Development, Validation, and Application of the 2. <scp>5D</scp> Finite‐Length Thin Layer ( <scp>FTL</scp> ) Element for Computing Dynamic Response of the Ground

ABSTRACT The classic finite element (FE) method suffers from low computational efficiency when dealing with wave propagation in unbounded domains, as a sufficient number of elements are required per wavelength. This issue becomes particularly pronounced in soil dynamics problems involving semi‐infinite ground. In this paper, we develop a 2.5D finite‐length thin layer (FTL) method to efficiently calculate ground vibrations. Based on the well‐established thin layer method, the ground is first discretized in the vertical direction, producing a series of thin layer elements. Through the quadratic eigenvalue analysis, the mode shapes of the thin layer elements are obtained. By superimposing the left‐ and right‐propagating mode shapes, the stiffness matrix of the 2.5D FTL element is constructed. Since the mode shapes are derived analytically, the length of the 2.5D FTL element is not restricted by the analyzing frequency or corresponding ground wavelength, significantly reducing the degrees of freedom (DOFs) of the ground model. The ground responses computed by the 2.5D FTL method are compared with those obtained using the classic dynamic flexibility method and the 2.5D FE method, demonstrating the high accuracy of the 2.5D FTL method. The 2.5D FTL element is subsequently incorporated into the 2.5D finite element, with the perfectly matched layer (PML) serving as an absorbing boundary. Numerical results exhibit good compatibility between the 2.5D finite element and the 2.5D FTL element. Additionally, a case study of ground vibrations from an underground tunnel is conducted, illustrating the capability of the proposed method in analyzing dynamic interactions between complex engineering structures and soils.