Torsional dynamics of end-bearing pile in non-homogeneous soil: variational approach coupled with Ritz solution

An analysis is developed for torsional dynamics of end-bearing pile foundations embedded in inhomogeneous soil deposits. The inhomogeneity of the soil deposit is incorporated in the analysis through an algebraic expression that can simulate linear, parabolic, and hyperbolic variation of shear modulus with depth. In the analysis, the pile is modelled as a one-dimensional elastic continuum, while the soil is a three-dimensional viscoelastic continuum. The Extended Hamilton’s Principle is employed to derive the governing differential equations describing pile and soil motions, which are solved employing Bessel functions and Ritz procedure, respectively. The accuracy of the analysis is verified against existing solutions in the literature. The proposed framework is further employed to study the influence of inhomogeneity. From the study, it is found that the effect of soil inhomogeneity on dynamic torsional stiffness, wave propagation, and pile-twist distribution cannot be neglected, especially for softer (pile-soil stiffness ratio greater than 500) soil deposits.