Evaluation of the Dynamic Impact of a Passing Vehicle on a Bridge Deck Due to a Damaged Expansion Joint

When a vehicle passes over a bridge, it may jump on the bridge due to a damaged expansion joint. The sudden jump induces a heavy dynamic impact on the bridge and therefore damages the bridge deck and girder. The traditional dynamic amplification factor defined by the current bridge design code shows the amplification of the static effects on the bridge. However, it only concerns the stable moving load induced by the vehicle. The sudden vehicle impact due to a damaged expansion joint sometimes exceeds the allowable design load, so it is important to evaluate the dynamic impact in practice. In fact, the dynamic impact can be approximately considered as a contact force between a damped harmonic oscillator and a beam due to the bilateral symmetry of the vehicle; therefore, a model-based approach using the bridge midspan acceleration is proposed in this study to approximately evaluate the impact force, where it is assumed as an exponentially damped sine function. This is a typical parametric model-based inverse problem. The conjugate direction method is used to determine the unknown parameters and the initial values are determined by a simple global search method. Since only five parameters are included, the proposed method is simpler than the conventional basis function-based methods. Numerical simulations were conducted to validate the proposed method. Generally, the proposed method performs well to identify the dynamic impact. In particular, the displacement measured directly from the bridge is preferred since the displacement obtained from the acceleration has numerical errors; the measurement noise in the range of 1% to 5% shows a slight influence on the proposed method; and the error of frequencies and mode shapes greatly affects the proposed method, especially for the maximum force.