Analytical Framework for Parabolic Soil Arching and Stress Evolution in Deep-Buried Twin Parallel Rectangular Tunnels

Abstract：Understanding the stress evolution of soil arching in deep-buried twin parallel rectangular tunnels is pivotal for ensuring their design safety and economic viability. However, accurately characterizing this complex geomechanical behavior remains a significant challenge. This study pioneers an innovative stress evolution model for soil arching by integrating structural arch concepts with limit equilibrium theory, establishing a rational parabolic arch axis, and systematically incorporating the influence of soil cohesion on the stress evolution of both elastic and frictional arches for the first time. The model rigorously derives the nonlinear increasing stress evolution equation in the limit state, and based on the friction angle, gravity, cohesion and overburden pressure within the soil body, it proposes the optimization calculation formula of the key arch parameters such as foot inclination, arch thickness, etc. Extensive numerical simulations across 72 scenarios (varying depth-tospan and spacing-to-span ratios) validate the model. Predictions of the minor principal stress within the soil arch, which non-linearly decreases and stabilizes with increasing tunnel spacing, show strong agreement with simulation outcomes. This research enhances the understanding of soil arching in deepburied twin parallel rectangular tunnels, offering crucial theoretical support and an efficient analytical tool for optimizing their design and ensuring construction safety.