<p>Based on the wave function expansion (WFE) method and expansion of the cylindrical wave into plane wave (ECPW) method, an analytical method for a circular lined tunnel embedded in the half-space unsaturated soil is developed. To develop the analytical method, the governing equations and corresponding potentials for the unsaturated soil are introduced first. The wavefield in the soil is decomposed into the free wavefield and scattered wavefield. The free wavefield in the unsaturated soil is determined by the incident waves as well as reflected waves from the surface of the soil. The scattered wavefield in the soil can be further divided into the direct and secondary scattered wavefields. The direct scattered waves due to the presence of the tunnel are cylindrical waves emitted from the tunnel, while the secondary scattered waves are the reflected waves of the direct scattered waves from the surface of the soil. To determine the secondary scattered waves for the tunnel, the ECPW method for the unsaturated half-space soil is proposed in this study. The wavefield in the tunnel lining consists of standing waves represented by Bessel functions. By using the expressions for the above wavefields, the equations for the unknown coefficients of the wavefunctions are derived. With the developed analytical method for the circular tunnel, some numerical results are presented.</p>

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Dynamic response of a circular tunnel buried in the half-space unsaturated soil to elastic waves

  • Yong-Hong Miao,
  • Jian-Fei Lu

摘要

Based on the wave function expansion (WFE) method and expansion of the cylindrical wave into plane wave (ECPW) method, an analytical method for a circular lined tunnel embedded in the half-space unsaturated soil is developed. To develop the analytical method, the governing equations and corresponding potentials for the unsaturated soil are introduced first. The wavefield in the soil is decomposed into the free wavefield and scattered wavefield. The free wavefield in the unsaturated soil is determined by the incident waves as well as reflected waves from the surface of the soil. The scattered wavefield in the soil can be further divided into the direct and secondary scattered wavefields. The direct scattered waves due to the presence of the tunnel are cylindrical waves emitted from the tunnel, while the secondary scattered waves are the reflected waves of the direct scattered waves from the surface of the soil. To determine the secondary scattered waves for the tunnel, the ECPW method for the unsaturated half-space soil is proposed in this study. The wavefield in the tunnel lining consists of standing waves represented by Bessel functions. By using the expressions for the above wavefields, the equations for the unknown coefficients of the wavefunctions are derived. With the developed analytical method for the circular tunnel, some numerical results are presented.