Huaibo Song
email: songhuaibo@mail.dlut.edu.cn

Huafu Pei
email: huafupei@dlut.edu.cn

Jean-Michel Pereira
email: jean-michel.pereira@enpc.fr

Anh Minh Tang

Chao Zhou
email: zhou@polyu.edu.hk

MSc Ph D Student

A simple load transfer method for energy pile groups

Keywords: load transfer method, energy pile group, thermomechanical behavior, geothermal energy

Various analysis methods have been developed to simulate the performance of energy pile groups subjected to thermal and mechanical loads. Although they considered the interactions between piles in the group, the 'sheltering-reinforcing' effect was usually ignored during the analysis, or the methods were not experimentally validated. Therefore, to address this gap, we propose an experimentally validated load transfer model that considers the 'shelteringreinforcing' effect for the thermomechanical analysis of energy pile groups. The proposed method modeled two well-documented full-scale field tests and two finite-element simulation cases. The comparison results showed that the proposed method could capture several essential aspects of the energy pile group, including thermally induced strain, stress, displacement, and group effects. Furthermore, a parametric analysis was performed to evaluate the effects of relevant parameters on the thermomechanical behavior of the energy pile group.

Introduction

Energy piles are environment-friendly technologies that have attracted increasing attention

Revised Manuscript (Clean Version) because of their effective solicitation of shallow geothermal energy [START_REF] Rotta Loria | Thermally induced deformation of soils: A critical overview of phenomena, challenges and opportunities[END_REF]. Unlike conventional pile foundations, the operation of an energy pile involves complex coupling between thermal, mechanical, and other physical fields (Bourne-Webb and Bodas Freitas 2020). It is also necessary to consider pile-pile and pile-slab interactions under thermalmechanical loading for energy pile groups [START_REF] Moradshahi | Effect of nearby piles and soil properties on the thermal behaviour of a field-scale energy pile[END_REF], Ravera et al. 2020a, 2020b[START_REF] Fang | Group Performance of Energy Piles under Cyclic and Variable Thermal Loading[END_REF]. Recently, understanding this complex mechanism, seeking simple approaches to describe it, and then applying it to the engineering design of energy piles has become a hot topic in energy pile research.

Numerous in situ field tests [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] Murphy | Evaluation of thermo-mechanical and thermal behavior of full-scale energy foundations[END_REF][START_REF] Faizal | Axial and radial thermal responses of energy pile under six storey residential building[END_REF], Sutman et al. 2019a, Fang et al. 2020, 2022[START_REF] Wu | Interactions of an Energy Pile with Several Traditional Piles in a Row[END_REF], 2021), small-scale laboratory model tests [START_REF] Kalantidou | Preliminary study on the mechanical behaviour of heat exchanger pile in physical model[END_REF], Yavari et al. 2016a, Yazdani et al. 2019b, Kong et al. 2020[START_REF] Song | Performance study of energy piles in different climatic conditions by using multi-sensor technologies[END_REF], and centrifuge model tests [START_REF] Ng | Centrifuge modelling of heating effects on energy pile performance in saturated sand[END_REF], 2016, 2021[START_REF] Ng | Energy pile group subjected to non-symmetrical cyclic thermal loading in centrifuge[END_REF] have been conducted to investigate the thermomechanical behavior of energy pile and pile groups. It is impractical to use experimental methods to comprehensively investigate the effects of all the factors on the performance of energy piles considering the enormous time-consuming and financial expense. Thus, the development of experimentally verified numerical methods to supplement the experimental methods is necessary to thoroughly study the thermomechanical mechanisms of energy piles. Various numerical approaches with different complexities have been used in previous years, including finite element models [START_REF] Yavari | A simple method for numerical modelling of mechanical behaviour of an energy pile[END_REF][START_REF] Rammal | Impact of thermal solicitations on the design of energy piles[END_REF], Garbellini and Laloui 2019a[START_REF] Nguyen | Long-term thermomechanical behaviour of energy piles in clay[END_REF][START_REF] Arzanfudi | A thermo-hydromechanical model for energy piles under cyclic thermal loading[END_REF][START_REF] Georgiadis | Heating and cooling induced stresses and displacements in heat exchanger piles in sand[END_REF], Sutman et al. 2020), finite difference models [START_REF] Suryatriyastuti | Understanding the temperatureinduced mechanical behaviour of energy pile foundations[END_REF], 2014[START_REF] Luo | Probabilistic design model for energy piles considering soil spatial variability[END_REF][START_REF] Najma | Incremental load transfer analysis of an energy pile under arbitrary mechanical and thermal loads[END_REF], Liu et al. 2022), and other theoretical models [START_REF] Rotta Loria | The interaction factor method for energy pile groups[END_REF], 2017a, Rotta Loria et al. 2018, 2020a, Garbellini and Laloui 2019a[START_REF] Iodice | Analytical Solutions for Ultimate Limit State Design of Thermal Piles[END_REF][START_REF] Iodice | A practical method to design thermally stressed piles[END_REF], Ravera et al. 2020a, 2020b[START_REF] Cui | Analytical solution for longitudinal vibration of a floating pile in saturated porous media based on a fictitious saturated soil pile model[END_REF][START_REF] Rashk | Analytical Solutions for Thermomechanical Soil-Structure Interaction in Single Semifloating Energy Piles Embedded in a Layered Soil Profile[END_REF], Liu et al. 2022, Song et al. 2022, Song and Pei 2022, Pei et al. 2022a). Among these, the load transfer method is commonly used for energy pile design because it overcomes the drawbacks of high time consumption, high computational cost, and high requirements of the complete numerical simulation method. The load transfer method is very user-friendly and well-suited for the engineering design of energy piles.

The load transfer method was initially proposed by Seed and Reese [START_REF] Seed | The action of soft clay along friction piles[END_REF] and then gradually applied to investigate the thermomechanical response of an isolated energy pile. For example, [START_REF] Knellwolf | Geotechnical Analysis of Heat Exchanger Piles[END_REF] developed a load transfer method using the threepolyline load transfer curve proposed by Frank and Zhao (1982). In situ isolated energy piles were modeled, and their thermomechanical behavior was analyzed. The comparison results between the simulations and the measured data showed good agreement. Sutman et al. (2019b) developed a model by incorporating the unloading-reloading response into the load transfer curve and validated it through field test results. The above studies demonstrate the applicability of the load transfer method for studying the thermomechanical response of an isolated energy pile. As an essential part of the energy pile group, the successful application of the single pile response model lays the foundation for developing a pile group response model.

Recently, several studies (Ravera et al. 2020a[START_REF] Fei | Analysis of energy pile groups subjected to nonuniform thermal loadings[END_REF], Liu et al. 2022) extended the load-transfer method to consider the thermomechanical interaction of energy piles in groups. Ravera et al. (2020a) modified the load transfer curve of an isolated energy pile in a group using a displacement factor that considered group effects. The field test results of an energy pile group consisting of four energy piles were used to validate the proposed method. A comparison between the simulated and measured results showed the suitability of the proposed method for analyzing the thermomechanical performance of the energy pile group. Nevertheless, it should be noted that the determination of the displacement factor is based on an empirical formula, which is proposed based on the fitting of the finite-difference modeling results of the 5×5 pile group [START_REF] Comodromos | Contribution to the design methodologies of piled raft foundations under combined loadings[END_REF]. A significant difficulty in applying this empirical formula to the analysis of the energy pile group is that the effect of the temperature on displacement factor cannot be considered. Thus, additional experiments or numerical simulations are required for specific analysis cases to comprehensively determine the appropriate displacement factors.

Besides, the load transfer method proposed by Ravera et al. (2020a) has some limitations in clarifying the thermomechanical behavior of energy pile groups because it cannot take into account the 'sheltering-reinforcing' effects of the energy pile group into consideration.

The 'sheltering-reinforcing' effects characterize the interaction between piles in groups and are considered in previous studies of conventional pile groups [START_REF] Mylonakis | Settlement and additional internal forces of grouped piles in layered soil[END_REF]Gazetas 1998, Wang et al. 2016). The results indicated that the calculated pile head displacement was overestimated without considering this effect, and the error increased significantly with increasing group size. For the energy pile group, the 'sheltering-reinforcing' effects act throughout thermomechanical loading, which can be observed in the field test results (Rotta Loria and Laloui 2017b, 2018, Fang et al. 2020). [START_REF] Liu | A simple method for analyzing thermomechanical response of an energy pile in a group[END_REF] proposed a load transfer method to rapidly calculate the response of an energy pile group in which they considered the reinforcing effect of neighboring piles in the group. The applicability of this method to pile groups was verified by comparing it with finite element simulations that did not consider the nonlinear pile-soil interaction (Rotta Loria and Laloui 2016). Nevertheless, the presence of the slab and the pile-slab-soil interaction had not been considered in their study, which would limit the scope of application of the method due to the importance of the slab in the energy pile group.

Besides, there is no adequate verification of whether the proposed model can accurately calculate the critical aspects of the thermomechanical responses of the energy pile group, including the pile axial strain, stress, and pile head displacement. Therefore, to address this gap, it is necessary to develop an experimentally validated model. This study aims to provide an experimentally validated simple load transfer model that considers the 'sheltering-reinforcing' effects for thermomechanical analysis of energy pile groups. Section 2 details the proposed model and the developed thermomechanical performance analysis algorithm for energy pile groups based on the proposed model. Section 3 verifies the results obtained by the proposed method using field tests and finite element simulations. A comprehensive sensitivity analysis of the parameters involved in the proposed model is presented in Section 4. Finally, conclusions are presented in Section 5.

Development of the load transfer model for the energy pile group

Some assumptions of the load transfer mechanism for energy piles are employed in this study: (1) the load-displacement relationship (i.e., t-z model) and pile and soil properties are assumed to be independent of temperature variations, based on the fact that previous studies suggested that the effect of temperature within the range of 5 -40 ℃ on soil and concrete properties is insignificant (Yavari et al. 2016b, Yazdani et al. 2019a[START_REF] Rotta Loria | Thermally induced deformation of soils: A critical overview of phenomena, challenges and opportunities[END_REF]; (2) the strain and stress analysis of the energy pile in the group is achieved by considering the pile-to-pile interaction in the pile group; (3) the interaction between the slab, energy piles in the group, and soil can be considered through assuming an additional spring connecting with the pile heads; (4) The influence of the axial deformation of the piles on the thermomechanical behavior of the piles is mainly considered in the study to simplify the calculation (Ravera et al. 2020a). The last assumption is based on the fact that a numerical study of energy piles [START_REF] Olgun | Thermo-mechanical radial expansion of heat exchanger piles and possible effects on contact pressures at pile-soil interface[END_REF]) and full-scale field studies [START_REF] Faizal | Axial and radial thermal responses of energy pile under six storey residential building[END_REF]) reported that the normal contact stress of the piles did not change significantly owing to their radial thermal expansion of the energy piles. Other studies on the load transfer analysis [START_REF] Knellwolf | Geotechnical Analysis of Heat Exchanger Piles[END_REF][START_REF] Chen | Parameters for Load Transfer Analysis of Energy Piles in Uniform Nonplastic Soils[END_REF] have also confirmed that the influence of radial deformation on the pile-soil axial interaction is negligible. Therefore, the present study did not consider the influence of the radial deformation of the energy pile.

Load transfer function at the shaft of the isolated energy pile

According to a previous study [START_REF] Lee | A simplified nonlinear approach for pile group settlement analysis in multilayered soils[END_REF], the nonlinear performance of the pile load displacement is divided into (i) the nonlinear relationship between the pile shaft shear stress and pile-soil relative displacement and (ii) the nonlinear stress-strain relationship of the surrounding soil induced by the pile shaft shear stress. [START_REF] Caputo | Pile foundation analysis: a simple approach to nonlinerity effects[END_REF] and [START_REF] Trochanis | Three-dimensional nonlinear study of piles[END_REF] divided surrounding soil into disturbed and undisturbed zones. The disturbed zone is a thin layer of soil on the soil/pile interface. The nonlinearity of the pile-soil interaction was concentrated in this interface. The area outside the interface is the undisturbed zone. Because this zone is subjected to a relatively low stress change, the stress-strain behavior of the soil is mainly elastic. The nonlinear response of pile groups primarily depends on the nonlinear characteristics of single piles, and the pile-pile interaction is elastic. The total shaft displacement at a certain depth (i.e., u) can be divided into pile-soil relative displacement (i.e., p) and the elastic displacement of the surrounding soil (i.e., s).Recently, these concept has been introduced into the thermomechanical analysis of energy pile group [START_REF] Fei | A simplified method for geotechnical analysis of energy pile groups[END_REF], Liu et al. 2022). As suggested by [START_REF] Lee | A simplified nonlinear approach for pile group settlement analysis in multilayered soils[END_REF], the thickness of the interface was assumed to be zero, which can provide a simplified mathematical processing method for simulating the pilesoil relative displacement and elastic displacement of the soil around the pile. Thus, the total pile shaft displacement can be expressed as follows:

u p s   (1)
The elastic soil displacement induced by pile shaft stress can be calculated using the expression proposed by Randolph and Worth (1978):

0 0 = ln = m r r s G r   (2)
where 𝐺 is the shear modulus of the soil, 𝑟 0 is the pile radius, 𝑟 𝑚 is the shear influence radius.

In this study, an exponential model was employed to calculate the pile-soil relative displacement of the pile-soil interface because it can better simulate the field test results without adopting complex fitting parameters [START_REF] Kezdi | Bearing Capacity of Piles and Pile Groups[END_REF]. The exponential model is expressed as

follows: max = 1 exp s u u G p                    ( 3
)
where τ is the pile shaft shear stress, 𝜏 𝑢 is the ultimate shear stress, 𝐺 𝑠,𝑚𝑎𝑥 is the initial stiffness of the pile-soil interface, the unit of which is kPa/m.

It should be noted that the deformation mechanisms of energy piles and conventional piles differ. For the energy pile, when the pile body is heated up, it expands, the upper part of the pile side friction decreases, and it is in the unloading stage. In contrast, the shaft shear stress at the lower end of the pile side increases and is in a loading state. When the pile body is cooled, it shrinks, and the situation is the opposite of that during heating. Therefore, Eq. (3) should be improved for the thermomechanical analysis of the energy pile. We developed a model by employing the improved Masing rule to simulate the loading-unloading-reloading path of the pile-soil interaction, and its expression can be written as Eq. ( 4). Further details can be found in (Pei et al. 2022b).

    ,max 0 0 0 0 1 exp s u u G p p                              ( 4
)
where 𝜂 denotes the loading and unloading branching judgment factor, 𝜂 = -1 and 𝜂 = 1 represent unloading and reloading conditions, respectively, 𝑝 0 denotes the relative displacement of the pile and soil corresponding to the stress reverse point, 𝜏 0 is the pile shaft stress corresponding to the stress reversal point. When 𝑝 0 and 𝜏 0 are equal to zero, Eq.( 4)

degenerates to the expression of the initial loading curve.

Substituting Eqs. ( 2) and (4) into Eq. ( 1), the total pile shaft displacement at a given depth can be expressed as Eq. ( 5):

  0 0 0 max 0 ln 1 u s u u p s p G                           (5)
where 𝑝 0 = 𝑢 0 -𝑠 0 = 𝑢 0 -𝜓𝜏 0 , and 𝑢 0 denotes the total shaft displacement of the pile corresponding to the shaft shear stress reversal point. Thus, Eq. ( 5) can be expressed using Eq.

(4), which is the load transfer function used to simulate the relationship between the pile shaft resistance and the relative pile-soil displacement.

    0 0 0 0 max 0 ln 1 u s u u u G                            (6)

Group interaction for energy piles considering 'sheltering-reinforcing' effect

As discussed in the previous section, the pile-soil-pile interaction in the pile group can be considered as linearly elastic and suitable for the principle of superposition. According to previous studies [START_REF] Randolph | An analysis of the vertical deformation of pile groups[END_REF], for the two energy piles system (𝑖 and 𝑗 ) subjected to thermomechanical loading, the vertical elastic displacement of the pile 𝑖 can be divided into three parts: (i) the displacement (𝑠 𝑖0 ) induced by its own load; (ii) the displacement (∆𝑠 𝑖0 ) induced by the 'sheltering-reinforcing' effect of pile 𝑗; (iii) the additional displacement (𝑠 𝑖𝑗 ) caused by 𝑗 pile under its own load. If the 'sheltering-reinforcing' effect is not considered, the total elastic displacement of 𝑖 pile can be written as follows:

0 i i i j s s s   (7)
In the proposed method, we consider the 'sheltering-reinforcing' effect. Therefore, the total elastic displacement of 𝑖 pile can be written as follows:

0 0 i i i i j s s s s    (8)
According to the formulation proposed by Randolph and Worth (1978), 𝑠 𝑖0 can be calculated as follows:

0 0 0 = ln si m i r r s G r  (9)
The shear stress of pile 𝑖 transferred to the side of pile 𝑗 can be expressed as follows: 0 0 , ( )

sij sji aij m aij r r s r s      (10)
where 𝑠 𝑎𝑖𝑗 denotes the distance between the axes of two piles. Considering the 'shelteringreinforcing' effects of pile 𝑗 on pile 𝑖, ∆𝑠 𝑖0 can be obtained by:

0 0 0 0 = ln ln sji sij m m i aij aij aij r r r r r s G s s G s     (11)
If the existence of pile 𝑗 is not considered, then the displacement at the position of pile 𝑗 caused by pile 𝑖 under its own load is:

0 0 0 = ln ,( ) sji m ji aij m aij r r s r s r G s    (12)
In addition, the shear stress transferred from pile 𝑖 to the side of pile 𝑗 (i.e., 𝜏 𝑠𝑖𝑗 ) reduces the displacement of pile 𝑗 as follows:

0 0 0 0 0 0 = ln ln sji sji m m ji aij r r r r r s G r s G r     (13)
Therefore, the additional displacement of pile 𝑗 induced by the load of pile 𝑖 can be expressed as follows:

0 0 0 0 0 ln ln sji m m ji ji ji aij aij r r r r s s s G s s r              (14)
According to the assumption that 𝜏 𝑠𝑖𝑗 = 𝜏 𝑠𝑗𝑖 = 𝜏 𝑠𝑖 [START_REF] Zhang | Simplified non-linear approaches for response of a single pile and pile groups considering progressive deformation of pile-soil system[END_REF], the additional elastic displacement of pile 𝑖 caused by the load of pile 𝑗 is equal to the additional elastic displacement of pile 𝑗 caused by the load of pile 𝑖, that is:

0 0 0 ln ln si m m ij ji aij aij r r r r s s G s s r             (15)
Thus, for a two-pile system, the total elastic displacement of pile 𝑖 can be obtained as follows:

0 0 0 0 0 0 0 ln ln ln ln si m m m m i i i i j aij aij aij aij r r r r r r r s s s s G r s s s s r                 (16)
For a group of 𝑛 piles, the total elastic displacement of pile 𝑖 can be calculated as follows:

  0 0 0 0 0 1, 1, 0 0 ln ln ln ln n n si m m m m i i i ij j j i j j i aij aij aij aij r r r r r r r s s s s G r s s s s r                                (17)
Therefore, the total shaft displacement of the energy pile 𝑖 is:

    0 0 0 0 max 0 = l n 1 u s i si s u u p s u G                              (18)
where 𝜓 , is the pile-pile interaction parameter, which can be written as follows:

0 0 0 1, 0 0 ln ln ln ln n m m m m j j i aij aij aij aij r r r r r r r G r s s s s r                          (19)

Load transfer function at the base of energy pile group

Similar to the definition of the pile-side displacement, the displacement at the pile end is the sum of the pile-soil relative displacement (i.e., 𝑝 𝑝 ) and the elastic displacement of the soil at the pile tip (i.e., 𝑠 𝑝 ). It can be written as

p p p u p s   (20)
The pile-soil relative displacement can be simulated using an exponential model (Liu et al., 2022), which can be calculated as follows:

max = 1 exp p p up p up G p                      (21)
where 𝜎 𝑝 is the pile tip resistance, 𝐺 𝑝𝑚𝑎𝑥 is the initial stiffness of the pile tip-soil interface;

𝜎 𝑢𝑝 is the ultimate pile tip resistance.

According to the improved Masing rule (Pei et al. 2022), the load transfer function for simulate the loading-unloading-reloading path of the pile-soil interaction at the pile tip can be written as

    max 0 0 0 0 1 exp p p p up p p p up p G p p                                (22)
Thus, the pile-soil relative displacement of the energy pile tip can be written as

  0 0 0 max 0 ln 1 p p u p p p p p pu p p p G                       (23)
where 𝜅 denotes the loading and unloading branching judgment factor, 𝜅 = -1 and 𝜅 = 1 represent unloading and reloading conditions, respectively, 𝑝 𝑝0 denotes the relative displacement of the pile tip and soil corresponding to the stress reversal point, 𝜎 𝑝0 is the pile tip resistance corresponding to the stress reversal point. When 𝑝 𝑝0 and 𝜎 𝑝0 equal zero, Eq. ( 22) degenerates to the expression for the initial loading curve.

According to [START_REF] Randolph | An analysis of the vertical deformation of pile groups[END_REF], the elastic vertical displacement of the soil induced by the pile tip resistance can be obtained as

  0 1 4 p p p soil r s G        ( 24
)
where λ is the model parameter. According to the studies in [START_REF] Lin | Interaction coefficients method for calculating piles group settlements considering reinforcing and restraining effect[END_REF], the pile-pile interaction at the pile tip is insignificant. Therefore, the total displacement of the pile tip can be expressed as follows:

  0 0 0 max 0 ln 1 p p u p p p p p p p p pu p u p s p G                           (25)
where 𝑝 𝑝0 = 𝑢 𝑝0 -𝑠 𝑝0 = 𝑢 𝑝0 -𝜆𝜎 𝑝0 , and 𝑢 𝑝0 denotes the total displacement of the pile tip corresponding to the pile tip resistance reversal point. Thus, Eq.( 25) can be expressed as Eq.( 26), which is the load-transfer function used to simulate the relationship between the pile tip resistance and the relative pile tip-soil displacement.

    0 0 0 0 max 0 ln 1 p p u p p p p p p p pu p u u G                            (26)

Pile-slab-soil interaction for the energy pile group

The pile-slab-soil interaction of the energy pile group is simulated using a spring linked to the pile head during the load transfer method, as adopted by [START_REF] Knellwolf | Geotechnical Analysis of Heat Exchanger Piles[END_REF]Ravera et al. (2020a). The spring stiffness is calculated by [START_REF] Randolph | Design methods for pile groups and piled rafts[END_REF][START_REF] Selvadurai | Elastic analysis of soil-foundation interaction[END_REF])

  2 0 1 s s l a b s l a b h s E B L k     (27)
where 𝐸 𝑠 is Young's modulus of the soil; 𝜈 𝑠 is Poisson's ratio of the ssoil; 𝐿 𝑠𝑙𝑎𝑏 and 𝐵 𝑠𝑙𝑎𝑏 are the length and width of the slab, respectively; and 𝜌 0 is a coefficient, which can be evaluated from the dimensions of the slab (Ravera et al. 2020a).

Parameters determination

As shown in Fig. 1, the proposed model has four parameters that are calculated as follows:

(1) Ultimate shaft resistance 𝜏 𝑢

The ultimate shear stress is the stress corresponding to the asymptote of the stress-strain curve, which is obtained by laboratory interface shear tests. If the test data are not available, the ultimate shear stress can be calculated as follows:

  s 1 sin tan u s z        (28)
where 𝜎′ 𝑧 is the effective overburden pressure, 𝜎′ 𝑧 = 𝛾 , 𝑧 for the homogeneous soil and

𝜎′ 𝑧 = ∑ 𝛾 𝑖 , 𝑧 𝑖 𝑛 𝑖=1
for the layered soil, where 𝛾 , is the effective weight of the soil. 𝛿 𝑠 is the friction angle of the pile-soil interface, which can be expressed by the soil friction angle (𝜑 s )

as 𝛿 𝑠 = 𝑡𝑎𝑛 -1 𝑠𝑖𝑛𝜑 s 𝑐𝑜𝑠𝜑 s 1+𝑠𝑖𝑛 2 𝜑 s (Pei et al. 2022b).

(2) Initial stiffness of the pile-soil interface 𝐺 𝑠𝑚𝑎𝑥 According to Randolph and Worth (1978), 𝐺 𝑠𝑚𝑎𝑥 can be obtained as follows:

smax 2 2 ln s m G G r D D  ( 29
)
where 𝐺 𝑠 is the soil shear modulus and 𝑟 𝑚 is the shear influence radius, which is related to the pile length and soil layer distribution. The value of the shear influence radius increases with increasing soil depth. It can be expressed by:

  s 2 1 m r L     ( 30
)
where δ is the soil shear modulus ratio, ν 𝑠 is the Poisson's ratio of the soil, L is the pile length. For homogeneous soils, the soil shear modulus ratio can be calculated as

δ = 𝐺𝐿 2 𝐺 𝐿 ⁄ ,
where 𝐺𝐿 2 and 𝐺 𝐿 are the soil shear modulus at the middle and tip of the pile, respectively.

For multilayered nonhomogeneous soils, the soil shear modulus ratio can be calculated as δ = ∫ 𝐺 𝑖𝑧 𝑑𝑧 𝐺 𝐿 𝐿 ⁄ according to [START_REF] Lee | Pile groups under negative skin friction[END_REF], in which 𝐺 𝑖𝑧 is the shear modulus of the soil layer and 𝑧 is the soil depth. According to [START_REF] Wong | Negative skin friction on piles in layered soil deposits[END_REF], the shear influence radius should adopt a value in the range of 0.5-2.5L when the length-to-diameter ratio of the pile falls within the range of 20-100.

( The initial shear stiffness of the pile tip, which can be calculated as 𝐺 𝑝𝑚𝑎𝑥 = 4𝐺 𝑠 𝜋𝑟 0 (1 -𝜈 𝑠 ) ⁄ .

Fig. 1 Steps of calculation for the determination of model parameters

Implementation for thermomechanical analysis of an energy pile group

Approaches such as the one-dimensional element and finite difference methods can implement the proposed load transfer model. Song and Pei (2022) improved the finitedifference method proposed by [START_REF] Chen | Parameters for Load Transfer Analysis of Energy Piles in Uniform Nonplastic Soils[END_REF], which was divided into mechanical and thermomechanical analyses, as shown in Fig. 2. During the mechanical analysis, the temperature change is set to zero and the pile is subjected to the mechanical load only.

Besides, no constraint is applied to the pile head since the pile only moves downwards caused by the mechanical load. The mechanical response could be obtained through an iterative procedure.

When the energy pile is subjected to heating/cooling, the pile expands or contracts, a null point (NP) is defined as the position below and above which the pile has opposite displacements.

In the thermomechanical analysis stage, the position of the NP should be assumed first, and then the element number above and below the NP should be determined. The displacement calculation of the element below the NP starts from the NP+1 element. Since the displacement of NP caused by the thermal load is zero, the initial displacement of this element is the displacement under the mechanical load. Taking this as the initial element, one iteratively calculates the displacement of all pile elements below the NP and calculates the stress of each element from the pile bottom element upward based on the displacement. The displacement and stress calculation methods for elements above the NP are similar to those below the NP.

The difference is that the stress is calculated sequentially from the downward pile head element. parameters for the present study were extracted from [START_REF] Guo | Investigation on the thermomechanical behavior of free constrained full-scale PHC energy pile in multi-layer strata[END_REF] and are shown in Table 1. The pile was continuously heated for 168 h at an average power of 3.44 kW. In this study, the heating durations of 24, 72, 96, and 168 h are selected to be modeled, corresponding to the pile temperature variations of 11.1, 13.2, 16.6, and 19.3 ℃. No mechanical load was imposed on the pile head during testing, thus the change in pile stress was caused by the thermal load only. In addition, the contact stiffness between the pile head and superstructure was not considered in this case study because there were no structural constraints on the top of the pile. Fig. 4 shows the thermally induced pile axial stresses obtained from the experiments and the model used in this study. A close agreement between the measured and computed values for all the heating steps is observed. The computed thermal stress meaningfully yields a value of zero at the pile head, which reflects the absence of restraint provided by any structural elements.

The thermal stress increases with the pile depth and decreases again towards the pile tip.

Differences between the simulations and measurements along the pile in the first two soil layers can be found. The reason may be attributed to the significant variations of the ultimate skin friction of the first three soil layers, i.e., 37.82, 12.4 and 106.4 kPa for the first, second and third soil layers, respectively. As the temperature change increases, the second layer of soil needs to mobilize more friction than under lower temperature changes to resist the significantly increased relative pile-soil displacement. Even the third soil layer may mobilize more friction when the second soil layer is incapable of providing enough friction to reach the limit equilibrium, which would induce the stress redistribution along the pile depth and thus explains the variation of the thermal stress of the pile body in the second layer of soil. A similar phenomenon can also be found in previous studies (Rotta Loria and Laloui 2018, [START_REF] Fang | Thermomechanical Behavior of Energy Piles and Interactions within Energy Pile-Raft Foundations[END_REF].

Tests of an energy pile group

The analysis case was a full-scale field test of a pile group consisting of four energy piles, as reported by [START_REF] Mimouni | Behaviour of a group of energy piles[END_REF] and Rotta Loria and Laloui (2017Laloui ( , 2018)). The energy piles (EP) have a diameter of 0.9 m and a length of 28 m; their arrangement is shown in Fig. 6a. The pile group joint has a slab of 26 m long, 0.9 m thick, and 10 m wide. The piles were placed in five soil layers as shown in Fig 6b . The top layer of the soil deposit was alluvial, reaching a depth of 8.6 m. The subsequent layer is a sandy-gravelly moraine with a thickness of 8 m. Below it, a thin bottom moraine layer is found and reaches a depth of 20.1 m. The last layer is molasses, reaching a depth of 28.9 m. The soil deposit was considered to be fully saturated with water since the groundwater table was located at the surface. The relevant parameters used in this study were extracted from existing studies or calculated according to the determination methods described in Section 2, as shown in Table 2. It is noted that Young's modulus of the Molasse layer provided by Ravera et al. (2020a) was in the range of 3000-7000 MPa, based on which the calculated shear modulus fell in the range of 1153.8 -2692.3 MPa.

The initial stiffness of skin friction and tip reaction of the load transfer in the Molasse layer were calculated according to the equations mentioned in section 2.5 and fell in the range of 318.2-742.5 MPa/m and 2176.5-5078.5 MPa/m, respectively. Therefore, this study conducted two kinds of simulations using the maximum and minimum values of the initial stiffness of skin friction and tip reaction estimated from the shear modulus. The four energy piles were subjected to a heating-passive cooling cycle during the test. In this study, the monitoring results of EP1 pile (see Fig. 6a) during the heating phase were used to validate the proposed model. The

FE simulations of energy pile groups

Saggu and Chakraborty (2016) conducted numerical studies of energy pile groups with spacings of 2.5 and 4 m using the finite element software Abaqus. In these studies, the pile group size was 3×2, and the slab was considered to be composed of the same concrete as the pile. The slabs were 15.5 m long, 1.2 m thick, and 12.9 m wide. All piles, 20 m long and 1m in diameter, were wished into a single layer of dry Ottawa sand. During the simulations, an axial load of 6000 kN was continuously applied to the slab, and all the piles were first heated and then recovered. The temperature changes were 21 and 2.8 ℃ at the heating and recovery ends, respectively. The parameters used in this study are listed in Table 3. A contact stiffness calculated as 401.7 MPa/m was considered in the study. The vertical stress at the end of the recovery phase was slightly higher than that under mechanical loading, because the pile did not return to the initial temperature. An interesting phenomenon is that the corner piles show a more significant thermal stress than the central piles because of the interaction effects, which is in agreement with previous studies [START_REF] Jeong | Thermally induced mechanical response of energy piles in axially loaded pile groups[END_REF][START_REF] Suryatriyastuti | On the understanding of cyclic interaction mechanisms in an energy pile group[END_REF]. A similar phenomenon can be observed in Fig. 9(d), (e), and (f) for the piles with 4.0 m center-to-center spacing. effect in the group. The difference between the results without and with consideration of the 'sheltering-reinforcing' effect tend to disappear when s/D is larger and the convergence is delayed if the number of piles increases. The displacement ratio obtained by the finite element simulation is the largest, and the results without and with consideration of the 'shelteringreinforcing' effect are smaller and smallest, respectively. The possible reasons, similar to those discussed by [START_REF] Liu | A simple method for analyzing thermomechanical response of an energy pile in a group[END_REF], are as follows:

(i)

The nonlinear interaction of the pile-soil interface is not considered in the finite element simulations of Rotta Loria and Laloui (2016). Thus, when the pile is subjected to the thermal load, the pile and soil will deform together, and there is no relative slip between them. However, the nonlinear pile-soil interaction is considered in the proposed model, which means there will be a relative slip between the pile and soil. The shaft resistance induced by surrounding soil will hinder the upward expansion of the pile. Therefore, the displacement ratio obtained by the finite element simulation is greater than that obtained by the model proposed in this study.

(ii) Even though the nonlinear mechanical properties of the interface have been considered, the calculation without considering the 'sheltering-reinforcing' effect would overestimate the displacement ratio of the pile.

Besides, the displacement ratio obtained in the free displacement field increases significantly when s/D=3. The reason may be that the shear displacement of the surrounding soil in the free displacement field varies according to a non-linear decreasing function with pile spacing and increases rapidly at smaller pile spacings [START_REF] Wang | Interaction factor for large pile groups[END_REF]. The comparison results show the importance of considering the 'sheltering-reinforcing' effect in estimating the energy pile group response and the relevance of the model proposed in the present study.

Parametric study

This section aims to study the influence of the pile-slab-soil interaction, pile spacing, pile position and number in a group using the present load transfer model. To this end, a series of simulations was conducted using the parameters listed in Table 4.

Effect of the pile-slab-soil interaction

To study the effect of the pile-slab-soil interaction on the thermomechanical behavior of an energy pile group, a 2×2 pile group and an isolated pile were modeled. The pile-to-pile spacing of the group was three times the pile diameter. The parameters used in simulations are

shown in Table 4. The piles were subjected to temperature changes of 10 and 30 ℃. Contact stiffness values of 0, 1, 3, 5, and 7 GPa/m were used in simulations. Fig. 10 shows the effect of the contact stiffness on the thermal vertical stress of the pile. It can be observed that more thermal stress was induced as the contact stiffness increased. The thermal stress generated at the pile head of the pile group was slightly larger owing to the pile-slab-soil interaction. Fig. 11 shows the effect of the contact stiffness on the maximum thermal vertical stress in the pile. It can be found that the maximum thermal stress in the pile in the group under the same contact stiffness was smaller than that of the isolated pile. This phenomenon has also been observed in previous studies [START_REF] Suryatriyastuti | On the understanding of cyclic interaction mechanisms in an energy pile group[END_REF], Ravera et al. 2020a). The thermally induced downward displacement of the pile under different levels of pileslab-soil interaction is compared in Fig. 12. According to the study of [START_REF] Najma | Incremental load transfer analysis of an energy pile under arbitrary mechanical and thermal loads[END_REF], the location of the NP (i.e., thermally induced displacement equal to zero) approaches the pile head with greater pile head constraint, which explains why the position of NP gradually moves upward as the contact stiffness increases. It is also observed that the absolute values of the pile head and end displacements decreased and increased, respectively, as the contact stiffness increased. Additionally, the NP of the pile group was lower than that of the isolated pile under the same constraint conditions. Fig. 13 presents the effect of the contact stiffness on the absolute value of the maximum thermal vertical displacement of the pile. Compared with the isolated piles, the pile group had larger thermally induced displacements under the same constraints; however, this difference became insignificant as the temperature change increased. 4. The pile-to-pile spacing of the group was three times the pile diameter. During the simulation, all the group piles were energy piles and subjected to a temperature change of 30 ℃. Besides, contact stiffness equal to zero was considered. Fig. 14 shows the vertical thermal displacement of the pile head subjected to different spacings. It can be observed that the thermal displacements decreased with increasing pile spacing, which is consistent with the results of [START_REF] Jeong | Thermally induced mechanical response of energy piles in axially loaded pile groups[END_REF][START_REF] Rotta Loria | The interaction factor method for energy pile groups[END_REF]. This may be because an increase in pile spacing weakens the pile interactions within the group. The mechanism was discussed in detail in a study by Rotta Loria et al.( 2016) on the interaction factor of energy-pile groups. In addition, the comparison results with and without considering the 'sheltering-reinforcing' effect, shown in Fig. 14, further indicate the advantage of the present method in the analysis of the response of the energy pile group. The difference between thermal stresses in the pile group and the isolated pile decreased as the temperature increased. However, the pile head displacement increased with the number of piles.

These results are consistent with those found by experimental and numerical studies(Rotta Loria and Laloui 2017b, Ravera et al. 2020a[START_REF] Fang | Group Performance of Energy Piles under Cyclic and Variable Thermal Loading[END_REF]) and validate the applicability of the present method to simulate the interactions and group effects of energy piles.

Discussion

In this study, we proposed an experimentally validated load transfer model that considers the 'sheltering-reinforcing' effect for the thermomechanical analysis of energy pile groups. The proposed method modeled two well-documented full-scale field tests and two finite-element simulation cases. The comparison results showed that the proposed method could capture several essential aspects of the energy pile group, including thermally induced strain, stress, displacement, and group effects. Also, we conducted a parametric analysis to evaluate the effects of relevant parameters on the thermomechanical behavior of the energy pile group.

Recently, several methods considering pile-pile interactions have been developed for the thermomechanical analysis of energy pile groups. For example, Rotta Loria and Laloui (2018) proposed an analytical model to analyze the vertical displacement and the increased deformation of energy pile groups subjected to thermal loads more comprehensively by defining a pile-soil-pile interaction factor. Iodice et al. (2021) provided a unified methodology involving a novel explicit formula for evaluating the maximum thermally induced axial load by establishing the effect of the actual restraint condition at the pile head as a function of the stiffness ratio between the inactive and the active pile subgroups. Nevertheless, the present study is different from the above studies. First, the present study aims to provide an experimentally validated simple load transfer model that considers the 'sheltering-reinforcing' effects for thermomechanical analysis of energy pile groups. The model can estimate all the thermomechanical behavior of energy pile groups involving vertical displacement, strain, stress, side friction, and group effects. This aim is very different from Rotta Loria and Laloui (2018) study, which mainly focuses on estimating the vertical displacement of the energy pile group.

Furthermore, this study developed the load transfer method for the single energy pile under thermomechanical loading by considering the pile-pile interaction in the group to make it suitable for the thermomechanical behavior of energy pile groups. This is different from the study of Iodice et al. (2021) because they fulfilled their aim by analyzing numerical simulation results and proposed the design procedure by using analytical solutions, which can be worked out to obtain explicit formulae for the direct computation of axial force in a multilayer soil.

Their practical method is more geared toward calculating the thermomechanical responses of single energy piles. Second, The present study considers both nonlinear pile-soil interaction and elastic deformation of the surrounding soil. The surrounding soil is divided into disturbed and undisturbed zones. The soil in the disturbed zone is a skinny layer of soil on the soil/pile interface. The nonlinearity of the pile-soil interaction was concentrated in this interface. The area outside the interface is the undisturbed zone. Because this zone is subjected to a relatively low stress change, the stress-strain behavior of the soil is mainly elastic. The pile-soil-pile interaction in the pile group is considered linearly elastic and suitable for the principle of superposition. The advantage of this approach is that it can consider the relative slip between piles and soil for the single pile and the interaction between piles-soil-pile in pile groups. Thus, the consideration of pile-soil-pile interaction in the present study is very different from the two studies (Rotta Loria & Laloui, 2018;Iodice et al., 2021).

One of basic assumptions of the simple load transfer method is that the mechanical behavior of the energy pile is governed by thermally induced pile axial deformation. Thus, the radial deformation induced by thermal loading is not considered in the present study. There is controversy about whether the influence of radial deformation of energy piles on the response of piles can be ignored in the study of simplified analysis methods. [START_REF] Wang | Posttemperature Effects on Shaft Capacity of a Full-Scale Geothermal Energy Pile[END_REF] and [START_REF] Faizal | Axial and radial thermal responses of a field-scale energy pile under monotonic and cyclic temperature changes[END_REF] showed that axial thermal strains were more restricted to thermal expansion than radial thermal strains, which indicated that the radial thermal strains are closer to that of the pile in free thermal expansion. On the contrary, the study by [START_REF] Mimouni | Behaviour of a group of energy piles[END_REF] showed that the radial thermal strains of the pile were much lower than the free thermal strains, indicating that stiffer soils provided higher restriction to radial thermal strains than the case reported by [START_REF] Wang | Posttemperature Effects on Shaft Capacity of a Full-Scale Geothermal Energy Pile[END_REF] and [START_REF] Faizal | Axial and radial thermal responses of a field-scale energy pile under monotonic and cyclic temperature changes[END_REF]. It suggests that building loads could affect the development of radial thermal strains along the pile length. [START_REF] Saggu | Cyclic Thermo-Mechanical Analysis of Energy Piles in Sand[END_REF] observed that the radial strains induced in a pile due to thermo-mechanical loading are higher than that induced due to only mechanical loading. Elzeiny & Suleimam (2021) pointed out that the horizontal pressure decreased by 2~5 kPa when colling the pile, which corresponds quite well with the average stress associated with the measured reduction in pull-out capacity.

Bourne-Webb et al. ( 2022) conducted numerical simulations and comprehensively investigated the problem. They reported that the horizontal stress changes induced by thermal loading have significant potential effects on the thermomechanical behavior of energy piles. The effects depend on the margin concerning the initial mobilization of the shaft resistance by the mechanical load. In summary, the studies mentioned above suggested that the horizontal thermally induced contact stresses would significantly influence the thermomechanical behavior of energy piles because of the radial expansion and contraction of the pile under heating and cooling.

However, these require a confirmation from field tests under building loads representing actual boundary conditions. It is noted that the existing studies have different opinions. [START_REF] Olgun | Thermo-mechanical radial expansion of heat exchanger piles and possible effects on contact pressures at pile-soil interface[END_REF] reported that radial contact pressures typically increase less than 15 kPa, which cannot fully explain the shaft resistance observed in heating tests. They thought that the increase of heat exchanger pile capacity in response to heating, observed in several small-scale laboratory studies, cannot be directly attributed to the increase of contact pressure at the soil/pile interface. [START_REF] Faizal | Axial and radial thermal responses of energy pile under six storey residential building[END_REF] conducted a field test of the energy pile and found that the magnitudes of the axial thermal strains were more constrained than the radial thermal strains at all depths, leading to the development of axial and radial thermal stresses of up to -4.5 and -0.015 MPa, respectively, for a change in average pile temperature of 24.1 ℃. The magnitudes of the radial thermal stresses with changes in pile temperature were significantly lower than the axial thermal stresses at all depths of the pile, indicating that the radial thermal expansion had found to be almost constant with pile depth and more significant than the pile length. However, when the pile was subjected to thermal loads, Rotta Loria and Laloui (2018) conducted finite element simulations and found that the shear radius was not constant with the pile depth and smaller than the pile length. In this study, the calculation of the shear radius is considered in a simplified method. For the multi-layered soil, the shear modulus and Poisson's ratio of each soil layer are different, which means there will be different values of shear radius for each soil layer. Thus, the calculated shear radius varies with pile depth but remains unchanged within the same soil layer through this simplified method. The simplified method mentioned above for the homogeneous soil will fail to obtain a shear radius varying with depth. The calculated shear radius remains unchanged within all the pile depths because the shear modulus and Poisson's ratio of the soil keep constant, which may adversely affect the application of the proposed simple load transfer method for energy pile groups in the homogeneous soil. Furthermore, the shear radius is greater than the pile length under mechanical loads and generally smaller than the pile length under thermal loads [START_REF] Randolph | Analysis of Deformation of Vertically Loaded Piles[END_REF]Rotta Loria & Laloui, 2018).

The proposed simple load transfer method for energy pile groups in the presented study can consider the combined thermal and mechanical loads. During the thermomechanical analysis, it is necessary to consider the shear radius induced by both mechanical and thermal loads.

Therefore, the shear radius induced by mechanical loads is employed for the thermomechanical analysis because the radius induced by mechanical loads is much greater than that induced by thermal loads.

Conclusions

We proposed a simple load transfer method for the thermomechanical analysis of an energy pile group subjected to thermomechanical loads. The proposed method was validated using full-scale field tests and finite element numerical simulations. In addition, a numerical analysis was performed to evaluate the effects of relevant parameters on the thermomechanical behavior of energy pile groups. The main conclusions are as follows:

(1) The results obtained with the proposed method were compared with those from fullscale field tests and FE simulations. The comparison indicated that the proposed model could capture the thermal strain, stress, and displacement of the energy piles in the group under thermal and mechanical loads.

(2) Under the same constraints and thermal loads, the energy piles in the group exhibited less thermal stress and larger thermal displacement than the isolated piles. The difference in the thermal stress and displacement between the single energy pile and the energy pile in groups increases with the temperature change increases.

(3) The maximum and minimum thermal stresses occurred at the corner and center piles, whereas the minimum and maximum thermal displacements occurred at the corner and center piles, respectively. In addition, the thermal displacement decreased with increasing pile spacing.

(4) The thermal stress decreased as the number of energy piles in the group increased under the same thermal load. The difference between thermal stresses in the pile group and the isolated pile decreased as the temperature change increased.

𝐾

  Fig.2Flow chart for computational thermo-mechanical analysis of energy piles (after Song

Fig. 3

 3 Fig.3Schematic of the soil and pile referring to the study of[START_REF] Guo | Investigation on the thermomechanical behavior of free constrained full-scale PHC energy pile in multi-layer strata[END_REF]

Fig. 4 Fig. 5

 45 Fig. 4 Experimental and modeled thermally induced pile axial stresses referring to the tests of Guo et al. (2018). (a) ΔT=11.1 ℃; (b) ΔT=13.2 ℃; (c) ΔT=16.6 ℃; (d) ΔT=19.3 ℃ Fig. 5 shows the measured and modeled thermal stress at different pile depths versus the

  temperature changes were 5, 10, 15, and 20 ℃, respectively. Additionally, an initial vertical mechanical load of 495 kN was calculated for the single pile tested by Rotta Loria and Laloui (2017). A contact stiffness calculated as 4450 MPa/m was considered. Besides, thermal stress means pile vertical stress induced by temperature changes only.

Fig. 6

 6 Fig.6 Schematic of (a) the energy pile foundation; (b) the soil stratigraphy (modified from Rotta Loria and Laloui 2017a, 2018a)

Fig. 7

 7 Fig.7shows the comparison between experimentally observed and computed thermal

Fig. 7

 7 Fig. 7 Comparison between experimentally observed and computed thermal vertical stresses variations. (a) ΔT=5℃; (b) ΔT=10℃; (c) ΔT=15℃; (d) ΔT=20℃

Fig. 8

 8 Fig.8shows the FE simulated and modeled pile axial stresses, referring toSaggu and

Fig. 8

 8 Fig. 8 FE simulated and modeled pile axial stresses referring to Saggu & Chakraborty(2016).

Fig. 9

 9 Fig. 9 Displacement ratio under the different pile spacings Fig.9 shows the displacement ratio for various pile groups under different pile spacings. It

Fig. 10 Fig. 11

 1011 Fig. 10 Effect of contact stiffness on the thermal vertical stress of the pile. (a) and (b) are the thermal vertical stress under a temperature change of 10 ℃ of an isolated pile and a pile in a 2×2 group, respectively; (c) and (d) are the thermal vertical stress under a temperature change of 30 ℃ of an isolated pile and a pile in a 2×2 group

Fig. 12 Fig. 13

 1213 Fig. 12 Effect of the contact stiffness on thermal vertical displacement of the pile. (a) and (b) are the thermal vertical displacement under a temperature change of 10 ℃ of an isolated pile and a pile in a 2×2 group; (c) and (d) are the thermal vertical displacement under a temperature change of 30 ℃ of an isolated pile and a pile in a 2×2 group

Fig. 14

 14 Fig. 14 Thermal displacement of the pile head under different pile spacing

Fig. 15

 15 Fig.15 shows a comparison of the profiles of the vertical thermal stress and displacement for

Fig. 15 Fig. 16

 1516 Fig. 15 Effect of pile arrangement in a group. Thermal vertical stress of the pile under (a) ΔT=10 ℃ and (b) ΔT=30 ℃; thermal vertical displacement of the pile under (c) ΔT=10 ℃; (d) ΔT=30 ℃

Fig. 17

 17 Fig. 17 Effect of the number of piles in the group. Thermal vertical stress of the pile under (a) ΔT=10 ℃ and (b) ΔT=30 ℃; thermal vertical displacement of the pile under (c) ΔT=10 ℃; (d) ΔT=30 ℃.

  𝜎 𝑣𝑏 , is the effective vertical stress at the pile tip; 𝑁 𝑞 and 𝑁 𝑐 are the load capacity coefficients, which can be calculated by 𝑁 𝑞 = 𝑒 𝜋𝑡𝑎𝑛𝜑 , 𝑡𝑎𝑛 2 ( 𝑁 𝑐 = (𝑁 𝑞 -1)𝑐𝑜𝑡𝜑 , , where 𝜑 , is the effective friction angle of the pile tip soil.

	𝜋+2𝜑 , 4 ),

3) Ultimate base resistance 𝜎 𝑢𝑝 𝜎 𝑢𝑝 can be calculated as 𝜎 𝑢𝑝 = 𝑐 , 𝑁 𝑐 + 𝜎 𝑣𝑏 , 𝑁 𝑞 , where 𝑐 , is the effective cohesion of the soil, (4) Initial shear stiffness of the pile tip 𝐺 𝑝𝑚𝑎𝑥

Table 1

 1 Soil parameters considered for modelling the field tests of[START_REF] Guo | Investigation on the thermomechanical behavior of free constrained full-scale PHC energy pile in multi-layer strata[END_REF]

	Variable	Soil layer, z [m]	Clay [0-4.3]	Silty clay 11.5] [4.3-	Clay 13.5] [11.5-	Clay 16] [13.5-	Silty [16-24] clay	Pile [24, -] tip	Pile
	Unit weight, 𝛾 𝑠𝑎𝑡 [𝑘𝑁/𝑚 3 ]	18.9	17.4	19.7	19.5	19.9	-	24.9
	Ultimate skin friction, 𝜏 𝑢 [𝑘𝑃𝑎]	2.6	6.5	10.3	22.9	31.9
	Young's modulus, 𝐸 [𝑀𝑃𝑎]	4.6	3.6	7.5	6.6	7.3	-	45700
	Shear modulus, 𝐺 𝑠𝑜𝑖𝑙 [𝑀𝑃𝑎]	17.1	13.9	28.5	25.2	15.1	-	-
	Friction angle, 𝜑 [∘]	10	6.6	6.8	18.4	17.3	-	-
	Initial stiffness of skin friction, 𝐺 𝑚𝑎𝑥 [𝑀𝑃𝑎/𝑚]	13.1	11.1	22.9	20.3	11.8	-	-
	Ultimate tip resistance, 𝑞 𝑏 [𝑀𝑃𝑎]	-	-	-	-	-	50	-
	Initial stiffness of tip reaction, -	-	-	-	-	1200	-

Table 2

 2 Soil and pile parameters considered for modelling the field tests referring to(Rotta Loria and Laloui 2017b, Ravera et al. 2020a)

	Variable	Soil layer, z [m]	Alluvial soil [0.0, 8.6]	Sandy-gravelly moraine [8.6, 16.6]	Bottom moraine [16.6, 20.1]	Molasse [20.1, 28.9]	Pile tip [24, -]	Pile
	Unit weight, γ sat [kN/m 3 ]	19.8	19	19.8	25.5	-	25

Table 3

 3 Soil and pile parameters considered in the present study referring to[START_REF] Saggu | Thermomechanical Response of Geothermal Energy Pile Groups in Sand[END_REF]

	Variable	Soil layer, z [m]	Ottawa sand [0, 20]	Pile tip [24, -]	Pile
	Unit weight, 𝛾 [𝑘𝑁/𝑚 3 ]		18	-	25
	Ultimate skin friction, 𝜏 𝑢 [𝑘𝑃𝑎]		31.6	-	-
	Shear modulus, 𝐺 𝑠𝑜𝑖𝑙 [𝑀𝑃𝑎]		32.6	-	-
	Friction angle, 𝜑 [∘]		32	-	-
	Initial stiffness of skin friction, 𝐺 𝑚𝑎𝑥 [𝑀𝑃𝑎/𝑚]	16.2	-	-
	Ultimate tip resistance, 𝑞 𝑏 [𝑀𝑃𝑎]		-	8.3	-
	Initial stiffness of tip reaction, 𝐺 𝑝𝑚𝑎𝑥 [𝑀𝑃𝑎/𝑚]	-	118.6	-
	Young's modulus, 𝐸 𝑃 (𝐺𝑃𝑎)		-	-	33.7
	Thermal dilation coefficient, 𝛼 𝑠 (𝜇𝜀/℃)		-	-	10

Table 4

 4 Soil and pile parameters considered in the present study Initial stiffness of skin friction, 𝐺 𝑠,𝑚𝑎𝑥 [𝑀𝑃𝑎/𝑚] 30 Ultimate tip resistance, 𝜎 𝑢𝑝 [𝑀𝑃𝑎] 10 Initial stiffness of tip reaction, 𝐺 𝑝𝑚𝑎𝑥 [𝑀𝑃𝑎/𝑚] 1500

	Variable

  ℎ contact stiffness between the pile head and slab 𝐿 length of the pile 𝐿 slab length of the slab 𝑁 𝑞 load capacity coefficients 𝑁 𝑐 load capacity coefficients 𝑃 mechanical load applied to the pile head 𝑝 pile-soil relative displacement 𝑝 0 relative pile-soil displacement corresponding to the stress reversal point 𝑝 p pile-soil relative displacement of the pile tip 𝑝 p0 relative displacement of the pile tip and soil corresponding to the stress reverse point 𝑟 0 pile radius 𝑟 𝑚 shear influence radius 𝑠 elastic displacement of the surrounding soil 𝑠 𝑖0 displacement of pile i induced by its own load 𝑠 ij additional displacement caused by 𝑗 pile under its own load 𝑠 aij distance between the axes of two piles 𝑠 p elastic displacement of the soil at the pile tip 𝑢 total shaft displacement at a certain pile depth 𝑢 0 total pile shaft displacement corresponding to the shaft shear stress reversal point 𝛼 𝑠 thermal dilation coefficient of the pile ∆𝑠 𝑖0 displacement induced by the 'sheltering-reinforcing' effects of pile 𝑗 δ soil shear modulus ratio 𝛿 𝑠 friction angle of the pile-soil interface 𝜂 loading and unloading branching judgment factor 𝜅 loading and unloading branching judgment factor 𝜈 soil Poisson's ratio of the soil 𝜎 p pile tip resistance

	𝜎 𝑢𝑝	ultimate pile tip resistance
	𝜎 𝑝0 𝜎 𝑣𝑏 ,	pile tip resistance corresponding to the stress reversal point effective vertical stress at the pile tip
	𝜎′ 𝑧	effective overburden pressure
	𝜏	pile shaft shear stress
	𝜏 𝑢	ultimate shear stress
	𝜏 0	pile shaft stress corresponding to the stress reverse point
	𝜑 s 𝜑 ,	friction angle of the soil effective friction angle of the pile tip soil

Acknowledgments

This research was supported by the National Natural Science Foundation of China (Grant Nos. 52122805 and 52078103) and the China Scholarship Council (CSC) (Grant No. 202106060093).

negligible effects on the development of axial thermal strains and stresses.

In some studies (Garbellini and Laloui 2019b[START_REF] Iodice | Analytical Solutions for Ultimate Limit State Design of Thermal Piles[END_REF][START_REF] Iodice | A practical method to design thermally stressed piles[END_REF], Liu et al. 2022), radial thermal effects are commonly considered relatively small compared to axial thermal effects when predicting the axial thermal response of energy piles due to the low diameter-tolength ratio of the pile. Some load transfer analysis methods have consistently validated and predicted the axial thermal response of field-and centrifuge-scale energy piles by neglecting the radial thermal effects [START_REF] Knellwolf | Geotechnical Analysis of Heat Exchanger Piles[END_REF][START_REF] Suryatriyastuti | A load transfer approach for studying the cyclic behavior of thermo-active piles[END_REF][START_REF] Chen | Parameters for Load Transfer Analysis of Energy Piles in Uniform Nonplastic Soils[END_REF][START_REF] Luo | Probabilistic design model for energy piles considering soil spatial variability[END_REF], Ravera et al. 2020a, Rotta Loria et al. 2020a[START_REF] Hu | Life-cycle probabilistic geotechnical model for energy piles[END_REF][START_REF] Najma | Incremental load transfer analysis of an energy pile under arbitrary mechanical and thermal loads[END_REF][START_REF] Fei | Analysis of energy pile groups subjected to nonuniform thermal loadings[END_REF]. Some numerical studies have also noted that radial thermal stresses in the energy pile are significantly low compared to the axial thermal stresses along the length of the pile [START_REF] Ozudogru | Analysis of friction induced thermomechanical stresses on a heat exchanger pile in isothermal soil[END_REF][START_REF] Gawecka | Numerical modelling of thermo-active piles in London Clay[END_REF]). Besides, preliminary numerical and analytical studies on energy piles [START_REF] Olgun | Thermo-mechanical radial expansion of heat exchanger piles and possible effects on contact pressures at pile-soil interface[END_REF][START_REF] Zhou | A novel cavity expansion-based analytical tool and its potential application for energy pile foundation[END_REF], along with a field study on an energy pile without end restraints [START_REF] Faizal | Axial and radial thermal responses of a field-scale energy pile under monotonic and cyclic temperature changes[END_REF]) have used cavity expansion analyses to confirm that no significant changes in pile-soil contact stresses are expected from the radial thermal expansion of the pile. However, these also need validation at various depths of a field-scale energy pile under building loads.

In the present study, a simple load transfer method was proposed for analyzing the thermomechanical behavior of energy pile groups. Therefore, the same assumption adopted by some studies, including the load transfer method for the thermomechanical analysis of energy pile and energy pile groups [START_REF] Knellwolf | Geotechnical Analysis of Heat Exchanger Piles[END_REF][START_REF] Suryatriyastuti | A load transfer approach for studying the cyclic behavior of thermo-active piles[END_REF][START_REF] Chen | Parameters for Load Transfer Analysis of Energy Piles in Uniform Nonplastic Soils[END_REF][START_REF] Luo | Probabilistic design model for energy piles considering soil spatial variability[END_REF], Ravera et al. 2020a, Rotta Loria et al. 2020a[START_REF] Hu | Life-cycle probabilistic geotechnical model for energy piles[END_REF][START_REF] Najma | Incremental load transfer analysis of an energy pile under arbitrary mechanical and thermal loads[END_REF][START_REF] Fei | Analysis of energy pile groups subjected to nonuniform thermal loadings[END_REF]) is employed to reduce the complexity of coupled thermomechanical analysis.

During the development of the simple load transfer model, the shear radius proposed by [START_REF] Randolph | Analysis of Deformation of Vertically Loaded Piles[END_REF] is employed to calculate the initial stiffness of the pile-soil interface, as shown in Eq.( 30). The shear radius is affected by pile length, shear modulus and Poisson's ratio of the soil. For the pile under pure mechanical loads, the shear radius has been


Eduardo Tomasi

César Fuguet

Christian Fabre

Frédéric Pétrot

Distributed Architectures Programming Models

come

SIMULATION OF A DISTRIBUTED SYSTEM

QEMU

QEMU is an open-source machine emulator. Multiple architectures can be executed in a single host. It provides a virtual model of an entire machine (CPU, memory and devices). We chose it for three main reasons:

IT IS FAST 1

It uses dynamic binary translation (DBT) to reach very high simulation speed. Also, QEMU's scalability on SMP machines is good [START_REF] Badaroux | To Pin or Not to Pin: Asserting the Scalability of QEMU Parallel Implementation[END_REF].

TCG PLUGIN

2

QEMU plugins provide interfaces to extend the simulator and add proper instrumentation. Plugins provide a mechanism to subscribe to events during translation and execution of instructions [START_REF] Cota | Cross-ISA machine instrumentation using fast and scalable dynamic binary translation[END_REF].

RISC-V 128

3

QEMU already has support for RV128 [START_REF] Portas | Fast simulation of future 128-bit architectures[END_REF]. Global memory in HPC might, in the next decade, exceed 2 64 bytes. It allows us to rethink the software architecture of supercomputers, including memory virtualization [START_REF] Waterman | Chapter 6, RV128I Base Integer Instruction Set, Version 1.7[END_REF].

Scalability

i$ d$ CPU i$ d$ CPU i$ d$ LLC$ DRAM GPU NIC
A cluster is a multicore computer that has its own memory hierarchy (multi-level caches and DRAM) and accelerators (such as GPUs). They are connected to each other through a high-performance communication network. MPI requires developers to expllictly define the communication and synchronization points. Also, pointers cannot be shared, which complexifies the transfer of structured data from one process to another. PGAS, on the other hand, eliminates the need for explicit communication, but introduces challenges related to data consistency and synchronization. To retrieve the metrics of interest, we need to monitor the code during execution. We need to know beforehand the virtual addresses of the MPI functions in the binary code. Through a QEMU plugin, we can monitor the translation blocks executed and profile the calls.

QEMU Extended with Plugins

We can gather metrics such as: number of instructions during a MPI call, number of system calls and number of memory accesses.

Results

Syscalls

Fig 1 .

 1 Fig 1. An example of a typical clustered architecture, as can be found in high performance computing (HPC).

Fig 2 .

 2 Fig 2. Shared Memory is used for parallelism inside a cluster, and Message Passing for parallelism between clusters.

Fig 3 .

 3 Fig 3. How to use QEMU to profile MPI calls.

Table II . Number of syscalls during MPI calls of NPB-DT. Table I. Number of syscalls during MPI calls of NPB-IS.

 II

					Syscalls
	Function		n p	1 cluster 2 clusters 4 clusters
	MPI Allreduce	1 2 4 8 16 32	0 93 78 80 85 144	4 41 3656 5056 4203 294	634 888 2379 2178 126 -	Function MPI Send	n p 5 8 16 32	1 cluster 2 clusters 4 clusters 9 9 10 10 10 10 11 12 15 19 22 -
	MPI Alltoallv	1 2 4 8 16 32	37 59 51 55 65 109	4763 7627 8529 8762 9756 10666	5488 5809 6792 7242 4361 -	MPI Recv	5 8 16 32	4 5 11 9	4 5 7 9	4 5 8 -
	No plugin		insn plugin	MPI plugin
	n p	MIPS MIPS Slowdown MIPS Slowdown
	1 2 4 8 16 32	74.3 101.6 126.2 155.3 170.0 101.6 64.2 80.6 92.3 97.9 203.2 102.9	13.6% 20.7% 26.9% 36.9% 40.2% 49.3%	40.0 48.7 53.7 60.0 64.5 72.3	46.1% 52.0% 57.4% 61.3% 62.1% 64.4%

Table III. Impact of the plugins during execution of NPB-IS.

This work was funded by the French National Research Agency (ANR) under grant agreement ANR-21-CE25-0016 (MAPLURINUM) shared memory.


Franck Lefèvre
email: franck.lefevre@latmos.ipsl.fr

Anna Fedorova

Alexander Trokhimovskiy

Denis Belyaev

Nicolay Ignatiev

Alexey Grigoriev

Natalia Savelyeva

Alexey Shakun

Kevin Olsen

Franck Montmessin

Shakun Alexey

Oleg Korablev

Observations of carbon monoxide (CO) by the Atmospheric Chemistry Suite (ACS) on board the Trace Gas Orbiter

CO in the atmosphere of Mars

Carbon monoxide (CO) is formed in the atmosphere of Mars through the photolysis of CO 2 at wavelengths shorter than 200 nm:

CO 2 + hν → CO + O (1)
Since the 1970s and the classic papers of [1,2] it has been known that OH and the trace amounts of oddhydrogen species (HO x ) produced by H 2 O degradation represent the main loss of CO and can efficiently recycle CO 2 from its photodissociation product:

CO + OH → CO 2 + H (2)
CO is therefore an important tracer of the catalytic chemistry that explains the remarkable stability of the Mars quasi-pure atmosphere of CO 2 .

The photochemical lifetime of CO is estimated from reaction (2) to 5 terrestrial years [START_REF] Lefèvre | The Atmosphere and Climate of Mars[END_REF]. This long lifetime does not authorize chemical variations of CO with local time or even at the seasonal timescale. Yet, observations show a pronounced seasonal cycle of the CO mixing ratio at high latitudes [START_REF] Krasnopolsky | [END_REF]5]. This phenomenon is not of chemical origin but a response to the condensation-sublimation cycle of CO 2 to and from the seasonal ice caps, which leads to enrichment-depletion of all non-condensable gases in polar regions. Thus, CO is also a good tracer of such processes and of atmospheric dynamics in general.

In terms of absolute amounts, previous measurements of Martian CO carried out from space or from the Earth indicate values of 700-1100 ppmv averaged over the atmospheric column [START_REF] Krasnopolsky | [END_REF]5]. Those abundances have historically been a challenge and remain unsolved for chemical models, which typically underestimate CO by a factor 2 to 8 [START_REF] Lefèvre | The Atmosphere and Climate of Mars[END_REF].

The fact that such a basic problem persists after decades of research may be indicative that an important process is missing or largely inaccurate in our understanding of the Mars photochemical system.

To date, only column-averaged amounts of CO have been measured on Mars and no measurements of the vertical distribution of CO have been published. Vertical profiles of CO will be provided for the first time by the instruments on board the Trace Gas Orbiter.

The Atmospheric Chemistry Suite (ACS)

The Atmospheric Chemistry Suite (ACS) package is an element of the Russian contribution to the ESA-Roscosmos ExoMars 2016 Trace Gas Orbiter (TGO) mission [6]. ACS consists of three separate infrared spectrometers, sharing common mechanical, electrical, and thermal interfaces.

Among the three spectrometers of ACS, the midinfrared channel (MIR) is a cross-dispersion echelle instrument dedicated to solar occultation measurements in the 2.2-4.4 µm range and achieves a resolving power of > 50000. With its unprecedented sensitivity and its spectral range that covers the 2.3 μm band of CO, MIR is well suited to retrieve accurate vertical profiles of CO from 10 km to about 140 km. In low dust conditions, we anticipate a sensitivity to CO of about 5 ppmv, i.e. less than 1% of the mean mixing ratio of CO on Mars. Measurements of the CO vertical distribution will also be possible with the thermal infrared (TIRVIM) channel of ACS, a Fourier-transform spectrometer encompassing the spectral range 1.7-17 µm. TIRVIM covers the strong CO band at 4.7 µm, which should allow the retrieval of accurate CO profiles in solar occultation mode, despite a lesser spectral resolution than MIR.

First observations of CO

The first vertical profiles of CO obtained by solar occultation from the MIR and TIRVIM channels of ACS, not retrieved yet at the time of writing, will be presented in this talk. They will be analysed in the context of Mars atmospheric dynamics and photochemistry. We will also present comparisons with three-dimensional simulations of Mars CO carried out with the LMD global climate model with photochemistry.

Acknowledgements

ExoMars is the space mission of ESA and Roscosmos. The ACS experiment is led by IKI Space Research Institute in Moscow. The project acknowledges funding by Roscosmos and CNES. Science operations of ACS are funded by Roscosmos and ESA.


Franck Montmessin

Nicholas Schneider

Justin Deighan

Sonal Jain

Scott Evans

Matteo Crismani

Michael Stevens

Daniel Lo

John Clarke

Michael Chaffin

Four years of upper atmospheric exploration at Mars with MAVEN and IUVS

à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Four years of upper atmospheric exploration at Mars with MAVEN and IUVS

Franck Montmessin [START_REF] Clarke | Variability of D and H in the Martian Upper Atmosphere Observed with the MAVEN IUVS Echelle Channel[END_REF], N. M Schneider (2), J. I. Deighan (2), S. K. Jain (2), J. S. Evans (3), M. Crismani [START_REF] Crismani | A persistent meteoric metal layer in the Martian atmosphere[END_REF], M. H. Stevens, (4) D. Y. Lo [START_REF] Gröller | Probing the Martian atmosphere with MAVEN/IUVS stellar occultations[END_REF], J. T. Clarke [START_REF] Jain | The structure and variability of Mars upper atmosphere as seen in MAVEN/IUVS dayglow observations[END_REF], M. S. Chaffin (2), M. Mayyasi [START_REF] Jain | The structure and variability of Mars upper atmosphere as seen in MAVEN/IUVS dayglow observations[END_REF], F. Lefèvre (1), A. Stiepen (2), E. Royer (2), Z. Milby (2), H. Groeller [START_REF] Gröller | Probing the Martian atmosphere with MAVEN/IUVS stellar occultations[END_REF], R. Yelle [START_REF] Gröller | Probing the Martian atmosphere with MAVEN/IUVS stellar occultations[END_REF], H. Nakagawa.

(1) LATMOS CNRS/UVSQ/UPMC/IPSL, Guyancourt/Paris, France, USA, (2) Laboratory for Atmospheric and Space Physics, University of Colorado at Boulder, (3) Computational Physics, Inc., (4) Space Science Division, Naval Research Laboratory, [START_REF] Gröller | Probing the Martian atmosphere with MAVEN/IUVS stellar occultations[END_REF] Lunar and Planetary Lab, University of Arizona, [START_REF] Jain | The structure and variability of Mars upper atmosphere as seen in MAVEN/IUVS dayglow observations[END_REF] Center for Space Physics, Boston University, [START_REF] Lo | Non-migrating tides in the Martian atmosphere as observed by MAVEN IUVS[END_REF] Tohoku University, Japan (franck.montmessin@latmos.ipsl.fr).

Abstract 1. MAVEN's Imaging UltraViolet Spectrograph (IUVS)

The Mars Atmosphere and Volatile EvolutioN mission (MAVEN) is a Mars orbiter equipped with instruments to study the current state of the Mars atmosphere, atmospheric loss processes, and their fundamental drivers. Most instruments make in situ measurements of particles and fields in the Mars environment and upper atmosphere. IUVS is the only remote sensing instrument for the study of Mars' atmosphere and its interaction with the plasma environment [START_REF] Mcclintock | The Imaging Ultraviolet Spectrograph (IUVS) for the MAVEN Mission[END_REF]. The instrument has two main channels for the study of the upper atmosphere at far-UV and Mid-UV wavelengths, plus an echelle channel capable of spectrally resolving hydrogen and deuterium Lyman alpha lines to measure the D/H ratio [START_REF] Clarke | Variability of D and H in the Martian Upper Atmosphere Observed with the MAVEN IUVS Echelle Channel[END_REF]. The instrument uses a scan mirror to obtain limb scans or disk maps and is mounted on an Articulated Payload Platform (APP) which maintains Mars pointing while the spacecraft bus and solar arrays maintain sun-pointing. The spacecraft travels on an elliptical orbit allowing limb scans to be obtained at periapse and full-disk imaging at apoapse, and scans of Mars corona in between [START_REF] Deighan | MAVEN IUVS observation of the hot oxygen corona at Mars[END_REF]. Thanks to the scan mirror, APP, and routine planning, the instrument observes with >50% duty cycles in a variety of repeating modes. On a bimonthly basis, the instrument performs two-day stellar occultation campaigns [START_REF] Gröller | Probing the Martian atmosphere with MAVEN/IUVS stellar occultations[END_REF] to probe atmospheric structure.

Key science results

By virtue of broad instrument capabilities and extensive observations, IUVS has observed the vast majority of phenomena discovered by prior UV instruments, and revealed a significant number of new phenomena as well. Observations of different phenomena can be individually optimized for spectral and two-dimensional resolution (through binning), as well as for sensitivity on daytime vs. night-time phenomena.

Dayglows and Nightglows

MAVEN/IUVS dayglow observations build on a rich history of prior UV studies by the Mariner missions and the SPICAM instrument on Mars Express. The dominant MUV emissions derive from solar excitation, ionization and dissociation of CO2, and subsequent ionization and dissociation products. The brightest FUV emissions are atomic emissions from the constituent atoms of CO2 and H2O, plus additional molecular bands originating with CO2 and its breakdown products. In addition to all spectral features observed by prior missions, IUVS has unambiguously observed and mapped the N2 Vegard Kaplan bands [START_REF] Evans | Retrieval of CO2 and N2 in the Martian thermosphere using dayglow observations by IUVS on MAVEN[END_REF][START_REF] Stevens | New observations of molecular nitrogen in the Martian upper atmosphere by IUVS on MAVEN[END_REF], and observed and mapped Mg + from meteor ablation [START_REF] Crismani | A persistent meteoric metal layer in the Martian atmosphere[END_REF]. The instrument also recorded the aftermath of the most intense meteor shower observed with scientific instrumentation, after the close passage of Comet Siding Spring past Mars in October 2014 [START_REF] Schneider | MAVEN IUVS observations of the aftermath of the Comet Siding Spring meteor shower on Mars[END_REF]. Limb scan dayglow observations have been powerful studies of spatial, seasonal and short-term variations in the thermosphere [START_REF] Jain | The structure and variability of Mars upper atmosphere as seen in MAVEN/IUVS dayglow observations[END_REF]. Longitudinal non-migrating tides have been observed in the peak emission altitudes [START_REF] Lo | Non-migrating tides in the Martian atmosphere as observed by MAVEN IUVS[END_REF].

The primary form of nightglow observed by IUVS is nitric oxide chemoluminescence. Nitrogen and oxygen atoms are liberated through molecular photodissociation on Mars' dayside. The atoms are then carried by thermospheric and mesospheric circulation patterns towards the winter pole, where they recombine and emit in the gamma and delta band of NO. IUVS limb scan observations [START_REF] Stiepen | Nitric Oxide Nightglow and Martian Mesospheric Circulation from MAVEN/ IUVS Observations and LMD-MGCM Predictions[END_REF] confirmed the basic geographic and seasonal emissions distribution predicted by modelling and observed by MEX/SPICAM. These observations also showed that the observed latitudinal emission distribution was not as sharply peaked at the winter poles as in models, an indication the circulation models may be missing important processes. Wave-3 tides were observed in equatorial regions at some seasons. Further apoapse imaging work with broader local time coverage is likely to distinguish between migrating, nonmigrating and stationary waves, offering further insights on their origin.

H and D observations above the exobase

The MAVEN IUVS instrument contains an echelle spectrograph channel designed to measure D and H Ly α emissions from the upper atmosphere of Mars. This channel has successfully recorded both emissions, which are produced by resonant scattering of solar emission, over the course of most of a martian year. The fundamental purpose of these measurements is to understand the physical principles underlying the escape of H and D from the upper atmosphere into space, and thereby to relate present-day measurements of an enhanced HDO/H 2 O ratio in the bulk atmosphere to the water escape history of Mars. Variations in these emissions independent of the solar flux reflect changes in the density and/or temperature of the species in the upper atmosphere. The MAVEN measurements show that the densities of both H and D vary by an order of magnitude over a martian year, and not always in synch with each other. This discovery has relevance to the processes by which H and D escape into space. One needs to understand the controlling factors to be able to extrapolate back in time to determine the water escape history from Mars at times when the atmosphere was thicker, when the solar flux and solar wind were stronger, etc. Further measurements will be able to identify the specific controlling factors for the large changes in H and D, which likely result in large changes in the escape fluxes of both species [START_REF] Mayyasi | The Variability of Atmospheric Deuterium Brightness at Mars: Evidence for Seasonal Dependence[END_REF].

Stellar occultations

Stellar occultations are a well-established tool for retrieving vertical profiles of density, temperature and composition in Earth and planetary atmospheres. As stars rise or set behind a planet's atmosphere, gases (and aerosols, if present) absorb light with their individual spectroscopic signatures. CO2 and O3 are the two gases readily identified in the IUVS wavelength range [START_REF] Gröller | Probing the Martian atmosphere with MAVEN/IUVS stellar occultations[END_REF]. Thousands of occultation events have been observed by SPICAM on Mars Express [START_REF] Montmessin | Stellar occultations at UV wavelengths by the SPICAM instrument: Retrieval and analysis of Martian haze profiles[END_REF] and vertical profiles have been used to understand and constrain models of the middle atmosphere [START_REF] Forget | Density and temperatures of the upper Martian atmosphere measured by stellar occultations with Mars Express SPICAM[END_REF]. To first order the vertical profile can reveal how the mesosphere has been raised, lowered or stretched out by heating or cooling processes. Statistically significant variations in the profiles are evidence of waves, tides or other perturbations.

IUVS has acquired data on Mars for more than one Martian year. During this time, beginning with March 2015 reported in [START_REF] Gröller | Probing the Martian atmosphere with MAVEN/IUVS stellar occultations[END_REF], hundreds of stellar occultations have been since observed, during 12 dedicated occultation campaigns, executed on average every two to three months. The occultations cover the latitudes from 80°S to 75°N and the full range longitude, and local times with relatively sparse sampling. From these measurements we retrieve CO2, O2, and O3 number densities as well as temperature profiles in the altitude range from 20 to 160 km, covering eight orders of magnitude in pressure from ∼ 2 × 10 1 to ∼ 4 × 10 -7 Pa. These data constrain the composition and thermal structure of the atmosphere. The O2 mixing ratios retrieved during this study show a high variability from 1.5 × 10 -3 to 6 × 10 -3 ; however, the mean value seems to be constant with solar longitude. We detect ozone between 20 and 60 km. In many profiles there is a well-defined peak be-tween 30 and 40 km with a maximum density of 1 -2 × 10 9 cm -3 . Examination of the vertical temperature profiles reveals substantial disagreement with models, with observed temperatures both warmer and colder than predicted. Examination of the altitude profiles of density perturbations and their variation with longitude shows structured atmospheric perturbations at altitudes above 100 km that are likely non-migrating tides. These perturbations are dominated by zonal wavenumber 2 and 3 with amplitudes greater than 45 %.

Ozone mapping

While ozone is mostly found closer to the surface of Mars, it also supplies information about the largescale circulation phenomena that extends deep in the mesosphere. At every apoapsis, IUVS activates its built-in scan to assemble a global mosaic of Mars in the MUV range where ozone can be retrieved for each individual FOV. This permits an acute characterization of ozone longitudinal and latitudinal behavior, providing unique insights into the shortterm dynamical chemical processes at work in the ozone annual cycle.

Data Access

All data, including higher-level products are archived for public use at NASA's Planetary Data System (PDS). All team publications indicate the data types used and reference the time period(s) utilized in the analysis. An instrument description and data format document ("Software Interface Specification) is also provided at the PDS.

Acknowledgements

FM acknowledges the support of CNES, the French space agency, for his activities as MAVEN CoI.


Alexander Lomakin
email: aleksander.lomakin96@gmail.com

Anna Fedorova

Oleg Korablev

Franck Montmessin

Gaetan Lacombe

Franck Lefèvre

High resolution spectra of CO2 ice based on SPICAM/MEX observations

à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Introduction

CO2 cycle on Mars defines fundamental processes both on surface and in atmosphere. On poles condensation of a large part of the atmosphere (up to 30%) results seasonal growth and retreat of polar caps [1], changing reflectance and emissivity of surface, that has dramatic consequences for energy budget [2] and changes local and global climate on the planet [START_REF] Hourdin | Workshop on Atmospheric Transport on Mars p[END_REF]. IR spectroscopy is one of the ways to measure abundance of carbon dioxide ice on Mars. CO2 ice has narrow features in NIR that allows to distinguish it from gaseous absorption in atmosphere. These features allowed to map distribution and seasonal evolution of condensation and sublimation of CO2 ice on polar caps [START_REF] Langevin | European Planetary Science Congress[END_REF]. Meanwhile, spectrum of carbon dioxide ice in NIR still hasn't been studied in details yet, because low resolution spectrometers cannot resolve weak sharp lines.

Observations

Since 2004 SPICAM IR spectrometer on Mars-Express has been carrying out measurements of the Martian atmosphere and surface in near-infrared range from 1 to 1.7 µm with the spectral power about 2000. The observations collected information about ices distribution on the surface for Martian years from MY27 to MY34. The analysis of SPICAM dataset related to surface features had not been made before. To process surface spectra of SPICAM and clean them from atmospheric signatures algorithm was developed based on the latest spectroscopic databases HITRAN2016 and Martian general circulation model v5.3. Here we present accurate high resolution spectra of Martian poles (figure 1) and seasonal maps for multi-annual distribution of carbon dioxide ice on surface of Mars.

Figure 1 :

 1 Figure 1: Comparison of SPICAM data and laboratory measurements by Hansen et al. (2005)

Acknowledgements

SPICAM operations are funded by CNES and Roscosmos. The data analysis by A.L., A.F. and O.K. has been supported by the Russian Government grant 14.W03.31.0017.