Ph.D Aylin Nouri
email: aylin.nouri@enpc.fr

Associate Professor, Ph.D Ali Noorzad
email: a_noorzad@sbu.ac.ir

Professor, Ph.D Jean-Michel Pereira
email: jean-michel.pereira@enpc.fr

Anh Minh Tang

MSc Candidate

Cyclically thermally-activated pile under combined axial/horizontal loads in saturated clay

Keywords: Repeated loading, Soil/structure interaction, Temperature effects List of notations Projected pile head axial displacement, mm Measured

In the present study, the influence of cyclic thermal loading on the mechanical response of an energy pile installed in saturated clay subjected to sustained combined axial/horizontal mechanical loading was investigated using physical modelling. After completion of the soil saturation process and prior to starting the thermo-mechanical loading, the pile fixation was released inducing pile head heave. When the rate of pile head heave became small, the model pile was subjected to compression axial loading of 100 N (i.e. 20% of the estimated ultimate axial load) followed by horizontal loading of 35, 71, and 109 N (corresponding to accumulative pile head horizontal displacements of 4%, 7%, and 12% of pile diameter) before subsequent 15 heating/cooling cycles. The results indicated that imposing heating/cooling cycles to the pile resulted in irreversible horizontal displacement, accumulating at a reducing rate as the number of thermal cycles increased. By the end of the 15 th cycle, the accumulated irreversible horizontal displacement was estimated at 0.57%, 1.15%, and 1.84% of pile diameter under the horizontal loads of 35, 71, and 109 N, respectively. Reversely, thermally induced pile head axial displacement at the end of the 15 th cycle is practically insignificant (smaller than 0.1% of pile diameter).

Introduction

The dual functionality of energy piles for supporting the structural loads and meeting the heating/cooling needs of the building imposes additional stresses/strains on the soil-pile system, which could affect the mechanical behaviour of the energy piles. Previous studies revealed that cyclic thermally-induced volume changes are much more predominant in clayey soils compared to sandy soils. Nevertheless, only a limited number of studies focused on the influence of thermal loading on the mechanical response of axially-loaded energy piles embedded in clayey soils by performing full-scale tests [START_REF] Laloui | Experimental and numerical investigations of the behaviour of a heat exchanger pile[END_REF][START_REF] Bourne-Webb | Energy pile test at Lambeth College, London: geotechnical and thermodynamic aspects of pile response to heat cycles[END_REF][START_REF] Akrouch | Thermo-mechanical behavior of energy piles in high plasticity clays[END_REF], centrifuge model tests [START_REF] Stewart | Centrifuge modeling of soil-structure interaction in energy foundations[END_REF][START_REF] Ng | Centrifuge modelling of energy piles subjected to heating and cooling cycles in clay[END_REF]Ng et al. , 2021a, b) , b) and 1-g small-scale physical model tests [START_REF] Yavari | Mechanical behaviour of a small-scale energy pile in saturated clay[END_REF][START_REF] Wu | Effect of stress history of saturated clay on engineering behaviour of an energy pile[END_REF][START_REF] Yazdani | Investigation of thermal loading effects on shaft resistance of energy pile using laboratory-scale model[END_REF][START_REF] Nguyen | Long-term thermo-mechanical behaviour of energy piles in clay[END_REF][START_REF] Tang | Physical modeling of the thermomechanical behavior of a geothermal pile[END_REF]. To the authors knowledge, the works of [START_REF] Vitali | Centrifuge modelling of the use of discretelyspaced energy pile row to reinforce unsaturated silt[END_REF] and [START_REF] Zhao | Thermally induced ratcheting of a thermo-active reinforced concrete pile in sand under sustained lateral load[END_REF] are the only available studies using centrifuge model tests to investigate the influence of monotonic heating and heating-cooling cycles, respectively, on the flexural behaviour of horizontally-loaded energy piles in sands. These studies indicate that (1) the heating operation reduces pile bending moment while causing no additional flexural stress, (2) imposing heating/cooling cycles results in accumulating irreversible horizontal displacement. Although such ratcheting has already been observed in axially loaded energy piles, its occurrence for energy piles subjected to inclined load has not yet been observed. This study thus aims to explore the influence mechanism of cyclic thermal loading on the mechanical response of a single model energy pile installed in saturated clay subjected to sustained combined axial/horizontal mechanical loading through physical modelling under normal gravity.

Experimental set-up

In order to use the results obtained from 1-g small-scale model tests to assess the thermo-mechanical response of full-scale energy piles, the test program was designed by considering the geometry difference between the smallscale pile and the full-scale pile. The experimental setup consists of a cylindrical steel soil tank (with , and ), whose internal surface was covered with a two-layer geotextile filter, wrapped in an expanded polystyrene sheet (Fig. 1).

Fig. 1. Schematic view of the experimental setup.

In order to minimize the heat dissipation rate, and maximize the roughness of the model pile surface, the outside surface of a closed-end aluminium tube (with , , and ) was coated with Fontainebleau sand. Given that the soil tank dimensions satisfy the following conditions: , and soil cushion below the pile toe , boundary effects could be considered negligible [START_REF] Boominathan | An experimental study on static and dynamic bending behaviour of piles in soft clay[END_REF][START_REF] Leblanc | Response of stiff piles in sand to long-term cyclic lateral loading[END_REF]. Kaolin clay powder (with , %, and )

was mixed with de-aired water to achieve an optimum water content of 29% [START_REF] Murillo | Elastic response of unsaturated soils[END_REF]. The grain-size scaling effect could be considered negligible in this study since the ratio is much larger than the proposed limit by Fioravante (2002). The model pile was first fixed to the centre of the tank and the soil was compacted by 50 mm thick layers around the pile to achieve a maximum dry density of (corresponding to ). The compacted clay is expected to show a double porosity structure with micropores (0.2 -2 μm) and macropores (5 -20 μm) [START_REF] Thom | Pore size distribution of unsaturated compacted kaolin: the initial states and final states following saturation[END_REF]. Although this installation method differs from a full-scale bored pile, it would still provide good soil-pile contact. However, a softer displacement response could be expected in the model pile due to some lesser degree of compaction of soil close to the pile. Finally, the soil mass was saturated for two months by slowly injecting de-aired water from the bottom of the soil tank. Using similar procedure, [START_REF] Nguyen | Long-term thermo-mechanical behaviour of energy piles in clay[END_REF] showed that two months was long enough a period for the soil mass to be fully saturated. During this saturation, the soil mass globally swelled, thus generating uplift forces on both pile shaft and toe. Afterwards, the pile fixation system was removed and a pile head heave was observed. When the rate of pile head heave became small (after 15 days), a 100 N dead-weight (i.e. 20% ) was placed on the pile head within seconds and was maintained for two hours to reach equilibrium without waiting for the soil to consolidate. Afterwards, horizontal load was applied in three steps by allowing water flow in the plastic bucket linked to the pile head through a piece of rope over a pulley. In the first, second, and third load steps, horizontal load was increased within 10 minutes from zero to 35 N, 35 to 71 N, and 71 to 109 N, respectively, corresponding to accumulative horizontal displacements of 4, 7, and 12%D, and maintained for more than 10 days at each loading level to reach equilibrium and to consolidate the soil prior to the cyclic thermal loading. At the end of each load step, 15 heating-cooling cycles with temperature variation of ±5 ℃ around an ambient temperature of 20 ℃ (consisting of a 3-hour heating phase followed by a 3-hour cooling phase and eventually, an 18-hour recovery phase) were imposed to the pile by circulating water in fitted aluminium U-shaped tube linked to a temperature-controlled water bath and a peristaltic pump. The heating and cooling phases of each cycle in the model pile simulate 6 months of temperature changes of ℃ in a full-scale concrete pile of 0.8 m in diameter. This temperature variation is within the range of 3-37 °C of field-scale energy piles [START_REF] Jiang | Thermo-mechanical behavior of driven energy piles from full-scale load tests[END_REF]). It should be noted that the model test could recreate the thermal and mechanical strains similar to field ones.

Results

In Fig. 2 As illustrated in Fig. 3, prior to the application of horizontal mechanical and cyclic thermal loads, the pile head moves axially by about -0.015%D due to the compressive axial loading of 100 N. This negligible pile head settlement could be attributed to the counteracting effect of the swelling-induced uplift forces.

Fig. 3 Changes in pile head axial displacement with time during the compressive axial loading period

As can be seen in Fig. 4, during the application of horizontal loading at each load step, the pile head horizontal displacement increases rapidly with the increase of horizontal load, then keeps on increasing at a reducing rate under the constant horizontal load and reaching 4%D, 7%D, and 12%D at the end of the first, second and third load steps, respectively. Meanwhile, the pile head heaves immediately after increasing the horizontal load, which might be due to further mobilization of the uplift force on the pile shaft due to the tendency of soil located in front of the pile close to the surface to heave. Afterwards, under the constant horizontal loads of 35 and 109 N, the pile head heave initially fluctuates around a steady value of 0.27%D and 0.12%D for about ten days, then begins to decrease gradually and reaches 0.22%D and 0.09%D at the end of the 19-day and 14-day period, respectively. However, under the constant horizontal load of 71 N, pile head heave fluctuates around a steady value of 0.12%D within a period of 11 days. The gradual reduction of pile head heave could be attributed to the pile being pulled downwards by the mechanicallyinduced consolidation and creep of the surrounding clay [START_REF] Fellenius | Results from long-term measurement in piles of drag load and downdrag[END_REF]. As shown in Fig. 5 (a)-(c), at any level of horizontal loading, the pile head heaves during the heating phase then settles quickly during the subsequent cooling phase, and heaves again during the recovery phase. Meanwhile, it also moves horizontally throughout the entire thermal cycle, except when the horizontal load equals 35 N, the recovery phase could not lead to the pile head horizontal displacement. By the end of each thermal cycle, the model pile keeps accumulating axial and horizontal movements instead of returning to its initial position before the thermal cycle, which means that irreversible displacements occur in both horizontal and axial directions. 123

As illustrated in Fig. 6, under the horizontal loads of 35, 71, and 109 N, the irreversible horizontal displacement rapidly increases to 0.09%D, 0.17%D, and 0.25%D during the first thermal cycle, then continues to increase at a decreasing rate with the increasing number of cycles, reaching 0.57%D, 1.15%D, 1.84%D at the end of the 15 th cycle, respectively. Thermally-induced irreversible horizontal displacements could be explained by the combined effect of both soil and pile contraction and build-up of excess pore water pressure, contributing to the reduction of horizontal effective stress acting on the pile shaft and subsequently, the reduction of passive soil resistance.

Additionally, thermally-induced soil consolidation and creep could contribute in turn to a time-dependent increase in horizontal displacement during the recovery phase. Evidence of these phenomena are available in previous works [START_REF] Akrouch | Thermo-mechanical behavior of energy piles in high plasticity clays[END_REF][START_REF] Wu | Effect of stress history of saturated clay on engineering behaviour of an energy pile[END_REF][START_REF] Ng | Centrifuge modelling of energy piles subjected to heating and cooling cycles in clay[END_REF]Ng et al. , 2021a, b), b). The gradual accumulation of thermally-induced irreversible horizontal displacements during thermal cycles could be caused by thermally-induced passive soil resistance mobilization. This kind of ratcheting response was similarly observed for axially-loaded energy piles embedded in clay reported by [START_REF] Nguyen | Long-term thermo-mechanical behaviour of energy piles in clay[END_REF], [START_REF] Wu | Effect of stress history of saturated clay on engineering behaviour of an energy pile[END_REF] and [START_REF] Ng | Centrifuge modelling of energy piles subjected to heating and cooling cycles in clay[END_REF]Ng et al. ( , 2021a, b), b), and for horizontally-loaded energy pile embedded in dry sand reported by [START_REF] Zhao | Thermally induced ratcheting of a thermo-active reinforced concrete pile in sand under sustained lateral load[END_REF]. It is also inferred from Fig. 6 that under the horizontal loads of 35 and 71 N, the first cycles induce irreversible axial displacement up to -0.03%D and -0.05%D, respectively. This negligible settlement is fully compensated by the pile head heave during subsequent cycles. However, under the horizontal load of 109 N, the first cycle induces irreversible heave up to 0.05%D, which almost remains constant during subsequent cycles and gains an increment of only 0.02%D. This reverse trend could be attributed to the uplift force on the pile shaft effectively mobilized in previous loading steps. It is further worth noting that the accumulated thermally-induced irreversible axial and horizontal displacements under the horizontal load of 71 and 109 N might be influenced by the accumulated irreversible displacements induced by previous loading steps. Overall, with increase in horizontal load, thermal cycles tend to cause a higher irreversible horizontal displacement, resulting in a negligible irreversible heave at the pile head.

Conclusions

The main conclusion of this study is that under the combined axial/horizontal mechanical loading, imposing heatingcooling cycles to the pile results in irreversible horizontal displacement at the pile head, accumulating at a reducing rate as the number of thermal cycles increases. After 15 heating-cooling cycles, the amount of accumulated thermally-induced irreversible horizontal displacement is estimated at 0.57%D, 1.15%D, and 1.84%D under the horizontal loads of 35, 71, and 109 N, respectively. Reversely, thermally-induced pile head axial displacement at the end of the 15 th cycle is practically insignificant (smaller than 0. 1%D). At higher horizontal loads, thermal cycles induce a higher irreversible horizontal displacement, resulting in a negligible irreversible heave. It is recommended that thermo-mechanical tests are performed with a more significant number of heating/cooling cycles to determine a stabilization threshold of the thermally-induced irreversible pile head horizontal displacement. This study is subject to some limitations, including (1) the absence of pore-water pressure measurement, (2) partial rotational restraint at the pile head, (3) uncertainty about the consolidation degree of the soil mass, (4) the existence of swelling-induced heave, (5) mismatch of the thermal properties of aluminium and concrete, (6) inability in simultaneous scaling of both strength and stiffness of the prototype pile, and (7) inability to reproduce the soil stiffness, stress level and excess pore water pressure within the soil mass at the prototype scale. However, the obtained qualitative results could provide insight into the thermally-induced ratcheting behaviour of mechanically-loaded piles.

  grain-size, Projected pile head horizontal displacement, mm

  , the continuous line represents the measured pile head heave immediately after removing the fixation system for the first 15-days before starting thermo-mechanical testing, while the dashed line shows the pile head heave extrapolated for the subsequent 90 days during thermo-mechanical testing. The measurements indicate that the pile head heaves rapidly with time in the first days and continues to heave at a reducing rate reaching 6.8% D after 15 days. The reason for this heave could be the pre-mobilized uplift forces on both pile shaft and toe, arising from the saturation-induced soil swelling in the vicinity of the fixed-headed pile[START_REF] Lalicata | Experimental observation on a laterally loaded pile in unsaturated silty soil[END_REF][START_REF] Yunlong | Pile behavior modeling in unsaturated expansive soils[END_REF].

Fig. 2

 2 Fig. 2 Time dependent heave of the pile head after removing the fixation system, measured and extrapolated curves

Fig. 4

 4 Fig. 4 Changes in horizontal load, pile temperature, and pile head axial and horizontal displacements with time during thermo-mechanical loading stage (Displacement readings at the pile head are zeroed before starting thermo-mechanical testing. The swelling-induced pile head heave has been subtracted from the measured total pile head heave. The dashed line demonstrates displacements extrapolated for the subsequent 15 days at the end of each loading step).

Fig. 5

 5 Fig. 5 Magnified view of the thermal-loading period at the end of (a) the first load step, (b) the second load step, and (c) the third load step.

Fig. 6

 6 Fig. 6 Pile head irreversible axial and horizontal displacements versus the number of heating-cooling cycles (mechanically-induced pile head axial and horizontal displacements due to consolidation and creep of the surrounding clay have been subtracted from the measured total displacements during the thermal-loading period of each respective load step).


Hung Quoc

Jean-Michel Vu

Anh Minh Pereira

Tang

Dr Anh Minh Tang

Effect of fines content on soil freezing characteristic curve of sandy soils

Keywords: temperature of spontaneous nucleation, hysteresis, soil freezing characteristic curve, residual water content

Soil freezing characteristic curve (SFCC) represents the relationship between soil temperature and unfrozen water content of soil during freezing and thawing processes. In this study, SFCC of sandy soils was determined in laboratory. Pure sand was mixed with clay at various contents (0, 5, 10, 15, and 20% of the total dry mass) and the mixtures were compacted to their respective maximum dry density. Compacted specimens were then placed in a close and rigid cell and the soil's temperature was decreased step-by-step to freeze the soil water and then increased back to thaw it. During this thermal cycle, soil's temperature and volumetric water content were monitored in order to determine the SFCC. The results show that SFCC was strongly dependent on the fines content: at higher fines content, the temperature of spontaneous nucleation was lower and the residual unfrozen volumetric water content was higher.

Introduction

Frozen soil consists of mineral particles, liquid water, ice and gas. It is formed from unfrozen soil during freezing, when a fraction of liquid water solidifies into ice at temperatures sufficiently low below 0 °C [START_REF] Andersland | An Introduction to Frozen Ground Engineering[END_REF]. This phase change causes significant modifications of physical-hydraulic-mechanical properties of soils [START_REF] Andersland | Frozen Ground Engineering[END_REF]. The freezing-thawing process is encountered in cold regions, seasonal cold regions as well as construction works using artificial ground freezing technique. Two main consequences of this process that need to be mentioned are frost heave and thaw settlement. These phenomena can induce damages to infrastructure [3][START_REF] Han | In situ monitoring of frost heave pressure during cross passage construction using ground-freezing method[END_REF][START_REF] Zhang | Analysis of frost heave mechanisms in a highspeed railway embankment[END_REF][START_REF] Yu | Engineering risk analysis in cold regions: State of the art and perspectives[END_REF].

The freezing-thawing process in porous media has been investigated not only in civil engineering and geosciences but also in physics [START_REF] Akyurt | Freezing phenomena in ice-water systems[END_REF][START_REF] Chen | A study of supercooling phenomenon and freezing probability of water inside horizontal cylinders[END_REF][START_REF] Kozlowski | Some factors affecting supercooling and the equilibrium freezing point in soil-water systems[END_REF][START_REF] Kozlowski | Soil freezing point as obtained on melting[END_REF][START_REF] Mishima | The relationship between liquid, supercooled and glassy water[END_REF]. While bulk water melts at 0 °C, water in porous media melts at temperatures below 0 °C because of physical interactions between water and solid particles [START_REF] Enninful | A novel approach for advanced thermoporometry characterization of mesoporous solids: Transition kernels and the serially connected pore model[END_REF][START_REF] Schreiber | Melting and freezing of water in ordered mesoporous silica materials[END_REF][START_REF] Petrov | Curvature-dependent metastability of the solid phase and the freezing-melting hysteresis in pores[END_REF]. Freezing process of a soil sample (where heat is extracted from the sample with a constant rate) can be divided into three steps (as shown in Fig. 1): (i) supercooling with release of sensible heat; (ii) first water freezing with release of latent heat;

(iii) further water freezing with release of sensible heat. In the first step, during cooling (extraction of heat from soil), soil temperature decreases to reach a certain value from that it cannot decrease anymore. This value is called temperature of spontaneous nucleation T sn where the first ice embryo nucleus forms because it attains the critical size [START_REF] Anderson | Undercooling, freezing point depression, and ice nucleation of soil water[END_REF][START_REF] Anderson Dm | Ice nucleation and the substrate-ice interface[END_REF].

Formation of ice crystals releases latent heat and thus increases soil temperature. From T sn , soil temperature increases to reach another value which is called freezing temperature T f , where it remains on a plateau for a while. During this second step, soil water is gradually frozen along with releasing latent heat. After that, within the third step, soil temperature decreases with further water freezing. Freezing temperature T f , also considered to be equal to thawing temperature T t at which soil state changes from frozen to unfrozen, is usually used as a boundary value index to distinguish between frozen soil and unfrozen soil [START_REF] Wan | Experimental study on the freezing temperatures of saline silty soils[END_REF][START_REF] Zhang | Variations of the temperatures and volumetric unfrozen water contents of fine-grained soils during a freezing-thawing process[END_REF][START_REF] Yu | A framework for constructing elasto-plastic constitutive models for frozen and unfrozen soils[END_REF]. These characteristic temperatures (T sn and T f ) were investigated in several studies [START_REF] Anderson | Undercooling, freezing point depression, and ice nucleation of soil water[END_REF][START_REF] Zhang | Variations of the temperatures and volumetric unfrozen water contents of fine-grained soils during a freezing-thawing process[END_REF][START_REF] Ayers | Freezing point of water in a soil as related to salt and moisture contents of the soil[END_REF].

Fig. 1 Freezing process of soil-water system. Soil freezing characteristic curve (SFCC) represents the relationship between the temperature and the quantity of liquid water in soil. It is one of the most essential data in studying the freezing-thawing process in soils. On the one hand, several SFCC models were empirically developed. From SFCC obtained experimentally, empirical models were proposed using power, piecewise or exponential functions [START_REF] He | An analysis of vapour transfer in unsaturated freezing soils[END_REF][START_REF] Teng | A mathematic model for the soil freezing characteristic curve: the roles of adsorption and capillarity[END_REF][START_REF] Anderson | Predicting unfrozen water contents in frozen soils from surface area measurements[END_REF][START_REF] Kozlowski | A semi-empirical model for phase composition of water in claywater systems[END_REF][START_REF] Kozlowski | Unfrozen Water Content in Representative Bentonites of Different Origin Subjected to Cyclic Freezing and Thawing[END_REF][START_REF] Ye | Assessment of radionuclide transport uncertainty in the unsaturated zone of Yucca Mountain[END_REF][START_REF] Ge | Exchange of groundwater and surface-water mediated by permafrost response to seasonal and long term air temperature variation[END_REF][START_REF] Tice | The prediction of unfrozen water contents in frozen soils from liquid limit determinations[END_REF]. On the other hand, SFCC can be derived from soil water characteristic curve (SWCC). This approach is based on the theory of similarity between freezing-thawing and drying-wetting processes that is illustrated by Clapeyron equation [29][30][START_REF] Zhang | Development and Testing of a Frozen Soil Parameterization for Cold Region Studies[END_REF][32][START_REF] Liu | Physically Based Equation for Phase Composition Curve of Frozen Soils[END_REF][START_REF] Zhang | Canopy effect caused by vapour transfer in covered freezing soils[END_REF][START_REF] Zhou | Practical models describing hysteresis behavior of unfrozen water in frozen soil based on similarity analysis[END_REF][START_REF] Sun | A multisurface elastoplastic model for frozen soil[END_REF][START_REF] Kebria | An algorithmic framework for computational estimation of soil freezing characteristic curves[END_REF]. More generally, various physical models were developed based on theory of capillarity, sorption or that of interface pre-melting [START_REF] Watanabe | Amount of unfrozen water in frozen porous media saturated with solution[END_REF][START_REF] Zhou | Application of the Generalized Clapeyron Equation to Freezing Point Depression and Unfrozen Water Content[END_REF][START_REF] Ishizaki | Premelting of ice in porous silica glass[END_REF]. Most of the existing SFCC models consider the effect of fines content but this effect is considered in different ways. For instance, some empirical models used specific surface or liquid limit as input data while physics-based models consider absorption parameters of soil. Due to the diversity of SFCC models, there is no unified standard for choosing SFCC in numerical simulations [START_REF] Bai | Theory and application of a novel soil freezing characteristic curve[END_REF].

In addition, except few models (e.g., [START_REF] Zhou | Practical models describing hysteresis behavior of unfrozen water in frozen soil based on similarity analysis[END_REF]), most of the existing ones consider a unique relationship between unfrozen water content and temperature. However, this relation obtained on the freezing path can differ from that of that of the thawing path; at a given temperature, water content of the freezing path can be higher than at of the thawing path. This hysteresis is usually ignored in the models.

To determine SFCC in the laboratory, a soil specimen is usually subjected to a freeze-thaw cycle, while unfrozen water content is measured. Although controlling specimen's temperature is technically feasible, measuring unfrozen water content is much more challenging. Several methods and techniques have been developed to evaluate the unfrozen water content at negative temperature, including dilatometry [START_REF] Koopmans | Soil freezing and soil water characteristic curves[END_REF][START_REF] Patterson | The measurement of unfrozen water content by time domain reflectometry: results from laboratory tests[END_REF], gas dilatometry [START_REF] Spaans | Examining the use of time domain refiectometry for measuring liquid water content in frozen soil[END_REF], adiabatic calorimetry [START_REF] Anderson | The unfrozen interfacial phase in frozen soil water systems[END_REF][START_REF] Kolaian | Calorimetric determination of unfrozen water in montmorillonite pastes[END_REF], isothermal calorimetry [START_REF] Tice | The prediction of unfrozen water contents in frozen soils from liquid limit determinations[END_REF], differential scanning calorimetry [START_REF] Kozlowski | Soil freezing point as obtained on melting[END_REF][START_REF] Kozlowski | A comprehensive method of determining the soil unfrozen water curves[END_REF][START_REF] Yong | Prediction of Salt Influence on Unfrozen Water Content in Frozen Soils[END_REF], X-ray diffraction [START_REF] Anderson | Migration of interlamellar water during freezing and thawing of Wyoming bentonite[END_REF][START_REF] Anderson | Physics, chemistry, and mechanics of frozen ground: a review[END_REF], time/frequency domain reflectometry (TDR/FDR) [START_REF] Stähli | Measurement of water and solute dynamics in freezing soil columns with time domain reflectometry[END_REF][START_REF] Zhou | Simultaneous measurement of unfrozen water content and ice content in frozen soil using gamma ray attenuation and TDR[END_REF][START_REF] Schafer | Estimating soil-water characteristic curve from soil-freezing characteristic curve for mine waste tailings using time domain reflectometry[END_REF] and pulsed nuclear magnetic resonance (P-NMR) [START_REF] Watanabe | Amount of unfrozen water in frozen porous media saturated with solution[END_REF][START_REF] Tice | Unfrozen water contents of submarine permafrost determined by nuclear magnetic resonance[END_REF][START_REF] Li | Pulsed NMR Measurements of Unfrozen Water Content in Partially Frozen Soil[END_REF]. Among these methods, TDR and P-NMR are the two most common ones. P-NMR is widely acknowledged as a highly accurate and non-destructive technique. However, the equipment required for this technique is generally expensive [START_REF] Yoshikawa | Comparing unfrozen water content measurements of frozen soil using recently developed commercial sensors[END_REF]. Compared to P-NMR, TDR/FDR can be used in the laboratory as well as in the field and it is cheaper, quicker, and more portable. With TDR, unfrozen water content is inferred from the measurement of apparent dielectric constant of soil using an empirical equation [START_REF] Topp | Electromagnetic determination of soil water content: Measurements in coaxial transmission lines[END_REF]58] or dielectric mixing models [START_REF] Stähli | Measurement of water and solute dynamics in freezing soil columns with time domain reflectometry[END_REF][START_REF] Roth | Calibration of time domain reflectometry for water content measurement using a composite dielectric approach[END_REF][START_REF] Watanabe | Measurement of unfrozen water content and relative permittivity of frozen unsaturated soil using NMR and TDR[END_REF]. It is noted that several factors such as temperature or bound water can affect its accuracy.

Several studies have determined SFCC in the laboratory in both freezing and thawing processes [START_REF] Zhang | Variations of the temperatures and volumetric unfrozen water contents of fine-grained soils during a freezing-thawing process[END_REF][START_REF] Ishizaki | Premelting of ice in porous silica glass[END_REF][START_REF] Koopmans | Soil freezing and soil water characteristic curves[END_REF][START_REF] Li | Pulsed NMR Measurements of Unfrozen Water Content in Partially Frozen Soil[END_REF][START_REF] Spaans | The Soil Freezing Characteristic: Its Measurement and Similarity to the Soil Moisture Characteristic[END_REF][START_REF] Bittelli | A thermodielectric analyzer to measure the freezing and moisture characteristic of porous media[END_REF][63][START_REF] Horiguchi | Experimental studies with frozen soil in an "ice sandwich" permeameter[END_REF]. These studies recognized that hysteresis exists in SFCC in which the unfrozen water content is different in thawing and freezing processes at the same temperature. Hysteresis in freezing-thawing process was believed to be similar to that of wetting-drying process. However, the mechanism inducing hysteresis in SFCC is complex and it may be influenced by several effects such as supercooling, pore blocking, capillarity, free energy barriers, contact angles and electrolytes [START_REF] Li | Pulsed NMR Measurements of Unfrozen Water Content in Partially Frozen Soil[END_REF][START_REF] Bittelli | A thermodielectric analyzer to measure the freezing and moisture characteristic of porous media[END_REF]. It is also noted that hysteresis is significant at temperatures between -2 °C and 0 °C [START_REF] Koopmans | Soil freezing and soil water characteristic curves[END_REF][START_REF] Kruse | Adsorbed cation effects on unfrozen water in finegrained frozen soil measured using pulsed nuclear magnetic resonance[END_REF][START_REF] Hu | Review of algorithms and parameterizations to determine unfrozen water content in frozen soil[END_REF] and that it should not be ignored due to impacts on unfrozen water content on frost heaving [START_REF] Hoekstra | Moisture movement in soils under temperature gradients with the cold-side temperature below freezing[END_REF][START_REF] Torrance | Chemical factors in soil freezing and frost heave[END_REF], creep behaviour of frozen soils [START_REF] Arenson | Effects of volumetric ice content and strain rate on shear strength under triaxial conditions for frozen soil samples[END_REF][START_REF] Zhang | Variation behavior of pore-water pressure in warm frozen soil under load and its relation to deformation[END_REF] as well as thermal regime of frozen ground [START_REF] Darrow | Thermal modeling of roadway embankments over permafrost[END_REF].

Beside hysteresis effect, it is found that the shape of SFCC depends also on several factors, including liquid limit [START_REF] Tice | The prediction of unfrozen water contents in frozen soils from liquid limit determinations[END_REF], stress condition [START_REF] Mu | Stress Effects on Soil Freezing Characteristic Curve: Equipment Development and Experimental Results[END_REF], salt content and solute types [START_REF] Watanabe | Amount of unfrozen water in frozen porous media saturated with solution[END_REF][START_REF] Ming | Investigation into Freezing Point Depression in Soil Caused by NaCl Solution[END_REF], initial water content or degree of saturation [START_REF] Suzuki | Dependence of unfrozen water content in unsaturated frozen clay soil on initial soil moisture content[END_REF][START_REF] Wu | Solute and water effects on soil freezing characteristics based on laboratory experiments[END_REF][START_REF] Jia | An NMR-based investigation of pore water freezing process in sandstone[END_REF], types of soil [START_REF] Zhang | Variations of the temperatures and volumetric unfrozen water contents of fine-grained soils during a freezing-thawing process[END_REF][START_REF] Bittelli | A thermodielectric analyzer to measure the freezing and moisture characteristic of porous media[END_REF][START_REF] Kruse | Adsorbed cation effects on unfrozen water in finegrained frozen soil measured using pulsed nuclear magnetic resonance[END_REF], pore-size distribution [START_REF] Li | Pulsed NMR Measurements of Unfrozen Water Content in Partially Frozen Soil[END_REF], and fines content [START_REF] Zhang | Variations of the temperatures and volumetric unfrozen water contents of fine-grained soils during a freezing-thawing process[END_REF][START_REF] Tice | The prediction of unfrozen water contents in frozen soils from liquid limit determinations[END_REF][START_REF] Li | Pulsed NMR Measurements of Unfrozen Water Content in Partially Frozen Soil[END_REF]63]. Among these factors, fines content can influence others (liquid limit, pore-size distribution and types of soil). As far as fines content is concerned, by determining unfrozen water content of several clays, a silt and a gravel, Tice et al. [START_REF] Tice | The prediction of unfrozen water contents in frozen soils from liquid limit determinations[END_REF] observed significantly different unfrozen water contents at the same temperature below 0 °C. Tian et al. [63] carried out tests on three soils corresponding to three clay contents and found that unfrozen water degree of saturation also changed in different ways in both freezing and thawing processes. For soils containing higher clay fraction, unfrozen water degree of saturation was higher at any given temperature below freezing point and the hysteresis loop was smaller. The same findings concerning SFCC were obtained in the study of Zhang et al. [START_REF] Zhang | Variations of the temperatures and volumetric unfrozen water contents of fine-grained soils during a freezing-thawing process[END_REF] on silty clay, and silt and in the study of Li et al. [START_REF] Li | Pulsed NMR Measurements of Unfrozen Water Content in Partially Frozen Soil[END_REF] on silty clay, fine sand, and medium sand. Some other authors also investigated different soils but the effect of fines content was out of their focus [START_REF] Teng | A mathematic model for the soil freezing characteristic curve: the roles of adsorption and capillarity[END_REF]30,[START_REF] Tice | Unfrozen water contents of submarine permafrost determined by nuclear magnetic resonance[END_REF][START_REF] Bittelli | A thermodielectric analyzer to measure the freezing and moisture characteristic of porous media[END_REF].

The present study aims at systematically investigating the effect of fines content on the SFCC of sandy soils. Clean sand was mixed with clay at dry state firstly and water afterward to obtain sandy soils with clay content of 0, 5, 10, 15, and 20% prior to compaction at the Proctor maximum dry density followed by a saturation phase. The specimen's temperature was then decreased progressively to freeze the soil specimen in undrained conditions prior to applying the thawing process. During this freezing-thawing cycle, soil's temperature and unfrozen water content were measured. After the introduction, the second section of this paper presents the materials and experimental methods. Experimental results are presented in the third section, before being discussed in the fourth section.

Materials and experimental methods

Experimental setup

The experimental setup is shown in Fig. 2 and the details of the sensors used are presented in Table 1. Soil specimen was contained in a rigid metallic cylindrical cell (150 mm in height and 150 mm in diameter). The cell was immerged in a temperature-controlled bath (F38-EH JULABO with ±0.03 °C accuracy). Soil temperature was measured with a PT100 sensor, soil volumetric water content was measured with a ML2x Thetaprobe sensor, and soil suction was measured with a tensiometer. As Thetaprobe sensor measures soil apparent dielectric constant ( ) which is the ratio of the dielectric permittivity of a substance to free space, soil unfrozen volumetric water content ( ) was estimated from measured by using empirical equations of Smith and Tice [58] (1) and Topp et al. [START_REF] Topp | Electromagnetic determination of soil water content: Measurements in coaxial transmission lines[END_REF] (2) for frozen and unfrozen states of soil, respectively. Equation ( 2) was used only for the initial state (before the occurrence of freezing) and for the final state where thawing is complete. Equation ( 1) is used where ice is expected to exist in soil (i.e. after the occurrence of freezing and before the completion of thawing).

Table 1: Properties of sensors using in freezing-thawing tests.

Material

Fontainebleau sand was carefully mixed with Speswhite kaolin clay at dry state using an automatic mortar mixer in order to obtain sandy soils with fines content (dry mass of clay divided by dry mass of soil) of 0, 5, 10, 15, and 20%. The physical properties of sand and clay are shown in Table 2 and Table 3, respectively. Fig. 3 presents the grain size distribution of these soils. In this study, the name of each soil corresponds to its clay content (for instance, S10 corresponds to a soil having 10% of clay in dry mass). Prior to the preparation of the soil specimens, each soil was carefully mixed with distilled water using the mortar mixer to obtain optimum water content (determined from the Normal Proctor compaction curves obtained on the same soils [START_REF] Boussaid | Sols intermédiaires pour la modélisation physique : application aux fondations superficielles[END_REF]). Afterward, wet soil was packed in a plastic bag for at least 24 h to ensure the homogenisation of water content, prior to compaction in the cylindrical cell to reach its maximum dry density. Fig. 3 Grain size distribution curves.

Experimental procedure

After soil compaction in the cell, sensors were installed as shown in Fig. 2 and an insulating cover made of expanded polystyrene was placed in order to avoid heat exchange between soil specimen and ambient air. The whole system was then transferred inside the temperaturecontrolled bath. Prior to the freezing-thawing test, soil specimen was saturated by injecting water from the bottom of the specimen during 0.5 to 2 days depending on fines content. After the saturation (when a layer of water of 10 mm was visible on the top of the specimen), the temperature of the bath was first set at a temperature between 0 °C and -1 °C (slightly higher than the expected T sn ). Each test started with the cooling path. The bath temperature was decreased in steps of 0.1 °C to freeze the soil pore water. Once the freezing was triggered, the temperature continued to be decreased in steps of 0.2 °C until -2 °C or -3 °C to observe the change of liquid water content during further cooling. Afterward, during the heating path, the bath temperature was increased in steps of 0.2 °C until 0 °C to thaw the frozen soil. During both cooling and heating paths, the bath temperature was changed to the subsequent step only when soil temperature and volumetric unfrozen water content (measured by the sensors) had reached their equilibrium state. The equilibrium state was considered reached when these two quantities did not change (< 0.05 °C for temperature and < 1% for water content) during at least 2 h.

The test program is shown in Table 4. The test number shows the soil tested (S0 to S20) followed by the number of replicate test (T1 to T4). At least two tests were performed for each soil. Tests T1 were performed following the procedure described above to obtain the complete SFCC curves. For the other tests (T2, T3, T4), only the freezing path of the same procedure was performed in order to replicate the characteristic temperatures.

Experimental results

Typical test (S10-T1)

As an example, the results of test S10-T1 are shown in Fig. 4 where soil temperature, suction, and volumetric unfrozen water content are plotted versus elapsed time for the cooling path. As shown in Fig. 5, when the bath temperature was changed from -1.5 °C to -1.6 °C (at 76 h), soil temperature changed to -1.6 °C after a few minutes. At 77 h, while the bath temperature was still maintained at -1.6 °C, soil temperature increased abruptly to -0.1 °C prior to a progressive decrease and reached the imposed temperature (-1.6 °C) again at 83 h. Soil suction started to increase at 78 h and reached a maximum value of 300 kPa prior to fall down to 100 kPa. At 77 h, soil water content decreased abruptly from 28% to 26% prior to decrease progressively to 3 % at 82 h. These results are representative of a freezing process in soil (Fig. 1) where the phase before 77 h corresponds to the supercooling step. At 77 h, soil water started to freeze: soil temperature increased abruptly because of latent heat release prior to decrease because of heat diffusion toward the liquid surrounding the cell; soil suction increased quickly because of the cryogenic suction induced by ice formation in the pore space (the sudden decrease of suction from 300 kPa to 100 kPa corresponded to the cavitation of the tensiometer, after this moment, the sensor did not provide anymore the real soil suction); volumetric water content decreased because of ice formation. From these typical results, the following parameters were defined to characterise the freezing process (see Figure 5): (i) temperature of spontaneous nucleation, T sn ; (ii) freezing point, T f ; (iii) residual volumetric unfrozen water content, θ r (the value recorded at temperature equal to T sn ) ; (iv) duration of the temperature plateau, t p ; (v) duration of the freezing process, t f .

After the freezing process (from 83 h), decrease of temperature induced slight decrease of volumetric unfrozen water content (see Figure 4) while soil suction measurement was no longer available because of the cavitation of the tensiometer. From the results shown in Fig. 4, Fig. 5 and Fig. 6, volumetric unfrozen water content obtained at the end of each step is plotted versus the corresponding soil temperature for test S10-T1 in Fig. 7. These results correspond to the SFCC of soil S10 obtained from test S10-T1, which include both freezing and thawing paths.

Effects of fines content

SFCC of all soils are shown in Fig. 8 where volumetric unfrozen water content was plotted versus temperature. As the initial volumetric water content (which depends on soil dry density) was different from one soil to the others, it is thus difficult to analyse the effect of fines content from these results. For this reason, volumetric unfrozen water content was used to calculate unfrozen water degree of saturation ( ; where is the volumetric unfrozen water content at saturate state). Fig. 9 shows SFCC of all soils where unfrozen degree of saturation was plotted versus temperature. For each soil, from the initial saturated state, when soil temperature decreased from 0 °C, soil remained saturated with unfrozen water. When temperature reached the temperature of spontaneous nucleation, freezing was triggered inducing significant decrease of unfrozen water degree of saturation. After this step, cooling induced only slight decrease of unfrozen water degree of saturation. During the heating path, unfrozen water degree of saturation increased gradually with temperature and the relationship between these two quantities was significantly different from the cooling path for all soils. In order to quantitatively assess the effects of fines content, temperatures of spontaneous nucleation T sn and freezing point T f were plotted versus fines content (Fig. 10). The results

show that the temperature of freezing point was close to 0 °C for all soils. The results were quite repeatable (with variation less than 0.1 °C) and only a slight trend of decrease of T f when fines content increase could be observed. For T sn , results showed a higher scattering (up to 0.5 °C, except for test at 0% of clay content where this value varied from -0.4 °C to -1.5 °C). In general, T sn is lower at a higher clay content.

Fig. 10 Temperatures of spontaneous nucleation and freezing point versus fines content Fig. 11 shows the residual unfrozen water content θ r (the value determined at a temperature equal to T sn , see Fig. 5) versus fines content. A good repeatability (with a scattering of 0.5 %) could be observed. The results show that residual unfrozen water content was higher at a higher fines content.

Fig. 11 Residual unfrozen water content versus fines content.

Fig. 12 presents the duration of the temperature plateau t p and the duration of the freezing process t f (see the definition on Fig. 5) versus fines content. Results of t p were quite scattering for 0 and 5% of fines content, varying from 0.80 to 4.40 h. They were more repeatable at higher fines contents. A general decrease of this duration when the fines contents increased could be observed. Results of t f varied between 5 and 10 h (except one test, S0-T1 where it was very long, 37.50 h). These results did not show any clear trend.

Table 5 shows the obtained characteristic parameters of all tests for better comparison. Fines content

(%) (°C) (°C) (-) (h) t f (h) S20-T1 20

Discussion

In this study, in order to determine the relationship between unfrozen water content and temperature during a freezing-thawing cycle, large soil specimens (150 mm in height and 150 mm in diameter) were prepared in order to embed several sensors within the soil mass. To minimise thermal and any other gradients, soil temperature was changed by small steps and equilibrium was checked at the end of each step prior the subsequent step. At equilibrium, the soil temperature and unfrozen water content were thus supposed to be homogeneous within the specimen. Similar large soil specimens were equally used in previous studies investigating SFCC with TDR method for measurement of unfrozen water content [START_REF] Zhang | Variations of the temperatures and volumetric unfrozen water contents of fine-grained soils during a freezing-thawing process[END_REF][START_REF] Schafer | Estimating soil-water characteristic curve from soil-freezing characteristic curve for mine waste tailings using time domain reflectometry[END_REF][START_REF] Wu | Solute and water effects on soil freezing characteristics based on laboratory experiments[END_REF]78]. Smaller specimens were used when measurements were performed by pulsed-NMR method [30,63,[START_REF] Ma | Soil freezing and soil water retention characteristics: connection and solute effects[END_REF]. In several previous works, specimens were immerged in a cooling bath with constant cooling rate or at low temperature (between -15 °C and -30 °C) and kept for several hours [START_REF] Wan | Experimental study on the freezing temperatures of saline silty soils[END_REF][START_REF] Ming | Investigation into Freezing Point Depression in Soil Caused by NaCl Solution[END_REF][START_REF] Wan | Study on ice nucleation temperature and water freezing in saline soils[END_REF][START_REF] Bing | Laboratory investigation of the freezing point of saline soil[END_REF]. For determining SFCC, unfrozen water content was measured at various controlled temperatures [START_REF] Zhang | Variations of the temperatures and volumetric unfrozen water contents of fine-grained soils during a freezing-thawing process[END_REF][START_REF] Schafer | Estimating soil-water characteristic curve from soil-freezing characteristic curve for mine waste tailings using time domain reflectometry[END_REF][START_REF] Wu | Solute and water effects on soil freezing characteristics based on laboratory experiments[END_REF][START_REF] Jia | An NMR-based investigation of pore water freezing process in sandstone[END_REF]78,[START_REF] Ma | Soil freezing and soil water retention characteristics: connection and solute effects[END_REF]. The difference between two successive controlled temperatures in these studies varies between 0.3 °C and 5 °C. In the present work, temperature steps of 0.1 °C and 0.2 °C were chosen before the occurrence of freezing phenomenon and afterward, respectively, in order to determine more accurately the freezing point, the temperature of spontaneous nucleation and the SFCC.

The measurement of unfrozen water content in the present study was converted from the measurement of apparent dielectric constant. In this study, under the influence of temperature, dielectric constant of each phase in soils changes, particularly those of water and ice [START_REF] Wraith | Temperature effects on soil bulk dielectric permittivity measured by time domain refiectometry: Experimental evidence and hypothesis development[END_REF][START_REF] Haynes | CRC Handbook of Chemistry and Physics, 97th Editi[END_REF].

Several models exist to estimate moisture content from unfrozen soil apparent dielectric constant [START_REF] Stähli | Measurement of water and solute dynamics in freezing soil columns with time domain reflectometry[END_REF][START_REF] Schafer | Estimating soil-water characteristic curve from soil-freezing characteristic curve for mine waste tailings using time domain reflectometry[END_REF][START_REF] Topp | Electromagnetic determination of soil water content: Measurements in coaxial transmission lines[END_REF][58][START_REF] Roth | Calibration of time domain reflectometry for water content measurement using a composite dielectric approach[END_REF][START_REF] Watanabe | Measurement of unfrozen water content and relative permittivity of frozen unsaturated soil using NMR and TDR[END_REF][START_REF] Birchak | High dielectric constant microwave probes for sensing soil moisture[END_REF][START_REF] He | Application of multiphase dielectric mixing models for understanding the effective dielectric permittivity of frozen soils[END_REF][START_REF] Nagare | Laboratory calibration of time domain reflectometry to determine moisture content in undisturbed peat samples[END_REF]. The most used is Topp's empirical model [START_REF] Topp | Electromagnetic determination of soil water content: Measurements in coaxial transmission lines[END_REF] but it is not compatible with frozen soils [START_REF] Spaans | Examining the use of time domain refiectometry for measuring liquid water content in frozen soil[END_REF]58,[START_REF] Zhou | Simultaneous measurement of unfrozen water content and ice content in frozen soil using gamma ray attenuation and TDR[END_REF]. Otherwise, Smith and Tice Hysteresis of SFCC (difference between the freezing and the thawing curves) is usually attributed to the same factors inducing hysteresis in SWCC, such as the effect of electrolytes, pore geometry, pore blocking, effect of contact angle and change in pore structure [78].

Actually, in a freezing process, increasing solute concentration by forming ice from water increases the effect of electrolyte. Otherwise, forming ice also changes soil skeleton that affects matric potentials of soils. In addition, the hysteric behaviour is also mainly attributed to supercooling of pore water [START_REF] Zhang | Variations of the temperatures and volumetric unfrozen water contents of fine-grained soils during a freezing-thawing process[END_REF][START_REF] Tice | Unfrozen water contents of submarine permafrost determined by nuclear magnetic resonance[END_REF][START_REF] Bittelli | A thermodielectric analyzer to measure the freezing and moisture characteristic of porous media[END_REF]63]. Instead of freezing at 0 °C, pore water is necessarily supercooled at lower temperature. In the present work, an insignificant hysteresis of was observed for all soils below T sn (at frozen state). First, the effect of electrolytes can be ignored. Second, temperature below T sn of -1 °C to -2 °C corresponds to a suction of 1 MPa to 2.5 MPa following the Clapeyron equation. This high range of suction corresponds mainly to water in micropore (intra-aggregates) in the clay matrix where SWCC is also reversible. As a result, hysteresis of SFCC observed in the present work could be contributed mainly to supercooling. After the triggering of freezing, SFCC obtained at temperature lower than T sn were generally reversible (see Fig. 8 & Fig. 9).

Results shown in Fig. 9 demonstrate significant effect of fines content on the thawing path of SFCC; at a given temperature, a higher unfrozen water degree of saturation was obtained at a higher fines content. These results are consistent with the findings of previous works [START_REF] Tice | The prediction of unfrozen water contents in frozen soils from liquid limit determinations[END_REF][START_REF] Li | Pulsed NMR Measurements of Unfrozen Water Content in Partially Frozen Soil[END_REF]63,[START_REF] Zhang | Variation behavior of pore-water pressure in warm frozen soil under load and its relation to deformation[END_REF]. Following these studies, Gibbs-Thompson equation can be used to relate the pore size distribution and the thawing path of SFCC; a lower temperature corresponds to a smaller pore.

In the present work, soil having higher fines content would have a larger volume of micropores (inter-aggregates and intra-aggregates pores) a lower volume of macropores (space between sand particles).

T sn determined in this study can be associated to supercooling. Fig. 10 shows that this parameter generally decreased with an increase of fines content and it was measured with a relatively high scattering. For bulk water, T sn depend on numerous factors such as sample volume, cooling velocity, the presence and concentration of solutes, the presence of solid impurities, effects of external fields (impulse waves, electromagnetic radiation, etc.) [START_REF] Kozlowski | Some factors affecting supercooling and the equilibrium freezing point in soil-water systems[END_REF][START_REF] Fletcher | The chemical physics of ice[END_REF][START_REF] Uzu | On the Freezing of the Droplets of Aqueous Solutions[END_REF]. In the case of soils, additional factors can be soil components and their fractions. Many studies determined T sn of various soils and found that increasing clay content in soils decreases temperature of spontaneous nucleation to lower range [START_REF] Anderson | Undercooling, freezing point depression, and ice nucleation of soil water[END_REF][START_REF] Zhang | Variations of the temperatures and volumetric unfrozen water contents of fine-grained soils during a freezing-thawing process[END_REF]. These studies focused on clays or clay and silt and these results agree with sandy soils in the present study.

It is noted that the supercooling is considered as a necessary phase to activate nucleation process and it appears in both cases, either in free pure water or within the porous volume of soils. Because of the high value of released latent heat, about 334 J/g, which appears during nucleation process, water needs to be supercooled at T sn for equilibrating energy before crystallization. According to Yershov [START_REF] Yershov | General Geocryology[END_REF], T sn is remarked as the temperature at which embryo nuclei form and grow to the critical sizes, about 472 H 2 O corresponding to 10 -26 m 3 .

The relatively high scattering of results obtained in the present work can be thus explained by the random behaviour of the crystallization process. The slight effect of fines content on T sn can be explained by the effect of soil pore size distribution on the supercooling: soil having a higher fines content would have higher volume of micropores, and T sn is generally lower in a smaller pore.

Numerous studies investigated T f and showed that T f depends on many factors such as salt content [START_REF] Ayers | Freezing point of water in a soil as related to salt and moisture contents of the soil[END_REF][START_REF] Ming | Investigation into Freezing Point Depression in Soil Caused by NaCl Solution[END_REF][START_REF] Wan | Study on ice nucleation temperature and water freezing in saline soils[END_REF][START_REF] Banin | Effects of Salt Concentration Changes During Freezing on the Unfrozen Water Content of Porous Materials[END_REF][START_REF] Han | Experiments on the initial freezing point of dispersive saline soil[END_REF], salt types [START_REF] Wan | Experimental study on the freezing temperatures of saline silty soils[END_REF][START_REF] Bing | Laboratory investigation of the freezing point of saline soil[END_REF], initial water content [START_REF] Anderson | Undercooling, freezing point depression, and ice nucleation of soil water[END_REF], soil types [START_REF] Kozlowski | Soil freezing point as obtained on melting[END_REF][START_REF] Zhang | Variations of the temperatures and volumetric unfrozen water contents of fine-grained soils during a freezing-thawing process[END_REF]30,[START_REF] Li | Pulsed NMR Measurements of Unfrozen Water Content in Partially Frozen Soil[END_REF][START_REF] Cannell | Freezing-point depressions in stabilized soil aggregates, synthetic soil, and quartz sand[END_REF][START_REF] Kozlowski | A simple method of obtaining the soil freezing point depression, the unfrozen water content and the pore size distribution curves from the DSC peak maximum temperature[END_REF], etc. In the present study, T f was found close to 0 °C for all soils. This result can be explained by two main reasons: soils were studied at saturated state and fines content is sufficiently low. Bing and Ma [START_REF] Bing | Laboratory investigation of the freezing point of saline soil[END_REF] obtained similar results with saturated sandy soil containing less than 7.5% of clay. Furthermore, freezing point remains constant also above a certain value of water content for all soils [START_REF] Kozlowski | Some factors affecting supercooling and the equilibrium freezing point in soil-water systems[END_REF][START_REF] Bing | Laboratory investigation of the freezing point of saline soil[END_REF][START_REF] Wen | Experimental study on unfrozen water content and soil matric potential of Qinghai-Tibetan silty clay[END_REF]. Actually, for the soils considered in the present study, with relatively low contents of low plasticity kaolin clay, the amount of bound water should be negligible and T f should be similar to that of bulk pure water, i.e. close to 0 °C.

Residual unfrozen content was found higher at a higher fines content (Fig. 11). It is believed that residual unfrozen relates almost directly to the amount of specific surface of soils.

According to several studies [START_REF] Zhang | Variations of the temperatures and volumetric unfrozen water contents of fine-grained soils during a freezing-thawing process[END_REF][START_REF] Tice | The prediction of unfrozen water contents in frozen soils from liquid limit determinations[END_REF]30,[START_REF] Li | Pulsed NMR Measurements of Unfrozen Water Content in Partially Frozen Soil[END_REF]63], unfrozen water content remaining in soils at the same temperature decreased in the following order: clay, silts, sands and gravel.

Following Bing and Ma [START_REF] Bing | Laboratory investigation of the freezing point of saline soil[END_REF], only free water was frozen when freezing is triggered. Unfrozen water should then correspond to bound water. According to Tian et al. [63], the amount of bound water in soils is proportional to the thickness of the electric double layer and specific surface area. In the present study, a higher fines content corresponds to a higher specific surface area and then a higher amount of bound water.

The duration of temperature plateau, t p , would depend then on the amount of latent heat released when freezing is triggered. This amount mainly depends on T sn, as shown in Table 5.

As the results of T sn show significant scattering and a general slight increase when fines content increased (Fig. 10), similar trends were observed with t p (Fig. 12). The duration of the freezing process, t f , which is much longer than t p , correspond to the thermal diffusion of latent heat released during the whole freezing process. This duration would depend thus mainly on the thermal diffusivity of the frozen soil (which at the same time evolves during freezing).

Conclusions

The results obtained in this study show that fines content in sandy soils significantly influenced the soil behaviour under a freezing-thawing cycle. Based on the investigation of five levels of fines content (varying from 0 to 20 %), the following conclusions can be addressed:

-When the temperature decreased from 0°C, freezing was triggered at T sn inducing a sudden decrease of from the saturated state to the residual state. Afterward, continued to decrease but with a lower rate. The subsequent heating induced an increase of (which represents a progressive melting of frozen water).

-The thawing path of SFCC was strongly dependent on the fines content; at a given temperature, a higher was observed for a higher fines content.

-T sn was higher at a higher fines content and varied between -1.0 °C and -2.0 °C.

-T f varied between 0°C and -0.2 °C, only a slight decrease of T f with an increase of fines content was observed.

-(varied from 1 % to 7 %) was higher at a higher fines content.

-t p was found scattering and slightly decreased when fines content increased.

-t f was found independent of fines content.

The findings of the present study would be helpful to predict the soil behaviour under freezing-thawing process. That would imply several applications in cold regions and also in geotechnical engineering ground improvement by artificial ground freezing.

Fig. 2

 2 Fig. 2 Schematic view of the experimental setup. (1) Temperature-controlled bath; (2) Soil specimen; (3) Temperature controlling system; (4) Temperature-controlled liquid (30% ethylene glycol + 70% water); (5) Metallic cylindrical cell; (6) Insulating cover; (7) Temperature sensor; (8) Tensiometer; (9) Soil water sensor; (10) Thermal conductivity probe (results are not presented in this study); (11) Data logger system.

From - 1 Fig. 4

 14 Fig. 4 Soil temperature, volumetric unfrozen water content and suction versus elapsed time during the cooling path of test S10-T1.

Fig. 5

 5 Fig. 5 Soil temperature, volumetric unfrozen water content and suction versus elapsed time during the freezing process of test S10-T1 (detailed view from 70h to 86 h).

Fig. 6

 6 Fig.6shows the results of test S10-T1 during the heating path. During this path, temperature was increased by steps of 0.2 °C from -2.8 °C to 0 °C. It induced thawing of frozen water (corresponding to a gradual increase of unfrozen water content).

Fig. 6

 6 Fig. 6 Soil temperature and volumetric unfrozen water content versus elapsed time during the heating path of test S10-T1.

Fig. 7

 7 Fig. 7 Soil freezing characteristic curve determined from test S10-T1.

Fig. 8

 8 Fig. 8 Soil freezing characteristic curve (volumetric unfrozen water content versus temperature) for all soils.

Fig. 9

 9 Fig. 9 Soil freezing characteristic curve (unfrozen water degree of saturation versus temperature) for all soils.

Fig. 12

 12 Fig. 12 Duration of the temperature plateau and duration of the freezing process versus fines 284 content. 285

  [58] proposed a model based on comparison of unfrozen water content measured from NMR and TDR methods for 25 soils covering a wide range of specific surface areas. For this reason, in the present work, the model of Smith and Tice[58], which provides an accuracy of ±3% compared to measurements from NMR method, was used for frozen soils.

Table 2 .

 2 Physical properties of sand.

	Property

Table 3 :

 3 Physical properties of clay.

	Property

Particle diameter < 0.002 mm (%) 79 Particle diameter > 0.01 mm (%) 0.5 Maximum dry density, ρ d,max (Mg/m 3

) 1.45

Table 4 :

 4 Physical properties of soils.

	Test No.	Fines content	Dry	Porosity	Test duration
		(%)	density	(-)
			(Mg/m 3 )		(h)
	S20-T1	20	1.98	0.25	754
	S20-T2	20	1.96	0.26	26
	S15-T1	15	1.99	0.25	712
	S15-T2	15	2.00	0.25	64
	S10-T1	10	1.91	0.28	590
	S10-T2	10	1.90	0.28	153
	S5-T1	5	1.78	0.33	817
	S5-T2	5	1.78	0.33	143
	S5-T3	5	1.78	0.33	190
	S0-T1	0	1.67	0.37	756
	S0-T2	0	1.67	0.37	286
	S0-T3	0	1.67	0.37	75
	S0-T4	0	1.68	0.37	187

Data availability

The datasets generated during and/or analysed during the current study are available from the corresponding author on reasonable request.

Funding and Competing interests

No funding was received for conducting this study.

The authors have no competing interests to declare that are relevant to the content of this article.