Determining Anti-plane responses of a semi-circular alluvial valley embedded in a single layered half-space: Fid-Bau Portal

Determining Anti-plane responses of a semi-circular alluvial valley embedded in a single layered half-space

Shyu, Wen-Shinn / Teng, Tsung-Jen / Chai, Juin-Fu / Chou, Chuen-Shii

Abstract This paper proposes a modified hybrid computational method, comprising finite element method and a Lamb series for a single layered half-space, to derive displacement amplitude ( $| u_{y j}^{A V} |$ ) in a field that includes a semi-circular alluvial valley (SCAV) embedded within a single layered half-space subjected to shear horizontal (SH) waves. Variations in $| u_{y j}^{A V} |$ associated with depth (from the free surface through the SCAV and layered medium to the half-space) and site effects were also examined under various incident angles ( $θ_{2}$ ) and dimensionless frequencies ( $ζ$ ). Our analytical solutions, based on a theoretical model of the single layered half-space, revealed the thickness effects and the resonance frequencies (RFs) under various $θ_{2}$ , due to a soft layered medium. We compared the resulting $| u_{y j}^{A V} |$ value with those of an SCAV embedded in a half-space (i.e., $| u_{y j}^{a v} |$ ) and theoretical solutions based on a single layered half-space (i.e., $| u_{y j}^{f} |$ ) under RFs with various $θ_{2}$ . We discovered that due to the embedding of an SCAV in the single layered half-space, the thickness effects created by that space were a major contributor to site effects. The response amplitudes at the free surface were also magnified by the enlargement effect of the SCAV. Additional numerical simulations were conducted to obtain responses of $| u_{y j}^{A V} |$ under $ζ$ ranging from 0.01 to 2.0. These results support our discovery that thickness effects dominate the site effects. This paper provides a valuable reference to further our understanding of site effects associated with surface irregularities in the single layered half-space.

Graphical abstract The hybrid method, comprising FEM and a Lamb series for a single layered half-space, was applied in conjunction with transfinite interpolation to study the effects of a semi-circular alluvial valley embedded within a single layered half-space, incident angle of SH waves ( $θ_{2}$ ), and dimensionless frequency ( $ζ$ ) on the displacement amplitude ( $| u_{y j}^{A V} |$ ) near and along depth of the topography. Display Omitted

Highlights • Anti-plane scattering problem of single layered half-space was studied. • FEM and a Lamb series were applied in conjunction with TFI to study displacement in the field. • We detailed thickness effects and enlargement effect in the scattering problem of topography.