An analysis for the torsional dynamic response of end-bearing pile foundations embedded in a layered transversely isotropic geomaterial (soil/rock) is presented. The deformation of the transversely isotropic soil or rock is described by the method of separation of variables. The elasticity theory for a viscoelastic medium with frequency independent hysteretic material damping, and the Extended Hamilton's Principle are utilised to derive the differential equations describing pile and soil motions. The differential equations are solved analytically in an iterative algorithm. The accuracy of the analysis is verified with existing studies reported in the literature for pile foundations embedded in a homogeneous and layered soil deposit. The effect of the degree of anisotropy on the pile-soil response - dynamic pile-head stiffness, distribution of pile rotation and torque with depth, dimensionless soil displacement function for various values of pile slenderness and pile-soil stiffness ratios in a homogenous soil deposit is investigated. Design charts of static pile-head stiffness in a homogeneous soil deposit for a wide range of pile-soil stiffness and pile slenderness ratios, and degree of anisotropy are also reported. The effect of soil layering for a pile embedded in a two-layered soil deposit is also studied.

Anisotropy is an inherent characteristic of subgrade soils, causing significant variations in the dynamic behavior of the pile embedded in them under different loading conditions. This research develops a novel model to examine, for the first time, the dynamic behavior of an end-bearing pile embedded in an anisotropic elastic medium subjected to vertical S-waves. The pile is modeled as a Euler-Bernoulli beam, while the surrounding soil is treated as a transversely isotropic (TI) elastic material. The one-dimensional free-field and three-dimensional scattered-field motions in the TI elastic medium under S-waves are obtained within the frame of dynamic continuum model. The developed model is checked for accuracy against established analytical solution. Key parameters, such as the anisotropic modulus ratio of the TI soil, pile radius, are systematically studied to assess their effects on the kinematic behavior of the system. Results reveal that the soil anisotropy would significantly alter the kinematic behavior of the pile and surrounding soil system, notably impacting the amplification factors for pile displacement and rotation and the horizontal movement of the soil. These findings highlight the necessity of considering soil anisotropy in the seismic design and analysis of pile foundations to ensure structural safety and performance under earthquake.