A Novel Double-Layer Plastic Zone Elastoplastic Model and Analytical Solutions Considering the Freezing Temperature Gradient of Surrounding Rock in Cold Region Tunnels

Abstract

The frost heave force and the plastic zone caused by the frost heave of the surrounding rock are the primary causes of tunnel frost damage. Current research mainly focuses on the plastic damage caused by the frost heave rock zone on the inner layer rock, while neglecting the damage caused by the outer layer rock. It will not accurately evaluate the stability of tunnels in cold regions. A new elastoplastic calculation model of the tunnel surrounding rock double-layer plastic zone in cold regions is proposed to reveal the failure law of the surrounding rock under frost heave based on thermodynamics and elastic-plastic mechanics theory. The stress field and radius of the surrounding rock in the two-layer plastic zone are determined using the Unified Strength Theory. The radius and stress distribution of the double-layer plastic zone obtained by the theoretical solution are in accordance agreement with the numerical calculation, which verifies the correctness of the theoretical solution. The case analysis of the Yuximolegai Tunnel shows that the thicknesses of the inner and outer plastic zones of the surrounding rock reach 0.57 and 2.34 m, respectively. The outer plastic zone caused by non-uniform frost heaving of the surrounding rock has a larger influencing range than the inner plastic zone. The double-layer plastic zone expands rapidly with the increase in the volumetric frost heave coefficient and elastic modulus of the surrounding rock, but are significantly suppressed by the in-situ stress. The influence of lining thickness and non-uniform frost heave coefficient on the plastic zones is relatively minor, yet their impact on the frost heave force should not be overlooked.