Reliability analysis of supporting pressure in tunnels based on three-dimensional failure mechanism

Based on nonlinear failure criterion, a three-dimensional failure mechanism of the possible collapse of deep tunnel is presented with limit analysis theory. Support pressure is taken into consideration in the virtual work equation performed under the upper bound theorem. It is necessary to point out that the properties of surrounding rock mass plays a vital role in the shape of collapsing rock mass. The first order reliability method and Monte Carlo simulation method are then employed to analyze the stability of presented mechanism. Different rock parameters are considered random variables to value the corresponding reliability index with an increasing applied support pressure. The reliability indexes calculated by two methods are in good agreement. Sensitivity analysis was performed and the influence of coefficient variation of rock parameters was discussed. It is shown that the tensile strength plays a much more important role in reliability index than dimensionless parameter, and that small changes occurring in the coefficient of variation would make great influence of reliability index. Thus, significant attention should be paid to the properties of surrounding rock mass and the applied support pressure to maintain the stability of tunnel can be determined for a given reliability index.