Sparse Polynomial Chaotic Expansion for Uncertainty Analysis of Tunnel Stability

Uncertainty is an intrinsic property of rock engineering because of the complicated geology conditions, rock failure mechanism ambiguity, and the nonlinear mechanical behavior of surrounding rock mass. We developed a novel framework to handle the uncertainty by combing the Sparse polynomial chaotic expansion (SPCE), numerical model, and reliability method. The SPCE model was used to map the complex relationship between the response of the surrounding rock mass and its uncertainty. The first-order reliability method (FORM) evaluated the reliability index and failure probability. Based on the SPCE model and FORM, a simple global optimization algorithm (SHGO) seeks design points and corresponding reliability indexes. A circular tunnel verified the developed framework with a close-form solution. The reliability index, design point, and failure probability were in excellent agreement with the FORM and Monte Carlo simulation. This indicated that the SPCE model could be used as a surrogate model for the analytical solution to approximate the tunnel response (including deformation and size of the plastic zone). Then, the developed framework was employed in a horseshoe tunnel by combing with the numerical model. The results further proved that the developed framework is feasible and effective for handling uncertainty in rock engineering. Furthermore, the developed framework is effective, efficient, and accurate for reliability analysis and provides a helpful tool to approximate the response of rock structure to avoid the time-consuming numerical model in practical rock engineering.