System Reliability of Concrete Dams with Respect to Foundation Stability: Application to a Spillway

Structural reliability analysis is not widely used for the design and assessment of concrete dams. In this paper, the system reliability of a spillway structure consisting of two monoliths is calculated. Limit state functions are defined from the failure modes sliding in the concrete rock contact, sliding in the rock mass, and adjusted overturning. Random variables in the limit state functions are defined by stochastic distributions. These are defined based on site investigations and laboratory tests from samples taken at the dam. Simulations and information from the literature are used for the remaining variables. The safety index is calculated by the first-order reliability method for each failure mode and monolith, and the system reliability is approximated by direct integration of the bivariate normal distribution. The output is the safety index including associated sensitivity values at the single failure mode, monolith, and system levels. The results show that the system safety is governed by a persistent rock joint beneath one monolith. A system reliability analysis is found to be a useful tool in the dam risk management process as it can be used to calculate the probability of failure and to identify important failure modes and variables.