Analysis For Antiplane Surface Motion Of Several Typical Sites

The effect of site conditions on the seismic ground motion is a research subject which is complicated but having important theoretical and applied value. Several typical sites are chosen in this paper in order to investigate the main points of wave function expansion method applied to elastic wave scattering problems. Antiplane scattering analytical solution for the alluvial valley of shallow circular-arc cross-section is investigated, which has practical engineering value. After that, features of antiplane surface motion for several typical sites are studied in details by use of superiority of analytical solutions in probing into objective regularity.The main achievements of this paper could be summarized as follows:(1) Wave function expansion method involved in the scattering problem of elastic wave is summarized, and key points of the wave function expansion method and its application in the elastic wave scattering problem of local sites are studied. Since the antiplane scattering problems of local sites could be divided into two kinds: interior and exterior problems, main points to solve the problems are Graf's addition theorem. So two expressions and suitable range of the Graf's addition theorem are studied hi the paper. Moreover, an auxiliary function method for mixed boundary-value problems are also discussed in this paper.(2) There are no reports on the analytical solution of antiplane scattering of shallow circular-arc cross-section alluvial valley because of limit of the special functions, although it possesses practical engineering values. The convergence and precision of the analytical solution in this case are studied and discussed to fill the space of the research. The results of studying indicate: the solutions are convergent even for the alluvial valley of small depth-to-width ratio and it has high precision. After that, antiplane surface motion features of the shallow alluvial valley of small depth-to-width ratio are investigated in details. The results indicate that surface displacement amplitudes of alluvial valley will not reduce when the alluvial valley become shallow. The maximum amplitudes will move to high frequency with depth-to-width ratio becoming small.(3) Comparison analysis for antiplane surface motion features between the circular-arc cross-section alluvial valley and the single overburden layer is investigated in details in this paper. The comparison results indicate: The surface displacement amplitudes of the alluvial valley have similar form of variation with the incident frequency to those of the single overburden layer when the verticalwaves are excited. The surface displacement amplitudes of the single overburden layer are lower limit of the alluvial valley. The surface displacement amplitudes of the single overburden layer can't be amplified, while some places on the surface of the alluvial valley will be amplified when the grazing waves are excited. The amplitudes will be more notable with depth-to-width arising of the alluvial valley in this case. The notable torsion effects of the surface ground motion above the alluvial valley are illustrated and the torsion effects become stronger as the frequency of the incidence is higher.(4) Antiplane surface motion of the underground circular soft inclusion and the underground homogeneous soft interlayer is investigated in this paper. The results indicate: surface displacement amplitudes just above the soft inclusion of small depth-to-width ratio is amplified and soft interlayer of small depth-to-thickness ratio is amplified to a certain degree, and moreover, the latter is lower limit of the former.(5) Antiplane surface motion of underground circular hard inclusion and underground homogeneous hard interlayer is investigated. The results indicate: The surface displacement amplitudes just above the underground circular hard inclusion is reduced, while surface motion on both two sides are significantly amplified when the vertical waves are excited. The surface motion on the side o...