Statistical Damage Constitutive Model Of Rocks Based On Brittle-ductile Transformation Characteristics And Its Parameter Inversion

As a natural geological material with defects,rock has multi-component,heterogeneous and cross-scale complex structure.Its constitutive model and parameter determination have always been an important content in the field of geotechnical engineering.Therefore,based on the method of theoretical analysis and example verification,this paper comprehensively uses the statistical damage theory,continuum mechanics theory and rock triaxial compression test to analyze the deformation process and mechanical properties of rock.On this basis,the brittleness evaluation method,strength criterion,damage model and constitutive model of rock are deeply studied.Firstly,on the basis of summarizing the previous research results,the existing brittleness indexes based on strength characteristics,stress-strain curve,mineral composition and fracture toughness are summarized and analyzed.On this basis,the pre peak stress growth rate,amplitude and post peak stress-strain relationship are comprehensively considered,and the evaluation method of rock brittleness characteristics based on full stress-strain curve is proposed,The results show that this method can not only qualitatively describe the brittleness characteristics of different kinds of rocks,but also quantitatively describe the brittleness characteristics of the same kind of rocks in different states.Secondly,the brittle ductile transformation characteristics of rock caused by confining pressure effect are analyzed.According to the fact that Mohr Coulomb strength criterion is only applicable to the prediction of rock stress eigenvalues under low confining pressure level,the concept of critical confining pressure is introduced,and a nonlinear strength criterion considering brittle ductile transformation characteristics is proposed;On this basis,aiming at the problem that the existing models are not suitable for the simulation of rock deformation and failure process under high stress state,the statistical damage theory is introduced.Based on the damage model considering the characteristics of residual strength,a statistical damage constitutive model which can simulate the brittle ductile transformation process of rock and is suitable for a large range of stress variation is established.The determination method of model parameters is given,and through parameter analysis,It is revealed that the fundamental reason why the existing statistical damage constitutive model can not simulate the brittle ductile transformation characteristics is the lack of rock strength criteria that can reflect the large range variation of confining pressure level and the neglect of the important influence of stress eigenvalue on the model curve;At the same time,the verification shows that the model can well simulate the triaxial compression deformation and failure process of marble from low confining pressure to high confining pressure.Finally,aiming at the defects and shortcomings that the existing models are difficult to reflect the initial damage characteristics and post peak deformation and failure characteristics,a rock geometric damage model considering initial damage is proposed;In addition,according to the characteristics that the Weibull distribution parameters m and F0 obtained by the peak point method can not better simulate the post peak deformation and failure characteristics,a parametric rock geometric damage model is constructed.On this basis,the statistical damage constitutive model of strain softening rock is established and modified,and the determination method of model parameters is given.The results show that the model established in this paper can better simulate the deformation characteristics of each stage of rock,Especially the post peak deformation and failure characteristics.