Probabilistic analysis of tunnels considering uncertainty in peak and post-peak strength parameters

Abstract

Stability analysis of rock tunnels is a complex problem because of various types of uncertainties present in the rock mass properties and hence probabilistic approaches are used to systematically consider these uncertainties in the analysis. While the uncertainty in deformation modulus and peak strength parameters has been considered previously it has been observed that the uncertainty in post-peak strength parameters is generally neglected in earlier studies. Post-peak strength parameters are among the most important factors which significantly influence the plastic zone development and displacements around the tunnel and hence neglecting uncertainty in post-peak strength parameters is not appropriate. In the current study, a quantitative approach based on the Geological Strength Index (GSI) has been used to estimate the uncertainty in peak strength, residual strength and deformation parameters. Then the uncertainty in yield zone and displacement around the tunnel is estimated using Hong’s point estimate method coupled with finite element method. The approach was used to estimate the displacements around tunnels of different shapes in three case studies in average quality rock mass and the predicted displacements were compared with the in-situ measurements. A comparison is provided with the generally adopted conventional probabilistic approach in which uncertainty in peak strength parameters and deformation modulus is considered and rock mass is assumed as elastic-perfectly plastic. It was observed that predicted displacements were matching well with the measured displacements for all the tunnels by considering uncertainty in residual strength parameters while displacements were underestimated when the conventional approach was used. A parametric study was conducted to estimate the influence of Coefficient of Variation (COV) of different parameters on the plastic zone development and displacements of rock tunnel by selecting one of the case studies. It was observed that COV of yield zone depth and displacement was varying with the COV of the intact rock properties and thus influencing the probability of failure.