Pile foundations are the primary means of supporting offshore structures. In many instances the maximum stresses occurring during the life of a pile result from pile driving during installation. The Eleventh Edition of the "API Recommended Practice for Planning, Designing and Constructing Fixed Offshore Platforms"1 provides guidance for selecting minimum pile cross-sectional areas for various pile hammer sizes. Analysis indicates that for some cases the values indicated by the API criterion may not be sufficiently conservative to prevent pile failure during driving, and in others it may be overly conservative. This study provides information on the significance of some of the important variables involved hopefully leading to the development of an improved API criterion. The scope of this paper is limited to the calculation of the maximum dynamic stresses imparted to a pile upon impact. A large hammer system for large piles is used for the comparison. Stress profiles are obtained for six cases having increasing degrees of complexity to provide some indication of the influence of the various parameters. The results are presented starting with a simple impact system and progressing to more complicated models incorporating features commonly found in actual pile driving systems. Two approaches are investigated for modeling the system. They are the continuous and discrete mass approaches. Results for the distributed mass system are obtained using the finite difference time integration procedure developed by E.A.L. Smith.2 Transient modal analysis is used for further verification.
This paper addresses problems associated with modeling the systems and in interpreting the solution results. Specific problems addressed are the modeling of the pile hammer ram, anvil and cushion together with the pile itself. The mathematical overshoot that often occurs when using discrete systems to predict the pile stresses is discussed.
In addition to the more complex analytical procedures discussed, approximate simplified formulas are presented which may be easily used as an aid for estimating the maximum dynamic stresses. These should prove useful in design and serve as a guide in making field decisions.
The two approaches .used for modeling the systems are the continuous and discrete mass approaches. Results for the discrete mass systems are investigated using the finite difference time integration procedure developed by E.A.L. Smith2 and transient modal analysis. The finite difference and modal analysis procedures operate on the governing partial differential equation to form either a set of algebraic equations or ordinary differential equations. For the linear one dimensional wave equation considered here, both procedures yield virtually the same results and differ only in methodology.
The propagation of stress waves in elastic media has been extensively analyzed. Timoshenko and Goodier3 for instance provide a modern treatment. For simple one dimensional impact, it can be shown that a compressive stress wave travels down the pile having a magnitude of
(Mathematical equation) (Available in full paper)
This is the basic traveling wave equation.
The wave action at the boundaries between different media is treated by equating the forces and material particle velocities at the discontinuities between media.
