Challenges in Computational Modeling of Liquefaction-Induced Ground Deformations
Zhaohui Yang and Ahmed Elgamal
University of California, San Diego
1. Introduction
In recent years, observations from physical model experiments (centrifuge, 1g shake-table, and
field testing) have significantly advanced our knowledge of many soil response mechanisms
associated with liquefaction (O'Rourke et al. 1999). Results from these experiments have
generated a large database for calibration/verification of computational models.
Computationally, significant advances have also taken place. For instance, the introduction of
state-dependent dilatancy into sand constitutive modeling (Manzari and Dafalias 1997, Li and
Dafalias, 2000) allows for a unified treatment of sand behavior at different relative densities with
a single set of model constants.
Despite the great progress in both physical and numerical modeling of liquefaction, a number of
challenges still remain. In this paper, our discussion is focused on three major issues that
potentially have a significant impact on the reliability of computational results: 1) fluid migration
patterns during liquefaction, 2) strain localization and its impact on residual strength evaluation,
and 3) estimates of in-situ soil states, including degree of saturation, stress-induced anisotropy
( k 0 value), and material anisotropy (particle orientation).
2. Fluid migration during liquefaction
Vertically non-uniform fluid migration
The issue of possible evolution of weak shear interfaces due to non-uniform fluid flow has been
under investigation by many researchers (Scott and Zuckerman 1972, Liu and Qiao 1984,
Arulanandan et al. 1988, Elgamal et al. 1989, Kutter and Fiegel 1991, Kokusho 1999, Kokusho
et al. 1999, Kulasingam et al. 2001, Malvick et al. 2002). Many natural and man-made
liquefiable sand deposits contain finer, more impervious silty or clayey layers (a typical example
is soil strata generated by the hydraulic fill process, Seed 1987). During the liquefaction-induced
fluid migration process, entrapment underneath a stratum of relatively lower permeability may
occur, forming a water-rich seam thereby. The shear strength along this seam may approach
zero. In the case of a sloping liquefiable soil profile, such an excessively weak interface may
cause large lateral ground deformation (and lateral loading on underground structures). Since a
water interlayer might not dissipate for hours or even days after the earthquake, lateral
deformations may thus take place long after the end of the shaking (delayed flow failure).
The delayed flow-failure mechanism above was inferred from a number of earthquake case
history studies worldwide, such as the failure of one of the Mochikoshi-Tailings-Dam dikes in
the 1978 Izu-Ohshima-Kinkai, Japan Earthquake (Ishihara 1984, Harder and Stewart 1996), and
the failure of the Tapo Canyon Tailings Dam in the 1994 Northridge, California Earthquake
(Harder and Stewart 1996). Berrill et al. (1997) and Boukouvalas et al. (1999) also report on
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delayed flow failures in slopes and bridge foundations. In a recent centrifuge testing series
conducted at U.C. Davis, Kulasingam et al. (2001) and Malvick et al. (2002) point out that water
interlayer formation depends on: 1) initial relative density and the volume of the liquefiable sand
below the low-permeability layer, 2) base motion amplitude and duration, and 3) the
permeability ratio (or difference) between the two layers. Pilot computational modeling of waterinterlayer effects on liquefaction-induced lateral deformation are also underway (Yang and
Elgamal 2001).
Lateral fluid migration
At sites of spatially varying water table (pressure head), lateral fluid migration (from locations of
higher pressure head towards lower pressure-head zones) may exert large static driving force on
soil mass (Li and Ming 2001). This lateral driving force can subject the soil to greater
susceptibility to flow failure or larger extent of lateral spreading. This important issue was
addressed by Li and Ming (2001), in computational simulations of Upper San Fernando Dam
response during the 1971 earthquake.
3. Strain localization and its impact on residual strength
Residual strength is typically referred to as mobilized shear resistance at large shear strains
(under constant pressure and volume). Assessment of soil residual strength is commonly done
through laboratory sample tests. However, observations from a large number of laboratory
sample tests (e.g., Han and Vardoulakis 1991, Han and Drescher 1993, Finno et al. 1997,
Alshibli et al. 2000a, b, Nemat-Nasser and Okada, 2001) have shown that, under large shear
deformations: 1) non-uniformity in terms of concentration of shear deformations (shear bands)
and redistribution of pore fluid seem to be an intrinsic characteristic of soil response, and 2) the
critical-state or steady-state soil response may only occur inside the shear bands, and not
necessarily everywhere in a test sample. The direct consequence of strain localization is that
traditional stress/strain measurements from soil samples in fact only result in nominal values of
residual strength, which are strongly dependent on sample geometry and load pattern.
Computationally, in order to uniquely capture the high deformation gradients associated with
strain localization, it is necessary to introduce a very small time scale (e.g., viscoplasticity
approach, Loret and Prevost 1990) or length scale (e.g., stress/strain gradient approach, Chang et
al. 2001; Cosserat continuum approach, Vardoulakis and Sulem 1995) in the constitutive model.
Either choice in turn requires very dense spatial and/or temporal discretization (i.e., small
element sizes and/or time steps), considerably increasing the computational cost. Still,
uncertainties in initial soil states may not ensure accuracy in modeling natural soil response (see
Section 4 below).
4. Determination of initial states
Liquefaction susceptibility at a particular site is largely dictated by initial conditions of the site,
including spatial distributions of soil density, permeability, degree of saturation, material fabric,
and stress states. The importance of soil density has long been recognized and extensively
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studied, and the effect of permeability is briefly discussed above. In this section, computational
modeling aspects of the other three conditions are summarized.
Degree of saturation
In many liquefaction evaluation procedures and computational programs, soil below the water
table is assumed to be fully saturated. Laboratory sample experiments conducted by Ishihara et
al. (2001) show that degree of saturation in a sand sample may significantly affect its
liquefaction resistance (for instance, cyclic strength of a 62% relative density Niigata Sand is
doubled when saturation ratio is reduced from 100% to 90%). In addition, soil permeability is
also known to be a function of saturation. Recently, constitutive models have been proposed
(e.g., Muraleetharan and Nedunuri 1998, Sun et al. 2000, Muraleetharan and Yang, 2001) to
model this effect numerically.
Stress-induced anisotropy
Anisotropic soil behavior due to the difference between vertical and lateral normal stresses is
often referred to as stress-induced anisotropy ( k 0 ≠ 1 ). The initial k 0 values are very important
in dictating: 1) the initial mean effective confinement at a given location, and 2) the rate of pore
pressure buildup at the early phase of lateral shaking (causing the lateral stresses approach the
vertical stress). Many computational soil models that incorporate kinematic hardening (or
rotational hardening) mechanisms are able to reflect stress-induced anisotropy. However, a major
difficulty is in that no technique has been found to be able to simply and reliably measure in-situ
k 0 values.
Inherent (fabric) anisotropy
Different from stress-induced anisotropy, inherent anisotropy is often believed to be a result of a
particular pattern of particle orientation (fabric), and is not significantly modified by the loading
process. Results from laboratory sample tests show that soil residual strength is strongly affected
by rotation of the principal stress directions when the fabric anisotropy is present (Mulilis et al.
1977). Since principal stress directions may change dramatically during seismic loading, the
effect of fabric anisotropy can be very important. A small number of models (e.g., Matsuoka and
Sakakibara 1987, Li 2001) have been developed to reproduce the experimentally observed soil
plastic response during the rotation of principal stress directions. However, a major challenge in
modeling of inherent anisotropy, again, is the lack of reliable measurement of in-situ fabric
distribution.
5. Conclusions
A number of challenges associated with computational modeling of soil liquefaction response
were briefly discussed. Some implications from this discussion are:
1) There is a need for reliable measurement of in-situ soil initial states including spatial
distribution of permeability, water flow pattern, degree of saturation, k 0 value, and particle
orientation (fabric).
2) Experimental quantification of the variations of the above factors during liquefaction, and
their influence on soil residual strength.
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3) Refined computational modeling of liquefaction (e.g., to capture high pressure/displacement
gradients) requires direct and detailed measurements of soil deformation/fluid migration
patterns from physical models, and from field evidence, which are currently scarce.
Acknowledgements
The authors are grateful for the research funding provided by the Pacific Earthquake Engineering
Research Center (PEER), under the Earthquake Engineering Research Centers Program of the
National Science Foundation (Award Number EEC-9701568), the United States Geological
Survey (Grant No. 99HQGR0020), and the National Science Foundation (Grant No. 0084616).
References
Alshibli, K.A., Sture, S., Costes, N.C., Frank, M.L., Lankton, M.R., Batiste, S.N., and Swanson,
R.A. (2000a). "Assessment of localized deformations in sand using X-ray Computed
Tomography," Geotechnical Testing Journal, ASTM, 23(3), 274-299.
Alshibli, K.A., Sture, S., and Batiste, S.N. (2000b). "Experimental evaluation of bifurcation
phenomena in sands," Plastic and Viscoplastic Response of Materials and Metal Forming, Proc.,
8th Intl. Symposium on Plasticity and Its Current Applications, July 16-20, Whistler, Canada,
A.S. Khan, H. Zhang, and Ye Yuan (Eds.), NEAT Press, Fulton, MD, 276-278.
Arulanandan, K., Yogachandran, C., Muraleetharan, K. K., Kutter, B. L., and Chang, G. S.,
(1988). "Laboratory Flow Slide During Earthquake Simulation, Centrifuge 88, Corte, J.-F., ed.,
Paris, Balkema, Rotterdam, April, pp. 539-544.
Berrill, J.B., Christensen, R.J., Keenan, R.J., Okada, W., and Pettinga, J.R. (1997). "Lateral
spreading loads on a piled bridge foundation," Proc., Intl. Conf. on Soil Mechanics and
Geotechnical Engineering, Seismic Behavior of Ground and Geotechnical Structures: Special
Technical Session on Earthquake Geotechnical Engineering, Balkema Publisher, Rotterdam,
Netherlands, 173-183.
Bouckovalas, G. D., Gazetas, G., and Papadimitriou, A. G. (1999). "Geotechnical Aspects of the
1995 Aegion, Greece, Earthquake," Proc., 2nd Intl. Conf. on Earthquake Geotechnical
Engineering, Balkema Publisher, Rotterdam, Netherlands, 2, 739-748.
Chang, C.S., Shi, Q., and Matsushima, T. (2001). "First strain gradient elasto-plastic model for
strain localization analysis," Proc., Mechanics and Materials Summer Conference, June 27-29,
San Diego, CA.
Elgamal, A. –W., Dobry, R., and Adalier, K. (1989). "Study of Effects of Clay Layers on
Liquefaction of Sand Deposits Using Small-Scale Models," Proc, 2nd US-Japan Workshop on
Liquefaction, Large Ground Deformation and Their Effects on Lifelines, T. D. O'Rourke and M.
Hamada (eds.), 145-160, NCEER, SUNY-Buffalo, Buffalo, NY (Report NCEER-89-0032).
4
Finno, R.J., Harris, W.W., Mooney, M.A., and Viggiani, G. (1997). "Shear bands in plane strain
compression of loose sand," Géotechnique, 47(1), 149-165.
Han, C. and Vardoulakis, I. (1991). "Plane strain compression experiments on water-saturated
fine-grained sand," Géotechnique, 41(1), 49-78.
Han, C. and Drescher, A. (1993). "Shear bands in biaxial tests on dry coarse sand," Soils and
Foundations, 33(1), 118-132.
Harder, L.F. and Stewart, J.P. (1996). "Failure of Tapo Canyon Tailings Dam," J. of
Performance of Constructed Facilities, ASCE, 10(3), 109-114.
Ishihara, K. (1984). "Post-earthquake failure of a tailings dam due to liquefaction of the pond
deposit," Proc., Intl. Conf. on Case Histories in Geotechnical Engineering, Univ. of MissouriRolla, St. Louis, MO, 3, 1129-1143.
Ishihara, K., Tsuchiya, H., Huang, Y., and Kamada, K. (2001). "Recent studies on liquefaction
resistance of sand - effect of saturation," (CD-ROM), Keynote Lecture, 4th Intl. Conf. on Recent
Advances in Geotechnical Earthquake Engineering and Soil Dynamics, March 26-31, San Diego,
CA, Prakash, S. Ed.
Kokusho, T. (1999). "Water Film in Liquefied Sand and Its Effect on Lateral Spread," Journal of
Geotechnical and Geoenvironmental Engineering, 125(10), 817-826.
Kokusho, T., Kojima, T. and Nonaka, N. (1999). "Emergence of water film in liquefied sand and
its role in lateral flow," Proc., 12th World Conf. on Earthquake Engineering (CD-ROM),
Auckland, New Zealand, No. 0946.
Kulasingam, R., Malvick, E.J., Boulanger, R.W., and Kutter, B.L. (2001). "Void redistribution
and localization of shear strains in model sand slopes with silt seams: report on first year
activities," Proc., U.S.-Japan Joint Workshop and Third Grantees Meeting, August 15-16,
Seattle, WA, 74-85.
Kutter, B.L. and Fiegel, G.L. (1991). "Mechanism of sand boil formation in layered soils as
observed in centrifuge test," Proc, 3rd US-Japan Workshop on Earthquake Resistant Design of
Lifeline Facilities and Countermeasures for Soil Liquefaction, T. D. O'Rourke and M. Hamada
(eds.), 279-292, NCEER, SUNY-Buffalo, Buffalo, NY (Report NCEER-89-3008).
Li, X.S. and Dafalias, Y.F. (2000). "Dilatancy for cohesionless soils," Geotechnique, 50(4), 449460.
Li, X.S. (2001). "An anisotropic parameter for critical state modeling of sand response," Proc.,
2001 Mechanics and Materials Summer Conference, June 27-29, San Diego, CA.
Li, X.S. and Ming. H.Y. (2001). "Seepage effects on flow deformation of earth dam," Proc.,
2001 Mechanics and Materials Summer Conference, June 27-29, San Diego, CA.
5
Liu, H. and Qiao, T. (1984). "Liquefaction Potential of Saturated Sand Deposits Underlying
Foundation of Structure", Proc, 8th World Conference on Earthquake Engineering, San
Francisco, California, Vol. III, July, 199-206.
Loret, B. and Prevost, J.H. (1990). "Dynamic strain localization in elasto-(visco-)plastic solids,
Part 1: General formulation and one-dimensional examples," Computer Methods in Applied
Mechanics and Engineering, 83, 247-273.
Malvick, E.J., Kulasingam, R., Kutter,B.L., and Boulanger, R.W. (2002). "Void redistribution
and localized shear strains in slopes during liquefaction" Proc., Int. Conf. on Physics Modeling
in Geotechnics, St.Johns, Newfoundland, Canada, Radu Popescu, Ed., Balkema (in printing).
Manzari, M. T. and Dafalias, Y. F. (1997). "A Critical State Two-Surface Plasticity Model for
Sands," Geotechnique, 49(2), 252-272.
Matsuoka, H. and Sakakibara, A. (1987). "A Constitutive Model for Sands and Clays Evaluating
Principal Stress Rotation," Soils and Foundations, 27(4), 73-88.
Mulilis, J.P., Arulanandan, K, Mitchell, J.K., Chan, C.K., and Seed, H.B. (1977). "Effects of
Sample Preparation on Sand Liquefaction," J. Geotechnical Engineering Division, 103(2), 91108.
Muraleetharan, K.K., and Nedunuri, P.R. (1998). "A bounding surface elastoplastic constitutive
model for monotonic and cyclic behavior of unsaturated Soils." Proceedings (in CD ROM), 12th
Engineering Mechanics Conference, ASCE, La Jolla, CA, 1331-1334.
Muraleetharan, K.K. and Yang, Y. (2001). "Stress-strain behavior of unsaturated soils: an
elastoplastic approach," Proc., Mechanics and Materials Summer Conference, June 27-29, San
Diego, CA.
Nemat-Nasser, S. and Okada, N. (2001). "Radiographic and microscopic observation of
shearbands in granular materials," Geotechnique, 51(9), 753-765.
O'Rourke, T.D., Bardet, J.-P., Hamada, M., (Eds.). (1999). Proc. seventh U.S.-Japan Workshop
on Earthquake Resistant Design of Lifeline Facilities and Countermeasures Against Soil
Liquefaction, Technical Report MCEER-99-0019, November 19.
Scott, R. F., and Zuckerman, K. A. (1972). "Sandblows and Liquefaction," The Great Alaska
Earthquake Of 1964-Engineering Publication 1606, National Academy of Sciences,
Washington, D.C., 179-189.
Seed, H. B. (1987). "Design problems in soil liquefaction," J. Geotechnical Engineering, 113(8),
827-845.
6
Sun, Matsuoka, Yao and Ichihara. (2000). "An elastoplastic model for unsaturated soil in threedimensional stresses," Soils and Foundations, 40(3), 17-28.
Vardoulakis, I. and Sulem, J. (1995). Bifurcation Analysis in Geomechanics, Blackie Academic
and Professional, Glasgow, U.K.
Yang, Z. and Elgamal, A. (2001). "Sand Boils and Liquefaction-Induced Lateral Deformation,"
(CD-ROM), Lessons Learned From Recent Strong Earthquakes, Proc., 15th Intl. Conf. on Soil
Mechanics and Geotechnical Engineering, 23 – 25 August, Istanbul, Turkey, A.M. Ansal, Ed.
7