基于嵌套思路的饱和孔隙-裂隙介质本构理论

Constitutive Theory of Saturated Pore-fracture Media Based on Nested Way

为了指导本构建模工作,需要建立饱和孔隙-裂隙介质的一般本构理论框架.首先,从混合物理论和嵌套思路出发,获得饱和孔隙-裂隙介质的能量平衡方程.其次,根据热力学功共轭特性确定了饱和孔隙-裂隙介质本构方程的应变状态变量和应力状态变量.再次,根据热力学局部平衡假定,获得饱和孔隙-裂隙介质的自由能势函数一般本构方程.最后,从一般自由能势函数本构方程出发,获得孔隙骨架和裂隙骨架变形相互耦合的各向同性线弹性方程.当孔隙骨架和裂隙骨架变形解耦时,该方程能够退化到Khalili线弹性方程.研究表明,在小应变情况下固相应变可分解为裂隙骨架应变、孔隙骨架应变与固相材料体应变之和;当混合物均匀化响应原理成立和流相材料本构模型与单相一致时,裂隙骨架应变、孔隙骨架应变、固相材料体应变、裂隙流相材料体应变和孔隙流相材料体应变分别唯一决定裂隙介质有效应力、孔隙介质有效应力、固相材料真实压力、裂隙孔压和孔隙孔压;当自由能函数是状态变量的二次函数时,可获得线弹性本构模型.

A general constitutive theoretical framework of saturated pore-fracture media need be formulated to guide constitutive modeling.Firstly,based on the mixture theory and nested way,the energy balance equation of saturated pore-fracture media is obtained.Secondly,according to the thermodynamic work conjugation behaviors,the strain and stress state variables of the constitutive equation for saturated pore-fracture media are determined.Thirdly,based on the assumption of local equilibrium of thermodynamics,the general free energy potential constitutive equations are obtained for saturated pore-fracture media.Finally,deriving from the general free energy potential constitutive equations,an isotropic linear elastic equation is obtained taking into account the coupling of pore and fracture skeleton deformations.When the pore and fracture skeleton deformations are uncoupled,the equation is degenerated into Khalili’s linear elastic equation.The researches show that,the solid phase strain can be decomposed into the sum of fracture skeleton strain,pore skeleton strain and volumetric strain of solid material in the case of small strain;When the mixture homogenous response principle is valid and the fluid material constitutive model is the same as the single fluid one,the fracture skeleton strain,pore skeleton strain,volumetric strain of solid material,volumetric strain of fluid material in fractures and volumetric strain of fluid material in pores uniquely determine the effective stress of fractured media,effective stress of pore media,real pressure of solid material,fracture pressure and pore pressure,respectively.A linear elastic constitutive relation can be achieved when the free energy function is a quadratic function of state variables.