INTERNATIONAL SOCIETY FOR SOIL MECHANICS AND GEOTECHNICAL ENGINEERING

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LIQUEFACTION-INDUCED UPLIFT OF BURIED STRUCTURES INSIGHTS FROM THE STUDY OF AN IMMERSED RAILWAY TUNNEL

Thaleia TRAVASAROU 1, Weiyu CHEN2, and Jacob CHACKO3

ABSTRACT

Light buried structures surrounded by liquefiable soils are susceptible to uplift during large earthquakes. Liquefaction-induced uplift, often referred to as “floatation”, has been commonly associated with significant displacements and is usually considered the result of a force-based buoyancy mechanism. Resistance to such mechanism is provided by the available shear strength of the liquefiable soil and a reverse end bearing capacity. We explored the mechanism of uplift in the context of the vulnerability and retrofit studies for an existing 5.8-km long immersed railroad tunnel located 15 km from the San Andrea fault in the Bay Area of California. The tunnel, built in the 1960’s, was placed in a trench excavated into the native soils and backfilled with loose gravel and sand. Two-dimensional effective stress dynamic soil- structure-interaction analyses complemented by two project-specific centrifuge experiments estimated relatively small tunnel uplift. Based on the analyses results and experimental observations we concluded that the governing mechanism of uplift is a displacement-limited ratcheting phenomenon associated primarily with co-seismic movement of soil under the tunnel. The amount of uplift is related primarily to the extent of liquefiable soils, their relative density, the differential weight between the buried structure and surrounding soil and amplitude and duration of shaking. Additional, sources are related to volumetric expansion of soil due to water inflow and potential heaving of soft soils. The methodology developed to assess the uplift vulnerability for this critical structure led to an improved understanding of liquefaction- induced uplift and the adoption of a no-retrofit strategy with significant cost savings. It also provides a framework for the future assessment of liquefaction-induced uplift vulnerability for a range of structures.

Keywords: Liquefaction, immersed tunnel, uplift, centrifuge, soil-structure-interaction, numerical analyses

OVERVIEW OF LIQUEFACTION-INDUCED UPLIFT

Uplift of light structures buried in liquefiable soils has been observed during large earthquakes (e.g., Seed, 1967; Koseki, Matsuo, Ninomiya, & Yoshida, 1997; Yasuda and Kiku, 2006), and reported during shaking table tests (e.g., Koseki et al., 1997; Yasuda et al., 1994; Tamura et al., 1997), and centrifuge tests (e.g., Adalier et al. 2002 and 2003, Sasaki and Tamura, 2004). In most of the cases involving strong shaking large uplift (i.e., sometimes on the order of meters) was observed. As a result liquefaction- induced uplift has traditionally been referred to as “floatation” (e.g., Seed, 1967; Tamura et. al., 1997; Yasuda et al., 1994) suggesting a mechanism related to equilibrium of vertical forces. This concept implies that during strong shaking the soil liquefies fully (i.e., 100 percent excess pore pressure) turning into a viscous fluid and imparting upward buoyancy forces on the buried structure. Hence some researchers proposed (e.g., Koseki et. al., 1997; Tamura et. al., 1997) that uplift vulnerability be assessed using limit equilibrium stability analyses. We refer to this force-equilibrium involving the assumption of buoyancy as the “force-based” concept for the uplift mechanism. This concept implies that uplift occurs

1 Senior Engineer, Earthquake Group, Fugro West, Inc., e-mail: [email protected] 2 Senior Engineer, Earthquake Group, Fugro West, Inc. 3 Principal, Earthquake Group, Fugro West, Inc. 5th International Conference on Earthquake Geotechnical Engineering January 2011, 10-13 Santiago, Chile rapidly after soil liquefaction and is related to large displacements. However, observations from physical model tests suggest that structural uplift occurs primarily co-seismically (e.g., Sasaki and Tamura, 2004, and Koseki et al., 1997) which would be in contrast to a force-based mechanism. Until recently limited literature existed on liquefaction-induced uplift of tunnel structures. A combination of centrifuge model testing (Adalier et al. 2002 and 2003) and numerical analyses (Yang et. al., 2004, Naesgaard et al., 2004) were performed for the George Massey Tunnel in Vancouver, Canada to help guide the decision for retrofit. In this case tunnel uplift was judged to be substantial and a stone column retrofit plan was proposed to limit uplift deformations.

We studied the mechanism of liquefaction-induced structural uplift in the context of the analytical and experimental work performed to assess the vulnerability to uplift and need for retrofit of the Bay Area Rapid Transit (BART) submerged railway tunnel near the city of San Francisco. At the onset of the project, there was consensus in the scientific community regarding the liquefaction susceptibility of the very loose gravels and sands surrounding the tunnel under strong design shaking. However, due to the limited data and documentation of liquefaction-induced uplift in the literature the expected consequences of soil liquefaction for the tunnel were not obvious and potential catastrophic uplift associated with a force-based mechanism could not be precluded. The extensive numerical analyses and testing performed subsequently for this project, and discussed in this paper, helped gain improved understanding of the uplift mechanism which was found to be primarily a displacement-limited ratcheting phenomenon. In the case of the BART tunnel the implications of the governing uplift mechanism estimating relatively small displacements enabled the adoption of a no-retrofit strategy with substantial cost benefits. The analyses performed for the BART tunnel project provide a framework that can be used in the future to evaluate the liquefaction-induced uplift vulnerability for a range of buried structures.

BART OFFSHORE TRANSBAY TUBE PROJECT DESCRIPTION

The Bay Area Rapid Transit (BART) Offshore Transbay Tube (TBT) is a 5.8 km-long immersed cut and cover railway tunnel built in the 1960s and connecting San Francisco to Oakland in the high seismicity Bay Area in California (Figure 1a). The TBT is the most important transportation infrastructure in the Bay Area carrying more than 300,000 passengers daily. It is located at close distances of about 14 km and 9 km, respectively, from the San Andreas and Hayward faults with estimated characteristic magnitudes of 7.9 and 7.25 and relatively high slip rates on the order of 17 and 9 mm/year. The project design spectra for outcropping “soft rock” corresponding approximately to a 1,000-year return period Bechtel (2005) are presented in Figure 1b and show high ground motions with peak ground acceleration of about 0.63g.

The TBT was constructed in a trench excavated into the native soils (Figure 2). After trench excavation an approximately 1.2-meter-thick layer of gravel was placed and screeded level. Prefabricated segments of tube, approximately 100 meters-long each, were immersed and connected together. The equivalent unit weight of the TBT is approximately 1.1 times that of sea water. Backfill material consisting of gravel was then tremmied around the sides of the tube section to about the middle height. Sand fill material was subsequently pumped in to provide a minimum cover of about 1.5 meters above the TBT. Natural sedimentation formed a soft impermeable layer of surficial mud.

The relative density of the trench backfills was inferred by 36 pairs of Cone Penetration (CPT) soundings Fugro (2007b) performed at about 1.5-meter distance from the tunnel edge on either side of the tunnel. Permeability was estimated with in-situ tests and empirical correlations based on gradation curves. Table 1 summarizes the soil properties interpreted from all available data. In both the gravel and sand fill the tip resistance is relatively uniform and low, with median values corresponding to relative density of about 5th International Conference on Earthquake Geotechnical Engineering January 2011, 10-13 Santiago, Chile 35% and 40%, respectively. The permeability of the gravel fill and foundation is large with best estimate values of 1 to 5 cm/s, while permeability in the sandy fill is approximately 100 smaller.

2.0 Matched Motions

Design Spectra 1.6 1.2 5 % Damping

0.8 0.4

Spectral Acceleration (g) 0.0 0.01 0.1 1 10 Period (s)

Figure 1. a) Location of BART offshore immersed tunnel with respect to major faults, b) Project design acceleration spectrum and seven spectrally-matched time histories

Surficial mud Sand fill Stiff clay

Gravel fill Gravel foundation

Figure 2. Typical cross-section of immersed tunnel and surrounding trench backfills

Table 1. Key trench backfill properties Dr (%) Permeability (cm/s) qc1N Unit best estimate best estimate SOIL TYPE best estimate Weight N (16%-84% (16%-84% 1,60 (16%-84% percentiles) (kN/m3) percentiles) percentile) Sand Fill 50 (32-70) 40 (35-45) 0.01 (0.002-0.1) 1.9 7 Gravel Fill 33 (25-48) 35 (30-40) 1 (0.3-10) 2.1 6 Gravel 33 (25-48) 35 (30-40) 1 (0.3-10) 2.1 6 Foundation

5th International Conference on Earthquake Geotechnical Engineering January 2011, 10-13 Santiago, Chile

DYNAMIC SOIL-STRUCTURE INTERACTION ANALYSES

Constitutive Model and Numerical Methods Fully-coupled effective-stress dynamic soil-structure interaction analyses were performed in FLAC using the constitutive model UBCSAND for the liquefiable soils (Beaty and Byrne, 1998). The model parameters were calibrated with emphasis on capturing the liquefaction triggering response and post- liquefaction accumulation of plastic shear strains (Giannakou et al., 2010; Fugro, 2008). The primary input parameter is the value of the energy and overburden corrected blowcount, N1,60, of the standard penetration test (Table 1). A typical FLAC grid is shown in Figure 3. Lateral free field boundaries were used to simulate free field conditions. The model was excited with a) one of the design input motions (i.e. TCU078 recording from the 1999 M7.6 ChiChi earthquake matched to the design spectra, Figure 1b), and b) the 090 horizontal component of the Yerba Buena Island (YBI) recording during the 1999 M6.9 Loma Prieta earthquake.

TC

STIFF CLAY TL TR A B STIFF CLAY (OBM)

STIFF CLAY (OBM)

DENSE SAND (UAM)

HARD CLAY (LAA) Input Depth – Base Rock Figure 3. Typical finite difference grid used in FLAC. Soil types in the area outlined with dashed lines is shown in greater detail in Figure 2.

Representative Results Figure 4 presents the time histories of tunnel uplift recorded at the tunnel center and two sides, together with time histories of excess pore pressures in the foundation gravel beneath the tunnel centerline and at the same elevation to the side (Figure 3). Relatively small uplift of around 0.08 m was estimated for the stronger TCU078 motion, while no uplift was estimated for the weaker YBI motion, despite the development of excess pore pressures of similar amplitude in the gravel foundation. Uplift occurs primarily co-seismically, and correlates well with the onset and end of strong shaking. However, it correlates less agreeably with excess pore pressure in the underlying gravel. In fact, uplift is negligible for the weaker YBI motion in spite of the development of large excess pore pressures in the foundation gravel. Also, for the design TCU078 motion it stops after the end of strong shaking despite excess pore pressure remaining large. Figure 5 presents the vectors of soil displacement with alternate cycles of strong ground motion. It appears that during shaking additional inertial demands are generated under alternate pulses of shaking resulting in: a) generation of excess pore pressure and associated reductions in soil strength in the liquefiable trench backfills, b) periodic exceedances of the reduced soil capacity and c) associated soil movement. As evidenced by Figure 5 and the tunnel trajectory shown in Figure 6a, the lighter tunnel is being pushed sideways and upwards in a ratcheting manner by the heavier and softened liquefiable soil. Those displacements resulting from shearing of the soil during strong shaking occur co- seismically and are not recovered after the end of shaking. One useful implication of this ratcheting nature of uplift is that the liquefaction process does not need to be modeled explicitly in numerical analyses to assess the effects of uplift. Instead, it suffices that the key effect of liquefaction (i.e., the 5th International Conference on Earthquake Geotechnical Engineering January 2011, 10-13 Santiago, Chile overall reduction of soil’s strength) be modeled with simplified assumptions in total stress analyses. Figure 6b compares the uplift time history estimated from total stress analyses where the liquefiable soil was modeled with reduced undrained shear strength of Su/p’= 0.17. In this case, this value may be considered as a spatial and temporal “average” of soil strength during the TCU078 event. In general, this approach may be used for calibration of soil properties of the liquefiable soils for input in 3-dimensional analyses where comprehensive liquefaction models are not widely available and reducing computational time is important.

0.12 0.12 YBI 0.08 0.08 TC 0.04 TL 0.04 TR 0

Tube UpliftTube (m) 0 Tube UpliftTube (m)

60 60 initial effective stress (B) initial effective stress (B) 40 40

20 20 B (beneath) A (adjacent) Exc. PP (kPa) Series3 (kPa) PP Exc. 0 0

0.5 0.1 0.25 0.05

0 3 0 3 Acc (g)

-0.25 Acc (g) -0.05 -0.5 -0.1 0204Time (s) 0600204Time (s) 060

Figure 4. Tunnel uplift, excess pore pressure in the foundation gravel beneath and adjacent to the tunnel, and input acceleration time histories for the design TCU078 (left) and YBI (right) motions

(a) One strong motion cycle (b) Subsequent cycle

Figure 5. Movement of liquefiable soil around the tunnel and ratcheting displacement of tunnel with alternate cycles of ground motion

5th International Conference on Earthquake Geotechnical Engineering January 2011, 10-13 Santiago, Chile

0.1 0.15 Effective Stress 0.08 Total Stress 0.1 0.06

0.04 Uplift (m) Uplift

Uplift (m) 0.05

0.02

0 0 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0 1020304050 Time (s) Horizontal Disp. (m) Figure 6. a) Tunnel trajectory for the TCU078 motion, b) comparison of tunnel uplift from detailed effective stress and approximate total stress analyses

CENTRIFUGE TESTING AND BACK ANALYSES

Two centrifuge experiments were performed at the centrifuge facility of the University of California at Davis (UC Davis), in September and December of 2007 (Kutter et. al., 2008, Chiou et al. 2010) with the goal to provide additional insights into the mechanism of uplift and form a reference for additional calibration and validation of the numerical methods. Figure 7 shows the idealized design cross-section and the as-built model before shaking for the first centrifuge experiment. Recorded time histories of tube uplift and excess pore pressure beneath and adjacent to the tube (sensors in Figure 7) are shown in Figure 8 for both the TCU078 design event and the simulation of the Loma Prieta earthquake (YBI motion). Similar to the predictions of the preliminary numerical models negligible uplift occurred during the small amplitude YBI motion despite the rise of excess pore pressure beneath the tunnel to about 70%-80% of the initial effective stress. For the design TCU078 motion the majority of uplift occurred co-seismically and was relatively small, on the order of 0.25m. Simulations performed after the experiment (calibration methodology presented in Giannakou et al., 2010) estimated the co-seismic portion of uplift satisfactorily. Real time recordings from high speed cameras and soil deformation patterns following model excavation suggest that uplift is primarily related to movement of the soil surrounding the tube towards and underneath the tube. As an example, Figure 9 shows columns of colored sand initially placed vertically adjacent to the tube having displaced downwards and towards the tunnel post-earthquake. Moreover, a black marker of sand originally placed at the corner of the tube displaced beneath the tube by about 1 meter (prototype scale) during shaking. Similar behavior was obtained from the fully-coupled dynamic effective stress analyses performed after the experiments (Travasarou and Chacko, 2008; Fugro, 2008).

DTV1 Sand

Stiff Clay Gravel P4 P5 Gravel

Figure 7. Idealized cross-section for first centrifuge experiment and front view of as-built centrifuge model

5th International Conference on Earthquake Geotechnical Engineering January 2011, 10-13 Santiago, Chile

0.3 0.3

0.2 0.2 Observation 0.1 0.1 Simulation Tube Uplift (m) Tube Uplift (m) 0 0 60 60

40 40

20 20 Excess PP (kPa) 0 Excess(kPa) PP 0 0.8 0.2 0.4 0.1 0 0 Acc. (g) Acc. -0.4 (g) Acc. -0.1 -0.8 -0.2 0 20 40 60 80 100 120 0 102030405060 Time (s) Time (s) Figure 8. Tunnel uplift, excess pore pressure beneath the tunnel, and input acceleration time histories for the design TCU078FN (left) and YBI (right) motions.

a b

~ 1 m

X-displacement contours -2.50E+00 ft -1.50E+00 -5.00E-01 5.00E-01 1.50E+00 2.50E+00

Figure 9. Displacement of sand toward and beneath the tunnel from the experimental observations and numerical back-analyses

POST-EARTHQUAKE UPLIFT THROUGH WATER FLOW

A second component of uplift may be related to migration of pore water in response to an existing gradient during or after the end of shaking. Figure 10 presents time histories of recorded uplift (sensor DTV1) and pore pressures (sensors P4 and P5) from the beginning until a few minutes after shaking, from 5th International Conference on Earthquake Geotechnical Engineering January 2011, 10-13 Santiago, Chile the first BART centrifuge experiment. During strong shaking the contractive soils around and beneath the tube generate excess pore pressure. As the particles within those soils settle into a denser state the pore fluid generated redistributes within the model in accordance with the prevailing pressure gradients. The initial gradients are such that pore water flows partially under the tube in response to the difference in pore pressure adjacent and beneath the tube and partially upwards to the surface. After the end of shaking additional flow of water occurs from regions adjacent to the tube to regions beneath the tube resulting in volumetric expansion of the soils beneath the tube and causing post-earthquake uplift. Once the pore pressures beneath the tube equalize with those adjacent to the tube there is no more tendency for water to flow beneath the tube and uplift ceases. As the pore pressures dissipate from the backfills, the pore fluid from beneath the tube tends to flow out and the tube settles back down. In this case a small fraction equal to about 10 to 15 percent of the total uplift occurs after the end of shaking and is largely recovered by settlement over the next few minutes following the end of shaking. This additional uplift can be captured by post-earthquake analyses using reduced soil bulk modulus compatible to the volumetric strains observed in the field after soil liquefaction as described by Fugro (2008).

200 0.3

) 0.25 150 0.2

100 0.15 Uplift (m) P5 0.1 50 Pore Pressure (kPa Pressure Pore P4 0.05 DTV 1 0 0 0510 Time (min)

Figure 10. Tunnel uplift and history of pore pressures beneath the tunnel and at the same elevation adjacent to the tunnel observed in the centrifuge (sensor locations shown in Figure 7)

POST-EARTHQUAKE STABILITY

The concept of “floatation” of light structures buried in liquefiable soils is based primarily on the notions that upon liquefaction the soil looses its capacity to resist shear forces thus behaving as a heavy fluid, and that the weight differential between the light structure and the surrounding heavier soil results in net upward “buoyancy” forces. As shown in Figure 11a, an upward force imparted on a buried structure would mobilize a reverse end bearing resistance mechanism. Hence a factor of safety against uplift could be computed as the ratio of the resistance forces to the driving forces as:

Freverse_ end _bearing + Fshear _ strength FSuplift = (1) (γ soil −γ structure )⋅Vstructure

As suggested by this qualitative equation if shear stresses from differential weight are high enough and/or reduction in soil strength is low enough a “force-based” uplift mechanism could develop. The likelihood of that would depend on: a) the weight differential between the buried structure and surrounding soil, b) the soil’s relative density affecting the amount of strength reduction experienced during and post-shaking, c) the geometry which will control the reverse end bearing resistance (for example if the extend of liquefied soil beneath the buried structure is small the reverse end bearing capacity may increase 5th International Conference on Earthquake Geotechnical Engineering January 2011, 10-13 Santiago, Chile substantially). This mechanism could develop post-earthquake under “static” conditions, due to migration of pore water and subsequent loss of strength in critical layers. In the case of the BART TBT the potential for a force-based mechanism post earthquake was explored through simplified static total stress analyses where the undrained shear strength ratio (Su/p’) of the trench backfills was reduced progressively until unrestrained uplift of the tube was observed. Figure 11b presents the effect of the Su/p’ on the stability of the tube. For values of Su/p’ greater than about 0.05 the tunnel appears stable and uplift is associated with small movements. If Su/p’ were to reduce further uplift would increase rapidly showing the potential for a post-earthquake instability and pop-up. For the BART tube, the threshold of soil strength allowing the force-based mechanism to develop is low compared to what would be estimated from empirical relationships for soils with Dr ~ 35-45%. Hence it was considered that the tunnel would be stable post- earthquake. However, there may be conditions where this value is higher and comparable to the residual strength of the liquefiable soils surrounding the structure. In those cases large displacements associated with a force-based mechanism may occur and retrofit considerations are warranted.

1 0.3m 0.75

0.5

0.25 Tube Uplift (m) Uplift Tube 0 Loose sand 0 0.02 0.04 0.06 0.08 0.1 Su/P' of Trench Soils

Figure 11. a) Shear strain developed in loose sand as a result of an imposed displacement of ~0.3m in the tunnel indicating the mobilization of a reverse end bearing capacity against uplift, b) potential for post-earthquake uplift as a function of undrained shear strength

INSIGHTS ON LIQUEFACTION-INDUCED UPLIFT

Liquefaction-induced uplift of light buried structures is usually considered the result of a force-based buoyancy mechanism associated with very large displacements. This phenomenon has been referred to in the literature as “floatation”. Resistance to the development of this type of mechanism is provided by the shear strength of the soil surrounding the buried structure and the mobilization of reverse end bearing. Both sources of resistance are large at the onset of shaking and the factor of safety against uplift forces in the absence of soil liquefaction is typically high. During strong shaking soil liquefaction and associated reduction in shear strength may occur, depending on soil properties, geometry, and unit weight differential between the buried structure and the surrounding soil. If shear stresses from the differential weight are high enough and/or the reduced soil strength is low, uplift may occur as a result of a net upward force imparted on the structure, thus allowing the development of a force-based mechanism.

In the absence of conditions favoring a force-based mechanism, additional inertial demands are generated under the cyclic shaking pulses resulting in periodic exceedance of soil capacity and movement of the heavier soil which tends to displace the lighter structure in a ratcheting manner. The buried structure is effectively driven by the displacement of the weakened – by the generated pore pressure – soil in response to the alternate cycles of strong ground motion in a ratcheting manner. We refer to this mechanism as displacement-limited ratcheting uplift mechanism because it is controlled and limited by the volume of soil available to displace toward the buried structure and follows the earthquake pulses in a ratcheting 5th International Conference on Earthquake Geotechnical Engineering January 2011, 10-13 Santiago, Chile manner. In the end, the magnitude of movement depends on factors affecting both the demand and the capacity side of the problem. On the demand side larger uplift movements are expected for stronger shaking amplitude, larger shaking duration, and small ratios of structure density to density of surrounding soils. On the capacity side, larger uplift is expected for looser backfill soils, and larger extent of liquefiable soils around a buried structure. The ratcheting, displacement-limited mechanism is in contrast to a perceived “force-based” mechanism attributed to a buoyancy-related net upward force constantly applied on the buried structure resulting in uncontrolled displacements.

Although the primary source of uplift is related to shearing of the liquefiable backfill soils there may be secondary uplift sources. Those are associated with heaving of the soft soils surrounding the trench (Fugro, 2008) and water flow towards the tube in response to a pressure gradient after the end of shaking (e.g., Figure 10). Water flow may occur partially during shaking and more commonly occur post- earthquake in response to an existing pressure gradient. However this displacement appears reversible as pore pressures dissipate and equalize.

PROJECT SUMMARY

In the case of the BART TBT project the relatively small uplift displacements estimated can be explained by the nature of the displacement-limited ratcheting uplift mechanism in combination with favorable characteristics of the geometry and properties specific to this project: a) the small thickness of the gravel foundation, b) the large permeability of the liquefiable soils which reduces the duration over which the liquefiable soil has a reduced strength, and c) the existence of impermeable soils around the trench limiting the potential for water to feed in the system.

Additional 3-dimensional total stress analyses were performed to explore the sensitivity of uplift estimates to 3-dimensional effects such as the presence of the tube, structural discontinuities along the tube length and varying soil properties. These analyses, presented in detail by Fugro (2008) show that uplift induced stresses in the tube are within capacity (Figure 12). As a result a no-retrofit strategy was recommended for the project with substantial cost benefits.

The work performed for the TBT project led to an improved understanding of liquefaction-induced uplift and provides a framework to evaluate the vulnerability to uplift for a range of buried structures.

Moment in vertical plane 250,000 200,000 150,000 100,000 50,000 0 -50,000

Moment, kip-ft Moment, -100,000 -150,000 Z -200,000 Y -250,000 0 50 100 150 200 250 300 350

X Length along the tube, ft Figure 12. a) Three dimensional finite difference grid, b) comparison of bending moment demand to effective moment capacity for all seven design ground motions

5th International Conference on Earthquake Geotechnical Engineering January 2011, 10-13 Santiago, Chile

ACKNOWLEDGEMENTS

We would like to thank Professor Peter Byrne for sharing his experience and insights regarding numerical modelling of liquefiable soils and liquefaction-induced uplift and Professor Bruce Kutter for his resourcefulness and invaluable contribution during the centrifuge testing effort.

REFERENCES

Adalier, K., Abdoun, T., Dobry, R., and Phillips, R. (2002), “George Massey Tunnel Seismic Retrofit Final Design – RPI Centrifuge Test Results,” Technical Report prepared for Buckland and Taylor, LTD., Dep. of Civil and Environmental Engineering, Rensselaer Polytechnic Institute, February. Adalier, K., Abdoun, T., Dobry, R., Phillips, R., Yang, D., and Naesgaard, E. (2003), “Centrifuge modeling for seismic retrofit design of an immersed tube tunnel,” International Journal of Physical Modelling in Geotechnics, pp. 23-35 Bechtel (2005). “Development of seven sets of spectrum compatible time histories for slope stability analysis of the BART Transbay Tube for both DBE and LDBE Target spectra,” Interoffice memorandum, October 12. Beaty, M., and Byrne, P.M., (1998). “An effective stress model for predicting liquefaction behavior of sand,” Proceedings of a Specialty Conference, Geotechnical Earthquake Engineering and Soil Dynamics, ASCE pp. 766-777, Seattle. Chang, D., Travasarou, T., and Chacko, M.J., (2008). “Numerical evaluation of liquefaction-induced uplift for an immersed tunnel,” 14th World Conference on Earthquake Engineering, October 2008, Beijing, China, Paper No 06-0085. Chiou, J.C., Kutter, B.L., Travasarou, T., and Chacko, J.M., (2010). “Centrifuge modeling of seismically induced uplift for the BART Transbay Tube,” Journal of Geotechnical and Geoenvironmental Engineering, accepted. Fugro West, Inc (2008). “Final report – No densification assessment, Offshore Transbay Tube (TBT) Seismic Retrofit Project” Prepared for Bechtel Infrastructure Corporation, BART Earthquake Safety Program, July. Giannakou, A., Travasarou, T., Ugalde, J., Chacko, J.M., and Byrne, P., (2010). “Calibration methodology for liquefaction problems considering level and sloping ground conditions,” 5ICEGE, Chile. Naesgaard, E., Yang, D., Byrne, P.M., and Gohl, B. (2004), “Numerical Analyses for the Seismic Safety Retrofit Design of the Immersed Tube George Massey Tunnel,” 13th World Conference on Earthquake Engineering, Vancouver, B.C., Canada, August 1-6, Paper No. 112. Itasca Consulting Group Inc. (2006a), “Fast Langrangian Analysis of Continua (FLAC2D),” version 5.0 Koseki, J., Matsuo, O., Ninomiya, Y., and Yoshida, T. (1997), “Uplift of sewer manholes during the 1993 Kushiro-Oki earthquake,” Soils and Foundations, Vol. 37, No. 1, pp. 109-121. Kutter, B.L., Travasarou, T., and Chiou, J.C. (2008), “Centrifuge testing of the seismic performance of a submerged cut and cover tunnel in liquefiable soil ,” GEESD IV, Sacramento. Seed, H.B. (1967), “Soil stability problems caused by earthquakes,” Report, Soil Mechanics and Bituminus Materials Research Laboratory, University of California Berkeley, January 1967. Travasarou, T., and Chacko, J.M. (2008). “Liquefaction-induced uplift mechanics of immersed tunnel,” 3d Hellenic National Conf. of Earthquake Engineering and Engineering Seismology, Athens, in Greek. Yang, D., Naesgaard, E., Byrne, P., Adalier, K., and Abdoun, T. (2004), “Numerical model verification and calibration of George Massey tunnel using centrifuge models,” Canadian Geotechnical Journal, Vol. 41, pp. 921-941. Yasuda, S., and Kiku, H. (2006), “Uplift of sewage manholes and pipes during the 2004 Niigataken-Chuetsu earthquake,” Soils and Foundations, Vol. 46, No. 6, pp. 885-894.