Axial stiffness of floating pile foundations and rigid footings with Vlasov-Leont′ev foundation model and expressions for a rigid disk

In the manuscript, a hybrid formulation to evaluate the axial dynamic and static head stiffness of pile foundations and rigid footings floating in a homogeneous half-space is demonstrated. In the formulation, the soil adjacent to the pile is modeled with the Vlasov-Leont′ev foundation model, and the underlying soil beneath the pile is modeled by a spring-dashpot system. The spring-dashpot system is described with expressions obtained from the solution of a vertically vibrating rigid massless disk on the surface of a homogeneous half-space. The expressions are obtained from the literature reported by several authors. The results obtained from the proposed formulation and the expressions are compared with rigorous formulations in the literature for pile foundations and rigid footings. It is found, the formulation demonstrated produces accurate dynamic and static head stiffness for pile foundations and rigid footings. Besides, it captures the essential mechanics of a foundation floating in a homogeneous half-space. Based on an investigative study, it is found, the expression proposed by Veletsos and Verbic accurately models and simulates the homogeneous half-space underneath the pile foundations and rigid footings.