Reliability based design optimization for a rock tunnel support system with multiple failure modes using response surface method

Reliability-based design optimization (RBDO) is applied to a rock tunnel support system, considering the ground-support interaction and the parametric uncertainties. Both reliability index approach (RIA) and performance measure approach (PMA) are employed as the RBDO algorithms. The first-order reliability method (FORM) and the response surface method (RSM) are used to perform the reliability analysis. The shotcrete thickness and its installation position are considered as two design variables to be optimized in an illustrative example of a circular rock tunnel. The influence of the two design variables on the reliability results is first investigated with respect to three failure modes, namely, the support capacity criterion, the tunnel convergence criterion and the rockbolt length criterion. Then, the proposed RBDO procedure is used to seek for the design variables of minimum shotcrete thickness and the optimal installation position for the rock tunnel example. The computational efficiency and stability between RIA and PMA are compared. The influences of the rock mass quality, the variation of the shotcrete thickness and the target reliability requirement on the optimized results are also investigated and discussed.