基于声子晶体理论的饱和地基上周期性高架桥与隧道结构振动特性研究

Based on the theory of the phononic crystal and the saturated soil dynamic theory, the vibration characteristics of the periodic viaduct and tunnel in the saturated soil are analyzed from the calculation the vibration energy band of the periodic structure, the vibration and wave propagation of the periodic structure due to a moving load. Mainly include the several aspects below: using the transfer matrix method and the coupling vibration between the pile and soft foundations, a numerical model for analysis of the energy band of an "open"-type periodic viaduct in out-of-plane or in-plane vibration is developed. The energy band of the periodic tunnel-soil is computed and harmonic analysis of the displacement responses within the pass bands and band gaps of the periodic structure are investigated with the FEM/BEM method. By using the Floquet transform method, the mathematics model of the dynamic responses of the periodic viaduct and the tunnel under moving loads is established and the numerical solution of the vibration isolation via multiple pile rows is given. The scattering effect of a tunnel embedded in the homogeneous or layered saturated soil during propagation of Rayleigh wave is studied using the analytical function and BEM-FEM method. The purposes of this project are to discuss the rules and effects of the coupling vibration between the basic cell and the soft foundation as well as their physical properties on the energy band of the periodic structure. The reasons of the energy band of the periodic structure are also presented. Moreover, the influence of the moving loads on the vibration of the periodic structure and the surrounding environment as well as the effectiveness of the vibration isolation via multiple pile rows is investigated. The results of this research can be used to provide a new idea for the seismic design of the viaduct or tunnel foundation in the saturated soft soil and the vibration control of the periodic structure. It has active guidance meaning and applied value to the engineering practice.

项目基于声子晶体理论及饱和土体理论，从周期结构振动能量带计算、移动荷载引起周期结构振动与传播等方面，开展周期性高架桥与隧道结构振动特性分析，主要包括：利用桩-土共同作用及传递矩阵法，建立饱和土体上"开放式"周期性高架桥结构平面外、平面内振动能量带计算模型；采用有限元-边界元法，建立周期性隧道-土层能量带与谐波激励下禁带、通带内位移响应计算模型；引入Floquet变换，建立移动荷载与周期性高架桥、隧道结构相互作用以及周期性多根多排桩隔振数值模型；结合解析函数法与BEM-FEM，分析饱和地基中隧道结构对Rayleigh波场散射效应等。主要研究目标是：分析基本元与软土地基耦合振动及其物理性质等对能量带分布的影响，揭示周期性结构能量带产生机理。考察移动荷载对周期结构及周边环境振动影响规律以及排桩隔振效果。为饱和软土地基上高架桥、隧道等周期结构抗震设计、隔振减振控制等提供一种新的理论基础与工程指导。

利用周期结构所具有的振动特性，可为结构的抗震设计、减振控制提供了一种新思路。如通过合理设计周期性高架桥结构的几何参数和材料参数，保证地震主要形式的能量波在高架桥、隧道结构本身通带频带范围内，否则，具有较大能量的地震波难以通过高架桥结构，引起能量急剧增加造成结构破坏。基于此，根据国家自然科学基金（No：51269021）项目研究计划安排，开展了相关系列研究，已出版专著1部，发表论文22篇，其中SCI/EI检索15篇。项目进行了以下研究：(1)建立了周期性高架桥结构能量带特征方程，分析了周期性高架桥结构平面内振动的能量带分布特征；(2)结合Wolf算法，推导了描述周期性高架桥波场局部化的Lyapunov正指数，分析了平面外振动失谐引起局部化现象；(3) 根据饱和土Biot 理论及孔洞边界特性，建立了半无限饱和土体中孔洞对波场散射问题的边界元积分方程；(4) 在计算域内采用Galerkin加权余量法，推导了3D无限、有限域全耦合饱和土体固结的比例边界有限元方程；(5) 基于比例边界有限元法与Fourier积分变换，建立频域—波数域内的比例边界有限元方程，分析了移动荷载作用下半无限弹性空间中地铁隧道动力响应。项目研究表明：对于水平梁-梁及水平梁-桥墩间的弹簧连接的周期性高架桥结构，在平面内振动时结构中存在三种复晶格波；增大周期性高架桥结构水平梁刚度、水平梁-梁弹簧刚度，将提高结构中振动波传播速度，振动传播距离也会增大；随振动频率增加，周期高架桥结构失谐引起局部化现象明显；随饱和土体中流、固二相耦合程度增大，孔洞应力集中系数增大，孔洞的散射作用增强；随荷载移动速度增大，地铁隧道振动波传播到土体表面，引起的土体振动有放大增强的现象，将会对地铁隧道上部结构的安全性造成一定影响。计算结果还表明：高架桥结构设计时，结构基本主频不能在较小频率区域，否则极易引起能量集中，造成结构破坏。项目的实施为饱和软土地基上高架桥、隧道等周期结构抗震设计、隔振减振控制等提供一种新的理论基础与工程指导。