基于横观各向同性层状介质模型的复杂场地地震效应研究

Site response has always been regarded as an important research topic. However, few studies have been reported to investigate this subject by considering soil as an anisotropic medium. Transversely isotropic (TI) medium has been widely acknowledged as a reasonable mechanical model in presenting the anisotropy properties of soil and is very convenient for engineering application. Therefore, it has important theoretical significance and practical application value to carry out research by introducing the TI medium model to the study of site response. Firstly, the IBEM based on the dynamic stiffness matrix and the Green’s functions of uniformly distributed loads established in isotropic (TI) medium, is extended into the layered elastic (saturated) medium to develop the corresponding two dimensional, two and a half dimensional and three dimensional IBEM. Then, systematic theoretical study and application study on complex site response are performed based on the layered elastic (saturated) medium model. This project aims at finding out the essential differences on wave scattering by complex site in the TI medium and in the isotropic medium, clarifying the influence of the soil anisotropy parameters on the seismic ground motion and on the seismic response spectrum, and ultimately promoting the development of studies on site response in anisotropic medium. This study will provide a new method and thought for wave field simulation in a TI layered half-space, which will also offer a theoretical basis for the works of Earthquake Damage Prediction, Seismic Zoning and Earthquake Resistance Protection of important engineering structures, especially important to the accuracy in determining the ground motion parameters of the area with significant soil anisotropy.

场地效应是重要的研究课题，然而目前在土的各向异性方面仍鲜有研究。横观各向同性(TI)介质被公认为是描述土体各向异性的合理力学模型且便于工程应用，将其引入场地效应研究具有重要理论意义和实用价值。项目首先将申请者各向同性介质中建立的基于动力刚度矩阵和均布荷载动力格林函数的间接边界元方法(IBEM)平行拓展到TI层状弹性(饱和)介质，发展相应的二维、2.5维和三维IBEM。进而系统开展基于TI层状弹性(饱和)介质模型的复杂场地效应理论研究与应用研究。项目力图揭示TI介质中复杂场地地震波散射与各向同性情况的本质差异，阐明土体的各向异性参数对地震动和反应谱的影响规律，推动场地效应研究在各向异性介质方面的发展。研究成果可为TI层状半无限介质中波场模拟提供新的方法思路；为场地条件复杂地区震害预测、地震区划和重大工程抗震设防等工作奠定理论基础，尤其为场地土各向异性显著地区地震动参数的精确确定提供理论依据。

复杂场地的地震动效应已在多次地震观测和震害调查中得到证实，然而现有研究大都基于各向同性介质模型。横观各向同性（TI）介质作为各向异性的一种特例，是描述土体各向异性的合理力学模型且便于工程应用，采用该介质模型开展场地效应研究具有重要的理论意义和应用价值。.基于以上研究背景，项目首先建立了一套以均布荷载动力格林函数为基本解的间接边界元方法（IBEM），进而系统深入的开展了基于TI介质模型的复杂场地地震效应问题研究。取得主要成果包括，求解TI弹性（饱和）介质波动方程，建立了层状TI弹性（饱和）半空间的精确动力刚度矩阵；进而推导了均布斜线、移动斜线和斜面荷载（孔压）的系列动力格林函数；进而以该系列格林函数为基本解，建立了层状TI弹性（饱和）半空间中地震波场模拟的一套IBEM（包括二维、2.5维和三维）；最后基于建立的这套IBEM，系统研究了层状TI弹性（饱和）场地中典型局部地形（凹陷、盆地和山体等）地震效应问题。. 研究结论包括：土体TI性质的引入改变了波在土体中的传播机理，导致了土层中透射波（反射波）与散射波动力相互作用的改变；土层TI介质参数改变了场地的动力特性，使得不同TI介质模型对应的地表位移幅值和分布差异显著；共振频率的阶数越高，不同TI参数对应放大谱的峰值以及峰值频率差异越大，说明土体的TI性质对高频地震动有着更为显著的影响。本项目推动了场地效应研究在各向异性介质方面的发展，提高了场地效应数值模拟的精度。另外，项目成果（精确动力刚度矩阵和IBEM）还被成功应用于了土-结构相互作用、列车高速运行地基环境振动和地铁隧道对弹性波的散射问题求解，探讨了TI介质参数的影响。项目研究具有显著的科学意义和广阔的应用前景。