Anti-plane response induced by an irregular alluvial valley using a hybrid method with modified transfinite interpolation

Abstract This paper proposes a novel strategy for the investigation of displacement amplitude ( | u y | ) near and along an irregular alluvial valley subjected to shear horizontal ( SH ) waves. The irregular alluvial valley in this study comprises a partially filled alluvial valley and a circular-arc-layered alluvial valley. Modified transfinite interpolation (MTFI) was used to obtain the coordinates of nodes and determine the sequence of node numbering in the inner finite region, including the irregular alluvial valley. The proposed hybrid method, comprising finite element method and a Lamb series, was applied in conjunction with MTFI to study the effects of irregular alluvial valley geometry, the incident angle of SH waves ( θ ), a dimensionless frequency ( η ), and a filling ratio (FR) on | u y | . Semi-circular canyons and semi-circular alluvial valleys were also examined. We describe in detail the amplification of | u y | at the surface of the alluvial valley and discuss the reasons for the formation of the maximum amplitude ( | u y | max ) as well as its position. Interestingly, FR was shown to play an important role in determining the value of | u y | , and variations in θ and η dominate the patterns observed in | u y | . Our numerical simulation results help to elucidate site effects in irregular alluvial valleys as well as a wide range of subjects related to geological structures.