Anti-plane response caused by interactions between a dike and the surrounding soil

Abstract This paper proposes a novel strategy for the investigation of displacement amplitude ( | u y | ) near and along symmetric dikes comprising a trapezoidal structure with a circular-arc foundation when subjected to shear horizontal ( SH ) waves. Materials in the half-space dealt with two types of dike: (1) soft dikes, and (2) hard dikes. Modified transfinite interpolation (MTFI) was used to obtain the coordinates of nodes and determine the sequence of node numbering in the inner finite region, which included a dike and a semi-circular-arc annulus. MTFI was shown to overcome the difficulties involved in the meshing of irregularity. The proposed hybrid method, comprising finite element method and a Lamb series, was applied in conjunction with MTFI in order to study the effects of dike material, the incident angle of SH waves ( θ ), and a dimensionless frequency ( η ) on | u y | . We briefly describe a closed-form solution to the problem of rigid semi-cylindrical foundations proposed in a previous study and then conducted a comparison of theoretical solutions and numerical results obtained using the proposed hybrid method. In the case of soft dikes, the natural fixed-base frequency of the foundation was close to the quasi-resonance frequency (QRF), which resulted in a maximum value of | u y | ( | u y | max ) at the top of the trapezoidal structure for various η . However, in the case of hard dikes, the | u y | max at the top of trapezoidal structure and in the dike foundation appeared at various QRF due to the fact that the movement of a hard dike is close to a rigid body motion. Energy absorption in a soft dike was shown to be superior to that of a hard dike, based on the fact that the shape of the deformed soft dike was more complex than that of the hard dike, and a number of displacement peaks observed inside the soft dike may be indications of damage within the dike that must be taken into account. Interestingly, the proposed hybrid method with MTFI provides a better understanding of the soil-structure interaction, compared with results obtained in previous studies.