Improved Methods for Forward and Inverse Solution of the Wave Equation for Piles

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This doctoral research project at the University of Tennessee at Chattanooga is now complete, and we are pleased to present the following:


This dissertation discusses the development of an improved method for the static and dynamic analysis of driven piles for both forward and inverse solutions. Wave propagation in piles, which is the result of pile head (or toe) impact and the distributed mass and elasticity of the pile, was analysed in two ways: forward (the hammer is modelled and the pile response and capacity for a certain blow count is estimated) or inverse (the force-time and velocity-or displacement-time history from driving data is used to estimate the pile capacity.) The finite element routine developed was a three dimensional model of the hammer, pile and soil system using the Mohr-Coulomb failure criterion, Newmark’s method for the dynamic solution and a modified Newton method for the static solution. Soil properties were aggregated to simplify data entry and analysis. The three-dimensional model allowed for more accurate modelling of the various parts of the system and phenomena that are not well addressed with current one-dimensional methods, including bending effects in the cap and shaft response of tapered piles. Soil layering was flexible and could either follow the grid generation or be manually input. The forward method could either model the hammer explicitly or use a given force-time history, analysing the pile response. The inverse method used an optimization technique to determine the aggregated soil properties of a given layering scheme. In both cases the static axial capacity of the pile was estimated using the same finite element model as the dynamic method and incrementally loaded. The results were then analysed using accepted load test interpretation criteria. The model was run in test cases against current methods to verify its features, one of which was based on actual field data using current techniques for both data acquisition and analysis, with reasonable correlation of the results. The routine was standalone and did not require additional code to use.

Dynamic Pile Testing Results
Crescent Foundation Demonstration Test Pile – Vulcan SC9 Hammer
Kenner, Louisiana

Brian Mondello and Sean Killingsworth
May 2014

This report presents the results from dynamic pile testing, and related data analysis, performed during the initial drive testing of the subject Test Pile on April 30, 2014, at the above referenced jobsite location in Kenner, Louisiana. The primary test objective was the monitoring of the hammer/driving system performance. Additionally, the testing objectives included the monitoring of dynamic pile driving stresses, pile structural integrity, and pile static bearing capacity. These objectives were met by means of a Pile Driving Analyzer® (PDA), Model PAX, which uses the Case Method for numerical computations. An additional analysis was performed on a selected test record using the CAPWAP® computer program. Discussions on the testing equipment, analytical procedures, theory, application, and limitations are presented in Appendix A. Testing and analysis results are presented in Appendix B.

A video of the SC-9 hammer featured in Mondello and Killingsworth:

Dynamic Response of Footings and Piles

Wing Tai Peter To
PhD Dissertation
University of Manchester
February 1985

Dynamic response analyses can be regarded as stress wave propagation problems. The solution of such by the finite element method entails more consideration than static problems, since sources of inaccuracies such as dispersion, spurious oscillations due to mesh gradation, wave reflection at transmitting boundaries, as well as instability or inaccuracy due to temporal operators and discretisation can arise. The criteria for formulating a finite element model for dynamic response analysis have been investigated. Using the relatively simple von Mises soil model (satisfactory for undrained saturated clay) three categories of problems have been investigated:

  1. The dynamic response analyses of surface footings subjected to periodic and impact loading have been performed in order to evaluate the finite element model design criteria. An approximate analysis is also performed in reducing a three-dimensional indirect impact problem to a two-dimensional analysis.
  2. Vibratory pile driving is a relatively new but somewhat unreliable technique of pile installation. Penetration is instantaneous if conditions are right, but with the high hire charges and uncertainty in success the technique is unpopular, especially in clays. In the work presented it is shown that vibratory installation is possible in cohesive soils at the fundamental frequency for vertical pile translation, if a high enough dynamic oscillatory force is provided. Penetration mechanisms have also been exploited.
  3. On the other hand, impact pile driving is reliable and widely adopted in terrestrial as well as offshore construction. Experience in one dimensional wave equation analysis is discussed, and further numerical evaluation of the parameters involved has been carried out by a more elaborate axisymmetric finite element model. In cohesive soils a closed-ended pile may be driven more easily than an equivalent open ended pile, depending on the level of the internal soil column and the soil properties. In the light of the growing popularity of nondestructive determination of the axial load-carrying capacity of piles by dynamic methods, the possibility of correlating the soil resistance mobilised in dynamic conditions to the ultimate static capacity is queried. The semi-empirical Case method has been assessed in detail.

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