Timoshenko Beam Theory–Based Dynamic Analysis of Laterally Loaded Piles in Multilayered Viscoelastic Soil

A semianalytical method is developed to obtain the dynamic response of laterally loaded piles in a multilayered soil. In the analysis, the soil is modeled as a three-dimensional viscoelastic continuum with frequency-independent hysteretic material damping and the pile as a circular elastic Timoshenko beam. Unlike the Euler-Bernoulli beam that is conventionally used to model laterally loaded piles in various analytical, semianalytical, and numerical studies, the Timoshenko beam theory accounts for the effect of shear deformation and rotatory inertia within the pile cross-section that might be important for modeling short stubby piles with solid or hollow cross-sections and piles subjected to high frequency of loading. In the analysis, the soil displacements in the horizontal direction are expressed as products of separable functions, and the extended Hamilton’s principle in conjunction with the calculus of variations is used to obtain two sets of coupled differential equations governing pile and soil motions along with the relevant boundary conditions. The coupled equations are solved analytically and numerically following an iterative algorithm. The differential equation and boundary conditions governing pile motion are progressively reduced to model the pile as a Rayleigh beam and a Euler-Bernoulli beam; thus, a unified framework incorporating various beam theories for the dynamic soil-structure interaction of laterally loaded piles in a multilayered soil is developed. The accuracy of the present analysis is verified against the results of several analytical and numerical solutions available in the literature. It is shown from the solved example problems that rotatory inertia has practically no effect on the dynamic response of piles, whereas there is some effect of shear deformation on the response of piles with hollow cross-sections.