By the 1920’s dynamic formulae were well established in the driven pile industry. Without really consistent methods of static capacity estimation, and given the conservative nature of most foundation design, their weaknesses were not fully appreciated.
The event that brought their weakness to the forefront was the development of precast concrete piles. Dynamic formulae assume that the pile is a rigid mass, or at best a simple spring. In the process of driving these relatively new concrete piles, tension cracking was noted in the mid-section of the pile, something the dynamic formulae didn’t take into consideration.
It was left to the Australian civil engineer David Victor Isaacs in 1931 to propose that piles, like other bars, were subject to wave propagation, and that the tension cracking was due to reflected tension waves from the pile toe. It was a long process to sell the basic concept of wave propagation in piles, and then making their modelling a practical tool for estimating hammer-pile-soil performance during driving.
It’s interesting to note that the individual who made the wave equation for piles a practical reality–E.A.L. Smith–was Raymond Concrete Pile’s chief mechanical engineer and an equipment designer. Wave propagation in piles is a dynamic phenomenon, and until recently dynamic phenomena were not an important aspect of geotechnical engineering design.
Today both GRLWEAP and TNOWAVE–the most popular wave equation programs–have Vulcan hammer data included in their hammer database. On this site we feature a number of aids to estimating drivability of Vulcan and many other types of hammers using the wave equation, along with some of the history behind them:
- Isaacs and Glanville: The Beginnings of the Wave Equation for Piles
- Smith’s Wave Equation Program–the first numerical method
- Wave equation programs for free download or use (along with in-depth background information on the program being downloaded):
- Information on wave equation programs and routines developed by Vulcan or its personnel
- ZWAVE, Vulcan’s own wave equation program in the 1980’s
- Closed form solution of the wave equation for piles, the definitive work on the subject, from the 1990’s. Includes some of the background documents and derivative works.
- Improved Methods for Forward and Inverse Solution of the Wave Equation for Piles, a 3D FEA solution of the wave equation, with many referenced documents
- Differential Equations and Laplace Transforms in Soil Dynamics
- Other Monographs on the Wave Equation
3 thoughts on “Wave Equation Analysis”