The dynamic characteristics of the damage probability of a gravity dam

A first-order approximate probabilistic analytical method to investigate the damage of concrete gravity dams, based on the pseudo-excitation method (PEM), is proposed. This method constructs stochastic stiffness under stochastic stimulus using second-order perturbation. It involves the following steps. First, the PEM and the Mazar damage models are utilised to analyse the way to calculate the expected value and variance of the damage of a dam excited by a random earthquake load and a static load in the initial condition. Next, the evolutive process of the probability distribution of the tensile damage of a dam is analysed in the damage condition based on perturbation theory. Finally, a numerical example is given to verify and analyse the convergence and stability of this model. The calculated results show that the expected values of the probability distribution of the stochastic structure under a stochastic stimulus are steady under a second-order perturbation. The results indicate that, compared to PEM, the salient features of the method proposed provide a probabilistic analysis for the nonlinear response of a concrete gravity dam.