Numerical Modelling based on Asymmetric Elastic Wave Equations with High-speed Train Seismic Source over the Bridge

Abstract:

Due to the repeatability, definiteness and economy of high-speed train moving seismic source, high-speed-train seismology has been extensively studied by many researchers. The field data acquired in Dingxing provided by the joint research group of High-speed-train Seismology show that there existing a large amount of rotational ground-motions, which is difficult to describe by means of conventional continuum mechanics theory. In addition, the high-speed train runs on viaducts most of the time considering safety and stability. Therefore, the study on the asymmetric elastic wave equations with high-speed train seismic source passing over the bridge is in demand.

In this abstract, we simplify the moving high-speed train as combination of a series of the axle loads from the front and rear bogies of N cars, and built a simplified bridge pier model, as a result, train source expressions with N cars moving on land and on the bridge are given, respectively. Consider that the piers are inserted into the ground at a depth of a few tens of meters to reach the bedrock. When the high-speed train passes the piers, the piers will appear oscillating motion which is subjugated by the ground. The intensity of the oscillating motion gradually decays with the depth of the piers inserted into the ground. And the oscillating motion is relative to the micro-structure interactions of subsoil and bedrock in the frame of the generalized continuum mechanics theory, hence, we derive the asymmetric elastic wave equations based on the modified couple stress theory. Then, numerical modelling based on the asymmetric elastic wave equations is performed on the simplified bridge pier model with high-speed train source. Compared with the real data recorded when high-speed train passed the piers in Dingxing county, the seismogram in this case exhibits similar waveform features, and is mainly dominated by low-frequency energy around 10Hz and 25Hz, which matches the real data well. The numerical modelling proves that the bridge pier model we build basically accords with the physical facts.