Long-Term Stability Analysis for High Arch Dam Based on Time-Dependent Deformation Reinforcement Theory

Abstract

A high arch dam project causes an intense disturbance to its geological environment, with high in situ stress in the critical instability state, and the creep and damage of abutment rock mass resulting from the process of nonequilibrium evolution have a serious impact on the long-term safety of an arch dam. In this study, the long-term stability of an arch dam was evaluated with time-dependent deformation reinforcement theory (TDRT), in which plastic complementary energy (PCE) was used to judge the steady state or viscoplastic flow of the structure, the overstresses beyond the yield criterion were the driving force for nonequilibrium evolution of rock structures, and the unbalanced forces were the required reinforcement forces. Based on a viscoplastic model and asymptotic stability analysis, the principle of minimum plastic complementary energy was proved for perfect and hardening yielding, in which viscoplastic structures deform to the limit steady state at which the PCE is minimized under time-invariant loading and boundary conditions. Thus, the PCE is a reasonable and quantitative criterion for stability evolution, and unbalanced forces can be used to determine the reinforcement because they have a completely mathematical basis. The expression of PCE and unbalanced forces for the finite-element method (FEM) were programmed, the theory was implemented in a parallel FEM code, and the long-term safety of Jinping Arch Dam in China was evaluated.