Physics-Based and Machine-Learning Models for Braking Impact Factors

The effect of vehicle braking can significantly amplify a bridge deflection compared to that induced by a vehicle moving at a constant speed. However, the magnitude of this amplification depends on vehicle bridge interaction (VBI) phenomena activated by the road roughness. The road roughness triggers the vehicle dynamics, thus magnifying the interaction between the vehicle and the bridge. This paper proposes a probabilistic model for the amplification factor. The amplification factor is associated with the vehicle’s hard braking by the mid-span of the bridge under different road roughness classes. The amplification factor, defined as the ratio between the maximum deflections corresponding to a vehicle braking and moving at a constant speed, is estimated as a function of the mass, velocity, natural frequency and damping of the vehicle. The VBI model is obtained by discretizing the coupled governing equations using the finite difference method. The vehicle is modelled as a two-degrees of freedom system corresponding to the bouncing and pitching motions. The computational efficiency of this model supported an expensive set of analyses, where the parameter values were selected using the Latin Hypercube sampling scheme. The model outputs have been validated against a middle-span bridge’s measured experimental displacement response under different scenarios.