Statistical Damage Constitutive Model for Rocks Under High Temperature and High Confining Pressure Environments Based on the Weibull Distribution
Deep-seated rocks are typically found under high temperature and high confining pressure conditions.It has strong theoretical and practical significance to intensive research the constitutive relationship of deep-seated rocks for the exploration of deep-earth mineral resources,efficient utilization of geothermal energy,and stability analysis of rock masses.In order to investigate the constitutive relationship of rocks during the entire process of static triaxial compression under different temperature and confining pressure,based on the concept of macroscopic phe-nomenological damage mechanics,from the aspect of rock elastic modulus changing with temperature,an expres-sion of rock damage under temperature effects was obtained.Furthermore,based on the Weibull distribution and modified Mohr-Coulomb strength criterion,rock mesoscopic was homogenized.Combined with the statistical dam-age theory,a statistical damage expression of rocks was obtained under axial pressure;Subsequently,based on the extended strain equivalence principle,the two parts of damage were coupled to yield a coupled damage expression of rocks under high temperature and axial pressure.Combined with the consideration of rock residual stress following Lemaitre's strain equivalence hypothesis and the principle of effective stress,this coupled damage expression was considered.At the same time,the influence of the threshold of crack initiation within rocks was taking into account.The constitutive model was divided into two parts of before and after the threshold strain.This resulted in a segmented function form of a statistical damage constitutive model for rocks that reflects the impact of high temperature and high confining pressure.To validate the applicability and accuracy of the model,the model's constitutive curves for rocks were compared with experimental constitutive curves under different conditions of temperature(25,200,400,600,800,1 000 ℃)and confining pressure(0,10,20,30,40 MPa).The comparison results were favorable which in-dicated there is a critical temperature for rocks.Under constant confining pressure,it was observed that the strength of the rock initially increases and then decreases with increase of temperature;Under constant temperature,the ductility of the rock gradually enhances with increase of the confining pressure.
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