Lower and upper bounds for the drained three-dimensional stability of shallow tunnels using the Extended Matsuoka-Nakai yield criterion

The paper focuses on determining lower and upper approximations of the pressure required on the unlined part of a tunnel’s front under drained conditions. This work is carried out within the framework of classic limit analysis. In the last three decades, various approaches have been explored to enhance the understanding of the minimum pressure required for ensuring the stability of the massif during tunnel excavation under drained conditions. Methods for solving this problem are typically categorized as limit equilibrium methods, limit analysis methods, or elasto-plastic stress–strain calculations. However, the failure criterion used has almost invariably been the Mohr–Coulomb criterion. Despite its broad application, this criterion has certain limitations in evaluating the effect of the three principal stresses on the yield of earthy or rocky materials. Over time, alternative failure criteria have been proposed to address this issue, including one developed by Matsuoka and Nakai.

This work applies Limit Analysis theorems to this problem using an extended Matsuoka-Nakai criterion. Besides providing highly accurate stability factors for tunnels using this criterion, the novelty of this study also lies in the comparative analysis of numerical results with experimental data, demonstrating that the Matsuoka-Nakai criterion offers a more accurate model of the experimental data compared to the traditional Mohr–Coulomb approach.