Study On The Evolution Of Non-uniform Deformation And Failure And Statistical Damage Constitutive Model Of Rock

As a kind of heterogeneous natural geological materials,rock plays an extremely important role in the construction of geotechnical engineering and mine engineering,its deformation and failure laws are closely related to the occurrence of engineering geological disasters.And in the actual engineering practice,rock is often in different loading states.It is helpful to understand the failure mechanism of rock correctly to study the evolution laws of rock deformation and failure under different loading modes,which is of great significance to the safety design,construction and disaster prevention of geotechnical engineering and mine engineering.The key problem of studying the deformation damage evolution and failure of rock is to establish the constitutive model of deformation damage and failure.Considering the non-uniformity of rock,the basic theory of statistical damage mechanics is an effective method to study rock deformation and failure.Therefore,it is equally important to establish statistical damage constitutive equation based on the evolution laws of non-uniform deformation of rock.By investigating a large number of domestic and foreign literatures on rock deformation,damage and failure,and on the basis of summing up the previous research results,deformation and failure tests of rocks based on the digital speckle correlation method and the corresponding acoustic emission tests under different uniaxial loading modes were carried out and the evolution laws of non-uniform deformation of rock specimens under different loading modes,including the evolution of non-uniform deformation field,the displacements evolution of deformation localization bands and the evolution of deformation energy,were analyzed.In addition,the evolution laws of lateral expansion coefficients in the whole process of non-uniform deformation of rocks were analyzed and the micro-morphology of the fracture surfaces of rocks were observed by scanning electron microscope,and the failure types of rocks under different loading modes were studied.At the same time,the acoustic emission characteristics in the process of rock deformation under different loading modes were analyzed,and then the relationships between the degree of non-uniform defornation and acoustic emission characteristics of rocks were studied.Based on the evolution laws of non-uniform deformation field and the relationships between the degree of non-uniform deformation and acoustic emission characteristics under different loading modes,the damage variable of rock was defined with the degree of non-uniform deformation.Based on the basic theory of statistical damage and considering the nonlinear elasticity and residual stress of rock specimens,the statistical damage constitutive equations of rocks under uniaxial and triaxial compression were derived.Finally,the correctness and rationalities of the constitutive equations were verified by fitting test results.The main research contents and conclusions are as follows:(1)Study on the evolution laws of non-uniform deformation and failure of rock under uniaxial compressionBased on the digital speckle correlation method,the evolution of non-uniform deformation field,the displacements evolution of localization bands and the evolution of deformation energy of rock in the process of uniaxial compression were analyzed,the research results show that:The non-uniform deformation field gradually evolves with the increase of stress.The degree of non-uniform deformation changes linearly before plastic stage,and then changes nonlinearly.The degree of non-uniform deformation increases greatly at the moments of the start-up of deformation localization band,the stress drop during the pre-peak loading,the peak value of loading stress and the failure after peak loading.The displacements evolution of deformation localization band(including dislocation displacement and tension displacement)correspond well with the loading stress.The displacements of localization band change linearly before the plastic stage,then present nonlinear change.The displacements have a turning point at the time of the start-up of deformation localization band,and the rate of increase in displacement speeds up.The displacements of loealization band jump up at the time of stress drop during the pre-peak loading and suddenly change by a big margin at the time of failure after peak loading.There is a good correspondence between deformation energy evolution and loading stress of rock specimen.In which,before the time of the start-up of deformation localization band,the deformation energy of rock specimen gradually accumulates and the accumulative rate gradually increases.The energy accumulation begins to slow down from the time of the start-up of deformation localization band,and at the time of stress drop during the pre-peak loading and failure after peak loading,energy is released.(2)Study on the evolution laws of non-uniform deformation and failure of rocks under uniaxial constant amplitude cyclic loading and uniaxial graded constant amplitude cyclic loadingBased on the digital speckle correlation method,the evolution of non-uniform deformation field,the displacements evolution of localization bands and the evolution of deformation energy of rocks in the process of uniaxial constant amplitude cyclic loading and uniaxial graded constant amplitude cyclic loading were analyzed,the research results show that:In the process of constant amplitude cyclic loading,the non-uniform deformation field gradually evolves.The degree of non-uniform deformation undergoes slow evolution stage and accelerated evolution stage,and lags behind the loading stress in time.During the whole cycle process,the degree of non-uniform deformation increases with the increase of cyclic number when loading or unloading to the same stress.During each cycle,the degree of non-uniform deformation accumulates when loading and unloading to the same stress.Before rock failure,the value of the degree of non-uniform deformation at the bottom point of unloading stress will gradually approach the one at the peak point of loading stress,this phenomenon can be used as the precursory information of rock deformation and failure under constant amplitude cyclic loading.The evolution of the non-uniform deformation degree of rock under graded constant amplitude cyclic loading is basically the same.Only at the initial stage of the increase of graded peak stress,the value of the degree of non-uniform deformation and the lag time at the peak point of the degree of non-uniform deformation relative to the peak point of loading stress all increase greatly.In the process of constant amplitude cyclic loading,the displacements evolution of deformation localization bands is dominated by tension displacement,and the ultimate failure mode is tensile failure.The displacements of localization bands fluctuate with loading and unloading stress.They undergo slow evolution stage and accelerated evolution stage,and lag behind loading stress in time.During the whole cycle process,the displacements of localization bands increase with the increase of cyclic number when loading or unloading to the same stress.During each cycle,the displacements of localization bands accumulate when loading and unloading to the same stress.In addition,before rock failure,the displacements of localization bands at the bottom point of unloading stress will gradually approach the ones at the peak point of loading stress,this phenomenon can be used as the precursory information of rock deformation and failure under constant amplitude cyclic loading.The displacements of the localization band of rock under graded constant amplitude cyclic loading basically have the same change laws,but the value of the displacements of localization bands and the lag time at the peak point of the displacements of localization bands relative to the peak point of loading stress all increase considerably only at the initial stage of the increase of graded peak stress.In the process of constant amplitude cyclic loading,the deformation energy evolution of rock specimen lags behind the loading stress in time.When loading or unloading to the same stress,the deformation energy gradually accumulates with the increase of cyclic number,and in each cycle,when loading and unloading to the same stress,the deformation energy also accumulates.The deformation energy under graded constant amplitude cyclic loading basically has the same change laws,but the cumulative value of deformation energy and the lag time at the peak point of deformation energy relative to the peak point of loading stress all increase considerably only at the initial stage of the increase of graded peak stress.(3)Study on the evolution laws of non-uniform deformation and failure of rock under uniaxial graded cyclic loadingBased on the digital speckle correlation method,the evolution of non-uniform deformation field,the displacement evolution of localization band and the evolution of deformation energy of rock in the process of uniaxial graded cyclic loading were analyzed,the research results show that:The non-uniform deformation field of rock gradually evolves with the increase of graded peak stress and cyclic number,and the localization phenomenon becomes more and more obvious.After the start-up of localization band,the peak point of non-uniform deformation degree lags behind the peak point of loading stress.During the whole process of graded cyclic loading,the degree of non-uniform deformation increases with the increase of cyclic number when loading or unloading to the same stress.During each cycle,the degree of non-uniform deformation accumulates when loading and unloading to the same stress.The difference of the degree of non-uniform deformation between the peak point of loading stress and the bottom point of unloading stress increases with the increase of cyclic number.The specimens are mainly tensile and extrusion failure.During the whole process of graded cyclic loading,the extrusion displacement of localization band increases with the increase of cyclic number when loading or unloading to the same stress.During each cycle,the extrusion displacement of localization band accumulates when loading and unloading to the same stress.The extrusion displacements of localization band between the peak point of loading stress and the bottom point of unloading stress both increase greatly when the localization phenomenon first appears,and the difference between them increases with the increase of cyclic number.After the start-up of localization band,the peak point of deformation energy lags behind the peak point of loading stress.During the whole cycle,when loading or unloading to th?saine stress,the deformation energy gradually accumulates with the increase of cyclic number,and in each cycle,when loading and unloading to the same stress,the deformation energy also accumulates.The difference of the deformation energy between the peak point of loading stress and the bottom point of unloading stress increases with the increase of cyclic number.(4)Study on the failure types of rocks under different uniaxial loading modesBased on the digital speckle correlation method,the lateral expansion coefficients of rocks under different forms of uniaxial loading were calculated.It is found that the degree of lateral relative elongation of rock specimens all increases gradually during different forms of uniaxial loading,and this Poisson effect leads to the tensile failure of rock specimens.During the constant amplitude cycle,the degree of lateral relative elongation of rock specimens at the peak point of loading stress increases with the increase of cyclic number,but the increase rate decreases with the increase of graded peak stress.In addition,the fracture surfaces of rocks were observed by scanning electron microscope.Through the micro-morphology analysis of rock fractures,it is confirmed that the brittle tensile failure is dominant in rocks under different uniaxial loading modes.The microanalysis results are consistent with the previous macroanalysis results,which further reveals the influence of loading modes on the failure types of rock.(5)Study on the relationships between the degree of non-uniform deformation and the acoustic emission characteristics of rocks under different uniaxial loading modesThrough the study of the relationships between the degree of non-uniform deformation and the acoustic emission characteristics of rocks under different forms of uniaxial loading,it is found that there is a good corresponding relationship between them,in which:During the uniaxial compression process,the degree of non-uniform deformation at the start-up point of localization band increases greatly,and the accumulative ringing counts and accumulative energy of acoustic emission begin to accelerate.At the time of stress drop,the degree of non-uniform deformation increases greatly,the accumulative ringing counts and accumulative energy of acoustic emission increase sharply.In different forms of uniaxial cyclic loading process,the maximum point of the degree of non-uniform deformation corresponds to the starting point for the quiet period of acoustic emission signal,and the minimum point of the degree of non-uniform deformation is located in the quiet period of acoustic emission signal.The degree of non-uniform deformation is negatively correlated with the Felicity ratio in general,and with the cyclic number increasing,the degree of non-uniform deformation increases and the Felicity ratio decreases.(6)Study on the statistical damage constitutive models of rock based on the evolution of non-uniform deformationBased on the analysis of the variation of the degree of non-uniform deformation of rock specimens with axial strain under different uniaxial loading modes and the corresponding relationships between the degree of non-uniform deformation and the acoustic emission characteristics,the damage variable was defined with the non-uniform deformation degree,i.e.,the statistical index Sw of non-uniform deformation.The increment of Sw was assumed to accord with Weibull distribution relative to the axial strain and the statistical damage constitutive equation of rock under uniaxial compression was derived by considering the nonlinear elasticity and residual stress of rock specimen at the same time.Finally,the correctness and rationality of the constitutive equation were proved by fitting the experimental data.In the derivation process of the statistical damage constitutive equation for rock under triaxial compression,the damage variable was still defined with the degree of non-uniform deformation.The increment of Sw was assumed to accord with Weibull distribution relative to the combined effect of the strains of rock specimen in three directions,i.e.,the volume strain ?m,and the nonlinear elasticity and residual stress of rock specimen were also considered,the statistical damage constitutive equation of rock under triaxial compression was deduced.The correctness and rationality of the constitutive equation were proved by fitting experimental data.Finally,the influences of confining pressures on the parameters of statistical damage constitutive model were discussed.