Seismic Vulnerability of the Highway System

Task C2-2: Effect of Pile Spacing on the Lateral Stiffness of Pile Groups - Static Analysis Studies

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

Principal Investigator and Institution

Geoffrey R. Martin, University of Southern California


The primary objective of Task C2-2 is to determine an appropriate, yet practical, method for establishing the lateral load-deformation behavior of large pile groups in soft clays and sands. The focus of the task is on the use of conventional nonlinear "p-y" curves, coupled with multipliers appropriate for a given pile spacing. Such characterization is needed for static pushover analyses. In addition, a secondary objective is to establish an approach to determine an equivalent linear stiffness matrix for dynamic response analysis.


During Research Years 1 and 2, this task served to identify, formulate, and implement an appropriate numerical analysis methodology necessary to achieve the primary objective. This required investigation on several fronts. An extensive literature review provided information on practice and state-of-the-art approaches used for lateral load design. Suitable field test data on single piles and small pile groups were also obtained for calibration purposes. Given the absence of information on large pile groups, a survey questionnaire form was distributed to selected consultants and transportation agencies in various States, with a focus on collecting information on long span bridges and large pile group foundations typically used for such structures.

The influence of soil type on pile behavior required consideration of constitutive formulations for sand and clay. The observed influence of dilatency effects on sand behavior may require a more sophisticated constitutive formulation compared with the commonly adopted Mohr-Coulomb constitutive model. A constitutive model based on bounding surface concepts was therefore identified for implementation.

Numerical modeling of the pile group problem required assessment of various strategies. An initial investigation used a line element to model the pile and rigid spokes to account for pile diameter effects, and invoked symmetry simplifications to reduce the problem to manageable proportions. This approach provided promising results but, in order to capture diameter effects in a more rigorous fashion, a move to a continuum pile model was considered more appropriate. Such a modeling approach was available in the 3-D nonlinear finite difference program FLAC3D, and this program was adopted to achieve the primary objective of the research.

The focus of Research Year 3 will be to complete the numerical work and rationalize the results in the form of p-y curves and multipliers for given spacing, fixity, and soil conditions; and completely document all work in the form of a final report with appropriate design guidelines. The scope of work includes the following three subtasks:

Subtask 1 - The following analyses will be conducted:

Phase Item


Calibration  Pile Group Emulation of field test behavior using small pile group load tests.
Research Analyses  Internal Pile Simulate behavior of internal pile in large pile group using periodic boundary simplification.
External Pile Simulate side-by-side behavior using two-pile group with fixed boundaries.
Simulate leading row-trailing row behavior using two-pile group with fixed boundaries.

Subtask 2 - Development of appropriate recommendations for designing large pile groups using p-y curves and multipliers, including use of the program GROUP for pushover analyses, and development of recommendations for determination of equivalent linear stiffness matrices.

Subtask 3 - Completion of final report documenting all work on the task from Research Years 1 through 3, including worked examples on representative large pile groups.


  • Recommendations for designing large pile groups using p-y curves and multipliers.
  • Worked examples on representative large pile groups.
  • Final technical report document all aspects of this 3-year task.

Technical Challenges

Most of the technical challenges associated with this task have already been resolved in connection with the numerical difficulties encountered in Research Year 2. A remaining challenge is the satisfactory simulation of the large pile group behavior.

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