Study On Mechanical Properties Of Deep Marble Under Quasi-static Loading And Unloading

During the excavation and support of deep underground hydraulic engineering(such as underground powerhouse and diversion tunnel),the surrounding rock undergoes a complex stress process from stress equilibrium being broken to stress redistribution.Different engineering activities usually cause different disturbance intensity,which will influence rock mechanical properties in different response.The mechanical properties of deep rocks are significantly different from those of shallow rocks,and with the increase of buried depth and original rock stress,dynamic disasters such as rock burst and large-scale collapse caused by excavation disturbance have become more frequent.Therefore,in-depth study of the mechanical properties of deep-buried rock under high stress during excavation disturbance is of great importance for safe and efficient excavation and prediction of engineering disasters.Based on the MTS815 Rock Mechanics System of Key Laboratory of Deep Earth Science and Engineering(Sichuan University),Ministry of Education,this paper carries out laboratory tests on Jinping marble under five different stress paths,which are respectively uniaxial and triaxial with quasi-static strain rate,loading and unloading of different initial confining pressures and unloading of different unloading rates.From the aspects of conventional mechanical parameters,energy dissipation rate,characteristic stress,constitutive relation and dilatancy,the study on the change law of mechanical properties is carried out in an all-round way.The specific research content and conclusions are as follows:(1)Through the discreteness analysis of physical parameters such as density and P-wave velocity of marble,the grouping of test samples is carried out to improve the reliability of the follow-up test results.There are totally 39 rock samples in the test.In loading test,sample density?is in the range of 2.786 g/cm³ to 2.820 g/cm³,and the P-wave velocity V_p is in the range of 3311 m/s to4541 m/s.In unloading test,sample density?is in the range of 2.781 g/cm³ to 2.860 g/cm³,and the P-wave velocity V_p is in the range of 3497 m/s to 4132 m/s.The range,mean,standard deviation and variation coefficient of???/?_max?V_p and V_p/V_pmax are calculated respectively.The standard deviations of?,?/?_max and V_p/V_pmax are less than 1,and the variation coefficients are all less than 10%,which meets the requirements of the test specification.(2)Considering the influence of excavation disturbance on the mechanical properties of deep-buried marble,laboratory tests under five stress paths were carried out to analyze the variation law of stress-strain curves,peak stress,peak strain,deformation parameters and failure modes.The stress-strain curve under different stress paths can be divided into five stages of crack closure,linear elasticity,crack initiation,rapid crack expansion and post-peak failure.In uniaxial state,with the increase of strain rate,the pre-peak non-linear characteristics of marble gradually weaken and the degree of post-peak stress drop increases.In the triaxial state,as confining pressure increases,the stress plateau increases and post-peak stress drop decreases.For peak stress,it decreases gradually in uniaxial state while increases slightly in triaxial state with strain rate increasing.As confining pressure increases,peak stress gradually increases when constant confining pressure loading and unloading,but unloading peak stress is lower than loading peak stress under the same confining pressure.With the increase of unloading rate,peak stress increases under the initial confining pressure of 50MPa.Comparing uniaxial and triaxial state,peak strain of uniaxial marble is less than triaxial at the same strain rate.Under constant confining pressure loading and unloading conditions,peak strain gradually increases as confining pressure increases,and declines as unloading rate increases.The elastic modulus and Poisson's ratio obtained in elastic stage are used to analyze the deformation characteristics of marble under loading state,while the deformation modulus and the generalized Poisson's ratio are used under unloading state.As the unloading progresses,the deformation modulus decreases,but the generalized Poisson's ratio increases first and then remains unchanged.The failure modes of marble are different in different states.The brittle failure characters of marble become more obvious with strain rate and unloading rate increasing,the plastic failure characters get more obvious with confining pressure increasing,and marble exhibits s nonlinear dilatancy phenomenon under confining pressure.(3)Focusing on the change law of total strain energy,elastic strain energy and dissipation energy in the process of deformation and failure of deep-buried marble under different stress paths,the evolution process of different energy with the increase of stress is analyzed.In uniaxial stress state,the pre-peak energy dissipation is small,and the pre-peak energy evolution is mainly the storage of elastic strain energy.While in triaxial state,the increment of pre-peak elastic strain energy is small,but dissipation energy increases obviously.The influence of unloading on energy evolution is mainly embodied in dissipation energy,which turns and increases rapidly after unloading point.According to the variation law of energy dissipation,the energy evolution process of marble can be divided into four stages:low energy dissipation,slow increase of energy dissipation,pre-peak dilatancy and post-peak failure.(4)The ratio of dissipated energy to total strain energy was defined as energy dissipation rate to illustrate the progressive failure process of marble,and the characteristic stress was determined on this basis.Based on the characteristic stress point corresponding to the change law of energy,the mechanical performance of deep buried marble is analyzed.With the increase of stress level,the energy dissipation rate curves under different test conditions all show a trend of increasing first to decreasing and then increasing rapidly and finally slowly increasing.The closure stress?_ccis determined by the maximum value of energy dissipation rate,and crack initiation stress?_ci and damage stress?_cd are respectively determined by lateral strain difference method and volume strain method.Under quasi-static strain rate,the influence of strain rate on uniaxial and triaxial mechanical properties is analyzed according to the corresponding characteristic energy of ?_ci,?_cd and peak stress ?_cs,respectively,the influence of unloading and unloading rate on the mechanical properties of marble is analyzed by using the characteristic energy law corresponding to?_cs.(5)The damage variable was defined according to the energy dissipation rate.With the increase of stress,the damage variable of marble gradually decreases before closure stress,then increases slowly,and it increases in a power function when stress exceeds damage stress.Considering the difference of mechanical properties under uniaxial and triaxial conditions and the deterioration of mechanical properties in unloading state,the constitutive relations under uniaxial,triaxial loading and unloading conditions are established respectively,and the correctness of constitutive models is verified by the test data.(6)Based on the significant dilatancy phenomenon after the failure of the marble,the apparent dilatancy angle is determined by combining the volume strain and the energy dissipation rate respectively,through the nonlinear volume change characteristics under different stress paths,the deformation and failure mechanics characteristics of deep-buried marble are studied deeply.Under different stress paths,the volumetric strain increases first and then decreases with the increase of axial strain.According to this law,the apparent dilatancy angle?_VS,which is related to strain,is obtained,based on the energy dissipation rate,a new index-?_EDR is proposed to measure the dilatancy of marble by energy dissipation.Under different initial confining pressures,the variation of ?_{V S} and ?_EDR with loading and unloading conditions is consistent,but the variation of ?_{V S} and ?_EDR under uniaxial and triaxial with quasi-static strain rate and different unloading rates is contrary.According to the variation of deformation parameters and failure modes in marble,the variation of dilatancy characteristics under the above three stress paths is consistent with that of?_EDR,which shows that it is more universal.(7)Combined with the nonlinear characteristics of energy evolution,the self-restraint model of elastic strain energy is established and verified.The bifurcation and chaos in the energy evolution of marble are studied by means of nonlinear dynamical system.In the process of deformation and failure of marble,the self-inhibition model of energy evolution is established by combining the expression that the elastic strain energy has the mechanism of self-promotion and self-inhibition,and the model is verified by the pre-peak elastic strain energy-deviatoric stress relationship under different stress paths,which shows that the model can simulate the evolution of elastic strain energy well.The deformation and failure process of marble based on Logistic equation can be divided into three stages:stable region,period doubling bifurcation region and chaotic region.With the increase of stress,the energy evolution changes from elastic energy storage to energy dissipation.