Reliability analysis of bolt-supported tunnels regarded as homogenized structures

This paper presents a reliability analysis of deep tunnels reinforced by fully grouted bolts using a homogenization approach. From the constitutive viewpoint, the anisotropic elastoplastic behavior of bolted rock mass is formulated in the context of the homogenization method. Reliability design analysis is undertaken considering the configurations of both radial and face bolts used separately or in association. The combination of rock bolting associated with classical shotcrete lining is also addressed. Restricting to deep tunnels and axisymmetry conditions, a simplified analytical approach followed by finite element numerical modeling are developed in the framework of the homogenization method. Reliability analyzes are performed using the Monte Carlo simulation (MCS) and the first-order reliability method (FORM). The response surface method (RSM) provides analytical approximations to enable reliability analyses without time-consuming computational models. The results show excellent correlation between the obtained reliability parameters, which emphasizes the relevancy of the adopted reliability methods. Structural failure probabilities below or close to 1.0% were obtained in all cases studied for the best structural tunnel conditions.