This paper presents an exact, analytical solution to the boundary value problem of the anti-plane (SH) waves scattering by an isosceles triangle hill on an elastic half-space by using the wavefunction expansion method. An appropriate regionmatching technique is introduced to divide the half-space containing a triangle hill into two subregions. Then, the wavefield expression of each subregion is constructed in terms of an infinite series in two coordinate systems, respectively. Furthermore, a Graf’s addition formula is derived to unify the coordinate system and solve the unknown coefficients in the wave functions. Finally, numerical results are calculated to illustrate the effects on ground motion due to the existence of an isosceles triangle hill. This paper revises the existing analytical methods, and aims to provide a benchmark for numerical method verification and a reference for engineering practice.

Seismic response for an isosceles triangle hill subjected to anti-plane shear waves / Song, Yunqiu; Li, Xinzhu; Yang, Zailin; Yang, Yong; Sun, Menghan. - In: ACTA GEOTECHNICA. - ISSN 1861-1133. - 17:(2020), pp. 275-288. [10.1007/s11440-021-01216-7]

### Seismic response for an isosceles triangle hill subjected to anti-plane shear waves

#### Abstract

This paper presents an exact, analytical solution to the boundary value problem of the anti-plane (SH) waves scattering by an isosceles triangle hill on an elastic half-space by using the wavefunction expansion method. An appropriate regionmatching technique is introduced to divide the half-space containing a triangle hill into two subregions. Then, the wavefield expression of each subregion is constructed in terms of an infinite series in two coordinate systems, respectively. Furthermore, a Graf’s addition formula is derived to unify the coordinate system and solve the unknown coefficients in the wave functions. Finally, numerical results are calculated to illustrate the effects on ground motion due to the existence of an isosceles triangle hill. This paper revises the existing analytical methods, and aims to provide a benchmark for numerical method verification and a reference for engineering practice.
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Utilizza questo identificativo per citare o creare un link a questo documento: `https://hdl.handle.net/11583/2977683`