Stability analysis of twin horse-shoe shaped tunnels in rock mass

Abstract

This study examines the stability of a single and twin horse-shoe shaped unlined tunnels laid in rock media and loaded with surcharge pressure on ground surface. The tunnels are assumed to be sufficiently long so that the plane strain analysis remains applicable. The failure of rock mass is governed by the generalized Hoek-Brown (GHB) yield criterion. The analysis has been performed by using the lower bound finite elements limit analysis in conjunction with the power cone programming (PCP). No assumption needs to be associated with either the smoothing of the yield surface or fixing the value of the exponent in the GHB criterion. For a given cover to diameter ratio of the tunnels, the maximum permissible value of the surcharge pressure on ground has been computed ensuring the stability of the tunnels. Apart from the different basic material yield parameters (GSI, mi and σci), the effect of clear spacing (S) between the twin tunnels on the results has also been studied. Failure patterns have also been explored for a number of cases to identify the region of the plastic shear zone. The computations reveal that the optimal spacing (Sopt), beyond which the tunnels behave like isolated ones, remains almost independent with respect to the material parameters and increases continuously with an increase in H/B; the value of Sopt/B increases from 2.5–3.0 for H/B = 1 to 13.0–14.0 for H/B = 6. The computational results have been duly validated and even compared with the different available solutions for square and circular twin tunnels in rock media.