Dr Charles Aaron Spicer

Nadine Christelle

Professor Gopal Santana Phani Abadie

Madabhushi

Anchor Pile Design for Floating Offshore Wind Turbines

Keywords: Floating Offshore Wind, Tension Leg Platform, Anchor Pile Design, Cyclic Loading, 1g Testing, Sand

As the world is working towards accelerating the global transition to clean power, the development of floating offshore wind turbine (FOWT) technologies is becoming increasingly important. The design of robust anchors that can sustain severe cyclic loads from the wind, waves and currents, for a large number of cycles, is central to the deployment of future floating wind farms. This paper presents experimental work to further understand and improve the design of driven anchor piles in sandy soils for Tension Leg Platforms (TLPs). It involves laboratory tests at 1g, scaled to represent a typical anchor pile, designed following original guidelines for floating offshore wind turbine anchors from the ABS (American Bureau of Shipping). The test programme involves selected axial load cases to investigate stable, meta-stable and unstable behaviour, and demonstrates that the factors of safety currently recommended by the ABS are insufficient, leading to premature failure of the anchor pile. However, the results show good agreement with published cyclic interaction diagrams, originally devised for the design of piles under cyclic axial loading. A set of empirical laws are derived from the experimental results to predict the number of cycles to failure and the change in pile ultimate pull-out capacity due to cyclic loading. This work suggests a revised direction for the design of anchor piles under cyclic loading.

INTRODUCTION

As the offshore wind industry expands into deeper waters, the superstructures and foundations of fixed-bottom offshore wind turbines are becoming increasingly large and expensive. Floating offshore wind turbines (FOWTs) provide a promising solution to accessing deeper waters, and their technological development is of increasing importance. However, while floating wind farms are technically feasible, the experience and knowledge in relation to their technology and design is still very much in its infancy.

Anchors and mooring systems could represent over 10% of the capital expenditure of an installed farm, and therefore optimized and robust designs could have a positive impact on the future developments of floating wind (The Carbon Trust, 2015). As floating wind develops, the design of anchors to severe long-term repeated cyclic environmental loads will be of preeminent concern, with very little work presently published in literature to assess their design and how it might affect the fatigue life of the mooring lines and floating structure. Some early work on axial pull-out capacity of piles was reported by Madabhushi and Haigh (1998). Current design guidelines mostly rely on knowledge-transfer from oil and gas floating platforms (e.g. ABS (2013)), and fixedbottom wind turbine foundations (e.g. DNV-GL-ST-0119 (2021), DNV-GL- ST-0126 (2018)).

This paper focusses on the design of anchor piles in sand for use with Tension Leg Platforms (TLPs, Figure 1(a)). TLPs are one of the promising floating offshore wind structure types, and comprise highly buoyant platforms which are tethered to the seabed by high tension vertical tendons attached to anchors. In sandy soils, anchor piles are a good anchor type to tether the TLP [START_REF] Abs | Offshore Anchor Data for Preliminary Design of Anchors of Floating Offshore Wind Turbines[END_REF]. External forces on the TLP such as the wind, waves and current create a purely tensile cyclic load on the anchor (Figure 1(b)). This cyclic load could cause excessive uplift displacement if not accounted for in design. This paper presents experimental work to further understand the behaviour of anchor piles in sand for TLPs. A range of one-way constant amplitude cyclic axial loads are applied to a model pile in sand at 1g, designed to represent a typical anchor pile for a TLP [START_REF] Abs | Offshore Anchor Data for Preliminary Design of Anchors of Floating Offshore Wind Turbines[END_REF]. The pile displacement is measured and the test results are used to (i) assess factor of safety methods for cyclic design, and (ii) compare with published stability diagrams for axially loaded piles [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]. The results are also used to provide the basis for a set of empirical laws which can be used to estimate (i) the number of cycles sustained by the pile before failure, and (ii) the change in the pile's ultimate holding capacity.

Traditional Anchor Design Methods

The design of anchor piles under axial tensile loads is commonly achieved using the same design practices as for (mono)piles, typically using the t-z curves method (DNV-GL, 2018; 2021). However, there is limited recommendation with regards to how the effects of cyclic loading should be accounted for, as this is not a critical loading condition for offshore wind monopiles.

The effect of cyclic loads can be accommodated for through the estimation of the ultimate holding capacity in the mooring line used for monotonic design, multiplied by factors of safety that are based on experience and conservative assumptions [START_REF] Puech | Advances in axial cyclic pile design: contribution of the SOLCYP project[END_REF]. This commonly accounts for all cyclic case scenarios, and aims at estimating which would be the worst through weighting via load factors. DNV-GL (2021) recommends estimating the design anchor resistance from a sum of the characteristic mean and dynamic tensions, multiplied by load factors in the range of 1.0 to 2.86 (see [108][109][110][111]. The design method for monotonic loading (traditionally the t-z curves method) is then used. The ABS design method for TLP anchor piles (ABS, 2013) is similar. In its method the ultimate holding capacity of the anchor pile, TULT, is determined by multiplying the maximum expected load on the pile for a given load case, TMAX, by the factor of safety, FOS, for that specific load case. TULT is then taken as the maximum of all the obtained values as shown in Equation 1. The factor of safety FOS is equal to 3 for normal loading and 2.25 for extreme loading. This definition can also be used to define the maximum tolerable cyclic load on an anchor pile, and will be used in this respect in the following

𝑇 𝑈𝐿𝑇 = max(All 𝑇 𝑀𝐴𝑋 × FOS) (1)

Cyclic Stability Diagrams

A better design tool for the cyclic axial loading of piles is an interaction diagram, also called a cyclic stability diagram. Cyclic stability diagrams have mainly been developed for pile design to axial cyclic loading, and recent contributions from the SOLCYP project (SOLCYP, 2012) have enabled the establishment of a framework for both sand and clay, for piles subjected to both tensile and compressive cyclic loads, based on both field and laboratory tests [START_REF] Puech | Advances in axial cyclic pile design: contribution of the SOLCYP project[END_REF]. These diagrams, of which the principles are summarized in Figure 2, synthesise the effect of the mean and cyclic loading amplitude TMEAN and TCYC (Figure 1(c)), on the number of cycles to a pile's failure, Nf. The failure criteria typically taken to define these zones are whichever occurs first of a pile head displacement, δ, exceeding 10% of the pile diameter, or a pile head displacement displaying a sudden rapid increase, indicating shaft failure [START_REF] Silva | Influence of cyclic axial loads on the behaviour of piles driven in sand[END_REF]. Cyclic load case scenarios are then identified to be in one of three zones:

• stable (i.e. "safe") zone: characterised by a slow increase of accumulated displacements that effectively stabilize after a certain number of cycles, typically Nf > 1000. • meta-stable zone: where a rapid increase in deflection and pile failure is observed for cycle number 100 < Nf < 1000. • unstable zone: typically characterised by rapid accumulation of displacement and abrupt reduction in ultimate holding capacity at low cycle number, i.e. Nf < 100.

The interaction diagram design tool can therefore be used to ensure that the amplitude of cyclic loading applied to a pile will only ever lead to safe stable behaviour [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].

Empirical Evolution laws

Jardine and Standing (2012) data also form the basis for the derivation of a simple empirical formula for predicting the reduction of a pile's shaft resistance, and therefore the reduction in its ultimate holding capacity, ΔTULT, with cycle number, N as shown in Equation 2 [START_REF] Andersen | Cyclic resistant geotechnical design and parameter selection for offshore engineering and other applications[END_REF].

∆𝑇 𝑈𝐿𝑇 𝑇 𝑈𝐿𝑇 = 𝐴 (𝐵 + 𝑇 𝐶𝑌𝐶 𝑇 𝑈𝐿𝑇 ) 𝑁 𝐶 (2)
A, B and C are constants equal to -0.126, -0.1 and 0.45 respectively, and are derived to fit the data from Jardine and Standing (2012).

Figure 2. Principles of cyclically loaded stability diagrams for axially loaded piles

EXPERIMENTAL METHOD

Testing equipment

The cyclic test rig used in this study was originally designed and developed by [START_REF] Rovere | Cyclic loading test machine for caisson suction foundations[END_REF] to apply cyclic axial loading on small-scale model suction piles in sand, and was then modified to investigate the lateral loading of piles in sand (Leblanc, Houlsby, & Byrne, 2010a;[START_REF] Leblanc | Response of stiff piles to random two-way lateral loading[END_REF][START_REF] Abadie | Cyclic Lateral Loading of Monopile Foundations in Cohesionless Soils[END_REF][START_REF] Abadie | Rigid pile response to cyclic lateral loading: laboratory tests[END_REF]. It was adapted here to perform long-term cyclic axial loading on a long slender pile, with the set-up shown in Figure 3.

One-way cyclic loading was applied through a motor driving a rotating mass, Mass 1, located at the end of a lever arm. Mass 2 is chosen to balance the weight of the supporting arm and motor, in order to apply a oneway sinusoidal tensile load on top of the pile via Cable 1. The motor frequency is 0.106 Hz, mimicking the frequency of wave loading. Two LVDTs located at the pile head enable to measure the pile deflection, with data acquired via the DASYLab software. A load cell located along Cable 1 enable to check the applied load onto the pile.

Sample Properties

The experimental tests were conducted in dry Hostun sand HN31 (Table 1) at 1g to mimic the drained conditions typically achieved for long-term wave-induced cyclic loading. In order to limit the effects of dilation at this very low confining stresses, a repeatable low relative density DR = 8% was achieved by pouring the sand manually from a very low drop height. The pile was "wished in place" by pouring the sand carefully around it in order to preserve the soil-shaft interface and suppress the effects of friction fatigue from installation. This also enabled more consistent and repeatable results in terms of measured ultimate holding capacity, TULT, in the sand.

Pile Geometry

The ABS design guidelines (ABS, 2013) recommend an anchor pile aspect ratio L/D = 50 in sand to tether TLP offshore wind turbines. At model-scale, the pile dimensions were limited by the size of the laboratory container (Figure 3), to a value of L = 950 mm and a pile diameter of D ≈ 19 mm in order to leave a reasonable clearance of 2.6 D between the pile and the bottom of the container.

The ABS also recommends a diameter over thickness ratio D/t = 40 for steel piles to ensure sufficient axial stiffness. However, achieving this ratio would have led to an unreasonably thin steel pipe, that are commercially unavailable (e.g. t ≈ 0.47 mm). Instead, an acrylic pipe with wall thickness t = 3.0 mm was chosen, and the dimensionless axial stiffness ratio, λ, was scaled adequately to match full-scale anchor piles [START_REF] Randolph | Analysis of deformation of[END_REF].

𝜆 = 4𝜋𝐸𝑡 𝐷𝐺 0 (3)
Where E is the Young's modulus and G0 the average initial shear modulus of the sand down the pile length.  is typically around 170 for a prototype anchor pile, designed following the ABS guidelines [START_REF] Jardine | Pile load testing performed for HSE cyclic loading study at Dunkirk, France[END_REF]. Using the framework from [START_REF] Hardin | Shear Modulus and Damping in Soils: Design Equations and Curves[END_REF] to assess a value of G0 = 13.1 MPa of the laboratory sample, an acrylic pipe of dimensions provided in Table 2 was selected, providing a value of  = 160.

Finally, the shaft-soil interaction obtained with this choice of pipe material was too smooth to mimic the tensile behaviour typically obtained at higher confining stresses. To improve coupling at the interface, the acrylic pipe was coated using P60 sandpaper (0.6 mm thick), increasing the pile outer diameter to 19.2 mm and leading to the final anchor pile dimensions listed in Table 2.

Test Programme

The test programme involved a series of monotonic pull-out tests, aimed at determining both the ultimate holding capacity TULT of the test pile in the sand, and the repeatability of the testing procedures (PO-1,2,3, Table 3). This was followed by a series of cyclic loading tests, for which the idealized input signal is provided in Figure 1(c) and Table 3.

The range of one-way cyclic load cases was chosen to investigate the effects of both the load amplitude (TCYC) and the load magnitude (TMAX), by varying the dimensionless loading ratios TCYC/TMAX and TULT/TMAX (which corresponds to the load factor of safety FOS of Equation 1). The two load amplitudes tested, correspond to a "normal" and "extreme" case [START_REF] Suzuki | Initial Design of Tension Leg Platform for Offshore Wind Farm[END_REF][START_REF] Abs | Floating Wind Turbines[END_REF][START_REF] Crozier | Design and Dynamic Modeling of the Support Structure for a 10 MW Offshore Wind Turbine[END_REF][START_REF] Matha | Model Development and Loads Analysis of an Offshore Wind Turbine on a Tension Leg Platform, with a Comparison to Other Floating Turbine Concepts[END_REF], and have amplitudes TCYC/TMAX of 0.2 and 0.4 respectively. Three factors of safety were tested: FOS = 2.6, 2.0 and 1.4. The two larger ratios are as close as experimentally possible to the values recommended in the ABS design method for extreme and normal loading (3.0 and 2.25 respectively), both expected to lead to a stable behaviour according to the ABS. The ratio of 1.4 was added to this study to ensure an unstable cyclic behaviour for later comparison with the work on stability diagrams by [START_REF] Tsuha | Behaviour of displacement piles in sand under cyclic axial loading[END_REF].

The stable cyclic tests were stopped after ~8000 cycles, which was enough cycles to ensure a stable behaviour [START_REF] Jardine | Field axial cyclic loading experiments on piles driven in sand[END_REF]. They were then followed by a monotonic pull-out test to estimate the degradation of the ultimate holding capacity caused by cyclic loading and friction-fatigue.

MONOTONIC RESPONSE

The results of the monotonic tests are shown in Figure 4. The differences observed between the tests evidence some experimental error caused by model preparation. However, the discrepancy is within the expected experimental error for this type of 1g test. The curves display a peak response, which naturally defines the ultimate holding capacity of the pile TULT = 125.2 ± 13.9 N. This is followed by a rapid softening of the pile response, caused by a loss of shaft resistance that induces a loss in tension in Cable 1 once the pile has reached capacity.

The API pile design method (API, 2000) was used to make predictions of the ultimate holding capacity of the test pile, considering two cases: (i) a smooth pile surface (TULT,API,S), with a soil-pile friction angle of δ = 15˚ and (ii) a more realistic prediction of the sand-coated pile used in this paper, considering a rough pile surface, (TULT,API,R), with δ = 22˚ [START_REF] Tomlinson | Foundation Design and Construction[END_REF]. This gives ultimate capacities of TULT,API,S = 80.3 N and TULT,API,R = 119.3 N (reported in Figure 4).

-1 Monotonic Pull-out - 1 - - - - - - PO-2 Monotonic Pull-out - 1 - - - - - - PO-3 Monotonic Pull-out - 1 - - - - - - CYC-E-1.4 0.

CYCLIC RESPONSE

Figure 5 shows the comparative tension-displacement curve response of an unstable, meta-stable and stable case. The number of cycles that can be sustained by the pile during cyclic loading can be defined as follows, depending on what is most critical for design (Figure 6, Table 3):

• Ni is the number of cycles before a change from stable to meta/un-stable behaviour, defined by the inflexion point, after which the second derivative of the δ-N curve becomes positive. • N0.1D is the number of cycles after which the pile displacement is greater than 0.1D, i. This definition enables comparison with data in the published domain, but offers a more conservative estimate than the definition adopted by [START_REF] Tsuha | Behaviour of displacement piles in sand under cyclic axial loading[END_REF]. These definitions are illustrated in Figure 6(a), together with the evolution of the pile head displacement with cycle number. In Figure 6(b) ∆δ is defined as the cyclic pile head displacement relative to the initial monotonic displacement. It is normalised by δs which is the pile head displacement resulting from the application of TMAX in a static load test (PO-Avg).

Factors of Safety

First, the results can be used to assess factors of safety methods for TLP pile anchors in sand. Table 3 provides an overview of the results obtained for the tests. The selected factors of safety chosen for extreme (CYC-E) and normal (CYC-N) load events must ensure a stable behaviour at all times. The results show that a factor of 2.6 for "Normal"i.e. long-term operationalloading is sufficient (see test CYC-N-2.6 in Table 3). However, a factor of safety of 2 for extreme load (CYC-E-2) is likely to be unconservative if a stable behaviour is targeted. In practice, it would be best to assess the number of cycles expected for each load type, and ensure that Nf is reasonably smaller than this critical number for this load case. This is what cyclic stability diagrams provide. The two sets of results show good agreement, and the interaction diagram correctly predicts the stable, metastable or unstable behaviour of all but one cyclic test, CYC-E-1.4, which is however aligned with another meta-stable test that failed around the same number of cycles in this zone. The exact stable, meta-stable and unstable zones and cycle numbers are likely to vary with soil conditions and pile parameters [START_REF] Tsuha | Behaviour of displacement piles in sand under cyclic axial loading[END_REF], and further work is needed to improve this data base for future design.

Cyclic Stability Diagrams

Prediction of number of cycles to failure

In addition to stability diagrams, predicting the number of cycles to failure can be aided by empirical equations. The results in Table 3 clearly show that an increase in the amplitude of cyclic loading TCYC/TMAX, or a decrease in the factor of safety TULT/TMAX, both have a detrimental effect on the value of Nf. [START_REF] Jardine | Field axial cyclic loading experiments on piles driven in sand[END_REF] demonstrated that the ratio TCYC/TULT is the most important load ratio driving the response of the pile (e.g. Equation 2). A power law was fitted to the experimental results for Nf = N0.1D as a function of TCYC/TULT, with the results shown in Figure 8:

𝑁 𝑓 = 0.06 ( 𝑇 𝐶𝑌𝐶 𝑇 𝑈𝐿𝑇 )

-5

(5)

The data from [START_REF] Jardine | Field axial cyclic loading experiments on piles driven in sand[END_REF] and [START_REF] Tsuha | Behaviour of displacement piles in sand under cyclic axial loading[END_REF] are also displayed in Figure 8 for comparison. The difference in the results can in part be explained by the more conservative approach adopted in these two studies than the definition chosen for Equation 4 in this paper. Equation 5 can be used to directly provide the threshold values for which TCYC/TULT enables stable (0.14) and meta-stable (0.23) behaviours. Safe stable behaviour therefore corresponds to a factor of safety of 1.24 for the normal load case (for which TCYC/TMAX = 0.2), and 2.48 for the extreme load case (for which TCYC/TMAX = 0.4).

Change in pull-out capacity

Figure 9 shows the results of the pull-out tests following the stable cyclic loading tests CYC-N-2.6 and CYC-N-2. In both tests TULT degraded from 125.2 to 99.3 N (TULT,DEG), a 21% reduction in strength (∆TULT = 25.9 N). This is typical of piles subjected to cyclic (wave) loading, where the shaft capacity typically reduces massively due to friction fatigue during cyclic loading [START_REF] Poulos | Pile behaviour-theory and application[END_REF][START_REF] Dejong | Interface Load Transfer Degradation During Cyclic Loading: A Microscale Investigation[END_REF].

For the unstable and meta-stable tests, the test pile experienced shaft failure during cycling when TULT degraded to such an extent that TULT = TMAX, and ΔTULT = TMAX -TULT. The results were compared with Equation 2, and the values of A, B and C optimised using linear regression (Figure 9, Equation 6).

∆𝑇 𝑈𝐿𝑇 𝑇 𝑈𝐿𝑇 = -0.26 (-0.08 + 𝑇 𝐶𝑌𝐶 𝑇 𝑈𝐿𝑇 ) 𝑁 0.43 (6) 6shows that for very long-term cyclic loads characterised by TCYC/TULT < 0.08, no cyclic degradation of the ultimate holding capacity is expected. This would correspond to typical operational conditions of the FOWT in quiet sea.

CONCLUSIONS

This paper presents the results of an experimental campaign aimed at investigating the suitability of existing design methods for anchor piles subjected to tensile cyclic loads. The results show that the use of large factors of safety, as recommended in current design guidelines might be sufficient for certain load case scenarios but neither provides an accurate design method, nor accounts for cycle number.

A more rigorous approach consists of using stability diagrams, from which empirical evolution laws can be derived for design. The framework introduced by Jardine and Standing (2012) and [START_REF] Tsuha | Behaviour of displacement piles in sand under cyclic axial loading[END_REF] can be directly applied for more accurate design and provides a reasonable assessment of (i) the number of cycles to failure, and (ii) the degradation of the ultimate holding capacity of the anchors. Further work using centrifuge modelling would enable the completion of these models at representative soil stress levels and pile dimensions.

ACKNOWLEDGEMENT

The authors are thankful for the support of the Schofield Centre in conducting this project, and the support provided while conducting the last tests at the start of the COVID-19 pandemic. The authors are also thankful for the fruitful discussions with Tobias Möller. 2012) and [START_REF] Tsuha | Behaviour of displacement piles in sand under cyclic axial loading[END_REF]. The trendline of Equation ( 5) is also plotted.

Figure 1 .

 1 Figure 1. (a) Schematic representation of a TLP-supported FOWT (b) Realistic tendon tension load, operating conditions (Crozier, 2011) (c) Idealised tensions applied during test programme; definitions of TMAX, TCYC and TMEAN shown on test CYC-E-1.4

Figure 3 .

 3 Figure 3. (a) Schematic of Test Rig (b) Test Rig and data acquisition computer (c) LVDT, load cell and pile set-up (b) (c)

  Figure 5. T-δ response of: (a) test CYC-E-1.4, unstable (b) test CYC-E-2, meta-stable (c) CYC-N-2.6, stable(stopped after 8556 cycles)

Figure 4 .

 4 Figure 4. T-δ response of the monotonic pull-out tests PO-1,2,3

Figure 7

 7 Figure 7 shows the experimental results from Jardine and Standing (2012) also reported by Tsuha et al. (2012) for one-way tensile cyclic loading tests. The large-scale piles were tested with the facilities of the GOPAL (Grouted Offshore Piles Alternating Loading) research project, on 7 open-ended driven piles in dense Dunkirk sand (DR ≈ 75%), of L = 19 m in length and D = 457 mm in diameter (L/D = 41.6), and plugged at ~60% of the embedded length. The results obtained in this paper have been added to the diagram for comparison. The numbers labelled on the figure correspond to the number of cycles at failure, Nf.

Figure 6 .

 6 Figure 6. Evolution of pile head displacement with cycle number (a) Test CYC-E-1.5, and definition of Ni, N0.1D, and Ns, (b) Compared accumulated pile displacement ∆δ of all 5 cyclic tests, with an example trendline plotted for test CYC-E-1.4 used to define Na

Figure 7 . 3 >

 73 Figure 7. Cyclic stability diagram with the number of cycles to failure Nf marked fromRichard and Standing (2012) and reported by[START_REF] Tsuha | Behaviour of displacement piles in sand under cyclic axial loading[END_REF] and superimposed with this test campaign's results.

Figure 8 .

 8 Figure 8. Evolution of cycle number as a function of TCYC/TULT for this campaign's test results and the one-way cyclicresults from[START_REF] Jardine | Field axial cyclic loading experiments on piles driven in sand[END_REF] and[START_REF] Tsuha | Behaviour of displacement piles in sand under cyclic axial loading[END_REF]. The trendline of Equation (5) is also plotted.

Figure 9 .Figure 10 .

 910 Figure 9. Pull-out tests after stable cyclic loading, with PO-Avg scaled to match the curves

Table 1 .

 1 Properties of Hostun Sand[START_REF] Mitrani | Liquefaction Remediation Techniques for Existing Buildings[END_REF][START_REF] Heron | The Dynamic Soil Structure Interaction of Shallow Foundations on Dry Sand Beds[END_REF]

	Property	Description	Value
	emin	Minimum void ratio	0.555
	emax	Maximum void ratio	1.01
	Gs	Specific gravity	2.65
	ϕcrit (degrees)	Critical angle of friction	33
	d50 (mm)	Mean particle size	0.424
	Cu	Uniformity coefficient	1.67

Table 2 .

 2 Anchor Pile Properties

	Property	Description	Acrylic pipe	Acrylic pipe + sand paper
	L (mm)	Length	950	950
	D (mm)	Total pile outer diameter	18	19.2
	t (mm)	Pile wall thickness	3.0	3.6
	L/D	Aspect ratio	52.8	49.5
	λ	Dimensionless axial stiffness	160

Table 3 .

 3 Test programme and results overview (see definition of load characteristics in Figure1(c))

	Test	𝐓 𝐌𝐀𝐗 𝐓 𝐔𝐋𝐓	𝐓 𝐂𝐘𝐂 𝐓 𝐌𝐀𝐗	𝐓 𝐂𝐘𝐂 𝐓 𝐔𝐋𝐓	𝐓 𝐌𝐄𝐀𝐍 𝐓 𝐔𝐋𝐓	FOS TULT/TMAX	Number of cycles	Ni	N0.1D	Na	Ns	Nf	Response
	PO


X Xu

C N Abadie

T Möller

G Della

T S Da

Silva Burke

On the use of high-resolution distributed fibre optic sensing for small-scale geotechnical experiments at 1g 1

Keywords: sinkhole, 1g experiments, fibre optic sensing

The use of distributed fibre optic sensing (DFOS) is becoming increasingly popular for strain measuring and monitoring. While the technology is efficient in the field, its use for strain measurement in geotechnical model-scale experiments is currently limited, mostly because of a lack of spatial resolution in the DFOS technologies. However, recent developments now enable high spatial resolution measurements, for example, with the use of Rayleigh Scattering technology for the fibre and the Luna ODiSI 6100 DFOS analyser. This technology is becoming increasingly popular for use in small-scale experiments, mainly for structural monitoring. For geotechnical applications, there are a few technological barriers that presently limit their use in the laboratory. However, there are great advantages in using this technology, mainly to measure strain deformation continuously along the fibre at the core of a soil sample. This paper explores the possibility of using high-resolution distributed fibre optic sensing for small-scale geotechnical experiments at 1g, using a trapdoor rig that mimics the formation of a sinkhole. The fibre optic is embedded in the soil above the trapdoor to measure subsidence, and different laying techniques are explored, aiming at enhancing the coupling between the fibre optic cable and the surrounding soil at low confining pressures. This work aims at widening the range of instrumentation available to measure strain in small-scale geotechnical experiments, offering a complementary technique to conventional instrumentations.

INTRODUCTION

Small-scale physical modelling at 1g is commonly used in soil mechanics to investigate soil behaviour and geotechnical failure mechanisms (Muir Wood, 2006). The measurement of ground displacements is central to most experiments and is also used to further validate and refine analytical and numerical models. Conventional instrumentation, such as linear variable displacement transducers (LVDTs), only capture the displacement at limited discrete locations and directions, while more recent techniques, such as Particle Image Velocimetry (PIV), can only capture strain profiles at a soil sample boundary (ground surface, or transparent boundary).

Distributed fibre optic sensing (DFOS) has emerged as a powerful tool for continuous, high temporal and spatial resolution mapping of subsurface ground movement, and enable measurement of temperature, strain, and acoustic energy distributions along the entire length of a fibre optic sensing cable [START_REF] Kechavarzi | Distributed fibre optic strain sensing for monitoring civil infrastructure: a practical guide[END_REF][START_REF] Xu | Monitoring of tunneling intercepted end-bearing piles using distributed fibre optic sensing[END_REF]. To date, this technology has mostly been used and deployed in the field, with DFOS cables embedded in trenches on the ground surface and back-filled by in-situ soil to monitor ground cracks, horizontal displacements and ground settlements [START_REF] Klar | Monitoring tunneling induced ground displacements using distributed fiber-optic sensing[END_REF][START_REF] Zhang | Role of the interface between distributed fibre optic strain sensor and soil in ground deformation measurement[END_REF]. This is because the incorporation of DFOS cables into the ground could provide significantly improved information on the location and magnitude of subsurface ground movement and subsidence.

However, for small-scale geotechnical experiments, conventional DFOS offers limited advantages, mostly because of the restrictions on spatial resolution (typically 1 m for Brillouin optical time-domain reflectometry (BOTDR)) and also the sampling frequency (acquisition time of several minutes per measurement). [START_REF] Beemer | Investigation of an OFDR fibre Bragg system for use in geotechnical scale modelling[END_REF] The recent developments of the OFDR Luna ODiSI 6100 DFOS analyser enable better use of DFOS in smallscale experiments, using cost-effective cables, a spatial resolution of 0.65 mm to 2.6 mm and an acquisition rate of 25 Hz to 250 Hz.

Nevertheless, for strain measurement directly within a soil sample, the accuracy from DFOS relies on sufficient soil-cable coupling, especially for 1g tests, which typically have very low overburden pressure [START_REF] Zhang | Role of the interface between distributed fibre optic strain sensor and soil in ground deformation measurement[END_REF].

This paper explores the impact of different cable installation techniques in improving the data quality of measured ground movements induced by underground subsidence at 1g. Both the soil-cable interface properties and cable fixities are investigated and recommendations on the best laying techniques are provided through comparison with PIV data.

SINKHOLE SMALL-SCALE EXPERIMENTS

The experiments replicated the formation of a sinkhole using a 2D plane-strain trapdoor rig, actuated with a hydraulic piston and equipped with an acrylic window (Fig. 1). The box has internal dimensions of 790 mm × 200 mm × 560 mm, with a trapdoor width of 100 mm. Detail on the experimental setup is provided by [START_REF] Möller | Distributed fibre optic sensing for sinkhole early warning: experimental study[END_REF].

A 200 mm high soil sample was carefully prepared using Hostun HN31 sand at selected relative densities using a sand pourer [START_REF] Madabhushi | A new automatic sand pourer for model preparation at University of Cambridge[END_REF]. Scaling of soil sample properties at 1g meant that a relative density of ~50% corresponds to a relative density of ~80% in the field [START_REF] Möller | Distributed fibre optic sensing for sinkhole early warning: experimental study[END_REF]. The soil strain field was assessed using PIV [START_REF] Stanier | Improved image-based deformation measurement for geotechnical applications[END_REF].

Linear variable differential transformers (LVDTs)

were employed to verify the trapdoor displacement , and experiments were terminated at 𝛿 = 20 𝑚𝑚 . However, only the first 3.5 mm are of interest in this paper, with a focus on 𝛿 = 2 𝑚𝑚, which corresponds to the early stages of the sinkhole formation [START_REF] Möller | Distributed fibre optic sensing for sinkhole early warning: experimental study[END_REF] when it is the most essential to detect subsidence-induced strain in the soil.

The high-resolution Rayleigh-based distributed fibre optic sensing system Luna ODiSI 6100 was used to log DFOS cable strain. This analyzer is based on the optical frequency domain reflectometry (OFDR) technique, and a spatial resolution of a 2.6-mm was adopted for the experiments, with a frequency of 25 Hz. A 2-mm diameter tight-buffed polyurethane-coated DFOS cable (C07, Nanzee Sensing, Suzhou, China) was used. [START_REF] Zhang | Role of the interface between distributed fibre optic strain sensor and soil in ground deformation measurement[END_REF] showed that it is suitable for monitoring soil deformation, thanks to its excellent strain transfer capability and low Young's modulus (200 MPa). The DFOS cable is capable of withstanding moderate impacts during installation, and can easily be pre-strained and directly integrated into loose granular soils. DFOS cables were embedded at 50 mm intervals throughout the entire height of the soil sample to capture and compare the strain profiles with that from the PIV (Fig. 1(a)). At each layer, two separate DFOS cables, rear and front cables were installed independently to enable direct comparison (Fig. 1(b)).

CABLE INSTALLATION TECHNIQUES

Soil-cable interface

To enhance the soil-cable coupling, one DFOS cable was uniformly coated with a layer of sand (Fig. 2). This was achieved by applying a very thin layer of glue on the cable and rolling it in the sand. This increases the soilcable friction angle, with negligible impact on other cable properties (e.g. Young's modulus).

Cable fixities at each layer end

Each cable layer was typically pinned at both edges of the box to replicate the effect of overburden pressure in an infinitely long cable; excess slack between the two ends was removed before the cable was fixed in position. Three other cable fixing methods were also explored to investigate the effect of releasing the pre-tension in the cable on the measurement: (1) leaving the cable in a loose state; (2) guiding the cable through a tube (Fig. 3(a)); and (3) introducing a slack loop into the DFOS cable in the vicinity of the trapdoor (Fig. 3(b)). Table 1 summarizes the test programme reported in this paper.

Effect of soil-cable interface

Fig. 4 shows typical strain profiles obtained with the C07 cable for targeted densities of DR=50% and DR=95% and compared with PIV data for DR=50%. All profiles display a double-peak with a central dip, which corresponds to the location of the sinkhole. A very similar signature strain profile can be obtained with the sand-coated cable, yet with more pronounced peaks and dips, as well as greater inclination, providing more acute data for post-processing. In addition, sand-coating enables to restore a near-zero strain at the edge of the sample for DR=50%, which was targeted to mimic an infinitely long cable. Nevertheless, an order of magnitude difference is observed with the PIV data, which is in line with the observations from [START_REF] Zhang | Role of the interface between distributed fibre optic strain sensor and soil in ground deformation measurement[END_REF].

The soil-cable friction was derived from the strain gradient along the DFOS cable:

𝜏 = - 𝐸𝐷 4 𝑑𝜀 𝑑𝑥 (1)
where D is cable diameter and E is Young's modulus. Fig. 5 shows that the sand-coated cable offers much higher friction (max 1.56 kPa) compared to that of the standard cable (max 0.82 kPa).

The distributed strain profiles could also be integrated along the DFOS cable to obtain the cable axial deformation. Thus, the friction-displacement curves for both standard and sand-coated cable at every 2.6 mm ICPMG 2022

10th International Conference on Physical Modelling in Geotechnics 19(Mon) -23(Fri) September 2022 / KAIST, Daejeon, Korea could be derived. Fig. 6 shows that the standard C07 cable exhibits softening behaviour at larger trapdoor displacements than the sand-coated cable, providing insight into the results of Fig. 4 and Fig. 5.

Effects of cable fixities

Fig. 7 compares the strain signature profiles for the four different fixities. First, in the case of the standard C07 cables, the loose cable picks up boundary effects, with non-zero strain experienced at x/B = -4. The tubeguided cable similarly picks up strain at the boundaries, but engages more strain around the trapdoor zone, thanks to its freedom at the end. However, none produce a very satisfactory signal to locate the peaks, which the loose sand-coated C07 cable displays best. Fig. 7 also shows that fixities have a lesser impact on the strain profiles of the sand-coated cables. Finally, Fig. 8 shows that all four cables experienced similar soil-cable interface friction, with limited influence of fixities.

CONCLUSIONS

Small-scale sinkhole tests in granular soils were performed with a 2D plane-strain trapdoor rig to explore the application of high-resolution distributed fibre optic strain sensing for sinkhole early warning detection, by examining different cable laying techniques. The results show that a continuous loose sand-coated cable, pinned at the end of each soil layer provides a good quality measurement of soil strain profile and enabled the most accurate location of the sinkhole. The only (and main) difference compared with PIV data is the order of magnitude of the measured strains, which will be further explored through numerical modelling by the authors. Nevertheless, this paper demonstrates the value of using DFOS technology for subsurface strain profile measurement in small scale experiments at 1g.

Fig. 1

 1 Fig.1 Layout of FO strain sensing cables in plane-strain trapdoor test: (a) Elevation view; (b) Plan view.

Fig. 2

 2 Fig.2 DFOS cables in trapdoor experiments: (a) Sand-coated cable; (b) Standard DFOS cable.

Fig. 3

 3 Fig.3 Fixing conditions of DFOS cables in the trapdoor test: (a) Cable guided through a tube; (b) Loop introduced to provide cable slack.

Fig. 4

 4 Fig.4 Comparison of strain signature profiles (δ = 2 mm).

Fig. 5

 5 Fig.5 Comparison of friction profiles (δ = 2 mm).

Fig. 6

 6 Fig.6 Comparison of friction-displacement relationships between C07 (blue) and sand-coated C07 cables (red) (δ = 2 mm; z = 50 mm, DR=50%).

Fig. 7

 7 Fig.7 Effects of cable fixities on strain signature profiles (z = 50 mm, DR-48 & DR-52).

Fig. 8

 8 Fig.8 Effects of cable fixities on friction profiles (z = 50 mm, DR-48 & DR-52).

Table 1 .

 1 Cable installation techniques attempted

	Test ID	Dr	Soil-cable interface Fixing
		(%)		condition
	DR-96	96	Polyurethane &	Tape-fixing
			Sand-coated
	DR-48	48	Polyurethane (×2)	Loose & Tubed
	DR-52	52	Sand-coated (×2)	Loose & Slack

ACKNOWLEDGEMENTS

The authors are grateful to CSIC (EPSRC (EP/N021614/1) and Innovate UK (920035)) for funding and supporting this work. They are also thankful to the Schofield Centre and Professor Gopal Madabhushi, for their support with laboratory experiments and fruitful discussion with Professor Emilio Bilotta, Dr Geoff Eichhorn and Dr Cedric Kechavarzi.


Alex Coiret

Pierre-Olivier Vandanjon

Romain Bosquet

Tristan Soubrié

Guillaume Baty

Experimental assessment of wind influence on high-speed train energy consumptions

Keywords: Railways, energy consumptions, energy model, wind, aerodynamics, high-speed train

Ifsttar and RFF have developed an energy model of high-speed trains in order to determine the influence of infrastructure geometry and environment on train power consumptions. Validation of this model is based on full scale tests performed for the Rhine-Rhone high-speed line acceptance of work (in 2011). This paper aims to evaluate if wind influence is a relevant parameter for the model. This involves numerical determination of aerodynamic coefficients for various wind and ground configurations and their use for the calculation of the aerodynamic efforts. Atmospheric characteristics are extrapolated from meteorological measurements thanks to the AROME numerical model, over the whole Rhine-Rhone line. Most remarkable results show for a moderate train speed (about 47 m/s), a rearward oriented wind of only 5,5 m/s lowers by 30% the power due to aerodynamic forces applied on the train, or raises it similarly if it is forwardly oriented. In conclusion, this work points out that wind influence is of first importance for computing energy consumption.

Résumé

L'Ifsttar et RFF ont développé un modèle énergétique des trains à grande vitesse dans le but de déterminer l'influence de la géométrie et de l'environnement des infrastructures sur les consommations énergétique des trains. La validation de ce modèle est basée sur des essais grandeur nature réalisés lors de la réception de la ligne à grande vitesse Rhin-Rhône (en 2011). Cet article vise à évaluer si l'influence du vent doit être prise en compte dans ce modèle. Cela implique la détermination numérique de coefficient aérodynamiques pour plusieurs configurations de vent et de terrain et leur utilisation pour le calcul des efforts aérodynamiques. Les caractéristiques atmosphériques sont extrapolées de mesures météorologiques à l'aide du modèle numérique AROME, sur l'ensemble de la ligne Rhin-Rhône. Les résultats les plus remarquables montrent que pour une vitesse modérée de train, d'environ 47 m/s, un vent arrière de seulement 5,5 m/s diminue de 30 % l'énergie due aux efforts aérodynamiques appliqués sur le train, ou l'augmente similairement s'il est orienté frontalement. En conclusion, ce travail montre que l'influence du vent est de première importance. Mots-clé: Voies ferrées, consommations d'energie, modèle énergétique, vent, aérodynamique, train à grande vitesse.

Introduction

Railways, thanks to their low rolling resistance, overtake road and air in energy-efficiency for short and medium travel. Nevertheless, rail transportation is not always competitive in terms of travel times, compared to air transport for long travels or door to door road transport for short distances. Higher speeds are then required for maintaining railways competitiveness, but this trend paradoxically lowers its initial energy efficiency advantages [START_REF] Martin | Train performance and simulation[END_REF], especially for short inter-stop distances [START_REF] Feng | Optimization of target speeds of high-speed railways trains for traction energy saving and transport efficiency improvement[END_REF]. Then, the optimization of rail transportation should involve energy and mobility criteria (Coiret, 2012 ;[START_REF] Smith | Energy and environmental aspects of high-speed rail, 2nd International Conference on Road and Rail Infrastructure[END_REF], Vandanjon, 2012). In this context, Ifsttar and RFF have developed an energy model of high-speed trains, validated with full scale tests at the occasion of the acceptance of work of the Rhine-Rhone line (in 2011). Infrastructure geometry, train dynamics and electric consumption have been used to build an energy model but wind influence was not integrated in first attempt since local weather conditions was not continuously accessible during the tests. This last point remained to be assessed. In this context, this work, handled by Andheo and Ifsttar, aims to determine the level of wind induced aerodynamical forces, compared to other forces including aerodynamic forces due to the train speed. Various wind conditions, train speed and topological situations are considered to assess the wind influence.

Aerodynamic model

Field determination of atmospheric characteristics

The wind influence was chosen to be studied on several trains running on the Rhine-Rhone high-speed line. Indeed, electrical power consumptions and infrastructure characteristics are known for these runs. An energy model has been developed and validated with these data. Wind influence could be integrated in this model. Atmospheric characteristics (wind speed and direction, pressure and temperature) were determined over the whole Rhine-Rhone line (about 140 km) for the 25 days of tests conducted in 2011 for its acceptance of work. The numerical model AROME [START_REF] Seity | The AROME-France convective scale operational model[END_REF] was used to compute these wind fields from measurements at several surrounding weather stations (figure 1 : example of computed wind field).

The wind defined at a height of 10 meters is converted to a local wind along the train line, by applying atmospheric boundary conditions and specific environmental masks to take into account cities or forest. The equation (1) gives the wind intensity for a z height, relatively to the z0 rugosity height (here 0.05m, considering mostly countryside), d a moving length (here equal to 0.7×h), and k the Von Karman constant (0.4). Hypothesis leads to a value of u(3m) equal to 0.75×u (10m). Land influence is later taken into account thanks to a shading criterium of less than 100 m forests or urban areas.

u ( z )= u * k ln ( z-d z 0 ) (1)

High-speed train aerodynamics modeling

In parallel, aerodynamic coefficients of the experimental high-speed train (ALSTOM TGV Duplex) were computed. Navier-Stockes equations have been resolved on a simplified geometrical model by using auto-adaptive Cartesian meshes (figure 3, table 1). The longitudinal coefficient Cx fits with the value retained by the concerned norm and other data [START_REF] Raghunathan | Aerodynamics of high-speed railways train[END_REF]. It is of great importance since this coefficient is used for computing aerodynamic forces. Other coefficients match less the norm, for example, Cz is 56% lower than the normative value. This is due to issues of modeling the underside of the train, but it virtually does not affect the needed tractive forces, since its influence is negligible facing the Cx coefficient. Eventually, the considered Cx coefficient is a combination of data issued from literature on the detailed geometrical model and influence due to side wind as numerically computed on the simplified one.

Results

Computed coefficients are integrated in numerical simulations for the 15 selected train runs , on a full train, for various wind angle direction and relative elevations to the natural ground. At last, power is computed all along the itineraries, while considering situations with or without wind. The computation of the power is based on the equations (2). These equations give the aerodynamic F force and M momentum from the C and Cm force and moment coefficients, and from the air density (ρ), the S and L reference surface and length (S=10 m 2 ; L = 3 m), and from the speed of the air flow velocity (V).

F= 1 2 ρ S V 2 C M = 1 2 ρS L V 2 Cm (2)
The power induced by aerodynamic forces is computed as the product of the axial force Fx and the relative wind speed. The power that would have been consumed without wind is also calculated to estimate the wind effect on energy consumption. It is simply the product of the axial force without wind and the train speed. The wind effect is then the gap between the two power levels, as used on Figure 6 in ordinate.

Here, three particular runs are considered (figure 6). The green curve labelled 29034 corresponds to a train traveling at high speed in a weak mean wind. The blue and red curves, labelled respectively 29001 and 30002, correspond to a train traveling at a moderate speed for two quite different wind mean speeds (the wind and train speeds are given in figures 4 and 5 for theses two test runs).

One worthwhile result is that for a weak wind (2 m/s) and a train traveling at high speed (95 m/s), wind influence is of +5% and -5% on power due to aerodynamic forces on the train, respectively on front and rear wind sections of the itinerary (test run labelled 29034 on figure 6). This result is deduced from the analysis of the 29034 test run between the 70 and 120 km abscissae (section for which the mean speed is of 95 m/s).

Another result is that for a moderate train speed (about 47 m/s), a stronger rear wind (5.5 m/s) lowers the needed power by 30% compared to the case without wind, and a front wind of 3 m/s raises it by 20% (respectively test runs labelled 29001 and 30002 ; see figures 4, 5 and 6 at the pk distance of 70 km).

Conclusions

In conclusion, this work based on a large set of full-scale experimental data, on the reconstitution of the wind field and the numerical simulation of the aerodynamic forces, points out that wind influence on total aerodynamic power consumption is of first importance. Indeed, for the less sensible case, with a weak wind and a high train speed, wind influence has been found to be netherless noticeable, of the order of 5% of power due to aerodynamic forces on the train. For a more sensible case, with a wind speed about 5,5 m/s and a moderate train speed of 47 m/s, the wind field is accountable of variations on this power as high as 30%.

In perspective, the work will contribute to the developpement of a complete wind model as a component of the Ifsttar and RFF energy model.

Fig. 1 .

 1 Fig. 1. Wind field plotted from AROME data, around the 140km high-speed line (at 13h, the 29/08/2011).

Fig. 2 .

 2 Fig. 2. Classification of the runs on the train speed, and relative wind speed (each colored spot represent a test run).

Fig. 3 .

 3 Fig. 3. Transverse and frontal views of the numerical discretization of the train.

Fig. 4 .

 4 Fig. 4. Train speed (left) and computed wind speed (right) for the 29001 test run along the curvilinear distance pk (km)

Table 1 .

 1 Aerodynamic coefficients for the trailer, with a 5 degrees wind incidence angle.

		C x	C y	C z	Cm x	Cm y	Cm z
	Norm	0.157	0.484	-0.294	-0.317	-0.119	-1.013
	Simulation	0.148	0.555	0.128	-0.334	-0.235	-1.036
	Variation to the norm (%)	-6	15	-56	5	97	2

Corresponding author: alex.coiret@ifsttar.fr

Acknowledgements

The authors thank Meteo-France for their delivery of wind field calculations and Inexia for the train measurements.


Diarmid M Xu

N Abadie

Gopal Madabhushi

John M Harris

Richard J S Whitehouse

C N Abadie

S P G Madabhushi

Response of armour rock-scour protection to earthquake-induced liquefaction for offshore wind applications

Keywords: offshore renewable, centrifuge testing, scour protection, seismic loading, particle image velocimetry

des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

INTRODUCTION

Offshore wind is an established but expanding industry that is key to the global energy generation of the future. Worldwide many countries are looking to accelerate significantly their production of offshore wind power, with new developments in seismically active regions such as North America and South Asia. For example, Taiwan is aiming to install 1.5 GW per year, targeting 15 GW by 2035 (Bureau of Energy, Ministry of Economic Affairs, 2021). However, there is very little understanding and experimental data currently available to evidence the behaviour of large-diameter monopile foundations under seismic loads, in particular when installed in liquefiable soils [START_REF] Seong | Seismic response of offshore wind monopiles in cohesionless soils[END_REF].

As part of the foundation system, rock scour protection is commonly used to mitigate or remediate scour around the foundation, caused by the erosion of the soil due to the action of waves and currents [START_REF] Harris | Foundation Scour as a Geohazard[END_REF]. The formation of a scour hole around a monopile foundation will both reduce its capacity and stiffness as the embedded depth is reduced, thus altering the structure's natural frequency. When large scour holes are expected, and mitigation is required, an 8 m diameter pile will have a 30 m diameter × 1.5 m high layer of graded rocks deposited around the monopile to protect against scour. The bottom filter layer typically consists of 0.1 to 0.2 m diameter rocks, poured to a height of approximately 0.5 to 1 m. This is then covered by an armour layer, for example made of 0.5 m rocks, over 1 m in height. Alternatively, a layer of widely graded rocks of ~ 1.5 m thickness can provide both functions.

This method currently remains the most costeffective choice to remediate scour in offshore wind. Recent developments on scour protection for offshore wind turbines have provided better understanding of the effectiveness of different types of protection and their effect on restoring structural stiffness [START_REF] Mayall | Flume tank testing of offshore wind turbine dynamics with foundation scour and scour protection[END_REF]. However, the seismic behaviour of rock scour protection, specifically settlement induced by liquefaction, is not well understood, with limited data currently available in published literature [START_REF] Escribano | Stability of scour protection due to earthquake-induced liquefaction: Centrifuge modelling[END_REF]. As a result, current design guidelines offer limited or conservative procedures to protect against scour with seismic action (DNV GL, 2016, DNV 2021). Notably, the centrifuge tests performed by [START_REF] Escribano | Stability of scour protection due to earthquake-induced liquefaction: Centrifuge modelling[END_REF] show settlements in the region of 0.05 m (Test S02) and a delay to the onset of liquefaction due to the increase in overburden pressure from the presence of the rock berm. This test was performed with 0.5 m diameter armour rocks located on liquefiable loose sand (Table 1).

In this paper, the results of a dynamic centrifuge test are presented, with the aim of comparing to the findings of [START_REF] Escribano | Stability of scour protection due to earthquake-induced liquefaction: Centrifuge modelling[END_REF], and extending the research to incorporate soil displacements below the berm. The centrifuge test, DMX01, contains two models, one with rock, one without. As the sand was poured to fill the entire model box, the only difference between the two sides is the presence of rock, allowing direct comparison. In addition, Particle Image Velocity (PIV) was deployed to capture soil displacements.

EXPERIMENTAL METHODOLOGY

Models design

This paper examines the results of a dynamic test, performed in the 10 m-diameter Turner beam centrifuge at the Schofield Centre [START_REF] Madabhushi | Centrifuge Modelling for Civil Engineers[END_REF] at an enhanced gravity of 50 g. Centrifuge modelling enables reduced scale model tests to be performed while preserving stress-strain behaviour of the soil by scaling up the gravity by a factor of N, with N = 50 in this paper. A set of scaling factors relate the model to the prototype response, following [START_REF] Schofield | Cambridge Geotechnical Centrifuge Operations[END_REF].

The model was prepared in a 730 mm × 250 mm × 400 mm container, with a front acrylic window to enable PIV. A servo hydraulic shaker was used to simulate a series of earthquakes [START_REF] Madabhushi | Development of a servo-hydraulic earthquake actuator for the Cambridge Turner beam centrifuge[END_REF].

Figure 1 shows model DMX01, with dimensions at prototype scale. The two partitions of the sample were separated by a thin, flexible plastic divider, capable of deforming without adding any additional stiffness to the soil. The divider allowed lateral shaking but was impermeable to the methylcellulose used for saturation of the sample and stopped pore pressure transmission between the two partitions. Figure 2 presents the berm geometry where D50 is the rock diameter.

Rock berm design and model soil

The model rock berm was chosen to represent two layers of poorly graded large 1 m armour rocks with no filter layer in order to test the worst case senario. A midrange specific gravity for the rock Gs=2.62 was chosen representing standard rather than high density rocks with Gs~3 at this stage.

The sand model was poured in a loose state (relative density = 47 %) with Hostun HN31 sand, d50 = 0.44 mm, using an automatic sand pourer [START_REF] Madabhushi | A new automatic sand pourer for model preparation at University of Cambridge[END_REF]. It was then saturated using methylcellulose, with control over the flowrate during saturation using the "Cam Sat" system [START_REF] Stringer | Novel Computer-Controlled Saturation of Dynamic Centrifuge Models Using High Viscosity Fluids[END_REF]. Table 1 summarises the model properties.

One of the difficulties in scaling the geometry of rock armour for centrifuge modelling is that respecting the ratio between D50/d50 would lead to too fine sand particles, which are no longer cohesionless. However, reasonable scaling of the rock and sand particles is ensured if D50/d50 is greater than 15 [START_REF] Madabhushi | Centrifuge Modelling for Civil Engineers[END_REF], which was enforced here at 2273 (Table 1).

The berm geometry was designed with sufficient free sand on either side to allow the sand to flow and heave, thus not obstructing rock settlements. The size of the berm was limited by the size of the model box but was sufficiently large to represent berms in the field.

Load Sequence

Table 2 presents the earthquake sequences of the test. The voltage input (V) is a measure of the displacement amplitude and hence earthquake strength, with prototype peak bedrock accelerations (i.e. input motion) recorded for plotting. In DMX01, earthquakes of increasing strength were applied with EQ6 lasting for about 10 seconds at field scale.

Instrumentation

As layers of sand are poured, sensors are placed at selected depths. Pore water pressure transducers (PPT's) and piezoelectric accelerometers are buried in the sand to record pore pressures and accelerations in the sediment at specific locations.

DASYLab v13.0 was used to log data into text files for later processing. A logging rate of 6000 Hz was used for dynamic events, and a rate of 100 Hz was used for swing up, to record pore pressures and settlements as the g level increases from one to fifty.

The PIV camera used was the MotionBLITZ EoSens mini 2, model MC 3071. Images were captured at 1696×942 at 900 frames/sec, with a capture time of 1.5 seconds. These images were processed using geoPIV_RG [START_REF] Stanier | Improved image-based deformation measurement for geotechnical applications[END_REF].

TEST RESULTS

All sensor voltages were filtered, calibrated and zeroed in MATLAB using a bespoke script. An eighth order Butterworth filter was used to reduce phase shift. An approximate initial effective vertical stress has been calculated to identify the limit of liquefaction. For the EQ6 results presented, the selected input motion was a sine wave with an input of 2.5 V, this produced a peak ground acceleration of 0.17g (Figure 3).

DMX01 test data contrasts a key finding of [START_REF] Escribano | Stability of scour protection due to earthquake-induced liquefaction: Centrifuge modelling[END_REF] comparing the settlements of rock and of free field sand (Figure 3), but confirms that the increase of overburden pressure caused by the presence of the rock berm ensured that the excess pore pressure never exceeded the initial effective vertical stress (i.e. the red dashed line in Figure 4a).

It can be seen that the earthquake produced settlements in the region of 300 mm with a characteristic stop start motion instead of a smooth curve, where the soil stiffens and softens in alternate half cycles to allow the rocks to sink gradually. Comparing the input motion and LVDT recorded vertical displacements, the results exhibit a delay from the first cycle to the start of settlements. This is because a few earthquake cycles are required to build up excess pore pressure to partially liquefy the soil.

Figure 4 shows the excess pore pressures for the largest earthquake applied, the red dashed line shows the liquefaction limit. Although excess pore pressures are higher on the rock side, the increase in overburden pressure is far greater. In addition, the data shows that the build-up of excess pore pressure is slower on the rock side, this is because the sinking of rocks causes additional shearing and soil dilation, thus retarding the generation of excess pore pressures. Despite not reaching full liquefaction, these excess pore pressures still caused significant rock settlements. The results from the PIV displayed in Figure 5 demonstrate that the shallower sediments settle further compared to the deeper sediments under the rock berm. In this figure, a column of data points, 0.5 m to 3.0 m below the mudline is presented for clarity.

CONCLUSIONS

The data from the centrifuge test has shown that: 1. Rock berm settlements in the region of 300 mm are observed post seismic liquefaction (Figure 3), which is in contrast to the findings of [START_REF] Escribano | Stability of scour protection due to earthquake-induced liquefaction: Centrifuge modelling[END_REF]. 2. The presence of rock delays the onset of full liquefaction compared to the free-field sand (Figure 4). 3. Despite not reaching full liquefaction, large settlements still occurred. 4. The PIV technology deployed captures the sand failure mechanism during a dynamic centrifuge test. These results show that after a significant seismic event, there is indeed the need to inspect rock berms at offshore wind foundations and carry out remediation work as required. Future centrifuge tests are planned to investigate the effect on settlements of the rock size, type, mixed grading and berm geometry.

  on Physical Modelling in Geotechnics 19(Mon) -23(Fri) September 2022 / KAIST, Daejeon, Korea

  (a) Schematic and (b) Photo of test DMX01

Fig. 3 .

 3 Fig. 3. Settlement of the rock berm in EQ6.

Fig. 5 .

 5 Fig. 5. Comparison of sand settlement below the rock berm.

Table 1 .

 1 Armour rock data comparison. (D50 is used for scour rock grading, and d50 used for sediment grading. ts is the berm thickness/height.)

	Parameter	DMX01	(Escribano and	Field data
		(prototype)	Brennan, 2017)
	d50 (mm)	0.44	0.14	0.15
	D50 (mm)	1000	500	500-1000
	ts (mm)	2000	1500	1500
	ts/D50	2	3	3-1.5
	D50/d50	2273	3571	3333-6667
	Gs	2.62	-	2.5-3.0
	Fig. 2. Berm geometry for DMX01

10th International Conference on Physical Modelling in Geotechnics 19(Mon) -23(Fri) September 2022 / KAIST, Daejeon, Korea

Table 2 .

 2 Earthquake Sequence.

	Earthquake	DMX01
	EQ1	Sine sweep, 0.7V
	EQ2	Kobe, 0.2V
	EQ3	Sine wave, 50Hz, 10 cycles, 1.0V
	EQ4	Sine wave, 50Hz, 10 cycles, 1.5V
	EQ5	Sine wave, 50Hz, 10 cycles, 2.0V
	EQ6	Sine wave, 50Hz, 10 cycles, 2.5V


G Della Ragione
email: gianluigi.dellaragione@unina.it

T Möller

C N Abadie

X Xu

T S Da Silva Burke

E Bilotta

Fiber Optic Sensing for Sinkhole Detection in Cohesionless Soil

Keywords: Sinkhole, Trapdoor Test, Fiber Optic Sensing

Sinkholes are geo-hazards which can form suddenly without humanly visible pre-indication from soil surface settlement. An early warning system located below ground would enable to detect sinkhole-induced settlement before it reaches the surface, preventing possible damage to infrastructure and protecting lives. This paper focuses on the use of Distributed Fiber Optic Sensing (DFOS) as a solution for early detection of sinkhole formation. A series of small-scale experiments in controlled conditions are used to simulate the formation of a sinkhole. Fiber optics cables are laid in the soil specimen, and strains are collected using the LUNA ODiSi 6100 analyzer. The soil movements are observed through a Perspex window, collected with a camera and analyzed using Particle Image Velocimetry (PIV). Results indicate the ability of DFOS in detecting soil movements and underline the typical signature strain profile expected during sinkhole formation, indicating that at an early stage in the sinkhole formation, horizontal movements govern the strain profile within the cable. In conclusion, our study suggested that the DFOS technology can be used to detect, locate and estimate the size of a sinkhole, even though it has not possible to monitor the real strain level in the soil, due to a lack of shear transfer at the interface between the soil and the cable.

Introduction

A sinkhole is created by subsidence of a depression or hole in the ground, eventually creating catastrophic failure at the soil surface. This can be the result of (i) progressive sagging of the overlying deposit above the void, (ii) sudden collapse of brittle formations along failure planes [START_REF] Jennings | Sinkholes and Subsidence in the Transvaal Dolomite of South Africa[END_REF]. The genesis of a sinkhole depends on the complex geological structure and the hydrogeological setting of the soil. Nevertheless, the formation of a sinkhole implies that a void must develop at a certain depth and that a disturbing agent must arise to cause the soil to collapse within the void. The areas primarily exposed to these phenomena are karst terrains, which comprises limestone, dolomite, evaporites and gypsum. These are prone to being dissolved with underground water flow, due to their chemical composition, thus allowing the formation of a cavity which may collapse and cause a sinkhole.

Sinkholes can cause severe damage to the existing infrastructures and buildings [START_REF] Gutiérrez | Sinkhole hazards[END_REF][START_REF] Johnson | Salt dissolution and subsidence or collapse caused by human activities[END_REF][START_REF] Buchignani | Evaportie karst and sinkholes: a synthesis on the case of Camaiore (Italy)[END_REF], and in rare occasions can lead to fatalities [START_REF] Bezuidenhout | Surface subsidence and sinkholes in the dolomitic areas of the Far West Rand, Transvaal, Republic of South Africa[END_REF][START_REF][END_REF]. Monitoring systems are needed to prevent or reduce the risk of any damage. Existing monitoring techniques, such as satellite-monitoring (DInSAR), laser scanner, photogrammetry, total stations and high precision levelling, are focused on the measurement of movements at surface level. These techniques must allow some settlements and deformations in the soil body, before being able to detect the formation of a sinkhole. Therefore subsurface methods such as embedded Distributed Fiber Optic Sensors (DFOS) could detect sinkhole-induced strains and movements earlier, since they can be installed at depth in the ground.

This paper shows an experimental campaign carried out as part of the SINEW project [START_REF] Abadie | SINEW: SINkhole early warning[END_REF] to investigate the efficacy of this latter monitoring technique in detecting strain changes within the soil, induced by the formation of a sinkhole.

Methodology

Experimental Setup

Sinkholes can be simulated in the laboratory by means of trapdoor tests, both at 1g [START_REF] Möller | Distributed fibre optic sensing for sinkhole early warning: experimental study[END_REF] or in the geotechnical centrifuge [START_REF] Jacobsz | Trapdoor experiments studying cavity propagation[END_REF][START_REF] Da Silva | Centrifuge modelling of the behaviour of geosynthetic-reinforced soils above voids[END_REF]. In this paper, the experimental study was performed at 1g using a 790 × 200 mm rectangular rig, equipped with a trapdoor of width, B = 100 mm that can mimic the formation of a sinkhole, as shown in Fig. 1.

Samples were prepared using Hostun sand, with an average particle size, d 50 = 0.356 mm [START_REF] Da Silva | Centrifuge modelling of the behaviour of geosynthetic-reinforced soils above voids[END_REF]. Tests were prepared at increasing relative densities (D R = 20%, 52% and 88%) to allow comparison of sinkhole formation at different soil conditions. The sand was poured manually for D R = 20%, and using an automatic sand pourer for the higher densities. The sample height was H = 200 mm (H/B = 2). The DFOS cables were installed at heights of z = 50, 100, and 150 mm above the trapdoor and these layers were highlighted using dyed black sand to highlight the shear band during failure (Fig. 2). The cables were pinned at the edge of the box, and coated in sand to increase soil-cable interface coupling in selected experiments [START_REF] Xu | On the use of highresolution distributed fibre optic sensing for small-scale geotechnical tests at 1g[END_REF].

The DFOS analyzer used to collect strain within the cable is the Luna ODiSI 6100 [START_REF]Luna Innovation Incorporated: Optical Distributed Sensor Interrogator Model ODiSI 6100: Data Sheet[END_REF]. It is well adapted for small scale experiments in the laboratory due to the small spatial resolution and precise gauge length (2.6 mm used in this case). With a sample width of L = 790 mm, this provides ~300 sampling points in the FO cable at each level, enabling the establishment of a precise continuous distributed strain profile.

Images for the PIV analysis were acquired using a Canon Powershot G10 camera and the analysis was carried out using GeoPIV_RG [START_REF] Stanier | Improved image-based deformation measurement for geotechnical applications[END_REF].

Results

For a trapdoor displacement δ lower or equal to 1-2% of the trapdoor width, the soil is able to adjust and redistribute the stresses on an adjacent support [START_REF] Dewoolkar | Centrifuge modeling of granular soil response over active circular trapdoors[END_REF]. This behavior is known as arching [START_REF] Terzaghi | Stress distribution in dry and saturated sand above yelding trap-door[END_REF] and is regarded as the early phase of the sinkhole formation. This phase is the main focus of the work presented in this paper. Despite measuring the strain profile at three heights within the soil sample, the cable of most interest in this study is the one located at z = 150 mm, which represents a realistic embedded height that could be achieved during earthwork (~1 m depth from original soil surface at full scale).

Particle Image Velocimetry Analysis

The main results from PIV analyses consist in the settlement profiles at different heights above the trapdoor, which have been fitted using a modified Gaussian distribution [START_REF] Vorster | Estimating the effects of tunneling on existing pipelines[END_REF] according to the following equations: 2 (1)

S v (x) = S max • n/ (n + 1) + exp α • (x/i)
where S max is the maximum settlement at the trapdoor centerline, i is the distance from the trapdoor centerline of the inflection point, α is a shape factor to alter the location of the inflection point. Horizontal soil displacements from PIV are interpolated using a double Gaussian distribution, according to the following equation:

S h (x) = S hmax • {exp[-(x-b)/c]-exp[-(x + b)/c]} (3)
where S hmax is the maximum horizontal displacement while b and c are fitting parameters. Displacement profiles from PIV are shown in Fig. 3, demonstrating the adequateness of Eq. ( 1) and (3). From the displacement profiles, it is then possible to evaluate the strain which are representative of those experienced by the fibre optic cable using:

ε = x i+1 -x i + S h,i+1 -S h,i 2 + S v,i+1 -S v,i 2 0.5 /(x i+1 -x i ) (4)
This is needed for comparison with DFOS data, where horizontal and vertical displacement cannot be accessed.

Strain Profiles from DFOS

The experimental soil strain evaluated from fitted displacement profiles (Eq. ( 4)) are then compared with the experimental strain experienced by the fiber optic cables, obtained from the Luna ODiSI 6100 interrogator. Figure 4 shows a difference in strain magnitude between the fiber optic cable and the corresponding strain in the soil. This discrepancy might be related to a lack of shear transfer between the soil and the cable, induced by a lack of coupling and the low stress level at 1g. To further understand this behavior, detailed inspection of the fiber optic cable was performed numerically to enable better visualization of the cable deformation and strain profile [START_REF] Della Ragione | Numerical investigation of fibre optic sensing for sinkhole[END_REF]. Figure 5 shows a comparison between the experimental output from the interrogator and the numerical results for validation. The results concur with the experimental observations and demonstrate the impact of testing at 1g, and of the low stress level, on the cable's ability to follow soil movement, a difficulty that disappears at higher stress levels [START_REF] Abadie | SINEW: SINkhole early warning[END_REF][START_REF] Della Ragione | Numerical investigation of fibre optic sensing for sinkhole[END_REF].

This does not invalidate the use of 1g small scale experiments to further understand the use of DFOS for geo-hazard monitoring, as this is currently the most practical and cheapest way of generating experimental results using Rayleigh backscatter light analyzer. Moreover, the singular shape of the strain profile indicates the expected signature that one would expect from a sinkhole detection. The strain profiles obtained can reveal the position and the size prediction of the sinkhole, by looking at the position of the inflection point, as shown in Fig. 6, which pertains to experimental results.

Conclusions

Sinkholes are highly dangerous events for the health of infrastructures. Hence, to minimize or avoid the possible damages induced by a sinkhole, it is important to monitor soil deformations. A way to address this, is the use of an inexpensive fiber optic cable, buried at shallow depths, in the soil mass, that 'senses' the change in strain in the soil before its effects reaches the surface.

Different from civil structural applications (e.g. concrete structures, steel structures, etc.), where the fiber can be simply glued onto the surface, the effectiveness of DFOS in following soil movements is strongly dependent from the soil-cable interface and this limit has been considered as the main barrier to the use of this technology for geotechnical applications.

This paper illustrated the effectiveness of a relatively new technology (i.e. DFOS with Raileigh backscattering) in detecting soil movements.

Our study focused its attention on small scale trapdoor test, performed in controlled conditions at 1g. Results from PIV have been processed so that can be compared with data obtained by the fiber optic interrogator.

Despite DFOS technology is not able to follow the soil strain as expected, it is able to pick up an unequivocal profile of strain, induced by the trapdoor lowering, since the beginning of the test (i.e. δ ≤ 0.01 -0.02•B). In conclusion, our study suggested that the DFOS technology can be used to detect, locate and estimate the size of a sinkhole, even though it has not possible to monitor the real strain level in the soil, due to a lack of shear transfer at the interface between the soil and the cable.

Fig. 1 .

 1 Fig. 1. Experimental rig with plane strain trapdoor

Fig. 2 .

 2 Fig. 2. Image acquired from the Canon Powershot G10, used for PIV analysis

Fig. 3 .

 3 Fig. 3. (a) Vertical displacements, (b) Horizontal displacements from PIV for D R = 52% δ = 2 mm and z = 150 mm

Fig. 4 .Fig. 5 .Fig. 6 .

 456 Fig. 4. Soil strain from PIV and strain within the fiber optic cable for D R = 20% δ = 1 mm and z = 150 mm

Acknowledgements. We are grateful to CSIC (EPSRC (EP/N021614/1) and Innovate UK (920035)) for funding and supporting this work and Dr Jennifer Schooling and Prof. Giulia Viggiani for facilitating the collaboration between the University of Naples Federico II and the University of Cambridge, which enabled Mr Gianluigi Della Ragione's internship at CSIC within the Erasmus+ Programme. We are also thankful to the Schofield Centre and its Director, Prof. Gopal Madabhushi, for their support with the laboratory experiments. Fruitful advice and discussion with Prof. Malcolm Bolton, Prof. Sadik Oztoprak, Dr Sam Stanier and Prof. Giulia Viggiani were also very valuable for the development of this project.


Diarmid M Xu

Gopal Madabhushi

C N Abadie

John M Harris

Richard J S Whitehouse

S P G Madabhushi

Effect of rock density on the response of scour protection to earthquake-induced liquefaction for offshore wind applications

come   L'archive ouverte pluridisciplinaire

1 Introduction Offshore wind is an ever-growing industry with huge potential to meet the future demand of renewable energy (Global Energy Review 2021, 2021). As global energy usage increases, new offshore wind farm developments are being constructed in seismically active areas, such as North America and East Asia. The most common type of foundation selected for offshore wind turbines is the monopile, large diameter steel tubes that are hammered into the seabed (Deep Water, 2013).

In scour prone areas, rock dump is used to lay a rock berm around the monopile, either as a preventative measure or as remediation. Scour is a phenomenon where the water currents that collide with the foundation are redirected into vortices that erode away the sediment around the foundation [START_REF] Harris | Foundation Scour as a Geohazard[END_REF].

A typical berm geometry for an example 8m diameter pile would have a filter and armour rock layer spanning five and three times the monopile diameter respectively (The Rock Manual, 2007). Armour rock are typically larger, at 0.3m to 0.5m in diameter, they resist the push of the current whereas the filter rocks are smaller, 0.1m to 0.2m and they prevent the armour rocks from sinking into the sand. Each layer is around 0.5m to 1.0m thick. An alternative approach to the lays above is 1-2m of well graded rock (widely graded on a Particle Size Distribution plot) rock dump that can serve both functions. The exact rocks used varies per site so the dimensions and berm thicknesses given here are only representative values.

Both the monopile and rock dump are a common and cost-effective way of building turbine foundations, however, while the phenomenon of scour is relatively well documented and studied [START_REF] Harris | Scour Development around Large-Diameter Monopiles in Cohesive Soils: Evidence from the Field[END_REF] [START_REF] Harris | Foundation Scour as a Geohazard[END_REF] [START_REF] Whitehouse | Sediment transport and scour in the ocean environment -knowledge and future directions[END_REF], there is little data or research into the seismic behaviour of rock scour protection, specifically settlement induced by liquefaction [START_REF] Escribano | Stability of scour protection due to earthquake-induced liquefaction: Centrifuge modelling[END_REF].

Recent research has studied the effectiveness of different types of protection and their effect on restoring foundation stiffness and strength [START_REF] Mayall | Flume tank testing of offshore wind turbine dynamics with foundation scour and scour protection[END_REF], however, design codes provide limited or conservative methods (Standard DNV GL, 2016, Standard DNV GL 2021). Three options are given to design against scour for offshore monopiles:

• install scour protection before or shortly after foundation installation, or; • specify a pile embedment length that remains sufficiently long even after the most extreme case of scour, or; • "monitor and react", with appropriate pile embedment length designed with a scour allowance, and scour remediation work is only carried out if and when required.

It is also stated that scour must be considered during design but there is limited guidance on how this should be done. The three options are all costly, either due to over design of the foundation, or scour protection, or through the risk of future remediation. Therefore, understanding seismic impact is important.

Both [START_REF] Escribano | Stability of scour protection due to earthquake-induced liquefaction: Centrifuge modelling[END_REF] and [START_REF] Xu | Response of armour rock-scour protection to earthquake-induced liquefaction for offshore wind applications[END_REF] showed significant settlement of the scour protection rocks, of around 0.35m. In this paper, the results of two saturated dynamic centrifuge tests that continue the research of [START_REF] Xu | Response of armour rock-scour protection to earthquake-induced liquefaction for offshore wind applications[END_REF] are presented, with focus on the effect of rock density on rock settlement due to seismic liquefaction. Centrifuge tests named DMX02 and DMX03 differ only in the density of rock used, with DMX02 being the benchmark test using a mid-range rock specific gravity compared to a higher rock density in DMX03. In both tests, the rock and sand settlement, soil accelerations and pore water pressures were captured and compared.

2 Experimental Methodology

Centrifuge testing

A geotechnical centrifuge allows small scale models to be tested at elevated g levels, where the results, after scaling [START_REF] Schofield | Cambridge Geotechnical Centrifuge Operations[END_REF], can be converted to match that of prototype structures out in the field. Centrifuge testing mitigates the need to carry out scale testing on prohibitively large civil engineering structures, while still allow the study of the non-linear behavior of soils.

The centrifuge used in this study was the 10 m-diameter Turner beam centrifuge at the Schofield Centre [START_REF] Madabhushi | Centrifuge Modelling for Civil Engineers[END_REF]. Two saturated dynamic centrifuge tests were performed at 50g in a model container sized 730mm x 250mm x 400mm and a servo hydraulic shaker was used to simulate a series of earthquakes [START_REF] Madabhushi | Development of a servo-hydraulic earthquake actuator for the Cambridge Turner beam centrifuge[END_REF]. in DMX02 andDMX03, with only the rock density, but not the size or number of rocks used, being changed. Another slight variation was in the position of the sensors below the rock berm, in DMX03 more sensors were deployed, as shown in Figure 1. The sand was saturated with methylcellulose for scaling purposes. Figure 2 presents the berm geometry where D50 is the rock diameter. Sufficient space was given for the sand to flow and heave (so that the rock may settle) and to avoid boundary conditions.

Rock berm design

The model rock berm represented a simplified worst case scenario, of two layers of poorly graded large 1m armour rocks with no filter layer. Due to the size of the rocks (20mm) and the size of the container, a checker board grid of rocks were laid to form the rock berm. This procedure was repeated for both tests, meaning the size and number of rocks used was identical. DMX02 was the benchmark test, with a rock specific gravity of Gs=2.62. The heavier rocks of DMX03 had a Gs=2.88. Figure 3 shows the test models of both experiments. Note that the colours of the rocks are different but this has no effect on the results.

Table 1 is adapted from [START_REF] Xu | Response of armour rock-scour protection to earthquake-induced liquefaction for offshore wind applications[END_REF] and summarises the model rock dimensions and properties. If the ratio D50/d50, that of the rock and sand in the field, was kept the same in the model, the size of the sand grains would more closely resemble that of clay, and thus the sediment behaviour would be incorrect. [START_REF] Madabhushi | Centrifuge Modelling for Civil Engineers[END_REF] states that as long D50/d50 is greater than 15, reasonable scaling of the rock and sand particles would be ensured.

Model soil

The sand used was Hostun HN31, d50=0.44mm, a sand that is manufactured, not quarried. This means the physical properties of the sand can be tightly controlled and measured (void ratio emin=0.555, emax=1.01, specific gravity Gs=2.65). While not a suitable sand for construction, it is a reliable, medium grained sand for scientific research.

The sand was poured to be loose, at a relative density of 43% using an automatic sand pourer as described in [START_REF] Madabhushi | A new automatic sand pourer for model preparation at University of Cambridge[END_REF], to maintain uniformity and repeatability. After pouring, the sand was saturated with methylcellulose to ensure the correct liquid scaling. Saturation was achieved via controlled vacuum suction through a modified saturation system based on the system developed by [START_REF] Stringer | Novel Computer-Controlled Saturation of Dynamic Centrifuge Models Using High Viscosity Fluids[END_REF].

Load sequence

A series of four earthquakes were fired using the servo-hydraulic shaker [START_REF] Madabhushi | Development of a servo-hydraulic earthquake actuator for the Cambridge Turner beam centrifuge[END_REF], these are shown in Table 2. To begin, a small test earthquake (input Peak Ground Acceleration, i.e. bedrock acceleration, PGA~0.05g) is fired to ensure all systems and sensors are functioning correctly, this does not fully liquify the soil and little settlements occur. Next, two large earthquakes are fired (PGA~0.3g to 0.4g). Finally, to show that "soil remembers" its past loading history, a small earthquake (PGA~0.05g) is simulated to end the experiment, where little to no liquefaction or settlement is expected.

Instrumentation

Sensors were installed during the sand pouring process at regular depth intervals. Linear variable displacement transducers (LVDT's) at the top track rock settlement and sand heave, zero displacement is defined to be at the starting position of each earthquake. Pore water pressure transducers (PPT's) and piezoelectric accelerometers capture pore water pressure and soil accelerations. DASYLab v13.0 was used to log data into text files for processing later. A logging rate of 6000Hz was used for dynamic events, and a rate of 100Hz was used for swing up, to record pore pressures and settlements as the g level increases from one to fifty. Though that data is normally not used, if something were to go awry during the flight, these data could help identify the problem and when it occurred.

Test Results

All sensor voltages were first filtered, then calibrated and zeroed in MATLAB using a bespoke script, before being scaled to prototype scale. All results are presented at prototype scale. An eighth order Butterworth filter was used to reduce phase shift. An approximate initial effective vertical stress has been calculated to identify the limit of liquefaction, where ru=1 (the ratio of excess pore pressure and initial effective vertical stress).

Rock settlement

Figure 4 shows some exemplar data from DMX03, EQ2 (PGA=0.4g), of the rock settlements versus the input motion at the bottom in blue. It is seen that significant rock settlement occurs, in the region of 0.75m with the middle of the berm settling more than the sides, this is corroborated by Figure 5, a post test image of the model where the berm can be seen to have curved. It is also observed that the sand heaves due to the rock settlement. Lastly, the settlement history shows a characteristic start stop motion that matches that of the input motion.

The settlements at the berm centre for all earthquakes are summarized in Figure 6, where the settlement has been plotted against the Arias Intensity, a measure of the energy of an earthquake. The Arias Intensity is a value to compare earthquakes, for example, between a high amplitude, low cycle count quake and a low amplitude, high cycle one. From this data, it is seen that the grouping of higher settlement data points is reversed between the earthquakes for low and high Arias Intensities, i.e. in the case of low Arias Intensity, DMX02 resulted in higher settlements, whereas for high Arias Intensity, DMX03 was higher. This means that higher density rock settles more than mid-range density rock under full liquefaction (EQ2 and EQ3), but under partial liquefaction from smaller earthquakes, the settlement is less (EQ1 and EQ4). Figure 7 compares the time histories of EQ2 from both DMX02 and DMX03, the input motion is shown to be very similar, but the settlement from DMX03 is higher. In DMX03, 15 cycles of the sine wave was fired, instead of 10, but the comparative settlements shown in Figure 6 were taken at 10 cycles for both tests. As shown in [START_REF] Escribano | Stability of scour protection due to earthquake-induced liquefaction: Centrifuge modelling[END_REF] and [START_REF] Xu | Response of armour rock-scour protection to earthquake-induced liquefaction for offshore wind applications[END_REF], the addition of a rock berm will increase the initial effective vertical stress, and thus delay the onset of full liquefaction. This delay will reduce rock settlement for smaller earthquakes, where full liquefaction does not occur. However, for larger input motions, full liquefaction does occur, at which point the higher density rocks will in fact settle more than their lighter counterparts.

Soil liquefaction

From the plot of excess pore water pressure in Figure 8, it is shown that the soil reaches full liquefaction under the larger earthquakes of EQ2 and EQ3. The selected sensors form the central column in Figure 1. The liquefaction limit line is an estimation, taking into account the weight of sand and that of the rock berm prior to the earthquake. Full liquefaction is also confirmed in Figure 9 where decoupling can be seen in the (piezo recorded) acceleration time history. As the shallow regions of sand liquefy, they can no longer transfer shear waves, and thus the acceleration time trace "fades" as the input motion travels up the soil column. From the two centrifuge tests it can be seen that significant settlements can occur with any scour protection armour rock, however, under full liquefaction due to large earthquakes, the settlement of higher density rock will be greater compared to that of lower density rock.

Usually the rock to be used on a project is selected based on proximity to quarries, as a large proportion of the cost of rock dump is the transportation from the source to site. One reason high density rocks such as granite might be chosen, despite the higher unit cost than standard density rock, is to reduce the rock berm thickness required to ensure enough rock weight to resist scour currents and to add stiffness to the monopile foundation.

As seen from the results presented here, there is no major incentive to use high density rock dump to reduce scour protection rock settlement due to seismically induced liquefaction. For earthquakes producing high Arias Intensities, high density rock fill resulted in a 30% increase in the average and maximum recorded rock settlement in this study. However, a reduction of 75% settlement for quakes of low Arias Intensity was observed owing to the larger initial vertical effective stress imposed by the denser rocks.

Future planned work includes investigating the effect of rock size, rock grading and berm geometry on rock settlement post-earthquake. A monopile may also be included into future models. This research should form the basis for further research in the behaviour of rock scour protection in liquefiable soils.

Figure 1 .

 1 Figure 1. Test schematic of DMX03, prototype scale Figure 1 shows a cross section of the model for DMX03. The sand and rock formation remained identical in DMX02 and DMX03, with only the rock

Figure 2 .

 2 Figure 2. Berm geometry of DMX03, prototype scale

  a). Top down view of model DMX02 and (b) DMX03, part of the view is blocked by gantries that hold LVDT sensors. The blue cylinders are part of the servo-hydraulic shaker.

Figure 4 .

 4 Figure 4. Displacement time history from EQ2 of DMX03 for all LVDT's including the input motion

Figure 5 .

 5 Figure 5. Post DMX03 image of the rock berm, side view

Figure 8 .

 8 Figure 8. Excess pore pressure of EQ2, DMX03, central PPT stack, including liquefaction limit line (red) and input motion (blue)

Table 1 .

 1 Comparison of berm rock properties * D50 is used for scour rock grading, and d50 used for sediment grading. ts is the berm thickness/height.)

	Parameter DMX02	DMX03	(Escribano	Field data
		(proto-	(prototype)	and Brennan,
		type)		2017)
	d50 (mm)	0.44	0.44	0.14	0.15
	D50 (mm) 1000	1000	500	500-1000
	ts (mm)	2000	2000	1500	1500
	ts/D50	2	2	3	3-1.5
	D50/d50	2273	2273	3571	3333-6667
	Gs	2.62	2.88	-	2.5-3.0
	* (

Table 2 .

 2 Earthquake sequence for both DMX02 and DMX03

	Earthquake number	Earthquake
	EQ1	Kobe, 0.15V
	EQ2	Sine wave, 50Hz, 15 cycles, 2.50V
	EQ3	Sine wave, 50Hz, 15 cycles, 3.00V
	EQ4	Sine wave, 50Hz, 15 cycles, 0.75V

Acknowledgements

The authors acknowledge the generous funding from EPSRC and HR Wallingford that made this project possible, and the help and advice of the technicians at the Schofield Centre.