Probability Method Applied to Dynamic Pile-Driving Control

An energy approach previously developed as an alternative to the conventional dynamic pile-driving control methods (e.g., ENR and Gates formula) has been formulated in a probabilistic framework. The Smith-model parameters incorporated in the energy approach, including the damping factor and the quake, were treated as random variables whose mean values, standard deviations, and probability distribution functions were determined from a statistical analysis of a database of 204 pile cases. The Smith parameters for each pile case were derived from the back-calculation process in relation to the Case Pile Wave Analysis Program (CAPWAP) signal-match procedure. The first-order second-moment (FOSM) method was used in the probabilistic energy approach to compute the mean value and standard deviation of the pile capacity. A detailed description is given of the database, the statistical analysis results, and the mathematical formulation of the probabilistic energy approach. The developed probability approach was applied to the 204 pile cases. The agreement between the computed pile-capacity and the static load test results is either slightly better than or equally as good as the comparison between the traditional CAPWAP deduced pile-capacity and the static pile-load test results. The required inputs in the probabilistic energy approach are the energy delivered to the pile head during each hammer blow, the blow count per 0.3 m of pile penetration, the maximum velocity at the pile head, and the pile dimensions and elastic properties. The required instrument for this method is much simpler compared to that required by the Case and CAPWAP methods, leading it to be an attractive and economic method for pile-driving control in the field.