Numerical modelling for a simplified bridge pier model under high-speed train passage over the bridge

In this work, we simplify a moving high-speed train as combination of a series of the axe loads from the front and rear bogies of cars. We build a simplified bridge pier model, as a result, train source expressions with cars moving on land and bridges are given respectively. Considering that the piers are inserted into the ground at a depth of a few tens meters and reach the bedrock. When the high-speed train passes the piers, the piers will appear oscillating motion which is subjugated by the ground, and this oscillating motion is relative to the microstructure interactions of subsoil and bedrock in the frame of the generalized continuum mechanics theory. Hence, we derive the elastic wave equations based on the modified couple stress theory to perform numerical modelling for a simplified bridge pier model under high-speed train passage over the bridge. Based on the wave equation and the train source expressions, a theoretical seismogram of a moving high-speed train with 16 cars on the bridge are obtained. Compared with the real data recorded when a high-speed train passed the piers in Dingxing County, some conclusions are drawn.