Abstract

This paper presents a closed-form series solution of cylindrical SH-wave scattering by the surrounding loose rock zone of underground tunnel lining in a uniform half-space based on the wave function expansion method and the mirror image method. The correctness of the series solution is verified through residual convergence and comparison with the published results. The influence of the frequency of the incident cylindrical SH-wave, the distance between the wave source and the lining, the lining buried depth, and the properties of the surrounding loose rock zone on the dynamic stress concentration of the tunnel lining is investigated. The results show that the incident wave with high frequency always makes the dynamic stress concentration of the tunnel lining obvious. With the increase of the distance between the wave source and the tunnel lining, the stress around the tunnel lining decreases, but the dynamic stress concentration factor around the tunnel lining does not decrease significantly but occasionally increases. The ground surface has a great influence on the stress concentration of the tunnel lining. The amplitude of the stress concentration factor of tunnel lining is highly related to the shear wave velocity of the surrounding loose rock zone. When the property of the surrounding rock (shear wave velocity) changes more, the amplitude of the stress concentration factor is larger, that is, the stress concentration is more significant.

Highlights

  • The scattering of elastic waves by an underground cavity is one of the hot research topics in the fields of earthquake engineering, seismology, and geophysics due to its particular significance in seismic risk assessment, seismic microzonation, and the design of important facilities

  • The surrounding loose rock zone is assumed to be divided into four layers, and the properties of the loose rock zone are discussed in three cases as follows: Case 1: β1 2700 m/s

  • The closed-form series solution of cylindrical SHwave scattering by surrounding rock in a uniform half-space is obtained by using the wave function expansion method

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Summary

Introduction

The scattering of elastic waves by an underground cavity (or local topography) is one of the hot research topics in the fields of earthquake engineering, seismology, and geophysics due to its particular significance in seismic risk assessment, seismic microzonation, and the design of important facilities. The method of solving the problem of wave scattering can be divided into two kinds of methods: numerical method and analytical method. Numerical methods mainly include the finite difference method (FDM), finite element method (FEM), and boundary element method (BEM); the analytical methods mainly refer to wave function expansion methods. The numerical method can be applied to the cavity (or local topography) of any shape and various. Series Solution for Cylindrical SH-Waves site conditions and is more suitable for handling actual engineering problems. The analytical method is still necessary to solve some special regular cavity (or local topography) and boundary conditions. The analytical method is only suitable for relatively simple and regular models, it has an advantage over the numerical method in revealing the essence of the problem, and it can verify the accuracy of the numerical method

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