A novel semi-analytical solution to ground reactions of deeply buried tunnels considering the nonlinear behavior of rocks

Abstract

The nonlinearity of rock becomes more significant as the buried depth increases, which changes the stress redistribution and deformation patterns during tunneling. In this study, a newly proposed UHS model (unified strain-hardening and strain-softening constitutive model) and the finite difference method are applied to obtain a novel semi-analytic solution that is used to investigate the effects of nonlinear characteristics such as strain-hardening and strain-softening on the ground reaction. The yield surface and the plastic internal variable of the calculated node are consistent and are solved by iteration. The solution of differential equations is unnecessary. Therefore, the proposed solution can be used to accurately calculate the plastic internal variable and the stress state in the plastic zone without stress vibration in the strain-hardening zone that was often observed in previous solutions. The proposed model is validated via comparison to the classical solution and numerical results. Then, the influences of strain-hardening, strain-softening, and prestress on ground reactions are highlighted. The radius of the plastic zone and the displacement of the tunnel wall gradually decrease with increasing post-peak ductility. Considering strain-hardening characteristics would increase the radius of the plastic zone. Moreover, prestressing significantly reduces the plastic zone radius and tunnel wall displacement in deeply buried tunnels.