A Constitutive Model For Saturated Rock Mass Based On Double-stress Principle And Finite Element Program Development

Led by the "one belt and one way" strategy and the 14th Five-Year layout plan in recent years,large-scale range complex rock mass engineering projects have become more numerous and the resulting technical difficulties increase.According to the characteristics of large-scale rock mass engineering and the research status of rock mass,the most typical saturated multi-set jointed rock mass with low-order fracture system is studied,based on the theory of equivalent continuous media,from two aspects of constitutive model and finite element program development.It not only improves the theoretical system of rock mass constitutive theory,but also provides a new calculation model for numerical analysis and design of this kind of rock mass engineering,which is conducive to analysis and optimization comparison.Firstly,it should be clear that the premise for research based on the theory of equivalent continuous media is that multi-set jointed rock mass can be equivalent to porous continuous media.By determing the permeability and mechanical parameters of rock mass unit with quasi-constant and quasi-tensor criterion,the existence of REV in rock mass is checked to confirm whether the rock mass can be equivalent to porous continuous media,and the rock mass attribute parameters corresponding to the size of REV are taken as the equivalent continuity parameters.An example is given to show the steps for determining the equivalent continuity of multi-set jointed rock mass.It is proved that such rock mass with low-order fracture system can be regarded as porous continuous media when the joint spacing is dense and uniform.Secondly,the shortcomings of the previous constitutive theory of saturated porous media that the deformation of solid matrix can not be reasonably considered is overcome.Based on the universal principle of conservation of mechanical work and the theory of engineering mixtures,the double-stress principle of saturated porous media considering matrix compressibility under small strain is proposed by deducing and analyzing the universal equation of conservation of work of volume deformation of saturated porous media.That is to say,Terzaghi effective stress only determines the solid volume fractional strain;solid matrix pressure only determines the solid matrix volume strain;Terzaghi effective stress and solid matrix pressure together determine the solid phase volume strain.The double-stress principle lays a theoretical foundation for the establishment of constitutive model for saturated rock mass equivalent to porous continuous media.Thirdly,a intact rock damage constitutive model with Poisson's ratio varying with principal strain and a dynamic joint constitutive model with stiffness varying with joint deformation and joint stress are established,and the coupling damage effect of joint deformation on intact rock mass is discussed.The nonlinear constitutive model for multi-set jointed rock mass is obtained by integrating intact rock and joint model.Based on the mixture theory and double stress principle,the stress-seepage coupling effect of saturated porous media is studied,and the constitutive model for saturated multi-set jointed rock mass is established by synthesizing the characteristics of the nonlinear constitutive model of multi-set jointed rock mass.Finally,in view of the fact that in most of the finite element softwares(such as the UMAT subroutine of ABAQUS)which can be customized by users to calculate geotechnical mechanics problems,the constitutive models adopted are based on the effective stress principle without considering the compressive deformation of solid and fluid matrix,a new finite element program is developed in order to apply the double stress principle.The basic stress-seepage coupling equation of rock mass is derived from the constitutive model for saturated multi-set jointed rock mass.The finite element equation and element stiffness matrix are obtained by Galerkin weighted residual method and bivariate function integral method,and the finite element program is developed.The program considers the compressive deformations of intact rock and joint water,the nonlinearity of rock mass and the coupling of stress and seepage,and is used to simulate the excavation of deep-sea rock mass tunnel.The results of numerical analysis show that the finite element program established by the proposed constitutive model can simulate the engineering response of nonlinear saturated rock mass more truly and provide reference for design and construction.