This study numerically investigated the influence of downstream bed slopes of 0°, 5°, 10°, and 15° and bridge pier positions of 1.1 and 1.3 m on the impact force induced by a tsunami surge wave. Square, circular, and ogival bridge pier geometries were studied to evaluate the influence of geometry. The numerical model used in the study was validated against experimental benchmarks in the literature, and the pressure and impact force time histories were analyzed. The results confirm the suitability of the model for simulating this surge–structure interaction. The results show that the impact forces are significantly influenced by pier geometry. The square geometry recorded a maximum horizontal impact force of 1.73 and 3.32 times more than those for the circular and ogival geometries, respectively. The result further shows that increasing downstream bed slope causes a reduction in the recorded impact forces. The reduction is influenced by the pier geometry, with a maximum reduction of 23% for the square, 32% for the circular, and 38% for the ogival pier recorded as the downstream bed slope increases from 0° to 15°. The circular and ogival pier cases were found to have mitigated flow stagnation and pressure amplification relatively better than the square pier geometry. Slope-dependent reduction factors were proposed for possible incorporation into design guidelines. This study provides practical frameworks for design purposes.
Adekoya et al. (2026) studied this question.