Dynamic Response to Seismic Waves at the Shallow Slope Supported by Bolts

In the soil slope supported by bolts, longitude waves instead of transverse waves, generated by earthquakes, first reach the slope surface. With the dynamic response of the P (pressure) wave along the anchorage structure, first, a theoretical study was conducted to investigate the propagation characteristics of the interference superposition, generated by the SV (shear-vertical) and the P waves. The SV wave was formed by the wave, originating from the bottom and reflected from the free surface of the slope, whereas the latter was the incident P wave, propagating in the slope. In addition, the structural measures, restraining the seismic wave, and the characteristics of the restraint effect at the free segment of the bolt were investigated. According to the wave-way difference between the incident P wave and the reflected SV wave, the minimum critical slope angle, influenced by the interference at the shallow slope, and the maximum influencing depth of the dynamic response, acting vertically to the slope surface, were obtained. The results indicate that the maximum influencing depth linearly correlated with the slope angle. Furthermore, based on the propagation characteristics of the P wave along the bolt, and the coupled relation between the wave length and the anchorage design parameters, the axial acceleration of the wave propagating along the bolt axis was obtained. Then, the theoretical length of the anti-seismic bolt, subjected to seismic waves, and the compensation force of the anchorage structure were obtained. Finally, a numerical study, based on FlAC3D, properly verified the theoretical conclusions.