Simplification of earthquake induced vehicle bridge interaction contact simulation for urban viaducts

The possibility of motor vehicles parking on or slowly driving on the urban viaducts during earthquakes has been largely increased to a non-negligible level due to the traffic jams in most of modern cities. As a fact of the earthquake disaster investigation, detachment and collision between motor vehicles and the bridge deck endangered the safety of both drivers and the bridge structure itself. In recent studies, Hertz model was therefore proposed to simulate this nonlinear contact and collision behavior with the complexity and inefficient in solving the kinetic equilibrium equations of earthquake induced vehicle bridge interaction (VBI) system, and hence hindered the comprehensive numerical analysis. In this paper, two linearized contact models, that is, a piecewise linear tangent model derived by Taylor series expansion of the Hertz model and a piecewise secant model derived by least square method of error minimization of the Hertz model, are both proposed to simplify the simulation of the vehicle bridge contact behavior for earthquake induced VBI system. A total of 3*2041VBI parametric systems considering different vehicle masses, frequencies and ground motions, are calculated and statistically analyzed to compare the accuracy of each model with nonlinear Hertz model. Statistical analysis result shows that the vertical contact force calculated by two simplified models are acceptable in earthquake induced VBI analysis with less than 10% error in more than 99% analysis cases. However, the piecewise tangent model is more accurate than the piecewise secant model when the vehicle and bridge stay attached. If detachment occurs, the secant model would have higher accuracy in predicting the initial peak ground acceleration (PGA) of vehicle detachment from the bridge. Based on this result, a formula using the piecewise secant model for predicting the initial detachment PGA of vehicles from the bridge deck is proposed to simplify the increment dynamic analysis (IDA) method in further earthquake induced VBI analysis.