Non-limit state seismic earth pressure solution for finite soil mass considering intermediate principal stress

To investigate the distribution law of non-limit state seismic passive earth pressure in a finite soil mass under the translational (T-mode) pattern of a rigid retaining wall, and to overcome the limitations of existing seismic earth pressure models that cannot simultaneously account for wall displacement, soil arching effect, intermediate principal stress, and seismic temporal effects, this study establishes horizontal and vertical stress equilibrium equations for differential soil strips by combining the differential element method with the pseudo-dynamic method. An analytical solution for non-limit state seismic passive earth pressure considering intermediate principal stress is derived. Parametric analysis indicates that when soil arching effect and wall displacement are considered, the seismic passive earth pressure exhibits a nonlinear distribution along depth. At the same depth, the seismic passive earth pressure increases with larger internal friction angle, cohesion, displacement ratio, and intermediate principal stress coefficient, whereas neglecting the intermediate principal stress results in unconservative estimates. Under seismic loading, the resultant seismic passive earth pressure is amplified, and this amplification becomes more pronounced with increasing internal friction angle, especially when the base displacement ratio and soil cohesion are relatively high. For instance, at a normalized depth of 0.8, with all other factors held constant, increasing the internal friction angle by 33.33%, 66.67%, and 100% leads to normalized lateral pressure increases of 42.96%, 44.79%, and 44.67%, respectively. The proposed method provides a valuable theoretical reference for evaluating the seismic performance of retaining structures in underground engineering.