Dynamic Stresses in a Driven Pile During Installation-Classical Wave Equation Model Solution Using Partial Differential Equations

This paper derives and solves the governing dynamic wave equation of motion of a driven pile during the installation phase, when the driven pile is subjected to hammer blows. The pile is assumed as an elastic solid body. The equation of motion is a partial differential equation in space (axial coordinate) and time. The governing partial differential equation of motion is solved for installation boundary conditions, and simplified soil resistance models. The solution of the governing equation yields important design parameters, such as stress variation at any cross-section along the pile length with respect to time, and propagating wave speed. The resulting closed-form solution can be easily implemented using a standard spreadsheet or an engineering calculation program. This approach is compared with conventional wave equation analysis (WEAP) used in industry practice. The conventional wave equation analysis is based on discretization of the pile into mass-spring-damper elements (lumped parameter approach), rather than continuous modeling. The models and solutions from these two approaches are compared.