Macroscopic And Microscopic Interpretation Of Morphologies Of Failure Planes And Fracture Mechanism Of Hard Rocks Under Loading And Unloading Paths

The excavation of deep rock mass involves complex loading and unloading processes,and engineering disasters induced thereby happen frequently.Existing research into the mechanism of unloading failure of rocks generally uses traditional methods at the macroscopic scale while overlooks the microstructures in rocks.With the improvement of the testing means,it has become possible to characterize the evolution process of rock failure from the microstructural perspective.Failure planes,which record the deformation and failure process of rocks,contain rich microscopic failure information.Therefore,the analysis of failure planes of rocks allows researchers to reveal the essence of the failure.At present,the information about failure mechanism contained in failure planes of rocks under different unloading paths has not been well interpreted.Based on the loading and unloading tests of marble and the digital image processing technique,the correlation between 3d morphologies of failure planes and the failure mechanism was explored.The crack evolution mechanism and morphological characteristics of failure planes in the failure process of marble were quantitatively characterized through simulation tests by means of 3d particle flow code(PFC).Then,a constitutive model for rock failure based on morphological characteristics of failure planes was established.The main research results are shown as follows:(1)The loading and unloading tests for failure of marble under were conducted.On this basis,the research analyzed mechanical properties of marble throughout the deformation and failure process under unloading paths,explained influences of confining pressure and unloading rate on the elastic modulus,and provided changes of brittleness index of rock samples with increasing confining pressure and unloading rate.Test results indicated that the higher the stress level in the unloading was,the larger the damage stress and peak stress of rock samples;as the unloading rate increased,the damage stress,damage strain,peak stress,and peak strain all decreased.During the unloading of confining pressure,the confining pressure–elastic modulus curves gradually changed from linear to nonlinear ones,and the nonlinear characteristics became less evident with the growing unloading rate.At the same unloading rate,the decrease in the elastic modulus increased significantly with the increment of the initial confining pressure during unloading.Under the confining pressure of 10?40 MPa,the brittleness index ?B always increased with the rising unloading rate,and the fluctuation of the index ?B was found to be maximum under confining pressure of 40 MPa with the increasing unloading rate.(2)The scanning and analysis of 3d morphologies of failure planes in the marble under loading and unloading paths revealed that with the increase in the unloading rate,the elevations of measurement points of failure planes tended to be concentrated.Moreover,the higher the stress level during the unloading was,the greater the correlation coefficient of normal fitting for elevations of the measurement points.The amplitude parameter Sa and the fractal dimension D both reduced with growing confining pressure and the two were linearly correlated with confining pressure.The Sa and the D showed an increasing trend with the rising unloading rate.As the confining pressure and the unloading rate increased,a large amplitude parameter Sa corresponded to a large brittleness index B?.The cohesion c of rock samples decreased on the whole while the internal friction angle ? increased with the growth of the amplitude parameter Sa.The fractal dimension D was linearly correlated with the amplitude parameter of failure planes: a large amplitude parameter corresponded to a great fractal dimension.The fractal dimension D was found to grow with the increasing roughness coefficient JRC3 D of failure planes,and the two presented a quadratic positive correlation.(3)A 3d simulation model based on PFC was built for failure of marble during loading and unloading and the conversion between the unloading rate in the PFC simulation test(in MPa/step)and that in indoor test(in MPa/s)was provided as 1 MPa/s = 0.007 MPa/step.Based on characteristics of the relative displacement field,the 3d failure planes in the PFC simulation tests under loading and unloading paths were subjected to secondary screening and verification.The PFC3 D based simulation test revealed that there were obviously more tensile cracks than shear cracks in the loading process and shear cracks extended later than tensile cracks.Compared with the loading test,the numbers of tensile and shear cracks both reduced under the unloading path.As the unloading rate increased,the ratio of the number of tensile cracks to that of shear cracks exhibited an increase trend.Before reaching the peak stress,the number of cracks reduced abruptly with growth of the unloading rate.The influences of the unloading rate on the damage of rock samples were mainly shown in the propagation speed of cracks;while after reaching the peak stress,the instantaneous kinetic energy gradually increased with rising unloading rate and in the context,the influences of the unloading rate on the damage of rock samples were reflected in the intensity of damage.By analyzing the characteristics of failure planes in the numerical model,it was found that the ratio of the number of tensile cracks to that of shear cracks on failure planes under unloading paths was always larger than that under loading paths,and it increased to a larger extent under greater confining pressure.The ratio of the number of tensile cracks to that of shear cracks on failure planes was linearly positively correlated with both the amplitude parameter and the fractal dimension D.(4)On the basis of morphological characteristics of failure planes of the marble,a damage variable d was defined as a ratio of minimum to maximum fractal dimension of failure planes under the identical grid spacing.Moreover,by considering the influences of confining pressure on the elastic modulus during the deformation process of rocks,a modified constitutive model for failure of hard rocks under loading and unloading paths was established.The theoretical curves obtained by solving the constitutive model matched well with the test curves.This indicates that the model is able to describe the changing characteristics of overall behavior and strength of marble during deformation with changes in confining pressure.