Upper Bound Limit Analysis-Based Determination of the Influence of a Non-Associated Flow Rule on the Stability of Shallow Tunnels

On the basis of a non-associated flow rule and the upper bound theorem for limit analysis, the expression of surrounding rock pressure on shallow tunnels was derived by constructing a simple failure pattern. Strength reduction technique was applied to study the stability of shallow tunnels under certain levels of surrounding rock pressure; this analysis was based on the internal consumption and external energy conservation principle. The optimized upper bound solutions of surrounding rock pressure and the safety factor for shallow tunnels were obtained by nonlinear optimization methods. Results show that the dilatancy of geomaterials and the lateral pressure coefficient of surrounding rock significantly affect the surrounding rock pressure and stability of shallow tunnels. Furthermore, the lateral pressure coefficient is an important factor in relation to the stability of such tunnels.