Study On Generalized Strength Reduction Method For Nonlinear Failure Criteria

The linear failure criteria is always used to analyze slope stability in the traditional strength reduction method.However,a substantial amount of experimental evidence shows that most geomaterials follow nonlinear failure envelopes,whose nonlinear characteristic is significant especially in the range of small normal stresses.So that the approximation from the nonlinear failure criteria to the linear failure criteria will lead to an evident deviation from realistic results in stability calculation.In this paper,the generalized Hoek-Brown(HB)criterion and the non-linear Mohr-Coulomb(MC)criterion,two commonly used nonlinear failure criterias,are applied to the generalized strength reduction method(GSRFEM),and in this method,it need to reduce the instantaneous linearization strength parameters at the stress point.The specific research contents are as follows:(1)To study two strength parameters reduction methods based on HB criterion.Firstly,to directly reduce HB strength parameters with same proportions,and there are four strength reduction schemes to be compared in the aspect of reduction effect.Secondly,it is certainly worth determining the applicable range of the optimal HB parameter reduction scheme and the strength reduction scheme based on the equivalent MC.(2)In the study on the generalized strength reduction method,two instantaneous linearization strength reduction schemes are proposed to verify its rationality:Based on the stress field attained from the elasto-plastic analysis,the stress point dependent MC strength parameters can be reduced,and the resulting approach is denoted as Point-IL-SSRFEM;Since the strength parameters are required to be constant in each element for the conventional finite element method,the attained instantaneous strength parameters for stress points in each element shall be averaged and then reduced,and the resulting approach is denoted as Element-IL-SSRFEM.(3)There are three instantaneous linearization approachs,namely the approach of minimizing the FOS(ILmin_FOS),the geometric approach(ILGeo)and the bisection trial approach(ILBisec),which are investigated in conjunction with the generalized strength reduction method for the HB material model and the nonlinear MC material model,respectively.Based on the above research,the innovative achievements are as follows:(1)Due to the inherent nonlinear feature of HB criterion,both the three-parameter reduction scheme,which is belived to be the optimal one among four HB strength parameter reduction schemes,and the strength reduction scheme based on the equivalent MC,shall be only applicable when the value of HB input parameters is relatively small.(2)The calculation results of the rock slope example disclose that:compared to Element-IL-SSRFEM,Point-IL-SSRFEM has lower requirements for finite element meshing,what's more,the numerical accuracy and computational efficiency of Point-IL-SSRFEM are relatively higher.Hence,it is feasible to use GSRFEM to anlyse the stability of slopes based on the nonlinear failure criteria.(3)Based on a specific stress state,the instantaneous linearization strength parameters determined by the three instantaneous linearization methods are the same.Therefore,in the generalized strength reduction method,changing the instantaneous linearization method has little effect on its calculation result.(4)In the generalized strength reduction method,changing the instantaneous linearization method lead to the difference in computational efficiency,and ILGeo-GSRFEM is believed to be the optimal one for HB failure criterion,while ILmin_FOS-GSRFEM is the optimal one for nonlinear MC failure criterion.