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Physical and numerical modelling of pilefoundations subjected to vertical and

horizontal loading in dry sand

CONFERENCE PAPER SEPTEMBER 2014

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5 AUTHORS, INCLUDING:

Y. S. nsever

Uludag University

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Mehmet Yener zkan

Middle East Technical University

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Tatsunori Matsumoto

Kanazawa University

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Available from: Y. S. nsever

Retrieved on: 06 April 2016

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1 INTRODUCTION

Application of piled raft foundation design isincreasing in the world as an economic foundationsystem to reduce average and/or differential

settlement (e.g. Katzenbach & Leppla 2013;Yamashita 2012). The international CPRF-Guidelinehas been published by the International Society ofSoil Mechanics and Geotechnical Engineering(ISSMGE 2012).In their life time, these foundationsmay also be subjected to lateral loads such as windsand earthquakes. Experimental studies on piled raftssubjected to horizontal loading were carried out byHorikoshi et al. (2003), Matsumoto et al. (2004),Matsumoto et al. (2010) and so on. However, thedesign framework of piled rafts subjected to lateral

loading has not been established (Matsumoto, 2013).In order to understand the behaviour of piled raftfoundations under vertical and horizontal loading, aseries of vertical load test and cyclic horizontal loadtest on a 3-pile piled raft model were carried out indry sand model ground at 1-g field. Load tests of thecomponents of the piled raft model, such as raftalone and single pile, were also carried to investigatetheir interactions in the piled raft. Numericalmodelling of the load tests were conducted, aimingat obtaining more insight into the behaviour of the

piled raft subjected to vertical and horizontal

loading. A FEM software, PLAXIS 3D, was used forthis purpose. The hardening soil model wasemployed for modelling the sand behaviour.

2 OUTLINE OF MODEL TESTS

In order to investigate the pile model foundationsbehaviour, a series of load tests which includes staticvertical and horizontal loading of model foundations

(single pile, raft alone and piled raft) were consid-ered in the scope of this paper.

2.1 Test set-up

Drysilica sand #6, having a relative density, Dr, ofabout 70 % was used as a model ground. The

physical properties of the sand are summarised inTable 1. The mechanical properties of the sand wereobtained from triaxial CD tests as described later.

Table 1. Properties of model ground.Item Value

Density of soil particles, s(t/m3) 2.66

Maximum dry density, dmax(t/m3) 1.542

Minimum dry density, dmin(t/m3) 1.280

Maximum void ratio, emax 1.079Minimum void ratio, emin 0.725Median grain size,D50 0.423Coefficient of uniformity, Uc 1.880

Model ground was prepared in a laminar box thathad dimensions of 800 mm (in x-direction) x 500mm (iny-direction) with a depth of 530 mm (Figure1). The model ground was prepared by layers (10layers of 50 mm and one layer of 30 mm) in order tocontrol the density of the model ground. Each layerwas tamped until Drreached 70%.

Physical and numerical modelling of pile foundations subjected tovertical and horizontal loading in dry sand

Y.S.Unsever & M.Y. zkanDepartment of Civil Engineering, Middle East Technical University, Ankara, Turkey

T. Matsumoto, S. Shimono & K. EsashiGraduate School of Natural Science and Technology, Kanazawa University, Kanazawa, Japan

ABSTRACT: Vertical load test and cyclic horizontal load test on a 3-pile piled raft model were carried out indry sand model ground at 1-g field to investigate vertical and horizontal bearing mechanisms of the piled raftmodel. Load tests on the raft and single pile were also carried out separately to investigate their interactions onthe piled raft. Numerical modelling of the load tests were carried out, aiming at obtaining more insight into

the behaviour of the piled raft subjected to vertical and horizontal loading. A FEM software, PLAXIS 3D, wasused for this purpose. The hardening soil model was employed for modelling the sand behaviour. The soil

parameters were estimated from a series of consolidated drained triaxial tests of the sand. It is shown from theload tests that the behaviour of the piled raft is not mere summation of the components, but is largelyinfluenced by the interaction of the components as well as the level of the applied load.

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20

255

30

100

240

400

530

VDG-RVDG-L

HDG

LC-RLC-L

150 150

P1 P2 P3

800

Figure 1. Test setup for horizontal loading of piled raft.

Table 2. Properties of the model pile.Item ValueOuter diameter,D(mm) 20.00Wall thickness, t (mm) 1.1

Length,L(mm) 255Cross sectional area,A(mm2)

65.31

2nd moment of inertia,I(mm ) 2926.2Youngs modulus,E (N/mm ) 64000Poissons ratio, 0.31

mm

30

20

40

40

40

40

40

3515

20

SG1

SG2

SG3

SG4

SG5

SG6

vertical straingauges

shear straingauges

SH1-2

255

20

255

30

240

8080

80

80 80 404080

1.1

(a) Single pile (b) Piled raft

Figure 2. Single pile model and piled raft model.

Figure 2a shows the single pile model (SP) madeof aluminium, properties of which are summarised inTable 2. The pile was instrumented with straingauges at six levels to obtain axial forces, bendingmoments and shear forces induced in the pile duringloading tests. Piled raft (PR) model was composedof three model piles and a rectangular raft ofstainless steel having dimensions of 240 x 80 mmwith a thickness of 30 mm (Figure 2b). Centre-to-centre pile spacing, s, was 80 mm, 4 times the pilediameter, D = 20 mm (s/D = 4). The 3 piles wererigidly connected to the raft. Note that the sand

particles were adhered on the pile shaft and the raftbase to increase their friction resistance.

In horizontal loading test of the piled raft,vertical load was applied by placing five lead plates(497 N in total, Figure 1) prior to starting of thehorizontal loading, and then horizontal load wasapplied by means of rotating wooden rods and wiresin a displacement-controlled manner.

The detailed description of the tests is given byUnsever et al. (2014).

2.2 Triaxial CD tests of the sand and modelling

A series of triaxial CD tests of the sand having Dr=70 % were carried out under different confining

pressures, p0 (p0 = 11, 50, 100 and 150 kPa). Inaddition, a cyclic CD was conducted under p0= 100kPa. The soil specimens had a height of 100 mmwith a radius of 50 mm.

The test results, deviatoric stress, q, versus axialstrain, a, and volumetric strain, vol, versus a, are

shown in Figures 3 and 4, respectively. It is seen thatthe initial stiffness increases with increasing p0 andstress-strain relations exhibit non-linearity (Figure 3),and that a relatively large dilatancy occurs (Figure 4).

In order to model numerically the above observedbehaviour of the sand, the Hardening Soil model(HS model) (Schanz et al., 1999) was employed.Principle parameters of HS model are summarised inTable 3. The parameters except for Eoed, m and Rfwere estimated from the cyclic CD testwith kPa100ref

00 pp .

0 2 4 6 8 100

100

200

300

400

500

600

700

800

Silica sand #6

p0=150 kPa

p0=100 kPa (cyclic)

p0=100 kPa

p0= 50 kPa

p0= 11 kPa

Experiments

Hardening soil

Deviatoricstress,q

(kPa)

Axial strain, a(%) Figure 3. Deviatoric stress qversus axial strain a.

0 2 4 6 8 102

1

0

-1

-2

-3

-4

-5

-6

-7

p0=11 kPa

p0=150 kPa

p0=100 kPa (cyclic)

p0=100 kPa

p0= 50 kPa

p0= 11 kPa

Experiments

p0=150 kPa

p0=100 kPa

p0=50 kPa

Hardening soil

Vo

lumetricstrain,

vol

(%)

Axial strain, a(%)

Figure 4. Volumetric strain volversus axial strain a.

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Table 3. Material properties of the sand.Item Value

Secant stiffness,E50(kPa)* 29.56103

One-dimensional stiffness, Eoed(kPa)* 23.65103

Unloading/reloading stiffness,Eur(kPa)* 99.59103

Stress dependency parameter for stiffness, m 0.5Non-linear factor,Rf 0.75Poisson's ratio, 0.19

Internal friction angle, '(deg.) 43.2Dilatancy angle, (deg.) 15.8

* values for a reference stress, ref0

p = 100 kPa

It was assumed that Eoed= E50/1.2. The values ofm and Rf listed in Table 3 were determined so thatthe results of numerical simulations fit to themeasured results.

The results of the numerical simulations of theCD tests are compared with the measured results inFigures 3 and 4. The numerical modelling fairly

simulate the measured results, although the post-peak softening behaviours measured in the CD testsare not simulated using the numerical modelling.

3 NUMERICAL MODELLING OF LOAD TESTS

The numerical study was carried out by threedimensional finite element program, PLAXIS 3D.Figure 5 shows the finite element mesh of thevertical loading of the piled raft model, for anexample. Half of the model foundation and themodel ground were modelled due to symmetricconditions. Interface elements were arranged alongthe pile shafts and at the raft base. The finite elementmesh consists of 10-noded 29570 triangularelements for the piled raft model. Similar FEMmodelling was adopted for the cases of single pileand raft alone. In the case of the single pile, only thecentre pile was modelled without the raft and twoedge piles. Only the raft was modelled without thethree piles for the case of the raft alone.

The model sand ground was modelled throughout

using the HS model having the parameters listed inTable 3. The interface friction angle for the pile shaft

800240

40250

530

(mm)

Figure 5. Finite element mesh of the piled raft model.

and the raft base was estimated as 31.1 degrees fromthe horizontal loading test of the raft alone model onthe model ground.

The raft and the piles were assumed to be linearlyelastic. Although the model piles were hollowcylinders with an end plate, they were modelled bycombination of beam elements surrounded by solidelements, following Kimura & Zhang (2000). In the

hybrid modelling of pile, a large portion of thebending stiffness, EI, and axial stiffness, EA, of thepile are shared by the beam elements, still keepinglarge enough stiffness of solid pile elementscompared to the stiffness of the surrounding ground.The big advantage of the hybrid modelling of pile isthat axial forces, bending moments and shear forcesof the pile can be estimated easily from the factoredvalues of those of the beam elements.

The following FEM analysis procedure wasadopted:

Step 1: K0consolidation of the ground alone.Step 2: Setting the foundation in the model ground

and gravity calculation.Step 3: Calculation of loading process (placing of

weight plates is included, if present).

In the analyses, loading of the model wasperformed by displacement-controlled manner. Thedisplacement of the model foundation was increased

by 0.2 mm increment until 2.00 mm displacement,then the interval was increased to 0.4 mm andanalyses was continued until failure occurred.

4 EXPERIMENTAL AND ANALYTICALRESULTS

4.1 Vertical load test of the single pile model

Figure 6 shows the measured and calculatedrelationships of the pile head load and the pile headdisplacement, w. Both results have similar initialstiffness which is an important criteria in design.Although the calculated maximum capacity is about

67 % of the measured one, the calculated load-settlement relation is very close to the measuredcurve until this load.

3

2

1

00 100 200 300 400 500

Measured

Calculated

Vertical load, V(N)

Settlement,w

(mm)

Figure 6. Vertical load-pile head settlement relationship of thesingle pile.

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250

200

150

100

50

00 100 200 300

w/D 0.01 0.02 0.03 0.04 0.05

Mes.

Cal.

Axial force, Fa(N)

DepthfromG

.L.,z(mm)

Figure 7. Distribution of axial forces along the pile shaft.

The measured and calculated distributions of theaxial forces along the pile shaft at normaliseddisplacements, w/D= 0.01, 0.02, 0.03, 0.04 and 0.05are is given in Figure 7. There is reasonableagreement between the measurements and thecalculations, especially at small displacements.

4.2 Vertical load test of the raft alone model

Figure 8 compares the measured and calculated load-settlement relationships of the raft alone model. Inthe experiment, the maximum load of 3200 N wasattained at w = 8.5 mm. Post-peak softening

behaviour was observed and the residual ultimateload of 2915 N was obtained.

It is seen from Figure 8 that initial stiffness of theraft is simulated very well until w reaches 1.5 mm.After that settlement, the calculated stiffness of theraft is larger than the measurement. The calculatedmaximum load of 2972 N is comparable with the

measured residual load, although the analysis doesnot express the measured softening behaviour.

12

11

10

9

8

7

6

5

4

3

2

1

00 500 1000 1500 2000 2500 3000 3500

Vertical loading of full raft

MeasuredCalculated

Vertical load, V(N)

Se

ttlement,

w

(mm)

Figure 8. Load- settlement relationships of the raft alone.

4.3 Vertical load test of the piled raft model

The measured and calculated relationships of thevertical load and the settlement of the piled raft areshown in Figure 9. The measured and calculatedloads supported by the 3 piles and the raft in the

piled raft are also shown in the figure. It wasobserved in the experiment that the raft load attainsthe peak value of 2684 kN at w = 8.5 mm then

slightly decreases with increasing w. The behaviourof the raft in the piled raft is comparable with that ofthe measured in the vertical load test of the raft alonein Figure 8. In contrast, the behaviour of the piles inthe piled raft is totally different from that of thesingle pile. The load of the 3 piles in the piled raft is1692 N at w= 3 mm and 3184 N at w= 12 mm. Themaximum load of the single pile was 460 N at w= 3mm (see Fig. 6) and 633 N at w= 12 mm. That is,the load of the 3 piles in the piled raft is much higherthan 3 times the load of the single pile. This

tendency becomes significant for larger settlements.It is thought that the load transfer from the raft baseto the ground enhances the pile resistance in the

piled raft due to the resulting increase in the stiffnessand the strength of the soil surrounding the piles inthe piled raft. The calculation results fairly simulatethe above-mentioned experimental results, althoughthe calculated responses of the total load, the raftload and the 3 piles load exhibit bi-linear (elastic-

perfectly plastic) response.The proportion of vertical load carried by the 3

piles and the raft with the change in normalised

settlement, w/D, are given in Figure 10. As it ismeasured, the 3 piles take about 70 % of the appliedload at very early stage of loading, then the load

proportion taken by the 3 piles decreases withincreasing w/D and levels off at a value of 52 %when w/Dis 0.15. The load proportion taken by theraft, of course, has the counter trend. The calculationsimulates well the measured behaviour, although thecalculated proportion of the load by the 3 piles issmaller than the measurement.

12

11

10

9

8

7

6

5

4

3

2

1

00 1000 2000 3000 4000 5000 6000 7000

Total (Mes.) Total (Cal.)

3 piles (Mes.) 3 piles (Cal.)

Raft (Mes.) Raft (Cal.)

Vericaldisplacement,w

(mm)

Vertical load,V

(N)

Figure 9. Vertical load- settlement relationship of the piled raft.

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0.00 0.05 0.10 0.15 0.20 0.250

20

40

60

80

100

3 piles (Mes.)

3 piles (Cal.)

Raft (Mes.)

Raft (Cal.)Proportionofloadcarried

bye

achcomponent(%)

Nomarised settlement of piled raft, w/D

Figure 10. Load sharing of 3 piles and the raft.

0.00 0.05 0.10 0.15 0.20 0.25 0.300

200

400

600

800

1000

1200

P1&P3 (Mes.)

P2 (Mes.)

P1&P3 (Cal.)

P2 (Cal.)

Piles 1 & 3

(Edge piles)

Pile 2

(Centre pile)

Pile

loa

d

(N)

Normalised settlement of piled raft, w/D Figure 11. Vertical loads at edge and centre piles.

The vertical loads taken by the edge piles (P1 andP3) and the centre pile (P2) are plotted against w/Din Figure 11. It was measured that the edge piles (P1and P3) support slightly larger load than the centre

pile (P2) until w/D reaches 0.1, and thereafter P2supports larger load than the edge piles. The abovementioned response of the piles at smaller w/D issimilar to that of a piled raft having a rigid raft in auniform elastic ground. The larger load of P2 atlarger w/D is thought to be due to a larger stresslevel in the soil surrounding P2 caused by loadtransfer from the raft base to the soil.

Although higher initial stiffness of the pilesmeasured in the experiment is not simulated well inthe calculation, the calculation results in Figure 11simulate reasonably well the measured trendqualitatively.

4.4 Horizontal load test of the piled raft model

In the cyclic horizontal load test of the piled raftmodel, a vertical load of 497 N in total was appliedon the raft top prior to the start of horizontal loading.

Although cyclic horizontal loading was applied tothe model, the behaviour in the 1st loading inpositive direction is focused in this particular paper.

The measured and calculated relationships ofhorizontal load, H, and normalised horizontal

displacement, u/D, are shown in Figure 12. Themeasured and calculated resistances of the 3 pilesand the raft in the piled raft are also indicated in thefigure. The horizontal load carried by the 3 pilescontinues to increase with increasing u/D, whereasthe raft resistance tends to level off after u/Dexceedsabout 0.05. When measurements and calculations arecompared, it is seen that calculation overestimates

the experiment results. However, the calculatedtrends of the total load, the 3-piles load and the raftload comparable with the measurements.

0.00 0.05 0.10 0.15 0.20 0.250

100

200

300

400

500

600

700

800

Meas. Calc.

Total

3 Piles

Raft

Horizontalload,

H

(N)

Normalised horizontal displacement, u/D

Figure 12. Horizontal load-normalised horizontal displacementrelationship of the piled raft.

Figure 13 shows the change in the percentage ofhorizontal load carried by the raft against u/D. At the

beginning of the test, the horizontal load carried bythe raft is about 85%, and it decreases with

increasing u/Dand finally becomes constant around25%. The calculation simulates well the measuredbehaviour qualitatively and quantitatively.

0.00 0.05 0.10 0.15 0.20 0.250

20

40

60

80

100

Measured

Calculated

Perc.

ofh

orz.

loadcarriedbytheraft(%)

Normalised horizontal displacement, u/D Figure 13. Percentage of horizontal load carried by the raft.

The axial load carried by each pile of the piledraft is given in Figure 14. Before applying thehorizontal load, edge piles (P1 and P3) carry thesame amount of load, which is smaller than that ofthe centre pile (P2). After starting of the horizontalloading, the vertical load on the front pile (P3) starts

to increase, while the vertical load on the rear pile(P1) starts to decrease, which suggests that thecontact pressure at the raft base increases around P3and decreases around P1. The calculation simulatesthe measured trend of the changes of pile loads.

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0.00 0.05 0.10 0.15 0.20 0.25

-100-50

0

50

100

150

200

250

300

350

400Calc. Meas

Pile 1 (Rear pile)

Pile 2 (Centre pile)

Pile 3 (Front pile)

Pile

axialload

(N)

Normalised horizontal displacement, u/D

Figure 14. Axial load-displacement relationships.

-10 -8 -6 -4 -2 0 2 4

250

200

150

100

50

0

P2 in PR

Depthfrom

G.L.,

z

(mm)

Bending Moment, M(N.m)

Meas. Calc.

u/D= 0.02

u/D= 0.04

u/D= 0.06

u/D= 0.08

u/D= 0.10

Figure 15. Bending moments along the pile shaft for P2.

-10 -8 -6 -4 -2 0 2 4

250

200

150

100

50

0

P3 in PR

Depthfrom

G.L.,

z

(mm)

Bending Moment, M(N.m)

Meas. Calc.

u/D= 0.02

u/D= 0.04

u/D= 0.06

u/D= 0.08

u/D= 0.10

Figure 16. Bending moments along the pile shaft for P3.

The bending moments along the pile shaft for P2and P3 are given in Figures 15 and 16, respectively.The maximum negative bending moment occurs atthe top of each pile. Maximum positive bendingmoment occurs at depths of 0.55-0.60 of the pilelength. It is seen from comparison of Figures 15 and16 that bending moments generated in the front pileare larger than that of the centre pile. The same

behaviours were also observed in the experimentalstudy of Horikoshi et al. (2003). Although thecalculation overestimates the measured bendingmoments, the calculation simulates well the trends ofmeasured distributions in both piles.

5 CONCLUDING REMARKS

A series of vertical and horizontal loading tests onthe single pile, the raft alone and the piled raftmodels were carried out in dry sand to investigatethe resistance mechanisms of the piled raft. FEMmodelling of the experiments were conducted toobtain more insight into the mechanisms and to

explore a possible design approach.It was found from the load tests on the modelfoundations that the behaviour of the piled raft is notmere summation of the components, but is largelyinfluenced by the interaction of the components aswell as the level of the applied load.

The numerical modelling in which soil modelcapable of considering stress dependent behavioursuch as the Hardening soil model, was able tosimulate quantitatively well the experimental resultsof the vertical load tests on the single pile and the 3-

pile piled raft. However, the numerical modelling

simulated qualitatively the horizontal load test on thepiled raft. Consideration of anisotropic nature of thesand, for example, would be needed in future study.

REFERENCES

Horikoshi, K., Matsumoto, T., Hashizume, Y., Watanabe, T. &Fukuyama, H. 2003. Performance of piled raft foundationssubjected to static horizontal loads. IJPMG-International

Journal of Physical Modelling in Geotechnics 3(2): 37-50.International Society of Soil Mechanics and Geotechnical

Engineering. 2012. ISSMGE Combined Pile-Raft

Foundation Guideline (Ed. Katzenbach, R., Choudhury, D.).Katzenbach, R. & Leppla, S. 2013. Economic solutions forgeotechnical challenges like super high-rise buildings andurban tunnelling. Int. Conf. State of the art of pile

foundation and pile case histories, Indonesia, A1-1-A1-12.Kimura, M. & Zhang, F. 2000. Seismic evaluations of pile

foundations with three different methods based on three-dimensional elasto-plastic finite element analysis. Soils and

Foundations 40(5): 113-132.Matsumoto, T., Fukumura, K., Kitiyodom, P., Oki, A. &

Horikoshi, K. 2004. Experimental and analytical study onbehaviour of model piled rafts in sand subjected tohorizontal and moment loading, Int. Journal of Physical

Modelling in Geotechnics, 4(3): 1-19.

Matsumoto, T., Fujita, M., Mikami, H., Yaegashi, K., Arai, T.& Kitiyodom, P. 2010. Load tests of piled raft models withdifferent pile head connection conditions and their analyses.Soils and Foundations50(1): 63-81.

Matsumoto, T. 2013. Implications for design of piled raftfoundations subjected lateral loading. Proc. Int. Symp. on

Advances in Foundation Engineering, Singapore,113-136.Plaxis BV, Netherlands User Manuals, Plaxis 3D . 2013.Schanz, T., Vermeer, P.A. & Bonnier P.G. 1999. The

hardening soil model: Formulation and verification. InR.B.J. Brinkgreve., Beyond 2000 in ComputationalGeotechnics. Rotterdam: Balkema. 281-290.

Unsever, Y.S., Matsumoto, T., Shimono, S. & Ozkan, M.Y.

2014. Static cyclic load tests on model foundations in drysand. Geotech. Eng. Journal of SEAGS & AGSSEA 45(2)(accepted for publication).

Yamashita, K. 2012. Field measurements on piled raftfoundations in Japan". Proc. of Int. Conf. on Testing and

Design Methods for Deep Foundations, Kanazawa,79-96.