Use of Centrifuge Tests for the Validation of Innovative Concepts in FoundationEngineeringJ. GarnierHead of Soil Investigations and Soil Mechanics Division, Laboratoire Central des Ponts et Chaussées, Nantes, FranceA. PeckerChairman Managing Director, Géodynamique et Structure, Bagneux, FranceABSTRACT: The design of important civil engineering structures often introduces new concepts which havenot be validated by previous experience. Extensive use of numerical modeling may help understand thebehavior of structures under extreme loading conditions. However, this modeling requires an experimentalvalidation that only centrifuge tests may offer. This use of centrifuge tests as a validation tool is illustrated forthe foundations of the Rion Antirion bridge (Greece).1 INTRODUCTIONThe design and the conception of important civilengineering structures require the use ofexceptional tools for numerical modeling andexperimental validation. Among the mostappropriate experimental tools, model tests take upa privileged place. The complex behavior ofgeomaterials encountered either in foundation or inthe structure itself (earth dams for instance),requires that model tests be realized with theoriginal material. This requirement, and the strongstress dependence of the behavior of geomaterialsimpose that the gravity field be adequatelyreproduced.This paper illustrates the contribution ofcentrifuge tests in the validation of a newfoundation concept in seismic areas. Thisinnovative foundation concept is presently beingimplemented for the Rion Antirion bridge inGreece. Coupled to extensive numerical modeling,these tests proved the validity of the concept and ofthe theoretical tools developed for design.2 DESCRIPTION OF THE STRUCTUREThe Rion Antirion bridge is a unique structurewhich, within the framework of a B.O.T. contract,has been granted to the French Company Dumez-GTM by the Greek government. This bridge islocated near Patras, 250 km west of Athens, andwill constitute a fixed link between the Peloponeseand the Continent. The main bridge is a threespans cabled-stayed structure, with a total length of2 290 m; the central spans are 560 m long each. Itis located in exceptional environmental conditionscharacterized by a deep water depth (65 m), weakfoundation soils composed of alluvial deposits(alternate layers of silty sands, sandy clays andmedium plasticity clays) and a high seismic designmotion (peak ground acceleration of 0.48 g at theseabed level). (Combault - Morand 1998; Pecker -Teyssandier 1998)).To accommodate these environmentalconditions, the solution chosen by Dumez-GTM,the designer, consists in gravity base caissonsdirectly founded at the seabed level (figure 1).The foundation diameter, at the seabed level, isequal to 90 m extended by a cone with a diameterof 26 m at the sea level. The total height of onepylon is approximately 220 m among which 65 mare below water. The dead weight of one pier is ofthe order of 800 MN. To this permanent load, ahorizontal shear force of 600 MN and anoverturning moment of 20 000 MN.m.m aresuperimposed during the earthquake.
Figure 1: Pier ElevationIn view of the poor quality of the foundationsoils, a direction foundation on the in-situ soilscannot be foreseen and some kind of soilimprovement is required. The final scheme whichhas been chosen is presented in figure 2; it consistsof stiff inclusions driven at close spacing belowand outside the foundation. At the present designstage, 270 hollow steel pipes, 2 m in diameter,20 mm thick and 25 m to 30 m long, are driven at asquare mesh of 7 m x 7 m (figure 2).Figure 2. Pier foundationThese inclusions are not connected to the raft anda free draining gravel bed layer is laid on top of theinclusions below the raft. This layer preventssuction, allows uplift and sliding during theseismic excitation. This arrangement, whichenforces a capacity design philosophy infoundation engineering (Pecker 1998) limits theforces and moments transmitted to thesuperstructure and to the foundation soils.3 OBJECTIVES OF THE CENTRIFUGE TESTSThis totally innovative concept, at least in seismicareas, clearly calls for extensive theoreticalanalyses and experimental validation. Assophisticated as can be, the theoretical andnumerical tools do not have the capacity ofmodeling all the details of the behavior of thiscomplex scheme during an earthquake. Centrifugemodel tests were therefore undertaken with a three-fold objective:- validate the theoretical predictions of theultimate bearing capacity of the foundation undermonotonically increasing shear force andoverturning moment,- identify the failure mechanism of the foundationunder these combined loads,- assess the behavior of the foundation undervarious cyclic load paths.4 DESCRIPTION OF THE CENTRIFUGEFACILITY AND TEST SET UPThe three tests have been performed in the 200 g-tongeotechnical centrifuge at the LCPC Nantes center.The centrifuge was described by Corte and Garnier(1986). It is designed to carry a 2000 kg payload to100 g accelerations, the bucket surface is at a radiusof 5.5 m and the platform has a working space of 1.4m by 1.1 m.All tests have been carried out at 100 g onmodels at a scale of 1/100 (Figure 3). Thedimensions of the corresponding prototype are asfollows :Radius of the circular footing : Bf = 30 mInclusions: Length and diameter: D = 8.5 m andBi = 0.67 mWall thickness t = 6.7 mm (steel)Stiffness EI = 158 MN.m2Thickness of the ballast layer : 1.2 mFigure 3. Model foundation (scale 1/100)FoundationScour protectionMovable mass
The soil material has been sampled at locationof pier N17 of the Antirion approach viaduct andsent to the laboratory. The clay is dried at 60° for 24hours, water is added to bring the water content toabout w = 80% and the slurry is mixed undervacuum during 4 hours to get a homogeneousmaterial. The slurry poured into the cylindricalcontainers, 895 mm wide, is then consolidated infour successive layers. After consolidation, the 350inclusions are jacked into the clay sample at a squaremesh of 23 mm (2.3 m at prototype scale). Theballast layer is simulated by Fontainebleau sandpluviated on top of the clay (Figure 4).Figure 4. Inclusions jacked into the clay bedThe models are instrumented to measure :- Pore pressures at different locations below thefoundation- Soil settlements- Vertical and horizontal displacements of thefooting- Water table level (kept close to the clay layersurface)- Applied loads (shear force and overturningmoment)- Bending moment in 2 or 3 inclusions (Figure 4).A cone penetrometer actuator or a vane testdevice are located onto the container to determinethe clay characteristics during the 100 g tests. Forthe clay used in the tests, a linear relationship hasbeen obtained between CPT tip resistance qc andundrained shear strength Su both measured in flight:Su = qc / 14.7The loads applied to the foundation system havethree independent components:- vertical load V kept constant during the wholetests (V = 8.9 kN in Test 1 and 9.3 kN in Tests 2and 3, in prototype conditions). This load issimulated by the dead weight of the foundation.- horizontal shear force T applied at an elevationh=118 mm (11.8 m in prototype conditions) abovethe foundation level (top of the ballast layer). Ahydraulic servo-actuator is used and the horizontalload T produces an overturning moment T.h.- additional overturning moment M correspondingto a vertical load eccentricity. This overturningmoment is obtained by displacing a carriage and amovable mass using an electric motor and anendless screw (Figure 3). The position of thecarriage is monitored by a displacement transducer.An adjustable counterweight allows to balance allmoments to zero when the movable mass is at itscentral position.A typical loading path is shown in Figure 5below.Figure 5. Typical load pathPath OK-OK’ corresponds to cyclic horizontalshear force T when the vertical load is applied atthe center of the foundation. Paths AB and DC arealso cyclic shear force but the vertical load iseccentric (additional constant overturningmoment). Paths AD and BC are cyclic overturningmoment under a constant horizontal shear force T.Table 1 presents the loading programs of thethree tests. In order to be in undrained conditionsin the clay beds, frequency for cyclic loading ischosen as 0.1 Hz in shear T loading and 0.02 Hz incombined T-M loading.Table 1. Loading programs in Tests 1, 2 and 3 inprototype conditionsTestSequenceTest 1 Test 2 Test 31 10 cyclesT=+/-6.5 MN10 cyclesT=+/-5 MN10 cyclesT=+/-15 MN2 10 cyclesT=+/- 14 MN10 cyclesT=+/-15 MN10 cyclesT=+/-15 MN andM=+/-70 MN.m3 10 cyclesT=+/- 35 MN10 cyclesT=+/-15 MN andM =+/-70 MN.m10 cyclesT=+/-35 MNInstrumented tubesDOOverturning moment MShear force TAKBCK’
4 Static loading Tto failure10 cyclesT=+/-35 MN andM=+/-170 MN.m5 cyclesT=+/-35 MN andM=+/-170 MN.m5 Static loading T up tofailure5 cyclesT=+/-35 MN6 Static loading T up tofailure5 TESTS RESULTSEach clay model is consolidated at 100 g for two tofive hours before starting the loading tests. Theconsolidation ratio at the end of this 100 gconsolidation is close to U=100% in the upperreinforced layers. On the whole clay beds, U rangesfrom 74% to 95% depending on the clay sample.Results of the CPT tests performed in flight inTest 2 at the end of the 100 g consolidation areshown in Figure 6 and compared to the shearstrength profile observed on site:Su = 30 + 2.8 z (Su in kPa, z in m)It is obviously not possible to present all loadingtest results and only some data from Test 2 areshown as examples. First, Figure 7 gives the mainrecorded values vs. time in model units. Theloading sequences 1 to 5 indicated in Table 1 areclearly seen in the shear force T vs. time curve. Figure 6. Shear strength profiles from in flight CPTtests performed into the clay sample (Test 2)02468Verticaldisplacement(mm)-505101520Horizontaldisplacement(mm)0 100 200 300 400 500 600 700 800 900 1000 1100 1200 1300 1400 1500Time (seconde)-500-2500250500Shearforce(daN)D69D68Vertical Displacement of the foundationHorizontal displacement of the foundationLoad sequences1 2 3 4 5Shear force T-20020406080Porepressure(kPa)Pore presures - 128 mm below the clay surface100 mm out ofthe verticalbelow the centerof the foundation0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0-32-28-24-20-16-12-8-4040 20 40 60 80 100 120Undrained shear strength (kPa) with ratio Qc/Cu = 14.8Layer n°1 : saturated sand layerFinal clay tableBallast (Fontainebleau sand)InclusionCPT Tip resistance (MPa)Prototypedepthzp(meter)Cu(kPa)=2.8Z(m)+30
Figure 7. Test 2: horizontal load T, vertical and horizontal foundation displacements, pore pressure vs. time inmodel conditions.An example of relationship observed betweenfoundation displacement and cyclic shear force isshown in Figure 8 corresponding to sequence 2. Inthis case, large hysteresis is seen but displacementsstabilize with cycles.Figure 8. Test 2 : Horizontal displacement of thefoundation vs. cyclic shear force T (sequence 2)Tests have also shown that pore pressures maydevelop during loading. Figure 9 givesmeasurements done during sequence 4 by a PPTplaced 12.8 m deep in the clay and 10 m out of thevertical of the center of the foundation in thedirection of loading. The pore pressure variationdue to the five cycles goes from - 20 kPa to+80 kPa. It is sensitive to both the additionaloverturning moment M and to the shear force T.Figure 9. Test 2: Excess of pore pressure due tocyclic loading 12.8 m deep in the clay and 10 mout of the vertical of the foundation in the loadingdirection (sequence 4).The inclusions participate significantly in theresponse of the foundation system even underrelatively small loads. Figure 10 presents thebending moment profiles observed in inclusion P5during static loading up to failure (sequence 5).This 8.5 m long inclusion is placed at a distance of13.8 m from the center of the foundation in theloading direction (Figure 12). Maximum bendingmoment is located at mid-depth and increases withthe applied horizontal shear force. When the loadreaches T = 45 MN, bending moment in inclusionincreases much more rapidly.Figure 10. Test 2 : Bending moment vs. depth ininclusion P5 during loading sequence 5This critical load about 45 MN is also observedin the load vs. foundation displacement plotted inFigure 11. This figure presents the response of thefoundation system to the final static T loading upto failure (sequence 5 in table 1). At the beginningof sequence 5, the horizontal displacement of thefoundation is 0.48 m due to the previous cyclicsequences 1 to 4.-0.02 -0.01 0.00 0.01 0.02 0.03 0.04Horizontal displacement (meter)-18-16-14-12-8-6-4-2246812141618-20-1001020ShearforceT(MN)PullPush-1.8 -1.3 -0.8 -0.3 0.3-2.0 -1.5 -1.0 -0.5 0.0 0.5Bending moment in the inclusion P5 (MN*m)-8-7-6-5-4-3-2-101Depthintotheclay(meter)P5-4P5-3P5-5P5-2P5-1Clay bedBallast layer Inclusion P5Pull PushShear force T25.0 MN35.0 MN38.1 MN42.0 MN44.0 MN46.0 MN48.1 MN50.2 MN-600 -400 -200 0 200 400 600Additional overturning moment (MN*m)-30-1010305070-40-20020406080Porepressure(kPa)PullPush-40 -30 -20 -10 0 10 20 30 40Horizontal shear force T (MN)-30-1010305070-40-20020406080PullPush051015202530354045505560HorizontalshearforceT(MN)Pull0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0Horizontal foundation displacement (meter)
Figure 11: Test 2: Horizontal shear force vs.foundation displacement in loading sequence 5The loading curve in Figure 11 indicates a verystiff response up to a load about 43 MN at whichthe relative horizontal displacement is only 0.12 m.Displacement increases more rapidly after thisT=43 MN load that corresponds to failure. Thedisplacement controlled loading process continuesup to a horizontal displacement of 1.32 m (1.8 mfrom the beginning of the test). The carried shearforce T is then close to 50 MN.A view of a vertical cut done in the model afterthe centrifuge loading test is shown in Figure 12.The print of the circular footing is clearly seen andthe figure also indicates that clay deformation andinclusions rotation are much larger at the front ofthe footing in the loading direction.Instrumentedinclusion P5LoadingdirectionFigure 12. Test 2 : Vertical cut of the model after theloading test along the footing diameter in theloading direction.All three loading tests of foundation resting onthe reinforced clay have shown that neither theinitial stiffness nor the ultimate resistance tohorizontal loads are affected by the previous cyclicloading sequences even if some have been verysevere.6 COMPARISON WITH THEORETICALANALYSESThe theoretical tools developed to analyze thebehavior of the reinforced soil are based on a limitanalysis method (yield design theory; Salençon1990) and on the finite element method. The yielddesign theory allows the determination of theultimate loads that the foundation can withstandand therefore provides a means of estimating theultimate bearing capacity under various monotonicload paths. The finite element analyses giveadditional information, the displacements and therotations of the foundation, and provide a means ofestimating its seismic behavior.Due to the space limitations, the results of thecentrifuge tests will be compared only to those ofthe yield design theory. Figure 13 presents thekinematic mechanism used in the yield designtheory (Pecker, Salençon 1998). Under thecombined effect of the vertical load, horizontalshear force and overturning moment, thefoundation undergoes a rotation around point Ω,uplift along its left edge and the inclusions underthe right edge are strained and displaced; themaximum bending moment occurs approximatelyat mid-height of the inclusions, at the intersectionof the inclusions and of the kinematic mechanism.These results predicted by the yield design theoryare in very good agreement with those observedduring the centrifuge test: see figures 10 and 12 forcomparison (taking into consideration that infigure 12 the load is acting to the left whereas infigure 13 it is directed to the right).Figure 13. Kinematic mechanismIt is interesting to note that the finite elementanalyses predict the same failure mechanisms.For the three tests carried out in the centrifugefacility in Nantes and for five other tests carriedout in another centrifuge facility in Bordeaux, theresults of which are not reported herein, figure 14presents the comparison between the computedfailure loads (yield design theory) and themeasured ones. In Nantes, those failure loads weremeasured after cyclic loading, whereas inBordeaux, they were measured without any priorcyclic loads. In Nantes, the testing arrangement isidentical between the three tests and the load pathsare varied; in Bordeaux, the load path is identicalin the five tests but the other parameters are varied(number of inclusions, soil strength, vertical load).It appears from figure 14 that the trends arecorrectly predicted, that the predictions andΩωBλΒεα µδF
measurements are in very good agreement for theNantes tests and that the failure loads areunderestimated for the Bordeaux tests. However,during the tests in Bordeaux, it was noticed that atfailure, significant changes in the initial geometryof the system (formation of a soil bulging at thefront of the foundation) occur and that the failureloads were measured at very large displacements.If the "failure" loads are taken at the start of thechanges in geometry, the agreement betweenpredictions and measurements is also very good.Figure 14. Comparison of measured and computedfailure loadsFinally, the cyclic tests have shown that the systemexhibits a significant energy dissipation capacitywith the formation of fat hysteresis loops duringcyclic loading. The equivalent damping ratiocomputed from the hysteresis loops of figure 8 isequal to 18%, whereas the theoretical predictionsfrom the finite element analyses are of the order of15% at the same load level.In addition, even at very high cyclic load levels(75% to 80% of the failure load), the systemexhibits very small degradation; the hysteresisloops stabilize after a few number of cycles(figure 8); the permanent excess pore pressure isonly a small fraction (30%) of the initialhydrostatic pressure.7 CONCLUSIONThe centrifuge model tests have permitted thevalidation of this innovative foundation conceptproposed for the foundations of the Rion Antirionbridge. In addition, they were used to calibrate thetheoretical analyses and numerical tools developedfor the design of the foundations which requiresextensive parametric studies, which cannotobviously be carried out with the model tests.REFERENCESCombault J., Morand P. 1998. The exceptionalstructure of the Rion Antirion bridge in Greece.Proceedings of the IABSE Conference - Kobe(Japan).Corté J.F., Garnier J. 1986. Une centrifugeuse pourla recherche en géotechnique. Bull. Liais. Labo.P. et Ch. 146: 5-28Pecker A., Teyssandier J.P. 1998. Seismic designfor the Rion Antirion Bridge", Proc. Instn. Civ.Eng. Geotech. Engng., 131 pp. 4-11 - Paper11311.Pecker A 1998. Capacity design principles forshallow foundations in seismic areas. Keynotelecture, Proceedings XIth Europ. Conf. onEarthquake Engineering. Eds. Bisch, Labbé,Pecker - Balkema.Pecker A., Salençon J. 1998. Innovative conceptsin foundation engineering. 2ndJapan-UKWorkshop on implications of recent earthquakeson seismic risk, Tokyo Institute of Technology,April 6-9, 1998.Salençon J. 1990. Introduction to the yield designtheory. European Journal of MechanicsA/Solids 9, n° 5, pp. 477-500.0204060801001200 20 40 60 80 100 120Measured failure load (MN)Computedfailureload(MN)