Probabilistic Stability Analysis of a Tunnel Face in Spatially Random Hoek-Brown Rock Masses with a Multi-Tangent Method

Tunnel excavations in heavily fractured rock masses are often subjected to the high risk of face instability. To solve this problem, the probabilistic stability analysis of tunnel face is performed in this contribution, in which the fractured rock masses are modelled as spatially random media that follow the Hoek-Brown failure criterion. The method of Karhunen-Loeve expansion is adopted to characterize the spatial variabilities of Hoek-Brown parameters. Under this circumstance, the conventional tangent technique fails to integrate the Hoek-Brown failure criterion into the kinematical approach of limit analysis framework. Thus, the multi-tangent method which permits to use multiple tangent lines to represent the nonlinear Hoek-Brown failure envelope is proposed. A discretized three-dimensional failure mechanism of tunnel face is adopted to determine critical face pressures within the framework of limit analysis. Due to a large number of input variables required by the generation of random fields, the global sensitivity analysis and a sparsity scheme are employed to reduce the problem dimension. The method of spare polynomial chaos expansion is then employed to perform Monte Carlo simulation with a significant reduction of calls to the computationally expensive original model. Finally, the parametric analysis on the deterministic model and probabilistic model is performed to gain an insight into the proposed approach.

Automated summary

In this paper, a probabilistic stability analysis is conducted to investigate the face instability in tunnel excavations in heavily fractured rock masses. By modeling the fractured rock masses as spatially random media following the Hoek-Brown failure criterion, the method of Karhunen-Loeve expansion is used to characterize the spatial variabilities of Hoek-Brown parameters. The multi-tangent method is proposed to integrate the nonlinear Hoek-Brown failure envelope into the kinematical approach of limit analysis. The study also employs global sensitivity analysis and a sparsity scheme to reduce the dimensionality of the problem.