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首页> 外文期刊>Technical Gazette >Analytical Solution for 2D and 3D Lamb Problem in Saturated Soil Incorporating Effects of Compressibility of Solid and Pore Fluid
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Analytical Solution for 2D and 3D Lamb Problem in Saturated Soil Incorporating Effects of Compressibility of Solid and Pore Fluid

机译：饱和土壤中的2D和3D羊羔问题的分析解决方案掺入固体和孔隙流体压缩性的影响

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In this paper, to avoid the complexity, a simple and efficient analytical solution is derived for both 2D and 3D Lamb problems, respectively, in saturated soil under harmonic excitations. Unlike the existing solutions, the proposed solutions for both 2D and 3D Lamb problems in saturated soil under harmonic excitation are capable of well revealing the effect of compressibility of both liquid phase and solid phase on the ground displacements. By applying Fourier transforms and Hankel transforms on the governing equations of wave propagation in saturated soil, wave equations are transformed to ordinary differential equations. Combining the boundary conditions and draining conditions on the ground surface, the displacement solutions on the surface of saturated porous soil due to line and point harmonic excitations are derived, respec-tively. Then, the solutions in frequency domain are obtained by inverse integral transforms. In the meanwhile, for the sake of discussion without losing its generality, the non-dimensional solutions for three-dimensional Lamb problem are derived. The effectiveness and accuracy of the proposed solutions are demonstrated by employing three different approaches. Finally, parametric studies are conducted to investigate the effects of the governing parameters (i.e., exciting frequency, bulk modulus of soil matrix, and bulk modulus of pore fluid) on variation of non-dimensional displacement with the increasing distance away from the excitation source. The results indicate that, in contrast to the effect of the compressibility of soil matrix, the exciting frequency as well as the compressibility of the pore fluid play significant role in affecting the variation of displacement on ground surface subjected to excitations, which particularly highlights that the compressibility of the pore fluid should be carefully considered for evaluating the ground movements.
机译：在本文中，为了避免复杂性，在谐波激发下分别在饱和土壤中分别在饱和土壤中衍生简单而有效的分析解决方案。与现有解决方案不同，在谐波激发下饱和土壤中的2D和3D羊羔问题的提出解决方案能够良好地揭示液相和固相对压缩在地面位移上的压缩性的影响。通过在饱和土中的波传播的控制方程上应用傅里叶变换和嗜鲸变换，波动方程被转换为常规方程。结合边界条件和排出条件在地面，衍生出由于线和点谐波激发引起的饱和多孔土壤表面上的位移溶液。然后，通过逆积分变换获得频域的解。同时，为了讨论而不丢失其一般性，导出了三维羔羊问题的非维度解决方案。通过采用三种不同的方法来证明所提出的解决方案的有效性和准确性。最后，进行了参数研究以研究控制参数（即激发频率，土壤基质模量和孔隙流体的散装模量）对来自激发源的不断变化的非尺寸位移的变化。结果表明，与土壤基质的可压缩性的影响相比，令人兴奋的频率以及孔隙流体的可压缩性起着显着作用，在影响受激励的地面上位移的变化起作用，这特别突出了应仔细考虑孔隙流体的可压缩性以评估地面运动。

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