低山丘陵地形效应的三维有限元模拟

Three-dimensional finite element simulation of the topographical effect of low mountains and hills

摘要:

山地丘陵地形对地震动的分布有重要的影响,研究地形效应,有利于充分认识地震灾害风险,为减轻灾害损失做好防御措施。基于实际地形建立自贡西山公园观测台阵所在山体的三维有限元模型,研究开发黏弹性人工边界和SH波垂直入射前处理程序,开展动力学数值模拟；数值模拟结果与实际记录进行对比,并验证模型的合理性；研究分析低山丘陵山体对地震动强度及空间分布影响,以及峰值加速度与入射波频率、高程、坡度的关系。结果表明:低山丘陵山顶位置地震动峰值放大明显,而山脚凹陷位置地震动峰值存在削弱现象;地形效应与输入地震动频率密切相关,不同主频的输入地震动所造成的地表峰值加速度分布不同;较高主频的地震动可以凸显地形细节的影响;地表峰值加速度与高程具有较好的正相关关系,与坡度的相关关系较弱。综合高程和坡度拟合峰值加速度的效果优于仅使用高程或坡度的拟合,二元三次多项式拟合效果较好,可用于定量描述地形放大系数随高程和坡度的变化。

Abstract:

Mountainous and hilly topography affects the distribution of ground motion. The study of topographical effect enables the complete understanding of the risk of earthquake disasters and the implementation of preventive measures to reduce disaster loss. In this paper, a three-dimensional finite element model of the hill where the Zigong topographic array is located was established based on actual topography. A preprocessing program for setting viscoelastic artificial boundaries and vertical incidence of the SH wave was developed to carry out dynamic numerical simulations. The rationality of the proposed model was verified through the comparison of numerical simulation results with actual records. Analysis was conducted to determine the influence of low mountains and hills on the intensity and spatial distribution of ground motions and the relationship among peak ground acceleration and wave frequency, elevation, and slope. The results show the amplification effect of the top of the low hill on the peak ground acceleration, which is weakened by concave topography at the foot of the hill. The topographical effect is closely related to the frequency of input ground motion, and input ground motions with different dominant frequencies cause varied distributions of peak ground acceleration. A good positive correlation was observed between peak ground acceleration and elevation, but a weak correlation between peak ground acceleration and slope. The fitting effect of peak acceleration through the combination of elevation and slope is better than that when using only elevation or slope. The binary third-order polynomial exhibited a desirable fitting effect, which can be used to quantitatively describe the changes in topographical amplification coefficient with elevation and slope.