Inverse analysis for rock mechanics based on a high dimensional model representation

Mechanical parameters of rock mass are essential in rock engineering for stability analysis, supporting design, and safety construction. The inverse analysis has been commonly used in rock engineering to determine the mechanical parameters of the rock mass. In this study, a novel inverse analysis approach was proposed through combing high dimensional model representation (HDMR), Excel solver, and numerical model. HDMR was employed to approximate the nonlinear function between the mechanical parameters of rock mass and the response of rock based on the numerical model. Excel Solver was adopted to search the mechanical parameters of rock mass based on the HDMR model for the inverse analysis. The proposed method was verified and illustrated the performance of the proposed method by two tunnels. The mechanical parameters of rock mass were determined based on the displacement of surrounding rock mass and HDMR model using the Excel solver for the tunnels. The displacement and stress of surrounding rock mass were computed based on the determined mechanical parameters of rock mass by the proposed method. There was an excellent agreement with the real value or contour that was computed based on the actual mechanical parameters of the rock mass. The results demonstrated that the proposed method was practical and accurate. It also made it convenient to be applied to determine mechanical parameters of rock mass based on monitored information.