Probabilistic Analysis of Tunnel Stability in Spatially Variable Cohesive-Frictional Soil

This paper explores a probabilistic study of plane-strain tunnel stability in a spatially variable cohesive-frictional soil medium. The cohesion, friction angle, and the unit weight of soil are considered as random variables, which are assumed to be log-normally distributed. First, the multivariate cross-correlated random fields are discretized using the Karhunen-Loève expansion method in MATLAB for isotropic and anisotropic scale of fluctuation. A two-dimensional finite element model of a circular tunnel is then created in PLAXIS2D. FEM-based pressure-deformation approach is used for the determination of critical tunnel support pressure. This approach ensures the determination of the critical tunnel support pressure consistently in a repeatable manner. Using Monte-Carlo simulations, stochastic analysis is performed by repeatedly mapping random fields onto the finite element mesh in PLAXIS2D for multiple realizations. The input parameters include a mean cohesion of 10 kPa, a mean tangent of friction angle of tan 22°, and a mean unit weight of 16 kN/m³, each with coefficients of variation of 10%. Two cases were considered with ratios of horizontal to vertical scale of fluctuation as 1 and 10, respectively. The study assesses the effect of isotropic and anisotropic scale of fluctuation on the critical tunnel support pressure. The limiting tunnel support pressures from the random analyses are compared with the results of deterministic analyses to study the impact of spatial variability on tunnel stability. The mean critical tunnel support pressure and the failure probability of the tunnel for all the cases are presented.

Keywords: Tunnel, Cohesive-frictional soil, Spatial Variability, Anisotropic scale of fluctuation, Critical Tunnel support pressure.