Study On Damage Statistical Constitutive Model Of Frozen Gravelly Sand Based On Modified Parabola Criterion

With the expansion of human activity space and the accelerated development of the construction of the western part of the country,the number of major infrastructure projects in cold regions is increasing.With the acceleration of engineering construction in cold regions,it is necessary to study the mechanical properties of frozen soil to ensure the stability of structures in frozen soil regions.The research on the damage constitutive theory of frozen soil is an important topic in the field of geotechnical engineering.In this paper,the normal triaxial tests are carried out at different temperatures and confining pressures to study the stress-strain characteristics,volume change characteristics and strength characteristics of frozen gravelly sand.The damage statistical constitutive model of frozen gravelly sand is established The rationality of the model is verified by experiments.The main research contents and conclusions are as follows:(1)Conventional triaxial shear test at low temperature for frozen gravelly sand.Using MTS landmark 370.10 frozen soil triaxial tester,the conventional triaxial shear tests of frozen gravelly sand were carried out at four temperatures(-3 ℃,-4 ℃,-5 ℃ and-7 ℃)and five confining pressures(0.4MPa,0.7MPa,1.0MPa,1.5MPa and 2.0MPa).The results show that the deviator stress-axial strain curve of frozen gravelly sand shows strain softening characteristics,and the corresponding volume change curve shows the characteristics of shrinkage before expansion.The curve of deviating stress axial strain can be divided into initial linear elastic stage,elastic-plastic stage and strain softening stage.With the increase of the confining pressure,the maximum volume shrinkage and the maximum shear expansion of the specimen are smaller and smaller.At different temperatures,the volume change curves are basically similar,showing the phenomenon of volume expansion after shrinkage with the increase of axial strain,and with the gradual decrease of temperature,the strain softening trend is more and more obvious.The strength envelope is nonlinear,which can not be described by the Mohr Coulomb strength criterion.(2)Strength criterion of frozen gravelly sand.According to the strength characteristics of frozen gravelly sand,a nonlinear strength criterion for frozen gravelly sand is proposed based on envelope theorem and Mohr stress circle equation.In the complex stress state,the nonlinear characteristics of the strength envelope of frozen gravelly sand are considered in the P-Q plane.In the π plane,the strength envelope of frozen gravelly sand is assumed to conform to the shape characteristics of lade Duncan criterion,and the strength criterion of frozen gravelly sand under complex stress state is established.The strength envelope of frozen gravelly sand on P-Q plane is verified.The test results are in good agreement with the fitting results,which shows that the proposed strength criterion can better describe the strength characteristics of frozen gravelly sand under complex stress conditions.(3)Establishment and verification of damage statistical constitutive model for frozen sand with gravel.The distribution of micro cracks or micro holes in frozen soil is discrete and random.It is considered that the strength of micro elements in frozen soil obeys the Weibull distribution law.The modified parabolic strength criterion is introduced to describe the strength characteristics of micro elements in frozen soil.According to the theory of statistics and damage mechanics,a statistical damage constitutive model which can reflect the whole process of damage of frozen gravel sand is established.The results show that the constitutive model can better describe the strain softening characteristics and the characteristics of shrinkage and expansion.In addition,through the analysis of and F in Weibull distribution function＿The sensitivity analysis shows that the stress-strain curve changes from strain softening to strain hardening from 0.231 to 0.931＿0 increases from 5.278 to 28.278,and the stress-strain curve changes from strain softening to strain hardening.