Stability analysis of twin circular tunnels using shear strength reduction method

Abstract

This paper investigates the face stability of twin circular tunnels horizontally aligned in cohesive undrained soil under plane strain conditions. The shear strength reduction method in the two-dimensional finite-element limit analysis programme is used to obtain rigorous upper and lower bounds of the factor of safety (FoS) for various depth ratios (C/D) and centre-to-centre spacing ratios (S/D) between the tunnels. Since the undrained shear strength is not a function of the mean normal stress, stability results are independent of loading directions. Therefore, the stability (in collapse or blowout) for this problem is well expressed by using Broms and Bennermarks’ original stability number N = (σs + γH − σt)/Su. The variations of the FoS have been presented for different combinations of stability numbers (N) and geometries (C/D and S/D). The FoS and the stability number results are compared and validated by using the finite-difference method as well as other existing solutions available in the literature. The results from this study are summarised in stability charts for use by designers and practising engineers.