A nonlinear interface structural damage model between ice crystal and frozen clay soil

Sheng Shi,Feng Zhang ,2,KangWei Tang ,DeCheng Feng ,XuFeng Lu

1.School of Transportation Science and Engineering,Harbin Institute of Technology,Heilongjiang,Harbin 150090,China

2.State Key Laboratory of Road Engineering Safety and Health in Cold and High?Altitude Regions,CCCC First Highway Consultants Co.,Ltd.,Xi'an 710075,China

ABSTRACT The shear properties of ice?frozen soil interface are important when studying the constitutive model of frozen soil and slope stability in cold regions.Ⅰn this research,a series of cryogenic direct shear tests for ice?frozen clay soil interface were conducted.Based on experimental results,a nonlinear interface structural damage model is proposed to describe the shear properties of ice?frozen clay soil interface.Firstly,the cementation and friction structural properties of frozen soil materials were analyzed,and a structural parameter of the ice?frozen clay soil interface is proposed based on the cryogen‐ic direct shear test results.Secondly,a structural coefficient ratio is proposed to describe the structural development degree of ice?frozen clay soil interface under load,which is able to normalize the shear stress of ice?frozen clay soil interface,and the normalized data can be described by the Duncan?Chang model.Finally,the tangent stiffness of ice?frozen clay soil interface is calculated,which can be applied to the mechanics analysis of frozen soil.Also,the shear stress of ice?fro‐zen clay soil interface calculated by the proposed model is compared with test results.

Keywords:ice?frozen clay soil interface;cryogenic direct shear test;structural coefficient ratio;shear tangent stiffness;cementation

1 Introduction

As a composite geological material,frozen soil has more complex mechanical properties than unfro‐zen soil.Ⅰn recent years,with the rapid development of railways,highways and airport engineering in cold regions,the design of these projects requires a deep understanding for the mechanical and deformation characteristics of frozen soil(Maet al.,2005;Laiet al.,2016;Liet al.,2017).However,global tempera‐ture is rising,which in turn is accelerating degrada‐tion of permafrost,this degradation frequently causes foundation instability of structures in permafrost re‐gions which not only seriously endangers the con‐struction and operation of projects in cold regions,but also has a significance impact on the ecological envi‐ronment(Chenet al.,2020).Permafrost is formed from a combination of climate,geology and geogra‐phy.Under the influence of geology and geography at different scales,different levels of climate are formed,which determines the formation,succession and distri‐bution of permafrost.Ⅰn this process,ice lens with dif‐ferent thickness and shape are formed and randomly arranged within permafrost.Thus,the mechanical properties of permafrost are complex.Ⅰn addition,temperature sensitivity is due to the existence of ice crystals in permafrost while permafrost structure is due to the cementation of ice crystals.According to the distribution position and shape characteristics of ice lens in permafrost,permafrost structure can be di‐vided into overall structure,network structure and lay‐ered structure.Cryogenic structure is the direct sign of permafrost geology,such as syngenetic permafrost which is characterized by microlenticular cryostruc‐ture(Brayet al.,2006).The type of cryogenic struc‐ture controls the deformation and mechanical behav‐ior of frozen soils(Shur and Jorgenson,1998;French and Shur,2010;Bray,2012).Such cryogenic structure makes the study of permafrost more difficult.To fur‐ther study the mechanical properties of permafrost,it is necessary to have a basic understanding of the shear behavior of ice lens‐frozen soil interface.

Cryogenic direct shear test is an effective method to estimate the shear characteristics of frozen soil and interface of frozen soil?structure,which has been widely used by researchers(Murphy and McCartney,2014;Di Donnaet al.,2015).Bondarenko and Sa‐dovskii(1975)conducted an experimental study on the instantaneous freezing strength and long‐term freezing strength of the interface between frozen soil and rock.Their results show that temperature has a great influence on cohesion,but little influence on friction angle.Ladanyi(1995)indicated that the inter‐face freezing strength was affected by ice content,soil type,water content and other factors,and used the Mohr‐Coulomb law to describe the shear strength of interface.Ristet al.(2012)carried out a series of in‐clined shear box tests on permafrost sands,and found that the particle size of frozen soil is one of the deci‐sive factors for the interface friction angle.Liuet al.(2014)conducted a series of strength tests on the fro‐zen soil‐concrete interface.The results show that the peak shear strength and residual shear strength of in‐terface increase linearly with increasing of normal stress and decreasing of temperature.Yazdaniet al.(2019)studied the effect of thermal cycle on the shear strength of frozen soil‐pile interface by the tempera‐ture controlled direct shear apparatus.The results indi‐cated that temperature was the main factor affecting the interface strength.

The constitutive models of frozen soil were mostly developed from remolding samples,and the research mainly focused on the analysis of the stress?strain rela‐tionship obtained from tests,and using the elastic the‐ory and plastic theory to establish the constitutive model(Sayles,1973;Rottaet al.,2017).Arenson and Springman(2005)found that the creep rate of frozen soil increases when the temperature approached the melting point of ice,the reason is that the increasing unfrozen water content strongly affected the mechani‐cal response of frozen soil.Cudmani(2006)proposed an elastic viscoplastic constitutive model of frozen soil based on the response of time and temperature.Wanget al.(2014)proposed the viscoelastic plastic constitutive model of frozen soil by connecting Max‐well model,Kelvin model and Bingham model in se‐ries and the parabolic yield criterion was considered.Laiet al.(2014)simulated the deformation of frozen loess under complex stress path on the basis of super‐plasticity theory and complex stress path test.Yama‐moto and Springman(2014)investigated the creep be‐havior of frozen soil under triaxial stress when the temperature was close to the melting point.Amiriet al.(2016)established an elastoplastic constitutive mode of saturated frozen soils based on the theory of two‐stress state variables.Loriaet al.(2017)studied the nonlinear behavior of frozen soil in the process of deformation by combining the parabolic yield surface with the elliptical yield surface on the basis of the as‐sociated flow law.Aliet al.(2018)developed a new constitutive model of frozen soils by using the evolu‐tionary polynomial regression method,the model was trained and verified by a series of triaxial test data and used to simulate the entire stress‐strain curve of frozen soils.

With numerous random initial defects in frozen soil,and the development of research on mechanical behavior of frozen soil,a microstructure damage con‐cept of frozen soil was proposed based on experimen‐tal results.The theory of damage mechanics was grad‐ually introduced into the study of constitutive models of frozen soil.Laiet al.(2008)conducted a series of unconfined compression tests,and found that Weibull distribution function can accurately describe the strength characteristics of frozen soil.A statistical damage constitutive model of high?temperature fro‐zen silt was established based on the continuous dam‐age theory and statistical theory.Laiet al.(2009)pro‐posed the elastic‐plastic damage constitutive model of frozen soil based on the continuous damage theory and orthotropic damage variable,and the model can effectively simulate the stress‐strain process under high confining pressure.Liet al.(2009)established an improved statistical damage constitutive model of frozen soil by taking the strength of soil element as a random variable,and used Mohr Coulomb failure cri‐terion to estimate whether the soil element was dam‐aged.Laiet al.(2012)adoptedK?Stest method to de‐termine the strength distribution of warm ice?rich fro‐zen clay,and established a damage statistical constitu‐tive model by using Mises criterion as strength param‐eter of frozen soil unit.Yanget al.(2010,2014)de‐rived a viscoelastic plastic constitutive model of warm‐ice rich frozen sand by using the Weibull distri‐bution function to describe the development of dam‐age in the samples during the creep process.

With the rapid development of engineering con‐struction in cold regions,higher requirements have been put forward for the study of frozen soil.Since the ice‐frozen soil interface is the weakest medium in the internal structure of frozen soil under external load,it is necessary to consider the mechanical characteris‐tics of the ice‐frozen soil interface when studying de‐formation characteristics.However,the influence of the ice?frozen soil interface shear characteristics on the mechanical properties of frozen soil were ignored in the above constitutive models.Therefore,in the pro‐cess of establishing the constitutive models of frozen soil,considering the mechanical characteristics of ice‐frozen soil interface can accurately describe the stress‐strain properties of frozen soil under load.The interface tangent stiffness acts as an important parame‐ter in our study,but is difficult to determine in the ex‐perimental due to the effect of icecrystal cementation.

To study the shear behavior of ice‐frozen clay soil interface,a series of cryogenic direct shear tests under different conditions were carried out.Results show that shear stress of the ice‐dry clay soil interface acts as hardening type while the ice‐frozen clay soil inter‐face exhibits softening properties.The quantitative structural parameters of different normal stresses and initial void ratios were obtained based on the analysis of cementation and friction properties of frozen soil materials.The structural coefficient ratio was intro‐duced to establish the ice‐frozen clay soil interface constitutive model which can reflect the influence of ice crystal cementation.Calculated results shows that the structural coefficient ratio has well normalization effect on the influence of interface cementation and can connect the softening stress curve of ice‐frozen soil interface with hardening stress curve of ice‐dry clay soil interface.Finally,based on the modified Duncan‐Chang model,the shear tangent stiffness of ice‐frozen clay soil interface was obtained which can provide basic data for numerical calculation,and the proposed constitutive model of ice‐frozen clay soil in‐terface was verified by the test results.

2 Laboratory test and results

2.1 Sample preparation and testing method

The ice sample was made of distilled water in a mold with diameter of 61.8 mm and height of 20 mm at?20°C for 24 hours,then removed from the mold and stored in a refrigerator at a temperature of?20°C.The tested soil was extracted from Daxing'an Moun‐tains permafrost regions,located in northeastern Chi‐na.The specific gravity,plastic limit,liquid limit,and plastic index is 2.75,25.19%,36.98%and 11.79,re‐spectively.Purified water was mixed with soil at tar‐get moisture content and stored in a sealed bag for 12 hours to ensure uniform distribution of water,as presented in Figure 1a.

Figure 1 Test procedure of interface shear test

Afterwards,the ice sample was placed in the end of a prepared cylindrical copper mold with a diameter of 65 mm and height of 40 mm.According to the pre‐designed initial moisture content(i.e.,14%,16%,and 18%)and initial void ratio(i.e.,0.6,0.8,and 1.0),the soil was uniformly placed into the sample mold in lay‐ers based on the method of controlled dry density,and pressed slowly with a sample‐making machine until a certain height,and frozen at a temperature of?20°C for 24 h,as presented in Figure 1b.Ⅰn addition,to con‐duct the ice‐dry clay soil interface shear test,samples with initial void ratio of 1.0,0.8 and 0.6 were pre‐pared according to the method of controlled dry densi‐ty by using a mold with diameter of 65 and height of 20 mm.The samples were then placed in an oven at a temperature of 108°C for 24 hours to ensure that all the moisture in the sample evaporated,as presented in Figure 1c.

Finally,the cryogenic direct shear tests were con‐ducted at a temperature of?3°C with a modified di‐rect shear apparatus,and the ice‐frozen soil specimen or ice‐dry clay soil specimen was embedded in the temperature‐controlled shear box,as presented in Figure 1d.To ensure that the sample temperature is consistent with the test target temperature,the low temperature control time is 3 h during the test.The loading rate was set to 0.8 mm/min to push the shear box(ASTM,1998),and the samples after the tests are presented in Figure 1e.The design of test conditions is presented in Table 1.

Table 1 The designation of test conditions

2.2 Characteristics of interface deformation

The experimental results for shear stress?shear displacement curves of ice‐dry clay soil interface are depicted in Figure 2.One can found that the shear stress of ice‐dry clay soil interface behavior as harden‐ing type under different confining pressures and ini‐tial void ratios,the curve slope increases with increas‐ing of confining pressure,and increases with decreas‐ing of initial void ratio.The relationship between shear stress and shear displacement can be simulated by the hyperbolic model,expressed as:

whereτdis shear stress of ice‐dry clay soil interface,uis the shear displacement,aandbare the test parameters.

Figures 3?5 show the shear stress‐shear displace‐ment curve of ice‐frozen clay soil interface under dif‐ferent initial void ratios and initial moisture contents.Ⅰt is found that shear stresses exhibit a softening behavior under low normal stress The softening properties of ice‐frozen soil interface represent the magnitude of ice crystal cementation force at the interface,and the soft‐ening behavior of shear stress decreases gradually with decreasing of void ratio under the same normal stress.This is because when the normal stress is equal,the greater the ice crystal cementation force is,the more obvious the curve softening characteristics are.With in‐creasing of the initial void ratio of frozen soil,the ice content at the interface increases,and the correspond‐ing cementation force increases,thus,the softening be‐havior become obvious.With decreasing of initial void ratio,the content of ice crystals at the interface are less,the cementation force is decreasing,and the soften‐ing behavior is weakened.When the initial void ratio is high(e0=1.0),the original structure is not easily damaged under low normal stress(σn=50 kPa),and the shear stresses exhibit strong softening behavior.The normal stress has a great influence on the shear stress‐displacement curve when the initial void ratio is low(e0=0.6),and the higher the normal stress,the weaker the softening behavior.Once the shear stress reaches the peak point,initial damage to the interface structure occurs,and this damage is accumulating con‐tinuously with increasing of displacement until com‐plete failure occurs and finally the shear stress will be consistent with that of ice‐dry clay soil interface.

Figure 2 Shear stress‐shear displacement curves of ice‐dry clay soil interface under different conditions

Figure 3 Shear stress‐shear displacement curves of ice‐frozen clay soil interface under initial moisture content of 14%

Figure 4 Shear stress‐shear displacement curves of ice‐frozen clay soil interface under initial moisture content of 16%

Figure 5 Shear stress‐shear displacement curves of ice‐frozen clay soil interface under initial moisture content of 18%

Also,the softening behavior of the shear stress is obvious under high moisture content,and with in‐creasing of normal stress,the softening behavior grad‐ually weakens.At low normal stress(50 kPa),the soft‐ening behavior is positively correlated with initial void ratio and moisture content.With decreasing of initial void ratio,the stress curve changes from strong softening behavior to weak softening behavior.This is because the larger the initial void ratio,the greater the ice crystals content and the stronger the interface structure,thus,the softening behavior is more obvi‐ous.The comparison of Figures 3?5 show that the peak strength of ice‐frozen clay soil interface is sensi‐tive to the initial water content and increases with in‐creasing of initial water content.With change of ini‐tial water content from 14%to 18%,the increase of peak strength under different initial void ratios ranges from 123 kPa to 306 kPa under the normal stress of 50 kPa,while ranging from 161 kPa to 441 kPa under the normal stress of 100 kPa,and 223 kPa to 516 kPa under the normal stress of 200 kPa.With increasing of initial void ratio,the softening behavior of the curve became obvious with increasing water content.The explanation for this phenomenon is that at low temperature(?3°C),the increase of initial void ratio and water content greatly increases the content of ice crystal at the interface,which will inevitably increase the cementation force at interface and lead to an obvi‐ous softening behavior of the interface.

3 Theoretical foundation of ice?frozen clay soil interface constitutive model

3.1 Damage evolution mechanism of ice?frozen clay soil interface

For structural geotechnical materials, shear strength mainly consists of cohesive and friction,which play different roles at different strains.At the initial stage of loading,cohesion plays a major role.With increasing of strain,initial damage to cementa‐tion occurs and the contribution of cohesion to shear strength will decrease.Due to the decrease of cohe‐sion,friction gradually plays a key role in resisting shear strength with increasing of strain(Liuet al.,2016;Zhang and Liu,2019).

Because of the special environment of frozen soil,it is assumed that there is no water film in frozen soil.This film is completely transformed into ice crystals,thus,the frozen soil is mainly composed of soil skele‐ton and ice crystals.The cementation of ice crystals has a significant effect on mechanical properties of frozen soil as presented in Figure 6b.When the shear stress exceeds the peak point,initial damage to the ce‐mentation of ice crystals occurs,and the friction be‐tween ice and soil particles gradually plays a key role.The friction characteristics are mainly reflected in the interaction between soil particles and ice as presented in Figure 6a.Thus,the mechanical responses of ice‐frozen soil interface are determined by the cemen‐tation characteristics of ice crystals and the friction properties of soil particles.The damage of ice crystals in frozen soil causes the loss of cementation.There‐fore,the bonded ice crystals and slippage of soil parti‐cles should be considered when analyzing the me‐chanical properties of frozen soil.As presented in Fig‐ure 7a,the bonded elements and frictional elements were used to simulate the brittle properties of ice crys‐tals and slippage behaviors of soil particles,respec‐tively.The corresponding mechanical models are pre‐sented in Figure 7b.Ⅰn Figure 7,E,qandfrepresent elastic modulus,ice crystal cementation force and fric‐tion force between ice and soil particles,respectively.u0anducrepresent the shear displacement correspond‐ing to the peak stress point and the completely failure point of ice crystal cementation,respectively.

Figure 6 Schematic diagram of bonded elements and frictional element

3.2 Structural parameter of ice-frozen clay soil interface

The structural strength of the ice‐frozen clay soil interface can be reflected by the change of strength before and after the interface structure is damaged.Because the friction property of interface will be af‐fected by unfrozen water film and ice crystal after ce‐mentation is completely damaged,to simplify the cal‐culation,the influences of these factors were ignored.The difference of shear stress between the ice‐frozen clay soil interface and corresponding ice‐dry clay soil interface can be used to analyze the structure of the ice‐frozen clay soil interface.Figure 8 shows the shear stress‐shear displacement curve of the ice‐fro‐zen clay soil interface and ice‐dry soil interface.Ⅰt can be found that the shear stress of the ice‐frozen clay soil interface under the same displacement is larger than the corresponding ice‐dry clay soil interface.The shear stress ratio of the ice‐frozen clay soil interface and ice‐dry clay soil interface is able to describe the structural strength potential(structural strength)of the cementation characteristics of ice crystal at the inter‐face,which is expressed as follows:

whereτiandτdare the shear stresses of ice‐frozen clay soil interfaceand ice‐dry clay soil interface,respectively.

Figure 7 Mechanical elements and model for cementation and friction simulation

Figure 8 Test results of ice‐frozen clay soil interface and ice‐dry clay soil interface

3.3 Analysis of ice?frozen clay soil structural parameter

According to the test results of ice‐frozen clay soil interface and ice‐dry clay soil interface,the structural parameters of ice‐frozen clay soil interface under dif‐ferent shear displacements can be calculated by Equa‐tion(2).Figures 9?11 show the relationships between structural parametermand shear displacementu.From Figures 9?11,it can be found that the structural parametermcan be divided into two sections.Whenu＜u0(u0is the shear displacement corresponding to the peak shear stress in the shear stress‐shear displace‐ment curve)the original cementation of ice‐frozen clay soil interface is not damaged,with increasing of shear displacement,the interface structure plays a role,and the curve is ascending.When the curve reaches the peak point,the corresponding structural parameter ism0.Whenu＞u0,the curve shows a declining state,the cementation of ice?frozen clay soil interface is gradual‐ly damaged until completely lost,and the structural pa‐rameters tend to be a constant which equalsmb.The re‐lationship between structural parametersmand shear displacementucan be fitted by the generalized hyper‐bolic model,and can be expressed as:

whereα,β,χare model parameters,and the value un‐der different test conditions are presented in Table 2.

Figure 9 Relationship between structural parameters and shear displacement under initial moisture content of 14%

Figure 10 Relationship between structural parameters and shear displacement under initial moisture content of 16%

Figure 11 Relationship between structural parameters and shear displacement under initial moisture content of 18%

Table 2 Parameters of generalized hyperbolic model

3.4 Definition of ice-frozen clay soil interface damage function

During the change of ice‐frozen clay soil inter‐face structural parameter,the damage degree is re‐flected by damage functionD.Ⅰt is difficult to find the real value of structural strength when the shear stress corresponding to the rising section of the structural parameter curve is low,and the interface structural strength is not fully exerted.Therefore,the starting pointm0of the curve descent as the ini‐tial structural parameter reflects the beginning of structural damage(values listed in Table 3).Accord‐ing to Figures 9?11,whenu=u0,m=m0,D=0;whenu→∞,m=mb,D=1.The damage function can be de‐fined as:

wherem0is the initial structural parameter,mbis the structural parameter when the interface structure is lost.

According to Equation(4)and Table 3,the damage function can be calculated,as presented in Figures 12?14.One can found that initial interface damage oc‐curs whenu=u0during the shear process.Ⅰnterface damage enters the acceleration stage with increasing of shear displacement whenu＞u0.Once the structure of ice‐frozen clay soil interface is completely lost,the damage rate decreases gradually and tends to level.

Table 3 Structural parameters under different conditions

Figure 12 Relationships between damage function and shear displacement under initial moisture content of 14%

Figure 13 Relationship between damage function and shear displacement under initial moisture content of 16%

Figure 14 Relationship between damage function and shear displacement under initial moisture content of 18%

4 Constitutive model of ice-frozen soil consid‐ering structural effects

To consider the structure produced by the cemen‐tation of ice crystals in the nonlinear damage model of ice?frozen clay soil interface,the concept of struc‐tural coefficient ratio is introduced.The ratio repre‐sents structural performance when the interface is damaged,and also the proportion of structure in the evolution process of interface from structural integri‐ty to the state of complete failure.With increasing of the damage coefficient,the structural coefficient ra‐tio decreases.The structural coefficient ratio can be expressed as:

whereDis damage function.

By substituting Equations(1),(4)and(5)into Equation(2)can obtain:

Ⅰt can be seen from Equation(6)that the softening stress of ice‐frozen clay soil interface can be trans‐formed into the hardening stress of ice‐dry clay soil interface by the structural coefficient ratio.Therefore,the structural coefficient ratio defined in Equation(5)has a good normalization effect on the influence of in‐terface cementation,and the influence of ice crystal cementation can be reflected by hardening stress type without structural of the interface.

According to experimental results in section 2,the interface mechanical behavior under shear condition is similar to soil under triaxial test,where the princi‐ple of the Duncan‐Chang model is used to describe the shear properties of ice‐dry soil interface,although some concepts of this model needs to be revised.The confining stress is equivalent to the normal stress in the interface model. From Equation(6)S(m0?mb)can be replaced byτdwhich is de‐scribed by the Duncan Chang model,and the corre‐sponding initial tangent stiffness,failure ratio and tan‐gent stiffness at any point in the model can be ex‐pressed as:

whereτfandτultare the failure stress and progressive stress of ice‐dry clay soil interface,respectively.

Ⅰn addition,the initial stiffnesskiis related to the normal stressσn,and expressed as:

wherepais atmospheric pressure,Kandnare test parameters.

The failure stress of ice?dry clay soil interface can be expressed as:

whereφfis the friction angle during interface failure.

By substituting Equations(8)and(9)into Equa‐tion(7)can obtain:

From Equation(6),the nonlinear elastic constitu‐tive model of ice‐frozen clay soil interface consider‐ing the influence of structure can be expressed as:

Ⅰt is difficult to determine some parameters in the softening model when considering the effect of inter‐face structure,especially the tangent stiffness at any point.However,according to Equation(11),the inter‐face constitutive model of ice‐frozen clay soil and the corresponding model parameters can be obtained by introducing the structural coefficient ratio into the Duncan‐Chang model.On the basis of Equation(11),the initial tangent stiffness and tangent stiffness at any point of ice‐frozen clay soil interface considering structural influence can be expressed as:

The parameters ofK,n,φf,andRfcan be deter‐mined by the Duncan‐Chang model.

5 Parameters determination and model validation

The Duncan‐Chang model parameters of ice‐dry clay soil interface were determined by experimental data under different conditions(Table 4),and on the basis of these parameters,the tangent stiffnessktcan be determined.Then,by introducing the structural coefficient ratio,according to Equations(12)and(13)can obtain the initial tangent stiffnesskisand tangent stiffnessktsof the ice‐frozen clay soil inter‐face,which can be used to the finite element analy‐sis of frozen soil.The shear stress of ice‐frozen clay soil interface under different normal stresses,initial void ratios and initial moisture contents can be cal‐culated by substituting the test parameters(present‐ed in Tables 2?4)and Equations(3)?(5)into Equa‐tion(11),the calculated results were compared with test results.Figures 15?17 show the comparison between calculated results and test results of the ice‐frozen clay soil interface shear stress under dif‐ferent normal stresses,initial void ratios and initial moisture contents.Ⅰt is found that the calculated results are consistent with experimental data,illus‐trating the rationality of the model proposed in this research.

Table 4 Test parameters of ice‐dry clay soil interface

Figure 15 Comparisons between calculated results proposed by model and test results under initial moisture content of 14%

Figure 16 Comparisons between calculated results proposed by model and test results under initial moisture content of 16%

Figure 17 Comparisons between calculated results proposed by model and test results under initial moisture content of 18%

6 Conclusions

The mechanical parameters of ice‐frozen clay soil interface have an important influence on the deforma‐tion study of frozen soil.To investigate the mechani‐cal parameters and constitutive model of ice‐frozen clay soil interface considering ice crystal cementation,the concept of structural coefficient ratio was intro‐duced based on a series of cryogenic direct shear test results.The conclusions are provided as follows:

(1)The shear tests of ice‐frozen clay soil interface and corresponding ice‐dry clay soil interface with dif‐ferent initial void ratios were conducted at a tempera‐ture of?3°C.Ⅰt was found that the shear stress of ice‐dry clay soil interface exhibits hardening behavior,and increases with decreasing of initial void ratio.However,the shear stress of ice‐frozen clay soil inter‐face presents a softening property,which is positively correlated with initial void ratio and moisture content.

(2)Based on the analysis of the cementation and friction structural of frozen soil materials,the structural parameters proposed by the test results of ice‐dry clay soil interface and ice‐frozen clay soil interface have clear physical significance.These structural parameters can well reflect the deformation and failure characteris‐tics of ice‐frozen clay soil interface under load.

(3)To describe the structure produced by ice crys‐tals at ice‐frozen clay soil interface,the concept of structural coefficient ratio was introduced,which has a good normalization effect on the influence of inter‐face cementation.The shear stress of ice‐dry clay soil interface can be described by the Duncan‐Chang mod‐el,which is used as the normalized shear stress con‐sidering the structure effect.

(4)The tangent stiffness in the softening model is difficult to determine.The basic parametersφf,kiandRfwere determined by the Duncan‐Chang model with‐out considering structure.By introducing the structur‐al coefficient ratio,the tangent stiffnessktsof ice‐fro‐zen clay soil interface can be calculated,which is an important parameter to calculate the deformation of frozen soil.

Acknowledgments:

The research was supported the National Key Re‐search and Development Program of China(Nos.2016YFE0202400,2018YFC1505306),the National Natural Science Foundation of China(No.41971076),and the State Key Laboratory of Road Engineering Safety and Health in Cold and High?altitude Regions(No.YGY2017KYPT?04).