Research On The Characteristics Of Symmetrical Complex Local Topography Ground Motion Under SH Wave Action

Earthquakes are an inevitable natural disaster that seriously affects human production,life,and property safety.Research has shown that local topography is one of the key factors affecting seismic intensity.Local topographies with different geometric shapes lead to differences in seismic motion patterns,so studying the scattering of seismic waves by typical shaped local topographies is of engineering significance.However,analytical research on local topography with complex boundaries,especially convex topography,has encountered bottlenecks to some extent both domestically and internationally.Currently,it is necessary to explore new analytical solutions to overcome the difficulty in constructing wave field expressions caused by complex boundary conditions.A boundary condition decomposition technique,multi-region-matching technique(MRMT),is proposed in this thesis.The research content starts from the isosceles trapezoidal hill model,and introduces in detail the application of MRMT in this model.Two auxiliary boundaries are introduced into the isosceles trapezoidal hill model,and the wave field expressions in the sector-shaped subregion are constructed.In order to solve the unknown coefficients in the Fourier-Bessel series expressions in each subregion,the Fourier series expansion method in the complex field is employed to establish the infinite system of algebraic equation.Through a large amount of convergence analysis,the truncation terms of the series solution are determined to ensure the stable convergence of the calculation results.Then,the effects of topography parameters,such as the height,hilltop width,slope of the isosceles trapezoidal hill,the plane SH waves incident angle and dimensionless frequency,on ground motion are analyzed through numerical cases.It is found that the ground motion on the hillside is stronger than that on the hilltop,and the seismic weakening effect is generally only reflected on the surface of the hill.Subsequently,applying the frequency domain results as the transfer function and Ricker wavelet as the incident wave signal,a series of time domain results are obtained employing inverse fast Fourier transform.Through analysis,it is found that new cylindrical waves are generated at abrupt changes in the topography boundary,and multiple reflections of waves within the raised area can generate very complex seismic wave fields.Secondly,the flexibility of MRMT is fully utilized to expand the research of plane SH waves scattering and ground motions by complex hills and multi peak topographies.Since the construction of wave field expressions in each subregion is independent of each other,topography parameters are arbitrarily set without affecting the form of wave field expressions.Based on this advantage,the ground motion of the hill with complex slopes,the hill with twin peaks,the two adjacent triangular hills,hill-canyon-hill combination topography under the plane SH waves incident are discussed,and the influence of different boundaries on plane wave scattering and ground motion characteristic are analyzed.Through the comparison of displacement amplitudes,it can be seen that strong amplification of ground motion generally occurs near the peaks,and the shape of the hilltop has little impact on surface ground motion when the plane SH wave is incident horizontally.Finally,a shallow isosceles trapezoidal depression topography model is established employing MRMT,which overcomes the limitations of existing steep slope trapezoidal depression model.The two corners at the bottom of the depression are located inside the area enclosed by the auxiliary boundary,so the slopes of the model are gentle slopes smaller than45°,complementary to the steep trapezoidal depression topography model.Through a series of numerical examples,it is illustrated that the ground motion characteristics of shallow isosceles trapezoidal depression topography are different from the relevant conclusions of steep slope trapezoidal depression topography.Compared with isosceles trapezoidal hill topography,concave topography has a more significant seismic shielding effect on the flat surface of the back wave.When the plane SH wave is incident horizontally,the seismic motion patterns of concave and convex topographies are exactly opposite.The research work of this thesis proposes a decomposition technique for complex boundary conditions in theory.This technique can not only be used to analytically solve the scattering problems of plane SH waves by symmetric local topography,but also has theoretical application value for asymmetric topography models.On the other hand,this article analyzes the ground motion of various local topographies under the action of plane SH waves,and draws relevant conclusions that provide data support and theoretical basis for building site selection and structural seismic design in earthquake engineering.