Laboratory investigation on the mechanical behavior of ice-saturated frozen loess

XiangTian Xu ,YuanMing Lai ,JinYi Chai ,CaiXia Fan

1.Institute of Transportation,Inner Mongolia University,Hohhot,Inner Mongolia 010070,China

2.State Key Laboratory of Frozen Soil Engineering,Cold and Arid Regions Environmental and Engineering Research Institute,Chinese Academy of Sciences,Lanzhou,Gansu 730000,China

1 Introduction

The mechanical properties of frozen soil are an important subject of enquiry for the design of geotechnical engineering technologiesin cold regions.Previous studies show that the mechanical behavior of frozen soil was significantly influenced by ice content,temperature,strain rate,and confining pressure(Andersland and Akili,1967;Chamberlain,1972;Alkire and Andersland,1973;Bragg and Andersland,1981;Sayles and Carbee,1981;Liet al.,2004;Laiet al.,2013).As with unfrozen soil,the strength and deformation characteristics of frozen soil were affected by confining pressure.Due to the presence of ice in frozen soil,the mechanical properties are more sensitive to confining pressure.Many scholars concluded that the strength of frozen soil increases with an increase of confining pressure from a lower initial confining pressure,while the strength of frozen soil decreases with an increase of confining pressure from a higher initial confining pressure (Chamberlain,1972;Maet al.,2000).However,there are not many studies on the strength and deformation of ice-saturated frozen soil.This study investigates the influence of confining pressure on mechanical properties of ice-saturated frozen loess.

In order to study the damage of frozen soil in the loading process,some researchers investigated the evolution of the meso-structure and micro-structure of frozen soil during the deformation process by using scanning electron microscopes or CT scanning tests(Wuet al.,1996;Maet al.,1997;Linget al.,2003;Liuet al.,2005).A CT scanning test can certainly observe changes of the meso/micro-structure in frozen soil during the loading process.For the acquisition of reliable test data,in addition to a high standard of ex-perimental operation,this test requires expensive equipment such as the CT scanner.However,the damage of materials can be reflected and measured from the deterioration of the macro mechanical properties.To investigate the damage behavior of ice-saturated frozen loess from the viewpoint of deterioration of mechanical properties,a series of triaxial loading-unloading cycle (TLUC) tests have been carried out at-6 °C in this study.The TLUC test results showed that energy dissipation occurs in the unloading-reloading process.Energy dissipation increases with the increase of plastic strain and finally approaches a stable value.Furthermore,the elastic modulus change was observed with the strain.The elastic modulus of ice-saturated frozen loess increased with strain at the initial loading stage,and then decreased with an increase of strain.The degeneration of the elastic modulus was defined as the damage.The evolution of damage with plastic strain was analyzed.In addition,the influence of the confining pressure on the energy dissipation and damage of ice-saturated frozen loess was considered.

2 Experimental procedures

2.1 Sample preparation

The loess used for preparing the test specimens was obtained from Lanzhou,Gansu,which is a region of seasonally frozen soil.The grain size distribution of tested loess is shown in table 1.

Using a specially-made machine to form the specimen,the loess was mixed with 14% moisture content by weight first,and then kept for 6 hours with no evaporation to ensure the specimen’s uniformity.Cylindrical samples of frozen loess having diameter of 61.8 mm and height of 125.0 mm (so that the height/diameter ratio was greater than 2) were prepared in a tri-split copper mould in which the loess was compacted using a specially-made specimen machine.The mould was then closed and evacuated to remove air from the voids.After the loess was saturated with de-aerated distilled water,the saturated specimens were refrigerated together with the mould.They were quickly frozen under-30 °C to avoid frost heave.When the specimens were completely frozen,which usually takes 48 hours,the moulds were removed and the specimens were mounted with epoxy resin platen on two ends and covered with a rubber sleeve.Then,the specimens were kept in an incubator for over 12 hours under the target testing temperature of-6 °C to ensure that the specimens had a uniform temperature.The basic physical parameters of saturated loess specimens are listed in table 2.

2.2 Test procedure

The test equipment is a cryogenic triaxial apparatus improved from a MTS-810 material test system with 10,000 kg capacity.The technical indices and performance parameters of the equipment were detailed by Xuet al.(2011a).

Two loading modes for a triaxial test were adopted in this study.One is the traditional triaxial compression(TC) under various confining pressures used to investigate the effects of confining pressure on the mechanical properties of ice-saturated frozen loess.The TC tests were carried out at a constant strain-rate of 1.67×10-4/s.The confining pressure was varied from 0.5 MPa to 9.0 MPa under TC tests.The other loading mode is a static triaxial loading-unloading cycle(TLUC) under different confining pressures used to investigate the elastic modulus evolving with deformation (since we can define the damage according to the degeneration of elastic modulus) and the effect of confining pressures on the damage for ice-saturated frozen loess.The procedures of the TLUC test for frozen soil used in this study were proposed by Xuet al.(2011b).At first,the axial loading was exerted on the specimen under a given confining pressure until the axial strain reachedεa1,and then the first unloading began.After an unloading that made the deviator stress equal to zero (σ1-σ3=0),and another loading,that made the axial strain reachεa2,began,and so on toNcycles.In this study,seven loading-unloading cycles were carried out.As with the TC tests,the strain-rate of loading and unloading stage under TLUC tests is 1.67×10-4/s.The value of confining pressure adopted in the TLUC test is the same as that with the TC test.

Table 1 Particle fraction of Lanzhou loess (%)

Table 2 Basic physical parameters of the loess specimens

3 Test results and discussion

3.1 TC test results and analysis

Figure 1 shows TC test curves obtained under confining pressures changing from 0.5 MPa to 9.0 MPa for ice-saturated frozen loess specimens tested at-6 °C at a strain-rate of 1.67×10-4/s.It can be seen from figure 1a,the stress-strain curves of ice-saturated frozen loess under various confining pressures show strain-hardening behavior when the axial strain is less than 15%.Meanwhile,we find that the confining pressure slightly affected the stress-strain behavior of ice-saturated frozen loess.At lower confining pressures (<5 MPa),the stress-strain curves under different confining pressures nearly coincide with each other.This indicates that the stress-strain relation is not obviously affected by confining pressures in this phase.When the confining pressure exceeds 3 MPa,the stress-strain curves also coincide with each other.However,the stress-strain curves under this confining pressure range fall below the stress-strain curves at lower confining pressures.

The reason behind these phenomena is that the strength and initial stiffness of ice-saturated frozen loess (silty clay) is mainly governed by the cohesion of the ice matrix,and the interparticle friction is small.Therefore,the confining pressure has just a slight effect on the stress-strain behavior of ice-saturated frozen loess under either lower confining pressures or higher confining pressures.However,the ice is crushed at higher confining pressures,which makes the strength and initial rigidness of ice-saturated frozen loess at higher confining pressures less than that at lower confining pressures.Figure 1b shows volumetric strain characteristics under various confining pressures.It can be found that the volumetric deformation of ice-saturated frozen loess exhibited significant dilatancy,besides a slight bulk shrinkage which occurred in the initial deformation stage at lower confining pressures (<3 MPa).

To quantitatively describe the effects of confining pressure on mechanical behavior of ice-saturated frozen loess,the strength,or stress value corresponding to the strain of 15%,and initial tangent modulusEiat various confining pressures is shown in figure 2.From figure 2a,we can observe that the relation between strength and confining pressure can be divided into two phases.In the phase 1,the confining pressure ranges from 0.5 MPa to 3.0 MPa.In this phase,the strength of ice-saturated frozen loess is barely influenced by the confining pressures,so that the values of strength range from 2.4675 MPa to 2.5076 MPa.If considering the test tolerance of 1%,the difference of strength at various confining pressures in this phase can be ignored.This phenomenon indicates that the internal frictional angle of ice-saturated frozen loess is very small and that the strength is significantly controlled by the ice bond.In phase 2,the confining pressure ranges from 5.0 MPa to 9.0 MPa.Similar to the phase 1,the strength of ice-saturated frozen loess is also slightly affected by the confining pressure in phase 2.However,the strength at this phase changes from 2.1927 MPa to 2.2414 MPa,which is lower than that at phase 1.This shows that the strength of ice-saturated frozen loess at lower confining pressures is greater than that at higher confining pressures.Due to this the higher confining pressure causes a portion of the ice to crush or melt,which results in the degradation of the ice bond.In the range of the tested confining pressures,the difference of the maximum and minimum value of strength is 0.3149 MPa.

Figure 1 TC test curves

Figure 2 Strength and initial tangent modulus under different confining pressures

For the convenience of engineering application,the average value of strength under various confining pressures can be taken as the strength parameter.Then,the Mises’ strength criterion can be used to describe the strength behavior of tested ice-saturated frozen loess.

In this study,thekcan be determined by the average value of strength under various confining pressures.The average value of strength in this case is 2.3517 MPa.Under triaxial compression,it is known thatσ2=σ3,then equation(1)was simplified toσ1-σ3=We obtaink=2.3517/=1.3578 according to the TC tests.

From figure 2b,it can be found that the relation between the initial tangent modulus and the confining pressure can also be divided into two phases.In phase 1,the confining pressures make the intergranular contact of solid grains tighter,which enhances the stiffness of ice-saturated frozen loess.Therefore,the initial tangent modulus increases with the increase of confining pressure in this phase.However,with the further increase of confining pressure,the initial tangent modulus reaches a maximum value at a critical confining pressure,and then the initial tangent modulus decreases with the increase of confining pressure in phase 2.The degradation of the initial tangent modulus also indicates that the ice in frozen loess is crushed and melted under relative high confining pressures due to the stress concentration.However the changing range of the initial tangent modulus of ice-saturated frozen loess is relatively small,which varied between 62.1 MPa and 164.0 MPa.It is recognizably different from the corresponding test results regarding ice-saturated frozen sand and unsaturated frozen loess reported by other scholars (Chamberlain,et al.,1972;Parameswaran and Jones,1981;Xu,2012).This difference between two types of soils indicates that the mechanical properties of ice-saturated frozen clayey soil are significantly governed by the ice bond,and that the internal friction between particles is trivial and hardly affects its performance.

3.2 TLUC test results and analysis

Figure 3 shows the deviatoric stress-axial strain curves under TLUC test at various confining pressures.It indicates that the influence of confining pressure on stress-strain curves at the loading stage of TLUC tests is similar to that under TC tests.At a lower confining pressure phase (with the confining pressure less than 5 MPa),the stress-strain curves of the loading stage also nearly coincide with each other.When the confining pressure exceeds 3 MPa,the stress-strain curves are also slightly affected by the confining pressure.However,the stress-strain curves under this confining pressure range fall below the stress-strain curves at lower confining pressures.These show that the variation of strength and deformation characteristics of ice-saturated frozen loess with confining pressures under the TC and TLUC tests are similar.There are many existing studies on the effects of confining pressure on mechanical behavior of frozen soil under TC tests (Laiet al.,2013).Therefore,here we will not go into deeper discussion for this subject regarding TLUC tests.What the authors focused on here were the deformation characteristics and the variation of elastic modulus with varying strain observed in TLUC tests.It can be found from figure 3 that the frozen soil has considerable residual deformation after unloading to a zero stress state even if the strain is very low.This indicates that the deformation of frozen soil is mainly a case of plastic deformation and that the elastic deformation is hardly apparent.

Figure 3 Deviatoric stress-axial strain curves under TLUC tests

Figure 3 also shows that the hysteresis loops were formed by the unloading and reloading processes.The area of hysteresis loop represents the energy dissipation under the process of unloading-reloading.Table 3 lists the energy dissipation corresponding to each hysteresis loop under different confining pressures.There,the unit of energy dissipation is 10-2J/m3which is similar to the specific strain energy.Table 3 shows that the energy dissipation during the unloading-reloading process increases with the number of cycles under various confining pressures.What should be noted is that the rate of increase of energy dissipation is higher at the initial stage while the rate slows to gradual to decreasing with further cycles.This occurs because of the slope of stress-strain increases rapidly with strain at the initial stage and slowly at the later deformation stage.The energy dissipation during unloading-reloading process is mainly controlled by the plastic strain.Therefore,the relation between energy dissipation and plastic strain may be more valuable in that it reveals the evolution law of energy dissipation with plastic strain.

Figure 4 shows the relation between energy dissipation and plastic strain for ice-saturated frozen loess under different confining pressures.It indicates that the energy dissipation was affected by the confining pressure.The energy dissipation decreases with the increase of confining pressure.

However,the energy dissipation has no obvious change with the further increase of confining pressure when the confining pressure exceeds 7.0 MPa.According to the variation of energy dissipation with plastic strain,the following formula can be used to describe the evolution of energy dissipation with plastic strain.

where,Edis the energy dissipation,anda,b,care the test parameters relative to confining pressures,respectively.

Figure 4 Variation of energy dissipation with plastic strain under various confining pressures

It can be discerned from figure 3 that the hysteresis loops in the stress-strain curve can be approximated as straight lines.The slopes of these straight lines are the elastic modulus of ice-saturated frozen loess under different strains.Therefore,we can investigate the evolution of elastic modulus with strain.Here,the initial elastic modulus was defined as the slope of the initial stage of the stress-strain curve.Figure 5 shows the elastic moduli at different strains under various confining pressures.It can be seen from figure 5 that,under a given confining pressure,from zero strain to the first unloading,the elastic modulus increased with the increase of strain,after which it reached a peak value at the first unloading,then it decreased with a further increase of strain.For this reason,we can regard the state corresponding to the peak value of the elastic modulus as an undamaged state.The deterioration degree of the elastic modulus in the initial stage relative to the undamaged state was defined as initial damage.The initial damage showed that there were micro-cracks in the frozen loess,and micro-cracks were gradually closed in initial loading stage to result in the increase of stiffness.Yet with further development of deformation,new micro-cracks or macro-cracks would occur in the frozen loess,which exhibited degeneration of the elastic modulus.

Table 3 Energy dissipation at different number of cycles under various confining pressures

Figure 5 Elastic moduli at different strains under various confining pressures

Based on the fact that damage induces deterioration of the elastic modulus,the damage variable for ice-saturated frozen loess is defined as the following:

whereEuwas elastic modulus under the undamaged state which corresponded to the maximum elastic modulus under a given confining pressure in this study,whileE~was the elastic modulus under a damaged state.The damage variable can be used to describe the extent of the damage of ice-saturated frozen loess,which evolved with the plastic strain.In order to calculate the damage in each plastic strain under various confining pressures,the elastic modulus and the corresponding plastic strain under various confining pressures are listed in table 4.

According to table 4,the damage under its corresponding plastic strain has been calculated by equation(3).The change in damage with plastic strain under various confining pressures is shown in figure 6.It can be ascertained from figure 6 that the damage of ice-saturated frozen loess developed with plastic strain,which weakened its mechanical properties.In the initial strain stage,the damage rate was higher.With the development of strain,the damage rate was reduced.In the late strain stage,the damage rate became very low.The damage was also influenced by confining pressure.When the confining pressure was less than 1.0 MPa,the damage variable increased with confining pressure.The reason for this was that when the confining pressure was lower,its increase could induce the expansion of micro-porosities and micro-cracks in an ice-saturated specimen and cause the development of damage.However,the damage decreases with the further increase of confining pressure.This was because under higher confining pressures (from 1.0 MPa to 5.0 MPa),the confining pressure restricts the development of micro-porosities and micro-cracks.When the confining pressure exceeded 5.0 MPa,the ice in frozen loess was crushed and pressure melting occurred,which resulted in more micro-porosities and micro-cracks and thus an increase of damage.

4 Summaries and conclusions

This study presents an experimental investigation of the mechanical behavior of ice-saturated frozen loess by conducting triaxial compression tests and triaxial loading-unloading cycle tests under confining pressures of 0.5–9.0 MPa at-6 °C.The TC tests show that the strength and deformation characteristics were influenced by the confining pressures.The strength of ice-saturated frozen loess changes from 2.4675 MPa to 2.5076 MPa under confining pressures from 0.5 MPa to 3.0 MPa.When the confining pressures range from 5 MPa to 9 MPa,the strength decreases to a range of 2.1927 MPa to 2.2414 MPa due to the crushing of the ice or melting under higher confining pressures.The Mises’ strength criterion can be used to characterize the ice-saturated frozen loess based on the fact that the difference of strengths under various confining pressure is trivial.The initial elastic modulus increases with the increasing of confining pressure and reaches a maximum value at confining pressure of 3 MPa.However,it deceases with the further increase of confining pressure.

The TLUC tests show that the elastic deformation of frozen soil is very small in the total deformation.The hysteresis loop is formed in the unloading-reloading process.The area of the hysteresis represents the energy dissipation which increases with the increasing of plastic strain.In the initial strain stage,the dissipative rate was higher.With the development of plastic strain,the dissipative rate becomes smaller and gradually tends to a stable value.The confining pressure has an effect on the energy dissipation.These characteristics can be described by the equation(2).The energy dissipation increases with the increase of confining pressure when the confining pressure changes from 0.5 MPa to 7.0 MPa.However,the energy dissipation curves under confining pressures of 7.0 MPa and 9.0 MPa almost overlapped each other which indicated that the energy dissipation was not affected anymore by the confining pressure when it exceeded a critical value.According to the fact that the elastic modulus decreases with the increase of plastic strain,the deterioration of stiffness was defined as the damage of ice-saturated frozen loess.The damage increases with the increase of plastic strain.The development of damage is faster at the initial stage.With further increases of plastic strain,the damage rate gradually approaches zero,which indicates the damage is not evolved any longer with the plastic strain.The damage was also influenced by the confining pressure.The damage increases with the increase of confining pressure under lower confining pressures.At relatively higher confining pressures,the damage decreases with the increase of confining pressure.With the further increase of confining pressure,the damage increases with the increasing of confining pressure once again.

This research was supported by the National Natural Science Foundation of China (41301072,41230630,41101068),National Key Basic Research Program of China (973 Program No.2012CB026102),Natural Science Foundation of Inner Mongolia (2013MS0702),the Program of Higher-level talents of Inner Mongolia University (30105-125146),and the Open Project Program of the State Key Laboratory of Frozen Soil Engineering (SKLFSE201208).

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