Study On Damage Constitutive Model Of Shale Considering Macroscopic And Mesoscopic Defects

The constitutive relationship of shale is not only a description of the mechanical properties of shale,but also a theoretical basis for shale fracturing.Shale contains a large number of micro-and macro-defects,such as micro-cracks,cracks,bedding and so on.Defects affect the mechanical properties of shale.Therefore,macro-and micro-defects should be considered in the construction of shale constitutive model.Based on triaxial compression test and ABAQUS finite element software numerical simulation,the influence of micro and macro defects on the mechanical properties of shale is analyzed,and the damage constitutive model of shale considering micro and macro defects is established on the basis of rock mechanics theory.The results of this paper are as follows:(1)The numerical simulation results show that stress concentration is easy to occur at the meso-damage site;the existence of meso-damage affects the failure mode of rock samples;with the increase of the number of meso-damage from 0 to 20,the fracture pressure decreases from 18.04 MPa to 15.36 MPa,that is,rock is more vulnerable to failure.(2)The triaxial compression test results of shale show that the corresponding peak pressure of shale decreases from 106.2MPa to 72.3MPa when the fracture depth increases from 0 mm to 12.5 mm;when the number of cracks increases from 1 to 4,the peak pressure decreases from 85.5MPa to70MPa;the peak stress and elastic modulus of shale show concave variation with the increase of angle,and the peak stress corresponding to 45 degree cracks is the smallest.Its value is 85.5MPa;with the increase of the percentage of Crack Filler(calcite),the change of elastic modulus and peak stress is concave,that is to say,it first decreases and then increases,and the minimum value is 85 MPa when the content is 50%.Through the study of shale compression photographs,it is found that the main shear failure occurs in the sample,and the fracture surface is related to the fracture angle.(3)Assuming that rock micro-element strength obeys Weber distribution,and expresses micro-element strength with Mohr-Coulomb criterion,the micro-damage variable is deduced.According to fracture mechanics and damage mechanics,the macro-damage variable of uniaxial compression is deduced,and then the macro-damage variable and micro-damage variable are coupled.Finally,the damage constitutive model of shale considering macro-and micro-defects under uniaxial compression load is obtained,and the model is calculated.Comparing the stress-strain curves with the experimental data,it is found that they are in good agreement,which indicates that the uniaxial compression model is correct.(4)Based on the triaxial experimental data,the expression of micro-damage variable is derived by introducing measured stress and strain,and the expression of macro-damage variable under triaxial compression is derived from the equivalent flexibility matrix of fractured rock mass and the flexibility matrix of complete rock sample.According to the Lemaitre strain equivalence principle,the expression of damage variable coupled with macro-and micro-defects is derived,and finally the triaxial compression is established.By comparing the stress-strain curves of triaxial model with the experimental curves,it is found that they are in good agreement.By analyzing the influence of crack depth,angle and number on the peak stress,it is found that the law is the same as the experimental results,which can prove the correctness of the constitutive model.