Foundation Design for Liquefaction Induced Lateral Displacements
Geoffrey R. Martin, University of Southern California
The vulnerability of highway bridges to earthquake induced liquefaction related ground failures have been clearly demonstrated by the extensive damage observed in past earthquakes. Bridge damage associated with liquefaction during the 1964 Niigata, 1964 Alaska, 1990 Luzon, 1991 Costa Rica and 1995 Kobe earthquakes, for example, has graphically illustrated the nature of liquefaction related seismic design problems that need to be addressed at sites where potential liquefaction may occur.
Selected references illustrating the types of damage in past earthquakes are tabulated in Table 1. Further summary discussion is given in Section 2 of the report, where liquefaction induced lateral spreads involving both abutments and piers are the primary source of displacements leading to span collapse.
Table 1. Selected References Documenting Liquefaction Induced Damage
to Bridges or Piles in Past Earthquakes\
Tokimatsu and Asaka (1998) Kobe (1995) Hamada, M, (1992) Niigata (1964) Hall, J.F., and Scott, R.F. (1995) Luzon (1990) Iwasaki et. al.(1972) Costa Rica (1991)
Ross, et. al (1973) Alaska (1964) Youd, et. al. (1992) Costa Rica (1991) Youd, et. al (1993) Alaska (1964)
Costa Rica (1991)
Whereas the evaluation of the mode and magnitude of liquefaction induced lateral ground deformations involves considerable uncertainty and is the subject of ongoing research, the current state of the practice utilizes the Newmark sliding block approach on an assumed dominant failure plane within the liquefied zone. Hence free field displacements are defined by an estimated lateral displacement on a failure surface. Research to date to evaluate uncertainties in the Newmark approach is summarized in Section 3 of the report.
Where highway bridge site liquefaction problems are identified which are of concern in relation to the potential earthquake induced bridge damage modes associated with lateral spreads, mitigation methods need to be addressed. Apart from relocating the bridge to another less vulnerable site, two basic options are normally considered.
- Foundation/bridge structural design to accommodate the predicted liquefaction and related ground deformation demands. This requires soil-foundation structure interaction analyses to determine if the deformation and load capacity of the existing foundation/bridge system is adequate to accommodate the ground deformation demands without collapse or can meet prescribed performance criteria. If not, mitigation methods focused on strengthening the structural foundation system can be evaluated, and costs compared to the ground modification mitigation option described below.
- The use of site remediation techniques, where stabilizing measures or ground modification and improvement approaches are undertaken to prevent liquefaction and/or minimize ground displacement demands. Such methods include:
- Insitu ground densification of liquefiable soils in zones surrounding bridge piers, and in zones at or underneath the toe of approach fills, to reduce ground deformations to tolerable levels.
- The use of deep soil mixing using cement, to form stabilizing zones similar to those developed using ground densification techniques
- Other types of ground improvement such as dewatering, installation of gravel drains, or permeation grouting.
Liquefaction mitigation options through the use of soil remediation have been addressed in several tasks previously conducted under the MCEER/FHWA Highway Project DTAH61-92-C-00106, including a comprehensive report on ground remediation measures for liquefaction at existing bridge sites authored by Cooke and Mitchell (1999).
Although ground remediation techniques are often used at bridge sites to mitigate liquefaction induced lateral spreads, further research is needed on mitigation options related to foundation design or retrofit, as methods of soil improvement are often costly and time-consuming to implement. A number of case histories and a limited number of analyses have indicated that, with appropriate design, foundations can accommodate relatively large ground deformation demands from lateral spreads. Analysis approaches are discussed in Section 4 of the report. Three dimensional numerical analyses of pile soil interaction during lateral spreads, are described in Section 5 of the report.
The results of research conducted in this study are intended to establish: (1) practical analysis approaches to evaluate the ability of foundation systems normally associated with short to medium span bridges (pile footings and drilled shafts) to accommodate displacement demands arising from lateral spreads; (2) a case study data base (including verification studies using the above analysis approach) which will document field observations in past earthquakes and results of centrifuge modeling simulations; and (3) general guidelines on conditions suitable for structural retrofit or a structural mitigation option, together with design approaches.
The research summary provided below, documents progress to date on the project.
Observations on Lateral Spread Damage
With reference to the idealized bridge on a liquefiable site shown in Figure 1, based on observations in past earthquakes, damage modes associated with lateral ground deformation demands on the bridge leading to potential structural damage or bridge collapse include:
- Lateral deformation of abutments and piers arising from liquefaction induced flow failures or lateral spreads, leading to substructure pile damage and potential span collapse
- Liquefaction induced differential ground lurch at adjacent pier supports causing potential span collapse
Liquefaction induced bearing capacity failure of piled pier supports may also cause span collapse, but is not addressed in this study. Two representative examples of damage modes are given below.
The first example is the Magsayay Bridge damaged in the 1990 Luzon earthquake, and documented by Hall and Scott (1995). Figure 2 shows the collapse mode involving the collapse of four simple supported spans induced by about 2 meters of lateral spread at the west abutment. As the east abutment did not move, it could be argued that a continuous deck may have prevented collapse due to strut action.
The second example is that of the performance of the Landing Road Bridge in the 1987 Edgecumbe earthquake (New Zealand), documented by Berrill et. al. (1997). In this example, bridge approach spans to a riverbank were supported by concrete slab piers founded on battered prestressed concrete piles, as shown in Figure 3. Liquefaction induced lateral spreads in the liquefiable sand layer of the order of 2 meters were estimated. Observations from back analyses and excavations, indicated that the piles successfully resisted the passive pressures mobilized against the piers, albeit cracks in the piles suggested plastic hinges in the piles were on the verge of forming as shown schematically in Figure 3.
In the Kobe earthquake, field investigations using borehole cameras and slope indicators, showed that failures of piles in lateral spread zones concentrated at the interfaces between liquefied and non-liquefied layers, as well as near pile heads. Also lateral pile analyses using p-y methods together with estimated ground displacement profiles, were consistent with observed pile performance, (Tokimatsu and Asaka, 1998), as shown for example in Figure 4.
Figure 4. Site and Damage Characteristics for a Precast Concrete Pile Subjected to
a Lateral Spread in the Kobe Earthquake (After Tokimatsu and Asaka, 1998)
The most widely used analytical approach to determine lateral spread displacements, is that of the so called Newmark sliding block analysis method, where deformation is assumed to occur on a well defined failure plane and the sliding mass is assumed to be a rigid block. The approach requires initial pseudo-static stability analyses (to determine the critical failure surface and associated yield acceleration coefficient ky corresponding to a factor of safety of 1.0 - see Figure 5) and a design earthquake time history representative of ground motions at the base of the sliding mass usually assumed at the base of the liquefied layers. Cumulative displacements of the sliding mass generated when accelerations exceed the yield acceleration can then be computed using computer programs such as described by Houston et al. (1987).
Figure 5. Pseudo-Static Stability Analysis
The Newmark method has been used to study earthquake induced slope displacements in dams and natural slopes. However, a number of uncertainties are inherent in the approach due to the assumptions involved. In particular, for liquefaction induced lateral spreads, uncertainties include:
1. The point in time history when cyclic strength degradation or liquefaction is triggered.
2. The magnitude of the apparent post liquefaction residual resistance as discussed above.
3. The influence of the thickness of liquefied soil on displacement.
4. The influence of a non-rigid zone of deformation (the liquefied zone)
To evaluate assumptions 3 and 4, the one dimensional site response program DESRA-MUSC (Qiu, 1998) was modified (SDESRA-MUSC) to include a small slope angle to allow accumulation of downslope displacement during earthquake ground shaking, due to a constant imposed static shear stress in a yielding soil layer. The 100 foot soil column shown in Figure 6 on a slope of 2° was subjected to the 1940 El Centro earthquake, and progressive downslope displacements of the 10 ft soil crust deforming as a result of yield on the underlying 10 foot thick soft clay layer (simulating liquefied soil), computed. Shear stress - shear strain behavior of the soft layer is shown in Figure 7, and displacements shown on Figure 8. Displacements calculated using the Newmark method (using input accelerations at a depth of 20 ft) are also shown on Figure 8. Although displacements are somewhat larger, they show similar time dependent trends.
Figure 6. Soil profile used for analysis
Figure 7. Stress-Strain relationships for layer 2 (inclined site 1)
Figure 8. Displacement time histories
Structural Analysis of Pile Foundations
Given analysis results defining the magnitude of liquefaction induced lateraldeformations and the geometry of the most likely failure surfaces based on Newmark analyses, an assessment should be made to see if the shear and moment capacity of pile foundations is sufficient to prevent collapse of the bridge structure under the imposed displacement demands on the foundation system, prior to considering a ground remediation option. It is assumed in these analyses, that the effects of ground displacement can be decoupled from the effects of structural inertial loading.
The magnitude of moments and shear induced in pile foundations by ground displacements, may be computed using soil-pile interaction programs such as LPILE (Wang and Reese, 1998), where the assumed displacement field is applied to interface springs or p-y curves. Example of such analysis approaches are given by Jakura and Abghari (1994) O'Rourke et. al. (1994), Ishihara and Cubrinovski (1998) and Hamada (2000). In the liquefied zone, the soil is normally treated as a soft cohesive soil when calculating lateral spring characteristics (or p-y curves) where the maximum soil cohesion is assumed equal to the residual strength of liquefied soil. In some cases, large ground deformations may slide past the foundation system exerting full passive pressures in the process. However, foundations may remain intact without failure, as in the case history reported by Berrill et. al. (1997).
A refinement of the above approach, is to consider the reinforcing or pinning effects the piles or pile group have on the lateral stability, by representing the pile shear forces at the location of the failure plane as an equivalent shear strength in the calculation of yield accelerations used in the Newmark analyses. This becomes an iterative approach as shear forces are a function of displacements which in turn are reduced as shear forces increase.
The framework of a simplified design approach to be studied in the research project, is that developed and recommended for new AASHTO LRFD provisions, (NCHRP 12-49, 2000) and involves four basic elements, as described below:
1. Pseudo-static stability analysis to establish yield seismic coefficients;
2. Newmark sliding block analysis;
3. Assessments of the forces that can ultimately develop on a pile foundation system as soil movement occurs in the liquefied zone
4. Assessment of the likely plastic mechanisms that may develop in the foundations or substructure.
The rationale behind this approach is to determine the likely magnitude of lateral soil movement and assess the pile foundation and structure's ability to both accommodate this movement and/or potentially limit the movement.
The concept of considering a plastic mechanism in the foundation under the action of spreading forces and is tantamount to accepting substantial damage in the foundation. This is a departure from the normal seismic design philosophy for vibration induced structural inertial loading alone. The departure is felt reasonable because it is unlikely that the formation of a mechanism in the foundation will lead to structure collapse. The reasoning behind this is that spreading is essentially a displacement-controlled process. Thus the estimated soil displacements represent a limit on the structure displacement, excluding the phenomena of buckling of the piles or shafts below grade and the continued displacement that could be produced by large P-? effects. Buckling should be checked, and methods that include the soil residual resistance should be used. O'Rourke, et. al. (1994) provides a method for checking buckling.
The flow chart of the methodology for consideration of spreading is given in Figure 9. The primary feature of the proposed methodology is to evaluate the potential use of passive piles or pin piles to restrict the movement of soil and foundations to levels that are tolerable by the structure. The steps involved are described below:
Figure 9. Design flow chart
Step 1. The soil layers that are likely to liquefy are identified.
Step 2. A stability analysis is executed to determine the likelihood of soil movements, and to determine the extent of such movements. This would include the depths of soil likely to move and the extent of the likely soil failure block. Assessment of the impacts to a bridge structure can then be made by considering the proximity of failure block to the foundation system.
Step 3. The maximum lateral spread displacement of the soil is estimated. This may be accomplished using Newmark displacement charts or by a site-specific Newmark time history analysis.
Step 4. An assessment is made whether soil will continue to displace or flow around a stable foundation or whether movement of the foundation will occur in concert with the soil . The assessment requires a comparison between the estimated passive soil forces that can be exerted on the foundation and the ultimate structural resistances that can be developed by the structure. In cases where a crust of non-liquefied material may exist at the ground surface, the full structural resistance may be less than the displacement-induced passive forces, and in such cases the foundation is likely to continue to move with the soil. In many cases, it may be immediately obvious which condition is more likely.
Step 5. If the soil continues to displace around a stable foundation, then the foundation is designed to withstand the passive pressures created by the soil flowing around the structure. The induced forces are effectively the largest forces that the structure will experience, and for this reason it is conservative to design a structure for such forces.
Step 6. If on the other hand, the assessment indicates that movement of the foundation is likely in concert with the soil, then the structure must be evaluated for adequacy at the maximum expected displacement. The implication of this assessment is that for relatively large ground movements, soil displacements are likely to induce similar magnitude movements of the foundation. In this context, "large" is taken relative to the structural yield resistance. The resulting induced movements of the foundations may produce substantial plasticity or hinge zones in the foundations, and may induce relatively large reactions in the superstructure.
Step 7. If such deformations are not acceptable, two ways to restrict the foundation and substructure forces to values less than yield could be considered. The first method is to design the foundations to resist the forces that would accompany passive flow of the soil around the foundations. The other method would be to limit the ground movement by providing either ground and/or structural remediation. It is the structural option that provides a potential first path, and this makes use of the "pinning" or dowel action that pile or shaft foundations contribute as they cross the potential failure plane of the moving soil mass, to potentially reduce the magnitude of lateral displacement.
Step 8. The determination of the plastic mechanism that is likely to occur in the presence of spreading should be done in a reasonable manner. Due to the range of inherent uncertainties, great precision in the determination may not produce more accuracy. Simple estimates of the mechanism and its corresponding lateral resistance capability may be adequate.
Such estimates could be based on hinge development in stable or firm soil zones above and below (by say 2 pile diameters) the liquefiable layer. Maximum "pinning" shear could then be assumed equal to 2Mp/L where Mp is the plastic moment and L the distance between hinges. The lateral shear that produces the plastic mechanism can be adjusted downward to account for the driving effect of the P-Delta effect. Figure 10 illustrate first-order corrections for P-Delta effects.
Figure 10. Influence of P-Δ effects on pinning shear (after NCHRP, 2000)
A more precise method of determining the plastic mechanism would be to use an approach that ensures compatibility of deformations between the soil and piles (e.g., similar to LPILE) and which accounts for plastic deformations in the piles themselves (e.g., the program BSTRUCT, O'Rourke et. al., 1994).
Step 9. The system then must be assessed for a prescribed displacement field to represent the likely soil spreading deformation. From this analysis, an estimate of the likely shear resistance the foundation will provide is estimated and this shear can then be incorporated back into the stability analysis.
Step 10. If substantial resistance is provided, then its effect on limiting the instability driven movement of the soil block should be accounted for. This step is typically not included in current assessments of potential foundation movements, although inclusion of such resistance may often improve the structure's expected performance.
Steps 11 and 12. The overall displacement is re-calculated with the revised resistance levels considered. Once a realistic displacement is calculated, then the foundation and structural system can be assessed for this movement. It is at this point that more permissive displacements than for substructure design can be relied upon. This implies that plastic rotations, and potentially large ones, may be allowed to occur in the foundation under such conditions.
Step 13. If the structure's behavior is acceptable, then the design is complete; if not, then the engineer must assess whether to try to produce adequacy either through additional piles or shafts, and these may not need to connect to the foundation (passive piles) or the cap. Alternately, ground improvement approaches may be considered, such as, stone columns. The selection of structural or geotechnical remediation methods is based on the relative economy of the system being used.
The process is repeated by returning to Step 8 and modifying the available resistance until the slope is stabilized.
Modeling Soil-Pile Interaction Using FLAC
To validate simplified procedures for analyzing the effectiveness of pile pinning effects in reducing lateral spreads and at the same time ensuring pile survivability, the three dimensional computer program FLAC 3D is being utilized. The explicit finite difference formulation of the code which includes large strain simulation of continua, interface models, structural elements and a library of soil constitutive models, makes it ideal for modeling lateral spread problems and soil-pile interaction.
To date the program has been validated against limiting equilibrium stability methods for lateral spreads (Figure 11) and against the results of lateral load pile tests such as the Mustang Island lateral lead test (Figure 12 and 13). The program has also been used to evaluate the effects of fill slopes on p-y curves such as for the case of abutment pile loading (Figure 14).
Figure 11. FLAC lateral spread simulations
Figure 12. Soil failure mode in Mustang Island Test using FLAC 3D (x 10 magnification)
Figure 13. Comparison of p-y curve @ 1.83 m in Mustang Island Test
Figure 14. Effect of inclined slope angle on p-y curves using FLAC 3D
Future research will focus on studying lateral spread deformation and the interaction with bridge piles (abutment piles and toe pier pile groups). These studies will include pile moment capacity (elastic-plastic pile moment behavior) and provide the means to calibrate the simplified procedures discussed in the previous section.
The author acknowledges the contribution to the research program by Lee Marsh of Berger/ABAM Engineers Inc, a member of the NCHRP 12-49 Project Team, Section 4.1 of the report on a design approach was formulated by Lee Marsh during discussions held as part of the liquefaction study for the NCHRP 12-49 Project.
- Berrill, J. B., Christensen, S A., Keenan, R. J., Okada, W. and Pettinga, J R. (1997).
- "Lateral-spreading Loads on a Piled Bridge Foundation," Seismic Behavior of Ground and Geotechnical Structures, Proc., Special Technical Session on Earthquake Geotechnical Engineering, 14th ICSMFE, A. A. Balkema, Rotterdam, 173-183.
- Cooke,, H. G. and Mitchell, J. K. (1999).
- "Guide to Remedial Measures for Liquefaction Mitigation at Existing Highway Bridge Sites," Technical Report MCEER-99-015, Multidisciplinary Center for Earthquake Engineering Research, Buffalo, NY, 176 pp.
- Hall, J.R., and Scott, R.F. (1995).
- "Evaluation of Bridge Damage in the 1990 Luzon and 1991 Costa Rica Earthquakes", Southern California Earthquake Center, Task H-6 Report to Caltrans and the City and County of Los Angeles, on the Characteristics of Earthquake Ground Motion for Seismic Design.
- Ishihara, K. and Cubrinovski, M. (1998).
- "Problem Associated with Liquefaction and Lateral Spreading During Earthquake," Geotechnical Earthquake Engineering and Soil Dynamics III, ASCE, Geotechnical Special Publication, No. 75, Vol. 1, pp. 301-312.
- Jackura, K. A. and Abghari, A. (1994).
- "Mitigation of Liquefaction Hazards at Three California Bridge Sites," Proc., 5th U.S.-Japan Workshop on Earthquake Resistant Design of Lifeline Facilities and Countermeasures Against Soil Liquefaction, Technical Report NCEER-94-0026, NCEER, Buffalo, NY, 495-513.
- NCHRP 12-49 (2000), National Cooperative Highway Research Project 12-49,
- Comprehensive Specifications for the Seismic Design of Bridges - Liquefaction Study Report, October, 2000.
- O'Rourke, T. D., Meyersohn, W. D., Shiba, Y. and Chaudhuri, D. (1994).
- "Evaluation of Pile Response to Liquefaction-Induced Lateral Spread," Proc., 5th U.S.-Japan Workshop on Earthquake Resistant Design of Lifeline Facilities and Countermeasures Against Soil Liquefaction, Technical Report NCEER-94-0026, NCEER, Buffalo, NY, 457-478.
- Qiu, Ping (1998).
- "Earthquake Induced Nonlinear Ground Deformation analyses," Ph.D. Dissertation, University of Southern California
- Ross, G.A., Seed, H.B. and Migliaccio, R. R. (1969). "Bridge Foundation Behavior in Alaska Earthquake," J. Soil Mech. And Found. Div., ASCE, 95(SM4), 1001-1036.
- Tokimatsu, K. and Asaka, Y. (1998).
- "Effects of Liquefaction-Induced Ground Displacements on Pile Performance in the 1995 Hayogoken-Nambu Earthquake", Special Issue of Soils and Foundation, pp. 163-177.
- Wang, S.T. and Reese, L.C. (1998).
- "Designed Foundations in Liquefied Soils," Geotechnical Earthquake Engineering and Soil Dynamics III, ASCE Geotechnical Special Publication, No. 75, Vol. 2, pp. 1331-1343.
- Youd, T. L. (1992).
- "Liquefaction, Ground Failure and Consequent Damage During the April 22, 1991, Costa Rica Earthquake," Proc., NSF/UCR, U.S.-Costa Rica Workshop on the Costa Rica Earthquakes of 1990-1991, Effects on Soil and Structures, EERI Pub. No. 93-A, EERI, Oakland, CA, 73-95.
- Youd, T.L. (1993).
- "Liquefaction-Induced Damage to Bridges," Transportation Research Record No. 14311, National Research Council, National Academy Press, Washington, D.C., 35-41.