Seismic Vulnerability of the Highway System

Task C2-3: Effect of Pile Spacing on the Lateral Stiffness of Pile Groups - Dynamic Analysis Studies

Subject Area: Special Bridges - Ground Motion & Geotechnical Studies
 Research Year 3

Principal Investigator and Institution

I. Po Lam, Earth Mechanics, Inc.


Task C2-2 is completing the development of numerical approaches to investigate soil-pile interaction effects of large closely spaced pile groups subjected to lateral pseudo-static loading, expressed in terms of p-y multipliers. Based on the results of parametric studies conducted under the task, linearization then allows a determination of a static stiffness matrix as a function of pile configuration and soil type for use in structural analysis.

Under Task C2-3, an analytical framework for dynamic loading will be advanced to model and evaluate wave propagation and wave scattering effects for both large pile groups and large caissons, including quantifying the effects of modifying the input motions due to wave scattering and its influence on system damping from radiation of reflected waves. In addition to developing design guidelines, this task will provide an evaluation of the appropriate platform for implementation of soil-structure interaction principles for bridge design and analysis.


At the onset of the pile group research being conducted under MCEER Project 094, two fundamental objectives were identified to advance the state-of-practice regarding analysis of the type of foundation systems encountered for long span bridges, including large pile groups and caissons. These were:

  1. Improved accounting of the interaction of the stress and strain field in the soil due to superposition of loading from many adjacent piles in close spacing, commonly referred as pile group effects. Research under Task C2-2 has been focused on addressing pile group effects for static loading conditions. Results from Task C2-2 will directly apply to static pushover capacity analysis of large pile groups, as well as the characterization of foundation stiffness and material damping issues in a global model demand analysis. Results of these studies can be assessed against data from available on-going pile group experiments for typical 3x3 or 4x4 pile groups.
  2. Extending this effort to address pile group foundations under dynamic loading conditions, particularly in relation to how earthquake wave scattering of the foundation system will alter the near-field ground motion transmitted to the superstructure. In addition to pile groups, the wave scattering issue needs to be addressed for large diameter drilled shafts and sunken caisson foundations (typical foundations for long-span bridges) where the wave scattering effect becomes increasingly important.

Item (2) above has traditionally been treated by frequency domain solution computer codes such as SASSI or CLASSI. However, the overall global bridge model analyses for major long-span bridges are commonly analyzed by computer codes such as ADINA or ABAQUS using time history analyses. Because of a lack of a common platform for analyses, substructuring techniques are needed to implement results of wave scattering and foundation impedances from frequency domain solutions into the subsequent time domain global bridge analyses models. This two-step approach, typically done by separate groups of engineers (i.e., structural versus geotechnical analysts), conducted using different numerical platforms, often leads to confusion and delays in projects, and is generally not favored by practitioners.

There is a great interest in advancing the state-of-practice so that the wave propagation and scattering analyses can both be conducted in time domain, or in a numerical platform that is familiar to structural engineers. Then, both groups (geotechnical professionals who is familiar with wave propagation analyses, and structural engineers performing the global structural model) can work simultaneously on the same computer platform to contribute expertise to the total problem.

It is considered feasible to address many of the wave scattering or soil-structure interaction issues using time domain general utility computer programs that are commonly used by bridge designers working on long-span bridge projects. The approach of using a common platform by both structural engineers in structural response studies and by geotechnical engineers in soil-structure interaction analyses is considered to be more practical than the traditional substructuring method, and is likely to help avoid mistakes when transferring large volumes of ground motion and foundation submodel data to the subsequent structural model.

During Research Years 3 and Year 4, the knowledge obtained from Task C2-2 for pile groups will be advanced to address dynamic loading issues, particularly for wave scattering effects during the analysis of long-span bridges. In Research Year 3, the work will require calibration solutions for typical caissons and pile group configurations to ensure that the wave scattering treatment in time domain can be compatible to proven approaches (e.g., SASSI type analyses) within the context of linear elastic half-space assumptions. After confirmation of the basic time domain framework, an examination of the degree of change in the ground motion input affected by the scattering issue will be examined. Results from the Research Year 3 sensitivity studies will then be used to develop guidelines to account for wave scattering and radiation damping issues.

Work during Research Year 3 will consist of the following:

  1. Select typical pile groups, large diameter drilled shafts, and large caisson systems for soil-structure interaction analyses to be conducted in both the frequency domain (using programs such as SASSI) and in the time domain (using an analytical platform such as ADINA.
  2. Compare the results of these analyses to demonstrate that the time domain computer codes can yield similar wave propagation and wave scattering solutions as frequency domain solutions.
  3. Based on the results of sensitivity studies, develop guidelines for modifying the free-field site response ground motion criteria to account for wave scattering and radiation damping issues.


  • Assessment of whether frequency domain and time domain analysis approaches provide similarly accurate results for long-span bridge foundation systems.
  • Guidelines for modifying the free-field site response ground motion criteria to account for wave scattering and radiation damping.

Technical Challenges

Although the PI and agency staff are experienced in the use of the computer program ADINA, they have no experience in using the SASSI program. This will require careful modeling and results review considerations to ensure that the analyses are conducted correctly.

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