MSc • DSc José Antonio Schiavon

Antonio

Candidate

Cristina De Hollanda

MSc, DSc Cavalcanti Tsuha

Ing, HDR Luc Thorel

Behaviour of helical anchors subjected to cyclic loadings

Keywords: Helical anchors, uplift capacity, sand, cyclic loading, centrifuge modelling, field load tests, numerical modelling, tropical residual soil Ancoragens helicoidais, capacidade de carga à tração, areias, carregamento cíclico, modelagem física em centrífuga, provas de carga, modelagem numérica, solo residual Ancrages hélicoïdaux, capacité portante en traction, sable, chargement cyclique, modélisation en centrifugeuse, essais de chargement in situ, modélisation numérique, sols tropicaux résiduels Anchors & anchorages, sands, centrifuge modelling

Helical anchors, used widely to resist uplift loading for a variety of applications, including in transmission towers, pipelines, offshore structures, etc., are subjected to environmental cyclic loads that influence the anchor performance and may induce fatigue failure. However, the influence of cyclic loading on helical anchor behaviour is unknown. A comprehensive evaluation of the effect of cyclic loading on the load-displacement response of single-helix anchors in sandy soils is presented here, including an interaction diagram to help designers evaluate the impact of different conditions in cyclic loadings. The experimental work of this thesis includes geotechnical centrifuge modelling and field load tests. The centrifuge model tests were carried out with reduced scale models of helical anchors in sand, at IFSTTAR (Nantes, France). The field load tests were performed on helical anchors installed in a tropical residual soil of the Experimental Site of the University of São Paulo (São Carlos, Brazil). In addition, numerical modelling was used to predict the pre-and postcyclic responses of the single-helix anchors tested in a centrifuge. The main findings of this research are: (a) helical anchor behaviour is governed by helix bearing resistance, and no loss of helix bearing capacity was observed in the range of cyclic loadings tested, (b) the degradation of shaft resistance was noticed mainly during the first 100 cycles, when the accumulation of permanent displacements is more significant, (c) an interaction diagram showing the different conditions of cyclic stability is proposed from the results of the experimental data, (d) modified values of the bearing capacity factor in tension (Nq) are suggested for the estimation of post-cyclic uplift capacity of single-helix anchors in sand, (e) SCHIAVON, José Antonio Behaviour of helical anchors subjected to cyclic loadings 8 University of São Paulo and LUNAM University the installation effect of the anchor should be taken into account in the numerical model in order to obtain reliable predictions of the helical anchor performance.

As estacas helicoidais são largamente utilizadas para resistir a carregamentos de tração em uma variedade de aplicações como torres de linhas de transmissão de energia, dutos enterrados, estruturas offshore, etc. Estes tipos de estruturas são normalmente submetidos a carregamentos cíclicos que influenciam o desempenho de fundações por estacas helicoidais submetidas a esforços de tração, e podem induzir ruptura por degradação da capacidade de carga. Contudo, a influência do carregamento cíclico no comportamento das estacas helicoidais (ou ancoragens helicoidais, quando submetidas apenas a esforços de tração) é pouco conhecida. Uma avaliação abrangente do efeito de carregamentos cíclicos sobre o comportamento das ancoragens helicoidais é apresentada nesta tese, incluindo um diagrama de interação para auxiliar na avaliação do impacto de diferentes condições de carregamento cíclico. O trabalho experimental desta tese inclui modelagem em centrífuga geotécnica e ensaios de carregamento cíclico em estacas na grandeza real em campo. Os ensaios em centrífuga foram realizados com modelos reduzidos de estacas helicoidais em areia, no IFSTTAR (Nantes, França). Os ensaios de campo foram realizados em ancoragens helicoidais instaladas no solo residual tropical do Campo Experimental de Fundações da Universidade de São Paulo (São Carlos, Brasil). Além disso, modelos numéricos foram utilizados para simular os resultados do comportamento das ancoragens helicoidais ensaiadas em centrífuga nas condições pré-e pós-ciclos. Os principais resultados desta pesquisa são: (a) a capacidade de carga à tração da ancoragem helicoidal é controlada pela capacidade de carga da hélice, (b) a degradação da resistência por atrito lateral foi observada principalmente durante os primeiros University of São Paulo and LUNAM University RESUME SCHIAVON, J.A. Comportement des ancrages helicöidaux soumises à des chargements cycliques. 2016. 300 p. Thèse de Doctorat en cotutelle entre l'Université de Sao Paulo et l'Université Nantes Angers Le Mans, Sao Paulo, Sao Carlos, SP, 2016.

Les ancrages hélicoïdaux, largement utilisés pour résister à des efforts de traction pour une variété d'applications comme les pylônes électriques, les pipelines, les structures offshore, etc., sont soumis à des chargements cycliques qui influent sur la performance d'ancrage et peuvent induire une rupture par fatigue. Cependant, l'influence des sollicitations cycliques sur le comportement d'ancrage hélicoïdal est mal connue. Une évaluation approfondie de l'effet de charges cycliques sur la réponse effort -déplacement des ancrages avec une seule hélice dans les sols sableux est présentée, incluant un diagramme d'interaction pour aider à évaluer l'impact des différentes conditions de chargement cyclique. La partie expérimentale de cette thèse comprend des essais en centrifugeuse géotechnique et des essais de chargement in situ.

Les essais en centrifugeuse ont été effectués sur des modèles réduits d'ancrages hélicoïdaux dans du sable, à l'IFSTTAR (Nantes, France). Les essais de chargement in situ ont été réalisés sur des ancrages hélicoïdaux installés dans le sol tropical résiduel du site expérimental de l'Université de São Paulo (São Carlos, Brésil). De plus, la modélisation numérique a été utilisée pour prédire les réponses pré et post-cycliques des ancrages d'une hélice testée en centrifugeuse. Les principales conclusions de cette recherche sont: (a) le comportement d'un ancrage hélicoïdal est régi par la capacité portante de l'hélice, et aucune perte de capacité portante d'hélice n'a été observée pour la gamme de charges cycliques testée, (b) la dégradation de la résistance par frottement latéral sur le fut a été remarquée principalement pendant les 100 premiers cycles, lorsque l'accumulation des déplacements permanents est plus importante, (c) un diagramme d'interaction montrant les différentes conditions de stabilité This type of foundation is normally used to support structures, such as transmission towers, submerged pipelines, decks, offshore constructions, wind farms, etc. In these cases, the helical anchors are subjected to a series of loading and unloading cycles during their service life. These cyclic loadings change the soil conditions close to the anchor, and consequently affect the helical anchor behaviour.

However, despite the increasing use of helical foundations in the aforementioned applications, there are no studies that investigate and propose procedures to estimate the influence of cyclic loadings on helical anchor behaviour. In addition, there is no design instruction for the prediction of helical foundations' responses under cyclic loadings.

In investigations about the behaviour of conventional piles under tension cyclic loading, the cyclic response has been classified based on the displacement accumulation and on the degradation of shaft resistance. For high amplitude tension cyclic loadings, few cycles are sufficient to cause complete pile skin friction degradation and failure under tensile loading.

On the other hand, in cases of compression cyclic loadings with low cyclic amplitudes, a densification of the soil below the pile tip is observed, that causes an increase in pile capacity mainly due to a gain in base resistance.

The cyclic response of foundations or anchors depends on the characteristics of the cyclic loading, soil type and installation process.

In the case of helical anchors, the cyclic response is composed of two distinct parts:

shaft resistance response and helix bearing response. As the soil around the anchor is sheared and displaced (loosened) during installation, a tensile cyclic loading is supposed to cause the University of São Paulo and LUNAM University densification of the soil above the helix, consequently improving the helix bearing response during static loading. However, the shaft resistance may degrades faster compared to conventional piles, since the soil around the anchor shaft is disturbed by the installation process and is in a less dense condition. Therefore, to address these questions, the study reported here is focused on the behaviour of single-helix anchors subjected to tensile cyclic loadings.

The main motivations of this thesis are to contribute to the current unsatisfactory understanding of helical foundations behaviour and to help foundation designers predict helical anchors cyclic response, as the construction of guyed towers for Brazilian power transmission lines is increasing rapidly.

Objectives

Considering the need for a better understanding of the behaviour of helical anchors under cyclic loading, the main objective of the research reported here is to evaluate the effects of different combinations of cyclic loadings and of the number of cycles on the accumulation of anchor displacement and on the uplift capacity of single-helix anchors in sand.

Secondary objectives

-Evaluate the scale effects on the prototype results of the physical modelling of helical anchors in sand;

-Evaluate the contribution of shaft resistance to the uplift capacity of single-helix anchors;

-Verify the influence of the soil disturbance caused by the installation process on the cyclic behaviour of helical anchors in sand and in residual tropical soil;

University of São Paulo and LUNAM University -Development of numerical modelling to simulate the pre-and post-cyclic helical anchor response considering the soil disturbance caused by the installation process.

Justification

The fact that a large amount of helical foundations has been employed to support cyclic loadings of power transmission towers, added to the fact that the installation process of helical anchors causes soil disturbance, which directly affects the anchor's capacity and stiffness, indicates that it is necessary to understand in detail the performance of helical foundations under cyclic loadings.

Thesis organization

 Chapter 1 shows the motivations and the objectives of this thesis

 Chapter 2 provides background information on the principal topics involved in this research. The failure mechanism of single-helix anchors under tension is briefly discussed as well as the effects of the helical anchor installation on the anchor capacity.

The physical phenomena that influences the behaviour of foundations under cyclic loading is also included in a literature review about previous research on foundations under cyclic loading. Additionally, a brief description of centrifuge physical model tests and the scale effects that can affect the modelling results is presented.

 Chapter 3 presents the materials and methods employed in this work. This chapter is subdivided into three sections: centrifuge modelling, field experiments and numerical modelling.

 Chapter 4 presents and discusses the experimental and numerical results. This part is subdivided into three sections.

 Chapter 5 offers propositions to guide the prediction of the cyclic loading response of single-helix anchors in sand. In this chapter, Interaction Diagrams, recommendations concerning the numerical modelling of helical anchors, and equations to predict the cyclic accumulated displacement in sand are presented. In addition, values of post-cyclic bearing factors (Nq-pc) are proposed for the calculation of the post-cyclic uplift capacity of helical anchors in sand. Also, the results of post-cyclic bearing factors (Nq-pc) are compared to the pre-cyclic bearing factors (Nq).

 Chapter 6 presents the main conclusions of the thesis and suggestions for future research on this subject.

University of São Paulo and LUNAM University

LITERATURE REVIEW

Helical anchors

Helical anchors have been employed as foundations of structures subjected to vertical and horizontal actions (Figure 1b to 1e). In Brazil, this type of foundation has normally been used as a foundation for towers for power transmission lines, as guyed masts and selfsupporting towers. [START_REF] Merifield | Ultimate uplift capacity of multiplate helical type anchors in clay[END_REF].

A helical anchor consists of a steel shaft with a tubular or square cross-section, with one or more helical plates welded along the shaft (Figure 1a). The number of helical plates depends on the soil conditions and on the required capacity. These anchors are installed into the soil by means of torque application to the upper end of the shaft by mechanical means (Figure 2). Initially, together with torque effort, a downward force is applied to assist in the advancement of installation. This downward force must be sufficient to ensure that the anchor advances into the ground with a feed rate of 80 to 100% of the helix pitch. Insufficient force leads to a lower advance rate which can cause augering and affects the anchor uplift capacity [START_REF] Perko | Energy method for predicting the installation torque of helical foundations and anchors[END_REF]. According to various researchers (Hoyt & Clemence, 1989;Narasimha Rao et al., 1989;Ghaly & Hanna, 1991;Ghaly et al., 1991;[START_REF] Perko | Energy method for predicting the installation torque of helical foundations and anchors[END_REF][START_REF] Tsuha | Relationship between installation torque and uplift capacity of deep helical piles in sand[END_REF]Sakr, 2014), the uplift capacity of helical anchors can be correlated with the final installation torque. The torque measured at the end of installation (final penetration corresponding to 3 helix diameters) represents an indirect strength measure of sheared soil by helices (Hoyt & Clemence, 1989). The installation of the helical anchor is supposed to finish when the installation torque reaches the design value. [START_REF] Perko | Helix pier engineering handbook 2000[END_REF] list the main advantages of helical anchors compared to other types of foundation:

 The uplift capacity can be estimated using the installation torque;

 The anchors are removable and can be reused;

 Easy transportation to places difficult to access, compared to concrete;

University of São Paulo and LUNAM University  Can be installed under the water table ;    Less time to be installed compared to other types of deep foundation;

 Can be installed with small equipment in inaccessible places;

 Noise and vibration during installation are minimal;

 Can be galvanized to resist corrosion;

 There is no need for concrete moulds;

 This pile can be loaded immediately after installation;

 There is no soil residue;

 It is less harmful to the environment. [START_REF] Perko | Helical piles: a practical guide to design and installation[END_REF] reported that there are over 50 helical anchor manufacturing companies in at least twelve countries on four continents, and in the United States there are over 2000 installation contractors. Brazil is among such manufacturing countries, where companies have been installing helical anchors for nearly 15 years in Brazilian territory, primarily used as anchors of guyed masts and foundations of self-supporting towers [START_REF] Tsuha | Theoretical model to control on site the uplift capacit of helical screw piles embedded in sandy soil[END_REF]. These types of structures are subject to a series of loading and unloading cycles of variable load amplitudes, mainly due to environmental changes. In this case, the helical anchors should support cyclic loadings which largely depend on variation in wind force. Also, in the case of guyed towers, the cycles of temperature variation can cause length variation in electrical conductors and guy cables, and consequently cause variation in uplift loading. These cyclic loadings modify the stress condition in the soil mass close to the pile, and consequently change the helical anchor tensile and compressive capacities.

University of São Paulo and LUNAM University 2.1.1. Behaviour of helical anchor foundations under uplift axial loading

When conventional piles are subjected to tensile loads, the pile capacity depends on the shear resistance at the interface pile-soil (shaft resistance). However, the failure mechanism of helical anchors under tensile loading differs from the mechanism of conventional piles (cylindrical shape) mainly because: 1) generally the helix bearing resistance is more important than the shaft resistance, 2) the soil around the shaft is significantly disturbed by the helix penetration during installation.

Effects of helical anchor installation

During helical anchor installation, the soil around the shaft is traversed and disturbed by the passage of the helices (shearing and displacing the soil laterally and vertically), and consequently some characteristics of the soil are modified and the shaft resistance is affected.

Helical anchor installation disturbs the soil structure and changes the stresses in the soil mass above the helical plates. Tsuha et al. (2012a) observed a considerable influence of the different degrees of disturbance of sand penetrated one, two or three times by the helical plate.

However, for the anchor installed in loose sand, the final state of the sand above each one of the three helices was similar. The hypothesis explaining the effect of sand density is illustrated in Figure 3.

The different shades of grey in Figure 3 identify two different groups of sand condition: initial state of undisturbed sand and the final state of a sand mass penetrated by the helices. In Figure 3b, the different shades of grey correspond to four different groups of sand condition, which vary with the number of helical plates that penetrate through a particular zone of soil.

Figure 3. Hypothesis for sand disturbance after installation of a three-helix anchor: (a) loose sand; (b) dense sand (Tsuha C. , Aoki, Rault, Thorel, & Garnier, 2012a).

The movement of soil particles around a helical plate during the installation of a helical anchor was verified with a video by [START_REF] Kanai | A seismic retrofitting application by means of multihelix micropiles[END_REF]. The author observed that the soil at the lower edge of the helical plate starts moving towards the upper edge of the plate during anchor penetration. Figure 4 illustrates the mechanism observed.

Figure 4. Model for the movement of soil particles around a helical plate during installation, after [START_REF] Kanai | A seismic retrofitting application by means of multihelix micropiles[END_REF]. [START_REF] Komatsu | Development on battered pile with screw pile method (NS-ECO pile)[END_REF] carried out model tests on a small scale helical anchor (shaft of 40 mm diameter and 80 mm of helix diameter) in a cylindrical testing vessel to examine the effect of the anchor installation on soil. In Figure 5, the displacement of the soil mass can be visualized

University of São Paulo and LUNAM University after the installation of a single-helix model anchor. This author observed the following: (i)

the soil above the blade of the pile rises upwards, (ii) the soil close to the pile shaft is pulled down due to the shaft friction, and (iii) the soil beneath the blade is compressed.

Figure 5. Model anchor (one-helix) installed in sand, after [START_REF] Komatsu | Development on battered pile with screw pile method (NS-ECO pile)[END_REF] -adapted. Kulhawy (1985) mentioned that significant disturbance does occur within the cylindrical installation zone of the helical anchor, and the disturbance effect can be approximated by relating the disturbed properties to the in-situ soil properties. For the prediction of the anchor uplift capacity, Kulhawy recommended considering the disturbance effect on the shearing resistance along the disturbed cylinder.

A large increase in lateral stress around a helical anchor model was observed by [START_REF] Clemence | Measurement of lateral stress around multihelix anchors in sand[END_REF] after installations in dense soils. When the anchor was loaded to failure the lateral stress increased further. The authors attributed this increase to arching stresses and soil dilatant behaviour developed when the anchor traversed and sheared the soil.

Concerning the effect of installation on the shaft resistance of piles, [START_REF] Vesic | Tests on instrumented piles, Ogeechee River site[END_REF] observed a reduction in the shear stresses mobilized along the shaft at a given depth in the ground as the pile tip penetrates further. This behaviour has been referred to as "friction

University of São Paulo and LUNAM University fatigue" [START_REF] Heerema | Predicting pile drivability: heather as an illustration of the "friction fatigue" theory[END_REF]. During pile driving, the friction experienced by the pile shaft is presumed as large in the beginning and decreases gradually because of the abrasion between soil grains and shaft surface while the pile moves down due to the driving. The gradual decrease of shaft skin friction is a consequence of horizontal stress decrease of the surrounding soil. [START_REF] White | Displacement and strain paths during plane-strain model pile installation in sand[END_REF] observed that soil particles had broken in the interface zone adjacent to the pile shaft models when high stresses were generated below the model base, causing high irretrievable volume reduction. While the shearing along the pilesoil interface proceeds, this zone tends to exhibit further contraction, leading to a mechanism of shaft friction degradation.

Helical anchor uplift capacity

The behaviour of single-helix anchors is dependent on the helix embedment depth.

When the helical anchors are installed with the helix at shallow depths, a significant soil movement at the ground surface is observed at failure (shallow anchor behaviour).

Figure 6 presents the schemes of the failure surfaces in tests on multi-helix model anchors observed by Mitsch and Clemence (1985). Although these experiments have been carried out on multi-helix anchors, the mechanism of shallow anchor failure is clearly illustrated in the zone above the top helix in Figure 6a. In this situation, the anchor's capacity depends considerably on the depth of the top helix and the load is transmitted to the ground exclusively by the helices [START_REF] Trofimenkov | Screw piles as foundations of supports and towers of transmission lines[END_REF]Ghaly et al., 1991;[START_REF] Clemence | Prediction of uplift capacity for helical anchors in sand[END_REF]. The shallow anchor behaviour occurs until a certain critical helix embedment depth. When the helix depth exceeds this critical value (Hcr), the soil movement in the ground surface is not observed (deep anchor behaviour). In this case, the soil mobilization occurs in the zone around the helix (Figure 6b). The uplift capacity of helical anchors is dependent on the helix depth, and the load is transmitted to the soil by the helix and shaft [START_REF] Trofimenkov | Screw piles as foundations of supports and towers of transmission lines[END_REF]Ghaly et al., 1991;[START_REF] Clemence | Prediction of uplift capacity for helical anchors in sand[END_REF][START_REF] Tsuha | Relationship between installation torque and uplift capacity of deep helical piles in sand[END_REF]. The methods for the prediction of the helical anchor uplift capacity consist of theoretical approaches or empirical relationships. The most common theoretical methods are based on limit state analysis; such methods assume the individual bearing resistances of the helices.

Theoretical methods based on the cylindrical shear model, which assumes that a cylindrical failure surface is mobilized between the top and the bottom helices (Figure 6), are not discussed in this document, since the current study is focused on the behaviour of single helix anchors.

In practice, these theoretical methods are used to define the dimensions of helical anchors, such as the quantity and diameter of helical plates and the shaft [START_REF] Perko | Helical piles: a practical guide to design and installation[END_REF].

University of São Paulo and LUNAM University [START_REF] Perko | Helix pier engineering handbook 2000[END_REF] suggest that, when possible, engineers' decisions should be based on these methods in conjunction with installation torque measurements.

2.1.1.3. Individual bearing method: helix bearing and shaft resistances

According to [START_REF] Trofimenkov | Screw piles as foundations of supports and towers of transmission lines[END_REF], the value of the critical helix depth (Hcr) for the characterization of shallow and deep anchor behaviour is around 4-5 times the helix diameter (D). [START_REF] Healy | Pullout resistance of anchors buried in sand[END_REF] found values of the critical depth equal to 5D. Various authors have evaluated the value of the critical helix depth of anchors. Mitsch and Clemence (1985) reported a critical embedment ratio value of 5D for helical anchors in sand with relative density (Dr) between 44 and 90%. [START_REF] Trofimenkov | Screw piles as foundations of supports and towers of transmission lines[END_REF] and Vesic (1971) argue that the critical embedment ratio depends on the soil shear strength. Figure 7 presents the values of critical helix depth suggested by [START_REF] Das | Earth anchors[END_REF]. [START_REF] Trofimenkov | Screw piles as foundations of supports and towers of transmission lines[END_REF] were the first authors to present a formula (Eq. 3) expressing the uplift helix bearing capacity of a helical anchor as a function of dimensionless capacity factors (similar to Terzaghi's bearing capacity equation).

D ult z ' B Ac q    Eq. 3
where, qult is the ultimate bearing pressure; c is the soil cohesion;

A and B are bearing capacity dimensionless factors (Figure 9); ' is the soil unity weight; zD is the helix embedment depth.

Figure 9. Bearing capacity factors for helical anchors, after [START_REF] Trofimenkov | Screw piles as foundations of supports and towers of transmission lines[END_REF]. Mitsch and Clemence (1985) grouped experimental results of uplift tests on plate anchors and helical anchors, from various authors and presented values of uplift capacity factor (Nq) for helical anchors in sand (Figure 10). Thus, the helix bearing capacity can be given by Eq. 4. For deep behaviour helical anchors, Mitsch and Clemence (1985) propose to determine the shaft friction resistance based on the theoretical expression proposed by [START_REF] Tomlinson | Some effects of pile driving on skin friction[END_REF] for shaft resistance of piles in sand (Eq. 5). For helical anchors, Mitsch and Clemence (1985) presented values for the lateral earth pressure coefficient in uplift (Table 1).

 tan K q f u s  Eq. 5
where, q is the effective average (or mid-height) vertical stress 'zi on the element of the shaft length L; ' is effective unit weight of soil; zi is the ground depth i; Ku is the lateral earth pressure coefficient in uplift (see Therefore, the uplift capacity of a single helix anchor can be expressed by the combination of the helix bearing resistance with the shaft resistance as presented in Eq. 6.

       n s s h ult T A f A q Q 1 Eq. 6
where,

Ah is the helix net area (D 2 -d 2 )/4;
As is effective shaft surface area of each shaft segment with L length on which fs acts, and n is the number of shaft segments.

Foundations subjected to cyclic axial loadings

Over time, some structures are subjected to different types of actions of varying magnitude. Transmission towers, chimneys and other tall structures are submitted to a series of loading and unloading cycles due to wind action. Offshore platforms are structures subjected to wave action, characterized as a load which fluctuates during the structure's service life. Thus, foundations are required to support these cyclic loadings. However, foundation behaviour under cyclic loadings differs from monotonic behaviour.

A quasi-static cyclic loading is characterized by a condition in which the initial forces generated by low loading frequency can be assumed as negligible. For large loading frequencies, the inertia forces are relevant and the loading is dynamic [START_REF] Wichtmann | Explicit accumulation model for non-cohesive soils under cyclic loading[END_REF].

University of São Paulo and LUNAM University [START_REF] Youd | Compaction of sands by repeated shear straining[END_REF] observed no influence of the loading frequency within the tested range from 0.2 to 1.9 Hz. The limit between quasi-static and dynamic loading is also dependent on the cyclic loading amplitude. However, according to [START_REF] Wichtmann | Explicit accumulation model for non-cohesive soils under cyclic loading[END_REF], often this amplitude dependence is disregarded and the limit between quasi-static and dynamic loading is considered to be within about 5 Hz.

For the analysis of foundations under cyclic loadings, the main characteristics of the cyclic loading are: the number of cycles (N), the frequency of cycles (f), the mean load (Qmean) and the cyclic amplitude (Qcyclic). Figure 11 illustrates these parameters of cyclic loadings. In the case of anchor guyed cables of cell or transmission towers, a minimum load is applied under "no-wind" condition. In Figure 13, this pre-load (Qpre) corresponds to the minimum value of the tensile load that the anchor is subjected. The pre-load (Qpre) maintains the guy cable stretched during the tower service life.

The axial cyclic loading can involve one or two directions of loading. For one-way (OW) cycling the load is applied in only one way (compression or tension). For two-way (TW) cyclic loadings, tension and compression load is applied alternately. The path of the load may follow different functions, exhibiting linear, square, sinusoidal or other functions.

University of São Paulo and LUNAM University

Previous investigations have demonstrated that cyclic loading on piles can induce degradation in shaft resistance, and in some situations in pile base resistance [START_REF] Turner | Drained uplift capacity of drilled shafts under repeated axial loading[END_REF][START_REF] Al-Dhouri | Predicted and observed cyclic performance of piles in calcareous sand[END_REF][START_REF] Kouby | Behaviour of model piles subjected to cyclic axial loading[END_REF][START_REF] D'aguiar | Piles under cyclic axial loading: study of the friction fatigue and its importance in pile behavior[END_REF][START_REF] Li | Cyclic axial behaviour of piles and pile groups in sand[END_REF][START_REF] Tsuha | Behaviour of displacement piles in sand under cyclic axial loading[END_REF][START_REF] Thomassen | Experimental Investigations of Tension Piles in Sand Subjected to Static and Cyclic Loading[END_REF]. Even in small load amplitudes, cyclic failure has been observed in one and two-way cyclic loadings. [START_REF] Chan | Repeated loading on single piles in sand[END_REF] relate that failure can occur under one-way loading for a maximum load (Qmax) of 30% of the ultimate static value. [START_REF] Gudehus | Cyclic and monotonous model tests in sand[END_REF] presents the results of model tests in sand indicating that a maximum load, as small as 10% of the ultimate static load, can lead to pile failure. At higher cyclic load levels, e.g. 30%QT, failure occurs within about 40 cycles. In these experiments performed by [START_REF] Gudehus | Cyclic and monotonous model tests in sand[END_REF], failure was characterized by an increasing accumulation of permanent displacement with increasing numbers of cycles. Van [START_REF] Van Weele | Pile bearing capacity under cyclic loading compared with that under static loading[END_REF] deduced that displacement accumulation is due to continuous re-arrangement and crushing of particles. According to [START_REF] Poulos | Cyclic axial loading analysis of piles in sand[END_REF], two phenomena related to cyclic axial loading may influence the failure of a pile foundation: a) cyclic degradation (or reduction) of shaft skin friction and base resistance; b) accumulation of permanent displacement with increasing load cycles.

A description of the stress-strain response of soils according to three characteristic zones was proposed by [START_REF] Jardine | Some observations on the kinematic nature of soil stiffness[END_REF], as illustrated in Figure 12. Zone I corresponds to perfectly linear plastic behaviour delineated by the kinematic yield surface Y1. This yield surface Y1 falls within a larger Y2 surface where the stress-strain behaviour is non-linear though full recoverable behaviour is observed for complete load-unload cycles. According to [START_REF] Jardine | Some observations on the kinematic nature of soil stiffness[END_REF], the stress-strain loops typically involve hysteresis in which the dissipated energy is thought to be a result of local yielding and wearing at the inter-particle contacts.

According to [START_REF] Tsuha | Evaluation of the efficiencies of helical anchor plates in sand by centrifuge model tests[END_REF], load cycling within the Y2 surface does not lead to significant strain accumulation. If the cyclic shear strain amplitude during the cyclic loading University of São Paulo and LUNAM University exceeds a certain threshold value (and the Y2 surface is engaged) the soil microstructure is irreversibly altered resulting in stiffness and soil volume variations [START_REF] Vucetic | Cyclic threshold shear strains in soils[END_REF]. The stress paths move out towards the large scale Y3 yield surface with the soil exhibiting increasingly plastic and irrecoverable behaviour [START_REF] Tsuha | Behaviour of displacement piles in sand under cyclic axial loading[END_REF].

Stability of pile foundations under axial cyclic loadings

The number of cycles of loading needed to provoke pile cyclic failure depends on the mean cyclic load, the cyclic load amplitude, and the shaft and base resistances. An illustration of the influence of cyclic loading effects on shaft capacity of axially loaded piles in sand could be represented by an interaction diagram. [START_REF] Karlsrud | Piles in clay under cyclic axial loading: field tests and computational modeling[END_REF] and [START_REF] Poulos | Cyclic stability diagram for axially loaded piles[END_REF] were pioneers in presenting interaction diagrams (Figure 13) in which foundation cyclic stability can be evaluated. In this diagram, the mean and cyclic axial loads on a pile were plotted, and three regions were identified for a specified number of cycles (N): (1) a cyclically stable zone A in which no reduction in load capacity after N cycles is observed; (2) a metastable zone B in which cyclic loading causes some limited reduction of load capacity after N cycles; and (3) an unstable zone C in which cyclic loading results in failure of the pile within N cycles or less. The results of cyclic load-controlled tests performed on model piles in calcareous sand by Al-Douri and Poulos (1995) showed from the tests carried out-on 'virgin' piles (not previously failed) that the cyclic response is better than in piles that had been failed. In prefailed piles the cyclic loading led to failure in a small number of cycles. [START_REF] Jardine | Pile load testing performed for HSE cyclic loading study at Dunkirk, France. Two Volumes[END_REF] report results of field experiments into cyclic loading with full-scale piles in sand focusing mainly on axial shaft resistance in tension. One of the analyses reported by these authors explored the contours of number of cycles to failure in the cyclic loading coordinates Qmean/Qmax static and Qcyclic/Qmax static (Figure 14). -Stable: no failure occurs before 1000 cycles, with slow or decreasing rates of displacement accumulation.

-Unstable: failure develops with less than 100 cycles.

-Meta-Stable: failure is observed between 100 and 1000 cycles, or accumulated displacements do not stabilize at slow rates. Interaction diagrams obtained from cyclic tests in bored piles (compression) and in driven piles (tension) installed in sand are presented by [START_REF] Puech | Cyclic stability diagrams for piles in sands[END_REF]. These authors performed cyclic tests in centrifuge, calibration chamber and in situ (full scale tests). For the driven piles subjected to tensile cyclic loadings, [START_REF] Puech | Cyclic stability diagrams for piles in sands[END_REF] adopted the same failure criteria used by [START_REF] Tsuha | Evaluation of the efficiencies of helical anchor plates in sand by centrifuge model tests[END_REF], for the interpretation of shaft friction cyclic behaviour.

According to [START_REF] Puech | Cyclic stability diagrams for piles in sands[END_REF], the failure criteria definition for piles under cyclic compression loads is more complicated.

According to [START_REF] Benzaria | Cyclic axial load tests on bored piles in dense sands[END_REF], displacements are accompanied by a progressive mobilization of the pile toe capacity, therefore, the displacements generally tend to stabilize.

Therefore, the failure criteria should be defined in terms of an allowable displacement. In addition, the criteria can be attained in both increasing and decreasing rates of displacement accumulation. Figure 16 presents the displacement rates in the compression cyclic tests reported by [START_REF] Puech | Cyclic stability diagrams for piles in sands[END_REF].

Skin friction degradation in one-way cyclic loading

According to the findings of many researchers [START_REF] Boulon | Physical and numerical simulation of lateral shaft friction along offshore piles in sand[END_REF][START_REF] Poulos | Cyclic axial loading analysis of piles in sand[END_REF][START_REF] Lehane | Mechanism of shaft friction in sand from instrumented pile test[END_REF][START_REF] Al-Dhouri | Predicted and observed cyclic performance of piles in calcareous sand[END_REF]Foray et al., 1998;Fioravante, 2002;[START_REF] Lehane | Scale effects on tension capacity for rough piles buried in dense sand[END_REF][START_REF] Mortara | Cyclic shear stress degradation and postcyclic behaviour from sand-steel interface direct shear tests[END_REF], the skin friction response of piles in sand is mainly The shaft resistance is related to the soil tendency to dilate at the interface, that is a function of soil mineralogy, soil density, stress level, grain-size, pile diameter and interface roughness (Foray, 1991). The ratio of the dilatant zone thickness to the pile diameter is responsible for the large shaft resistance observed in small diameter piles; however, for relatively smooth steel piles the dilatant properties of the soil may be less important [START_REF] Houlsby | How the dilatancy of soils affects their behaviour[END_REF].

Regarding cyclic conditions in sand, [START_REF] Bowman | Mechanisms of set-up of displcaement piles in sand: laboratory creep tests[END_REF] argued that cyclic perturbations may allow friction slippage of particles, which would tend to accelerate the onset of volumetric dilation during soil creep. In contrast, [START_REF] Rimoy | On strain accumulation in a silica sand under creep and low level cyclic loading[END_REF] observed that low-level cycling accelerates the progression of creep but the volumetric strains are no longer reversed.

With respect to sand-steel interfaces, [START_REF] Mortara | Cyclic shear stress degradation and postcyclic behaviour from sand-steel interface direct shear tests[END_REF] observed a marked increase of the stress ratio (τ/σ) in low amplitude cycling in constant normal stiffness (CNS) direct shear tests. These observations are similar to those made by [START_REF] Yoshimi | A ring torsion apparatus for evaluating friction between soil and metal surfaces[END_REF] Uesugi et al. (1989) and [START_REF] Dejong | Interface load transfer degradation during cyclic loading: a microscale investigation[END_REF]. [START_REF] Yoshimi | A ring torsion apparatus for evaluating friction between soil and metal surfaces[END_REF] and [START_REF] Mortara | Cyclic shear stress degradation and postcyclic behaviour from sand-steel interface direct shear tests[END_REF] observed homogeneous deformations of the sand specimen for low shear

University of São Paulo and LUNAM University displacements. For higher values of shear displacement, strong distortions of the sand close to the interface were observed. All of these cited authors found a marked effect of densification at low amplitudes, leading to a stress ratio increase, which limits the decrease in normal stress, and results in a lower degradation rate.

Experiments performed on pile models in clay have shown that the degradation of shaft resistance occurs when the cyclic displacement exceeds 0.2% of the pile diameter [START_REF] Poulos | Influence of cyclic loading on axial pile response[END_REF]. Increasing cyclic displacement generates degradation and a loss of shaft resistance, reaching a limiting value for cumulative displacements about 1.5% of the pile diameter, after the first 10 or 20 cycles [START_REF] Poulos | Influence of cyclic loading on axial pile response[END_REF]. [START_REF] Urabe | Bearing capacity and pull-out resistance of wing piles during cyclic vertical loading[END_REF] reported through centrifuge testing that the shaft resistance reached an ultimate value when the pile head displacement was about 6-13% of the shaft diameter of model pile, and reduced significantly with increasing displacements. [START_REF] Li | Cyclic axial behaviour of piles and pile groups in sand[END_REF] verified that the majority of skin friction reduction occurs within the first 10 cycles in jacked and prejacked model piles. However, [START_REF] Poulos | Influence of cyclic loading on axial pile response[END_REF] mentions that the onset of degradation can vary considerably. According to [START_REF] Poulos | Cyclic axial loading analysis of piles in sand[END_REF], the shaft resistance degradation begins when the cyclic amplitude displacement exceeds the displacement required for full slip under static load test.

Based on the results of field tests at the Dunkirk site, [START_REF] Stuyts | Axial pile capacity of wind turbine foundations subject to cyclic loading[END_REF] observed that progressive densification of the soil around the pile occurs for cyclic axial loadings with an amplitude greater than 25% of the shaft resistance. In consequence of soil densification, the effective radial stresses on the pile-soil interface are reduced, resulting in a decrease of the normal stress on the pile-soil interface as well as the shaft capacity.

The reduction of radial stress during pile installation is possibly dependent on volume changes and stress level [START_REF] D'aguiar | Piles under cyclic axial loading: study of the friction fatigue and its importance in pile behavior[END_REF]. [START_REF] White | Friction fatigue on displacement piles in sand[END_REF] and [START_REF] Gavin | Effect of friction fatigue on pile capacity in dense sand[END_REF] relate the friction fatigue degradation to the University of São Paulo and LUNAM University number of shearing cycles during the pile penetration in the installation process. Therefore, comparing jacked and driven piles, the rate of degradation should be more significant in driven piles experiencing high blow counts. On the other hand, for continuous jacking piles, the rate of degradation should be considerably less. [START_REF] Gavin | Effect of friction fatigue on pile capacity in dense sand[END_REF] reported that cyclic loading caused no effect on the pile base resistance (or base stiffness) of displacement piles installed in dense sand. However, the shaft resistance of monotonically installed jacked piles, which had exhibited significantly high shaft resistance, showed large degradation during the initial load cycles, and at higher cyclic load levels. Furthermore, the horizontal effective stress at failure, acting monotonically and cyclically, were indistinguishable after a relatively small number of working load cycles. [START_REF] Urabe | Bearing capacity and pull-out resistance of wing piles during cyclic vertical loading[END_REF] observed that the shaft resistance of piles under cyclic tensile loadings exhibited greater degradation than in cyclic compressive loadings. According to these authors, the shear deformation during the downward movement increases the effective stress around the pile, while the uplift movement results in effective stress decrease.

The cyclic load amplitude causes significant influence on the cyclic degradation of shaft resistance. Le [START_REF] Kouby | Behaviour of model piles subjected to cyclic axial loading[END_REF] observed that friction degradation increases for greater displacement amplitudes (tests conducted with a displacement control). On the other hand, an increase in shaft resistance was observed after a few cycles of small cyclic amplitudes.

Similar observations were made by D' Aguiar et al. (2009).

The initial stress level does not influence significantly the cumulative contraction of sand within the shear zone surrounding the pile interface [START_REF] Li | Cyclic axial behaviour of piles and pile groups in sand[END_REF]. These authors reported that the skin friction degradation exhibited similar trend for model piles installed in different manners: pre-jacked, monotonically jacked and cyclically jacked. [START_REF] Li | Cyclic axial behaviour of piles and pile groups in sand[END_REF] concluded that independently of the installation procedure, similar amplitude cyclic loadings tend to provoke a similar decrease in radial stress with consequent shaft resistance decrease. given by the helix bearing resistance, similar to the pile base capacity. Therefore, some observations about the degradation of pile base resistance, and also about the bearing resistance of footings, can be useful in the study of helical anchors. [START_REF] Poulos | Bearing capacity of foundations on calcareous sand[END_REF] reported an effective reduction in the base capacity in model footings tests on sand as a result of large accumulated displacements at relatively high cyclic stress levels. Due to the scantly available data at that time, [START_REF] Poulos | Cyclic axial loading analysis of piles in sand[END_REF] suggested to ignore the cyclic degradation of base resistance in cyclic axial loading analysis in sand. [START_REF] Li | Cyclic axial behaviour of piles and pile groups in sand[END_REF] observed that although jacking installation causes densification of soil under the pile tip, a softening behaviour of the load-displacement response was observed during displacement-controlled cyclic loading on a jacked pile model in centrifuge. This softening is commonly expected for pre-jacked model piles (simulating buried piles) since the installation of this type of pile does not induce soil densification. For both cases of jacked and pre-jacked piles, the softening in the pile base resistance is due to a gap between the pile model base and the soil developed during the cyclic loading. However, for the case of jacked model piles, the softening phenomenon occurred after cyclic tests with larger settlements (65 mm for jacked piles and 5-20 mm for pre-jacked piles, both models with 63.5 mm diameter in prototypes), indicating that the large-amplitude cyclic axial loads can cause further densification of the zone of sand at the base of the jacked pile. Previous studies have indicated that the sand subjected to cyclic shear experiences a net reduction in volume with the number of cycles, until reaching a maximum density, even for dense sands with ID around 90% [START_REF] Ansell | A Cyclic Simple Shear Apparatus for Dry Granular Materials[END_REF][START_REF] Airey | Estimation of pile friction degradation from shearbox tests[END_REF].

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When the settlement is larger than 20 mm for the pre-jacked model piles, [START_REF] Li | Cyclic axial behaviour of piles and pile groups in sand[END_REF] observed that the pile base resistance increased with increasing settlement. Similar observations were made by Le [START_REF] Kouby | Behaviour of model piles subjected to cyclic axial loading[END_REF] and [START_REF] Benzaria | Contribution à l'étude du comportement des pieux isolés sous chargements cycliques axiaux[END_REF]. According to Le [START_REF] Kouby | Behaviour of model piles subjected to cyclic axial loading[END_REF], the soil around the pile is not remoulded as in the case of the jacked pile.

Therefore, the cyclic loading causes soil densification, leading to a reduction in the pile basesand particles contact and consequently a decrease in the stress at the pile base.

In two-way centrifuge cyclic tests, [START_REF] Urabe | Bearing capacity and pull-out resistance of wing piles during cyclic vertical loading[END_REF] observed an increase in the base resistance when a wing pile model (similar to a helical pile) is in the pushing direction, possibly because the sand moves beneath the base during the tension load and afterwards is densified during the compression load.

Plate anchors in sand subjected cyclic loadings

Plate anchors are used to support structures subjected to repeated uplift loadings as dry dock floors, transmission towers and offshore structures. This type of anchor essentially is comprised of a high strength rod fixed to a plate anchor installed by excavating the ground to the required depth followed by back filling and compacting with a good quality soil, different from helical anchors, for which the soil around the anchor was previously disturbed by the installation. The anchor's initial condition can be pre-stressed or dead (zero load). The reason for pre-stressing the anchors lies in the belief that this technique allows a reduction in the adverse effects of repeated loadings [START_REF] Hanna | Behaviour of dead anchors subjected to repeated and alternating loads[END_REF]. When subjected to cyclic loadings, dead anchors exhibit non-recoverable displacements, and the anchor's life will depend primarily on the load range for a particular limiting displacement. As the cyclic loads are applied, a progressive modification of the stress state occurs along the foundations resulting in a change in the anchor behaviour [START_REF] Hanna | Behaviour of dead anchors subjected to repeated and alternating loads[END_REF].

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Cyclic tests carried out by [START_REF] Hanna | Behaviour of dead anchors subjected to repeated and alternating loads[END_REF] on model dead anchors in sand revealed that the anchor experiences large displacements in the initial cycles with an increase in permanent displacements. In a bi-logarithmic plot with the rate of anchor displacement versus the number of cycles, the authors observed a decreasing linear trend of the displacement accumulation. With an increase in the number of cycles, the rate of displacement accumulation decreases but does not cease, and failure in the form of a sudden pull-out never occurs. The cyclic laboratory tests conducted by [START_REF] Petereit | The static and cyclic pullout behavior of plate anchors in fine saturated sand[END_REF] on anchor model plates in fine saturated sand showed a continuous anchor displacement even at maximum cyclic loads of 15%QT.

The anchor pre-stressing during the proof loading stage aims to reduce creep effects and stiffen the anchor system. [START_REF] Hanna | Behaviour of dead anchors subjected to repeated and alternating loads[END_REF] also investigated the effects of pre-loading the anchor with 75% of the anchor's uplift capacity (QT), and they observed that pre-loading does not produce any permanent stiffening effect. In contrast, when the anchor was subjected to 20,000 cycles with the applied loading varying from zero to 50%QT, a significant stiffening was noticed in the following cyclic loading (from 25%QT to zero). [START_REF] Hanna | Performance of prestressed anchors under slow repeated loadings[END_REF] showed that the use of a pre-stress load significantly reduces the displacements under the first cyclic loading and increases the anchor's life duration, by decreasing the permanent displacements at any cycle in comparison with the dead anchors. [START_REF] Hanna | Performance of prestressed anchors under slow repeated loadings[END_REF] also noticed that cyclic loadings with low mean loads (Qmean) tend to be more severe, i.e., a cyclic loading ranging from zero to 60%QT will generate greater accumulated displacements than a 30-80%QT cyclic loading. [START_REF] Beard | Holding capacity of plate anchors[END_REF] proposed contours limiting the number and magnitude of loading cycles to prevent failure due to cyclic creep, and suggests that the cyclic loadings with 2Qcyclic (double cyclic amplitude) lower than 5%QT can be ignored. Based on experimental observations, Andreadis and Harvey (1981) proposed a hyperbolic equation to describe the anchor response under cyclic loadings. In the case in which the permanent displacement experienced by a previous cyclic loading is known, these authors also propose a hardening ratio-total relative cyclic movement relationship.

Regarding the uplift resistance of wing plates of model piles under two-way cyclic loadings, [START_REF] Urabe | Bearing capacity and pull-out resistance of wing piles during cyclic vertical loading[END_REF] reported a significant decrease in the wing bearing resistance for piles with small ring area, under cyclic displacement amplitudes more than ±65 mm (in prototype values). This decrease was caused by the disturbance of the soil above the wing. [START_REF] Urabe | Bearing capacity and pull-out resistance of wing piles during cyclic vertical loading[END_REF] also show that the shaft resistance controls the cyclic tension response of the model pile for cyclic displacements less than ~30 mm. However, for larger displacement amplitudes, the wing plate controls the cyclic tension response. [START_REF] Chow | Drained cyclic capacity of plate anchors in dense sand: experimental and theoretical observations[END_REF] employed a macro-element modelling approach to interpret the behaviour observed in cyclic tests on plate anchors in dense sand. In this approach, an allowable combination of horizontal load (H), vertical load (V) and moment (M) acting on the anchor is represented by a surface in the H'-V'-M' space (Figure 17). To reproduce the effects of cyclic loadings, additional features should be considered in the model. If the soil experiences cyclic loading, the density and fabric changes and imposes an expansion of the yield surface [START_REF] Tatsuoka | Characterising the pre-failure deformation properties of geomaterials: theme lecture for plenary session no[END_REF]. Similar behaviour was described by [START_REF] Chow | Drained cyclic capacity of plate anchors in dense sand: experimental and theoretical observations[END_REF], with the anchors exhibiting changes in sand density and fabric, causing an expansion of the bounding and memory surfaces. However, the effects of density and fabric changes tend to disappear with large amounts of deformation, a situation in which both bounding and memory surfaces approach the ultimate failure surface [START_REF] Chow | Drained cyclic capacity of plate anchors in dense sand: experimental and theoretical observations[END_REF].

Cyclic behaviour of helical anchors in sand

The influence of cyclic loadings on the skin friction degradation of piles has been addressed by many studies in the literature. Also, the effect of cyclic loading on soils has been evaluated by triaxial tests on uniform samples. According to [START_REF] Ishihara | Undrained deformation and liquefaction of sand under cyclic stresses[END_REF], sand responses to monotonic and cyclic shearing depend on their fabric, initial state (void ratio and stresses) and degree of shearing.

For helical piles, the cyclic failure of the soil under the bottom plate (intact sand) in compressive cyclic loading could be evaluated with triaxial tests (the uniform and intact soil under the bottom plate). However, the cyclic response of helical piles under tension depends on the shear resistance of a soil-disturbed above the plates.

El Sharnouby and El Naggar (2011) present results of 15 compressive load cycles on a helical pile. According to the authors, the pile stabilized after a few cycles with a mean cyclic load and a maximum load respectively equals to 57 and 70% of the ultimate load.

Improvement of the monotonic load-displacement response was observed due to the performed load cycles, occurring an increase in stiffness.

The most prominent feature of helical anchor uplift capacity is the shear resistance of the disturbed soil in the cylinder above the plates. When this type of anchor is submitted to

University of São Paulo and LUNAM University cyclic loadings, the resisting forces are concentrated in the interface between intact soil and disturbed soil. Therefore, the cyclic response of helical anchors in sand depends of the shear resistance between disturbed soil and intact soil.

Probably, after a certain number of loading cycles (depending on the cyclic load amplitude), in one-way cyclic (in tension), the disturbed soil within the cylinder will be densified. In two-way cyclic (tension and compression), the pile response depends on the densification of the soil disturbed above the plates, and on the intact soil under the bottom plate. In that way, the behaviour of helical anchors under cyclic loading is complex.

Previous studies on helical anchors have related that cyclic loading promotes degradation on both coarse-grain and fine-grain soils and anchor performance. A reduction in horizontal stress occurs during the cyclic loading because of the sand particles movement from the edge of the helix to below the helix during repeated loading. As a consequence, a significant reduction in the anchor's capacity occurs [START_REF] Clemence | Dynamic Uplift Capacity of Helical Anchors in Sand[END_REF]. In the case of an expected inflow of soil into the cavity, [START_REF] Trofimenkov | Screw piles as foundations of supports and towers of transmission lines[END_REF] mentioned that the limiting value of the applied load cyclic conditions should be limited to between 60 and 70% of the anchor's uplift capacity in one-way cyclic loading, and from 30 to 40% of the uplift capacity in two-way cyclic loading. However, repeated load applications increased the stiffness of the soil-anchor system in some cases [START_REF] Andreadis | Embedded anchor response to uplift loading[END_REF].

According to [START_REF] Cerato | Effects of long-term dynamic loading and fluctuating water table on helical anchor performance for small wind tower foundations[END_REF], cyclic loadings at a relatively high cyclic/static load ratio may significantly increase uplift capacities and reduces long-term creep. If no preloading is performed, the anchors could present excessive displacements even at low loadings.

A general recommendation is to keep cyclic loads below 25% of the ultimate capacity of the anchor to minimize long-term creep [START_REF] Cerato | Effects of long-term dynamic loading and fluctuating water table on helical anchor performance for small wind tower foundations[END_REF]Ghaly & Clemence, 1998).

University of São Paulo and LUNAM University Cyclic loading was observed to improve the ultimate tension capacity in results

presented by [START_REF] Buhler | Design of dynamically wind-loaded helical piers for small wind turbines[END_REF]. The helical anchor named V13 was subjected to a series of two cyclic loadings with 33-39% and 33-65% of the predicted uplift capacity.

According to these authors, the densification of the soil above the helices during the cyclic loading is the most likely effect to explain the capacity increase. In addition, the cyclic load amplitude was observed to cause more influence on the anchor response rather than in the maximum load. Degradation of skin friction is believed to occur differently from degradation of base resistance; however, little conclusive data is available for helical anchor foundations.

Physical modelling in centrifuge

Full scale field tests are expensive and generally provide results with low repeatability.

It is difficult to reproduce closely controlled test conditions (Dickin & Leung, 1983). According to [START_REF] Hettler | Possibilities and limitations of 1-g model techniques[END_REF], 1g model tests are a useful tool to investigate mechanisms and slip surfaces. However, the 1g scaled models cannot reproduce the behaviour in geotechnical problems that are highly dependent on confining stresses, because the level of geostatic stresses that are reproducible in 1g reduced models are significantly less than the field stress conditions [START_REF] Kim | The role of the physical modeling in the design of geotechnical systems[END_REF]. To overcome this limitation of 1g models, geotechnical centrifuges are commonly used to compensate for the self-weight stress level [START_REF] Tsuha | A review of centrifuge model tests of helical foundations[END_REF].

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A centrifuge is essentially a sophisticated load form on which soil samples can be tested [START_REF] Taylor | Centrifuges in modeling: principles and scale effects[END_REF]. Experiments with small scale models in centrifuge can use the same material as the prototype and reproduce the same field of forces and mass in a full-scale structure [START_REF] Garnier | Physical modelling in geotechnics: state of the art and recent advantages[END_REF]. In centrifuge modelling, the intensity of the gravitational field generated by centrifugal acceleration must be inversely proportional to the reduction scale of the manufactured model [START_REF] Corté | L'essor de la modélisation en centrifugeuse en géotechnique[END_REF]. According to scaling laws, over a 1/n scaled model the applied centrifuge acceleration should be n times the earth's gravity (Garnier & König, 1998).

The scaling factor X * on a physical parameter X is the ratio of the value Xm in the model to the value Xp in the prototype (X * = Xm / Xp). Physical systems must satisfy fundamental laws of dynamics; thus, the dimensional analysis of physical relationships carries the following similarities:

* l * g * *    Eq. 7 2 * t * *    Eq. 8
where,  * is the scaling factor for stresses;  * is the scaling factor for bulk density; g * is the scaling factor for mass forces; l * is the scaling factor for distance measures;  * is the scaling factor for displacements; t * is the scaling factor for time.

The relationships presented in Eq. 7 and Eq. 8 can be grouped as follows: As soil behaviour depends on the stress history, which was previously detailed, scaled models must be subjected to the same stress state as the full-scale structure. This assumption leads to the following condition [START_REF] Taylor | Centrifuges in modeling: principles and scale effects[END_REF]:

1 *   Eq. 11
Table 2 presents the scaling laws derived from the equation of equilibrium (Eq. 11).

Table 2. Scaling law [START_REF] Fuglsang | The application of the theory of modelling to centrifuge studies[END_REF] successfully to investigate the performance of plate anchors (Ovesen, 1981;Dickin & Leung, 1983;Tagaya et al., 1988), and helical anchors (Levesque, 2002;Tsuha et al., 2007;Bian et University of São Paulo and LUNAM University al., 2008;Wang et al., 2013). However, the occurrence of scale effects can influence the results of model experiments of geotechnical problems in granular soils.

The reduced scale of models can induce scale effect in relation to the grain-size [START_REF] Balachowski | Scale effect in shaft friction from the direct shear interface tests[END_REF]. Dilation, roughness, and grain crushing influence the behaviour of granular soils, and the smaller the model is, the greater the effect of these phenomena on the model capacity (Klinkvort, Hededal, & Springman , 2013). Therefore, because the uplift capacity of a deep single-helix anchor is the sum of the shaft skin friction and the helix bearing capacity, for the centrifuge simulation of helical anchors in sand, it is fundamental to verify the occurrence of scale effects on the results of both components of anchor capacity.

Particle-size effects on shaft resistance

The particle size effect on the shaft resistance of piles is associated with shear band formation along the shaft. The shear localization in sand in plane strain compression and triaxial tests [START_REF] Desrues | An introduction to strain localisation in granular media[END_REF], and in direct shear apparatus [START_REF] Boulon | Numerical and physical behaviour under monotonous and cyclic loading[END_REF] indicate a mean thickness of the shear band of 10d50. In the case of sand-pile interfaces, the thickness of the dilatant zone is found as 10d50, independent of the shaft diameter [START_REF] Boulon | Physical and numerical simulation of lateral shaft friction along offshore piles in sand[END_REF]. [START_REF] Yoshida | Deformation property of shear band in sand subjeted to plane strain compression and its relation to particle characteristics[END_REF] observe that the shear band width is proportional to the grainsize and is comprised of between 10 and 20 times the average grain-size. Garnier and König (1998) mention that the shear band thickness is usually assumed to be 10 or 15d50.

An adequate model simulation of pile-sand interface can be ensured by following a minimum ratio between pile shaft diameter and average grain-size (d/d50). Previous studies on scaling effect on shaft friction have presented different limits of the ratio d/d50. Foray et al.

(1998) report that particle-size effects are negligible when d/d50 is greater than 200. Garnier and König (1998) affirm no significant grain-size effect when d/d50 is larger than 100 for pile

University of São Paulo and LUNAM University models with a rough shaft. Fioravante (2002) comments that scaling effects can be neglected for d/d50 greater than 30 to 50, despite the dispersion observed in the results.

The recommendations of the aforementioned studies to prevent scale effects in modelling pile shaft resistance in sand may not be suitable in the case of shaft resistance of helical anchor models due to installation effects. In the case of helical anchor installation, the anchor is penetrated into the soil by rotation, and consequently, significant disturbance occurs within the cylindrical installation zone around the shaft, which could influence the scale effects.

Particle-size effects on plate bearing capacity

Since there is no study available on particle size effects on the bearing plate resistance of helical anchor models, the recommendations of previous centrifuge model test investigations on footings and on plate anchors in sand were used by Tsuha et al. (2007) to define the minimum ratio D/d50 (D is plate diameter) to provide a satisfactory simulation of helical plate bearing resistance.

In the experiments of Yamaguchi et al. (1977) no difference was observed in the bearing capacity factor and load-settlement response of shallow foundations with the ratio of foundation width to an average grain size greater than 36. Ovesen (1979) investigated scaling effects in centrifuge tests on footing models in sand, and found that in experiments with a footing model diameter (D) larger than 30d50 no scale effect was observed. The results presented in Tatsuoka et al. (1997a) showed similar results between footing models with D/d50 a ratio of 33 and 50. Lau (1988) observed no evidence of serious particle size effects on footing models in sand with B/d50 ratios ranging from 165 to 8333.

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Three different scales of square plate anchors were tested by Ovesen (1981) in dense sand (g-levels ranging from 167g to 56g). In this cited work, no scale errors were found in models with a ratio between model width (B) and an average grain-size (d50) larger than 25.

From the aforementioned studies, for B/d50 ratios greater than 25, no difference in the anchor (or footing) response was observed. However, the minimum B/d50 or D/d50 ratio to avoid scale effects is still unknown, as there is no available centrifuge investigation on plate anchors using B/d50 ratios smaller than 25.

In the case of plate anchor models tested in centrifuge, the sand above the plate is placed in the container after the plate installation. Differently, in the case of centrifuge tests on helical anchors, the helical plate is penetrated into the soil by rotation after sand placement, and consequently, significant disturbance occurs within the cylindrical installation zone of the anchor. Also, the range of the ratio between plate and shaft diameters of helical anchors is usually lower than the ratios used for plate anchors. Therefore, these two differences probably could result in different values of the minimum ratio D/d50 necessary to avoid scale effects on helical anchor tests compared to the case of plate anchor and footing models.

Scale effects on helical anchor model tests

The values for the ratios D/d50 (plate diameter/average grain size) and d/d50 (shaft diameter/average grain size) observed in previous studies in order to avoid scale effects on bearing plate resistance and shaft resistance indicates that the shaft diameter should restrict the helical anchor model dimensions (greater d/d50 ratios are suggested compared to D/d50).

However, the shaft friction resistance corresponds to a very small portion of the total capacity of a helical anchor in sand. Therefore, scale effects on the shaft friction may not be significant compared to the scale effects on the helix bearing resistance.

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Centrifuge model investigations on helical anchors in sand can produce reliable simulations of anchor behaviour without influence of scale effects. For this, some relationships between grain and model size should be established in order to provide an accurate reproduction of prototype anchor-soil interaction. In the case of helical anchors, the helix-shaft-soil interaction is influenced by the grain-size in a particular manner.

The scale effects on shaft friction of helical anchors are related to the shaft diameter d similarly to the case of regular piles. However, the relationships between pile shaft diameter and d50 recommended to prevent scale effects on model tests may not be suitable for the simulation of shaft resistance of helical anchors, as the soil mass around the shaft (also the dilatant zone) is influenced by the previous installation of the helix.

In the case of helix bearing resistance, it is necessary to establish a helical plate component (such as the helical plate diameter or the effective helical radius) that can be related to particle size effects. In the case of plate anchors, the ratio between plate diameter D and the average grain size d50 is usually used to evaluate scale effects. However, the ratio between plate and shaft diameters is much better for plate anchors when compared to helical anchors. In the case of helical anchors, the net projected area of the helix is reduced; therefore, the ratio between helix diameter D and d50 cannot be the best parameter to explain the particle size effects on helix bearing resistance.

Therefore, to address the need to examine the scale effects on the results of centrifuge modelling of helical anchors in sand, in the current study a series of tests was conducted to investigate this problem. These tests were performed before the cyclic loading tests to help the decision regarding the optimal dimensions of the instrumented model anchor (shaft and helix diameter) to be fabricated for cyclic tests.

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MATERIALS AND METHODS

This chapter presents the materials and methods used in this study to evaluate the helical anchor behaviour under cyclic loading. For this evaluation two groups of tests were performed: laboratory model tests in centrifuges and field tests. Additionally, a numerical model was developed in order to simulate the pre-cyclic and post-cyclic uplift capacity of the anchors tested in centrifuges. Therefore, this chapter is divided into three main parts: centrifuge modelling, field tests, and numerical modelling.

Centrifuge modelling

The centrifuge modelling technique was used to evaluate the effects of cyclic loadings with different amplitudes on the helical anchor performance in sand, and to evaluate the particle-size effects in physical modelling of helical anchors in sand. For these two investigations, the sand sample reconstitution should be closely controlled to minimize the uncertainties related to the sand sample characteristics. Therefore, the samples were reconstituted through the sand raining method to provide repeatability of the characteristics of the various tested samples.

Installation and loading tests on the helical model anchors were performed with a servocontrolled hydraulic actuator that allows carrying out the experiments controlling the loading rate or the displacement rate.

The centrifuge experiments were performed in the IFSTTAR beam centrifuge (Figure 18). This centrifuge has a maximum radius of 5.50 m, and its swinging basket permits the installation of a container with 1.40 m in length, 1.15 m in width and 1.50 m in height, and with payload of 20 kN for experiments at 100g. The experiments for this thesis considered the ng centrifuge acceleration applied to the helix of the model anchor, taking into account the distance between the centrifuge spin axis and helix level to determine the application radius of the centrifuge acceleration, as presented in Figure 19. More details about the IFSTTAR geotechnical centrifuge can be found in [START_REF] Thorel | Mesures en macrogravité sur modèles réduits d'ouvrages géotechniques[END_REF].

Sand sample reconstitution

The centrifuge experiments were carried out in reconstituted sand samples prepared through the raining deposition technique inside rectangular steel strongboxes. In this technique, the sand is placed in an automatic hopper and pours through a slot to produce a uniform sand rain over the strongbox (Figure 20). The hopper moves in round-trips while the sand is deposed in thin layers on the bottom of the strongbox. The hopper horizontal speed is constant while the hopper passes over the strongbox. The sand drop height can be adjusted as well as the rate of flow by setting the horizontal speed and the slot width. The pluviation process is known for providing homogenous specimens and good repeatability [START_REF] Garnier | Physical modelling in geotechnics: state of the art and recent advantages[END_REF][START_REF] Küs | Pluviation des sables[END_REF][START_REF] Miura | A sample preparation method and its effect on static and cyclic deformation-strength properties of sand[END_REF]. The final dimensions of the sand sample are 1200 mm in length, 800 mm in width and 360 mm in depth. To assess the achieved density, at least two calibrated boxes were placed on the bottom of each strongbox. The centrifuge tests were performed in dry HN38 Hostun dense sand with a density index (ID) ranging from 94 to 99%. HN38 Hostun sand is a fine silica sand consisting of angular particles (sand extracted in Hostun, France). Hostun sand is used in other laboratory investigations, and its physical properties are well established (Flavigny, Desrues, & Palayer, 1990). [START_REF] Ternet | Reconstitution et caractérisation des massifs de sable. Application aux essais en centrifugeuse et en chambre de calibration[END_REF] These tests are discussed in more detail in the Appendix B and C.

Test system

In centrifuge, installation and loading were performed using a servo-controlled system fixed over a sand container. As illustrated in Figure 22, a motor was coupled with the servocontrolled system to rotate the helical anchor model during the installation. In some tests (listed in the Appendix K), a torquemeter was used to measure the installation torque (Figure 22a). The vertical displacement and the vertical force were monitored by displacement and force transducers, respectively. The registration of installation torque, displacement, and force was completed through an automatic data acquisition system installed in the centrifuge swinging basket. The data acquisition frequency was set at 10 Hz. More details concerning the measurement system are provided in Appendix F and in [START_REF] Thorel | Mesures en macrogravité sur modèles réduits d'ouvrages géotechniques[END_REF]. The main characteristics of the sensors used in the experiments are listed in Table 4.

The measurements of torque, displacement and force were converted into numerical data by an automatic data acquisition system placed in the centrifuge swinging basket.

Procedures for installation and monotonic tensile loading tests

The monotonic loading tests of the current research were carried out according to the procedures described in this section.

The installation of the helical anchor models into the sand sample was performed in flight by applying a constant rotation to the model anchor of 5.3 rpm (the field rotation rate normally varies from 5 to 20 rpm). During the model anchor installation, the vertical speed was set to permit the helix installation advances into the soil with a penetration rate of one pitch per revolution. In each container, a minimum axis-to-axis spacing of 10 times the helix diameter was kept between anchors to ensure no influence on the results.

Tensile loading tests were performed 3 minutes after the end of anchor installation. The anchor models were loaded at a vertical displacement rate of 0.3 mm/s. When the pull-out test was completed, the centrifuge was stopped to move the servo-control system over the next anchor model for testing.

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The sequence of the test procedure, from sample preparation to anchor testing in flight, is described below:

a) The sand sample is reconstituted by sand pluviation procedure.

b) The sand sample is placed in the centrifuge-swinging basket.

c) The servo-controlled system is installed over the strongbox.

d) Three consecutive stabilization cycles of centrifugation, with a 3 minute duration, with the maximum g-level planned for the tests in each container.

e) The model anchor is installed in flight.

f) Three (3) minutes of wait time after model installation (in flight).

g) The anchor pull-out test is carried out with a loading rate of 0.3 mm/s (in flight).

h) The centrifuge is stopped for repositioning the servo-controlled system for the next anchor test.

i) Steps e) through h) are repeated for the next anchor test.

Experiments on particle size effects

For centrifuge modelling studies it is necessary ensure that no scaling issues are influencing the results. An appropriate relationship between sand particle and model size has to be established in order to properly simulate the prototype pile-soil interaction. Previous studies on the soil particle size effect on plate anchors, footings and regular piles have been used as a scale effect reference for modelling helical piles. However, there is no certainty that limiting values of D/d50 reported in previous studies are valid for helical model anchors, since footing and plate models experience no reduction in effective diameter because of the shaft. In addition, the installation and the helix-shaft-soil interaction are influenced by soil grain-size differently than the scale effects on the shaft and the plate.

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Given the scenario above, an investigation about scale effects on the results of the centrifuge model on helical anchors in sand was carried out for this thesis before the cyclic tests, to assist in the decision about the dimensions of the instrumented anchor model fabricated for the cyclic tests.

The "modelling of models" technique was used in the current study to investigate the scaling effects on helical anchor models. In this technique, a large-scale model is assumed to be practically independent of scale effects. Different sizes of anchor models and g-levels were used to simulate the same prototype response. D/d50 and d/d50 ratios were varied but the D/d ratio was constant. Full similarity between model and prototype is achieved when identical non-dimensional response is observed between them.

Three reconstituted Hostun sand samples, with ID = 99% (Containers No. 8, 11 and 12), were prepared for these tests under acceleration levels ranging from 8.3 to 16.7g. All models were installed at the same relative embedment depth (zD) of 6D. Since the helical anchor models were fabricated with different helix diameters, the embedment depth of each model was adjusted to provide the same relative embedment depth (6D). The sequence of installation and loading tests started from the smallest to the largest scale model.

Helical anchor models for experiments on particle size effects

Four single helix anchor models with different sizes were used to provide a helical anchor prototype with 100 mm shaft diameter (full cross-section) and 330 mm helical plate diameter (D/d ratio equals to 3.3). The anchor models were composed of a steel helical plate welded to a round steel shaft, both fabricated with a maximum steel surface roughness Rmax of 4.87 μm. The results of the steel roughness analysis are presented in the Annex A.

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The helical plate embedment depth was equal to 6 times the plate diameter (1.98 m depth in prototype scale). The dimensions of the helical anchor models and their corresponding g-levels are presented in Table 5.

Figure 23 shows the four different single-helix anchor models tested in this investigation. The 6FH model differs from the others because this model was fabricated to be used in [START_REF] Tsuha | Theoretical model to control on site the uplift capacit of helical screw piles embedded in sandy soil[END_REF] research. The other models were fabricated especially for this investigation on particle-size effects. In the case of anchor models of smaller plate diameter, Figure 24 illustrates that the number of grains at the plate interface is reduced compared to the case of regular plate anchors.

In the current work, the particle size effect on the plate bearing resistance of helical anchors is proposed to be correlated to the helix effective radius w:

  d D . w   5 0 Eq. 12
where, w is the effective helical radius Three single-helix anchor models were used in this study: 6FH, 8FH and 10FH. The helix embedded depth for the three anchor models was 8D (see Table 5). The procedure of placing the model anchors during pluviation was intended to avoid any sand disturbance.

The sand pluviation in the strongbox was stopped when the sand level reached the helix embedment level. After that, the model anchor was placed on the sand sample and the sand deposition continued. Two parallel nylon lines were fixed on the top of the strongbox to maintain the anchor models in a vertical position. Figure 10 shows the nylon lines, four calibrated boxes and two helical anchor models already placed during the sand sample reconstitution. Figure 26 shows the sand sample with the anchor models after the pluviation. For the sample excavation after the anchor installation and pull-out test, it is necessary to moisten the sand sample. The water content was controlled by adding water over the strongbox to provide some temporary cohesion due to matric suction. The sand surface was protected by a geotextile to avoid erosion of the sample surface. The sample excavation (Figure 28) was done at least 6 hours after the addition of water.

Tomography

A helical anchor model fabricated in plastic (6HFp) was used to investigate the density changes in a sand sample after the installation (Figure 29). As the dimensions limits of the (Xray) CT scanner are 60 mm in the three axes, the helical anchor model was fabricated with the size corresponding to the 6FH model. The 6HFp was installed in flight with the helix at a 150 mm depth (7.5D). After installation, the plastic anchor model was pulled up 10 mm (0.5D), and then the centrifuge was stopped to disconnect the model. A steel coupling device was fabricated to permit an easy disconnection between the model and the servo-controlled system (Figure 30). The sand sample was moistened (as described in 3.1.5.1) to insert of two PVC tubes (external diameter = 55 mm and length = 170 mm) to extract the specimens for analysis (Figure 31). One PVC tube was used to recover the plastic model anchor + sand, and the other PVC tube was used to extract a non-disturbed sand specimen. The X-ray micro-tomography analysis was kindly performed by Dr. Christophe Dano with the micro-tomography apparatus of the Ecole Centrale de Nantes. The digital image processing was also performed by Dr. Dano.

Evaluation of shaft and helix bearing resistances

The evaluation of the individual contribution of shaft resistance and helix bearing resistance to the total helical anchor uplift capacity was done using two different methods: a)

comparison between the uplift capacity results of the fixed and removable helix model anchors; b) uplift tests on an instrumented helical anchor model.

The removable helix models (Figure 32) were constructed with a male-female connection with a square cross-section designed to transfer torque during installation and allow the separation of the anchor shaft from the helix during the shaft pull-out tests.

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Cyclic loading tests on single-helix anchor models in centrifuge

Cyclic tensile loading tests were conducted in this study to evaluate the effect of the combination of mean load and load amplitude, and of the number of loading cycles on the helical anchor response.

Cyclic loading tests with different combinations of load amplitude, mean load and number of cycles were performed in eight sand samples reconstituted with dry HN38 Hostun sand with a density index (ID) ranging from 94 to 99%.

Model 10FH, previously described in section 3.1.4.1, was cyclically tested in Containers No. 4, 5, 6 and 7. Model 10FHi, previously described in section 3.1.6, was tested in Containers No. 9, 10, 13 and 14. Both models had helix diameters equal to 33 mm and shaft diameters equal to 10 mm.

Cyclic loadings

One of the objectives of the cyclic loading tests was to evaluate the cyclic stability of single-helix anchors in sand using Interaction Diagrams. Therefore, the cyclic tests were performed in a range of pre-tensile load (Qpre) to reproduce the common range in the practice.

The application of a pre-tensile load intends to simulate the pre-tensile load of a helical anchor used to support guyed anchor towers, even in the absence of cyclic loadings. This pretensile load is equivalent to the minimum cyclic load (Qmin).

The cyclic loading characteristics Qmean and Qcyclic, normalized by the anchor uplift capacity before cycling (QT), are plotted in Figure 34, which presents all the cyclic tests performed for this research. The number of cycles to failure in each test can be marked in the plot. The contours of the number of cycles to failure (100 and 1000) define three stability zones. In the current research, the number of cycles of the cyclic tests ranged between 1000 and 3000. For cyclic loadings with greater maximum load (Qmax), a lower number of cycles were performed. Table 7 presents the main characteristics of the cyclic loadings. The installation of the helical anchor model was carried out to the maximum stroke of the servo-controlled system, which provided a helix embedment depth (zD) of 7.4D (244 mm in model scale). After the installation, the system was maintained standing at a minimum of 3 minutes and then, the pre-tensile loading (Qpre) was applied.

The pre-tensile load ranged from 10% to 50% of the anchor uplift capacity; however the majority of the tests were performed with pre-tensile loads between 10 and 30% (as showed in Table 7). After the application of the pre-tensile load and before starting the cyclic loadings, another three minute pause was taken. After the cyclic loading, a monotonic pull-out test was performed 3 minutes (or more) after the end of the cyclic test. Figure 35 illustrates the complete procedure of the cyclic load tests.

Tests with two consecutive cyclic loadings

Test series of two consecutive cyclic loadings with different Qmean and Qcyclic and a different number of cycles were performed to evaluate the influence of a previous cyclic loading on the anchor cyclic performance. In addition, the post-cyclic responses were compared to evaluate which sequence of cyclic loadings causes greater post-cyclic capacity degradation.

For the first test, a cyclic loading with a large amount of cycles (from 1000 to 3000 cycles) of small amplitude was performed on the anchor model. After that, still in flight, a cyclic loading with a larger amplitude and fewer cycles (from 300 to 1000 cycles) was carried out. After the second cyclic loading, a monotonic tensile load test was performed (Figure 37).

Field tests

Two single-helix anchors with an instrumented section above the helix were used to carry out monotonic and cyclic tests at the Experimental Foundations Site of the University of São Paulo at São Carlos. These anchors were manufactured by Vercon Industrial and were termed as 1MHA (monotonically tested helical anchor) and 1CHA (cyclically tested helical anchor -monotonic tests were also performed after each series of cyclic loading).

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The lead section of these single-helix anchors was composed of a cylindrical steel shaft with a 101.6 mm external diameter and a 7.1 mm wall thickness, and a helical bearing plate with a 305 mm diameter, a 12.5 mm plate thickness and a 75 mm pitch (Figure 38). The helical anchors were instrumented with strain gauges oriented in Wheatstone full bridge to measure the axial force in a shaft section 250 mm above the helix. Split steel sleeves covered the instrumentation to prevent damage during transportation and installation.

The strain gauges used were the PA-06-125BA-350-LEN simple unidirectional model polyamide based, designed steel, bondable type with a nominal resistance of 350 Ω. The strain gauges were bonded in pairs at opposite quadrants of the shaft cross section. In each pair, the strain gauges were bonded perpendicular to each other, one parallel and other perpendicular to the shaft's longitudinal axis.

The circuit was connected using a three-wire cable model 326-DFV manufactured by Vishay Precision Group. The cable comprises three twisted copper wires coated with tin with 0.404 mm diameter each wire (AWG 26).

The steel surface preparation for the strain gauges bonding was executed through the following process: i) solvent cleaning; ii) sanding (with sandpaper P60 and P120 grits); iii) cleaning with isopropanol; iv) application of conditioner and neutralizer; v) strain gauges fixing with cyanoacrylate adhesive.

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The cables connecting the instrumented section to the data acquisition system were placed inside the anchor shaft. The hole to pass the cables was sealed with adhesive joints and the external protection of the circuit was assured with a split steel sleeve.

The instrumented sections of both anchors were calibrated using a 500 kN capacity load cell with 0.5 kN resolution, a hydraulic actuator attached to a manual hydraulic pump, and a steel reaction frame (Figure 39). Data acquisition was performed using a P3 Vishay Micro-Measurements data acquisition system (Vishay Precision Group, 2011), registering the electrical signals of the load cell and of the strain gauges. The city of São Carlos is based on rocks of the "São Bento Group", constituted of sandstones of the "Botucatu Formation" and migmatites of the "Serra Geral Formation".

Above these rocks, conglomerates and sandstones of the "Bauru Group" and, then, Cenozoic

Sediments appear covering the whole region.

The typical geotechnical-geologic profile of the EESC-USP Experimental Site comprises a superficial layer of Cenozoic sediment composed of brown clayey sand (6 m thick), overlying a reddish clayey sand, originated from sandstone of the "Bauru Group"

(Figure 41). The action of weathering under local conditions causes a laterization process, which results in a very porous and collapsible material that is the superficial layer. A line of quartz pebbles and limonite separates the two soil layers. Figure 42 and Table 9 present the soil's granulometric characteristics at 3 different depths of the Experimental Site (3, 5 and 8 m depth).

Helical anchor installation and load test procedure

The helical anchors were installed on May 16 th , 2014. Each anchor was screwed into the ground with a hydraulic torque motor mounted on a backhoe loader, equipped with a digital torque indicator. The installation torque values were manually annotated every 0.5 m of penetration through the observation of the torquemeter display. Figure 43 shows the equipment used for the helical anchor installation and the torquemeter in detail.

The anchor 1CHA was tested monotonically and cyclically. Firstly, the 1CHA anchor was submitted to a monotonic tensile load test, and then, 4 cyclic and 4 monotonic tests were performed in an alternate fashion. Five monotonic tensile load tests were performed on reference anchor 1MHA, after the monotonic tests on anchor 1CHA were finished. Table 11 summarizes the loading tests carried out with both helical anchors. The monotonic and cyclic tensile load tests were performed using a hollow hydraulic jack with 450 kN capacity, and a reaction beam (composed of two 2.7 m long steel I-beams W530×92) centred over the anchor and resting on wood cribbing. A threaded rod was used to connect the hydraulic jack to the anchor. The applied load was measured using a 500 kN capacity load cell. The P3 Vishay Micro-Measurements data acquisition system was used to register the applied load. The anchor head displacements were monitored using four dialgauges with a resolution of 0.01 mm attached to two independent reference beams. Figure 44 shows the load test setup.

The axial load tests were conducted according to the Brazilian Standard ABNT-NBR 12131 [START_REF] Abnt | ABNT NBR-12131: Piles -static load test -test method[END_REF]. The load was applied in increments of 5% of the estimated anchor uplift capacity, with 5 minutes of maintained load for each load step. The loading was applied until an anchor head displacement equal or higher than 10%D was reached. The unloading was performed in 5 steps of 5 min until a load of 10% of the ultimate tension capacity was reached. The last unload step was maintained for 60 minutes. A preload of 4 kN was applied to the anchors to eliminate gaps in the connections of the shaft extension segments. After this procedure, the acquisition system was zeroed and the load test commenced.

The cyclic load tests were carried out with the same pre-tensile load (Qpre) in all of the tests, corresponding to 10% of the ultimate tension capacity obtained in the 1 st monotonic test on the anchor 1CHA (QT1). The characteristics of the cyclic load tests are presented in

Numerical modelling

Numerical analyses using the finite element method (FEM) were carried out with Abaqus/Explicit FEM suite to simulate the pre-and post-cyclic uplift response of the helical anchor tested in centrifuge.

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Parametric analyses of different properties of the soil disturbed by the anchor installation were carried out to evaluate the model response sensitivity of each parameter. The helical anchor prototype simulated in the numerical modelling presented the same geometrical characteristics as the prototype simulated in the centrifuge modelling. The measured and numerical results are compareble in this study.

Explicit and implicit (Abaqus/Standard) analysis

An explicit FEM analysis performs the incremental procedure and at the end of each of the increment updates the stiffness matrix changes based on the geometric and material changes. Then a new stiffness matrix is constructed and the following increment is carried out. In this type of analysis the increments are small enough to produce accurate results. One problem lies in the need for a large number of very small increments for accuracy, which causes a large computational cost along with it being time consuming. If the number of increments is not sufficient, the calculations tend to deviate from the correct solution. This is due to the fact that force balance is not strictly enforced, i.e., this method does not enforce force balance of the internal structure reaction forces with the externally applied loads.

An explicit analysis is a function of time. Thus, the velocity and acceleration, as well as the mass and damping, have to be considered. In an explicit method, Central Difference Time Integration (CDTI) is used to calculate field variables at respective nodal points. Since only a numerical solution is possible for a non-linear ordinary differential equation, the explicit method is particularly suited for non-linear problems (CAE ANALYSIS, 2011). It requires the inversion of the lumped mass matrix as opposed to that of the global stiffness matrix in the implicit methods. In the CDTI, the equation of motion is evaluated at the previous time step (tn-1, where tn is the current time-step).

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An implicit FEM analysis is analogous to the explicit analysis with the addition that, after each increment, Newton-Raphson iterations are carried out to ensure the force balance of the internal structure forces with the externally applied loads. Force balance is enforced to a specified tolerance. One drawback of the method is that during the Newton-Raphson iterations one must update and reconstruct the stiffness matrix for each iteration, and this can be computationally costly. However, larger increments are possible and the accuracy is typically higher than in the explicit case.

In an implicit scheme, displacement is not a function of time. Hence the velocities and accelerations which are time derivatives of displacement turn out to be zero and the mass and damping factors can be neglected. In order to solve a FEM problem using the implicit method, inversion of stiffness matrix is required. Very large deformation problems, such as crash analysis, can result in millions of degrees of freedom which effectively increase the size of the stiffness matrix. The larger the stiffness matrix, the longer the required computational time for its inversion. Hence, there is a need for an explicit method that would prevent the inversion of the stiffness matrix.

According to [START_REF] Helwany | Applied soil mechanics with ABAQUS applications[END_REF], implicit (static) analysis is the evident option for numerical simulations of footings since the load application is static, inducing no dynamic effects in the model. However, in situations with expected severe distortions, a static analysis may terminate when a few soil elements near a geometric singularity are excessively distorted. For this type of situation, progressive failure and post-failure conditions are able to be analyzed if explicit/dynamic formulations are used with caution. If the explicit/dynamic scheme is employed, the velocity of loading application must be very low to avoid "exciting" the finite element model.

In the current research, the Standard/Implicit analysis was chosen primarily for modelling the helical anchor response. However, excessive distortion of the soil elements

University of São Paulo and LUNAM University caused the termination of the analysis after a few millimeters of anchor displacement (around 5 mm). Therefore, explicit/dynamic analysis was chosen to simulate the quasi-static problem of the helical anchor model under tensile loading.

Model geometry, boundary conditions, finite elements and mesh characteristics

The numerical model was constructed with similar geometrical characteristics to the prototype simulated by the centrifuge modelling: a single-helix anchor with a helix diameter of D = 330 mm and a full cross-section shaft diameter of d = 100 mm. The numerical simulations comprised a unique helix embedment depth of zD = 7.4D, that is the helix depth adopted for the cyclic tests and some monotonic tests with models 10FH and 10FHi in centrifuge.

In the current investigation, the installation effect on the soil mass was considered in a simplified manner, assuming a cylinder of disturbed soil with different characteristics (compared with the undisturbed soil) around the anchor shaft. Therefore, the model geometry was constructed considering that the helical anchor was already installed into the ground. The geometrical characteristics and the model mesh are shown in Figure 45.

A distinct cylindrical zone of disturbed soil by the anchor installation was established according to experimental observations about the installation effects. The cylindrical zone of disturbed soil was considered with a radius 3 cm larger than the helix radius because the Abaqus software requires that any model part must have its left boundary over the axis of symmetry. Therefore, the disturbed soil above the helix and the soil below the helix were considered as the same material and therefore appropriate to be combined. Then a 3 cm  3 cm zone was created to the right of the helix to join the soil above with the soil below the helix.

Constitutive models

The numerical model basically involves two materials: i) steel for the anchor; ii) sand for the soil. The material behaviour for the helical anchor (steel) is assumed as linear-elastic with no material yielding given the low stresses generated by the applied loading.

The material properties used in the helical anchor are shown in Table 13. The density material for the anchor was chosen equals to the soil density to avoid convergence issues during the gravity loading step.

Table 13. Material properties considered for the helical anchor.

Young by [START_REF] Menétrey | Triaxial failure criterion for concrete and its generalization[END_REF] on the deviatoric stress plane [START_REF] Abaqus | User Manual: Abaqus Theory Guide[END_REF].

The mechanical properties of the undisturbed soil were obtained through triaxial tests (see Appendix C), and the bulk density was obtained with density boxes placed on the bottom of the strongboxes (Table 14). In addition, a numerical analysis of the triaxial tests with 3 confining stresses was carried out to compare the results.

A parametric analysis was carried out for the soil disturbed by the passage of the helix and shaft by varying the Young modulus and the internal friction angle of the soil. Thus, the agreement between the numerical and experimental results pre-and post-cycles was evaluated. These results are presented in section 6.

Table 14. Material properties considered for the undisturbed sand.

Young

Interfaces

The consideration of 3 different zones in the numerical model required the use of interaction models for the anchor-disturbed soil interface and for the boundary between the and the disturbed soil was modelled as a surface-to-surface contact with normal and tangential mechanical behaviours attributed. Normal surface behaviour was established as a "hard" pressure-overclosure relationship (no contact pressure until nodes are in contact; unlimited contact pressure once contact has been established), and the tangential surface behaviour was defined using the penalty friction formulation with an interface friction angle  =15º.

The nodes in the disturbed soil-undisturbed soil boundary were coupled using the tie interaction. This option imposes coupled interaction between pairs of surfaces. An additional verification was performed using the surface-to-surface contact option instead of the tie interaction. In this verification, the attributed interface normal stiffness was 110 10 N/m and the tangential behaviour considered an interface friction angle equalled to the disturbed soil's angle of friction. No difference was noticed comparing the results of both considerations for the disturbed soil-undisturbed soil interface.

Numerical analyses parameters

The analysis of the numerical model was comprised of 3 steps: i) initial (software default); ii) gravity loading; iii) tensile loading. In the initial step, a geostatic stress predefined field was attributed to eliminate material strain caused by the application of the gravity load in the subsequent step. This pre-defined field establishes the geostatic stress and the coefficient of lateral pressure before the application of gravity as a load in the second step.

The gravity was applied uniformly on the whole model. For the verification of scale effects for modelling helical anchors in sand, the value of uplift capacity (QT) of the anchor models was assumed to be the peak tensile force measured during the pull-out tests (Figure 48). The peak uplift capacity (QT (peak)), is very close to the tensile load related to a displacement of 10% of the plate diameter, (QT (0.1D)), as shown in Table 15 shows that the ultimate load was reached at a vertical displacement ranging from 10% to 16% of the helical plate diameter. The larger anchor models required slightly smaller displacements to attain the ultimate load; however, no clear trend was observed. probably occurred due to the variability in the sand samples and may not be attributed to particle size effects.

Previous studies on scale effects indicate that the values of bearing capacity and shaft resistance increase as the model size decreases (e.g. Ovesen, 1979 and1981;Foray et al., 1998;Garnier & König, 1998). The particle size investigation comprised monotonic tests on model anchors with w/d50 ratios ranging from 58 to 333. In this range of models assessed in this investigation, the almost horizontal trend line shown in Figure 49 suggests that no particle-size effect was observed for w/d50  58. The uplift capacity of the prototype simulated for this verification of scale effects was calculated by using Terzaghi's equation, as proposed in Adams and Klym (1972) for singlehelix anchors, and using bearing factor Nqu presented in Mitsch and Clemence (1985) for single-helix anchors in sand. The predicted value was 120 kN, which is approximately twice the measured mean value of uplift capacity (61 kN). Gavin et al. (2014) observed a similar difference between the results of numerical simulation and field experiments on a single-helix anchor in dense sand. These significant differences between the estimates and the measurements suggest that an important effect of the anchor installation is not considered in the prediction methods.

The results of installation torque necessary to install the anchor models tested in containers No. 11 and 12 are shown in Figure 50. Figure 51 shows that the final installation torque for models 10FH and 12FH is slightly greater than the results found for the other models. Models 10FH and 12FH were fabricated with a thicker helical plate (18.0 and 25.0 mm thickness in prototype scale, respectively) compared to models 6FH and 8FH (8.4 and 8.8 mm thickness in prototype scale) to avoid plate bending during installation. According to Sakr (2014), installation torque increases with helix thickness, since one of the torsional moment components acting on the helix is caused by the moment acting on side surface of outer perimeter of the helix. In addition, the thicker the helical plate, the greater the volume of the displacement soil by the passage of the helix.

Thus, the torque gain observed in models 10FH and 12FH is not evidence of a scale effect on the results of torque measurements. Accordingly, Figure 51 suggests that the installation torque was not influenced by scale effects. This verification highlights that the centrifuge modelling technique can be used successfully for investigations on the installation torque of helical foundations using anchor models with a ratio w/d50 greater than 58. Hoyt and Clemence (1989) proposed an empirical relationship between the installation torque and the axial uplift capacity of helical piles, given by Eq. 13:

D avg t T T K Q 3    Eq. 13
where,

Tavg-3D = average of the torque measured along the final distance corresponding to 3 times the helix diameter; Kt = torque correlation factor that varies with the shaft diameter.

To verify if the physical modelling well reproduced the field behaviour of helical anchors during installation and under tensile loading, Kt values were determined in this investigation, as presented in Table 15. The centrifuge tests provided Kt values of similar magnitude to the field measured value presented in Gavin et al. (2014) for a single-helix anchor with similar dimensions installed in dense sand. These authors found a Kt value of 13 m -1 , and the current centrifuge tests provided a mean Kt value of 15 m -1 . Therefore, no scale effect was observed in the simulation of a prototype Kt factor in the range of model sizes University of São Paulo and LUNAM University tested. On the other hand, the coefficients of variation of of installation torque and Kt factor indicate that the resisting forces acting on the helical anchor during installation are more variable than the forces acting on the anchor under tensile loading.

Evaluation of installation effect

The evaluation of the installation effects on the uplift capacity of helical anchors in dry sand was done in this study using the three different techniques described below. Figure 53a shows a photograph of the sand sample after the anchor installation. In this figure, the disturbed sand around the anchor is clearly observed. The sand is dragged down near the shaft and the soil above the helix rises upwards (as observed in [START_REF] Komatsu | Development on battered pile with screw pile method (NS-ECO pile)[END_REF].

Comparison between anchors in disturbed and undisturbed sand

Figure 54 illustrates the movement of the sand grains due to the helical anchor installation. Figures 57a andb show that the sand around the helix and around the shaft present different densities compared to the rest of the sand specimen. Close to the shaft, there are zones of both light and dark grey corresponding to dense and less dense sand, respectively (Figure 57a). This observation suggests that the sand disturbance is not uniform along the cylindrical zone above the helix, and that the configuration of dense and less dense zones depends on the patch followed by the helix. The same observation can be used for the zone around the helix illustrated in Figure 57b. This figure shows that the concentration of dark grey colour is more noticeable in one quadrant of the helix circumference. These observations support the hypothesis that during the model anchor installation, the traversed and displaced sand by shaft and helix during installation experiences different degrees of disturbance.

Possibly during the installation, the helix pushes up the undisturbed sand, and after the helix passage, the sand moves down to fill the gap created when the helix leaves this region. These sand layers are only slightly affected by the helix movement and, therefore, these layers of sand remain dense. Both anchor models had a helix embedment depth of 7.4D and the full-scale field test had a helix embedment depth of 6.1D (Gavin et al. 2014). Although the mean fraction of shaft resistance (obtained from tests on the instrumented piles of this study) is 18% of the total capacity (Figure 60), the results show that the centrifuge and field tests are comparable. (the Qpre value), and then to the mean cyclic load in tension (Qmean). As this procedure of increasing force in tension is monitored, the percentage of load resisted by the helix and by the shaft can be quantified.

From the results of the tests on the 10FHi model, the portion of load resisted by helix bearing corresponded to a mean value of 82% of the applied load, with a coefficient of variation of 12%. Figure 60 shows the ratio of the load on the helix to the maximum applied load (Qhelix/Qapplied) within the analysed test period.

University of São Paulo and LUNAM University Figure 62 presents a scheme of the helix-rod connection of the model anchors with a removable helix when there is a remaining torque after the anchor installation. Figure 62. Scheme of the additional contact in the helix-shaft connection due to torque.

Cyclic loading tests with 10FH and 10FHi

The cyclic loading investigation was conducted with the instrumented 10FHi and noninstrumented 10FH single-helix models with a helix diameter of 33 mm and a shaft diameter The monotonic capacity in tension (QT) was established as the peak tensile load independent of displacement. The ultimate load was found equal to 93.0 kN, in prototype value, for the 10FH model tested in container No. 5 (ID = 95%). About the same value was found in the pull-out tests of the 10FHi model: 92.7 kN for the first test and 94.5 kN for the second test, both carried out in container No. 9 (ID = 99%). Therefore, the monotonic capacity in tension (QT) was adopted as the average value of the three results, QT = 93.4 kN.

Helical anchor behaviour under cyclic tensile loading

After installation, the model anchors were cyclically tested in tension with values of Qpre varying from 0.08QT to 0.51QT (see Table 5, Chapter 3) to simulate the field minimum service load. In one-way cyclic loadings on regular piles (with no helices or wings), displacements greater than 0.1D have been commonly observed for Qcyclic lower than 0.3QT after 1000 cycles [START_REF] Tsuha | Behaviour of displacement piles in sand under cyclic axial loading[END_REF][START_REF] Puech | Cyclic stability diagrams for piles in sands[END_REF]. In the present research, the tests have shown the helical anchor model experiences 0.1D of accumulated displacement after 1000 cycles for cyclic loadings with Qcyclic from 0.2QT to 0.3QT, depending on the combination with Qmean.

However, the cyclic response of a helical anchor is not comparable to the response of conventional piles under cyclic tensile loading, as the role of the bearing helix controls the cyclic behaviour of this type of foundation. Figures 64a andb show that the first load cycle is observed to differ significantly from the following ones. The permanent displacement at the end of the first cycle was much larger compared to the subsequent cycles. The first cycle corresponds to the first loading on the disturbed sand above the helix; therefore, the subsequent cycle starts after a sand densification above the helix. [START_REF] Wichtmann | Influence of a cyclic and dynamic loading history on dynamic properties of dry sand, part II: cyclic axial preloading[END_REF] did not consider the deformations during the first cycle in the analysis of accumulation of deformations under cyclic loading since the analysis performed by these authors intended to investigate rules of cyclic displacement accumulation in sand specimens. Concerning the unloading branch of the first cycle, [START_REF] Wichtmann | Influence of a cyclic and dynamic loading history on dynamic properties of dry sand, part II: cyclic axial preloading[END_REF] argues that the strain generated in the three following quarters of the first cycle is negligible in comparison with the strain accumulated during the large number of subsequent cycles. In cyclic stability analysis, however, the displacements of the first cycles may be considered, since the initial conditions of the studied prototype does not involve the application of a pre-cyclic load greater than the maximum cyclic load (Qmax).

The results of the 5 th cyclic test carried out in container No. 9 (10FHi-5 -Cont. No. 9), presented in Figure 65, illustrate the effect of the application of a previous pre-tensile loading greater than the cyclic test Qmax (test 10FH-5 Cont. No. 4). For this case, at the end of the installation, a delay between stopping the vertical advance and stopping the helix rotation was observed. This mismatch caused an additional tensile force at the anchor head of about 64 kN, which pre-loaded the anchor with a greater value than the Qmax of this cyclic test. The occurrence of a large tensile load before the cycles increased the initial anchor stiffness and reduced the displacements of the first cycle. However, the results with no previous application of tensile loading (tests 10FHi-1 and 10FHi-2 in container No. 14) exhibit large displacements during the first cycle (Figure 65). (with a lower mean load and a lower cyclic amplitude condition) show that the anchor head displacement was 4.5%D after 1000 cycles, and 5.7%D after 2000 cycles. In the test with an intermediate condition of mean load and cyclic amplitude (Figure 66b), the maximum displacement achieved was 9.0%D after 1000 load cycles. The results of the test with a greater mean load and cyclic amplitude (Figure 66c) indicate a maximum anchor head displacement of 10.9%D at the last cycle (N = 300).

In Figure 66, the permanent displacement was much larger at the end of the first cycle than in the following cycles of the three tests. As mentioned before in this text, the first cycle includes the first loading on the sand above the helical plate, which is in a disturbed condition due to the anchor installation; therefore, the subsequent cycle starts after the sand densification above the helix. After a few cycles, during the unloading stages of each cycle, the results presented in

Figure 66 indicate that the force registered by the force gauge above the helix becomes greater than the applied force Also, the minimum tension force registered by the force gauge at the end of the unloading stage increases with the number of cycles. This occurs because at the beginning of the unloading stages the anchor movement alternates, and the anchor starts to move down. Consequently, at the end of the unloading stage a force below the anchor tip pushes up the helical anchor. When the applied tension load increases, the contact between the anchor tip/helix and the soil below the tip/helix is reduced and this force disappears. At the same time the sand grains move toward the "gap" formed beneath the anchor helix/tip.

After that, in the next unloading stage, the soil that fills the gap below the helix/tip will cause the registered pushing up force when the anchor moves down, as explained in Figure 67, and as discussed in section 4.2. This pushing-up force observed at the end of the unloading stage increased over the cycles and was greater tests of smaller cyclic amplitudes (Figure 66a), probably because the gap formed beneath the helix/tip is greater in larger cyclic amplitudes.

The assumptions illustrated in Figure 67 are corroborated by previous findings about the installation effects in section 4.2, and from Figure 56. The results of various tests in Figure 69, indicate that all the inflection points are placed along a straight line (separating non-linear from linear trends). This observation suggests that, after a number of cycles, the accumulated displacement can be predicted by a (logN)² function according to the combination of cyclic parameters as a mean load and a load amplitude.

Figure 70 presents typical curves of the displacement accumulation rate (the increment of accumulated displacement per cycle). The displacement rate is greater for higher values of cyclic amplitude and mean load. However, after a dozen cycles, the displacement rate drops to about 5% of the initial rate.

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Even at large cyclic loads (Qmax = 0.93QT) a significant decrease of the displacement accumulation rate is observed after a number of cycles.

For guyed tower anchors, a few cycles of cyclic loading with such intensity (0.93QT) would cause the anchor to fail cyclically due to excessive displacements. However, as the helix bearing resistance increased due to the soil densification above the helix during the cyclic loading, little or no loss in uplift capacity was observed in the post-cyclic monotonic test results. Therefore, the adjustment of the pre-stressed tower cables may be a repairing solution for excessive cyclic displacements of the anchor with no loss of capacity.

Figure 71 shows that no indication of displacement increase is observed after cyclic displacements of about 10%D. The displacement accumulation tends to decrease and stabilize at a given rate value depending on the cyclic loading intensity. Table 17 presents values of displacement accumulation rates of the three tests shown in Figure 71. The cyclic stiffness response is evaluated in this study using the parameters described in Figure 73 shows that the anchor axial stiffness enhances up to 4 times the initial stiffness, with more significant growth in the first 10 cycles for the tests on the 10FH model (Figure 73a). For the tests carried out on 10FHi model, the gain of anchor axial stiffness achieves a value from 1.7 to 3.6 times the initial stiffness, with more significant growth in the first 100 cycles (Figure 73b). For the first 10 cycles, the stiffness increase rate is higher in the tests on model 10FH (Figure 74a) than in tests on model 10FHi (Figure 74b). During the three cyclic tests on 10FH, with cyclic amplitudes up to 20%QT, the sand above the helix is densified and passes to an overconsolidated state. For the tests with higher cyclic amplitudes (34% and 42%QT), after a dozen cycles, a larger zone of sand above the helix is affected by the helix displacement and the sand densification continues. This effect can be verified by the late stiffness gain in the tests on the 10FHi model in container No. 14 (Figure 74b).

Shaft resistance degradation

Figure 75 presents the shaft resistance mobilized during the cyclic tests performed on the instrumented anchor model (10FHi). The initial value of the shaft resistance (Qshaft) varied from 2.8 kN to 28 kN in prototype values, which corresponds to 3% to 30% of the anchor uplift capacity (QT), respectively. Tests presenting greater values of skin friction (fs) were typically conducted with a larger Qmean. This observation indicates that a larger applied load induces a greater mobilization of the shaft resistance. Thus, in a one-way tensile cyclic loading with low values of Qmean and Qcyclic, the shaft resistance cannot be fully mobilized. On the other hand, in the cyclic loadings with higher cyclic amplitudes the shaft resistance is completely mobilized, and also exhibits the degradation of shaft resistance in early cycles. At the end of the cyclic test, the reduction in skin friction varies from 22% to 60% of the initial skin friction (N = 1), corresponding to a shaft load (Qshaft) ranging from 3% to 8% of the maximum applied load in the last performed cycle. Therefore, at the end of cyclic loading the shaft resistance is reduced to a very low value (almost nil), and the helix bearing resistance controls the anchor uplift capacity.

The results of this investigation showed that skin friction degradation is dependent on the cyclic loading magnitude and on the initial value of the shaft load (Qshaft). Figures 75a andb present the results of cyclic tests with U < 10%D after 1000 cycles for most cases (tests conducted in containers No. 9 and 10). In these figures, the skin friction degradation is observed over the entire test, indicating no stabilization. On the other hand, for cyclic tests with U  10%D the most significant degradation occurred before 100 or 200 cycles (Figures 75c andd). The helix bearing resistance controlled the behaviour of the model anchor since 70% to 97% of the applied load during the first cycles was resisted by the helix. In the last cycle, the portion of the applied load resisted by the helix was found to be from 92% to 97% of the maximum applied load. Figures 78a andc present the helix bearing mobilization during the cycles.

Greater shaft resistance was observed in the cyclic tests in container No. 9 and 10 in comparison with containers No. 13 and 14. In these cases, a smaller load was resisted by the helix (Figures 78a andc). However, as the skin friction degradation increases, the helix bearing also increases.

Figures 79b andd show the applied load resisted by the helix during the cycles normalized by the load resisted by the helix during the second cycle (N = 2).The majority of the cyclic tests performed on anchor model 10FHi showed a helix bearing resistance increase of up to 20% in relation to the value obtained in the first cycle (Figures 79b andd). This gain in helix bearing provided cyclic stability to the helical anchor, which resulted in a wide zone of Stable response in the interaction diagram is shown in section 4.5.7 (displacement limit criteria). Consequently, a narrow zone of Unstable response is noticed.

An increase in the helix bearing resistance of around 10% was observed after the first cycle of all tests. In the following cycles, an increase of helix resistance is observed up to 100 cycles for cyclic tests with higher cyclic amplitudes (Qcyclic ranging from 25 to 42%QT).

However, for cyclic loadings with smaller cyclic amplitudes (up to Qcyclic of around 20%QT) the helix bearing exhibits increase after 100 cycles. Figure 79 shows the contours of percentages of the helix bearing resistance increase during cyclic tests.

Q helix (N) / Q helix (N=2) Q helix (kN) Q helix (kN) Q helix (N) / Q helix (N=2)

Post-cyclic monotonic response

After the cyclic tests, monotonic uplift tests were performed to evaluate the influence of the cyclic loading on the post-cyclic response of the anchor.

No clear relationship was found between any cyclic loading parameter and the postcyclic capacity (QT-pc) variation. Generally, the post-cyclic uplift capacity was greater than the pre-cyclic monotonic capacity when the applied cyclic loading caused accumulated displacements greater than 10%D and up to 400 cycles (Figure 80a). Still, some cyclic tests with accumulated displacements smaller than 10%D exhibited a QT-pc greater than QT. Figure Table 19 summarizes the results of the post-cyclic monotonic uplift tests. The postcyclic capacity gain seems to be related to the minimum value of the mean cyclic load (Qmean).

The majority of the post-cyclic monotonic tests with a post-cyclic capacity greater than the pre-cyclic capacity were performed with Qmean between 45 and 67%QT. However, the The tests that exhibited a post-cyclic capacity increase also had a maximum cyclic load (Qmax) with values greater than 80%QT. Therefore, the gain in post-cyclic capacity occurred when the cyclic loading was performed with the Qmean maintained around 50%QT, and reaching to values of Qmax greater of 80%QT or more. A cyclic loading with such conditions of Qmean and

Qmax induces important densification of the sand above the helix, resulting in an increase in the helix bearing capacity. The cyclic loading also caused degradation of the anchor's post-cyclic uplift capacity in 15 of the 26 pull-out tests performed after cycling. In most of the cyclic tests that caused accumulated displacements (Uacc) smaller than 0.1D after 1000 cycles, a post-cyclic capacity reduction was noticed. In tests reaching Uacc  0.1D before 1000 cycles, although the limit displacement condition had not been attained, no capacity degradation was noticed for most tests except an increase of up to 8% of the post-cyclic capacity. Figure 81 shows the load-displacement response obtained for the three post-cyclic monotonic tests carried out on model 10FHi. This figure demonstrates that no loss in uplift capacity occurred after the cyclic tests. The cyclic loading caused densification of the disturbed soil above the helix, improving the helix bearing response. For cyclic tests of greater cyclic load amplitudes, the gain observed was higher. Figure 81 indicates that after cycles of higher load amplitude (10FHi-4 -Cont. No. 13), a stiffer response of the anchor was observed (smaller displacements of the anchor head compared to the other post-cyclic tests). Nevertheless, studies on the pile response to cyclic compressive loading have been performed

considering both base resistance and the skin friction responses to construct cyclic interaction diagrams [START_REF] Karlsrud | Piles in clay under cyclic axial loading: field tests and computational modeling[END_REF][START_REF] Poulos | Cyclic stability diagram for axially loaded piles[END_REF][START_REF] Airey | Estimation of pile friction degradation from shearbox tests[END_REF]1995;[START_REF] Puech | Cyclic stability diagrams for piles in sands[END_REF].

The helical anchor behaviour under cyclic tensile loadings is dependent on the joined responses of the shaft resistance and the helix bearing resistances. Therefore, the cyclic interaction diagrams in this study consider the set of helix bearing and shaft resistances in the analysis.

A Stable (S) response is defined for the cases in which the displacements of the anchor head accumulate slowly and do not reach values of 10% of the helix diameter (0.1D), during 1000 cycles or more. The Unstable (U) response is characterised by a rapid increase of the anchor head accumulated displacement reaching a limiting value of 0.1D during the first 100 cycles. For intermediate situations in which the anchor head reaches an accumulated displacement of 0.1D after 100 and before 1000 cycles, and the cumulative displacements increases at a moderate rate without stabilising, the cyclic response is classified as Meta-

Stable (MS).

Based on these categories of cyclic response, Figure 83 Although the analysis of displacement accumulation is necessary, the anchor performance is also dependent on the effect of the cyclic loading on the post-cyclic response.

This effect must not be neglected since the degradation and consequent reduction of the postcyclic anchor uplift capacity implies in a reduction in the foundation safety factor.

The results presented in section 4.5.6 show that the degradation of the post-cyclic uplift capacity occurred in cyclic loadings with accumulated displacements smaller than 10%D up to 1000 cycles.

On the other hand, for some cyclic tests with values of accumulated displacements larger than 10%D with less than 1000 cycles (sometimes less than 100 cycles), the post-cyclic monotonic capacity increased in relation to the pre-cyclic capacity. This fact is explained by the greater densification of the soil above the helix, causing the increase of helix bearing capacity.

Figure 85 presents the contours of the normalized post-cyclic uplift capacity varying with the cyclic parameters Qmean and Qcyclic. During low amplitude cyclic loadings, the sand densification is lower compared to the cases of higher cyclic amplitudes, and the accumulated displacements after 1000 cycles did not reach 10%D. In this case, the displacements are insufficient to compact a significant zone of sand above the helix. Thus, the loss in post-cyclic uplift capacity compared to the precyclic capacity is caused by the skin friction degradation.

In the case of high-amplitude cyclic loadings, the anchor displacement during the cyclic loadings re-arrange and compact the sand mass of a wide zone above the helix. This effect is responsible for avoiding reductions in the post-cyclic uplift capacity, although the shaft resistance is reduced after the loading cycles.

In some cyclic loading tests, despite the anchor accumulated displacement is greater than 10%D after a few cycles, no degradation of the post-cyclic uplift capacity was observed.

Therefore, a cyclic stability classification using the interaction diagram has proven un-suitable if only the displacement limit is the only criterion used to distinguish the cyclic responses.

Instead of evaluating the cyclic response merely based on the accumulated displacement, the cyclic behaviour of helical anchors should also be evaluated for the effects of the cyclic loading on the degradation of the anchor uplift capacity. Thereby, appropriate safety factors have to be used in the cyclic and post-cyclic stages of the helical anchor in service. Thus, two interaction diagrams are constructed in this study to separately evaluate the cyclic accumulated displacements and the post-cyclic capacity.

The first diagram (shown in Figure 83) provides information about the accumulated displacements during the cycles in order to guide the estimation of helical anchors displacement response under cyclic tensile loadings. The second diagram (Figure 86) provides the uplift capacity degradation. In field conditions, the intensity of the cyclic loadings varies according to the intensity of the acting forces on the structure. For guyed towers, as the main acting forces are due to wind action, the helical anchors can be subjected to sequences of cyclic loading of different amplitudes. Depending on the combinations of amplitudes, the helical anchor performance can be affected in different manners. Therefore, the effect of combining two successive and different cyclic loadings of different cyclic amplitude was also evaluated in this study, following a similar procedure shown in [START_REF] Blanc | Effects of cyclic axial loading sequences on piles in sand[END_REF].

Firstly, a cyclic loading test with 3000 cycles of low-amplitude (Stable) was carried out on model anchor 10FH, followed by 1000 cycles of a medium-amplitude cyclic loading, which lies at the limit between Stable and Meta-Stable, according to the limit displacement criteria of 10%D. After that, a second cyclic test was performed in an inversion of the order used for the first test. Both tests were conducted in container No. 6.

Figure 87a presents the load-displacement response of the first cyclic test (low amplitude followed by medium-amplitude cyclic loading) on anchor model 10FH (test 10FH-5). Both parts of the cyclic loading were carried out with the same pre-tensile load (Qpre or Qmin) of 17%QT, but with Qcyclic = 0.10QT for the first part of the test and Qcyclic = 0.28QT for the second part. The load-displacement response of the second cyclic test (10FH-6), which was carried out with the inverse sequence used for the first test is presented in Figure 87b.

Figure 87 shows that when a medium-amplitude cyclic loading (Qcyclic = 0.28QT) is performed before a low-amplitude cyclic loading, the accumulated displacements at the end of the cyclic loading is 42% smaller compared to the case in which a low-amplitude cyclic loading of Qcyclic = 0.10QT is applied first. The accumulated displacements at the end of test 10FH-6 corresponded to 9%D (Figure 87b), while in test 10FH-5 the accumulated displacements reached 15%D (Figure 87a). the accidental pre-loading at the end of the model installation compacted the sand above the helix, (2) during the installation of the anchor with smaller helix-pitch the soil above the helix is traversed more times compared to the model of the larger helix-pitch (10FHi), and as a consequence the level of sand disturbance is greater. However, no conclusions could be drawn about these observations.

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A 3 rd and a 4 th cyclic test on model 10FHi were performed with sequences of cyclic loading with different combinations of cyclic loading amplitudes, but with approximately the same Qpre value.

In the 3 rd cyclic test (10FHi-3 Cont. No. 14), for the first part of the cyclic loading a similar medium-amplitude to the first and second tests on 10FHi (Qcyclic = 0.28QT) was used (with a limit of stable and meta-stable cyclic responses using 10%D displacement criteria).

The second part of the 3 rd cyclic test consisted of 300 cycles with a high load amplitude, capable of causing accumulated displacements larger than 10%D before 100 cycles (Qcyclic = 0.39QT). The 4 th cyclic test was conducted using the inverse sequence of cyclic loadings (test 10FHi-4 Cont. No. 14).

Figure 89 presents the results of the 3 rd and 4 th cyclic tests conducted on model 10FHi.

The cyclic test with the higher amplitude applied first caused larger accumulated displacements, differently than that observed for the tests with sequences of medium and low amplitudes (Figure 88).

The medium-amplitude loading of tests 10FHi-6 and 10FHi-3, respectively in containers 9 (Figure 88b) and 14 (Figure 89a), caused a reduction in the displacement accumulation rate in both tests. When high-amplitude cyclic loading was carried out first, the accumulated displacement reached 13%D at the end of this cyclic loading part (Figure 89b).

When the medium-amplitude loading was applied first (Figure 89a), the accumulated displacement during the following cyclic loading (the high-amplitude loading) was 7%D. In the first part of the cyclic loading, an increase in the anchor axial stiffness was observed in three of the four tests on 10FHi (Figures 91a andc). The only case of stiffness decrease observed was in the first loading, because the anchor initial stiffness was higher than the other three tests, caused by an accidental pre-loading as explained previously.

On the other hand, two cyclic tests presented a stiffness decrease in the second part of the cyclic loading. The similarity between these two tests is in the smaller amplitude compared to the first part of the cyclic loading (Figures 91b andd). 10FHi-5 -Cont. 9 1 st : Q mean = 0.28Q T ; Q cyclic = 0.10Q T 2 nd : Q mean = 0.44Q T ; Q cyclic = 0.26Q T 10FHi-6 -Cont. 9 The post-cyclic response was also evaluated for 6 tests with two different cyclic loading sequences. Figure 92 shows that the greater pull-out capacities were observed after the two high-amplitude cyclic tests (10FHi-3 and 4, both in Cont. No. 14). For these cases, the postcyclic values of pull-out capacity are greater than the pre-cyclic (QT). All the cyclic tests using higher-lower loading amplitudes exhibited post-cyclic capacities greater than the tests with sequences of lower-higher loading amplitudes.

1 st : Q mean = 0.44Q T ; Q cyclic = 0.26Q T 2 nd : Q mean = 0.28Q T ; Q cyclic = 0.10Q T 10FHi-3 -Cont. 14 1 st : Q mean = 0.42Q T ; Q cyclic = 0.25Q T 2 nd : Q mean = 0.56Q T ; Q cyclic = 0.39Q T 10FHi-4 -Cont. 14 1 st : Q mean = 0.56Q T ; Q cyclic = 0.39Q T 2 nd : Q mean = 0.42Q T ; Q cyclic = 0.25Q T 1 st 2 nd 1 st 2 nd 2 nd 1 st 1 st 2 nd

Summary and conclusions

From the centrifuge testing programme carried out during this study, the following main observations were made about the behaviour of the helical model anchors under monotonic and cyclic loading: a) Comparable monotonic uplift capacity was found for anchor models with w/d50 ratio ranging from 58 to 117. For the same range of w/d50, the results of installation torque and torque correlation factor Kt were not affected by scale effects. In addition, the Kt values were found to be comparable to field measurements. These findings are valid for a D/d ratio equals to 3.3.

b) The sand disturbance in the cylindrical zone above the helix was not uniform with the depth. Contrast between less dense and denser sand was observed at a given cross-section of the cylinder of disturbed soil, indicating that the sand undergoes greater disturbance in the path the helix goes through.

University of São Paulo and LUNAM University c) Under monotonic tensile loading, the portion of the applied load resisted by helix bearing was found to be, on average, 82% of the applied load. After cycling, the portion resistance by helix bearing increased to 93% of the applied load, on average. This increase is mainly due to the degradation of the shaft friction resistance.

d) During the unloading stages (minimum applied load) of the cyclic tests, the tension force registered by the load cell above the helix was observed to become greater than the tension force applied to the anchor head. This minimum tension force registered by the load cell at the end of the unloading stage increases with the number of cycles. This phenomenon is related to the presence of the sand grains below the anchor does not allow the anchor to return to its initial starting elevation, thus with successive load cycles, the sand grains slowly creep underneath the anchor helix.

e) This study is focused on the cyclic behaviour of helical anchors used to support guyed tower under high wind speeds (low probability occurrence and low number of loading cycles). For this type of structure, the failure is associated with a specific displacement that will cause the slack of the cable. For this reason, this study is focused on the cyclic displacement response. For the cyclic loading conditions and numbers of cycles performed in the current study, no catastrophic anchor failure was observed.

f) Two different displacement accumulation trends were observed during the cyclic tests. These two trends were found to follow different functions. The transition from one trend to another was found to occur at specific values of cycle number (N) and accumulated displacement (Uacc). These specific values of N and Uacc were found to align in a straight line when the displacement accumulation response is analysed in a graphic of (logN)² versus Uacc for cyclic tests varying Qmean and Qcyclic.

g) The cyclic stability of helical anchors was suggested to be evaluated from the accumulation of displacements and from the degradation of the post-cyclic capacity. Thus, two interaction diagrams were constructed.

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RESULTS OF FIELD LOAD TESTS

Installation torque

The installation torque of both single-helix anchors tested at the Experimental Site of the University of São Paulo at São Carlos was registered every 0.5 m for the 15 m of anchor installation. The installation torque results are presented in Figure 93 and compared with the values reported by [START_REF] Tsuha | Theoretical model to control on site the uplift capacit of helical screw piles embedded in sandy soil[END_REF]. This author tested two double-helix anchors installed at the same site with 14.4 m depth. [START_REF] Tsuha | Theoretical model to control on site the uplift capacit of helical screw piles embedded in sandy soil[END_REF]) is equal to the helix diameter of the current study, in the current study the helix of 305 mm was installed deeper. Also, during the installation of top helix of the anchor 5C, the penetrated soil was already disturbed by the installation of the bottom helix, facilitating the penetration of the top helix, and reducing the installation torque.

Initial monotonic tension load test

The field experiments comprised: cyclic tensile loading tests on anchor 1CHA, and monotonic tensile loading tests on anchors 1MHA and 1CHA. Both anchors were instrumented to separate shaft and helix bearing resistances.

The anchor uplift capacity was established as the applied load to cause an anchor head displacement equals to 10%D (33 mm). This criterion is commonly adopted for helical anchors.

Figure 94 presents the load-displacement response for the uplift load tests on both 1MHA and 1CHA helical anchors. According to a limiting displacement criterion of 10%D, the uplift capacities of the first load test (QT1 2 ) were 89.1 and 97.6 kN respectively for 1MHA and 1CHA anchors.

The helix responses in both tests were identical in most load steps. During the last load step, the load registered in the shaft section above the helix was 77.2 kN for 1MHA and 2 QT1 is the reference uplift capacity obtained from the 1 st monotonic test for the calculation of the cyclic loading parameters.

60.3 kN for 1CHA (respectively, 87 and 62%QT). The shaft resistance (Qapplied -Qhelix) exhibited a peak approximately in the middle of the test (at a displacement of around 6%D or 18%d, where D and d were the helix and shaft diameters, respectively), followed by a decrease, which was more pronounced for anchor 1MHA. At the end of the load test, a negative skin friction and, consequently, a residual load at the helix was observed in both tests. The observed residual load was greater for the anchor 1MHA (Figure 94). Figure 95 presents a scheme of the reacting forces on the helical anchor during the first load tests. At the end of the unloading stage with no applied load on the anchor head, the skin friction prevents the rebound of the helix which causes the application of compressive forces on the soil above the helix. Therefore, to equilibrate the reacting forces on the helix caused by the compressed soil, the skin friction is reversed and becomes negative.

Cyclic loading tests on 1CHA anchor

In this section, the results of the cyclic tests and the subsequent monotonic load tests are presented and discussed in the same order in which the tests were performed (chronological order). In addition, the results of the monotonic tension load tests on 1CHA are compared with the results of the monotonic load tests on the reference anchor (1MHA), which did not experience cyclic loadings. Table 20 recapitulates the characteristics of the cyclic loadings carried out on anchor 1CHA. The four cyclic loading tests performed on anchor 1CHA are presented in Figure 96.

Monotonic tensile loading tests were conducted on this anchor before and after all cyclic

University of São Paulo and LUNAM University loading tests. In parallel to the monotonic tests on anchor 1CHA, monotonic tests were also conducted on reference anchor (1MHA).

The first cyclic test was carried out after the 1 st monotonic uplift test on 1CHA (Figure 96a). This first cyclic test was performed with cyclic parameters of Qmean = 0.15QT1 and Qcyclic = 0.05QT1 to evaluate the possible increase in the anchor's capacity due to lowamplitude cyclic loadings, typical in service conditions of guyed tower anchors. Due to the previous ultimate load applied on anchor 1CHA, Figure 96a shows that the cyclic loading caused very small displacements (around 0.1%D) during each cycle, with a negative accumulated displacement of the same magnitude. Despite causing large displacements that reached a limit condition of 10%D, the application of a single load cycle with a large amplitude of Qmax = QT1 (1 st monotonic load test) caused an improvement in the soil above the helix resulting in increased and the elimination of the accumulated cyclic displacements.

Negative accumulated displacements were observed during the cycles (Figure 96a) and can be explained by the negative skin friction on the shaft and the effects of the previous monotonic loading test on the soil above the helix.

Figure 96b shows that the registered load in the instrumented section (just above the helix) was virtually constant during the cycles. This constant load value during the cycles indicates that the shaft skin friction fluctuates between upward and downward sense depending on the magnitude of the applied force. Also in this figure, a decrease of the maximum load in the instrumented section helix occurred during the cycles (around 17%).

Since no helix bearing degradation is expected due to the helix bearing capacity increase after each monotonic tension load test, the decrease in the registered load in the instrumented section is probably due to the positive friction gain caused by the reversion of the negative skin friction. The results of the 2 nd monotonic load test conducted on anchors 1CHA (after the 1 st cyclic loading) and 1MHA are presented in Figure 97b. The ultimate applied load in this 2 nd monotonic loading test increased in around 55% in comparison with the 1 st load test. At the last load step of the 2 nd monotonic test, the applied tension load was equal to 154.0 kN and caused vertical displacements of 32.55 and 33.41 mm, respectively for 1MHA and 1CHA.

Therefore, no influence of the 1 st cyclic loading was observed on the post-cyclic response of anchor 1CHA. Both anchors exhibited a similar load-displacement response registered at the anchor head. However, differences were observed in the registered force in the instrumented section above the helix. In the instrumented section, a greater load (91%Qapplied) was observed for 1MHA anchor in the last load step in comparison with 1CHA (72%Qapplied).

Observing the shaft resistance (Qapplied -Qhelix), an increase was noticed at an anchor vertical displacement of around 5%d (or 1.6%D). After this peak, the shaft resistance decreased for 1MHA and slightly increase for 1CHA. Therefore, at the last load step, the shaft resistance achieved values of 13.9 and 44.2 kN respectively for 1MHA and 1CHA.

The 2 nd cyclic test was carried out after the 2 nd monotonic uplift test on 1CHA with Qmean = 0.25QT1 and Qcyclic = 0.15QT1. The maximum applied cyclic load (Qmax) corresponds to 26% of the ultimate load obtained during the 2 nd monotonic test on 1CHA. Figure 96c shows that no displacement increase occurred during the cycles and also no accumulated displacement was observed at the end of the cyclic test. Figure 96d shows a slight decrease of the maximum load measured in the shaft section just above the helix compared to the 1 st cyclic test (12% in the 2 nd cyclic test and 17% in the 1 st cyclic test). Also in Figure 96d, as in the 1 st cyclic test, the force registered in the instrumented section was greater than the applied load on the anchor head during the minimum cyclic load (Qmin or Qpre), indicating that reversion of shaft friction still occurs. After the 3 rd cyclic test, the 4 th monotonic tension load test performed on anchor 1CHA exhibited an ultimate load 17% greater than anchor 1MHA (Figure 97d), which had presented the greater ultimate load value in the previous (3 rd ) monotonic load test (Figure 97c). Besides the ultimate load increase of anchor 1CHA, the registered load in the last load step indicated no load increase in comparison with the previous monotonic test (3 rd ). The ultimate registered load in the instrumented section of this anchor was 129.0 kN in the 4 th monotonic tests.

Meanwhile, for the 3 rd test, the load in this section was 131.9 kN, which may indicate the ultimate helix bearing capacity was attained. In consequence, a shaft resistance increase was observed in anchor 1CHA. Identical behaviour was observed for the 4 th monotonic load test on anchor 1MHA; however, a lower shaft load was observed for this anchor.

Due to the observed increase of the ultimate load with the monotonic tension load tests, the last cyclic test (4 th ) was conducted with a higher cyclic load amplitude resulting in Qmax = 1.05QT1 and Qpre = 0.10QT1 to evaluate the anchor response to a large amplitude cyclic loading. Comparing with the results of the last monotonic test (4 th ) on anchor 1CHA, the maximum applied cyclic load (Qmax) corresponded to 50% of the ultimate load.

Figure 96g and h present the results of the 4 th cyclic test on anchor 1CHA. Similar displacement accumulation behaviour was observed during the 3 rd cyclic test. An initial accumulated displacement of around 0.7 mm was maintained until the end of the 4 th cyclic test with no increase during the cycles. Figure 96h shows that, for this 4 th cyclic test, the force registered in the instrumented section during the minimum cyclic load (Qmin) is inferior to the force applied on the anchor head, indicating no more signal of negative shaft friction, as observed in previous cyclic tests.

Figure 97e shows that the load-displacement response is similar for both anchors, with an ultimate load of anchor 1CHA slightly greater than that of anchor MHA1 (around 7% greater). Therefore, no degradation of the uplift capacity was noticed due to the application of University of São Paulo and LUNAM University the previous cyclic loading with a higher load amplitude (4 th cyclic test). The registered load in the instrumented section indicated similarities between the ultimate values of the last three monotonic tests (3 rd , 4 th and 5 th ). On the other hand, the shaft load increased by 27% in comparison to the previous monotonic test (4 th ). For the 5 th monotonic load test on anchor 1MHA, the increase in the shaft load was 111% in comparison to the 4 th monotonic test on this anchor.

Table 1 summarizes the results of the monotonic tensile load tests on both 1MHA and 1CHA anchors. Generally, the cyclic performance of the 1CHA helical anchor was affected by the monotonic load test performed before each cyclic test to simulate the ultimate loading of a blast of wind. In contrast, the cyclic load tests seem to not affect the monotonic behaviour of the helical anchor.

The load-displacement response of the first monotonic test on both 1MHA and 1CHA differed significantly from the results of the following monotonic tests (Figure 49). In addition, when the load-displacement responses are plotted according to the displacement history, each monotonic test appears to continue where the preceding test finished, perhaps with some capacity increase for anchor 1CHA.

Figure 49 shows clearly the improvement in the anchor response after each monotonic test on both anchors. The soil above the helices (described in Figure 41 of section 3.2.1) is a tropical residual soil, with a NSPT varying from 5 to 15 blows/30cm at the depth of the helix, with the bearing capacity disturbed by the helix penetration. Therefore, the monotonic tests improved the soil with low bearing capacity. If the helical anchors were installed in different soil, the improvement would probably be different. Figure 99 presents the registered load in the instrumented section in all monotonic tests according to the anchor's history of displacements. Both helix bearing and shaft resistance increased after the monotonic tests, however a greater increase of shaft resistance was observed for the anchor that experienced cyclic loadings. On the other hand, a slightly greater increase of helix bearing resistance was observed for the anchor that did not suffer cyclic loadings.

Additionally, Figures 96b,d

Q (kN)

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RESULTS OF NUMERICAL MODELLING

In the present study, the numerical modelling was carried out to simulate the pre-and post-cyclic uplift response of the helical anchor tested in centrifuge. The numerical model was constructed with the helical anchor installed into the sand mass.

Several preliminary numerical simulations were carried out to optimize the numerical model and the input parameters. When the Young modulus of the triaxial tests was considered for the undisturbed soil, the load-displacement responses of the preliminary numerical simulations resulted in poor agreement with the experimental results of the pre-cyclic monotonic tests. For these preliminary simulations, the numerical simulation resulted in a significantly less stiff load-displacement response compared to the measured response.

Therefore, increase values of Young modulus were used in the subsequent simulations. The parameters considered in the concluding analyses are shown in Table 22. Although the initial branch of some numerical load-displacement responses showed agreement with the experimental data, most numerical analyses overpredicted the anchor's ultimate tensile capacity from 45% to 147% in all the numerical simulations (considering that failure occurs for an uplift displacement of 10%D). Most of numerical simulations have not

 (º) 1 1 1 1 1 1 1 1 Interface shaft-soil  (

Failure mechanisms

From the observations of the results of preliminary and subsequent simulations, the difficulties in modelling helical anchors are recognized mainly in the reproduction of the ground conditions at the vicinity of the helical anchor.

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Two different movements occur during the anchor installation: i) displacement of the soil due to shaft advancement; ii) soil shearing and displacement due to the rotational and downward movements of the helix. The first action could resemble a jacked pile installation (cylindrical cavity expansion theory), leading the lateral earth pressure coefficient to increase at the vicinity of the shaft and densifying the surrounding sand; however, the helix movement during the anchor penetration would cause a decrease in soil shear strength and stiffness.

Few experimental data are available about the soil stress condition after the anchor installation. An example is the investigation with 1g model tests reported by Mitsch and Clemence (1985) in which they observed an increase in the lateral stresses during the helical anchor installation and during the anchor uplift loading. Nevertheless, the increase in the lateral stresses around the anchor would not be a trivial procedure for a numerical model with anchor as a wished-in-place element. Therefore, an alternative is to vary the parameters of stiffness and resistance of the soil around the anchor to try to reproduce the behaviour of the helical anchor.

Figure 102 compares the contours of vertical stress and vertical displacement of Tests 1 and 4 under a displacement of 0.1D. These contours highlight the differences in the failure mechanisms in models with different material stiffness. The simulation of Test 1 was performed with smaller values of Young modulus (Figures 102a andc) than of the Test 4

(Figures 102b andd). Thus, the vertical stresses in the Test 1 concentrated inside the cylinder of disturbed soil. In contrast, for the Test 4, higher levels of vertical stress can be visualized outside the cylinder. The same trend can be observed in the contours of displacement (Figures 102c andd). If no distinction of material would be made, the stresses and displacements outside the cylinder would be even larger. Figure 103 shows the contours of plastic equivalent strain (PEEQ) for Test 1 and Test 4.

Larger values of PEEQ are observed for the model with lower values of Young modulus (Test 1 -Figure 103a). Also, the plastic zone is larger for the Test 1 (Figure 103a). By using the

(c) (d) (a) (b)
feature of dividing the soil mass into two zones (undisturbed and disturbed), the formation of the failure surface can be observed between undisturbed and disturbed soil. This failure mechanism is more realistic and agrees with the experimental results (see section 4.2.2).

Overall post-cyclic monotonic response

The post-cyclic load-displacement response has been observed to exhibit a stiffness increase with a brittle behaviour (the anchor failure can be clearly identified with around 5 mm of anchor uplift displacement). Figure 104 presents two post-cyclic load-displacement responses that were typically observed in the centrifuge tests. Comparing the experimental results with the results of the numerical simulations, we observe that all numerical simulations provided a less stiff response. However, the ultimate uplift capacity was overpredicted by the numerical analyses, as occurred with the pre-cyclic response simulation. Figure 105 compares the helix bearing pressure obtained in the centrifuge tests and in the numerical analyses (the two numerical load-displacement responses that resulted closer to the experimental results).

PROPOSITIONS FOR THE DESIGN OF SINGLE-HELIX ANCHORS UNDER CYCLIC LOADING IN SAND

The results presented in the current study highlight the need to establish some guidelines for the design of helical anchors under cyclic loadings.

The observations from the cyclic tests reveal three topics of major significance:

-The effect of pre-failure and pre-loading on the anchor uplift behaviour: the reloading of a helical anchor that experienced failure during a previous loading test can cause excessive accumulated displacement and reduction of ultimate load of helical anchors in dense sand. However, for helical anchors with the helices installed in residual tropical soils of low to medium bearing capacity, the anchor response during reloading is improved compared to the first test, due to the compaction of the disturbed soil (destruction of soil structure of the residual soil during installation) above the helix.

-Displacement accumulation during cyclic loading: although the results of the present study have shown that no complete anchor pull-out occurs during the cyclic loading, the accumulated displacements generated during the cycles may reach the serviceability limit state.

-Increase or reduction of post-cyclic tensile capacity due to cyclic loadings: in addition to the analysis of displacement accumulation, the monotonic post-cyclic anchor performance should not be neglected, since degradation and consequent reduction of the post-cyclic anchor uplift capacity imply in reduction of the foundation safety factor.

For the first topic, concerning the effect of pre-failure and preloading on the helical anchor response, it is difficult to propose some design guideline, since this effect is dependent

University of São Paulo and LUNAM University on to soil type, and more tests are needed to confirm the trends observed in centrifuge and field tests. However, in some cases of helical anchors in tropical soils, conducting a preloading can improve the anchor response.

The other two topics have been rarely addressed and little information has been available to provide support for decisions in design of helical anchors.

Therefore, the following sections in this chapter offer some suggestions to guide the prediction of the cyclic loading response of single-helix anchors in sand. These recommendations are based on the results of the cyclic tests carried out on anchor models 10FH and 10FHi (in centrifuge) that represent a prototype of a single-helix anchor with D = 330 mm and d = 100 mm, and with helix embedment depth of 7.4D (at 2.44m depth).

However, for cyclic conditions different of the conditions tested in this study, the applicability of such recommendations should be verified by further studies.

Estimation of the cyclic accumulated displacements

A proposition to describe the displacement accumulation of a single-helix anchor in dense sand during cyclic loading is presented in this chapter. Simple equations have been developed based on the results of cyclic tests on models 10FH and 10FHi. These proposed equations relate the accumulated displacement with number of cycles and cyclic amplitude.

According to Buhler and Cerato (Design of dynamically wind-loaded helical piers for small wind turbines, 2010), the cyclic amplitude (Qcyclic) has greater influence on the anchor response than the maximum cyclic loading (Qmax). In the current study, the mean cyclic load (Qmean) was found to have minor influence on the model anchor behaviour than the cyclic amplitude. Therefore, the proposed expression to estimate the accumulated displacement at a given cycle (Uacc (N)) includes only the cyclic amplitude (Qcyclic).

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As previously discussed in section 4.5, the displacements generated by the first load cycle differ significantly from the following ones. According to Wichtmann (Explicit accumulation model for non-cohesive soils under cyclic loading, 2005), the deformations in the first cycle can differ materially from those in the following cycles, and therefore the first cycle is not suitable for the determination of the total strain amplitude. By the observation of Figure 69, the greater the cyclic amplitude (Qcyclic), the earlier is the transition point of displacement accumulation following the (logN)² rule. For the first cycles (before the transition point) the accumulated displacements are not properly estimated by a function type (logN)². Therefore, the procedure presented here proposes the use of two expressions to determinate the accumulated displacements. These two expressions were obtained by custom equation fitting, observing the correspondence between calculated and registered displacements in the test of mathematic functions and constants.

The application of one or other expression depends on the cycle number on which the accumulated displacement is required to be estimated. Figure 106 illustrates the situations in which both expressions are applied. At the initial cycles, when the number of cycles is less than the amount required to change the displacement accumulation trend, and is below and in the left side of the A-B line in Figure 106, Eq. 14 can be used to estimate the accumulated displacements. If the load cycle number N is greater, and is above and at the right side of the A-B line in Figure 106, Eq. 15 can be used. The load cycle number that corresponds to the transition point (Figure 106) between the two different displacement accumulation responses is called here Ntransition.

 

) N ( acc T max . T cyclic ) N ( acc U Q Q N log Q Q U 1 5 2 2 10       for Uacc (N) ≤ Uacc transition Eq. 14     onset acc T max . transition T cyclic ) N ( acc U Q Q N N log Q Q U       2 20 5 1 for Uacc (N) > Uacc transition
Eq. 15

The calculation of the Ntransition value for a given cyclic loading is proposed to be done through the Eq. 16. This equation corresponds to the A-B line equation in Figure 106, and has been determined by multiple linear regression considering the accumulated displacement at the Ntransition cycle number (Uacc onset)) as a function of number of cycles (N), cyclic amplitude (Qcyclic) and mean cyclic load (Qmean). Since both Uacc transition and Ntransition are unknown, a system of equations with Eq. 14 and Eq. 16 should be solved considering N = Ntransition in Eq. 14 to determine the value of Ntransition and Uacc transition.

. N log . Q Q . Q . U transition T cyclic mean transition acc     Eq. 16
Figure 107. Resolution of the system of equations with Eq. 14 and Eq. 16 through iteration procedure for a cyclic loading with Qcyclic = 0.2QT and Qmean = 0.3QT (prototype values).

The agreement between experimental and calculated values of Uacc is illustrated in The accumulated displacements of 2.5%D, 5%D and 10%D, depending on the cyclic parameters Qcyclic and Qmean, can be estimated using Figures 110a andb, for 100 and 1000 cycles, respectively.

The estimation of the number of cycles required to cause a certain anchor accumulated displacement is important to establish a service life period after which an adjustment of the pre-stressing load in the guy cable is necessary. Therefore, Figure 110 University of São Paulo and LUNAM University

Estimation of the post-cyclic capacity

The results of the cyclic load tests in centrifuge have shown that the post-cyclic tensile capacity was mainly affected by the mean cyclic load (Qmean) and by the number of cycles (N). Generally, for higher values of Qmean (50%QT or more), the cyclic loading caused a gain in post-cyclic uplift capacity. However, it is important to emphasize that the majority of the tests that exhibited gain in post-cyclic capacity was performed with less than 1000 cycles (the model anchor showed Uacc ≥ 10%D before 1000 cycles). In cyclic tests with 1000 cycles or more, the post-cyclic capacity typically showed a reduction up to 15% of the pre-cyclic capacity.

The pre-cyclic monotonic loadings in centrifuge have shown that the shaft resistance of the helical anchors was around 18% of the applied load, under loadings up to 65% of the anchor tensile capacity. On the other hand, in post-cyclic monotonic tests, the shaft resistance was around 7% of the anchor tensile capacity (with a maximum of 16%). Therefore, the postcyclic shaft resistance is suggested to be not considered for the prediction of the post-cyclic uplift capacity of helical anchors due to the small contribution to the post-cyclic capacity observed in the experiments.

A multiple regression was used to correlate the variation in the post-cyclic helix bearing capacity factor (Nq-pc) with N (number of cycles), Qmean and Qcyclic, resulting in the Eq. 17. For this regression, only the measured results of Nq-pc obtained from the tests on the instrumented pile were used, because in this case it was possible to separate the shaft resistance from the helix bearing resistance.

A comparison between the measured and calculated values of post-cyclic uplift capacity using Eq.4 is presented in Figure 111. For the calculated value of uplift capacity, the shaft friction resistance is not considered, in this post-cyclic helix bearing.

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98 1 285 0 1 236 0 100 433 0 2 2                             cyclic mean q pc q Q . Q . N . N N
(valid for the tested interval of 0.4 < Qmean/QT < 0.7) Eq. 17 The post-cyclic capacity (QT-pc) was found to be more dependent of N and Qmean, and less dependent on Qcyclic. Figure 112 illustrates the variation of the post-cyclic uplift capacity calculated using the Eq. 17. The reduction of the post-cyclic capacity seems to be more important when the helical anchors are subjected to a greater number of cycles, as shown in the comparison between Figure 112a andb. After 1000 cycles no capacity decrease was observed for Qmean /QT greater than around 0.40 in the centrifuge tests. This feature could be reproduced using Eq. 17 (Figures 112a andb). Although the cyclic tests with 1000 cycles and larger amplitudes have caused no reduction in post-cyclic uplift capacity, cyclic loadings with larger Qmax would reach first the limiting condition in terms of displacement, unlike the case of small amplitude cyclic loadings.

The post-cyclic response after cyclic loadings with Qmean /QT lower than 0.40 varies widely, and the variability is greater for smaller values of Qmean /QT. This observation indicates a more uniform post-cyclic response is expected for cyclic loadings with higher

Qmean, and the level of capacity reduction should vary only with the number of cycles. ii) In some cases with low mean load, the accumulated displacements did not reach 10%D after 1000 cycles; however, the post-cyclic uplift capacity presented some degree of degradation.

Therefore, this thesis proposed the use of an Interaction Diagram to evaluate the cyclic performance of helical anchors based only on the accumulated displacement response. Simple expressions have been presented to aid the preliminary evaluation of the cyclic behaviour of helical anchors in dense sand with helix embedment depth of around 7D. For different embedment depths, the application of these expressions should be verified. Based on these expressions, Interaction Diagrams have been drawn to assist the evaluation of the cyclic stability.

The study on the post-cyclic behaviour of helical anchors also provided insights and allowed the construction of a curve fitting to estimate the variation of post-cyclic uplift capacity due to the cyclic loadings.

The cyclic response of the single-helix anchor after a sequence of two different cyclic loadings was also evaluated in this research. In general, when cycles of intermediate amplitude are performed first, a reduction in the vertical displacements of the following cyclic loading is observed. On the other hand, when a sequence of cyclic loadings with intermediate and high amplitudes is carried out, the magnitude of the accumulated displacement is weakly

University of São Paulo and LUNAM University dependent on the loading order. Different stability criteria were proposed in this thesis from experimental data. The results and analyses presented here complement the database for the study of helical anchors under cyclic loadings and also provide guidelines for the design.

PART 2 -Field tests

The number of field cyclic tests on helical anchors is reduced compared to the number of cyclic tests performed in centrifuge for this investigation. As mentioned before in this text, cyclic loading tests on piles (or anchors) are much less time consuming and expensive using centrifuge compared to field tests. For this reason, the most part of this thesis is dedicated to centrifuge model tests.

For the field experiments cyclic tensile loading tests were performed on an instrumented single-helix anchor (instrumentation to distinguish shaft and helix bearing responses). This anchor was installed in a site of residual tropical soil (sandstone) at São Carlos, in Brazil.

Four series of cyclic loading tests were performed on this anchor, intercalated with monotonic tensile loading tests (after and before every cyclic test). The results of post-cyclic monotonic tensile load tests on this anchor were compared with the results of monotonic tensile load tests on an identical reference anchor which did not experienced cyclic loadings.

The main findings from these tests are: (i) occurrence of negative skin friction and consequent residual loads after anchor installation and uplift tests; however, for the anchor that experienced cyclic loadings, the negative friction decreased at the end of the unloading stage compared to the anchor that did not experience cyclic loadings; (ii) the effect of negative skin friction influences the cyclic response of the helical anchor; (iii) anchor response improvement was observed after every monotonic test on both anchors; this improvement was caused by soil compaction above the helices (the monotonic tests improved this disturbed soil which has low bearing capacity); (iv) the anchor's cyclic performance was

University of São Paulo and LUNAM University influenced by the preceding monotonic test; (v) cyclic load tests performed in this field investigation did not affect the monotonic behaviour of the helical anchor; (vi) both helix bearing and shaft resistances increased after the monotonic tests; however, a greater increase of shaft resistance was observed for the cyclically tested anchor. On the other hand, a slightly greater increase of helix bearing resistance was observed for the anchor that did not experienced cyclic loadings. The variation in the granulometric distribution due to reuse of the same batch of sand to reconstitute multiple samples was also investigated. Another sieve analysis was conducted on with the same sand batch after using this sand five times to reconstitute sand samples to carry out tests in centrifuge. In this second test, additional sieves were used to detail specific ranges of particle size.

A third sieve analysis was performed at the laboratory of soil mechanics of the Department of Geotechnical Engineering at EESC-USP. This sieve analysis used a sand sample from a new batch of HN38 Hostun sand, brought from France, to compare the resulting granulometric curves of the three sieve analysis. This third analysis was conducted using a different set of sieves of the two previous tests, with slightly different sieve openings.

Table 24 presents the percentage of cumulated passing material of the three tests. Figure 114 shows the three granulometric curves obtained from the three sieve analysis. In these three curves, the average grain size (d50) was found around 0.12 mm. No significant dispersion was observed among the resulting curves. The tests for determination of the maximum and minimum dry density were carried out according to the ASTM Standards D4253 (ASTM, 2014) and D4254 (ASTM, 2014), respectively. The maximum and minimum dry density were found, respectively, equals to 1554 kg/m³ and 1186 kg/m³, with a minimum void ratio of 0.70 and a maximum void ratio of 1.23.

Additional tests on sand specimens prepared according to the procedure described in [START_REF] Miura | A sample preparation method and its effect on static and cyclic deformation-strength properties of sand[END_REF] were carried out to verify the value obtained for the maximum dry density (d(max)). The sand specimen preparation consisted in using a multiple sieving pluviation apparatus. Various densities of sand specimens can be achieved when the rate of sand discharge is controlled. According to [START_REF] Miura | A sample preparation method and its effect on static and cyclic deformation-strength properties of sand[END_REF], when this procedure is performed with granular materials with relatively small uniformity coefficient, a very high density can be achieved without vibrating or impacting the specimen. In contrast with the results presented by [START_REF] Miura | A sample preparation method and its effect on static and cyclic deformation-strength properties of sand[END_REF] with Toyura sand (CU = 1.5 and d50 = 0.18 mm), the maximum dry density obtained with this procedure using the HN38 Hostun sand was only 3% greater than the result achieved with the test conducted according to the ASTM Standard A series of three triaxial compression tests was carried out in the laboratory of soil mechanics at the Ecole Centrale de Nantes. Sand specimens were reconstituted with dry HN38 Hostun sand in order to achieve a density index (ID) between 90 and 95% (the specimen reconstitution is difficult when a specimen of very dense sand is intended). The sand specimens with 100 mm diameter and 200 mm high were reconstituted by vibration and compaction of 5 layers using a two-part mould. The stability of the sand specimen during the mould removal was ensured by applying a negative pressure (suction) to the specimen.

The confining pressure was applied one hour before initiating the shearing stage, but no data was recorded during the application of the confining pressure. For the shearing stage, the axial displacement rate was set in 0.003 mm/s with data acquisition of the vertical displacement, axial load, confining pressure and volume variation of the water inside the cylindrical chamber. Figure 118a presents the sand specimen after reconstitution using the two-part mould. The sand specimen sealed and subjected to negative pressure is presented in Figure 118b. Figure 118c shows the triaxial test apparatus.

Figure 119a presents the stress-strain response of HN38 Hostun sand for three levels of confining stress. A volumetric expansion, typical behaviour of dense sands, is observed in Figure 119b. Table 25 presents some results of the triaxial tests. The Mohr-Coulomb envelope with the resulting strength parameters is presented in Figure 120.

Q cyclic / Q T Q mean / Q T Cyclic loading: Q mean = 0.324Q T Q cyc = 0.227Q T Q pre = 0.096Q T 1000 cycles Z D = 7.4D Q T =
Q cyclic / Q T Q mean / Q T Cyclic loading: Q mean = 0.334Q T Q cyc = 0.209Q T Q pre = 0.125Q T 520 cycles Z D = 7.4D Q T =
Q cyclic / Q T Q mean / Q T Cyclic loading: Q mean = 0.318Q T Q cyc = 0.097Q T Q pre = 0.221Q T 2000 cycles Z D = 7.4D Q T =
Q cyclic / Q T Q mean / Q T Cyclic loading: Q mean = 0.314Q T Q cyc = 0.156Q T Q pre = 0.158Q T 2000 cycles Z D = 7.4D Q T =
Q cyclic / Q T Q mean / Q T Cyclic loading: Q mean = 0.410Q T Q cyc = 0.224Q T Q pre = 0.186Q T 2000 cycles Z D = 7.4D Q T =
Q cyclic / Q T Q mean / Q T Cyclic loading: Q mean = 0.229Q T Q cyc = 0.144Q T Q pre = 0.085Q T 1000 cycles Z D = 7.4D Q T =
Q cyclic / Q T Q mean / Q T Cyclic loading: Q mean = 0.402Q T Q cyc = 0.225Q T Q pre = 0.177Q T 2000 cycles Z D = 7.4D Q T =
Q cyclic / Q T Q mean / Q T Cyclic loading: Q mean = 0.405Q T Q cyc = 0.269Q T Q pre = 0.136Q T 611 cycles Z D = 7.4D Q T =
Q cyclic / Q T Q mean / Q T Cyclic loading: Q mean = 0.405Q T Q cyc = 0.222Q T Q pre = 0.184Q T 1000 cycles Z D = 7.4D Q T =
Q cyclic / Q T Q mean / Q T Cyclic loading: Q mean = 0.516Q T Q cyc = 0.297Q T Q pre = 0.219Q T 1000 cycles Z D = 7.4D Q T = 93 daN
Q cyclic / Q T Q mean / Q T Cyclic loading: Q mean = 0.597Q T Q cyc = 0.222Q T Q pre = 0.374Q T 1000 cycles Z D = 7.4D Q T = 93 daN
Q cyclic / Q T Q mean / Q T Cyclic loading: Q mean = 0.694Q T Q cyc = 0.225Q T Q pre = 0.469Q T 1000 cycles Z D = 7.4D Q T =
Q cyclic / Q T Q mean / Q T Cyclic loading: Q mean = 0.551Q T Q cyc = 0.311Q T Q pre = 0.240Q T 1000 cycles Z D = 7.4D Q T = 93 daN
Q cyclic / Q T Q mean / Q T Cyclic loading: Q mean = 0.595Q T Q cyc = 0.346Q T Q pre = 0.248Q T 300 cycles Z D = 7.4D Q T =
Q cyclic / Q T Q mean / Q T Cyclic loading: Q mean = 0.447Q T Q cyc = 0.344Q T Q pre = 0.103Q T 500 cycles Z D = 7.4D Q T = 93 daN

Introduction

Helical piles have been used extensively to support tensile and compressive loads in a wide range of applications, such as transmission towers, pipeline anchors, foundations for commercial and residential buildings, solar panels, foundation repair, and retaining wall systems. These foundations are normally applied onshore; however, recently, the use of helical piles has been suggested as an innovative and attractive solution for foundations of offshore wind turbines [START_REF] Byrne | Helical piles: an innovative foundation design option for offshore wind turbines[END_REF], Spagnoli and Gavin 2015, Spagnoli et al. 2015). This type of foundation is composed of one or more helix welded to a steel shaft and is installed into the ground by rotation, causing the helical plate to screw through the soil. During the installation of a helical anchor, the cylindrical volume of the soil penetrated by the helices is disturbed by screwing the anchor into the ground, and these changes influence its uplift performance (Mitsch and Clemence, 1985). This installation effect depends on the soil type and on the soil initial condition.

The helical anchors, according to the plate relative depth and mode of failure, could be classified as shallow anchor or deep anchor. Different from the shallow anchor, the deep condition occurs when the failure surface does not extend to the ground surface. In this case, the anchor capacity is a combination of the helix bearing resistance and the shaft resistance [START_REF] Lutenegger | Uplift of shallow single-helix screw-piles[END_REF]. Normally, the bearing resistance is the predominant portion of the total capacity.

The uplift behaviour of helical anchors has been extensively investigated using laboratory 1 g models tests [START_REF] Clemence | Measurement of lateral stress around multihelix anchors in sand[END_REF]Mitsch and Clemence 1985;Narasimha Rao et al. 1989;Ghaly et al. 1991;Ghaly and Clemence 1998;etc.). However, to simulate cases where the anchor response is highly dependent on the confining stress, the use of geotechnical centrifuges is more appropriate to compensate for the soil self-weight stresses.

Centrifuge modelling allows for parametric studies with relatively small effort and low-cost compared to fullscale tests. For this reason, this modelling technique has been used successfully to investigate the performance of plate anchors (Ovesen 1981, Dickin and Leung 1983[START_REF] Dickin | Uplift behavior of horizontal anchor plates in sand[END_REF], Tagaya et al. 1988) and helical anchors (Levesque 2002, Tsuha et al. 2007, Bian et al. 2008, Wang et al. 2013). However, the occurrence of scale effects could influence the results of model experiments of geotechnical problems in granular soils. The reduced scale of models can induce scale effect in relation to the grain-size [START_REF] Balachowski | Scale effect in shaft friction from the direct shear interface tests[END_REF]. Dilation, roughness, and grain crushing influence the behaviour of granular soils, and the smaller the model is, the larger the contribution of these phenomena on the model capacity (Klinkvort et al., 2013). Therefore, as the uplift capacity of a deep single-helix anchor is the sum of the shaft skin friction and the helix bearing capacity, for the centrifuge simulation of helical anchors in sand, it is fundamental to verify the occurrence of scale effects on the results of both parts of anchor capacity. To address this need, this paper presents an experimental study with the aim of finding the appropriate dimensions of helical anchor models to simulate adequately the behaviour of single helix anchors in sand using centrifuge tests.

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Scale effect on helical anchor models in sand

The occurrence of the scale effect in centrifuge model tests on helical anchors in granular soils can be interpreted in terms of two different mechanisms: the particle-size effect on the shaft resistance and the particle-size effect on the helical plate bearing resistance.

2.1 Particle-size effects on the shaft resistance Scale effects observed on shaft resistance are related to the soil tendency to dilate at the interface, which is a function of soil mineralogy, soil density, stress level, grain-size, pile diameter and interface roughness (Foray, 1991). The particle size effect on the skin resistance of piles is associated with shear band formation along the shaft. The ratio of the dilatant zone thickness to the pile diameter is responsible for the large shaft resistance observed in small diameter piles; however, for relatively smooth steel piles, the dilatant properties of the soil may be less important [START_REF] Houlsby | How the dilatancy of soils affects their behaviour[END_REF]. Thus, an adequate model simulation of the pile-sand interface should to be assured by following a minimum ratio of the pile shaft diameter to the average grain-size (d/d50). Previous studies on the scaling effect on the shaft friction have presented different limits of the ratio d/d50. Foray et al.

(1998) reported that size effects are negligible when d/d50 is greater than 200. Garnier and König (1998) found no significant grain-size effect when d/d50 is larger than 100 for pile models with a rough shaft. Fioravante (2002) commented that scaling effects can be neglected for d/d50 greater than 30 to 50, despite the dispersion observed in the results.

The scale effects on the shaft friction of helical anchors are related to the shaft diameter d, similar to the case of regular piles. However, the relationships of the pile shaft diameter to d50 recommended to prevent scale effects on model tests are not appropriate for the simulation of shaft resistance of helical anchors, as the soil mass around the shaft (also the dilatant zone) is influenced by the previous installation of the helix.

Figure 1 shows a photograph of a helical anchor after installation, in flight, in the centrifuge of IFSTTAR (Bouguenais). This figure shows the disturbed sand around the anchor model installed in very dense HN38 Hostun sand. Therefore, based on the previous observation that the installation of the helix can influence the confining stresses around the shaft and the dilation mechanism, the values of the d/d50 ratio found in the literature for regular piles are not adequate for modelling the shaft resistance of helical anchors in sand.

Particle-size effects on the helical plate bearing resistance

Because there is no study available on the particle size effects on the bearing plate resistance of helical anchor models, the recommendations of previous centrifuge model test investigations on footings and on plate anchors in sand were used in Tsuha et al. (2007) to define the minimum ratio D/d50 (D is plate diameter) to provide a satisfactory simulation of helical plate bearing resistance. Yamaguchi et al. (1977) found no difference in the results of the bearing capacity factor and the load-settlement response of shallow foundations with the ratio of foundation width (B) to the average grain size (d50) greater than 36. Ovesen (1979) investigated scaling effects in centrifuge tests on footing models in sand and found no scale effect in experiments on footing model diameters (D) larger than 30d50. Lau (1988) observed no evidence of serious particle size effects on footing models in sand with B/d50 ratios ranging from 165 to 8333. The results of Tatsuoka et al. (1997) showed good agreement between the footing models with D/d50 ratio of 33 and 50.

Three different scales of square plate anchors were tested by Ovesen (1981) in dense sand (g-levels ranging from 167 g to 56 g). In this cited work, no scale errors were observed in models with the B/d50 larger than 25.

In the case of plate anchor models tested in a centrifuge, the sand above the plate is placed in the container after the plate installation. Differently, in the case of centrifuge tests on helical anchors, the helical plate is penetrated into the soil by rotation after sand placement, and consequently, significant disturbance occurs within the cylindrical installation zone of the anchor, as shown in Figure 1. In addition, the range of the ratio of plate to shaft diameters (D/d) is far superior for plate anchors compared to helical anchors. Therefore, these two differences probably result in different values of the minimum ratio D/d50 necessary to avoid scale effects on helical anchor tests compared to the case of plate anchor and footing models.

Centrifuge model investigations on helical anchors in sand can produce reliable simulations of the anchor behaviour without the influence of scale effects. For such simulations, some relationships of the grain to the model size should be established to provide an accurate reproduction of the prototype anchor-soil interaction. In the case of helical anchors, the helix-shaft-soil interaction is influenced by the grain-size in a particular manner.

In the case of the helix bearing resistance, it is necessary to establish a helical plate component (e.g., helix diameter or effective helical radius) that can be related to particle size effects. In the case of plate anchors, the ratio of the plate diameter D to the average grain size d50 appears to be a good parameter and is commonly used to evaluate scale effects. However, in the case of helical anchors, the net projected area of the helix is reduced in comparison to a plate anchor of same plate diameter. In addition, the ratio of the helical plate to the shaft diameters is variable, typically varying from 1.5 to 7.5. Therefore, the ratio of the helix diameter D to d50 is not the best parameter to explain the particle size effects on the helical plate bearing resistance. Accordingly, in the current work, the particle size effect on the bearing resistance is proposed to be correlated to the effective helical during the installation. The installation torque was measured by a torquemeter (indicated in Figure 5) only in two of the three containers tested in this investigation. The axial movement and loading on the anchor models were monitored by displacement and force transducers. The measurements of installation torque, displacement, and force were obtained by an automatic data acquisition system installed in the centrifuge swinging basket. More details regarding the IFSTTAR centrifuge can be found in [START_REF] Thorel | Mesures en macrogravité sur modèles réduits d'ouvrages géotechniques[END_REF].

Helical anchor models

Figure 6 shows the four different single-helix anchor models tested in this investigation. The anchor models were composed of a steel helical plate welded to a round steel shaft, both fabricated with a maximum steel surface roughness Rmax of 4.87 μm.

Four different scaling factors were estimated to provide a helical anchor prototype with a 100 mm of shaft diameter and a 330 mm helical plate diameter (D/d ratio equals to 3.3). The embedment depth of the helical plate was equal to 6 times the plate diameter (1.98 m depth). The dimensions of the helical anchor models and their corresponding g-levels are presented in Table 2.

Anchor installation and pull-out tests

The installation of the helical anchor models into the sand sample was performed in flight, applying a constant rotation to the model of 5.3 rpm (the field rotation rate normally varies from 5 to 20 rpm). The results of the final installation torque (Tf) and of the average torque measured at the final penetration of 3 helical plate diameters (Tavg-3D) are presented in Table 3. During installation by rotation, the vertical displacement rate was controlled to permit the helix to screw down through the sand sample with a rate of penetration of one pitch per revolution. In each container, a minimum centre-to-centre spacing of 10 times the helix diameter was kept between anchors to ensure no influence on the results.

The pull-out tests were performed three minutes after the end of anchor installations. The anchor models were loaded at a vertical displacement rate of 0.3 mm/s. When the pull-out was completed, the centrifuge was stopped to move the servo-control system over the following test location.

Test results

In the present study, the ultimate uplift capacity was assumed to be the peak tensile force measured during the pull-out test on the anchor model. As shown in Table 3, the peak capacity, QT (peak), is very close to the tensile capacity related to a displacement of 10% of the plate diameter, QT (0.1D). Figure 7 presents the load-displacement curves (in prototype values) obtained from the tensile loading tests on the anchor models. This figure shows that the results of ultimate uplift capacity obtained from the tests in containers 1 and 3 are more uniform than the results of the container 2 (Figure 7c). The variability of the results of the container 2 is probably due to the sample heterogeneity, as the other two samples provided uniform results for all models tested. Table 3 shows the results of ultimate uplift capacity (QT) and displacement (U) at failure found in Figure 7.

University of São Paulo and LUNAM University Therefore, to verify if the physical modelling well reproduced the field behaviour of helical anchors during installation and under tensile loading, the Kt values were determined in this investigation, as presented in Table 3. The centrifuge tests produced results of similar magnitude to the field-measured value presented in Gavin et al. (2014) for a single-helix anchor of similar shaft diameter installed in dense sand. These authors found a Kt value of 13 m -1 , and the current centrifuge tests provide a mean Kt value of 15 m -1 . In addition, as shown in Table 3, for the range of model sizes tested, no scale effect was observed on the simulation of a prototype Kt factor.

However, the results of the coefficient of variation of the installation torque (and Kt factor) indicate that the resisting forces acting on the helical anchor during installation are more variable than the forces acting on the anchor under loading (Table 3).

Conclusions

The use of a geotechnical centrifuge to investigate helical anchor behaviour is advantageous because field tests are time consuming, expensive, and difficult to be repeated or compared due to the natural soil variability.

However, scaling issues in modelling helical anchors have not been investigated previously. To address this problem, in the current study, pull-out tests on different reduced models of helical anchor in sand were performed in a centrifuge. All tested models simulated the same single-helix anchor prototype, with D = 330 mm, zD = 6D, and d = D/3.3. The findings presented here are valid for helical anchor models with D/d (helix/shaft diameters) ratios similar or greater than the one tested in this study. The performance of helical anchor models with smaller D/d ratios may be affected by scaling effect in a different manner due to the increase of the shaft resistance contribution to the total capacity. The main conclusions of this study are:

-A new parameter or relationship (ratio of the effective helical radius to the average grain size, w/d50) is proposed in this work to evaluate the scale effects on the results of the helical anchors uplift capacity in sand.

-The results of uplift capacity of all tested anchor models with the ratio w/d50 greater than 58 are comparable (mean value of 61 kN, with a coefficient of variation of 11%). Therefore, for the range of model sizes investigated, the influence of scale effects on tests results can be considered negligible.

-Although the minimum value of the shaft diameter/average grain size ratio evaluated in this study is 50 (much inferior to the recommended values in previous investigations regarding scale effects on shaft resistance), no scale effect on the uplift capacity results was observed. Accordingly, it is reasonable to assume that the particle size effects on helical anchor models in sand is related to effective helical radius /grain size ratio because the plate bearing capacity is the principal portion of the total capacity.

-The results of installation torque and torque correlation factor Kt obtained for the range of model sizes tested

were not affected by scale effects. In addition, this centrifuge modelling study provides results of the torque correlation factor Kt comparable to the field. Tables.

Table 1. HN38 Hostun sand characteristics.

Specific gravity of the sand particles Gs 2.64 a Maximum dry unity weight (kN/m 3 ) d(max)

  University of São Paulo and LUNAM University RESUMO SCHIAVON, J.A. Comportamento de ancoragens helicoidais submetidas a carregamentos cíclicos. 2016. 300 p. Tese de Doutorado em cotutela entre a Universidade de São Paulo e a Universidade Nantes Angers e Le Mans, São Paulo, São Carlos, SP, 2016.

  Procedures for installation and monotonic tensile loading tests _______________ 3.1.4. Experiments on particle size effects _____________________________________ 3.1.4.1. Helical anchor models for experiments on particle size effects ____________ 3.1.5. Installation effect ___________________________________________________ 3.1.5.1. Sand sample excavation ___________________________________________ 3.1.5.2. Tomography ____________________________________________________ 3.1.6. Evaluation of shaft and helix bearing resistances __________________________ 3.1.7. Cyclic loading tests on single-helix anchor models in centrifuge ______________ 3.1.7.1. Cyclic loadings _________________________________________________ 3.1.8. Tests with two consecutive cyclic loadings _______________________________ 3.2. Field tests _________________________________________________________ 3.2.1. Experimental site at EESC-USP _______________________________________ 3.2.2. Helical anchor installation and load test procedure ________________________ 3.3. Numerical modelling _______________________________________________ 3.3.1. Explicit and implicit (Abaqus/Standard) analysis __________________________ 3.3.2. Model geometry, boundary conditions, finite elements and mesh characteristics__ 3.3.3. Constitutive models _________________________________________________ 3.3.3.1. Numerical modelling of triaxial compression tests ______________________ 3.3.4. Interfaces _________________________________________________________ 3.3.5. Numerical analyses parameters _______________________________________ 4. RESULTS OF PHYSICAL MODELLING OF SINGLE-HELIX ANCHORS IN SAND _________________________________________________________________ 4.1. Particle-size effects ________________________________________________ University of São Paulo and LUNAM University Notations and Abbreviations EESC is the São Carlos School of Engineering IFSTTAR is the French Institute of Science and Technology for Transport, Development and Networks USP is the University of São Paulo c is the soil cohesion d is the shaft diameter d50 is the average grain-size emax is the maximum void ratio emin is the minimum void ratio f is the cyclic loading frequency fs is the skin friction resistance k is the anchor axial stiffness k(N=1) is the anchor axial stiffness at the 1 st cycle p is the helix pitch th is the helical plate thickness w is the effective helical radius zD is the helix embedment depth Ah is the helix net area As is the effective shaft surface area B is the square plate width Cu is the coefficient of uniformity D is the regular plate or helical plate diameter Dlower helix is the diameter of the lower helical plate of a multi-helix anchor Dupper helix is the diameter of the upper helical plate of a multi-helix anchor Gs is the specific gravity of the sand particles ID is the sand density index Ku is the lateral earth pressure coefficient in uplift N is the number of cyclesNf is the number of cycles to failure Nq is the bearing capacity factor Nq-pc is the post-cyclic helix bearing capacity factor Q is the tensile load on the anchor head Qapplied is the tension force applied on the anchor head Qcyclic is the axial cyclic load amplitude Qhelix is the tension force registered by the force gauge above the helix Qmax is the maximum cyclic load University of São Paulo and LUNAM University Qmean is the mean axial cyclic load Qmin is the minimum cyclic load Qpre is the tension force applied on the anchor head that simulates the field pre-cyclic load Qshaft is the shaft friction resistance QT is the ultimate tensile load QT1 is the ultimate tensile load obtained from the 1 st monotonic tension load test QTN is the ultimate tensile load obtained from the N th monotonic tension load test QT-pc is the post-cyclic ultimate tensile load QT (0.1D) is the assumed tensile capacity for an uplift displacement of 10%D QT (peak) is the peak tensile capacity Rmax is the maximum surface roughness T is the period of the cyclic loading Tavg-3D is the average torque for the final distance of penetration equal to three times the helix diameter Tf is the final installation torque Thelix is the resistant torque acting on the helical plates Tshaft is the torque generated by the contact between soil and pile shaft in the final of installation U is the vertical displacement Uacc is the accumulated vertical displacement U(peak) is the vertical displacement at the peak force value  is the interface friction angle  is the soil friction angle  is the soil unity weight ' is the soil effective unity weight d is the dry unity weight d(max) is the maximum dry unity weight d(min) is the minimum dry unity weight d(avg) is the average unity weight of the sand samples d(max) is the maximum dry density d(min) is the minimum dry density d(avg) is the average dry density of sand samples 1. INTRODUCTION Helical anchors have been widely used as foundation of power transmission towers in many countries. In Brazil, the use of helical anchors in the electrical power industry has increased markedly in recent years.

Figure 1 .

 1 Figure 1. (a) helical anchor configuration; (b), (c), (d), and (e) the use of helical anchors as anchors[START_REF] Merifield | Ultimate uplift capacity of multiplate helical type anchors in clay[END_REF].

Figure 2 .

 2 Figure 2. (a) installation equipment, after Schiavon et al. (2015); (b) torquemeter, after AB Chance Co. (2013); (c) coupling between extension segments, after Santos Filho (2014); (d) extension segment (own author).

Figure 6 .

 6 Figure 6. Failure surface in multi-helix model anchors, after Mitsch and Clemence (1985): (a) shallow top helix; (b) deep top helix.

Figure 7 .Figure 8 .

 78 Figure 7. Critical embedment depth a function of the angle of internal friction of soil, after[START_REF] Das | Earth anchors[END_REF].

Figure 10 .

 10 Figure 10. Bearing capacity factors for helical anchors in sand, after Mitsch and Clemence (1985) -adapted.

Figure 11 .

 11 Figure 11. Cyclic loading parameters, after Tsuha et al. (2012b) -adapted.

Figure 12 .

 12 Figure 12. Multiple yield surface, after Tatsuoka et al. (1997b).

Figure 13 .

 13 Figure 13. Main features of cyclic stability diagram (Poulos, 1988) -adapted.

Figure 14 .

 14 Figure 14. Interaction diagram presented by[START_REF] Jardine | Pile load testing performed for HSE cyclic loading study at Dunkirk, France. Two Volumes[END_REF] after studies evaluating the skin friction degradation of piles in sand under tensile cyclic loading (adapted).

Figure 15 .

 15 Figure 15. Cyclic interaction diagram, after Tsuha et al. (2012b).

Figure 16 .

 16 Figure 16. Displacement rate of cyclic compression tests in centrifuge simulating bored piles, after Puech et al. (2013) -adapted.

  influenced by: University of São Paulo and LUNAM University a) the interface friction angle; b) the variation of lateral stress, which is governed by the interdependence between the interface volumetric behaviour and the deformability of the sand around the pile shaft; c) the stiffness imposed by the soil on the interface, which depends on the pile radius and deformability of the soil; d) the initial stress level, which influences the dilation response of the interface; e) the type of loading (monotonic of cyclic), which determines dilation or contraction of the sand at the interface.

Figure 17 .

 17 Figure 17. Displacement rate of cyclic compression tests on bored piles: (a) system definition; (b) loading surface in the H-V-M space, after Cremer et al. (2001) -adapted.

  Therefore, parametric analyses of foundations and anchors are often performed by means of reduced scale models. Some experimental techniques used for tests on reduced scale models: a) experiments under normal gravity (1g) with the simple reduction of the model size; b) experiments in a calibration chamber; c) experiments in a geotechnical centrifuge.

  University of São Paulo and LUNAM University

Figure 18 .

 18 Figure 18. IFSTTAR geotechnical centrifuge.

Figure 19 .

 19 Figure 19. Centrifuge acceleration radius, after Tsuha (2007) adapted.

Figure 20 .

 20 Figure 20. Sample reconstitution.

  Paulo and LUNAM University no distinction will be made between total and effective stresses. The pluviation characteristics used to achieve a sand sample with such relative density were: slot width = 3 mm; drop height = 600 mm; horizontal speed = 18.5 cm/s (corresponding to 50 Hz equipment frequency); round-trip movements = 4. A verification of the sand sample bulk density according to the pluviation parameters are presented in the Appendix D.

  identified inhomogeneous zones in reconstituted sand samples in IFSTTAR caused by boundary effects. The density of the reconstituted sample by sand pluviation is affected by the strongbox walls in a 10 cm wide strip along the longer side and a 20 cm wide strip along the shorter side (Figure 21).

Figure 21 .

 21 Figure 21. Sand sample usable zone (dimensions in mm), after Rosquët (2004) -modified. Direct shear and triaxial tests were performed on reconstituted sand samples with

Figure 22 .

 22 Figure 22. (a) test system; (b) servo-controlled actuator.

Figure 24

 24 Figure24illustrates the effective contact area between anchor plate and granular soils,

Figure 24 .

 24 Figure 24. Helical anchor prototype simulated by anchor models of different sizes in the same sand sample.

D

  is the helix diameter d is the shaft diameter University of São Paulo and LUNAM University 3.1.5. Installation effect The installation effect on the sand penetrated by the helices influences the uplift behaviour of helical anchors. Therefore, for a better understanding of the cyclic response of helical anchors in this study, different techniques were used to investigate the effect of the anchor installation on the uplift capacity, and to visualise the installation effect and the failure mechanism. The influence of the installation effect on the helical anchor uplift capacity was investigated by comparing the model anchor response in two situations: a) model anchors were placed during the sand sample reconstitution by pluviation; b) model anchors were installed in flight. The pull-out test procedure was performed as described in section 3.1.3.

Figure 25 .

 25 Figure 25. Installation of the helical anchor models during pluviation.

Figure 26 .

 26 Figure 26. Sand sample reconstituted with helical anchor models placed during pluviation.

Figure 27 .

 27 Figure 27. Device for 12HF connection.

Figure 28 .

 28 Figure 28. Sample excavation for the visualisation of installation and failure mechanisms.

Figure 29 .

 29 Figure 29. 6FHp plastic model (dimensions in mm).

Figure 30 .

 30 Figure 30. Coupling device.

Figure 31 .

 31 Figure 31. Extraction of specimens (with and without a model anchor).

Figure 32 .

 32 Figure 32. Removable (RH) and fixed (FH) helix model anchors.

Figure 33 .

 33 Figure 33. 10FHi instrumented model.

Figure 34 .

 34 Figure 34. Points of experiments on the Interaction Diagram.

Figure 35 .

 35 Figure 35. Description of the cyclic loading test procedure (model scale).

A

  software produced by Moog Inc. is used in the IFSTTAR centrifuge to control the servo-controlled actuator in force or in displacement. All the cyclic tests performed in the current research were force-controlled to satisfy the cyclic loading parameters (Qmean and Qcyclic) specified for each test. In some cyclic loadings, the servo-controlled system could not properly follow the set point due to a bad configuration of the P.I.D. Moog parameters (servocontrol parameters in force). For a good agreement with the setpoint, the P.I.D. settings were adjusted to: P = 0.1, I = 0.1 and D = 0. Figure36illustrates the difference between cyclic loadings with coarse and fine P.I.D. adjustments.

Figure 36 .

 36 Figure 36. Cyclic loading with (a) coarse and (b) fine P.I.D. configuration.

For a second

  test, the inverse sequence of cyclic loadings was conducted: (a) the first, a few load cycles with large amplitudes were carried out; (b) next, a greater amount of cycles with smaller amplitudes was applied, and then; (c) a monotonic tensile load test was conducted on the anchor model. The installation, cyclic loading and pull-out tests were performed in the same manner as for the single cyclic loadings tests (see section 3.1.7).

Figure 37 .

 37 Figure 37. Two different cyclic loadings on the same helical anchor model.

Figure 38 .

 38 Figure 38. Instrumented lead section of the helical anchors tested (dimensions in mm).

Figure 39 .

 39 Figure 39. Calibration of the instrumented sections.

  University of São Paulo and LUNAM University

Figure 40 .

 40 Figure 40. São Paulo state, by de Abreu (2006) -adapted.

  Avg. Max. Temp. (º C) 28.0 28.0 28.0 28.0 25.0 24.0 24.0 27.0 28.0 28.0 28.0 25.0 27.0 Avg. Min. Temp. (° C) 18.0 18.0 17.0 16.0 13.0 12.0 12.0 13.0 15.0 16.0 16.0 18.0 15.3 Rainfall (mm) 268.7 227.4 136.7 59.4 49.7 32.1 15.5 26.6 58.9 132.8 164.9 240.1 1422.8

Figure 41 .

 41 Figure 41. Soil profile at experimental site of the University of São Paulo at São Carlos, Brazil, after Giachetti et al. (2004) and Machado (1998).

Figure 42 .

 42 Figure 42. Soil granulometric distribution of the EESC-USP Experimental Site, after Machado (1998).

Figure 43 .

 43 Figure 43. Installation of an instrumented helical anchor at the test site.

Figure 44 .

 44 Figure 44. Load test setup.

Figure 45 .

 45 Figure 45. Geometric and mesh characteristics, distances in centimetres (the numbers in parenthesis indicates the number of elements the line was divided).

Figure 46 .

 46 Figure46. Motion of mesh and material with Lagrangian, ALE and Eulerian methods(Abaqus, 2005).

  modulus E = 200000 MPa Poisson ratio ν = 0.3 Density ρ = 1555 kg/m³ For modelling the soil material (sand), the Abaqus software provides the following plastic constitutive models suitable for modelling problems involving soils: Mohr-Coulomb plasticity, extended Drucker-Prager, modified Drucker-Prager/Cap model and the Critical University of São Paulo and LUNAM University state (clay) plasticity model. In addition, the software allows the implementation of different constitutive models. The soil material (sand) was modelled with the Mohr-Coulomb plasticity associated with linear elasticity. The Mohr-Coulomb criterion assumes that yield occurs when the shear stress on any point in a material reaches a value that depends linearly on the normal stress on the same plane. The flow potential for the Mohr-Coulomb yield surface is chosen as a hyperbolic function on the meridional stress plane and the smooth elliptic function proposed

  modulus E = 50 MPa Poisson ratio ν = 0.3 Angle of internal friction ϕ = 47º Cohesion c = 0 Meridional eccentricity ϵ = 0.1 (software default) Deviatoric eccentricity e = (3 -sinϕ) / (3 + sinϕ) Coefficient of lateral pressure Ks =  / (1 -)Bulk density ρ = 1555 kg/m³3.3.3.1. Numerical modelling of triaxial compression testsThe triaxial compression tests on HN38 Hostun sand specimens were also numerically simulated with Abaqus/Explicit. The cylindrical sand specimen with a 100 mm diameter and 200 mm high was modelled in the axisymmetric condition. The vertical and horizontal displacements were restrained at the base and the left-hand boundary was the axis of symmetry. A confining stress was applied at the top and right-hand boundaries of the specimen and the deviatoric stress was applied to the top of the specimen by an axial displacement with a 0.05 mm/s displacement rate. The previously described elements CAX4Rwere used to compose the finite element mesh with 216 elements, each with approximately 1 mm side.

Figure 47

 47 Figure 47 presents the numerical modelling results of the three triaxial tests. A slightly

Figure 47 .

 47 Figure 47. Experimental and numerical results of triaxial compression tests: (a) σ3 = 50 kPa; (b) σ3 = 100 kPa; (c) σ3 = 200 kPa.

  Deviatoric stress (kPa) Deviatoric stress (kPa) Deviatoric stress (kPa) University of São Paulo and LUNAM University disturbed soil and the undisturbed soil. The interface between the anchor (helix and shaft)

  The third step involved the application of the tensile loading as vertical upward velocity acting on the shaft top surface. After testing different velocity values, no influence on the results was observed for velocities less than or equal to 2 mm/s. University of São Paulo and LUNAM University 4. RESULTS OF PHYSICAL MODELLING OF SINGLE-HELIX ANCHORS IN SAND 4.1. Particle-size effects

Figure 48 .

 48 Figure 48. Identification of the peak tensile force for the monotonic test on model 10FH in Container No. 12.

Figure 49 .

 49 Figure 49. Ultimate tensile load of helical anchor models of different sizes (in prototype values).

Figure 50 .

 50 Figure 50. Torque readings during the installation: (a) model 6FH, (b) model 8FH, (c) model 10FH and (d) model 12FH, in prototype values.

Figure 51 .

 51 Figure 51. Final installation torque, in prototype values.

  For a comparison between helical anchors in disturbed and undisturbed sand, pull-out tests were carried out on helical anchor models with a helix embedment depth of 8D, under two different conditions: a) model anchors placed in the sand sample during the pluviation to eliminate the soil disturbance caused by anchor installation; b) model anchors installed in flight to simulate the soil disturbance that occurs in field installation.The results of the six uplift tests conducted with the anchors in both conditions of sand disturbance are presented in Table16and in Figure52.

Figure 52 .

 52 Figure 52. Results of the pull-out tests with anchor models placed during the sand pluviation (not installed) and installed in flight, in prototype scale.

Figure 53 .

 53 Figure 53. Photographs of the sand sample after excavation around the 12FH model: (a) after model installation, and (b) after uplift loading.

Figure 54 .

 54 Figure 54. Installation effect: vertical and horizontal movement of sand grains that were aligned horizontally before the installation.

Figure 55

 55 Figure55shows the micro-tomographic images of the intact sand sample. Different

Figure 55 .

 55 Figure 55. Micro-tomographic images of the intact sand specimen collected from container No. 14.

Figure 56 .

 56 Figure 56. Micro-tomographic longitudinal section of the sand specimen with the plastic model anchor inside after a vertical uplift of 0.5D.

Figure 57 .

 57 Figure 57. Micro-tomographic images of the sand specimen with the plastic model anchor inside: (a) cross section at the shaft level; (b) cross section at helix level.

Figure 58 .

 58 Figure 58. Comparison between the results of Gavin et al. (2014) and tests performed on 10FH and 10FHi in zD = 7.4D (container No. 4, 5 and 9).

4. 3

 3 .2. Helical anchor response under reloading Two loading-unloading-reloading tests on anchor model 10FH were carried out to evaluate the monotonic anchor response after different levels of vertical displacement. For test 10FH-2 in container No. 4, the anchor model was loaded in tension to a vertical displacement of around 10%D. The second tensile loading test (10FH-1 in container No. 5) was conducted to a vertical displacement of the anchor head of approximately 1.2D. Figure 59 shows that the load-displacement responses of both tests are similar during the first loading stage. However, during the reloading stage, the anchor model that experienced a larger vertical displacement during the first loading exhibited a substantial reduction in the ultimate load. This occurred because the large displacement of the helix after the end of the first loading caused a gap below the helix, and a portion of sand moved to the gap, causing a decrease in sand density around the helix, and a consequent reduction in uplift capacity.

Figure 59 .

 59 Figure 59. Results in prototype values of the pull-out tests 10FH-2 in container No. 4 and 10FH-1 in container No. 5.

Figure 60 .

 60 Figure60. Registered load in the shaft section just above the helix compared with the applied load on the anchor head.

Figure 61

 61 Figure61shows the results of the uplift tests on the anchor models with a removable

Figure 61 .

 61 Figure 61. Load-displacement responses of the model anchors with removable helix (in prototype values).

  of 10 mm. The cyclic loading tests were carried out with different loading amplitudes (Qcyclic) and different pre-tensile loads (Qpre). The cyclic parameters are illustrated in Figure 11 of section 2.2. The basic parameters required to describe a cyclic loading are: mean load (Qmean), cyclic load (Qcyclic), frequency and number of cycles. Usually, Qmean and Qcyclic are normalized through the monotonic capacity in tension or compression. Therefore, before the series of cyclic tests, monotonic uplift tests were conducted on model anchors 10FH and 10FHi installed at the same embedment depth as the cyclic tests (zD = 7.4D). The load-displacement responses of the monotonic loading tests for models 10FH and 10FHi are presented in Figure 63. These results are utilized to define the ultimate load to be used for the determination of Qmean and Qcyclic values for the cyclic loading tests.

Figure 63 .

 63 Figure 63. Monotonic load-displacement responses of uplift tests with 10FH and 10FHi models (prototype values).

From a total of

  38 cyclic tests, only 33 tests have been analysed: 14 tests with anchor model 10FH and 19 tests with anchor model 10FHi. Results of 5 tests with 10FH model have not been used due to problems in maintaining the cyclic loading controlled in force in theappropriate range of load variation. In addition, due to a configuration error in programming the servo-controlling system, some tests initiated the cyclic loading before the pre-load being completely applied. Nevertheless, the results of these tests with cyclic loading starting prematurely were used in the analyses.

Figure

  Figure64apresents the pile head responses to axial cyclic loading in tension with a

Figure 64 .

 64 Figure 64. Load-displacement behaviour of cyclic tests with 10FH model: (a) Qpre  0.23QT; and (b) 0.09QT ≤ Qpre ≤ 0.14QT.

Figure 65 .

 65 Figure 65. Load-displacement behaviour of cyclic tests with 10FHi model with 0.08QT ≤ Qpre ≤ 0.17QT.

Figure 66 .

 66 Figure 66. Normalized load-displacement cyclic responses: (a) Qmean = 0.41QT and Qcyclic = 0.20QT; (b) Qmean = 0.51QT and Qcyclic = 0.29QT; (c) Qmean = 0.59QT and Qcyclic = 0.34QT.

Figure 67 .

 67 Figure 67. Gap formation and sand particles movement during the cyclic loading.

Figure 69

 69 Figure69presents the accumulated displacements plotted with the square of the

Figure 68 .

 68 Figure 68. Maximum and minimum values of vertical displacements with number of cycles in (a) and (b) linear scale; and (c) and (d) log scale.

Figure 69 .

 69 Figure 69. Accumulated displacements analysed in function of the logarithm of the number of cycles squared.

Figure 70 .

 70 Figure 70. Displacement accumulation rates in cyclic tests performed on the models: (a) 10FH; (b) 10FHi, in prototype values.

Figure

  Figure 70b presents the displacement accumulation rate of the cyclic tests on

Figure 71 .

 71 Figure 71. Displacement accumulation rates versus accumulated vertical displacements in cyclic tests performed with 10FHi model, in prototype values.

Figure 72

 72 Figure 72 based on the work of Rimoy et al. (2013).

Figure 72 .

 72 Figure 72. Stiffness and displacement cyclic parameters (adapted from Rimoy et al., 2013).

Figure 73 .

 73 Figure 73. Typical results of normalized axial cyclic stiffness (loading cyclic stiffness) for tests conducted on models: (a) 10FH and (b) 10FHi.

Figure 74

 74 Figure 74 compares the anchors' axial stiffness of the cyclic tests performed on models

Figure 74 .

 74 Figure 74. Typical results of axial cyclic stiffness for tests conducted on models: (a) 10FH and (b) 10FHi.

Figure 75 .

 75 Figure 75. Skin friction degradation: (a) and (b) cyclic tests in containers No. 9 and 10; (c) and (d) cyclic tests in containers No. 13 and 14.

Figure 76

 76 Figure76illustrates the level degradation of skin friction observed for the performed

Figure 76 .

 76 Figure 76. Maximum skin friction degradation observed in the cyclic tests.

Figure 77 .

 77 Figure 77. Contours of percentages of skin friction degradation: (a) fs (N)/fs (N=1) = 0.85; (b) fs (N)/fs (N=1) = 0.7; (c) fs (N)/fs (N=1) = 0.6; (d) fs (N)/fs (N=1) = 0.45.

Figure 78 .

 78 Figure 78. Helix bearing resistance: (a) and (b) cyclic tests in containers No. 9 and 10; (c) and (d) cyclic tests in containers No. 13 and 14.

Figure 79 .

 79 Figure 79. Contours of the increase of the maximum cyclic load registered in the force gauge above the helix: (a) Qhelix (N)/Qhelix (N=1) = 1.05; (b) Qhelix (N)/Qhelix (N=1) = 1.10; (c) Qhelix (N)/Qhelix (N=1) = 1.15.

Figure 80 .

 80 Figure 80. Post-cyclic ultimate tension load: (a) according to the number of cycles to failure; (b) according to the maximum cyclic load experienced during the cyclic loading carried.

  University of São Paulo and LUNAM University maintenance of the Qmean between these values was not the single cause of the capacity gain.

Figure 81 .

 81 Figure 81. Post-cyclic monotonic responses.

Figure 82

 82 Figure 82 compares the load registered in the force gauge above the helix (Qhelix) before

Figure 82 .

 82 Figure 82. Comparison between the load registered in the force gauge above the helix before and after the cyclic loading.

  Three categories of cyclic responses were used to classify the cyclic loadings of this study: Stable, Meta-Stable and Unstable, in accordance to[START_REF] Karlsrud | Piles in clay under cyclic axial loading: field tests and computational modeling[END_REF] and Poulos(1988). This categorization was applied to previous studies on the degradation of shaft resistance, e.g,[START_REF] Jardine | Field axial cyclic loading experiments on piles driven in sand[END_REF],[START_REF] Tsuha | Behaviour of displacement piles in sand under cyclic axial loading[END_REF] and[START_REF] Rimoy | Displacement response to axial cycling of piles driven in sand[END_REF].

  presents an interaction diagram only taking into account the limit accumulated displacement condition (10%D), indicating the zones of Stable, Meta-Stable and Unstable responses.

Figure 83 .

 83 Figure 83. Cyclic interaction diagram classifying cyclic responses only into account the limit displacement condition (10%D).

Figure 83

 83 Figure83illustrates a thin zone of unstable response. The lower limit line of the

Figure 84 .

 84 Figure 84. Contours for accumulated cyclic displacements equivalent to (a) 2%D, (b) 5%D, (c) 7%D and (d) 10%D.

Figure 85 .

 85 Figure 85. Contours of the normalized post-cyclic uplift capacity.

Figure 86 .

 86 Figure 86. Post-cyclic capacity interaction diagram.

Figure 87 .

 87 Figure 87. Load-displacement responses of tests with sequence of different cyclic loadings: (a) test 10FH-5 and (b) test 10FH-6, both in Cont. No. 6 (prototype values).

Figure 88 .

 88 Figure 88. Load-displacement responses of tests with different cyclic loadings sequences: (a) test 10FHi-5 and (b) test 10FHi-6, both in Cont. No. 9 (prototype values).

Figure 88

 88 Figure 88 indicates that during the initial cycles of the first cyclic loading, test 10FHi-5

Figure 89 .

 89 Figure 89. Load-displacement responses of tests with different sequences of cyclic loadings: (a) test 10FHi-3 and (b) test 10FHi-4, both in Cont. No. 14 (prototype values).

Figure

  Figure90ashows the vertical cyclic displacements for the four cyclic loading tests (with

Figure 91 .

 91 Figure 91. Normalized stiffness of the (a) first loading and (b) second loading of the test sequence; Anchor axial cyclic stiffness (in prototype scale) of the (c) first loading and (d) second loading of the test sequence.

Figure 92 .

 92 Figure 92. Post-cyclic monotonic tensile responses.

Figure 93 .

 93 Figure 93. Comparison of the installation torque of Tsuha's (2007) experiments with the current research.

Figure 94 .

 94 Figure 94. Results of the 1 st monotonic load tension tests performed on anchors (a) 1MHA and (b) 1CHA.

Figure 95 .

 95 Figure 95. Reacting forces on the helical anchor during the first tension load test.

Figure 96 .

 96 Figure 96. Results of the cyclic tests on 1CHA: (a) and (b) 1 st test Qmean = 0.15QT1 and Qcyclic = 0.05QT1; (c) and (d) 2 nd test Qmean = 0.25QT1 and Qcyclic = 0.15QT1; (e) and (f) 3 rd test Qmean = 0.35QT1 and Qcyclic = 0.25QT1; (g) and (h) 4 th test Qmean = 0.58QT1 and Qcyclic = 0.48QT1.

Figure 97 .

 97 Figure 97. Results of the monotonic tension load tests: (a) 1 st load test; (b) 2 nd load test; (c) 3 rd load test; (d) 4 th load test and (e) 5 th load test.

  , f, h and Figure 100 indicate that the negative skin friction (residual load) is reduced after a series of cyclic loadings.

Figure 98 .

 98 Figure 98. Monotonic load-displacement responses plotted according to the displacement history of each tested anchor.

Figure 99 .

 99 Figure 99. Registered load in the instrumented section above the helix plotted according to the displacement history of each tested anchor.

Figure 100 .

 100 Figure 100. Shaft friction plotted according to the displacement history of each tested anchor. 0 20 40 60 80 100 120 140 U (mm)

  Figure101shows the monotonic load-displacement responses of the numerical

Figure 101 .

 101 Figure 101. Comparison between numerical and experimental pre-cyclic monotonic responses.

  University of São Paulo and LUNAM University shown an asymptotic trend as exhibited in the experimental tests. The only two numerical tests that showed an asymptotic trend were the tests with greater Young modulus for both undisturbed and disturbed soils (Tests 5 and 6), leading to believe that the asymptotic trend can be obtained only for Young modulus greater than 70 MPa for the disturbed soil. On the other hand, tests with low values of both E and  may yield ultimate load values close to the experimental results, but with poor agreement with the initial branch of the experimental loaddisplacement response (e.g. Test 8). Gavin et al. (Field investigation of the axial resistance of helical piles in dense sand, 2014) also performed numerical simulations of a monotonic full-scale tensile test on a singlehelix anchor installed in dense sand with zD = 6.1D. The numerical result presented by these cited authors showed an overprediction in the ultimate uplift capacity of 120% more than the field result. Gavin et al. (Field investigation of the axial resistance of helical piles in dense sand, 2014) argues that their relatively poor prediction is related to significantly different strength and stiffness properties, and stress paths during loading of the numerical model (based on triaxial tests) compared with the field conditions. In addition, these cited authors mention that the anchor was modelled as a wished-in-place element, disregarding the effects of the installation procedure. Therefore, for the present numerical simulation, the effects of the anchor installation were simplistically simulated by a cylinder of disturbed soil above the helix, as recommended in Mosquera et al. (Discussion of "Field investigation of the axial resistance of helical piles in dense sand", 2015).

Figure 102 .

 102 Figure 102. Contours of vertical normal stress (values in Pa) for (a) Test 1 and (b) Test 4, and contours of vertical displacement (values in metres) of (c) Test 1 and (d) Test 4 for a vertical displacement of 10%D.

Figure 103 .

 103 Figure 103. Contours of plastic equivalent strain for (a) Test 1 and (b) Test 4.

Figure 104 .

 104 Figure 104. Comparison between numerical and experimental post-cyclic monotonic responses.

Figure 105 .

 105 Figure 105. Helix bearing resistance mobilized during experimental and numerical post-cyclic uplift load tests.

Figure 106 .

 106 Figure 106. Two different trends in displacement accumulation.

  Figure 107 illustrates the determination of both Uacc transition and Ntransition for a cyclic loading with Qcyclic = 0.2QT and Qmean = 0.3QT.

Figure 108 .

 108 Figure 108. Although a dispersion of 50% around the experimental values is observed, the

Figure 108 .

 108 Figure 108. Comparison between calculated and experimental values of the cyclic accumulated displacements (in prototype values).

Figure 109

 109 Figure 109 permits to estimate the number of cycles (Nf) required to cause a limiting

Figure 109 .

 109 Figure 109. Isovalues lines of cycles to cause a limiting accumulated displacement of 10%D.

  presents iso-values University of São Paulo and LUNAM University lines of accumulated displacements for 100, 500, 1000 and 2000 cycles that permits to estimate the number of cycles and consequently the service life duration in function of the cyclic parameters Qcyclic and Qmean.

Figure 110 .

 110 Figure 110. Isovalues lines of accumulated displacement (Uacc) after (a) 100 cycles, (b) 500 cycles, (c) 1000 cycles and (d) 2000 cycles.

Figure 111 .

 111 Figure 111. Comparison between measured and calculated results of post-cyclic helix bearing capacity.

Figure

  Figure 112b illustrates that after 2000 cycles almost all of the tests showed uplift

Figure 112 .

 112 Figure 112. Variation of the post-cyclic capacity (QT-pc) for (a) N = 1000 cycles and (b) N = 2000 cycles.

8. 1 .

 1 Recommendations for future work  Future numerical studies to simulate the behaviour of helical anchors under monotonic and cyclic loading should consider constitutive models that can reproduce hardening and cyclic degradation of soils. For modelling with wished-in-place element, the initial condition of the soil should be improved in order to better reproduce the lateral stresses around the anchor, and then, investigate the influence of the variation of lateral stresses on the anchor behaviour;  Physical modelling of helical anchors in calibration chamber to better investigate the modifications on the soil lateral stresses around the anchor after anchor installation.  Centrifuge model tests to investigate the behaviour of single-helix anchors under twoway cyclic loadings.  Centrifuge investigations on the effect of the number of helix on the cyclic response of helical anchors.  Centrifuge model tests to investigate the cyclic behaviour of helical anchors in loose sand and in cohesive soils.  Centrifuge model tests to investigate the behaviour of helical anchors under cyclic horizontal loadings. University of São Paulo and LUNAM University APPENDIX University of São Paulo and LUNAM University

Figure 116

 116 Figure 116 presents the vertical and horizontal displacement for the three tests. The Mohr-

Figure 116 .

 116 Figure 116. Results of the direct shear tests on HN38 Hostun sand (ID = 98%): (a) horizontal displacement vs shear stress; (b) horizontal displacement vs vertical displacement.

Figure 117 .

 117 Figure 117. Mohr-Coulomb envelope with peak values (c' = 0 and ' = 48°) and post-peak values at dH/D = 0.10 (c' = 0 and ' = 42°).

Figure 118 .

 118 Figure 118. (a) sample with two-part mould and (b) under suction.

Figure 119 .

 119 Figure 119. Triaxial test results: (a) stress-strain curves; (b) strain responses.

Figure 120 .

 120 Figure 120. Mohr-Coulomb envelope of HN38 Hostun sand (c' = 0 and ' = 47º).

Figure 127 .

 127 Figure 127. Additional efforts arisen on the force gauge due to model screwing.

Figure 128 .

 128 Figure 128. Torque applied vs measured force (compression is positive) in the force gauge above 10FHi helix.

Figure 132 .

 132 Figure 132. Installation torque of the 10FH model tested in container n. 9: (a) test 10FHi-5 and (b) test 10FHi-6.

Figure 133 .

 133 Figure 133. Installation torque of the 10FHi model tested in container n. 10: (a) test 10FHi-1; (b) test 10FHi-2; (c) test 10FHi-3; (d) test 10FHi-4; (e) test 10FHi-6 and (f) test 10FHi-7.

Figure 134 .

 134 Figure 134. Installation torque of the anchor models tested in container n. 11: (a) test 6FH-1; (b) test 6FH-2; (c) test 6FH-3; (d) test 10FH-1; (e) test 10FH-2; (f) test 10RH-1 and (g) test 12FH-1.

Figure 139 .Figure 140 .Figure 141 .Figure 142 .Figure 145 .

 139140141142145 Figure 139. Load-displacement response 10FH model tested in container n. 10: (a) and (b) test 10FH-4; (c) and (d) test 10FH-6; (e) and (f) test 10FH-7.

Figure 146 .

 146 Figure 146. Cyclic loading and pull-out test nº 10FH-6 with 10FH model in the 4 th container: (a) anchor location; (b) cyclic loading test on stability diagram; (c), (d) and (e) cyclic loading (results in model scale).

Figure 147 .

 147 Figure 147. Cyclic loading and pull-out test nº 10FH-2 with 10FH model in the 5 th container: (a) anchor location; (b) cyclic loading test on stability diagram; (c), (d) and (e) cyclic loading (results in model scale).

Figure 148 .

 148 Figure 148. Cyclic loading and pull-out test nº 10FH-3 with 10FH model in the 5 th container: (a) anchor location; (b) cyclic loading test on stability diagram; (c), (d) and (e) cyclic loading; (f) post-cyclic (results in model scale).

Figure 149 .

 149 Figure 149. Cyclic loading and pull-out test nº 10FH-4 with 10FH model in the 5 th container: (a) anchor location; (b) cyclic loading test on stability diagram; (c), (d) and (e) cyclic loading; (f) post-cyclic (results in model scale).

Figure 150 .

 150 Figure 150. Cyclic loading and pull-out test nº 10FH-5 with 10FH model in the 5 th container: (a) anchor location; (b) cyclic loading test on stability diagram; (c), (d) and (e) cyclic loading; (f) post-cyclic (results in model scale).

Figure 151 .

 151 Figure 151. Cyclic loading and pull-out test nº 10FH-6 with 10FH model in the 5 th container: (a) anchor location; (b) cyclic loading test on stability diagram; (c), (d) and (e) cyclic loading (results in model scale).

Figure 152 .

 152 Figure 152. Cyclic loading and pull-out test nº 10FH-1 with 10FH model in the 6 th container: (a) anchor location; (b) cyclic loading test on stability diagram; (c), (d) and (e) cyclic loading; (f) post-cyclic (results in model scale).

Figure 153 .

 153 Figure 153. Cyclic loading and pull-out test nº 10FH-2 with 10FH model in the 6 th container: (a) anchor location; (b) cyclic loading test on stability diagram; (c), (d) and (e) cyclic loading; (f) post-cyclic (results in model scale).

Figure 154 .

 154 Figure 154. Cyclic loading and pull-out test nº 10FH-3 with 10FH model in the 6 th container: (a) anchor location; (b) cyclic loading test on stability diagram; (c), (d) and (e) cyclic loading; (f) post-cyclic (results in model scale).

Figure 155 .

 155 Figure 155. Cyclic loading and pull-out test nº 10FH-4 with 10FH model in the 6 th container: (a) anchor location; (b) cyclic loading test on stability diagram; (c), (d) and (e) cyclic loading; (f) post-cyclic (results in model scale).

Figure 156 .

 156 Figure 156. Cyclic loading and pull-out test nº 10FH-1 with 10FH model in the 7 th container: (a) anchor location; (b) cyclic loading test on stability diagram; (c), (d) and (e) cyclic loading; (f) post-cyclic (results in model scale).

Figure 157 .

 157 Figure 157. Cyclic loading and pull-out test nº 10FH-2 with 10FH model in the 7 th container: (a) anchor location; (b) cyclic loading test on stability diagram; (c), (d) and (e) cyclic loading; (f) post-cyclic (results in model scale).

Figure 158 .

 158 Figure 158. Cyclic loading and pull-out test nº 10FH-3 with 10FH model in the 7 th container: (a) anchor location; (b) cyclic loading test on stability diagram; (c), (d) and (e) cyclic loading; (f) post-cyclic (results in model scale).

Figure 159 .

 159 Figure 159. Cyclic loading and pull-out test nº 10FH-4 with 10FH model in the 7 th container: (a) anchor location; (b) cyclic loading test on stability diagram; (c), (d) and (e) cyclic loading (results in model scale).

Figure 160 .

 160 Figure 160. Cyclic loading and pull-out test nº 10FHi-3 with 10FHi model in the 9 th container: (a) anchor location; (b) cyclic loading test on stability diagram; (c), (d) and (e) cyclic loading; (f) post-cyclic (results in model scale).

Figure 161 .

 161 Figure 161. Cyclic loading and pull-out test nº 10FHi-4 with 10FHi model in the 9 th container: (a) anchor location; (b) cyclic loading test on stability diagram; (c), (d) and (e) cyclic loading; (f) post-cyclic (results in model scale).

Figure 162 .

 162 Figure 162. Cyclic loading and pull-out test nº 10FHi-1 with 10FHi model in the 10 th container: (a) anchor location; (b) cyclic loading test on stability diagram; (c), (d) and (e) cyclic loading; (f) post-cyclic (results in model scale).

Figure 163 .

 163 Figure 163. Cyclic loading and pull-out test nº 10FHi-2 with 10FHi model in the 10 th container: (a) anchor location; (b) cyclic loading test on stability diagram; (c), (d) and (e) cyclic loading; (f) post-cyclic (results in model scale).

Figure 164 .

 164 Figure 164. Cyclic loading and pull-out test nº 10FHi-3 with 10FHi model in the 10 th container: (a) anchor location; (b) cyclic loading test on stability diagram; (c), (d) and (e) cyclic loading; (f) post-cyclic (results in model scale).

Figure 165 .

 165 Figure 165. Cyclic loading and pull-out test nº 10FHi-4 with 10FHi model in the 10 th container: (a) anchor location; (b) cyclic loading test on stability diagram; (c), (d) and (e) cyclic loading; (f) post-cyclic (results in model scale).

Figure 166 .

 166 Figure 166. Cyclic loading and pull-out test nº 10FHi-6 with 10FHi model in the 10 th container: (a) anchor location; (b) cyclic loading test on stability diagram; (c), (d) and (e) cyclic loading; (f) post-cyclic (results in model scale).

Figure 167 .

 167 Figure 167. Cyclic loading and pull-out test nº 10FHi-7 with 10FHi model in the 10 th container: (a) anchor location; (b) cyclic loading test on stability diagram; (c), (d) and (e) cyclic loading; (f) post-cyclic (results in model scale).

Figure 168 .

 168 Figure 168. Cyclic loading and pull-out test nº 10FHi-1 with 10FHi model in the 13 th container: (a) anchor location; (b) cyclic loading test on stability diagram; (c), (d) and (e) cyclic loading; (f) post-cyclic (results in model scale).

Figure 169 .

 169 Figure 169. Cyclic loading and pull-out test nº 10FHi-2 with 10FHi model in the 13 th container: (a) anchor location; (b) cyclic loading test on stability diagram; (c), (d) and (e) cyclic loading; (f) post-cyclic (results in model scale).

Figure 170 .

 170 Figure 170. Cyclic loading and pull-out test nº 10FHi-3 with 10FHi model in the 13 th container: (a) anchor location; (b) cyclic loading test on stability diagram; (c), (d) and (e) cyclic loading; (f) post-cyclic (results in model scale).

Figure 171 .

 171 Figure 171. Cyclic loading and pull-out test nº 10FHi-4 with 10FHi model in the 13 th container: (a) anchor location; (b) cyclic loading test on stability diagram; (c), (d) and (e) cyclic loading; (f) post-cyclic (results in model scale).

Figure 172 .

 172 Figure 172. Cyclic loading and pull-out test nº 10FHi-1 with 10FHi model in the 14 th container: (a) anchor location; (b) cyclic loading test on stability diagram; (c), (d) and (e) cyclic loading; (f) post-cyclic (results in model scale).

Figure 173 .

 173 Figure 173. Cyclic loading and pull-out test nº 10FHi-2 with 10FHi model in the 14 th container: (a) anchor location; (b) cyclic loading test on stability diagram; (c), (d) and (e) cyclic loading; (f) post-cyclic (results in model scale).

Figure 174 .

 174 Figure 174. Cyclic loading and pull-out test nº 10FHi-5 with 10FHi model in the 14 th container: (a) anchor location; (b) cyclic loading test on stability diagram; (c), (d) and (e) cyclic loading; (f) post-cyclic (results in model scale).

Figure 175 .

 175 Figure 175. Cyclic loading test 10FHi-1 in the 10 th container: (a) Qhelix/Qhead versus cycle number; (b) friction resistance versus cycle number; (c) displacement rate during the cyclic loading.

Figure 176 .

 176 Figure 176. Cyclic loading test 10FHi-2 in the 10 th container: (a) Qhelix/Qhead versus cycle number; (b) friction resistance versus cycle number; (c) displacement rate during the cyclic loading.

Figure 177 .Figure 178 .

 177178 Figure 177. Cyclic loading test 10FHi-3 in the 10 th container: (a) Qhelix/Qhead versus cycle number; (b) friction resistance versus cycle number; (c) displacement rate during the cyclic loading.

Figure 179 .

 179 Figure 179. Cyclic loading test 10FHi-6 in the 10 th container: (a) Qhelix/Qhead versus cycle number; (b) friction resistance versus cycle number; (c) displacement rate during the cyclic loading.

Figure 180 .Figure 181 .

 180181 Figure 180. Cyclic loading test 10FHi-7 in the 10 th container: (a) Qhelix/Qhead versus cycle number; (b) friction resistance versus cycle number; (c) displacement rate during the cyclic loading.

Figure 182 .

 182 Figure 182. Cyclic loading test 10FHi-2 in the 13 th container: (a) Qhelix/Qhead versus cycle number; (b) friction resistance versus cycle number; (c) displacement rate during the cyclic loading.

Figure 183 .Figure 184 .

 183184 Figure 183. Cyclic loading test 10FHi-3 on 10FHi in the 13 th container: (a) Qhelix/Qhead versus cycle number; (b) friction resistance versus cycle number; (c) displacement rate during the cyclic loading.

Figure 185 .

 185 Figure 185. Cyclic loading test 10FHi-1 in the 14 th container: (a) Qhelix/Qhead versus cycle number; (b) friction resistance versus cycle number; (c) displacement rate during the cyclic loading.

Figure 186 .Figure 187 .

 186187 Figure 186. Cyclic loading test 10FHi-2 in the 14 th container: (a) Qhelix/Qhead versus cycle number; (b) friction resistance versus cycle number; (c) displacement rate during the cyclic loading.

Figure 190 .

 190 Figure 190. 8FH model exhumation after uplift equals to 5.3 mm (0.2D): (a) entire anchor model; (b) helix in detail; (c) after removing the model anchor.

  is necessary to verify the minimum value of w/d50 ratio (Figure 2) to prevent any scale effect on helical anchor model in sand. The values for the ratios D/d50 (plate diameter/average grain size) and d/d50 (shaft diameter/average grain size) observed in previous studies to avoid scale effects on bearing plate resistance and shaft resistance indicate that the shaft diameter should restrict the helical anchor model dimensions (greater d/d50 ratios are suggested University of São Paulo and LUNAM University

Figures

  Figures

Figure 1 .

 1 Figure 1. Photograph of a helical anchor model in very dense sand after installation.

Figure 2 .

 2 Figure 2. Helical anchor prototype simulated by anchor models of different w/d50 ratios (different model sizes in the same sand sample).

Figure 3 .

 3 Figure 3. Mini-CPT results: (a) qc vs tip depth, (b) normalized tip resistance vs depth.

Figure 4 .

 4 Figure 4. IFSTTAR centrifuge.

Figure 5 .

 5 Figure 5. (a) test system; (b) servo-controlled actuator.

Figure 6 .

 6 Figure 6. Helical model anchors.

Figure 7 .

 7 Figure 7. Load-displacement curves of the tensile load tests: (a) and (b) container 1, (c) and (d) container 2, (e) and (f) container 3.

Figure 11 .

 11 Figure 11. Installation torque of helical anchor models of different sizes.

  tests performed by Unisol Laboratories b Estimated from at least two calibrated boxes placed on the bottom of each container c Measured from direct shear tests

Table 1

 1

);  is the interface friction angle. University of São Paulo and LUNAM University

Table 1 .

 1 Ku values recommended byMitsch and Clemence (1985).

	Angle of internal	Ku recommended values for
	friction of soil (º)	helical anchors
	25	0.70
	30	0.90
	35	1.50
	40	2.35
	45	3.20

  University of São Paulo and LUNAM University2.2.3. Behaviour of the pile base resistance in one-way cyclic loadingsStudies on pile base resistance under cyclic loading can contribute to the understanding of the behaviour of helical anchors. The largest contribution to the helical anchor's capacity is

  .

	Parameter	Notation Scaling factor
	Distance	u *	1/n
	Stress	 *	1
	Soil density	 *	soil	1
	Gravity	g *	n
	Displacement	 *	1/n
	Dynamic time	t * dyn	1/n
	Strain	 *	1
	Velocity	v *	1
	Acceleration	a *	n
	Frequency	f *	n
	Force	F *	1/n²
	Unit weight	 *	n
	Mass	m *	1/n³
	2.5.1. Scale effects
	Centrifuge modelling allows for parametric studies with relatively small effort and low-
	cost compared to full-scale tests. For this reason, this modelling technique has been used

  Table 3 lists the main characteristics of HN38 Hostun sand. Since the samples are dry,

Table 3 .

 3 HN38 Hostun sand main characteristics.

	Specific gravity of the sand particles	Gs	2.64
	Maximum dry unity weight (kN/m 3 )	d(max)	15.24
	Minimum dry unity weight (kN/m 3 )	d(min)	11.63
	Maximum void ratio	emax	1.226
	Minimum void ratio	emin	0.699
	Average grain size (mm)	d50	0.12
	Coefficient of uniformity	CU	1.97

Table 4 .

 4 Sensors features.

		Torque	Force	Displacement
	Feature	Sensor F62	sensor F97	sensor D SV2
	Range	50 Nm	1000 N	300 mm stroke
	Resolution	0.002 Nm	0.02 N	0.001 mm
	Linearity deviation	0.1%	0.15%	0.01%
	Hysteresis	0.1%	0.15%	0.004 mm
	Manufacturer	FGP	TME	TWK
	Model	CD1140-2	F 521 TC	Magnetostrictive displ. transd. MSE

Table 5 .

 5 Model piles characteristics.

	Model anchor designation	Shaft diameter Model	(d) in mm	Prototype	Helix diameter Model	(D) in mm	Prototype	Model	Helix pitch (p)	in mm	Prototype	Helical plate Model	thickness (t h )	in mm Prototype	Helix Model	embedment	(z D ) in mm Prototype	G-level	(g)	d/d 50	D/d 50	p / D
	6FH	6.0	100	20.0	330	1.6		26.7	0.5		8.4	120	1980	16.7	50	167	0.080
	8FH	8.0	100	26.6	330	1.4		17.5	0.8	10.0	160	1980	12.5	67	222	0.053

Figure 23. Helical model anchors with fixed helix.

  Table6presents the model anchor characteristics used for both analyses. The tests on the removable helix models were carried out in containers No. 2, 3 and 4. Tests on the instrumented anchor model 10FHi were carried out in container No. 9. The installation and loading test procedures were conducted as described in 3.1.3.

Table 6 .

 6 Models characteristics (model values).

	Model	Type d (mm) D (mm) Pitch (mm)	Helical plate thickness (mm)	zD/D g-level
	Prototype	fixed helix	100	330	41.2	25	various	-
	8RH removable helix	8	26	3.3	0.8	8	12.5
	10RH removable helix	10	33	4.1	1.8	7.4	10.0
	12RH removable helix	12	40	5	3	6	8.3
	8FH	fixed helix	8	26	1.4	0.8	8	12.5
	10FH	fixed helix	10	33	2.5	1.8	7.4	10.0
	12FH	fixed helix	12	40	3	3	6	8.3
	10FHi	instrumented	10	33	9.7	2.5	7.4	10.0

Table 7 .

 7 Characteristics of the cyclic load tests carried out.

	Sample Model nº Qmean/QT Qcyc/QT Pre-load/QT Cycles
	4	10HF-3	0.17	0.07	0.10
	4	10HF-4	0.23	0.14	0.09
	4	10HF-5*	0.32	0.23	0.10
	4	10HF-6*	0.42	0.32	0.10	63
	5	10HF-2*	0.53	0.21	0.32	520
	5	10HF-3	0.32	0.10	0.22
	5	10HF-4*	0.41	0.14	0.27	500
	5	10HF-5	0.41	0.09	0.32
	5	10HF-6*	0.33	0.16	0.18
	6	10HF-1	0.32	0.19	0.13
	6	10HF-2	0.41	0.22	0.18
	6	10HF-3	0.47	0.19	0.28
	6	10HF-4	0.47	0.23	0.23
	6	10HF-5	0.28	0.10	0.18 0.19
	6	10HF-6	0.45	0.26	0.19 0.18
	7	10HF-1	0.45	0.26	0.32
	7	10HF-2	0.28	0.10	0.18
	7	10HF-5	0.54	0.21	0.23
	7	10HF-6	0.40	0.23	0.14	700
	9	10HFi-3	0.52	0.29	0.12
	9	10HFi-4	0.41	0.27	0.18
	9	10HFi-5	0.27	0.15	0.17 0.18
	9	10HFi-6	0.41	0.22	0.17 0.17
	10	10HFi-1	0.28	0.10	0.30
	10	10HFi-2	0.45	0.28	0.22
	10	10HFi-3	0.45	0.28	0.21
	10	10HFi-4	0.27	0.10	0.37
	10	10HFi-6	0.52	0.22	0.51
	10	10HFi-7	0.52	0.30	0.47
	13	10HFi-1	0.41	0.20	0.16
	13	10HFi-2	0.60	0.22	0.24
	13	10HFi-3	0.67	0.16	0.14
	13	10HFi-4	0.69	0.23	0.25
	14	10HFi-1	0.48	0.31	0.08
	14	10HFi-2	0.55	0.31	0.10
	14	10HFi-3	0.51	0.37	0.18 0.17	300
	14	10HFi-4	0.60	0.35	0.17 0.17	300
	14	10HFi-5	0.51	0.42	0.34

* test results not considered in the analysis because of problems in the servo-controlled system configuration University of São Paulo and LUNAM University

Table 8 .

 8 Climate of São Carlos (Cepeagri, 2016).

Month Jan

Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Year

Table 9 .

 9 Granulometric fractions of soils according to NBR 6502[START_REF] Abnt | Rocks and soils -Terminology[END_REF] , after[START_REF] Machado | Application of elastoplasticity concepts to non-saturated soils[END_REF].

		Depth (m)	Sand (%)	Silt (%)	Clay (%)
		3.0		60.8		11.9	27.3
		5.0		66.7		5.90	27.4
		8.0		68.9		13.7	17.4
	Table 10. Soil characteristics obtained with undisturbed specimens, after Machado (1998).
	Prof. (m)	1	2	3	4	5	6	7	8	9
	Water content (%) 13.7	14.6	15.8	16.8	16.4	17.2	19.1	16.7	18.3
	d (kN/m 3 )	12.5	13.6	13.8	14.3	14.4	14.7	15.2	16.1	16.6
	 (kN/m 3 )	14.2	15.6	16.0	16.7	14.8	17.1	18.1	18.8	19.6
	Void ratio	1.17	0.99	0.96	0.90	0.88	0.84	0.78	0.68	0.63
	 (º) 1	-	29.0	-	-	31.2	-	-	26.4	-
	c (kPa) 1	-	0	-	-	10.5	-	-	26.9	-

1 obtained from saturated triaxial tests

Table 11 .

 11 Field tests on MHA1 and CHA1 anchors.

	Tested anchor	1MHA	1CHA
	1 st test	1 st monotonic 1 st monotonic
	2 nd test	2 nd monotonic	1 st cyclic
	3 rd test	3 rd monotonic 2 nd monotonic
	4 th test	4 th monotonic	2 nd cyclic
	5 th test	5 th monotonic 3 rd monotonic
	6 th test	-	3 rd cyclic
	7 th test	-	4 th monotonic
	8 th test	-	4 th cyclic
	9 th test	-	5 th monotonic

Table 12

 12

. The applied loading was registered every 25 seconds, and the anchor head displacements were registered 2 times per cycle, when the applied load reached the Qmax and Qmin values.

Table 12 .

 12 Characteristics of the cyclic load tests on anchor 1CHA.

	Cyclic test Qmean/QT1 Qcyclic/QT1	Number of cycles	Period (s)
	1 st test	0.15	0.05	50	60
	2 nd test	0.25	0.15	50	60
	3 rd test	0.35	0.25	50	60
	4 th test	0.58	0.48	50	60

Table 15 .

 15 This table shows that the QT results are similar in the range of models tested. The

variability in the results of container No. 11 is probably due to the sample heterogeneity, as the other two samples provided uniform results for all models tested.

Table 15 .

 15 Results of the investigation on the particle-scale effects.

	Sand sample	Model	d/d50	D/d50	w/d50	Tf (kNm)	Tavg-3D (kNm)	Kt (m -1 )	QT (0.1D) (kN)	QT (peak) (kN)	U(peak) (mm)	U/D
		8FHa	67	220	77	-	-	-	54	55	52.9	0.16
	Container	8FHb	67	220	77	-	-	-	51	53	48.3	0.15
	No. 8	12FHa	100	333	117	-	-	-	57	57	36.6	0.11
		12FHb	100	333	117	-	-	-	56	57	42.7	0.13
		6FHa	50	167	58	6.9	3.7	17	62	63	46.5	0.14
		6FHb	50	167	58	5.1	2.9	17	49	50	38.5	0.12
	Container No. 11	10FHa 10FHb	83 83	275 275	96 96	6.5 6.8	3.8 4.3	18 16	67 67	67 68	36.5 40.4	0.11 0.12
		12FH	100	333	117	8.9	8.9	6	55	55	32.7	0.1
		6FH	50	167	58	6.9	4.3	16	65	67	53	0.16
	Container	8FH	67	220	77	7.1	4.7	15	66	69	47.4	0.14
	No. 12	10FH	83	275	96	7.8	5.0	14	67	68	38.3	0.12
		12FH	100	333	117	10.2	6.9	10	65	66	38	0.12
					Mean	7.4	4.9	14	60	61	42.4
				Standard deviation	1.5	1.9	3.9	7	7	6.6
			Coefficient of variation	20%	37%	27%	12%	11%	16%

Figure 49 compares the ultimate uplift capacity according to the w/d50 ratio (effective helical radius/d50) of the model anchors with different sizes. The average ultimate load of the 13 tests is 61 kN, with an 11% coefficient of variation (COV). The variation in the QT results

Table 16 .

 16 Results of the uplift tests with model anchors in two different conditions.

	Test	Condition	zD/D	QT (kN)	U(peak) (mm)	U(peak)/D
	6FH Cont. No. 1	Placed before	8.0	38.5	45.9	0.14
	6FH-2 Cont. No. 11 Installed in flight	8.0	104.5	49.7	0.15
	8FH-1 Cont. No. 1	Placed before	8.0	31.4	51.2	0.16
	8FH-1 Cont. No. 2	Installed in flight	8.0	89.3	77.6	0.23
	10FH-1 Cont. No. 1	Placed before	8.0	55.8	52.6	0.16
	10FH-1 Cont. No. 2	Installed in flight	8.0	88.0	63.9	0.19

Table 17 .

 17 Displacement accumulation rates in tests with the 10FHi model (prototype values).

Table 18

 18 University of São Paulo and LUNAM University probably due to the different in the mean load (Qmean) of these tests (greater mean load for the test on the model 10FH). Comparing only the results obtained from the tests on model 10FHi, the influence of the cyclic amplitude is clear. For these cases, the cyclic tests with higher

	dependent on the cyclic loading amplitude and on the maximum cyclic loading. Similar
	observations were made by Rimoy (2013) that reported cyclic stiffness patterns varying
	mainly based on the cyclic amplitude in cyclic tests on conventional piles.
	For cyclic tests with Qcyclic varying from 10% to 15%QT the stiffness gain was less than
	in the cyclic tests with a Qcyclic of 34% and 42%QT. However, two cyclic tests with Qcyclic at

presents the results of the anchor's cyclic axial stiffness at the 1 st , 100 th and 1000 th cycle (or for a final cycle if N<1000). This table indicates that the stiffness increase is about 20%QT showed significant difference in stiffness gain, being 15.1 kN/mm for the 10FH test against 9.1 kN/mm for the test on model 10FHi, in prototype values. The difference is

Table 18 .

 18 Axial anchor stiffness in cyclic tests on models 10FH and 10FHi (prototype values).

							Axial anchor stiffness (kN/mm)
	Test Qmean/QT Qcyclic/QT Qmax/QT Cycles	Initial	N = 100 cycles	Final	Difference k(N=last) -k(N=1)
	10FH-4 Cont. No. 4	0.23	0.14	0.37	1000	5.9	17.4	18.1	12.2
	10FH-3 Cont. No. 5	0.32	0.10	0.42	1000	6.1	21.9	21.3	15.2
	10FH-1 Cont. No. 7	0.54	0.21	0.75	1000	4.8	19.9	19.9	15.1
	10FHi-3 Cont. No. 10	0.41	0.20	0.61	1000	12.8	21.3	21.9	9.1
	10FHi-1 Cont. No. 14	0.51	0.42	0.93	300	7.1	24.3	25.2	18.1
	10FHi-2 Cont. No. 14	0.45	0.34	0.79	500	8.6	24.7	25.8	17.2

Table 19 .

 19 Summary of results of the post-cyclic monotonic tests.

	Cont. No. Test No. Qmean/QT Qcyclic/QT Qpre/QT N (cycle)	QT-pc (kN)	QT post-cycles / QT	Qhelix post-cycles (kN)	Nq-pc
	4	10FH-3	0.17	0.07	0.10	1500	82.2	0.88	-	28.5
	4	10FH-4	0.23	0.14	0.09	1000	90.1	0.97	-	31.2
	5	10FH-3	0.32	0.10	0.22	2000	88.1	0.95	-	30.5
	5	10FH-5	0.41	0.09	0.32	2000	89.0	0.96	-	30.8
	6	10FH-1	0.32	0.19	0.13	2000	87.9	0.94	-	30.4
	6	10FH-2	0.41	0.22	0.19	2000	86.8	0.93	-	30.1
	6	10FH-3	0.47	0.19	0.28	2000	86.4	0.93	-	29.9
	6	10FH-4	0.47	0.23	0.23	1000	92.1	0.99	-	31.9
	7	10FH-1	0.54	0.21	0.32	2000	79.6	0.86	-	27.6
	7	10FH-2	0.40	0.23	0.18	2000	87.5	0.94	-	30.3
	7	10FH-3	0.52	0.29	0.23	2000	90.0	0.97	-	31.2
	9	10FHi-3	0.27	0.15	0.12	1000	100.0	1.08	-	34.6
	9	10FHi-4	0.41	0.22	0.18	1000	93.0	1.00	-	32.2
	10	10FHi-1	0.52	0.22	0.30	1000	88.1	0.95	93.3	32.3
	10	10FHi-2	0.52	0.30	0.22	1000	95.4	1.03	87.5	30.3
	10	10FHi-3	0.41	0.20	0.21	1000	93.3	1.00	86.8	30.1
	10	10FHi-4	0.60	0.22	0.37	1000	92.2	0.99	87.3	30.2
	10	10FHi-6	0.67	0.15	0.51	1000	98.1	1.06	82.4	28.5
	10	10FHi-7	0.69	0.22	0.47	1000	94.1	1.01	85.6	29.6
	13	10FHi-1	0.48	0.31	0.16	1000	91.1	0.98	89.4	31.0
	13	10FHi-2	0.55	0.31	0.24	1000	94.8	1.02	94.8	32.8
	13	10FHi-3	0.51	0.37	0.14	500	98.1	1.05	94.6	32.8
	13	10FHi-4	0.59	0.35	0.25	300	99.0	1.06	94.8	32.8
	14	10FHi-1	0.51	0.42	0.08	300	97.6	1.05	93.3	32.3
	14	10FHi-2	0.45	0.34	0.10	500	94.6	1.02	90.8	31.4
	14	10FHi-5	0.63	0.29	0.34	500	96.7	1.04	91.4	31.6

University of São Paulo and LUNAM University

Table 19

 19 also shows values of calculated post-cyclic bearing factors Nq-pc using the

measured results of pots-cyclic uplift capacity. For the calculation of Nq-pc values obtained from the tests on model 10FH (non-instrumented anchor model), the value of total uplift capacity was used (without subtracting the shaft resistance). For the tests on model 10FHi, the value of the measured helix bearing resistance was used for these estimates. However, as shown in this table, the Nq-pc values for all tests are very similar, as the portion of shaft resistance after the cyclic loadings are almost insignificant. The measured values of Nq-pc for all different types of cyclic tests are very similar (mean value of 31 with a coefficient of variation of 5%).

  University of São Paulo and LUNAM University b) a different number of helices and different helix diameter were used for the current study. For the work of[START_REF] Tsuha | Theoretical model to control on site the uplift capacit of helical screw piles embedded in sandy soil[END_REF] the helices diameters of double-helix anchor 5C were 254.0 mm and 304.8 mm, and for anchor 6C were 127.0 mm and 152.4 mm. Although the helix diameter of top helix of the anchor 5C

						Torque (kN.m)
		0	1	2	3	4	5	6	7	8	9 10
		0
								1MHA
		2						1CHA
								5C (Tsuha, 2007)
		4						6C (Tsuha, 2007)
	Helix depth (m)	6 8									Anchor 1MHA 1CHA 5C	Number of helices 1 1 2	D lower (mm) 305 305 254 D lower helix D upper helix D upper (mm) --304.8	d (mm) 101.6 101.6 73	z D lower (m) 15 15 14.4
		10									6C	2	254	304.8	73	14.4
		12
		14

Table 20 .

 20 Characteristics of the cyclic load tests on anchor 1CHA.

	Cyclic test Qmean/QT1 Qcyclic/QT1	Number of cycles	Period (s)
	1 st test	0.15	0.05	50	60
	2 nd test	0.25	0.15	50	60
	3 rd test	0.35	0.25	50	60
	4 th test	0.58	0.48	50	60

Table 21 .

 21 Summary of the results of the monotonic tensile load tests.

	Test No.	1MHA Qult (kN) Qhelix (kN)	Qs (kN)	1CHA Qult (kN) Qhelix (kN)	Qs (kN)
	1	89.1	77.2	11.9	97.6	60.3	37.3
	2	154.0	140.0	14.0	154.0	111.3	42.7
	3	204.0	181.0	23.0	186.0	131.9	54.1
	4	180.0	151.5	28.5	210.0	129.0	81.0
	5	217.0	156.7	60.3	241.0	131.1	109.9

Table 22 .

 22 Parameters of the concluding numerical simulations.

	Parameter		Test 1	Test 2	Test 3	Test 4	Test 5	Test 6	Test 7	Test 8
	E (MPa)	75	75	75	70	80	120	90	80
	Undisturbed		0.3	0.3	0.3	0.3	0.3	0.3	0.3	0.3
	soil	 (º)	47	42	42	42	47	48	48	42
		 (º)	6	6	6	6	6	6	6	6
	E (MPa)	50	50	50	50	70	90	90	45
	Disturbed		0.3	0.3	0.48	0.48	0.3	0.3	0.3	0.3
	soil	 (º)	37	33	33	33	33	37	42	33

Table 23 .

 23 Sieve analysis results

	Sieve opening		Passing material (%)
	(mm)	First test	Second test	Third test
	1.000	100.0	Not used	Not used
	0.595	Not used	Not used	100.0
	0.500	100.0	Not used	Not used
	0.400	Not used	100.0	Not used
	0.315	Not used	100.0	Not used
	0.297	Not used	Not used	99.9
	0.210	Not used	Not used	98.7
	0.200	96.1	96.4	Not used
	0.160	Not used	72.4	Not used
	0.149	Not used	Not used	74.1
	0.125	Not used	52.9	Not used
	0.105	Not used	Not used	41.1
	0.100	Not used	32.1	Not used
	0.080	17.8	15.7	Not used
	0.075	Not used	Not used	17.1
	0.063	6.2	6.0	Not used
	0.040	0.9	0.1	0.0

  Table 24 presents a summary of the characteristics of the HN38 Hostun used in centrifuge tests of this investigation.

Table 24

 24 Provided from tests carried out by Unisol Laboratories diameter (59.92 mm). The measures of vertical displacement were not reliable due to the low resolution of the available transducer in comparison to the range of the vertical displacements.

	. HN38 Hostun sand characteristics
	Specific gravity of the sand particles	Gs	2.64 a
	Maximum dry density (kg/m 3 )	d(max) 1554
	Minimum dry density (kg/m 3 )	d(min)	1186
	Maximum void ratio	emax	1.226
	Minimum void ratio	emin	0.699
	Average grain-size (mm)	d50	0.12
	Coefficient of uniformity	CU	1.97
	Coefficient of curvature	CC	0.99

a

Table 25 .

 25 Summary of results of the triaxial tests

	3 (kPa)	1 max (kPa)	(1 -3)max (kPa)	Ei (kPa)	E50 (MPa)	E50-reload (MPa)	ν	ϕ' (º)	ϕ'test end (º)
	50	374.9	324.9	42100	17500	97000	0.20
	100	652.8	552.8	64700	35700	92700	0.24	47	42
	200	1255.9	1055.9	62400	64400	127800	0.24

Table 27 .

 27 Characteristics of the model anchors.

	Model anchor	Shaft diameter	Helix diameter	Helix pitch	Helical plate
	designation	(d) in mm	(D) in mm	(p) in mm	thickness (th) in mm	p / D
	6H	6	20	1.6	0.5	0.08
	8H	8	26.6	1.4	0.8	0.053
	10H	10	33	2.5	1.8	0.076
	12H	12	40	3	3	0.075
	10FHi	10	33	9.7	1.5	0.294

Table 28 .

 28 Summary of centrifuge tests with helical pile models (cont.) University of São Paulo and LUNAM University Appendix L. Installation torque in centrifuge tests, in model values

	Cont.			Dr	G-level					Obtained
	No. Model Test No.	(%)	(g) zD/D	Study Installation Type of load	measures
		10FHi	10FHi-1	99	10	7.4 Mon. + cycl. load.	In flight Monot. + cycl.	F; U
		10FHi	10FHi-2	99	10	7.4 Mon. + cycl. load.	In flight Monot. + cycl.	F; U
	9	10FHi	10FHi-3	99	10	7.4	Cyclic loading	In flight	Cyc. + mon.	F; U
		10FHi	10FHi-4	99	10	7.4	Cyclic loading	In flight	Cyc. + mon.	F; U
		10FHi	10FHi-5	99	10	7.4	2 cyclic loadings	In flight	Cyc. + mon.	F; U; T
		10FHi	10FHi-6	99	10	7.4	2 cyclic loadings	In flight	Cyc. + mon.	F; U; T
		10FHi	10FHi-1	98	10	7.4	Cyclic loading	In flight	Cyc. + mon.	F; U; T
		10FHi	10FHi-2	98	10	7.4	Cyclic loading	In flight	Cyc. + mon.	F; U; T
	10	10FHi	10FHi-3	98	10	7.4	Cyclic loading	In flight	Cyc. + mon.	F; U; T
		10FHi	10FHi-4	98	10	7.4	Cyclic loading	In flight	Cyc. + mon.	F; U; T
		10FHi	10FHi-6	98	10	7.4	Cyclic loading	In flight	Cyc. + mon.	F; U; T
		10FHi	10FHi-7	98	10	7.4	Cyclic loading	In flight	Cyc. + mon.	F; U; T
		6FH	6FH-1	99	16.7	6.0	Scale effect	In flight	Monotonic	F; U; T
		6FH	6FH-2	99	16.7	8.0	Inst. effect	In flight	Monotonic	F; U; T
		6FH	6FH-3	99	16.7	6.0	Scale effect	In flight	Monotonic	F; U; T
	11	10FH	10FH-1	99	10	6.0	Scale effect	In flight	Monotonic	F; U; T
		10FH	10FH-2	99	10	6.0	Scale effect	In flight	Monotonic	F; U; T
		12FH	12FH-1	99	8.3	6.0	Scale effect	In flight	Monotonic	F; U; T
		10RH	10RH-1	99	10	6.0	Shaft friction	In flight	Monotonic	F; U; T
		6FH	6FH-1	99	16.7	6.0	Scale effect	In flight	Monotonic	F; U; T
	12	8FH	8FH-1	99	12.5	6.0	Scale effect	In flight	Monotonic	F; U; T
		10FH	10FH-1	99	10	6.0	Scale effect	In flight	Monotonic	F; U; T
		12FH	12FH-1	99	8.3	6.0	Scale effect	In flight	Monotonic	F; U; T
		10FHi	10FHi-1	99	10	7.4	Cyclic loading	In flight	Cyc. + mon.	F; U; T
	13	10FHi	10FHi-2	99	10	7.4	Cyclic loading	In flight	Cyc. + mon.	F; U; T
		10FHi	10FHi-3	99	10	7.4	Cyclic loading	In flight	Cyc. + mon.	F; U; T
		10FHi	10FHi-4	99	10	7.4	Cyclic loading	In flight	Cyc. + mon.	F; U; T
		10FHi	10FHi-1	99	10	7.4	Cyclic loading	In flight	Cyc. + mon.	F; U; T
		10FHi	10FHi-2	99	10	7.4	Cyclic loading	In flight	Cyc. + mon.	F; U; T
	14	10FHi	10FHi-3	99	10	7.4	Cyclic loading	In flight	Cyc. + mon.	F; U; T
		10FHi	10FHi-4	99	10	7.4	2 Cyclic loadings	In flight	Cyc. + mon.	F; U; T
		10FHi	10FHi-5	99	10	7.4	2 Cyclic loadings	In flight	Cyc. + mon.	F; U; T
		6FHp	6FHp	99	16.7	7.5 Inst. eff. (tomogr.)	In flight	Monotonic	F; U; T

University of São Paulo and LUNAM University

The sand density index in the site is not clearly reported inGavin et al. (2014), in[START_REF] Gavin | Base load -displacement response of piles in sand[END_REF], in[START_REF] Igoe | The development and testing of an instrumented open-ended model pile[END_REF] and in[START_REF] Doherty | Soil properties at the UCD geotechnical research site at Blessington[END_REF]. A ID = 100% is reported for reconstituted sand samples for triaxial tests for the site characterization, however there is no clearly indication of the site ID. Estimations performed by the present author using the correlation proposed byJamiolkowsky et al. (2003) with the CPT results presented byGavin et al. (2014) have indicated a ID value around 95%.

University of São Paulo and LUNAM UniversityAnnex A. Roughness of 10FH helical pile model

University of São Paulo and LUNAM University Annex B. Features of the force gauge in the model 10FHi

Acknowledgements

I would like to express deep gratitude to Professor Cristina Tsuha for believing in me and for giving me the opportunity to conduct this study. I only have to thank her for all that I have learned on work, scientific methodology, analysing, reasoning and writing. Without her guidance, encouragement, enthusiasm and support, this research would not have happened. I would also thank her for all the efforts made to materialize the Brazilian-French joint supervision of this thesis.

I thank Professor Luc Thorel, not only for co-supervising this research, but for the invaluable experience shared while I was a visiting student at IFSTTAR, and for the trips to Brazil to organize this research. I appreciate the discussions, suggestions, collaborations with this research and also the efforts made during all the process to conclude the joint supervision process. I would like to thank all the professors of the Department of Geotechnical Engineering of the University of São Paulo, especially to Prof. Cintra and Prof. Orencio. I would also like to thank all the technicians and staff of the Department of Geotechnical Engineering of the University of São Paulo: Oscar, Zé Luiz, Dito, Antonio, Décio, Clever, Maristela, Neiva, Álvaro, Herivelto and Toninho. I would like to thank to Mathieu Blanc, Alberto Bretschneider and Sandra Escoffier for the agreeable fellowship during my stay at IFSTTAR. I am greatly thankful to the IFSTTAR Acknowledgements SCHIAVON, José Antonio Behaviour of helical anchors subjected to cyclic loadings 282 University of São Paulo and LUNAM University This research was supported by the program USP-COFECUB grant No. UcMa 132/12, by the Brazilian Agency CAPES (Ministry of Education) and by the French Institute of Science and Technology for Transport, Development and Networks (IFSTTAR), France. The authors would like to thank to P. Gaudicheau, P. Audrain, S. Lerat, A. Neel, D. Macé and C. Favraud for their valuable contributions.

The 3 rd series of monotonic tension load tests was performed on anchor 1CHA (after the 2 nd cyclic test) and 1MCA (reference). The uplift capacities of the anchors increased compared to the previous test. Also, an asymptotic trend (more clear failure indication) of the applied load began to be observed for vertical displacements of around 6%D in both 1CHA and 1MHA 3 tests (Figure 97c). The maximum applied load attained greater values for the load test on 1MHA (204 kN) than for 1CHA (186 kN).

Comparing the shaft resistance values (Qapplied -Qhelix) obtained in the 2 nd and 3 rd monotonic loading tests, increases of 9.0 and 11.4 kN (64% and 27%) were observed for 1MHA and 1CHA, respectively.

The application of a single load cycle with a large amplitude of Qmax = QT(N) (in a monotonic loading test) has been shown to cause no damage to the anchor behaviour in both 1MHA and 1CHA anchors. At least, in the results of the first three monotonic tests, each time the anchors were re-tested monotonically, the ultimate load increased.

The results of the 3 rd cyclic test (Figures 96e andf) also illustrate the anchor performance improvement due to the previous application of a single cycle with large amplitude (during the monotonic loading test). In this cyclic test, cyclic loading with Qmean = 0.35QT1 and Qmean = 0.25QT1 caused an accumulated displacement of 0.60mm after 50 cycles; however, this accumulated displacement was generated in the first load cycle, and no further increase of accumulated displacement was noticed for the following 49 cycles.

During the 3 rd cyclic test, the Qhelix/Qapplied ratio decreased in comparison to the 2 nd cyclic load test (Figure 96d andf). While in the 2 nd cyclic test the maximum registered load in the instrumented section was Qhelix = 0.94Qapplied, in the 3 rd test the maximum load was Qhelix = 0.71Qapplied, indicating an increase in shaft resistance mobilization.

Appendix A. Characteristics of the HN38 Hostun sand HN38 Hostun sand is a fine silica sand consisting of angular particles is extracted in Hostun village, 66 km far from Grenoble, France. The characterization tests conducted with the HN38 Hostun sand were:

 Test for determination of the Specific Gravity of the sand particles (Gs);

 Test for determination of the Particle-Size Distribution;

 Test for determination of the maximum and minimum dry density;

The specific gravity of sand particles (Gs) was obtained from tests carried out by Unisol

Laboratories following the French Standard NF P94-054 [START_REF] Afnor | NF P94-054 Détermination de la masse volumique de particules solides des sols[END_REF]. The specific gravity of the HN38 Hostun sand was Gs = 2.64.

The particle-size distribution of the HN38 Hostun sand was carried out according to the French Standard NF P94-056 [START_REF] Afnor | Sols: reconnaissances et essais, Analyse granulométrique, méthode de tamisage à sec après lavage[END_REF] at the IFSTTAR laboratory. Figure 113 shows the equipment used in the tests. Five calibrated boxes were positioned at the bottom of the rectangular strongbox to determine the relative density of the sand sample reconstituted with HN38 Hostun sand. To maintain the same particle drop height during the tests, the hopper was stopped after a certain number of round-trip movements, depending on the slot opening: after 4 round-trip movements for 2 mm of slot opening; for 3 mm and 2 mm of slot opening, the hopper the drop height was verified after 3 and 1 round-trip movements, respectively.

Figure 121 shows the configuration of the calibration boxes inside the strongbox.

Table 26 lists the variation of the pluviation parameters and the results. Five penetrometric tests (mini-CPT) were carried out in container 3 at 10g and at a constant penetration rate of 10 mm/s. Figure 122 shows the IFSTTAR mini-CPT equipment.

These tests intended to evaluate the vertical and horizontal homogeneity of the sand sample tested. The results of the five mini-CPT tests are presented in Figure 123. Appendix F. Data acquisition system and servo-controlled hydraulic actuator

In the IFSTTAR Centrifuge, the on-board measurements during the tests are performed with the Spider8 (8-channel modules) data acquisition modules manufactured by HBM. The control of the data acquisition system is done with the DASYLab software via a graphical programming interface that enables to register the data on an external hard drive backup and facilitates the data duplication on a dedicated network space. Any type of sensor can be conditioned (full bridge, half-bridge, voltage source, temperature probe) with a sampling frequency up to 1200 Hz. Positioned in the centrifuge basket, Spider modules are then connected via a parallel link to a central processing unit at the centrifuge swing [START_REF] Thorel | Mesures en macrogravité sur modèles réduits d'ouvrages géotechniques[END_REF].

Figure 124. Spider data acquisition modules [START_REF] Thorel | Mesures en macrogravité sur modèles réduits d'ouvrages géotechniques[END_REF].

The hydraulic servo-actuator is equipped with a Moog electro-hydraulic servo-valve which is capable of operating up to 100g. The oil supply is provided by a stationary hydraulic power unity on the stator side (flow rate of 6.8 litres/minute at 50 °C under 15 MPa).

Appendix H. Calibration of the 10FHi force gauge

The force gauge of the model anchor 10FHi was calibrated in tension with a universal press (Figure 125a). A support base was used to attach the pile head to the press base (Figure 125b). Figure 126 presents the calibration curve of the force gauge at the shaft section above the helix of the model 10FHi.

During the first experiments with the model 10FHi (tests 10FHi-1 and 10FHi-2 in Container No. 9) we observed that the readings of this force gauge were being affected by the installation torque. Thus, a preliminary verification was done with the model anchor out of the sand sample and with no axial loading. The top of the model anchor was maintained attached to the servo-controlled actuator and a torque was applied to the anchor tip using a manual torque wrench. The axial force was observed to increase as the applied torque increased. This occurred because the force gauge has screws on both sides to attach both helix and shaft to the force gauge. Thus, as the torque increases, the shaft and the helix tend to be screwed even more into the screws of the force gauge. Figure 127 illustrates this mechanism. As consequence, the data registered with the force gauge above the helix are required to be corrected as a function of the applied torque. This correction was done by calibrating the arisen load in the force gauge due to the torque application.

The calibration was performed using the same servo-controlled system and the torquemeter used in the model anchor installation in centrifuge. As performed in the preliminary verification aforementioned, the top of the model anchor was maintained attached to the servo-controled actuator and a torque was applied to the anchor tip using a manual torque wrench. The applied torque was registered by the torquimeter attached to the servocontrolled system, and the load in the force gauge was monitored. As the torque increased, the force gauge indicated a compressive force in a linear correlation. Figure 128 presents the curve for the correction of force gauge readings with the applied torque.

University of São Paulo and LUNAM University compared to D/d50). However, the shaft friction resistance contributes to a very small portion of the total capacity of a helical anchor in sand as demonstrated in [START_REF] Schiavon | Experimental investigation on the helical pile behaviour under cyclic tensile loading[END_REF]. This author performed a series of pull-out tests on an instrumented model of a single-helix anchor, installed in the same sand sample used in the current investigation; in this case, the shaft capacity varied from 12 to 22% of the total uplift capacity of the helical anchor. Therefore, noting that the predominant portion of the uplift capacity of the investigated helical anchor is related to the helical plate bearing resistance; the scale effects evaluated in the current study are predominantly influenced by the ratio of the effective helical radius to the average grain size.

Experimental programme

The current study aims to verify the particle size effect on the uplift response of helical anchor models in sand tested in a centrifuge. To achieve this objective, four different helical anchor models, fabricated to simulate the same prototype of a helical anchor, were installed in dry dense sand samples and tested in a centrifuge. The pullout tests were performed on each model anchor at least three times to verify the repeatability and reproducibility of the measured results of uplift capacity. Therefore, three containers were equally prepared to allow the number of tests required for this purpose.

The scale effects on the helical anchor capacity were verified from the experimental results using the technique "modelling of models" described in Ovesen (1979). In this cited work, anchor models of different sizes and glevels were used to simulate the same prototype response in the same sand, and the full similarity is achieved when an identical response is observed between model and prototype. This author used this technique to evaluate scale effects on the bearing resistance.

The helical anchor models were installed and tested in three reconstituted sand samples prepared by a raining deposition technique. The sand samples were placed in a rectangular container of 1200 mm in length, 800 mm in width, and 360 mm in depth.

The centrifuge experiments were performed in reconstituted dry HN38 Hostun sand, which is a fine silica sand consisting of angular particles (sand extracted in Hostun, France). The Hostun sand is used in other laboratory investigations, and its physical properties are well established (Flavigny et al., 1990). The experiments were performed in sand samples with sand relative density of 99%. Table 1 illustrates the characteristics of HN38 Hostun sand. Figure 3 shows the results of mini-CPT tests (cone diameter = 12 mm) carried out in a preliminary container, prepared only to evaluate the vertical and horizontal homogeneity of the sand sample tested in the current investigation. The experiments were conducted in the IFSTTAR geotechnical centrifuge [START_REF] Corté | Une centrifugeuse pour la recherche en géotechnique[END_REF]), which has a radius of 5.50 m, a maximum payload of 2000 kg, and a maximum acceleration of 200 g (Figure 4).

Test system

The anchor model installations and pull-out tests were performed using a servo-control system fixed over the sand container. As illustrated in Figure 5, a motor was coupled to the system to rotate the helical anchor models

University of São Paulo and LUNAM University The average ultimate load obtained from the 13 tests is 61 kN, with a small coefficient of variation (COV) of 11%. The variation in the QT results probably occurred due to the variability in the sand samples and may not be attributed to particle size effect because there is no clearly defined trend.

The estimated uplift capacity of the prototype simulated in this study, using Terzaghi's equation as proposed in Adams and Klym (1972) for single-helix anchors, and the uplift capacity factor Nqu presented in Mitsch and Clemence (1985) for single-helix anchors in sand, was 120 kN, which is approximately twice the measured uplift capacity. A similar difference was observed in the numerical simulation of the field experiments of Gavin et al.

(2014) on a single-helix anchor in dense sand. The prediction of these authors provides a result of the uplift capacity two times greater than the field measurements. These significant differences between the estimates and the measurements suggest that there is an important installation effect, not considered in the p rediction methods, that influences the single-helix uplift capacity in dense sand, as illustrated in Figure 1.

Table 3 and Figure 9 show that the ultimate load was reached at a vertical displacement in the range of 10% to 16% of the helical plate diameter. The larger anchor models required slightly smaller displacements to attain the ultimate load; however, as shown in Figure 9, no clear trend was observed.

The findings reported in Ovesen (1979 and1981), Foray et al. (1998), Garnier and König (1998), and in other studies indicate that the results of bearing capacity and shaft resistance increases as the model size decreases.

Therefore, the almost horizontal trend line plotted in Figure 8 suggests that no scale effect was identified for the range of models evaluated in this investigation: d/d50  50, and w/d50  58.

The results of the installation torque of the anchor models tested in the containers 2 and 3 are presented in Figure 10 and 11. Figure 11 shows that the values of the final installation torque obtained for the models 10H and 12H (in prototype value) are slightly greater than the results found for the other models. The models 10H and 12H

were fabricated with greater helix thickness (18.0 and 25.0 mm in prototype scale, respectively) compared to the models 6H and 8H (8.4 and 8.8 mm) to prevent bending during the installation (see Table 2); therefore, as the installation torque increases with the helix thickness (Sakr, 2014), this torque gain probably is not caused by a scale effect. Accordingly, Figure 11 indicates that the installation torque was not influenced by scale effects for the range of w/d50 and d/d50 evaluated, as observed in Figure 8 for the uplift capacity. This finding is important because the average torque measured at the final penetration of 3 times the helix diameter is used to predict and to verify the ultimate capacity during anchor installation. Hoyt and Clemence (1989) proposed an empirical relationship of the installation torque to the axial uplift capacity of helical piles, given by Eq. 2:

where Tavg-3D = average of the torque measured along the final distance corresponding to 3 times the helix diameter Kt = torque correlation factor that varies with the shaft diameter