Dynamic response of unlined tunnels in soil with random properties

The analysis of underground structures under various environmental and mechanical loads is fraught with uncertainty. In this work, a simple perturbation-based probabilistic model is employed for modeling the complex composition of the geological material surrounding the underground opening. In addition, boundary elements are used for modeling the geometry of the problem, which is basically assumed to be that of an unlined cavity in the halfspace under plane strain conditions. The transient nature of the loading is taken into account through use of the Laplace transform with respect to the time variable. In a series of examples depicting some representative cases, the effect of material stochasticity is reflected in the presence of a non-zero, time dependent covariance matrix defined at the nodes of the discretized structure. In essence, the use of a uni-dimensional random field for representing the pressure and shear wave velocities of the geological medium is an alternative way for modeling the combined effects of heterogeneity, the presence of discontinuities, etc., which alter the simple, yet basic assumption that the ground can be modeled as a homogeneous viscoelastic semi-infinite continuum.