numerical model verification and calibration of george massey

Numerical model verification and calibration ofGeorge Massey Tunnel using centrifuge models

Dan Yang, Ernest Naesgaard, Peter M. Byrne, Korhan Adalier, and Tarek Abdoun

Abstract: Dynamic soil–structure interaction analyses were carried out for the seismic retrofit design of the immersedGeorge Massey Tunnel, both to predict and study soil liquefaction and related tunnel movements and to design groundimprovement. The proposed ground improvement included ground densification using vibroreplacement stone columnsalong both sides of the tunnel and seismic gravel drains adjacent to the outer edge of the densified zones. The den-sification and drainage were proposed to locally mitigate soil liquefaction and reduce displacements of the tunnel totolerable levels. Centrifuge model tests with base shaking to simulate earthquake effects were conducted to verify andcalibrate the numerical models. This included simulating the effects of ground densification and drainage on reme-diating tunnel movements. This paper presents the principal results from the dynamic analyses, the centrifuge modeldesign and testing procedure, the class A predictions of the centrifuge tests, and discussions of the centrifuge test re-sults and numerical model calibrations.

Key words: immersed tunnel, seismic retrofit, soil liquefaction, design verification, centrifuge testing, numerical calibra-tion.

Résumé : On a réalisé des analyses dynamiques de l’interaction sol–structure pour l’ajustement à rebours de laconception sismique du tunnel George Massey immergé, pour prédire et étudier la liquéfaction du sol et les mouve-ments conséquents du tunnel, de même que pour concevoir des améliorations du terrain. Les améliorations du terrainproposées comprenaient la densification du terrain en remplaçant le sol par des colonnes de pierres installées par vibra-tion le long des deux côtés du tunnel, et des drains de gravier sismiques adjacents aux bords extérieurs des zones den-sifiées. La densification et le drainage ont été proposées pour atténuer la liquéfaction du sol et réduire les déplacementsdu tunnel à un niveau tolérable. Des essais sur modèle au centrifuge avec vibration à la base pour simuler les effets detremblement de terre ont été réalisés pour vérifier et calibrer le modèle numérique. Ceux-ci comprenait la simulationdes effets de la densification et du drainage du sol sur le comfortement des mouvements du tunnel. Cet article présenteles principaux résultats des analyses dynamiques, la conception du modèle centrifuge et la procédure d’essai, les pré-dictions de classe A des essais au centrifuge et les discussions des résultats de l’essai au centrifuge, et les calibragesdu modèle numérique.

Mots clés : tunnel immergé, ajustement à rebours sismique, liquéfaction du sol, vérification de la conception, essai parcentrifuge, calibrage numérique.

[Traduit par la Rédaction] Yang et al. 942

Introduction

The 629 m long immersed George Massey Tunnel passesunder the south arm of the Fraser River to connect the Cityof Richmond and the Municipality of Delta, British Colum-bia. It is a major infrastructure in the Greater Vancouver area(Fig. 1). The tunnel was completed in 1959. Based on cur-

rent seismic design standards, the precast concrete structureis grossly underreinforced in the longitudinal direction. Thetunnel comprises six 105 m long precast concrete segmentswith rectangular cross section (Fig. 2). Each segment wasbuilt in a graving dock located just downstream of the tun-nel. The segments were then floated into place and sunk intoa shallow trench excavated into the loose Fraser River sands,silty sands, and silts. The trench was backfilled with loosesand underneath and along both sides of the tunnel using ajetting method. Gravel and rock fill were laid on top of thejetted sand and over the tunnel for scour protection and toprovide weight to counter buoyancy. A generalized soil pro-file based on the site investigations for the original construc-tion (Hall et al. 1957) and by the owner, the Ministry ofTransportation of British Columbia (Gillespie 1991), isshown in Fig. 3. The soils are unconsolidated deltaic andmarine sediments of Holocene age and extend to approxi-mately 300 m depth at the site (Britton et al. 1995).

The design criteria set out by the owner was that the tun-nel should be retrofitted to withstand both an equivalent mo-

Can. Geotech. J. 41: 921–942 (2004) doi: 10.1139/T04-039 © 2004 NRC Canada

921

Received 22 January 2003. Accepted 15 March 2004.Published on the NRC Research Press Web site athttp://cgj.nrc.ca on 9 October 2004.

D. Yang.1 Buckland & Taylor Ltd., 101-788 HarboursideDrive, North Vancouver, BC V7P 3R7, Canada.E. Naesgaard. Trow Associates Inc., 7025 Greenwood Street,Burnaby, BC V5A 1X7, Canada.P.M. Byrne. Civil Engineering Department, University ofBritish Columbia, Vancouver, BC V6T 1W5, Canada.K. Adalier and T. Abdoun. Civil Engineering Department,Rensselaer Polytechnic Institute, Troy, NY 12180-3590, USA.

1Corresponding author (e-mail: [email protected]).

ment magnitude 7.0 nearby nonsubduction earthquake and amoment magnitude 8.2 distant subduction earthquake with-out collapse or loss of life. Modification of firm ground mo-tions occurs due to the large depth of recent Holocene sandyand silty deposits at the site. The nonsubduction earthquakehas a 10% probability of exceedance in 50 years (475 yearreturn period), a peak ground acceleration (PGA) of 0.25g,and a peak ground velocity (PGV) of 0.25 m/s. Its two or-thogonal horizontal records were fitted to a uniform hazardresponse spectrum (UHRS). The subduction event has aPGA of 0.15g, and its two orthogonal horizontal recordswere fitted to a deterministic spectrum. Figure 4 shows thefirm ground response spectra of the two design earthquakes.

The seismic retrofit design is a challenging soil–structureinteraction analysis problem requiring estimation of possibleearthquake effects on the existing tunnel–soil system andevaluation of various remediation measures. The critical fac-tors to be evaluated in the geotechnical analysis include ex-cess pore pressure generation, soil liquefaction triggering,and ground displacement related to soil liquefaction, includ-ing tunnel flotation, lateral movement, and post-liquefactionconsolidation settlement.

Predicted dynamic behaviour of the tunnel–soil system

Two-dimensional (2D) dynamic soil–structure interactionanalyses on transverse and longitudinal sections were per-formed using the computer program FLAC (Itasca Con-sulting Group Inc. 2000). Total stress and effective stressliquefaction triggering constitutive models developed byP.M. Byrne and M. Beaty at the University of British Co-lumbia were used.

The total stress approach evaluates triggering of liquefac-tion by tracking the dynamic shear stress history on the hori-

zontal plane, τxy , within each element (Beaty 2001). The ir-regular shear stress history caused by the earthquake isinterpreted as a succession of half cycles, with the contribu-tion of each half cycle to triggering determined by its maxi-mum value of τcyc, equal to τst – τxy , where τst is the staticbias existing prior to dynamic loading. Each half cycle ofτcyc is transformed into an equivalent number of cycles Neqat τ15, the value of τcyc required to cause liquefaction in 15cycles. Liquefaction is triggered when Σ Neq exceeds 15.This approach was used to simulate a case history of the Up-per San Fernando Dam and its observed seismic responseduring the 1971 San Fernando earthquake (Beaty and Byrne1999).

The effective stress approach uses an incremental elastic–plastic effective stress formulation based on an assumed hy-perbolic relation between stress ratio and plastic shear strain(Byrne et al. 1995; Puebla et al. 1997). The constitutivemodel, namely UBCSAND, has been developed for predict-ing the liquefaction response of granular soils. It representsthe behaviour of the soil skeleton including its shear-volumecoupling response. As a plasticity model, it includes such fea-tures as a yield surface, a nonassociative flow rule, and defini-tions for loading, unloading, and hardening. It is a variation ofthe FLAC Mohr–Coulomb model. The effect of any porefluid is accounted for through its volumetric stiffness. Themodel is fully coupled so that the effects of pore-water floware included. This model was used to simulate monotonic andcyclic element tests and centrifuge tests and field observationsfrom the Wildlife Site seismic array (Puebla et al. 1997;Beaty and Byrne 1998; Byrne et al. 2004).

Two-dimensional transverse section models were devel-oped to study the tunnel flotation and lateral displacementmechanism, and 2D longitudinal models were created to in-vestigate longitudinal migration of liquefied soil under thetunnel and post-liquefaction consolidation settlements. Thekey elastic and plastic stiffness parameters for the modelsare dependent on stress level and density. The stress compo-nent is directly accounted for in the analysis procedure, andthe density component is based on corrected standard pene-tration test (SPT) blow count (N1)60. Major soil parametersused in the numerical models are given in Table 1. The mostcritical soil property, (N1)60, for the loose sand, fill, andgravel was selected based on the field cone penetration test(CPT) sounding results at the tunnel site. Figure 5 shows abasic transverse model with horizontal riverbed. The tunnelwas modelled as elastic beam elements. A numerical modelwith a ground slope on one side was created by modifyingthe geometry of the basic model. The numerical models withdensification zone or gravel drain treatment adjacent to thetunnel were created by increasing the (N1)60 value in thedensified zones or changing the permeability of the soil col-umns representing gravel drains. After evaluating several op-tions, ground treatment using densification by stone columnsand seismic gravel drains on each side of the tunnel waschosen to reduce the risk of tunnel flotation and excessivelateral displacement. In addition to ground treatment, thetunnel section will be reinforced structurally to improve itsductility and to control the size of cracking. More detaileddescriptions of the geotechnical and structural seismic retro-fit design and analysis of the tunnel are given in Yang et al.(2003) and Taylor et al. (2003).

© 2004 NRC Canada

922 Can. Geotech. J. Vol. 41, 2004

Fig. 1. George Massey Tunnel location plan.

© 2004 NRC Canada

Yang et al. 923

Fig. 2. Typical cross section of the tunnel (not to scale). RC, reinforced concrete.

Fig. 3. Generalized soil profile along the tunnel (not to scale).

Fig. 4. Firm ground design response spectra with 5% damping.

The effective contact pressure on the underside of the tun-nel is close to 18 kPa, which is much less than the effectiveoverburden stress in the soil at the same elevation adjacentto the tunnel. Field evidence and centrifuge and shaking ta-ble tests (Kimura et al. 1995; Nakata et al. 1991) for tunnelsin a similar situation have shown that liquefaction results ina reduced strength and stiffness of sand soils that can causethem to “flow” underneath a tunnel (like a reversed bearingfailure). Figures 6a and 6b show the tunnel flotation andlateral movement mechanism under the existing ground con-dition predicted by the soil–structure interaction analyseswhen liquefaction occurs. In Fig. 6a with level ground, thetunnel moved 0.57 m upward and very little laterally at theend of the 80 s earthquake shaking. In Fig. 6b with a 9°slope, the tunnel moved 0.25 m upward and 0.97 m laterallyat the end of shaking. When a slope exists, the lateral move-ment of the liquefied soils dominated the tunnel displace-

ment (Fig. 6b). High pore pressure generated by liquefactionadjacent to the tunnel also causes water to flow to the lowerpressure area under the tunnel and slowly push it up. Thislatter effect takes time and continues after the end of earth-quake shaking. It is also supported by the centrifuge testdata presented later in the paper.

The 2D longitudinal numerical models used the stratifiedsoil profile (Fig. 3) interpreted from the site investigationsand CPT tests. The densification zones and gravel draintreatment adjacent to the tunnel were not modelled by the2D longitudinal model. Their effects were studied by the 2Dtransverse models. The immersed tunnel, two ventilationbuildings, and two approaches were included in the longitu-dinal model. The immersed tunnel was represented by con-tinuous weightless beam elements with appropriate sectionshear and bending stiffness, sandwiched by two layers ofelastic soil elements having the buoyant weight of the tun-

© 2004 NRC Canada


Native sand Native siltRock andgravel fill

Sandfill overtunnel

Jettedsand fill

Soil parameters for all analysesSPT (N1)60 (blows/300 mm) 2–15a — 25 10 5–6Cohesion (Pa) — 8×104–10×104 — — —

Parameters for effective stress analysisPeak friction angle, φf (°) 34 — 45 34 34Constant-volume friction angle, φcv (°) 33 — 33 33 33

Parameters for total stress analysisInternal friction angle, φ (°) 34 — 45 34 34Elastic bulk modulus, B (Pa) 3.0×107 – 6.5×107 1.4×108 – 1.7×108 2.7×107 1.3×107 1.0×107

Shear modulus at small strain, Gmax (Pa) (Beaty andByrne 1999)

—b —b —b —b —b

B/Gdyn 10.0c 10.0c 10.0c 10.0c 10.0c

B/Gliq 50.0d 50.0d 50.0d 50.0d 50.0d

Mobilized residual strength, Sr (Pa) (Beaty 2001) —e —e —e —e —e

Residual shear strain, γr Sr /Gliq Sr /Gliq Sr /Gliq Sr /Gliq Sr /Gliq

a(N1)60 of native sand was randomly varied with a mean of 6 and a coefficient of variation of 30%.bGmax = 440[(N1)60]

1/3Pa(σ m′ /Pa)1/2, where Pa is atmospheric pressure and σ m′ is mean effective confining stress.

cFor saturated, nonliquefied elements, where Gdyn is equivalent shear modulus of nonliquefied soil during cyclic loading.dFor saturated, liquefied elements, where Gliq is post-liquefaction shear modulus during loading.eSr = σ vo′ 0.025 exp[0.16(N1)60], where σ vo′ is initial vertical effective stress.

Table 1. Major soil parameters used in the numerical analyses for the tunnel design.

Fig. 5. A basic transverse model showing mesh, boundary conditions, and material sections.

nel, which is much lighter than the surrounding soil. For thelongitudinal model, both elastic and inelastic beam elementswere studied. Each of the elastic soil layers had one half ofthe tunnel thickness and appropriate nonliquefied soil stiff-ness. These elastic soil elements were nonliquefiable. Thelongitudinal models were analyzed using both total stressand effective stress methods. The results from both analysesshowed that the loose sand layers under the tunnel and theriverbanks liquefied and that these liquefied soils movedtowards mid-river. This caused the tunnel midsections toheave upwards slightly. The liquefied soils also consolidatedduring the post-liquefaction and post-earthquake settlementphase. A differential settlement of up to 0.6 m within a dis-tance of 250 m along the tunnel was predicted from the lon-gitudinal models.

In the longitudinal models, the magnitude of tunnel move-ments may be overpredicted (as opposed to the real three-dimensional (3D) situation) because the effects of soildensification beside the tunnel were not taken into account.Nevertheless, the longitudinal models gave insight into thecharacteristics of soil liquefaction and its mechanism of mi-gration under the tunnel.

Need for numerical model verification andcalibration

During the final design phase, questions arose as to the re-liability of the numerical predictions, especially consideringthe high cost of the proposed ground improvement. Justifica-tion of the numerical analyses and viability of the ground

improvement design were needed. Seismic simulation ofthe tunnel using the centrifuge at Rensselaer PolytechnicInstitute (RPI), Troy, NY (http://www.rpi.edu/~dobryr/centrifuge), was chosen after considering different physicalmodelling options, which included centrifuge testing, shak-ing table testing, and upward hydraulic gradient testing.

© 2004 NRC Canada

Yang et al. 925

Fig. 6. (a) Tunnel flotation observed in total stress analysis (zoom view). (b) Ground and tunnel displacements observed in effectivestress analysis (zoom view).

D10 (mm) 0.09D50 (mm) 0.15Specific gravity, Gs 2.67Maximum void ratio, emax 0.887Minimum void ratio, emin 0.511Maximum dry unit weight (kN/m3) 17.33Minimum dry unit weight (kN/m3) 13.87Water permeability, k (m/s)

At Dr = 40% 6.6×10–5

At Dr = 60% 5.6×10–5

At Dr = 91% 2.3×10–5

Test viscous pore fluid, k (m/s)a

At Dr = 40% 2.6×10–6

At Dr = 90% 9.4×10–7

Internal friction angle (°)At Dr = 40% 33At Dr = 60% 36

Note: All of the listed values are based on laboratory tests at 1gconditions.

aRPI laboratory test results at 1g.

Table 2. Material properties of Nevada No. 120 sand (afterArulmoli et al. 1992).

Three small-scale tunnel models embedded in saturatedloose sand without and with densification or gravel drainagezone treatment were tested in the centrifuge to check andcalibrate the numerical model.

This paper will focus on the centrifuge testing and the nu-merical model calibrations using the centrifuge test data.

Design of centrifuge tests

The main objectives of the centrifuge testing were to cali-brate and validate the numerical models. The following spe-cific goals were set during the design of the centrifugemodels: (i) to understand dynamic behaviour of a 2D (crosssection) tunnel and soil model; (ii) to investigate the extentof liquefaction and liquefaction characteristics; (iii) to ob-serve tunnel flotation, settlement, and lateral movements in asloping ground condition; (iv) to study the effects of ground

© 2004 NRC Canada


Fig. 7. Typical grain-size distribution curves for Nevada and Fraser River sands.

Fig. 8. Sketch showing centrifuge model dimensions (model scale, with all dimensions in centimetres).

Fig. 9. A near-surface time history from SHAKE91 analysis (du-ration 80 s).

densification and gravel drainage zones; and (v) to measurepore pressure generation and dissipation during and follow-ing earthquake shaking.

Similar research was conducted previously by others us-ing both centrifuge model testing (Kimura et al. 1995; Hiro-oka et al. 1995) and shaking table testing (Nakata et al.1991; Tanaka et al. 1995). These earlier tests confirmed thatthe common failure modes of a buried tunnel (or a buriedpipeline) in loose liquefiable backfill consist of a combina-tion of uplift (i.e., upward flotation), rotation, and sliding,similar to those predicted by the numerical analyses(Figs. 6a, 6b). The available literature also describes thestudies conducted to mitigate the tunnel or pipeline failurescaused by earthquake-induced soil liquefaction. The counter-measures against soil liquefaction and structure failureincluded ground densification around the buried structures,gravel drain walls along the sides of the structures, sheet pilecutoff walls, and sheet piles with vertical drainage capacityalong the sides of the structures. All these countermeasureswhen properly designed were effective in mitigating soil liq-uefaction related failures. Results from the soil–structure in-teraction analyses with the different ground retrofit schemesand the associated costs were evaluated. The methods ofground densification and gravel zones were selected for cen-trifuge testing. A test with no treatment was also conducted.

A 1:100 scale tunnel model immersed in saturated loosesand and viscous methylcellulose fluid (25 times the viscos-ity of water) was selected for testing. A 380 mm deep,710 mm long, and 356 mm wide laminar rectangular boxwas used as the model container. Due to restrictions of thesize of the laminar box and the maximum centrifugal accel-eration that can be safely achieved with the chosen modelcontainer, and considering the soil–tunnel horizontal dimen-sion aspect ratio, the scaled model had a smaller prototypethan the actual tunnel. The prototype tunnel simulated by thecentrifuge tests had a cross section of 18 m (width) by 9 m(height) and an effective contact pressure of 5.6 kPa at the

underside of the tunnel, compared with the 24 m width and18 kPa effective contact pressure of the actual tunnel.

The model tunnel was made of aluminum. The actual tun-nel has a bitumen waterproof coating protected by timberplanks. The tunnel–soil interface friction coefficient of thecentrifuge models is roughly equal to that of the actual tun-nel.

Nevada No. 120 sand was used in the models. This is afine, uniform, subrounded, clean sand with material proper-ties as given in Table 2. Its grain-size distribution is essen-tially parallel to that of Fraser River sand (field soil) butfiner by a factor of about 2. In Fig. 7, the effective grain size(D10, in mm) for the Fraser River sand is 0.19 mm, whereasD10 for the Nevada sand is 0.09 mm. The permeability of theFraser River sand would be roughly four times that of theNevada sand based on the Hazen (1930) empirical equation,i.e., coefficient of permeability k (in cm/s) = c(D10)

2, wherec is a constant with a value in the range of 1.0–1.5. The per-meability of the Nevada sand, when saturated with viscousfluid (a methylcellulose solution having a viscosity 25 timesthat of water), would be 4 × 25 = 100 times less than that ofthe Fraser River sand. At 100g, permeability increases by afactor of 100. Therefore the permeability of the Nevada sandused in the centrifuge tests approximated the permeability of

© 2004 NRC Canada

Yang et al. 927

Fig. 10. A typical instrumentation layout (model scale, with all dimensions in centimetres). Lh, horizontal transducer; Lv, vertical trans-ducer; Dr, relative density of soil.

Fig. 11. Numerically predicted displacement vectors at the endof shaking for model 2.

the Fraser River sand that surrounds the existing tunnel. Thedrainage gravel used in one of the models was subangular,2.8–4.75 mm in diameter (with a D10 of around 3 mm), andwith a water permeability at 1g of 6.8 × 10–2 m/s.

The final centrifuge model configurations were kept sim-ple to ensure that they were suitable for numerical calibra-tion and validation purposes. Three tests were conducted:one with no ground retrofit (model 1), one with 10 m widedensification zones on each side of the tunnel (model 2), andone with 10 m wide walls of pervious gravel material oneach side of the tunnel (model 3). Figure 8 shows a sketchof the centrifuge model dimensions. All three models weretilted 2° during the tests to simulate a sloping ground condi-tion at the riverbed.

Centrifuge testing procedure

The centrifuge testing procedure, which includes prepara-tion and placement of sand, gravel, and tunnel and control ofsoil density for the three models tested, is described in detailin Adalier et al. (2002, 2003). Some important aspects re-lated to numerical modelling are reiterated herein.

The one-dimensional (1D) input horizontal motion used incentrifuge testing was the motion taken at the underside ofthe tunnel from 1D site response analysis obtained by propa-gating the design earthquake motions from the firm groundelevation through a 300 m thick soil column, using the com-puter program SHAKE91. Figure 9 shows the near-surfacetime history selected for centrifuge testing. The time historyrecord had a duration of 80 s and a PGA of 0.156g. The 1Dbase horizontal excitation that was delivered by the shakeron the centrifuge had slightly different frequency content be-cause of mechanical limitations. The very high and very lowfrequency content was filtered out from the record to becompatible with the limitations of the shaker. The modifiedmotion still had an overall energy level similar to the motionshown in Fig. 9. The dynamic (earthquake shaking) portionof the tests lasted only 0.8 s on the centrifuge due to scalingof time by 1/100. The total duration of the centrifuge testswas about 300 s, however, to allow time for pore pressuredissipation and consolidation of the liquefied soils.

The following instrumentation was monitored during thetests: (i) pore pressure transducers (PPT) located in loosesand, densification zones, and gravel zones; (ii) accelerome-ters located at the base of the laminar box, in sand, at theground surface, and on the tunnel; and (iii) linear variabledisplacement transducers (LVDT) located at ground surface,on the tunnel, and attached to the rings of the laminar box. Atypical instrumentation layout is shown in Fig. 10.

Spaghetti noodles were embedded in the foundation soilbefore testing to provide vertical marker lines to measure theinternal deformations of the soils. Detailed manual measure-ments of the model surface and box ring deformations weretaken at the end of each test. Then the model was left to par-tially dry for 3–4 days. The specimen was finally dissectedcarefully to measure final locations of the spaghetti noodles,accelerometers, and pore pressure transducers. Photographswere taken before and after each test, and detailed visualobservations were made.

Class A predictions of centrifuge tests

Fully coupled effective stress analyses with the programFLAC and the subroutine UBCSAND were used to makeclass A predictions (predictions made prior to conductingthe tests) of the centrifuge tests, including earthquake-

© 2004 NRC Canada


Output parameterScaling factor(model: prototype)

Model 1(loose sand)

Model 2(10 m widedensification)

Model 3(10 m widegravel zone)

Peak tunnel heave (m) 1:100 0.25 (0.27) 0.13 (0.14) 0.12 (0.04)Peak tunnel lateral movement (m) 1:100 0.59 (0.68) 0.50 (0.35) 0.40 (0.30)Maximum soil displacement (m) 1:100 1.52 (1.50) 1.20 (1.30) 1.03 (1.10)Peak tunnel horizontal acceleration (g) 100:1 0.10 (0.11) 0.13 (0.08) 0.095 (0.095)

Note: Numbers in parentheses are the results from the centrifuge tests.

Table 3. Results from class A predictions of centrifuge models presented in prototype scale.

Fig. 12. Displaced stacked rings of the laminar box containingmodel 3.

© 2004 NRC Canada

Yang et al. 929

induced tunnel movements and pore pressure generation anddissipation.

The numerical models of the centrifuge tests were built atmodel scale. The force and flow in the numerical modelswere allowed to reach static equilibrium under gravitationalacceleration (1g). Higher gravitational fields between 1g and100g were then applied to the numerical models in eightstages. At each stage, the force and flow were allowed toreach equilibrium. Consolidation and geometry change ef-fects with increasing gravity were taken into account in themodels until 100g was reached. The gravitational field was

inclined 2° from the vertical plane to simulate the slope ap-plied to the centrifuge model container. The original inputmotion shown in Fig. 9 was used in the class A predictions,as no actual recorded centrifuge input base motions wereavailable at the time. The input motion was applied parallelto the base of the numerical models.

Figure 11 shows the deformed grid and displacement vec-tors at the end of earthquake shaking for model 2. A sum-mary of results from the class A predictions of the threecentrifuge tests is shown in Table 3. The actual centrifugetest results are also shown in Table 3 in parentheses. The

Fig. 13. (a) Recorded accelerations (accel) from model 1. (b) Recorded accelerations (accel) from model 2. (c) Recorded accelerations(accel) from model 3.

class A predictions were in close agreement with the actualtest results, with respect to tunnel upward and lateral move-ments, soil displacement, and tunnel acceleration.

Results of centrifuge model tests andcomparison with class A predictions

The centrifuge test results and numerical analysis resultsare presented and discussed herein using prototype scales,unless otherwise noted.

Figure 12 shows a post-test photograph of the displacedstacked rings of the laminar box containing model 3. Mea-

surement of displacements of the rings gave an indication ofsoil deformations at the two vertical boundaries. The test re-sults are shown in Figs. 13–15. Note that earthquake shaking(the input motion) lasted 80 s (prototype scale) (so the accel-eration records in Fig. 13 are presented for the first 80 s),and the total test duration with detailed recording lasted90 000 s (prototype scale). Only the initial 300 s portion(prototype scale) of other recorded data is plotted in Figs. 14and 15.

The acceleration records (Fig. 13) revealed the followingfeatures regarding the dynamic behaviour of the tunnel andsoil system:

© 2004 NRC Canada


Fig. 13 (continued).

(1) Attenuation of the horizontal input motion occurred at thetunnel. This is shown by comparing the accelerometerreading a10 (tunnel horizontal) with readings a1 and a2 re-corded at the base of the model. Readings of accelerome-ters a1 and a2 should be the same, as they are both on therigid base of the centrifuge box. The ratios of the peak ac-celerometer reading a10 to the peak accelerometer readinga1 for the three tests shown in Fig. 13 are 0.11/0.1561 =0.7, 0.073/0.1561 = 0.5, and 0.09/0.1561 = 0.6, respec-tively. The attenuation is believed to be due to base isola-tion caused by the liquefied soil around the tunnel.

(2) Directional bias and dilation (suction) induced spikesoccurred in the upslope liquefied soil as shown by one-sided spikes in the accelerometer reading a12. Less biaswas observed in the downslope accelerometer a9 due toless dilation effect in the downslope liquefied soil.

The displacement transducer readings (Fig. 14) indicatedthe following features regarding the tunnel and soil move-ments:(1) The tunnel and soil vertical (Lv(2), Lv(4), and Lv(5)) and

horizontal (Lh(3), Lh(6), and Lh(7)) movements occurredmainly within the first 40 s of earthquake shaking.

© 2004 NRC Canada

Yang et al. 931

Fig. 13 (concluded).

© 2004 NRC Canada


Fig. 14. (a) Recorded displacements (Displ.) from model 1. (b) Recorded displacements (Displ.) from model 2. (c) Recorded displace-ments (Displ.) from model 3. Lv, vertical transducer; Lh, horizontal transducer.

(2) Only minor consolidation settlement (Lv(5)) and minorlateral spreading (Lh(6)) of the liquefied soil were ob-served during the post-earthquake phase.

Measured excess pore pressures are shown in Fig. 15.Also shown are excess pore pressure ratio values, Ru =u/σvo′ , where u is the excess pore pressure, and σvo′ is theinitial vertical effective stress. Ru = 0 indicates zero excesspore pressure, and Ru = 1 indicates zero effective stress anda state of complete liquefaction. Ru values in excess of 0.85are indicative of a large loss in stiffness and strength and es-sentially a state of liquefaction. These excess pore pressuresand the vertical marker lines indicated the following:

(1) Liquefaction appeared to initiate near the soil surface andpropagate downwards. Figure 15d shows that liquefactionat the depth of 5 m took place first at 6.4 s with Ru >0.93. Liquefaction at the depth of 10 m followed closelyat 6.6 s with Ru = 1.0. The peak Ru at depths of 15.5 and21 m occurred at 8.3 and 18.5 s, respectively. Full lique-faction did not take place at these depths in loose sand(peak Ru = 0.75 and 0.61, respectively), however.

(2) The groundwater flow mechanism and associated tunnelflotation observed in Figs. 6a and 6b are supported bythe pore pressure data (Fig. 15a) and the tunnel move-ment (Fig. 14a) obtained from the centrifuge test withno ground treatment (model 1). Pore pressure transduc-ers P5, P6, P9, P10, P11, P12, and P13 around the tun-nel reached their peak readings at 7–9 s of shaking,roughly the same time of the peak acceleration shown inFig. 9. The loose sand around the tunnel started to liq-uefy at this time and move towards the lower pore pres-sure zone (shown in pore pressure readings P7 and P8of Fig. 15a) beneath the tunnel. This caused the tunnelto move 0.27 m upward (shown in displacement trans-ducer reading Lv(4) of Fig. 14a) at the end of testing.

(3) Only the upper 10–12 m (out of 25 m) of loose sand (P5and P10 readings in Figs. 15a and 15b and P10 readingin Fig. 15c) and the very loose sand layer directly underthe tunnel (P7 and P8 readings) liquefied.

The effects of densification and gravel zones on tunnelflotation and horizontal movements measured from the threecentrifuge tests are shown in Figs. 16 and 17 and Table 3.Both densification and gravel zones immediately along thesides of the tunnel were effective in reducing the tunnelmovements, although with a similar treatment width thegravel zone method was slightly more effective than thedensification method. This is likely due to the high perme-ability of the gravel zones which limited the buildup of ex-cess pore pressure as shown in the pore pressure transducerreadings P4, P6, P9, P12, and P13 of Fig. 15c.

The final deformations of the tunnel and soils at the endof three centrifuge tests mapped after the drying and dissec-tion procedure are shown in Fig. 18. The tunnel deforma-tions shown in Fig. 18 do not necessarily represent the peaktunnel heave, as the tunnel settlement during the post-earthquake phase (due to excess pore pressure dissipation)had offset some tunnel heave. Peak tunnel heave and lateralmovements are given in Figs. 16 and 17.

The aforementioned features observed during centrifugetesting were generally in agreement with the class A predic-tions. The predicted tunnel and soil movements and the tunnelhorizontal accelerations matched the test results reasonablywell, as shown in Table 3. Additional numerical model cali-brations were conducted after the centrifuge tests, however, tofine-tune the soil parameters and the numerical models.

© 2004 NRC Canada

Yang et al. 933


© 2004 NRC Canada


Fig. 15. (a) Recorded excess pore pressures (EP Pre.) from model 1. (b) Recorded excess pore pressures (EP Pre.) from model 2.(c) Recorded excess pore pressures (EP Pre.) from model 3. (d) Normalized excess pore pressures (EP Pre.) for model 1. d, depth.

© 2004 NRC Canada

Yang et al. 937


Fig. 16. Class A predictions and measured and calibrated tunnelvertical movements at Lv(4) showing effects of densification andgravel zone: (a) model 1, (b) model 2, and (c) model 3.

Fig. 17. Measured and calibrated tunnel horizontal movements atLh(3) showing effects of densification and gravel zone: (a) model1, (b) model 2, and (c) model 3.

© 2004 NRC Canada


Fig. 18. Calibrated displacements (values in parentheses): (a) model 1, no ground improvement; (b) model 2, with densification zones;and (c) model 3, with gravel zones.

Numerical model calibrations

Numerical model calibrations were carried out by usingthe base motions from the three centrifuge tests. The re-corded base motions among the three tests were slightly dif-ferent, even though the input motion was same. The goal ofthe numerical calibrations was to fine-tune the model param-eters so that calculated and recorded displacements, acceler-ations, and pore pressure responses would match.

The final calibrations should provide the design engineerswith a better understanding of the soil parameters critical tothe prediction of soil liquefaction and tunnel movement be-haviour. The soil density as represented by (N1)60 values(corrected SPT blow counts) for loose sand and gravel weredetermined to be the most important soil parameters. Elasticand plastic soil moduli used in the analyses were functionsof (N1)60. The (N1)60 values used in the class A predictionswere determined based on an empirical relationship of(N1)60 = 32(Dr)

2, where Dr is the relative density of soil.This empirical equation was developed for Nevada sandfrom cyclic simple shear tests reported in VELACS projectdocuments and by University of California, Berkeley(Arulmoli et al. 1992; Kammerer et al. 2000). The centrifugetests showed that soil liquefaction first occurred near the soilsurface and progressed downwards. This evidence suggeststhat the soils were densified with increasing depth prior tothe earthquake shaking due to consolidation from the centri-fuge spin-up. The settlement of the model soil recordedduring centrifuge spin-up confirmed the occurrence of den-sification of the loose sand. No in-flight penetration test datawere available, however, to verify the density variation withincreasing depth within the model. For this study, the (N1)60values were adjusted during the final calibrations to be in-creasing with an increase in depth. Table 4 shows the (N1)60values before and after final calibrations.

Selected calibration analysis results are shown inFigs. 16–20. The final calibration analyses yielded resultsonly slightly different from the class A predictions. Fig-ure 16 shows the class A predictions (before calibration) oftunnel vertical movements, as compared with the centrifugeresults and the calibrated numerical predictions. Changesmade in the input to the calibrated numerical models includethe following: (i) the three recorded base motions were usedas input motions in lieu of the original input motion; and(ii) the revised (N1)60 values that allowed for soil densifi-cation during spin-up were used.

The tunnel movements were calibrated to be slightly onthe conservative side, as shown in Figs. 16–18. The ratiosof the calibrated numerical results to the centrifuge resultsvaried for the different numerical models. Overall, the final

predicted movements were in good agreement with the mea-sured data from the centrifuge tests.

Comparison of the accelerations in Fig. 19 shows that therecorded acceleration responses at the tunnel (accelerometerreadings a10 and a11), including the attenuation effectcaused by liquefaction, were simulated well by the numeri-cal models. The directional bias and dilation induced spikesoccurring in the upslope liquefied soil shown in a12 ofFig. 19c were also captured in the numerical modelling, al-though they were not as distinct. The spikes in the accelera-tion response are believed to be due to dilation. This results

© 2004 NRC Canada

Yang et al. 939

Loose sand (Dr = 40%)Dense sand and densification zone(Dr = 90%) Gravel zone (Dr = 40%)

Before After Before After Before After

5; constant 6–14; increasingwith depth



Table 4. Corrected SPT blow count (N1)60 values before and after the final numerical calibrations of centri-fuge models.

Fig. 19. Calibrated accelerations: (a) a10, tunnel horizontal mo-tion, model 1; (b) a11, tunnel vertical motion, model 1; and(c) a12, directional bias in liquefied sand, model 3.

in a sudden reduction in excess pore pressure and a relatedsudden increase in shear strength which curtails downslopemovement. Increasing the dilation in the loose sand modelwould likely result in a better match with the measuredhigher accelerations.

Comparison of the excess pore pressure generation anddissipation in Fig. 20 shows that the excess pore pressure re-sponses in model 1 (both P6 and P7 in loose sand), model 2(P6 in the densification zone and P7 in loose sand), andmodel 3 (P5 in loose sand and P6 in gravel) were simulatedreasonably well by the numerical models. The negative ex-cess pore pressure seen in P6 of Fig. 20b was caused by thedilative behaviour in the densified sand. It appears that thenumerical model slightly overpredicted the dilative behav-iour in the dense sand.

The centrifuge test results and numerical analyses led to afinal retrofit design that included both ground densificationusing vibroreplacement stone columns and seismic gravel

drains adjacent to the densified zones (Fig. 21). The widthof densification zones and the location of seismic graveldrains (e.g., at the outer edge, in the middle, or at the inneredge of the densified zones) were selected based on para-metric studies using the numerical models. Cost, structuralperformance (mainly crack width and tunnel leakage predic-tions), and the various uncertainties in the design were con-sidered in selecting the densification width and location ofdrains.

Conclusions

The centrifuge tests confirmed that the design earthquakemotion would likely trigger liquefaction in the loose sandand cause upward and lateral tunnel movements. These weremajor concerns during final design. The centrifuge tests alsoconfirmed the ability of the numerical models to predict thesoil and tunnel behaviour. The class A numerical predictions

© 2004 NRC Canada


Fig. 20. Calibrated excess pore pressures (EP pressure): (a) model 1, no ground improvement; (b) model 2, with densification zones;and (c) model 3, with gravel zones.

were in good agreement with the centrifuge test results. Thecentrifuge test results were used to fine-tune the numericalmodels for use in the final ground retrofit design.

The centrifuge test results demonstrated that both grounddensification and gravel drainage zones were effective inremediation of earthquake-induced tunnel movements. Theseresults led to a final retrofit design that included both grounddensification using vibroreplacement stone columns and en-hanced drainage using seismic gravel drains adjacent to thedensified zones.

Centrifuge testing gave the design engineers confidence inusing the numerical analysis results to assist the ground im-provement design.

Acknowledgements

The writers wish to thank Mr. William Szto and Dr. DonGillespie from the Ministry of Transportation of British Co-lumbia for permission to publish this paper and their coordi-nation and technical contribution during the project. Thewriters thank the project manager Dr. Peter R. Taylor ofBuckland & Taylor Ltd., the senior structural engineerDr. Hisham Ibrahim of Buckland & Taylor Ltd., and thegeotechnical specialist Dr. Blair Gohl of Pacific Geo-dynamics Inc. for their technical assistance and special con-tributions to the work. The peer reviewers were Prof. PeterM. Byrne (also a coauthor) and Prof. Don Anderson ofthe University of British Columbia. Special thanks go toDr. Ricardo Dobry of Rensselaer Polytechnic Institute andDr. Ryan Phillips of C-CORE, who were part of the centri-fuge testing team for the project. The design team includedBuckland & Taylor Ltd. (Primary consultant), Trow Associ-ates Inc., Pacific Geodynamics Inc., Ben C. Gerwick Inc.,AMEC, Levelton Engineering, Dr. W. Tseng of InternationalCivil Engineering Consultants Inc., and Dr. M. Collins of theUniversity of Toronto.

References

Adalier, K., Abdoun, T., Dobry, R., and Phillips, R. 2002. GeorgeMassey Tunnel seismic safety retrofit final design — RPI centri-fuge test results. Department of Civil and Environmental Engi-neering, Rensselaer Polytechnic Institute, February 2002.

Adalier, K., Abdoun, T., Dobry, R., Phillips, R., Yang, D., andNaesgaard, E. 2003. Centrifuge modeling for seismic retrofit de-sign of an immersed tube tunnel. International Journal of Physi-cal Modeling in Geotechnics, 3(2): 23–32.

Arulmoli, K., Muraleetharan, K.K., Hosain, M.M., and Fruth, L.S.1992. VELACS laboratory testing program — soil data report.The Earth Technology Corporation, Irvine, Calif. Report to theNational Science Foundation, Washington, D.C.

Beaty, M. 2001. A synthesized approach for estimatingliquefaction-induced displacements of geotechnical structures.Ph.D. thesis, University of British Columbia, Vancouver, B.C.

Beaty, M., and Byrne, P.M. 1998. An effective stress model forpredicting liquefaction behaviour of sand. In GeotechnicalEarthquake Engineering and Soil Dynamics III: Proceedings ofa Specialty Conference, Seattle, Wash., 3–6 August 1998.Edited by P. Dakoulas, M.K. Yegian, and R.D. Holtz. AmericanSociety of Civil Engineers, Geotechnical Special Publication 75,pp. 766–777.

Beaty, M., and Byrne, P.M. 1999. A simulation of the Upper SanFernando dam using a synthesized approach. In Proceedingsof Slope Stability and Landslides, 13th Annual Vancouver Geo-technical Society Symposium, Vancouver, 28 May 1999. Van-couver Geotechnical Society. pp. 63–72.

Britton, J.R., Harris, J.B., Hunter, J.A., and Luternauer, J.L. 1995.The bedrock surface beneath the Fraser River delta in BritishColumbia based on seismic measurements. In Current research1995-E. Geological Survey of Canada, Paper 1995-E, pp. 83–89.

Byrne, P.M., Debasis, R., Campanella, R.G., and Hughes, J. 1995.Predicting liquefaction response of granular soils from self-boring pressuremeter tests. In Static and Dynamic Properties ofGravelly Soils, ASCE National Convention, San Diego, Calif.,23–27 October 1995. Edited by M.D. Evans and R.J. Fragaszy.American Society of Civil Engineers (ASCE), GeotechnicalSpecial Publication 56, pp. 122–135.

Byrne, P.M., Park, S.-S., Beaty, M., Sharp, M., Gonzalez, L., andAbdoun, T. 2004. Numerical modelling of liquefaction and com-parison with centrifuge tests. Canadian Geotechnical Journal,41: 193–211.

Gillespie, D. 1991. Massey Tunnel site investigation, 1991. Minis-try of Transportation of British Columbia, Vancouver, B.C.

Hall, P., Broendum-Nielsen, T., and Kivisild, H.R. 1957. Deas Is-land Tunnel. Journal of the Structural Division, ASCE, 83(ST6):1436-1 – 1436-44.

Hazen, A. 1930. Water supply. In American civil engineers hand-book. Edited by M. Merriman, T. Merriman, and T.H. Wiggins.John Wiley & Sons, New York.

Hiro-oka, A., Okamura, M., Takemura, J., and Kimura, T. 1995.Dynamic behaviors of compacted sand surrounded by liquefiedloose sands. In Proceedings of the 1st International Conferenceon Earthquake Geotechnical Engineering. Edited by K. Ishihara.A.A. Balkema, Rotterdam, The Netherlands. pp. 681–686.

Itasca Consulting Group Inc. 2000. Fast Lagrangian analysis ofcontinua (FLAC), version 4.0. Itasca Consulting Group Inc.,Minneapolis, Minn.

© 2004 NRC Canada

Yang et al. 941

Fig. 21. Schematic ground improvement design (not to scale).

© 2004 NRC Canada


Kammerer, A., Wu, J., Pestana, J., Riemer, M., and Seed, R. 2000.Cyclic simple shear testing of Nevada sand for PEER CenterProject 2051999. Geotechnical Engineering Research ReportUCB/GT/00-01, University of California, Berkeley, Calif.

Kimura, T., Takemura, J., Hiro-oka, A., Okamura, M., andMatsuda, T. 1995. Countermeasures against liquefaction of sanddeposits with structures. In Proceedings of the 1st InternationalConference on Earthquake Geotechnical Engineering. Edited byK. Ishihara. A.A. Balkema, Rotterdam, The Netherlands.pp. 1203–1224.

Nakata, H., Miyake, K., and Muraoka, T. 1991. Shaking table testsof submerged tunnel in sandy ground. In Proceedings of the In-ternational Conference on Geotechnical Engineering for CoastalDevelopment: Theory and Practice in Soft Ground – Geo-Coast’91, Yokohama, Japan, 3–6 September 1991. Japan Coastal De-velopment Institute of Technology, Tokyo. pp. 483–486.

Puebla, H., Byrne, P.M., and Phillips, R. 1997. Analysis ofCANLEX liquefaction embankments: prototype and centrifugemodels. Canadian Geotechnical Journal, 34: 641–657.

Tanaka, Y., Komine, H., Tohma, J., Ohtomo, K., Tochigi, H., Abo,H., and Fukuda, S. 1995. Area of compaction to prevent upliftby liquefaction. In Proceedings of the 3rd International Confer-ence on Recent Advances in Geotechnical Earthquake Engi-neering and Soil Dynamics, St. Louis, Mo., 2–7 April 1995.University of Missouri-Rolla, Rolla, Mo. Vol. 1, pp. 269–274.

Taylor, P.R., Ibrahim, H.H., and Yang, D. 2003. Seismic retrofit ofa concrete immersed tube tunnel. In Concrete Structures in Seis-mic Regions: Proceedings of the Federation International duBeton (FIB) and International Association for Bridge and Struc-tural Engineering (IABSE) Symposium, Athens, Greece, 6–8 May2003. TEE Technical Chamber of Greece, Hellenic ConcreteSection, Athens, Greece. CD-ROM. Paper 221.

Yang, D., Naesgaard, E., and Gohl, B. 2003. Geotechnical seismicretrofit design of George Massey Tunnel. In Proceedings of the12th Pan-American Conference on Soil Mechanics and Geo-technical Engineering, Cambridge, Mass., 22–26 June 2003.MIT, Cambridge, Mass. pp. 2567–2574.

numerical model verification and calibration of george massey

Documents