基于2.5维有限元饱和土地基中空沟隔振性能研究

基于Biot饱和多孔介质U-W格式动力控制方程，采用Galerkin法和Fourier变换，推导了饱和土体2.5维有限元方程及黏弹性人工边界，建立了饱和土地基中空沟分析模型，并在波数域中进行求解，通过快速Fourier变换（FFT）进行波数展开，获得三维空间域中结果。算例分析了移动荷载作用下均质饱和土地基、分层饱和土地基、上覆单相弹性层饱和土地基3种饱和土地基模型中空沟的隔振效果。结果表明：饱和土地基中空沟的隔振效果不仅与空沟自身深度有关，还与地基中成层土体的分界面以及土体参数有关，波在不同土体分界面上的透射和反射会影响空沟的隔振效果；饱和土地基中上覆单相弹性层厚度对空沟的隔振效果影响显著，随着上覆单相弹性层厚度的增加，饱和土地基中空沟的隔振效果变好。

Study of vibration-isolation efficiency of open trench in saturated ground by 2.5D finite element method

Based on the U-W formula of governing equations of Biot’s theory for the saturated porous medium, the corresponding 2.5D finite element method (FEM) equations and the viscoelastic absorbing boundary are deduced by introducing Galerkin method and Fourier transform. The solution in wave-number domain can be obtained firstly from the built model for open trenches in the saturated ground; then the fast Fourier transform (FFT) is applied to gain the results in 3D space domain. For the moving loads, the vibration-isolation effects of open trenches in three saturated grounds (homogeneous saturated ground, layered saturated ground and saturated ground with upper layer being single-phase elastic medium) are investigated. It’s found that not only is the vibration-isolation efficiency of open trenches related to the trench depth, but also it’s affected by the interface properties and parameters varying of the layered soil media. The transmission and reflection of waves in different soil interfaces have great influences on the vibration-isolation effects of open trenches. Besides, the thickness of the upper single-phase elastic layer can greatly affect the vibration-isolation efficiency of open trenches in the saturated ground; as the thickness of the upper single-phase elastic layer becomes larger, the vibration-isolation efficiency of open trenches in the saturated ground gets improved.