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为研究层状饱和场地中沉积谷地对斜入射地震波的三维散射问题,建立了求解问题的2.5维间接边界元方法。通过沿沉积谷地轴线方向的傅里叶变换将三维问题降为二维问题,进而在沉积谷地的截面内进行边界单元的离散和求解,求得沉积谷地截面内的动力响应,然后再将截面内计算结果沿沉积谷地轴线方向进行波数展开即可求得任意位置动力响应。通过与弹性情况的比较验证了方法的正确性,并以均匀饱和半空间和基岩上单一饱和土层中沉积谷地对斜入射平面SH波的三维散射为例进行了数值计算和分析。研究发现沉积谷地对SH波的三维散射与二维散射之间存在显著差异;饱和情况(透水或不透水)与干土情况沉积谷地附近地表位移的差别很大;另外层状饱和半空间中沉积谷地和均匀饱和半空间中沉积谷地对斜入射SH波的放大作用也存在显著差别。
In order to study the three-dimensional scattering of obliquely incident seismic waves in sedimentary valleys in layered saturated terrain, a 2.5-D indirect boundary element method for solving the problem is established. The three-dimensional problem is reduced to a two-dimensional problem by the Fourier transform along the axis of the sedimentary valleys, and then the boundary elements are discretized and solved within the section of the valley. The dynamic response in the valley of the valley is calculated, and then the cross- Calculation results along the valley direction of the valley valley wave number can be developed to obtain the dynamic response at any position. The correctness of the method is verified by comparison with the elastic case. The three-dimensional scattering of obliquely incident plane SH wave is calculated and analyzed with the sediment valley in a homogeneous saturated half-space and a single saturated soil bedrock as an example. It is found that there is a significant difference between the three-dimensional scattering and the two-dimensional scattering of the SH wave in the sedimentary valleys. The difference of surface displacement near the sedimentary valleys in the saturated soil (permeable or impermeable) There is also a significant difference in the amplifying effect of obliquely incident SH waves in the valleys and in the uniformly saturated half-space sedimentary valleys.