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在Biot饱和多孔介质理论的基础上,应用Fourier级数展开和Hankel变换方法,将Biot波动方程转化为一组二阶常微分方程;运用薄层法在竖向进行离散求解,最终得到层状饱和地基Lamb问题的解答。针对薄层法仅能在有限深度内求解的不足,根据旁轴近似原理,对饱和半空间频率–波数域内的刚度矩阵进行二阶Taylor级数展开,得到适合于薄层法底层边界的通用旁轴近似解答,提高了薄层法的计算效率。最后,通过两个计算实例验证了本文解答。
Based on the theory of Biot saturated porous media, the Biot wave equation is transformed into a set of second-order ordinary differential equations by applying Fourier series expansion and Hankel transformation. Finally, the layered saturated solution Answer to the ground Lamb problem. According to the principle of paraxial approximation, the second-order Taylor series expansion of the stiffness matrix in the frequency-wavenumber domain of the saturated half-space is carried out to solve the problem that the thin-layer method can only be solved within the finite depth. Axis approximate solution to improve the calculation efficiency of thin layer method. Finally, we verify the solution of this paper by two examples.