Physics-Based Probabilistic Models for the Reliability Analysis of Bridges

This paper presents a general formulation for developing physics-based probabilistic models and explains their implementation in the reliability analysis of bridges and the modeling of their deterioration. The formulation of physics-based probabilistic models combines a computationally convenient representation of the governing physical laws with an analytical correction term. The governing physical laws may appear in the form of differential equations, design code expressions, or algorithmic procedures as in the push-over analysis. The correction term removes the implicit bias in predictions based on the governing physical laws and improves the model accuracy. A model error term is also included to capture the remaining unexplained uncertainty in model predictions. The physics-based probabilistic models predict the response quantities of interest (e.g., deformation capacity of a bridge) as a function of state variables that define the structural system, such as geometric quantities, material properties, initial and boundary conditions, and external loads. The paper presents stochastic differential equations for modeling the deterioration of the state variables based on thermodynamics laws. A reliability problem is then formulated to evaluate the time-varying failure probability using the developed probabilistic models. As an example, the paper presents a probabilistic model for the drift capacity of reinforced concrete bridge columns retrofitted with fiber-reinforced polymer composites and develops fragility functions conditioning on the drift demand.