Time-varying reliability calculation of bridges considering non-normal variable correlation

A method for time‐varying reliability calculation of RC bridges considering random deterioration process

“…Live loads, such as those caused by vehicles, occur randomly and have a short duration of action, which increases the likelihood of bridge damage. As these critical loads have a short duration of action, they are regarded as impulsive stochastic processes, such as Poisson stochastic processes 31 . Assuming that a series of mutually independent load times occur at times$${t_1},{t_2}, \ldots ,{t_n}$$, with corresponding load events $${S_1},{S_2}, \ldots ,{S_n}$$ and resistance values $$R({t_i})$$, the probability of the bridge being reliable over its service life period (0, T ] can be expressed as Equation (): $$$$\begin{equation}L(T) = P\left\{ {R({t_1}) > {S_1} \cap R({t_2}) > {S_2} \cdots \cap R({t_n}) > {S_n},t \in \left( {\left.$$…”

“…As these critical loads have a short duration of action, they are regarded as impulsive stochastic processes, such as Poisson stochastic processes. 31 Assuming that a series of mutually independent load times occur at times𝑡 1 , 𝑡 2 , … , 𝑡 𝑛 , with corresponding load events 𝑆 1 , 𝑆 2 , … , 𝑆 𝑛 and resistance values 𝑅(𝑡 𝑖 ), the probability of the bridge being reliable over its service life period (0, 𝑇] can be expressed as Equation (2):…”