@article{Toan Luong_Nghiem_2022, title={VERTICAL DYNAMIC RESPONSE OF A FRICTION PILE IN MULTILAYERED SOIL}, volume={23}, url={https://geomatejournal.com/geomate/article/view/3233}, abstractNote={<p>A semi-analytical-numerical method is developed to investigate the vertical dynamic response of a single pile embedded in multilayered soil. The governing differential equation for the pile and soil settlements is derived using the energy principles and variational approach that can consider both normal and shear strains in the vertical direction. The soil displacement in the vertical direction is expressed in terms of the pile displacement in the vertical direction and a decay function in the radial direction. The pile is modeled by a series of elements and the differential equation for each element is solved by applying the finite element method where exact shape functions are employed. The iterative algorithm is adopted to solve the pile settlement and the pile head impedance instead of solving simultaneously many equations and the proposed method is implemented in a computer code to obtain the solution. The validation of the proposed method is performed via a comparison of the pile head impedance and static stiffness with those from existing methods in the literature for both end-bearing and friction piles in homogeneous and multilayered soils. The pile head impedances calculated using the proposed method match well those obtained from approximate analytical solutions and are in good agreement with those from the three-dimensional finite element analyses at zero frequency.</p>}, number={96}, journal={GEOMATE Journal}, author={Toan Luong, Hiep and Nghiem, Hien}, year={2022}, month={Aug.}, pages={1–10} }