To study the correlation between the evolutionary behavior of different morphologies of fractures within natural rocks and the cumulative damage degree of the rocks,a phonomenology theory was applied to classify the rocks into three components:intact rock microelements,closed-form fracture microelements and open-form fracture microelements.The differential kinetic equations of rock fracture evolution were developed based on the logic of biotope growth,and the expressions for the evolution of closed-form and open-form fractures under compression were solved semi-analytically,so as to quantify the conversion relationships among different compoenents of microelements in the process of compression.The evolutional curves of the open-form fractures show a downward and then upward trend,reflecting the evolution rule of the initial open-form fractures before and after the compaction stage,which accords with the stress-strain curves during the nonlinear compaction stage.Subsequently,the semi-analytical expression of rock fracture evolution was used to define a global damage variable,which can precisely quantify the global damage degree of the rock during the initial stage,the compaction stage,the elastic-plastic stage,and the post-peak stage respectively,and the damage constitutive model was proposed based on the above fracture evolution mechanism and the global damage variable.Finally,based on the theoretical deduction of differential equations,strength criteria,and multi-objective optimization,the parameters of the damage constitutive model were determined by various means.The stable solutions for the initial proportions of the three components of the rock and the three fracture conversion factors are obtained,which enables the simulation of the stress-strain curve during the rock compression process.The results show that in the case study of coal rock and carbonaceous shale,the proposed damage constitutive model can well features the stress-strain characteristics and fracture evolutional law of different rocks under different confining stresses,and the simulation results of our model are basically in line with the experimental results.
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