Ground Motion Of Isosceles Trapezoidal Hill-Canyon Combined Topography Under SH-Waves

Diverse forms’ topographies may exacerbate the seismic response of the ground surface and expand the earthquake disasters’ threat to human life and property in the process of seismic wave propagation.On the side,in real life,the complex topography generated by the shaping of the natural environment and the needs of human’s live and production is widely available.Therefore,it is of great significance to evaluate the influence of partial topography on surface motion under the action of seismic waves from different perspectives in seismology and seismic engineering,which can provide a theoretical foundation for the response analysis of complex topography to seismic waves in practical application.Based on the complex function method and wave function expansion method,the seismic response of composite topography of the isosceles trapezoidal convex topography with two various shapes’ canyons(semicircle,V-shaped)under SH wave incidence by using multiregion-matching technique is mainly investigated in this paper,and the rigorous series analytical solutions of the scattering problem of corresponding model are obtained.Firstly,taking advantage of auxiliary boundary method to introduce the semicircular auxiliary boundaries to divide the two composite topography models into multiple subregions,respectively.The displacement field expressions when diverse boundary conditions are met in each subregion are constructed via employing the wave function expansion method and complex variable function method,and the corresponding of the analytical expressions of the stress components to the wave field on the basis of the constitutive relation are received.Introducing complex variable to unify the coordinate systems in the complex plane,and the infinite algebraic equations are established according to the boundary conditions such as displacement and stress continuity at the auxiliary boundaries.Under the condition of ensuring the accuracy and convergence of results,the unknown coefficients of the expressions of the wave fields in each subregion are given by truncating the finite terms by utilizing the FourierBessel series expansion method.For the sake of confirming the correctness of the results,the verification method of model degradation was used to compare the obtained results with previous studies,it is observed that the results in this paper had a high degree of compatibility with the existing research results.Eventually,numerical results calculated are given and the responses of different influence factors to the amplitude of surface displacement of composite topography are discussed,for instance,frequency,the slope of the trapezoidal hill,incident angle,the distance between two topographies,the radius of semicircular canyon,the center angle of V-shaped canyon etc.The results illustrate that the interaction between the isosceles convex topography and the canyon can be negligible when the distance between the two topographies increases by tens of times.With the increase of incident angle and frequency,the displacement amplitudes have noteworthy oscillation trend and also affect the variation of its maximum displacement amplitude.If the isosceles trapezoidal convex topography is steeper,the oscillation form of the displacement amplitude is more violent.For the two complex topographies in this paper,the amplitude of V-shaped canyon is more violent than semicircular canyon’s amplitudes when set as the parameters are same.The remaining factors also have a certain impact on the ground motion of the composite topography.