Study On Elastoplastic Constitutive Model Of Frozen Sand Considering Particle Breakage

Particle breakage is a basic phenomenon of granular materials under high stress.The research shows that there is significant particle crushing in frozen sand during triaxial shear.Up to now,little research has down on the particle breakage characteristics of frozen soil and the constitutive model considering the particle breakage applied to frozen soil have been carried out at home and abroad.The cold region of China is widely distributed,and the engineering in cold regions are developing rapidly.Under high stress conditions,the particle breakage of frozen soil seriously affects the stability and durability of the engineering in cold regions.The problem of particle breakage affecting frozen soil engineering has become an engineering problem which has been insufficient in the past and is becoming more and more important at present.In view of above-mentioned problems,low temperature triaxial compression tests of frozen sand under different temperatures and confining pressures is carried out in this paper.Based on the triaxial test results,the stress-strain characteristics,volumetric deformation characteristics,strength characteristics and particle crushing characteristics of frozen sand are studied,and the elastoplastic constitutive model and the non-linear strength criterion considering particle crushing are established.The main contents are as follows:（1）Based on the conventional triaxial test results of frozen sands with temperature conditions of-3℃,-5℃,-7℃and-10℃and confining pressure conditions of 0.5 MPa,1 MPa,2 MPa,4 MPa and 8 MPa respectively,it is found that frozen sands swell first and shrink later during triaxial shear,and the deviation stress-axial strain curve shows strain softening characteristics.Through screening the frozen sand samples before and after triaxial shear,the grain grading curves of frozen sand before and after shear are obtained.It is found that the content of coarse particles decreases obviously and the content of fine particles increases obviously after shear,which indicates that the particle crushing phenomenon of frozen sand is more obvious during triaxial shear.The influence of confining pressure on particle crushing characteristics is studied by using Hardin’s relative particle crushing rate B_r as a measure of particle crushing,which demonstrates that the relative particle crushing rate Br increases with the increase of confining pressure.（2）The triaxial test results of frozen sand show that the stress ratio of frozen sand varies nonlinearly with strain in the shear process.Consequently,the stress ratio M_cr proposed by Ueng and Chen in the energy balance equation considering particle crushing is modified to the stress ratio M which varies with strain.Then,the energy consumption of frozen sand during triaxial shear is analyzed by using the modified energy balance equation considering particle crushing,and the effects of confining pressure on energy consumption of particle crushing are studied.It is found that the frictional energy is realized as a trend of accelerated growth during the shearing process.The energy consumption of particle crushing has a good hyperbolic relationship with strain during triaxial shear,and is significantly affected by confining pressure.The energy consumption of particle crushing increases with the rise of confining pressure.（3）Based on the energy balance equation of frozen sand considering particle crushing,the yield function is established,the associated flow rule are adopted,and the hardening parameters are determined by a rebound test.Then,An elastoplastic constitutive model of frozen sand considering particle breakage is established.The model is used to simulate the stress-strain characteristics of frozen sand,which is compared with the indoor experimental result,and the results show that the model can better simulate the strain softening and dilatancy characteristics of frozen sand.（4）Shen Zhujiang’s double yield surface model has obvious advantages in reflecting the dilatancy,stress path influence and stress history influence of soil.In view of this,Based on the Shenzhujiang double yield surface model,a modified double yield surface model suitable for frozen sand is established.In order to better describe the three-stage characteristics of the deviation stress-axial strain curve of frozen sand,the parameter tangent modulus E_t of Shenzhujiang double yield surface model is modified.In order to make the model consider the influence of particle breakage,the energy tangent equation considering particle breakage is introduced to correct the volume tangent modulusμt in the original model.Finally,a modified double yield surface elastoplastic model suitable for description of strain softening,shear dilatancy,elasticity and particle crushing characteristics of frozen sand is established.Compared with indoor test results,the modified model has better applicability for frozen sand.