Seismic Vulnerability of the Highway System
Pile Group Effects
Geoffrey R. Martin, University of Southern California
Ignatius Po Lam, Earth Mechanics Inc.
Piled foundations are a common foundation type for long span bridges and typically consist of pile groups containing a large number of piles cast into a substantial pile cap, an example of which is shown in Figure 1. Such large pile groups can pose a significant challenge in terms of characterization for design purposes. This is certainly the case in seismic bridge design where the ensuing soil-pile-structure interaction influences global behavior. A workshop held at the University of Southern California in 1995 brought together design professionals and academia to discuss this issue of soil-pile-structure interaction in the context of long span bridge design.
The 1995 workshop sought discussion and debate on analysis issues involved in the seismic analysis of bridges accounting for the effect of the foundations. Of the various issues discussed and identified as requiring further research in order to be satisfactorily understood, the most important to be identified was the understanding of the importance and the physics of group action under both static and dynamic loads. Lack of adequate test data and poor understanding of effects such as nonlinear soil behavior and interference from seismic induced pile movements (kinematic interaction) were particular aspects identified as in need of research. Uncertainty on how different types of foundation configurations (number and spacing of piles) and bridge characteristics (mass, natural frequency and height of pier) were affected by such issues was also made apparent.
In concluding the workshop a clear need for more guidance on pile group design was identified. Both experimental and analytical work was required to alleviate unknowns in design. Benchmark cases providing a datum for analytical studies were also required with attention to detail an important factor. There was also an urgent need to develop analysis methods to adequately reproduce group effects, and it was recommended that a move be made to initiate research efforts to improve the state of the art in this area.
These findings provided the impetus for the Task C2-2 : Pile Group Effects research program, with the basic aims of the program being: (a) To help clarify issues surrounding large pile group behavior using numerical analysis techniques, and (b) develop practical analysis methodologies for use in design practice with input from design professionals. In the overview that follows the various issues and design considerations involved in the seismic design of large pile group foundations are discussed. This discussion serves to summarize the background to the research at hand and illuminate important aspects involved. An outline of the research strategy that has been developed is then provided, followed by details of progress made in Year 1.
Pile group behavior is fraught with various issues, particularly from a seismic design standpoint. A growing pool of field and centrifuge tests are emerging that have been instructive in this matter, and the more salient issues to emerge in connection with pile group behavior are discussed as follows:
Cyclic Degradation: Multi-directional earthquake shaking causes load reversals on piles within the group leading to loss of stiffness. Stiffness degradation has been attributed to both remolding of the soil as the pile repeatedly pushes against the soil, and gapping where permanent soil deformation results in a gap forming between the pile and soil. Quantification of these effects for pile group behavior is lacking.
Soil Type: Sand and clay pose different problems in terms of soil-pile interaction. Clays usually suffer from strength degradation due to cyclic loading. However, densification of sands due to cyclic vibration is possible, and constant infilling of potential gaps that form around piles is a commonly observed phenomena due to the cohesionless nature of the sand. Hence sands pose a different type of problem where the effects of cyclic loading may in fact increase the interaction amongst piles in the group, rather than diminishing the interaction as is usually the case with clay soils. Quantifying this effect is also an issue not yet resolved.
Wave Propagation: Wave scattering (i.e. radiation damping) effects associated with kinematic interaction are usually neglected due to the dominating effect of inertial response and accompanying hysteretic damping. However, studies have shown that radiation damping is important in modeling soil-pile-structure interaction for single piles, and this issue needs to be clarified with respect to large pile groups.
Loading Rate: The rate of loading can cause an increase in lateral resistance but it is unclear how this phenomenon relates to cyclic degradation and whether both phenomena oppose each other or whether cyclic degradation dominates with increase in the number of load cycles. Pore pressure behavior could also be linked with loading rate effects where dilation effects have been observed to increase the strength of the soil around piles. Such phenomena require clarification in the context of large pile groups.
Pile Cap - Pile Interaction: The investigation work carried out to date has mostly concentrated on pile behavior without serious consideration of the effect of the pile cap. A significant portion of lateral resistance of a pile group can come from rocking behavior of the pile cap, where alternate compression and tension loading in the piles is coupled with lateral movements. In the large pile group case this mode of lateral resistance may feature prominently.
Size Effect: The mere size of a large pile group is also an issue that requires consideration. Field and centrifuge testing has been undertaken on pile groups up to 4 x 4 configuration only, but a large pile group foundation system may involve hundreds of piles with a pile cap dimension greater than the pile length. Hence, different behavioral mechanisms may apply requiring consideration of factors normally ignored. The inertial effect of the soil mass contained within the pile group is a prime example.
Although serving more as a qualitative vehicle to demonstrate the types of phenomena at play, the field and centrifuge testing has helped to quantify some pile group effects. These include the lateral load distribution amongst rows of piles within the pile group, and reduction in lateral resistance of trailing piles due to the 'shadowing' effect. Such group effects are represented by the so called p and y multipliers that adjust p-y curves derived from single pile load tests. The discrete approach to pile design, encompassing p-y curves for lateral behavior and t-z curves for axial behavior, is the most common approach to pile design in practice. It is therefore important to present pile group findings in a form compatible with the discrete approach, if they are to be effective in design practice.
While p-y and t-z curves are an effective rationalization of continuum effects, there still remains a serious lack of test data on which to characterize pile group behavior. A recently completed research program, the National Cooperative Highway Research Program (NCHRP) 24-9, involved field-testing of pile group configurations with up to 12 instrumented piles, under both static and dynamic loading (Statnamic loading device). This will provide much needed data on dynamic pile group behavior but is still restricted to relatively small pile groups. Recourse to a numerical approach is the only practical means of investigating large pile groups, with judicious use of single and small pile group field and centrifuge test data for verification purposes.
Three-dimensional numerical analysis formulated within a finite element or finite difference computational framework, and assigned with analytical models seeking to capture the important, serves to simulate the type of behavior expected in the field. This approach is appropriate for research purposes but becomes prohibitive in design practice. Linearization of pile group behavior is therefore sought to lesson the computational burden. Lam et al. (1998) discuss such an approach where all the actions of the soil-pile system are condensed into a linearized foundation stiffness matrix that represents the behavior of the node located at the interface of the superstructure and foundation. This technique embodies the substructuring approach to analysis and is used in modeling pile group foundations for bridges to overcome complexities in the design process.
The substructuring approach helps to streamline the design process but also invites ignorance between the geotechnical and structural designers. The need for interaction between geotechnical and structural disciplines during the design process is often emphasized. Both parties should be aware of simplifications employed and the inherent limitations associated with them. This highlights the need to qualify pile group effects where simplifying assumptions have been made. This is an important consideration for large pile group behavior where the size of the problem will necessitate such an approach.
The basic research objective is to improve characterization of large pile groups and this will be achieved using numerical techniques in conjunction with input from design practice. In order to establish a baseline for numerical analyses, the establishment of a database on long span bridges is a first consideration. Information will be compiled on large span bridges representative of regions throughout the United States. The information will include the pertinent information required as input to adequately characterize the foundation behavior, and will include both existing and proposed structures.
The analytical portion of the research project requires familiarity with analysis methodologies and command of numerical techniques. A literature review will therefore be carried out to establish appropriate analysis methodologies and assess the various numerical techniques available. Field and centrifuge tests will also be identified for use as benchmark cases against which numerical analyses can be validated. Test data will need to be easily obtainable in order that a common basis of comparison will be provided for future studies.
Numerical assessment of pile group behavior will be carried out in two stages. The first stage will be concerned with static behavior of pile groups using key small pile-group tests (i.e. benchmark cases) identified in the literature review. The effect of soil behavior will be investigated by use of advanced constitutive models and compared against results using more standard models such as Mohr-Coulomb. Assessment of large pile group behavior will be undertaken once model behavior has been sufficiently calibrated with the benchmark cases.
Large pile group analysis will be undertaken using representative problems selected from the long span bridge database. Comparison with other design methodologies will then be made with input from design practice. Formalization of static analysis behavior will follow using linearization techniques to establish equivalent linear soil properties. This will enable comparison of group effects obtained with conventional linear analysis methods, providing an additional check on analysis results. A move to characterization of dynamic pile group behavior will form the second stage of the numerical assessment. This will be undertaken by applying the equivalent linear soil properties in elasto-dynamic analyses to evaluate the importance of dynamic effects such as kinematic interaction. Results will be compared with existing analytical models and behavior formalized.
Design guidelines will be established based on the static and dynamic findings. These will incorporate industry parameters for implementation into design-office analysis tools. Onus on practice-orientated design guidance will be ensured by seeking comments from design professionals throughout the preparation phase. Example analyses will be included in the final document as applied to pile groups representative of long span bridges in both the Western and the Eastern United States.
Literature Review: An extensive literature review of pile behavior was undertaken with over 150 individual papers and various key publications and conference proceedings obtained. Approximately one-third of the papers relate to pile group behavior, and only one-third of these provide design information that can be readily applied in practice. Overall the topic of research is more inclined to analytical and experimental investigation rather than applied research. These findings were expected and just confirm the need for more design guidance.
Survey Questionnaire: A combined questionnaire form was distributed to selected consultants and DOT engineers in April 1999. The questionnaire sought information on long span bridge foundation systems (Task C2-2) and seismic and retrofitting techniques (Task C1-1). Response to Task C2-2 has been poor with only three completed questionnaires received to date. Furthermore, of the three responses received only one applies to a long span bridge, where long span bridges have been classified in this study as bridges of any structural type over water or land, with spans greater than about 150m. The long span bridge is located in Brunswick, Georgia, and comprises a cable-stayed structure under construction, with a main span length of approximately 380m. The foundation system consists of 40, 1.8m diameter by 22m long drilled-shaft pile groups embedded into a 35m by 22m pile cap.
Numerical Analysis: Considering that a typical large pile group foundation consists literally of forests of piles, a first concern is how to model this effectively. An initial approach to this problem, utilizing the three-dimensional nonlinear finite element program DYNAFLOW (Prevost, 1998), invoked the concept of periodic boundary conditions. In this approach the large pile group is considered as infinite rows of piles extending in both directions. The concept is illustrated in Figure 2 where the notion of infinite bounds is seen to enforce periodic displacement conditions between piles, necessary in order to satisfy displacement compatibility between each tributary region. Deformations at adjacent points along the periodic boundaries are therefore identical; for example, deformations at points A and B on Figure 2 are identical, likewise for points C and D. Further simplification arises by making use of symmetric boundaries through the centerline of the piles and through the midpoint between piles, assuming the loading direction as indicated on Figure 2.
Detailed information on various long span bridges in the State of California have been obtained independently and are listed in Table 1. Further efforts will be made to gather information on more long span bridges in Year 2 of the project.
Table 1: Bridge Survey Listings
Structure Name Location Bridge Type Foundation System Vincent Thomas Bridge Long Beach,CA Suspension 0.4m breadth driven steel pile groups New Carquinez Bridge Soleno,CA Suspension 0.8m diam. cast-in-steel-shell pile groups Old Carquinez Bridge Soleno,CA Suspension 0.5m diam. concrete & timber pile groups San Francisco-Oakland Bay Bridge Oakland,CA
Timber pile groups Coronado Bridge San Diego,CA Box Girder 1.35m driven hollow concrete pile groups Richmond San-Rafael Richmond,CA Box Girder 0.4m breadth driven steel pile groups
The resultant finite element mesh model, comprising half a pile and the surrounding soil region, is shown in Figure 3. Adjacent nodes along each boundary were slaved together to provide displacement compatibility. The soil region, representing undrained clay, was modeled using eight-node brick elements utilizing an elastic perfectly plastic constitutive model based on Von Mises failure criterion. Elastic beam elements were used to model the pile. To account for diameter effects, the pile resembled a bicycle wheel in plan. Spokes, represented by rigid beam elements, were connected to a flexible hub (beam element) that was assigned the properties of the pile. The outer ends of each spoke were in turn connected to nodes of radial soil elements that formed an outer rim the size of the pile diameter.
The periodic boundary condition model represents lateral loading of a single row of piles in the plane perpendicular to the row. This is probably a fair representation of the inner rows of piles in a large pile group, but would not apply to the outer rows where the assumption of infinite extent of piles no longer suffices. Nevertheless, an indication of relative behavior can be made by undertaking analyses for different pile spacing, and this is achieved in the model by varying the size of the surrounding soil region. Results in the form of extracted p-y curves corresponding to 3, 6 and 24 pile-diameter spacing are indicated in Figure 4, where both lateral force and moment pile-head conditions were investigated. Also shown are results using the more conventional p-y based beam-column method of analysis, where the p-y curves were based on typical single pile criteria, but then a trial-and-error process used to match the 3-D finite element results as closely as possible.
The trial-and-error process consisted of adjusting p-y curves using both p and y multipliers in order to backfit the finite element results. The results then indicate that the 24 pile-diameter solution is akin to a single pile solution, as in this case no distortion of the original p-y curves was required. In the 3 and 6-pile diameter cases the results indicate comparatively lower lateral resistances at greater deflections, reflecting the type of group behavior that has been observed in field and centrifuge tests. The periodic boundary condition approach therefore fits observed behavior and will serve as an effective modeling tool to help characterize large pile group behavior. However, the analysis undertaken is a specific case and further research using this approach is clearly required in order that more general conclusions can be drawn.
Following the initial studies using DYNAFLOW, an evaluation of the 3-D nonlinear finite difference program FLAC3D (Itasca, 1997) resulted in it being chosen to undertake numerical analyses. In general terms FLAC3D is an explicit finite difference program. This separates it from other competing programs, such as DYNAFLOW, that usually employ finite element techniques to solve the discretized system. Also, FLAC3D differs from most other finite difference schemes in that the dynamic equations of motion are included in the formulation to solve static as well as dynamic problems. In this way the nature of the static formulation of FLAC3D can be considered as a form of dynamic relaxation, using numerical damping of fictitious inertial terms in order that iterations can proceed to converge to the static solution.
Approaching the problem in this way can have an advantage over the finite element approach, as the method is well suited to modeling non-linear systems such as pile group systems. The explicit time marching scheme employed by FLAC3D easily accounts for non-linear constitutive laws, and the solution process progresses without the need of forming 'stiffness' matrices that are typical of finite element schemes. This provides significant savings in terms of memory requirements, and this is an important consideration with 3-D formulations where memory demands are often restrictive. Also, a unique and clearly advantageous aspect of FLAC3D is the ability of users to implement their own constitutive models using a built-in programming language. This will provide a means of investigating the effect of soil type through use of advanced constitutive models.
The difference between sand and clay behavior is often obscured by use of computationally convenient but rather simplistic constitutive models. The greater influence of dilatancy on sand behavior requires more sophisticated constitutive formulations that can address both inelastic shear and volumetric behavior in a more appropriate manner. Both density and confining stress must also be taken into account to properly predict behavior. A promising constitutive model, based on the work of Wang et al. (1990), uses bounding surfaces to dictate inelastic behavior and will be implemented to assess the effect on pile group behavior. Comparison with more conventional soil models, such as Mohr-Coulomb, will also be investigated.
Initial validation studies are being carried out for FLAC3D that include analysis of single pile field tests and checking FLAC3D solutions against DYNAFLOW solutions. Analysis of a single pile lateral load test, reported by Matlock (1970), is presented to provide an example of the capabilities of FLAC3D. Soil at the test site was described as soft, slightly overconsolidated marine clay, and the test setup involved laterally loading a 0.33m diameter, 12.8m long steel pile with free-head conditions. Bending moments were accurately measured along the pile and differentiated to provide p-y curves at various depths.
In FLAC3D a continuum is made up of solid grid regions called "zones", and the zones can be distorted to fit the shape of the structure being analyzed. In the Matlock (1970) analysis the soil zone was assigned with an elasto-plastic Mohr-Coulomb material model, and the pile zone was assigned a linear elastic model. Behavior between the pile and soil was modeled by inserting an interface between the pile and soil zones. An interface possesses pressure dependent frictional-type properties (i.e. cohesion and friction angle) in directions normal and parallel to the pile axis. Integration of shear and normal forces at the interface grid points, and tracking of lateral deformation at the pile center, enabled p-y curves to be extracted for comparison with the field test results.
The results of the analysis are shown in Figure 5 and indicate good agreement. Other modes of loading behavior are being analyzed to check overall behavior of FLAC3D and thus ensure validity.
Calibration: Analysis of key field and centrifuge tests undertaken on relatively small pile groups will serve to further calibrate FLAC3D for the large pile group analyses. Table 2 lists the field and centrifuge tests that are being considered for static calibration purposes.
Table 2 : Calibration Tests for Static Pile Group Behavior
Location Configuration Spacing Soil Type Reference Lewisburg, Pa 3 x 2 3.6B Cohesive Kim et al. (1976) Brittany, France 3 x 2 3B/2B Clay and Silty Sand Meimon et al. (1986) Illinois 2 x 4 2.6D Sand Holloway et al. (1992) Houston, Texas 3 x 3
Stiff Clay Brown et al. (1987) Houston, Texas 3 x 3 3D Medium Dense Sand Brown et al. (1987) Stuart, Florida 4 x 4 3D Medium Dense Sand Ruesta & Townsend (1997) Utah 3 x 3 3D Clays and silts Rollins et al. (1998a, b) Centrifuge 3 x 3 3D/5D Loose and Dense Sand McVay et al. (1995) North Carolina 4 x 3 3D Sandy Silts and Clay NCHRP 24-9 Auburn Univ. 4 x 3 3D To be advised NCHRP 24-9
Year 2 Research Plan
Validation and calibration efforts are being undertaken to provide assurance of numerical results and are helping identify the intricacies and pitfalls that designers can be faced with when modeling pile group foundations. Following this, large pile group analyses utilizing periodic boundary conditions will be investigated and methodologies formulated for use in design practice. Transformation of behavioral trends into 'user-friendly' mechanisms such as p-y curves will be a main goal of this phase of the research. Culmination of this work will be application of the analysis methodology to representative problems as identified from the long span database in progress.
Rationalization of static pile group behavior will provide a suitable framework for future dynamic characterization. During Year 2, evaluation of the linearization approach to dynamic analysis will be undertaken as a precursor to dynamic analyses, with initiation of preliminary studies envisaged.
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