Finite strain solution for the surrounding rock of deeply buried tunnels based on the nonlinear strength characteristics

The strength of the surrounding rock in deeply buried tunnels exhibits obvious nonlinear variation with increasing confining pressure, and its significant characteristic of high in-situ stress makes it difficult to accurately assess the mechanical responses of the surrounding rock in the tunnel excavation. This paper introduced the nonlinear strength characteristics of rock and established a logarithmic strain equation for the surrounding rock of deeply buried tunnels. Considering the commonly overlooked strain-hardening characteristics of rock in previous studies, the internal variables were solved using the plastic shear strain of the current node during the iterative finite difference process. An analytical method coupling elasto-plasticity with finite strain for surrounding rock was proposed, based on the unified strain-hardening, strain-softening constitutive model and the nonlinear dilatancy model. When the model reverted to small strain analysis, the analytical results aligned with classical theoretical solutions, validating the effectiveness of the proposed method. Analysis results of influential parameters reveal that neglecting the nonlinear attenuation of the rock dilatancy coefficient leads to an underestimation of the plastic zone range of the finite strain of surrounding rock. As the rock dilatancy characteristics increase, the displacement of the tunnel wall, the radius of the residual zone and the plastic zone gradually increase, and the increment is pronounced with decreasing confining pressure. The strain-softening characteristics of rock predominantly affect the proportion of the residual and softening zones of the surrounding rock, leading to changes in displacement of the surrounding rock. Enhancing this characteristic significantly reduces the radius of the plastic zone. The consideration of rock strain-hardening characteristics is crucial for evaluating the plastic zone range of surrounding rock. However, the increased strain-hardening characteristics exerts minor impact on the radius of the plastic zone, primarily altering the proportion between the softening and hardening zones of the surrounding rock. The method proposed in this paper can effectively evaluate the plastic zone range of finite strain of surrounding rock in deeply buried tunnels, offering theoretical guidance for the design of the supporting structure system. © 2024, Central South University Press. All rights reserved.