基于概率密度演化的锈蚀混凝土梁时变可靠性分析

The limit state function for corroded reinforced concrete beams was established, in which the non-uniformity coefficient of corrosion was introduced to consider the non-uniformity of corrosion and randomness of steel bars. Then, according to the principle of conservation of probability, the generalized probability density evolution equation of the limit state function for corroded reinforced concrete beams was derived. Meanwhile,the finite difference method of TVD (total variation diminishing) difference scheme was recommended. Next, the time-dependent reliability calculation method based on the probability density evolution theory was proposed for corroded reinforced concrete beams through 'absorption boundary conditions'. Further, the generalized probability density evolution equation and the calculation results of time-varying reliability were shown by taking three corroded reinforced concrete beams as examples. Moreover, the accuracies of the probability density evolution and the time-dependent reliability calculation were investigated through one million-scale of Monte Carlo simulation and the two-norm error index. The comparison results of the second-order moment information and the reliability show that the probability density evolution method can accurately capture the probability density evolution information of corroded reinforced concrete beams during its service period with a relative low calculation cost, and then accurately predict the time-varying reliability.