| Strategies for performing probabilistic finite element analysis of dynamically-loaded structures in nonlinear continua are presented. The application is the response of tunnels in rock subjected to stress-wave loading, which is well-suited for efficient probabilistic methods because the problems require computationally-intensive numerical calculations and also possess significant uncertainties in material properties and loading. The probabilistic methods employed, however, are general and can be applied to any problem in structural or solid mechanics. An analytical model is developed for a circular tunnel in a Mohr-Coulomb material subjected to static axisymmetric pressure. Several numerical tunnel models are also developed that employ an explicit dynamic finite element solution. Significant attention is paid to the development and validation of the deterministic finite element constitutive model. Strategies are developed, implemented, and verified for treating non-normal correlated random variables and for computing probabilistic sensitivity measures from sampling information. Efficient and accurate probabilistic methods are applied to the tunnel models and their use is demonstrated with several examples. |
