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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。
Based on Biot saturated porous media UW format dynamic governing equations, the 2.5-D finite element equation and viscoelastic artificial boundary of saturated soils are deduced by Galerkin method and Fourier transform. The analytical model of hollowed-out soil is established in the wave number domain Solve and wave number expansion through Fast Fourier Transform (FFT) to get results in 3D space domain. An example is given to analyze the vibration isolation effect of hollow gound under saturated soil foundation, layered saturated soil foundation and saturated soil foundation with overlying single-phase elastic layer under moving loads. The results show that the vibration isolation effect of the hollow channel in saturated soil is not only related to the depth of the empty channel, but also to the interface of the layered soils in the foundation and the parameters of the soil. The transmission and reflection of the waves at different soil interfaces Which affects the vibration isolation effect of the empty trench. The thickness of the overlying single-layer elastic layer in saturated soil has a significant effect on the isolation effect of the empty trench. With the thickness of the overlying single-layer elastic layer increasing, the vibration isolation effect of the hollow trench in saturated soil Better.