An analytical solution for the dynamic response of an end-bearing pile subjected to vertical P-waves considering water-pile-soil interactions

A three-dimensional water-pile-soil model is developed to investigate the dynamic responses of end-bearing pile under vertical P-waves. The soil and pile are modelled as linear viscoelastic media with hysteretic material damping, and the water is modelled as linear acoustic medium. The proposed model considers the radial and vertical equilibria of pile-soil and pile-water as well as three-dimensional wave scattering. The total dynamic response of the system can be expressed as the sum of the free-field response and scattered-field response. The water-soil interaction is considered in the free-field response, while it is neglected in the scattered-field response. Through a precise theoretical derivation, a closed-form solution is obtained for the total response of the waterpile-soil system. The present solution is compared with several other methods to verify the validity of the method. The effects of several factors, such as soil thickness, water depth, pile radius, pile modulus and soil modulus on the dynamic response of the pile head are studied. The results indicate that it is necessary to consider the water-pile-soil interactions in the design of piles that are installed in offshore areas.