Green’s function for elastic wave equation with high-speed train seismic source over the viaduct

Abstract:

High-speed train seismology based on the high-speed train source has being research focus, due to the repeatability, determinacy and economy of the high-speed train source, meanwhile, the amplitude spectrum of seismic wave induced by high-speed train is broadband and discrete. Nowadays, several models have been established to describe the physical process of exciting seismic waves when high-speed trains running on ground. However, it is worth noting that the high-speed train runs on viaducts most of the time considering the safety and stability. Therefore, the solution to the elastic wave equation with high-speed train moving seismic source over the viaduct is of great theoretical and practical significance.

In this abstract, we focus on the seismic source caused by moving high-speed train passing over the viaduct, and the analytical formula of Green's function for elastic wave equation with high-speed train moving seismic source is derived.

We simplify the moving high-speed train as combination of a series of the axe loads from the front and rear bogies of N cars. While the trains pass by the viaduct, they exert force on the viaduct through axle loads, and the effect of each axle load is independent. Then the seismic source caused by moving high-speed train propagate to the underground media through the piers which are inserted into the ground at a depth of a few tens of meters to reach the bedrock. Therefore, the high-speed train source can be regarded as a linear superposition of a series of moving point sources, and the high-speed train source expression can be given. According to the linear superposition characteristics of the high-speed train source, we derive the Green's function for elastic wave equation with a moving point source on the free surface. Then, the Green's functions with multiple moving point sources are linearly superimposed to obtain the analytical formula for high-speed train moving seismic source. The analytical formula for the high-speed train moving seismic source is used to perform numerical calculations on a simplified viaduct pier model. The theoretical seismograms of a moving high-speed train with 16 cars passing over the viaduct have been obtained.