A Hybrid Second-Order Exponential Cone Programming–Based Lower Bound Finite-Element Limit Analysis Framework for Rock Tunnels in Anisotropic Rock Masses

Abstract

In this study, a new conic optimization technique, hybrid second-order exponential cone programming (HSOECP) in the framework of lower bound finite-element limit analysis, has been developed. This framework combines the specific features of a second-order cone and an exponential cone to capture the nonlinearity of the modified Hoek–Brown criterion developed for anisotropic rock masses recently. In the modified Hoek–Brown criterion, both inherent strength anisotropy owing to the variation of the uniaxial compressive strength of intact rock (σcβ) and structural anisotropy based on the anisotropic rock mass rating (ARMR) classification system were considered. The proposed methodology has been applied to study the stability of unlined circular tunnels in anisotropic rock masses. The maximum ground surcharge (σs) for which the tunnel is at its failure state has been obtained and presented in nondimensional form considering the influence of σcβ, ARMR, material constants (mi), inherent strength anisotropy parameter (kβ), unit weight (γ), and tunnel cover depth (C) and diameter (D). The computations were carried out using self-developed codes in MATLAB 2022b version. For C/D = 1 with mi = 5 and [(σcβ)/(γD)] = 50, the value of [(σs)/(γD)] with ARMR = 40 and kβ = 0.2 is approximately 283 times lower than that for ARMR = 100 and kβ = 1. Moreover, at ARMR = 40, the value of [(σs)/(γD)] for kβ = 0.2 is 18.33 times lower than that for kβ = 1. Increasing the tunnel cover depth significantly enhances tunnel stability, with a higher rate of improvement for lower C/D values. The influence of inherent strength anisotropy is found to be lower compared to the structural anisotropy of rock mass on the stability of unlined tunnels.