Mechanics Characteristic And Constitutive Model Studies Of Limestone Under Cyclic Loading Condition

With more and more kinds of geotechnical engineering are constructed,during the construction and using,they often encountered cyclic loading,the failure characteristics of rock under cyclic load perfect the theoretical research of rock under complex stress,and they are the frontier problem in engineering field,also have important significance to ensure the safety and stability of engineering.In this paper,based on the limestone of a water conservancy and hydropower engineering area,five laboratory mechanical tests(acoustic wave test,uniaxial compression test,conventional triaxial test and uniaxial cyclic test and triaxial cyclic test)were carried on limestone.The mechanical properties of limestone in different deformation zones under cyclic loading are analyzed,and the mechanical properties and macro failure mechanism of limestone under different loading conditions are compared.Then,the energy evolution law of rock in different deformation zones is analyzed through the stress-strain curve of rock under cyclic loading.Finally,using the cyclic loading test results,the fatigue constitutive model of limestone based on the internal variables theory and simplified constitutive models for different rock under certain conditions are established.The main conclusions of this paper are:(1)Through static limestone under uniaxial compression specimens the stress-strain curves of limestone is obtained under static uniaxial compression,the shape of curves before peak load is divided into two types(i.e.: obvious plastic deformation and unapparent plastic deformation type),the shape of curves after peak load can be divided into three types(i.e.the stress drop and the stress drop fast recovery type,stress drop multistage type);the stress-strain curves under static triaxial compression are similar with the static uniaxial compression when the confining pressure is 2 ~ 6MPa the curve before the peak load shows the plastic deformation stage,and the curve after the peak load shows the stress drop rebound,when the confining pressure is 8 ~ 12 MPa,the curve before the peak does not show the plastic deformation stage,the curve after the peak load shows rapid drop type and multi drop type;under dynamic single axis and three axis circulation,the stress-strain curves of failure apecimensare highly similar.The stress-strain curves in the reduction zone are both changed from sparse to dense,and the stress-strain curve in the area of reduction is changed from dense to sparse.According to the standard of non representative value,the compressive strength of limestone under static uniaxial compression condition is 175 MPa,the deformation modulus is 23.6GPa,the Poisson's ratio is 0.1.(2)Under the uniaxial and triaxial cyclic loading test,the deformation parameters of limestone are similar with the evolution of cyclic times in different deformation zones.At the reduce zone,the dynamic modulus of elasticity increases gradually with the increase of cyclic times,and the dynamic Poisson's ratio,the residual axial strain and residual volume strain decreases gradually.When the axial load is near the critical load value,the relative change of dynamic modulus of elasticity and dynamic Poisson's ratio is relatively small,and the residual axial strain,the residual volume strain increase gradually.At the increase zone,the dynamic modulus of elasticity decreases gradually,the dynamic Poisson's ratio,the residual axial strain and residual volume strain increase gradually.(3)Under the uniaxial and triaxial cyclic loads,the deformation parameters of limestone are similar with the evolution of axial vibration load.The dynamic modulus of elasticity and dynamic Poisson's ratio increases gradually with the increase of axial vibration load,and the residual axial strain and residual volume strain gradually decrease.(4)When the confining pressure is 0~4MPa,the dynamic modulus of elasticity of limestone increases firstly and then decreases with the increase of confining pressure,while the dynamic Poisson's ratio decreases firstly and then increases.When the confining pressure is 4~8MPa,the dynamic modulus of elasticity increases with the increase of confining pressure,and the dynamic Poisson's ratio decreases gradually with the increase of confining pressure.Under the pressure of 0~8MPa,the residual axial strain and residual volume strain show a tendency to decrease with the increase of confining pressure.(5)It can be obtained through limestone macroscopic destruction under different experimental conditions that: failure form of limestone is mainly to tensile failure in the conditions of static uniaxial compression test;static triaxial compression in the three conditions,when the confining pressure is 0 ~ 4MPa,mainly in tension and shear failure.And when the confining pressure is greater than 4 ~ 12 MPa,mainly by crushing and single shear failure forms;failure modes of rock under uniaxial cyclic loading for tensile failure;triaxial cyclic loading,the main damage form of limestone to shear failure.The compressive strength of limestone under different test conditions has different relation:Rjs>Rds,Rjd>Rdd,Rjs>Rjd,Rds>Rdd.So the effects of dynamic loads on the stability of rock mass in practical engineering is notable.experimental data obtained through the shear strength parameters of viscosity,cohesion limestone static test conditions,the cohesion is 46.39 MPa,the internal friction angle is 50.39 °,the dynamic test conditions for cohesion is 15.95 MPa,internal friction angle is 63.41 °.(6)In the uniaxial and triaxial cyclic loading test,the energy parameters of limestone are similar with the evolution of cyclic Week in different deformation zones.When the specimen is under the axial vibration load or the critical axial vibration load,the unit volume energy and the elastic deformation energy of the unit will not change significantly.while the unit volume dissipation energy decreases gradually and the elastic energy index increases gradually;When the specimen is in the critical axial vibration load,the unit volume can decrease with the increase of the cycle slip,the elastic deformation energy of the unit increases gradually with the increase of the cycle slip.The dissipation energy of unit volume can still decrease gradually.The elastic energy index is gradually increasing with the increase of cyclic times.(7)Under the uniaxial and triaxial cyclic loading test,the energy parameters of limestone increase gradually with the increase of axial vibration load;Through the analysis of the evolution of the energy parameters of limestone in different deformation zones with the confining pressure.When the axial vibration load is in the reduce zone,the unit volume vary little with the increase of confining pressure,moreover,the unit volume will decrease gradually.It can be seen that the dissipation energy of the unit increase and the elastic energy index decreases gradually;When the reduce zone axial vibration loads,the unit volume decrease gradually with the increase of confining pressure,and the elastic deformation of unit volume is reduced.In addition,the dissipation energy of unit volume energy increases and the elastic energy index decreases gradually.(8)When the deformation of limestone enters into expansion area,even if the unload enters to reduced area,the mechanical properties of the specimen show the properties of expansion area.(9)According to the stress-strain curve under cyclic loading,using the residual axial strain as the internal variable,the Fatigue constitutive model of limestone is established,and simplified constitutive models suitable for different lithology and certain conditions are proposed based on the existing data and previous studies,and the model parameters are analyzed in detail.Finally,the origin software is used to verify the rationality of the constitutive model and simplified model of cyclic loading.According to the comparison between the experimental data and fitting results,the rationality of each model is verified.