Nonlinear finite-element-based structural system failure probability analysis methodology for gravity dams considering correlated failure modes

Abstract

The structural system failure probability (SFP) is a valuable tool for evaluating the global safety level of concrete gravity dams. Traditional methods for estimating the failure probabilities are based on defined mathematical descriptions, namely, limit state functions of failure modes. Several problems are to be solved in the use of traditional methods for gravity dams. One is how to define the limit state function really reflecting the mechanical mechanism of the failure mode; another is how to understand the relationship among failure modes and enable the probability of the whole structure to be determined. Performing SFP analysis for a gravity dam system is a challenging task. This work proposes a novel nonlinear finite-element-based SFP analysis method for gravity dams. Firstly, reasonable nonlinear constitutive modes for dam concrete, concrete/rock interface and rock foundation are respectively introduced according to corresponding mechanical mechanisms. Meanwhile the response surface (RS) method is used to model limit state functions of main failure modes through the Monte Carlo (MC) simulation results of the dam-interface-foundation interaction finite element (FE) analysis. Secondly, a numerical SFP method is studied to compute the probabilities of several failure modes efficiently by simple matrix integration operations. Then, the nonlinear FE-based SFP analysis methodology for gravity dams considering correlated failure modes with the additional sensitivity analysis is proposed. Finally, a comprehensive computational platform for interfacing the proposed method with the open source FE code Code Aster is developed via a freely available MATLAB software tool (FERUM). This methodology is demonstrated by a case study of an existing gravity dam analysis, in which the dominant failure modes are identified, and the corresponding performance functions are established. Then, the dam failure probability of the structural system is obtained by the proposed method considering the correlation relationship of main failure modes on the basis of the mechanical mechanism analysis with the MC-FE simulations.