The variational projection method (VPM): A modern technique to simulate the seismic response of shallow alluvial valleys

Ávila-Carrera, R.; Sánchez-Sesma, F. J.

doi:10.1016/j.soildyn.2013.02.004

Cited by 2 publications

(1 citation statement)

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“…Among these idealized simplified models, the most popularly adopted ones are those of the fully filled type, especially those in trapezoid shapes (e.g., Bard and Bouchon 1980;Kawase and Aki 1989;Takenaka et al 1996;Makra et al 2005; Kham et al 2006;Gelagoti et al 2010). Various numerical approximation methods were devised to evaluate the dynamic site response (e.g., Aki and Larner 1970;Boore et al 1971;Dravinski et al 1991;Clements and Larsson 1994;Fu and Bouchon 2004;Dravinski 2007;Ávila-Carrera and Sánchez-Sesma 2013). Nowadays, tremendous progress in parallel processing and faster processors has boosted the growth of mesh discretization techniques.…”

Section: Introductionmentioning

confidence: 99%

Ground motions around a semi-circular valley partially filled with an inclined alluvial layer under SH-polarized excitation

Chang¹,

Tsaur

2014

Earth Planet Sp

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A simplified mathematical model, composed of a semi-circular valley partially filled with an inclined alluvial layer under plane SH-wave incidence, is presented. To evaluate the site response theoretically, a rigorous series solution is derived via the region-matching technique. For angular wavefunctions constrained by an inclined free surface, the original form of Graf's addition formula is recast to arbitrarily shift the local coordinate system. The valley geometry, filling material, angle of incidence, and wave frequency are taken as significant parameters in exploring the site effect on ground motions. Also included are the frequency-and time-domain computations. Two canonical cases, the semi-circular vacant canyon and the fully filled semi-circular alluvial valley, with exact analytical solutions, and the partly horizontally filled case previously studied, are taken to be particular cases of the proposed general model. Steady-state results show that the peak amplitudes of motion may increase at low frequencies when the filling layer inclines to the illuminated region. At low-grazing incidence, the phenomenon of wave focusing becomes evident on the shadow side of the filling layer. Transient-state simulations elucidate how a sequence of surface waves travel on the topmost alluvium along opposite directions and interfere with multiple reflected waves within the filling layer.

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