Wave Equation Technique For Estimating Driven Pile Capacity

A one-dimensional wave equation based algorithm for estimation of shaft and toe resistance of driven piles using High Strain Testing (HST) data is presented. The pile is represented by a uniform elastic bar, while the soil around the pile is assumed as a homogenized isotropic medium, and Smith model is adopted to represent soil-pile interaction in the wave equation analysis. In most cases, the displacement of pile particles along pile shaft is greater than recoverable soil deformation (i.e., soil quake in Smith model). Therefore, static shaft resistance could be reasonably assumed to be totally mobilized during pile driving. Smith damping factor is used to account for combined dynamic and rate effect. Force and velocity time histories measured at the pile head are used as input boundary conditions in an analytical solution of the one-dimensional wave equation. As a result, two unknown parameters, static shaft resistance and Smith damping factor, can be incorporated into the one-dimensional wave equation and determined analytically for the time duration prior to the first downward wave reaching the pile toe. Then, soil resistance and Smith damping factor at pile toe can be further determined. The advantage of the proposed analysis technique is that the Smith damping factor and the static soil resistance can be directly determined based on the closed-form solution of the one-dimensional wave equation, which is computationally efficient. Numerical examples are given to illustrate the use of the proposed method to determine the pertinent Smith model constants and the static resistances.