| Terrain condition is an important factor affecting the seismic effect of the site.Slope topography usually has a significant amplification effect on seismic waves,and its mechanism is closely related to the propagation process of seismic waves in the slope.Therefore,the application of seismic wave propagation theory to study the analytical solution of slope seismic response has important theoretical and practical significance for showing the propagation process of seismic wave in slope,revealing the general characteristics of slope seismic effect,and guiding the anti-seismic design of slope.Due to the differences in the external shape,internal structure and material properties of the slope,the propagation of seismic waves in the slope is a very complex dynamic process.In order to facilitate theoretical research,the slope is generalized into a trapezoidal section composed of the ground,slope surface and top surface.The slope is regarded as a homogeneous elastic isotropic material.At the same time,it is assumed that the seismic wave propagating from the deep earth to the slope is plane wave,and the seismic wave is divided into P wave and SV wave.Based on the theory of seismic wave propagation,the seismic response models of slope surface and slope top under the action of vertical incident seismic waves are established respectively,and various seismic wave functions causing slope response are deduced.The wave field superposition method is used to synthesize these seismic waves to obtain the analytical solution of slope ground motion,and then the corresponding amplification factor expression is obtained.In order to facilitate the application of analytical solution for practical calculation,a calculation program is written with MATLAB software,based on which the seismic effect of slope under the action of vertical incident seismic waves is studied,and the influence of Poisson’s ratio on the seismic effect of slope is analyzed.The results show that:(1)Under the action of vertical incident seismic waves,the seismic P wave only has a certain seismic effect on the top of the steep slope,while the SV wave usually has obvious seismic effects on the slope and the top of the slope,and the seismic effect caused by the seismic SV wave is stronger than the P wave.(2)Under the action of vertical incident SV waves,the displacement and dynamic stress amplification coefficients at the slope surface reach the maximum when the slope angle is equal to the critical angle of total reflection of SV waves.The displacement and dynamic stress amplification coefficients at the top of the slope appear double peaks at the same time with the slope angle,and the peak positions appear near the critical angle of SV waves and between 70°and 80°.(3)Whether the incident seismic wave is P wave or SV wave,whether the reflection coefficient is real or complex,whether the slope top or slope surface,the dynamic stress is unidirectional stress,and the direction is parallel to the free surface(slope surface or top surface).There is a linear relationship between the dynamic stress amplification coefficient at the slope surface and the reflection coefficient of the reflected P wave(Rpp or Rsp),and the variation of the two(Rpp or Rsp)with the slope angle is completely consistent.(4)Under the action of vertical incident seismic waves,the site effect of the slope is closely related to the Poisson’s ratio of the site stratum parameters.Regardless of whether the incident wave is P wave or SV wave,the site effect of the slope increases with the decrease of Poisson’s ratio. |
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