Nonlinear Visco-Elasto-Plastic Model for Surrounding Rock Incorporating the Effect of Intermediate Principal Stress

Abstract

This paper focuses on the influence of intermediate principal stress on visco-elasto-plastic solution of surrounding rock. Assuming that the surrounding rock satisfies the spatially mobilized plane (SMP) failure criterion, the H-Kelvin model was adopted and improved by considering the effect of intermediate principal stress. For elasto-plastic surrounding rock, an analytical approach was presented. For strain-softening surrounding rock, the potential plastic zone was subdivided into a finite number of concentric annuli and a numerical model for calculating the stress and displacement of each annulus was presented. Thus, based on SMP failure criterion and the improved H-Kelvin model, the nonlinear visco-elasto-plastic models considering the effect of intermediate principal stress were proposed for elasto-plastic and strain-softening surrounding rock, respectively. The accuracy of the proposed approaches were validated with the published results. Comparisons show that the long-term creep deformation based on M-C failure criterion is 9.4 mm which is 34.3% greater than the results of SMP failure criterion. Taking the safety factor as 1.5, the proposed model is applied in predicting the long-term deformation of Shangxinzhai Tunnel, the deformation is calculated to be 8.5 cm which is 29.2% smaller than the designed value.