Abstract The dynamic response of a transversely isotropic, multilayered and poroelastic seabed under the action of two-dimensional water waves is investigated via a recently developed semi-analytical method. The coupled governing equations of motion are based on the Biot's complete poroelastodynamic model, expressed in the (u,p) form. The potential-function method is introduced to express the unknown primary quantities such that the general solution in each layer is obtained with six undetermined coefficients. By virtue of the stable and efficient dual variable and position method, a general recursive relation for the displacements, stresses and pore pressure among different layers is established. The semi-analytical solutions for the layered seabed with two typical bottom boundary conditions are derived. Particularly, for the homogeneous transversely isotropic seabed, exact solutions are also derived for different bottom boundaries. The accuracy and reliability of the solutions are verified against existing solutions. Selected numerical examples are further presented to study the effect of anisotropic stiffness, anisotropic permeability and material layering on the wave-induced pore pressure and effective stresses.

中文翻译：

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横向各向同性多层多孔弹性海床中波浪引起的动态响应

摘要 通过最近开发的半解析方法研究了二维水波作用下横向各向同性、多层和多孔弹性海床的动力响应。运动的耦合控制方程基于 Biot 的完整多孔弹性动力学模型，以 (u,p) 形式表示。引入势函数法来表达未知的初级量，使得每一层的一般解都由六个未定系数获得。利用稳定高效的双变量位置法，建立了不同层间位移、应力和孔隙压力的一般递推关系。推导出具有两种典型底部边界条件的层状海床的半解析解。特别，对于均匀的横向各向同性海床，还推导出了不同底部边界的精确解。解决方案的准确性和可靠性已根据现有解决方案进行验证。进一步介绍了选定的数值例子，以研究各向异性刚度、各向异性渗透率和材料分层对波浪引起的孔隙压力和有效应力的影响。