基于快速多极边界元法三维饱和复杂场地地震波传播与散射宽频模拟

The propagation characteristics of seismic waves in fluid-saturated rock and soil layers are significantly different from those in single-phased soil medium. Aiming at quantitative simulation of large-scale three-dimensional seismic wave motion in poroelastic complex sites, the inclined disc surface load and fluid-source dynamic Green's function in poroelastic layered half space and a full space are firstly derived based on the single-porosity and double-porosity models of saturated medium. Then a fast broadband multi-pole indirect boundary element method (FMM-IBEM) for inhomogeneous two-phased medium will be developed, combined with the multi-level multi-pole expansion technique: the Green's functions are expanded by Taylor series (low frequency) or by a plane wave expansion with diagonal transfer (high frequency). This new method can significantly reduce the storage and computation requirement of traditional method for solving large-scale problems. Based on the FMM-IBEM, we will study the scattering of seismic waves in wide-band frequencies by complex layered alluvial basin, valley, inclusions group, etc. Through a large amount of parametric analysis, this project strives to clarify the influence characteristics of the incident wave, the complex alluvial structure, the topography feature etc. on ground motion, to reveal the model conversion, the focusing effect and resonance scattering phenomenon in layered saturated sedimentary basins, and to quantitatively investigate the damping nature of multi-scattered waves around the inclusions and cracks. We will also analyze the dynamic changes of the pore water pressure and fluid, and the ground motion amplification characteristics at different depths. Finally, the research can provide new efficient algorithms for studying the wave motion in inhomogeneous saturated medium, and provide a theoretical basis for seismic zoning, the city planning and the seismic design of engineering structures for complex saturated sites.

地震波在流体饱和岩土层中传播特性同干土场地情况具有显著差异。针对大尺度饱和复杂场地三维地震波动模拟问题，首先基于单一/双重孔隙饱和两相介质模型，推导饱和层状半空间及全空间斜面圆盘荷载、流量、孔压动力格林函数；进而结合多层多极子展开技术，对格林函数进行泰勒级数展开（低频）和平面波展开及对角转移（高频），建立饱和两相不均匀介质宽频快速多极间接边界元法，大幅降低普通方法所需计算量与存储量。据此开展饱和复杂沉积盆地、河谷、地下夹杂群等对地震波散射宽频模拟与大规模参数分析，力求阐明入射波特性、饱和场地波速结构、地形特征等对地震动影响规律，揭示饱和沉积盆地对地震波转换、聚焦效应及共振散射机制，量化饱和夹杂、裂隙群等对地震波多次散射衰减因子，分析不同深度孔压、流量动态变化及地震动放大特征。最终为饱和不均匀介质大规模波动问题分析提供新型高效算法，为复杂饱和场地地震区划、城市规划、工程抗震等提供理论依据。

滨海河谷地带多为饱和岩土场地。地震波在流体饱和岩土层中传播特性同干土场地情况具有显著差异，饱和两相介质波动方程宽频求解相比单相介质更为复杂困难。针对大尺度饱和复杂 场地三维地震波动模拟问题，首先基于单一/双重孔隙饱和两相介质模型，推导了饱和层状半空 间及全空间斜面圆盘荷载、流量、孔压动力格林函数，建立了饱和介质地震波动间接边界元求解方法；进而结合多层多极子展开技术，对格林 函数进行泰勒级数展开（低频）和平面波展开及对角转移（高频），建立饱和两相不均匀介质 宽频快速多极间接边界元法，大幅降低普通方法所需计算量与存储量。针对随机地震动模拟，发展了基于乘法降维法的单相及饱和复杂场地地震动模拟方法；建立了含随机裂隙群山体场地地震波动快速多极边界元方法。通过同理想条件下精确解析解结果进行对比，验证了 FMM-IBEM的求解精度、效率和高频数值稳定性。在此基础上，针对饱和复杂沉积 盆地、河谷、地下夹杂群等对地震波的宽频散射宽频，开展了精细化数值模拟与大规模参数分析，阐明了入射波特性、 饱和场地波速结构、地形特征等对地震动影响规律，揭示了饱和沉积盆地对地震波转换、聚焦效 应及共振散射机制，量化了饱和夹杂、裂隙群等对地震波多次散射衰减因子，分析不同深度孔压 、流量动态变化及地震动放大特征。在随机波动方面，系统揭示了地震波入射下岩土参数随机性对二维、三维沉积盆地位移幅值均值、变异性的影响，阐明了岩土参数随机性在二维、三维沉积盆地中的传递特性；考察了沉积河谷水深、孔隙率、沉积层厚度等关键参数对含水层饱和沉积场地地震动参数的影响规律。项目研究为饱和不均匀介质大规模波动问题分析提供了一种新型高效算法，为复杂饱和场地地震区划、城市规划、工程抗震等提供了重要理论依据。