Load Test on Full Scale Bored Piles Groups _ Salgado 2012

8/13/2019 Load Test on Full Scale Bored Piles Groups _ Salgado 2012

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Load tests on full-scale bored pile groups

Guoliang Dai, Rodrigo Salgado, Weiming Gong, and Yanbei Zhang

Abstract: The interactions between closely spaced piles in a pile group are complex. Very limited experimental data areavailable on the loading of full-scale bored pile groups. This paper reports the results of axial static load tests of both full-

scale instrumented pile groups and single piles. The load tests aimed to ascertain the influence of number, length, and

spacing of the piles on pile group load response. Experiments varied in the number of piles in the group, pile spacing, type

of pile groups, and pile length. All piles had a diameter of 400 mm. Two-, four-, and nine-pile groups with pile lengths of

20 and 24 m were tested. As the isolated piles and some piles in the pile groups were instrumented, the load transfer and

loadsettlement curves of both piles in isolation and individual instrumented piles in the groups were obtained. The

interaction coefficient for each pile in the group was back-calculated from the measured data. The interaction coefficients

are shown to be dependent on pile proximity, as usually assumed in elastic analyses, but also on settlement and on the size

of the group.

Key words: pile groups, load transfer, settlement ratio, interaction coefficient.

Rsum : Les interactions entre des pieux placs a proximit les uns des autres dans un groupe de pieux sont complexes.

Trs peu de donnes exprimentales sont disponibles sur les chargements de groupes de pieux foncs, a lchelle relle.

Cet article prsente les rsultats dessais de chargement statique axial sur des groupes de pieux et des pieux individuels

instruments a lchelle relle. Les essais de chargement visaient a confirmer linfluence du nombre, de la longueur et de

lespacement des pieux sur le comportement de groupes de pieux. Les essais ont permis de varier le nombre de pieux dans

un groupe, lespacement entre les pieux, le type de groupe de pieux et la longueur des pieux. Tous les pieux avaient un

diamtre de 400 mm. Des groupes de deux pieux, de quatre pieux et de neuf pieux, avec une longueur de 20 m et de 24 m

respectivement, ont t tests. Puisque les pieux individuels et quelques pieux a lintrieur des groupes ont t

instruments, les courbes de transfert de charge et de tassement total ont t obtenues autant pour les pieux isols que pour

les pieux individuels faisant partie dun groupe. Le coefficient dinteraction pour chaque pieu dans le groupe a t rtro-

calcul apartir des donnes mesures. On a dmontr que les coefficients dinteraction dpendent de la proximit des

pieux, tel que normalement suppos dans les analyses lastiques, mais aussi du tassement et de la taille du groupe.

Mots-cls : groupe de pieux, transfert de charge, ratio de tassement, coefficient dinteraction.

[Traduit par la Rdaction]

Introduction

Infrastructure construction in China has proceeded at a fastpace. Many large-span bridges have been built across theYangtze River, across the Yellow River, and even across theocean. Examples include the Jiangyin Yangtze River Bridge,Runyang Yangtze River Bridge, Sutong Yangtze RiverBridge, Hangzhou Bay Sea Bridge, and Donghai Sea Bridge.As an illustration of this type of foundation in engineeringpractice, the two main-span foundations of the Sutong YangtzeRiver Bridge consist of 131 117 m long piles with diameters inthe 2.82.5 m range with pile caps having plan dimensions of

50 m by 48 m and thickness varying between 5 and 13 m.These bridges all have large spans and consequently requirepiles with large load capacity in pile-based foundation solu-tions. This in turn leads to the use of a large number of pileswith large diameters and long lengths (sometimes referred toas super long piles, which might be generally thought of aspiles with lengths greater than 100 m or slenderness ratio

(length to pile diameter) greater than 100) and an associatedneed for more refined designs. In pursuing more refined de-signs, one of the areas where real data from instrumentedstructures is most lacking is pile groups.

Settlement analyses of pile groups (e.g., Poulos 1968;Butterfield and Banerjee 1971; Randolph and Wroth 1979;Poulos and Randolph 1983; Poulos 1989; Chow and Teh 1991;Lee 1993a, 1993b; Mandolini and Viggiani 1997; Mylonakisand Gazetas 1998; Randolph 2003; Leung et al. 2010) arebased on a variety of approaches, which include boundary-element methods, the hybrid load transfer approach, and thefinite element method. Despite some theoretical advances in

the analyses and prediction of pile group behavior in the lastfew decades, analyses are still based largely on simplificationsof the problem and of the constitutive behavior of the soil.Consequently, static load tests on groups remain the mostreliable means of assessing pile group response under designloads. Some model and field pile group vertical load tests havebeen performed (Whitaker 1957; Hanna 1963; Barden and

Received 8 November 2011. Accepted 31 July 2012. Published at www.nrcresearchpress.com/cgj on 8 November 2012.

G. Dai and W. Gong. School of Civil Engineering, Southeast University, No. 2 Sipailou, Nanjing, Jiangsu, 210096, China.R. Salgado and Y. Zhang. School of Civil Engineering, Purdue University, 550 Stadium Mall Drive, West Lafayette, IN 47907, USA.

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

1293

Can. Geotech. J. 49: 12931308 (2012) Published by NRC Research Pressdoi:10.1139/t2012-087
mailto:[email protected]://dx.doi.org/10.1139/t2012-087http://dx.doi.org/10.1139/t2012-087mailto:[email protected]


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Monckton 1970;Cooke et al. 1980; Briaud et al. 1989; Ismael2001;Bai et al. 2006; Yetginer et al. 2006); however, due tothe difficulties and cost of full-scale load tests, most pile grouptests were scaled down regardless of whether they were per-formed in the field or laboratory. There are few full-scale, insitu boredpile group load tests reported in the literature ( Baiet al. 2006).

The absence of rigorous methods of analysis and the scar-city of full-scale high-quality data from instrumented loadtests on single piles and pile groups means that the use ofconventional methods to design large-scale, heavily loadedpile foundations with very long pile lengths requires extracaution. Some research has been done on super-long singlepiles (Wei 1996; Fei 2000; Yu 2002; Fang 2003; Xie et al.2003). Results from this research show three key characteris-tics of super-long, large-diameter piles that differ from con-ventional piles: (i) pile weight is a larger percentage of pilebearing capacity; (ii) accounting for pile compression becomesmore important in settlement estimation; (iii) mobilization ofbase resistance requires excessive pile head settlements due togreater axial compressibility of the pile, which implies that

ultimate loads will be associated with much greater ratios ofshaft to base resistance. Although most published work onlong piles has focused on single piles, long piles are most oftenused in groups. The typical approach in a project involvinglong piles is to load-test single piles for verification and toestimate pile group settlement by approximate methods.

The present paper aims to start filling this knowledge gap byanalyzing full-scale, in situ bored pile group tests. The aim ofthe tests and analysis is to investigate the following crucialissues in particular: (i) rates of the pile head and pile base loadmobilization with settlement; (ii) variation of the shaft resis-tance, which is responsible for the difference between thesetwo rates, between single piles and piles in a group in variousarrangements; (iii) proportion of load applied on a pile capshared between the piles in the group; (iv) pile group effi-ciency variation with settlement.

Experimental program

Pile configurationsAs summarized in Table 1, the field load tests were per-

formed on: (i) an isolated single pile with length L 20 m;(ii) an isolated single pile withL 24 m; (iii) a two-pile groupwith spacing sp 2.5B (where B is the pile diameter of400 mm) and L 20 m; (iv) a two-pile group with sp 3.0Band L 24 m; (v) a four-pile group with sp 2.5B and L 20 m; (vi) a four-pile group with sp 3.0B and L 24 m;(vii) a nine-pile group with sp 2.5B and L 20 m; (viii) anine-pile group with sp 3.0Band L 24 m. All piles in theexperiments had a diameter, B, of 400 mm. The concrete

strength (fcd

) was 25 MPa for both the piles and the caps. Allcaps were reinforced with 12 mm rebars at a two-way spacingof 150 mm. The concrete reinforcement cover was 70 mm inthe caps and 35 mm in the piles.

In this paper, tests on isolated single piles are denoted DZ. Pilegroup tests are denoted QZ. The suffix L is used to indicate thatthe pile length,L, is 24 m (and so is longer than 20 m, the lengthfor the other set of piles). For example, QZ2 represents the two-pilegroup with shorter pile length and QZ2L indicates the two-pile groupwith longer piles. Finally, a dash after the pile group reference

followed by a number indicates a specific pile within that group. Forinstance, QZ21 is a reference to pile No. 1 in the QZ2 group. Thelayout of the testing area is shown in Fig. 1.

Site characterizationThe test site was located in Jiangning, Nanjing, China, and

the ground at the site was level. The subsoil of the test site is

the QinHuai River floodplain. One auger boring (BH) wasdrilled at the test site to a depth of 29.50 m. This boringshowed a uniform, thick soft clay layer starting at 17 m andextending all the way to the bottom of that boring (and, fromknowledge of the site, beyond). This auger boring depth was11B(B 400 mm, the pile diameter) deeper than the test pilebase for piles with 24 m length. Static cone penetration tests(CPTs) were performed in the vicinity of BH to give a con-tinuous record of the soil resistance with depth. Figure 2showsall four CPT logs available for the site, the locations of whichare identified in Fig. 1. As CPTu is not commonly used inChina, pore-water pressure measurement was not possiblewith the cone used.Table 2summarizes the soil properties ofeach soil layer crossed by the test piles. The subsoil profile

includes multiple layers of silt and clay. The thickness of eachlayer was identified based on CPT data. Soil samples wereobtained by using split-spoon samplers. The ground waterlevel was found at a depth of 2.60 m.

Pile installation and instrumentationThe piles were installed using the slurry method. Pile in-

stallation started on 28 June 2008 and ended on 3 August2008. The piles were drilled to depths of 20 or 24 m andprotruded 0.1 m above ground level. A 0.4, 0.8 or 1.2 m thickreinforced concrete cap was subsequently poured on the pilegroups and single piles. The eight caps were completed all atonce between 513 August 2008.Figure 1shows a layout planof the test piles and pile groups. The pile caps rested on the

ground and may be considered rigid for practical purposes.The pile spacing was 2.5Bin groups QZ2, QZ4, and QZ9 and3.0B in groups QZ2L, QZ4L, and QZ9L. Details of the pilespacing in the groups and dimensions of the pile caps issummarized inTable 1.

Axial forces along the depth were monitored by two straingauges installed evenly at each cross section for all test piles.There were six instrumented sections in each instrumented pile(as shown inFig. 2). A vibrating-wire load cell measured the piletop load of each pile in the pile groups (for four- and nine-pilegroups) during the loading process. Fourteen vibrating wire cellswere used in total, one each on the top of the following piles: QZ4-1,QZ4-4, QZ4L-1, QZ4L-4, QZ9-1, QZ9-4, QZ9-5, QZ9-6, QZ9-9,QZ9L-1, QZ9L-4, QZ9L-5, QZ9L-6, and QZ9L-9.

Test procedureThe load tests were performed using the kentledge load

method. The dead load applied by square precast concretepiles was placed evenly on the reaction platform, before thetest. The length of the reaction beams was 12 m and thedistances between the supporting points and the center ofthe pile caps were all larger than 5 m. It is possible that, for thenine-pile group, this distance might not be sufficient to avoidcreating an impact on values of measured settlement. How-ever, this impact would be negligible except for small loadsand settlements. The dead load was 1.2 times the estimatedultimate load of the test pile group. Load was applied by

1294 Can. Geotech. J. Vol. 49, 2012

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hydraulic jacks. A pump was used to push the oil into the jacksthrough high-pressure oil hoses.

Settlements were measured at four locations on the uppersurface of the cap using four displacement transducers. Theaxial loads transferred along the instrumented piles were mea-sured by strain gauges, which were mounted on the steel bars.

The real strain of the steel bar was obtained from

[1] s K b

where Kand b are strain gage calibration factors and is thereading from the sensor.

The real strain in the concrete was assumed to be the sameas that of the steel bar. The axial force applied on the pile is

[2] P sAs cAc sEsAs cEcAc

whereis stress, is strain, Eis the elastic modulus, A is thecross-sectional area, and the subscripts s and c are used torepresent the steel bar and concrete, respectively. The elasticmodulus of the concrete was measured as 29.2 GPa, whichwas obtained by performing axial compression tests on sixconcrete samples with sizes 100 mm 100 mm 300 mm,28 days after formation.

Table 1. Summary of field tests.

No.

No. of

piles

Pile

length (m)

Pile

spacing

Pile cap sizes (length width

height; all in metres)

Slenderness

ratio,L/B

DZ1 1 20 N/A 0.4 0.4 0.4 50

DZ1L 1 24 N/A 0.4 0.4 0.4 60

QZ2 2 20 2.5B 1.8 0.8 0.8 50

QZ2L 2 24 3.0B 2.0 0.8 0.8 60QZ4 4 20 2.5B 1.8 1.8 0.8 50

QZ4L 4 24 3.0B 2.0 2.0 0.8 60

QZ9 9 20 2.5B 2.8 2.8 1.2 50

QZ9L 9 24 3.0B 3.2 3.2 1.2 60

Fig. 1. Layout plan of test piles and pile groups (all dimensions in millimetres).

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The load tests were slowly maintained load tests, with nounloadreload loops. The main procedure is as follows:

1. For a single pile, the loading increment was one-tenth ofthe estimated ultimate load capacity. For pile groups, theload increment was one-fifteenth of the estimated ultimateload.

2. The displacements were measured 5, 10, 15, 30, 45, and60 min after each load increment and then once every30 min thereafter.

3. The difference between the displacements at 30 min and1 h after application of each load increment was calculated.If this difference was less than 0.1 mm, then the next loadincrement was applied.

4. Loading was discontinued if any of the following condi-tions were satisfied:

a. The total displacement was 40 mm (0.1B) and thedisplacement at the pile tops was 5 times the dis-placement there at the beginning of the load increment.

b. The total displacement was 40 mm and the displace-ment did not stabilize after 24 h of loading.

Analysis of load test results

Single pile test resultsThe loadsettlement curves for the two single piles (Fig. 3)

show that these two curves are almost identical for bearingcapacity Q 900 kN, corresponding roughly to 0.6Qult, withultimate bearing capacity, Qult, defined based on the tradi-tional 10% relative settlement criterion (Salgado 2008). ForQ 900 kN, the settlement at the pile top is greater for DZ1than for DZ1L at the same load. The ultimate bearing capacity

Fig. 2. CPT site logs, in terms of cone resistance qc versus depth, and layout of strain gauges in the test piles (all dimensions in metres).

Table 2. Soil properties.

Direct shear test,

curve-fit strength

envelope

One-dimensional

consolidation test

Soil

Thickness

(m)

Unit weight,

(kN/m3)

Void

ratio,

e0

Plasticity

index,

Ip

Liquidity

index,

IL

Cohesion

(kPa)

Internal

friction

angle,

12

(MPa1)

Es

(MPa)

Fill 2.6 19.2 0.76 16.0 0.42 38 17.4 0.30 6.07

Clay 2.0 19.6 0.71 17.2 0.28 50 18.5 0.23 7.65

Silt 5.6 18.5 0.85 5.8 0.60 11 22.5 0.25 7.56

Silt intermixed with silty sand 7.3 18.8 0.79 5.0 0.64 13 23.7 0.20 8.88

Soft clay 11.6 17.4 1.24 21.7 0.96 15 8.3 0.67 3.40

Note:12, coefficient of compressibility; Es, Youngs modulus of soil.




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tlement. The single pile settlement is generally smaller thanthe corresponding pile group settlement at the same averageload per pile when the load is relatively large. The Rs valuesfor the two-pile groups are however close to unity. The initialvalues ofRs (at small loads) are also close to unity, indicatinglittle interaction between the piles.

Shaft resistances and base resistances of individual pilesThe average unit shaft resistance, qs, between strain

gauge levels can be calculated from the load transfercurves. Figure 9 shows the distributions of unit shaft resis-tance both for the single pile and for some instrumented pilesin groups QZ2L, QZ4L, and QZ9L at intermediate load stepsduring the load tests. Tables 3 and 4 show the unit shaftresistance for the single piles and the individual instrumentedpiles in the pile groups when the settlement for tested pile or

Fig. 6. Load versus settlement for single piles and pile groups. sp, spacing of pile group.

Q (kN)

w

(mm)

Fig. 7. Loadsettlement curves for the single pile and average

loadsettlement curves for the pile groups: (a) L 20 m; (b) L

24 m.

0

10

20

30

40

50

60

70

0 500 1000 1500 2000

Q (kN)

w

(mm) DZ1

QZ2

QZ4

QZ9

0

10

20

30

40

50

60

70

0 500 1000 1500 2000

Q (kN)

w(mm) DZ1L

QZ2L

QZ4L

QZ9L

(a)

(b)

Fig. 8. Settlement ratio, Rs, versus pile group settlement for all

pile groups: (a) with L 20 m; (b) with L 24 m.

0

1

2

3

4

5

6

7

Settlementratio,

Rs

Pile group settlement (mm)

QZ2QZ4

QZ9

0

1

2

3

4

5

6

7

Settlementratio,

Rs


QZ2L

QZ4L

QZ9L

(a)

(b)




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Fig. 9. Distribution of unit shaft resistance for single piles and for instrumented piles in the pile groups: (a) DZ1L; (b) QZ2L-1; (c) QZ4L-

1; (d) QZ4L-4; (e) QZ9L-1; (f) QZ9L-4; (g) QZ9L-5.

0

5

10

15

20

25

Depth(m)

Unit shaft resistance (kPa)

280kN

700kN

1120kN

1540kN

0

5

10

15

20

25

Depth(m)


400kN

1200kN

1800kN

2400kN

3000kN

0

5

10

15

20

25

Depth(m)


720kN

1800kN

2880kN

3960kN

5040kN

0

5

10

15

20

25

Depth(m)


720kN

1800kN

2880kN

3960kN

5040kN

0

5

10

15

20

25

Depth(m)


1440kN

3600kN

5760kN

7920kN

10080kN

0

5

10

15

20

25

Depth(m)


1440kN

3600kN

5760kN

7920kN

10080kN

0

5

10

15

20

25

Depth(m)


1440kN

3600kN

5760kN

7920kN

10080kN

(a) (b)

(c) (d)

(e) (f)

(g)

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pile group is 40 mm (0.1B).Figure 9shows that the unit shaft

resistance is close to a limit value at shallower locations, but

that is not the case for deeper locations along the pile. In

practical terms, this means that the end of the load tests on the

single piles corresponds to a state at which the shaft resistance

mobilized along the entire pile is less than the limit shaft

resistance.

The limit shaft resistances were calculated using the

pile design methods proposed by Salgado et al. (2011),

which capture the dependence of the unit shaft resistance on

the clay undrained shear strength, the normal effective stress

on the pile shaft, and the difference between the critical-state

friction angle and the minimum residual friction angle. The

equations used for calculation of unit shaft resistance for clay

are

[3] qsL su

[4]

su

v

0.05A1 (1 A1) expv

pA(c r,min)A2

where su is the undrained strength of soil, v is the in situ

vertical effective stress at the depth whereqsLis calculated,pAis the reference stress value (100 kPa), c is the critical-state

friction angle, andr,minis the minimum residual state friction

angle. The equation allows calculation ofqsLfor c r,min

0, 5, and 12, with interpolation allowing estimation for

additional values of this difference.

The value ofA1 is determined from

[5] A1 0.4 c r,min 120.75 c r,min 5A2 is a coefficient determined using

[6] A2 0.4 0.3 lnsu

v

The equations used for calculation of unit shaft resistancefor sand are

[7] qsL (Ktan)v

whereKis the coefficient of lateral earth pressure and is theinterface friction angle mobilized at the pilesoil interface.

The lateral earth pressure coefficient is calculated by therelationship proposed byLoukidis and Salgado (2008):

[8] KK0

exp(0.2K0 0.4)C1

expDR1001.3 0.2 lnv

pAwhereK0is the initial coefficient of lateral earth pressure andDR is the relative density of the sand. Loukidis and Salgado(2008)found that the coefficient C1is equal to 0.71 for angularsands and 0.63 for rounded sands and suggested a value of 0.7be used in calculations for clean sands in general.

Table 3. Measured unit shaft resistance (kPa) for the single pile and pile groups with pile length 20 m.

Measured unit shaft resistance (kPa)

Soil depth (m) Soil DZ1 QZ2-1 QZ4-1 QZ4-4 QZ91 QZ9-4 QZ9-5

0.00.5 Fill 31.9 33.8 21.5 24.3 16.9 16.8 19.8

0.52.6 Fill 29.6 31.9 20.9 22.7 17.8 15.9 17.9

2.64.6 Clay 86.6 89.1 68.6 72.3 68.6 63.9 65.9

4.610.2 Silt 64.8 67.8 47.9 49.3 43.3 45.4 46.4

10.217.5 Silt with silty sand 62.5 62.8 44.8 42.4 41.2 36.0 41.1

17.519.5 Soft Clay 25.5 27.7 17.5 21.9 17.5 16.1 18.1

Table 4. Measured unit shaft resistance (kPa) for the single pile and pile groups with pile length 24 m.

Measured unit shaft resistance (kPa)

Soil depth (m) Soil DZ1L QZ21-1L QZ4L-1 QZ4L-4 QZ9L-1 QZ9L-4 QZ9L-5

0.00.5 Fill 32.6 31.5 25.9 28.0 24.5 24.6 23.3

0.52.6 Fill 32.1 29.8 26.0 27.8 23.3 23.2 22.8

2.64.6 Clay 89.1 86.1 69.8 72.1 81.6 74.2 68.9

4.610.2 Silt 62.1 60.5 47.5 50.1 52.9 48.0 41.6

10.217.5 Silt with silty sand 59.2 55.6 45.6 46.0 49.9 46.7 31.6

17.523.5 Soft Clay 22.4 21.9 15.6 16.6 17.3 13.3 11.9




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The relative density, DR (%), of the sand is calculatedthrough the correlation with CPT test results proposed bySalgado and Prezzi (2007)

[9] DR

ln

q

cpA

0.4947 0.1041c 0.841 ln

h

pA0.064 0.0002c 0.0047 lnh

pAwhereqcis the tip resistance from CPT test results and h

is the

lateral earth pressure.The top soil layer from 0 to 10 m has a qcvalue of roughly

2 MPa in a material that is a mix of sand, clay, and silt andcould be treated either as a loose sand layer or a stiff clay layer.The lower and upper bound values of limit shaft resistancescorresponding to the clay layers can be obtained by setting c

r,min 0 and 12 and taking OCR 1 to obtain a conservative

lower bound.K0for the sand layer was assumed equal to 0.5. Thecalculated lower bounds of the limit shaft resistances for the 20and 24 m long piles are1290 and 1440 kN, respectively, when themixed soil in the top 10 m is treated as a clay. The calculatedupper bound of the limit shaft resistances for the 20 and 24 mlong piles are 2000 and 2340 kN, respectively, when the mixedsoil in the upper 10 m is treated as a sand.

It can be seen from these comparisons that the conservativelower bound estimates are of the order of but slightly less than themobilized shaft resistance and that upper bound estimates exceedit, which is consistent with indications that the shaft resistancemeasured in the tests may have approached but was not fullymobilized by its limit value at the time the load test was stopped.

The implication of these considerations is that, for slender pileswith little to no base resistance, superstructure ultimate limitstates can be reached without full mobilization of shaft resistance.

Tables 3and4 show that the limit unit shaft resistances ofQZ2-1 and QZ2L-1 are very close to those of DZ1 and DZL1,respectively, which indicates that the pile interaction in the two-pile groups is relatively small. The limit unit shaft resistances atcomparable locations down the pile for QZ4-1 and QZ4-4 aresimilar in the last loading step, but their values are less than thatof the corresponding single piles. The group effect intensifies forQZ9 and QZ9L, leading to lower unit shaft resistances.

The pile head loads were measured using load cells. Thepile base resistance of each of the instrumented piles was taken

as the axial force measured at the last instrumented section,located 1m from the pile base. The pile head and base loads areshown inTable 5and Fig. 10for the nine-pile groups and forthe single piles under different load levels.

FromTable 5andFig. 10for QZ9 and QZ9L, it can be seenthat the corner piles have the largest pile load, followed by theside and then central piles, as expected. This confirms intuitionbased on elasticity solutions that if the pile cap is flexible andthe loads on every pile are as a result the same, the center pilewould be expected to settle the most, showing that it has thelowest stiffness. When imposing the same settlement on all piles,we would therefore expect the center pile to carry the smallest

Table 5. Top and base loads for single piles and individual instrumented piles in the nine-pile groups at three different load levels.

Load 9360 kN Load 7200 kN Load 5760 kN

Pile No.

Base load

(kN)

Top load

(kN)

Ratio

(%)

Base load

(kN)

Top load

(kN)

Ratio

(%)

Base load

(kN)

Top load

(kN)

Ratio

(%)

QZ9-1 (corner) 22 979 2.25 15 832 1.80 0 660 0.00

QZ9-4 (edge) 40 943 4.24 7 748 0.94 0 630 0.00

QZ9-5 (center) 86 1060 8.11 15 740 2.03 3 580 0.52

QZ9L-1 (corner) 27 1060 2.55 11 832 1.32 0 681 0.00

QZ9L-4 (edge) 50 1123 4.45 17 748 2.27 8 605 1.32

QZ9L-5 (center) 59 896 6.58 28 677 4.14 8 548 1.46

Fig. 10. Pile head and base loads versus pile group load for the

nine-pile groups: (a) L 20 m; (b) L 24 m.

0

200

400

600

800

1000

1200

Piletoporbase

load(kN)

Pile group load (kN)

QZ9-1: top

QZ9-1: base

QZ9-4: top

QZ9-4: base

QZ9-5: top

QZ9-5: base

0

200

400

600

800

1000

1200

1400

Piletoporbaseload(kN)

Pile group load (kN)

QZ9L-1: top

QZ9L-1: base

QZ9L-4: top

QZ9L-4: base

QZ9L-5: top

QZ9L-5: base

(a)

(b)

Dai et al. 1301



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load, as indeed observed. This order reverses when the base loadis considered instead (although base loads are small, so compar-

isons must be made cautiously). The experimental results seem to

capture an aspect of pile group response that is not often com-

mented on. The base of the pile located towards the center of the

group is more constrained because of the surrounding piles,

which may lead to a greater base resistance.

Because of symmetry, the head and base loads for piles in

two-pile and square four-pile groups are expected to be the

same. As seen earlier, that is not the case for the piles in thenine-pile groups. The ratio of the individual pile load to

the average individual load in the group, Qi/Qav, is tabulated in

Tables 6and7.The key for the identification of the individual

piles in each group is shown in Fig. 1. The load on the outer

piles of each group is observed to be greater than the average

load Qav. The same result is illustrated inFig. 11.

For QZ9, the ratio of pile head load of QZ9-1 (the cornerpile) to an average of the pile head load during the loadingprocess fluctuates between 0.94 and 1.08. The ratio of QZ9-4(the side pile) is in the range from 0.91 to 1.06, and the ratioof QZ9-5 (the center pile) is between 0.75 and 1.02. For

QZ9L, the corner, edge, and central pile ratios fluctuate be-

tween 1.02 and 1.15, 0.89 and 1.13, and 0.71 and 0.86,respectively. What emerges clearly from these numbers is thelower load at the center.

Figure 12 shows individual pile load versus group settle-

ment curves for QZ9 and QZ9L. For comparison, the load

settlement curves of DZ1 and DZ1L are also shown in Fig. 12.

For small group loads, for which linear elastic solutions would

be most applicable, a random load distribution is obtained,

with no definite pattern. When Q10%is approached, there is a

redistribution of the load, and the position of the pile within

the group begins to influence the load it carries. Generally, at the

same settlement, the load on an individual pile within the group

is always less than the load for the corresponding single pile.

Implied interaction coefficients

Elasticity-based solutionsConsiderable work has been done on the calculation of the

settlement of pile groups. Most proposed methods are based on

linear elastic solutions. A realistic solution to the settlement

Table 6. Values ofQ/Qav in group QZ9.

Total load on

pile group,

Q(kN)

Average load

per pile,

Qav Q/9

Measured load

for QZ9-1,

Q1 (kN) Q1/Qav

Measured load

for QZ9-4,

Q4 (kN) Q4/Qav

Measured load

for QZ9-5,

Q5 (kN) Q5/Qav

1440 160 154 0.96 169 1.06 120 0.75

2160 240 260 1.08 249 1.04 206 0.86

2880 320 340 1.06 303 0.95 287 0.903600 400 430 1.08 390 0.98 354 0.89

4320 480 500 1.04 470 0.98 430 0.90

5040 560 580 1.04 538 0.96 474 0.85

5760 640 660 1.03 630 0.98 580 0.91

6480 720 766 1.06 710 0.99 637 0.89

7200 800 832 1.04 748 0.94 740 0.93

7920 880 900 1.02 870 0.99 820 0.93

8640 960 998 1.04 935 0.97 900 0.94

9360 1040 979 0.94 943 0.91 1060 1.02

Table 7. Values ofQ/Qav in group QZ9L.

Total load onpile group,

Q(kN)

Average loadper pile,

Qav Q/9

Measured loadfor QZ9L-1,

Q1 (kN) Q1/Qav


Q4 (kN) Q4/Qav


Q5 (kN) Q5/Qav

1440 160 185 1.15 142 0.89 114 0.71

2160 240 260 1.08 249 1.04 176 0.73

2880 320 305 0.95 351 1.10 260 0.81

3600 400 430 1.08 450 1.13 311 0.78

4320 480 535 1.11 452 0.94 376 0.78

5040 560 602 1.08 538 0.96 445 0.80

5760 640 681 1.06 605 0.95 548 0.86

6480 720 766 1.06 691 0.96 585 0.81

7200 800 832 1.04 748 0.94 677 0.85

7920 880 900 1.02 921 1.05 759 0.86

8640 960 998 1.04 935 0.97 812 0.859360 1040 1060 1.02 1123 1.08 896 0.86




11/22

calculation of the pile group still evades the profession, as itrequires modeling of the installation of the piles (in the rightsequence) and then their loading using an analysis that accu-rately captures soil element behavior, strain localization, andlarge displacements.

The analytical approach with the best chance of eventuallybecoming a general design method accounting for pile groupeffect is based on quantification of interaction between piles.This interaction is expressed through the concept of the coef-ficient of interaction, ij, which is equal to the ratio of thesettlement of pile i to the settlement of pile j when pile j isloaded. Using this concept, the settlement of any pile i in thegroup with a rigid cap is expressed through (Salgado 2008)

[10] wi j1

n

ij Qj

Ktj

where wi is the settlement of pile i, ij is the influence factorbetween i and j, Qj is the load acting on pile j, and Ktj is thestiffness of pilej (in the sense of how much load is required tohave unit pile head settlement).

Straight application of this equation would lead to dif-ferent settlements for different piles in the group. Salgado(2008)shows how group settlement can be calculated for thecase of a rigid cap, when every pile settles by the sameamount.

The interaction coefficients are usually calculated by usingconcepts from elasticity theory. For example, according toRandolph (2003)

[11] ij (L, )ln(rm/spij)

ln(2rm/B) 0

where

[12] Qb

wbEpAp

4Gbrs

1

1

EpAp

[13] kEpAp[14] rm 0.25 2.5(1 )GGL 0.25

GL

GbL

where (L, ) is the factor containing the pile-reinforcing effect, given inMylonakis and Gazetas (1998); rmis the magical radius proposed by Fleming et al. (1992) atwhich the settlement w of the ground surface becomes zero;

Fig. 11. Ratio of the individual pile load to the average individual

load,Qi/Qav, for the two nine-pile groups: (a)L 20 m; (b)L 24 m.

0.00

0.20

0.40

0.60

0.80

1.00

1.20

1.40

0 200 400 600 800 1000 1200

Qav(kN)

Qi/Qav

QZ9-1QZ9-4

QZ9-5

0.00

0.20

0.40

0.60

0.80

1.00

1.20

1.40

0 200 400 600 800 1000 1200

Qi/Qav

Qav(kN)

QZ9L-1

QZ9L-4

QZ9L-5

(a)

(b)

Fig. 12. Individual pile load versus group settlement relationship

for the two nine-pile groups: (a) L 20 m; (b) L 24 m.

Q (kN)

w

(mm)

0

10

20

30

40

50

60

70

0 500 1000 1500 2000

Q (kN)

w

(mm)

DZ1L

QZ9L-1

QZ9L-4

QZ9L-5

(a)

(b)

Dai et al. 1303



12/22

spij is the spacing between the pair of piles considered (pile iand pile j);Qbis the pile base load; wbis the settlement; Episthe Youngs modulus of the pile; Apis the sectional area of thepile; Gb is the shear modulus at the pile base and within thebearinglayer, following the notation by Randolph and Wroth(1978);rsis the radius of pile ( B/2);v is the Poissons ratioof the soil;kis the Winkler constant (also called a modulus of

subgrade reaction);Gis the average shear modulus of soil overthe length of the pile;GLis the shear modulus at the pile shaftwith the bearing layer.

This approach offers a useful framework for analysis, butthe reliance of the expressions on elastic parameters makes itdifficult to use them in practice. The interaction coefficientsshould, in reality, change with settlements. Based on theresults of the load tests, the individual values of the interactioncoefficients of each pile in the group can be back-calculatedbecause the total load applied on the group and the load on onepile of each type (i.e., corner, side or center) are recorded.Assuming that all piles located symmetrically in the groupcarry the same load, with some adjustment to make sure thatthe individual loads add up to the total load on the group, we

can obtain as many equations for the interaction coefficientsas there are pile types. Depending on the pile group geom-etry, there will be as many equations as there are unknowncoefficients. In cases where there are not enough equations,it is possible to use eq. [11] to generate supplementaryequations.

As the load was not measured on top of every pile in thegroup, but only in one pile of each type of pile (as perthe symmetries in the group), we first assume piles to carry thesame load as the load measured for the pile of a given sym-metry, then add up the loads. There will be a difference withrespect to the load measured for the entire group, which is thenallocated to the piles proportionally.

Calculation of influence coefficients

Formulation for a two-pile groupFor the two-pile group, we have a single unknown and also

only one equation. So the settlement of the group will be

[15] wg w1 w2 j1

n

ij

Qj

Ktj(1 12)

Q

Kt

Formulation for a four-pile groupIn the four-pile group, there is only one pile type because of

the symmetries present, so there is only one equation, but thereare two unknowns because a pile interacts differently with the

pile next to it than with the pile in the opposite corner. So wecan write eq. [10] once for the group settlement

[16] w1 wg j1

n

ij

Qj

Ktj(1 212 14)

Q

Kt

where11 1, and12 13and 14need to be determined.The additional equation that is needed comes from eq. [11],which allows us to express the ratio of the two interactionfactors as

[17]12

14

ln(rm/sp12)

ln(rm/sp14)

The CPT data indicates that the soil above and below 17 mis the same, which means the shear moduli GLfor the bottomlayer and Gb for the base layer are the same, with their ratiothen equal to 1. The ratio of the average shear moduluscalculated over the entire length of the pile to the shearmodulus at the level of the base of the pile is approximately1.5 by using the correlation of shear modulus versus qcofLeeet al. (2009) for sandysilty material and Mayne and Rix(1993)for clay. The Poissons ratio is taken as 0.45, as the

load test was done under essentially undrained conditions asfar as the clay is concerned. This leads to rm 2.06L, or41.2 and 49.4 m, respectively, for the 20 m long and 24 m longpiles. The spacing in the group with 20 m long piles is sp 2.5B; it is 3B in the 24 m long piles. For the pile group with20 m long piles

[18]12

14

ln41.2/[(2.5)(0.4)]

ln41.2/[(2.52)(0.4)] 1.10

and the system of equations for the four-pile groupbecomes

[19] 12 1.1014 0

[20] 1 212 14 Ktwg

Q

It turns out that substitution ofrm 49.4 m for the groupwith 24 m long piles yields the same value of12/14(1.10),so the equations are the same as for the group with 20 m longpiles.

Formulation for a nine-pile groupIn the case of the nine-pile groups, there are three types of piles,

which we will calla, b, and c. Piles 1, 3, 7, and 9 in Fig. 1 are of typea. Piles 2, 4, 6, and 8 are of type b. Pile 5 is of type c. As thecoefficient of interaction for any two piles depends on the dis-

tance between the two piles, there are a number of equalities toexplore

[21] 12 23 45 56 78 89 14 47 25 58 36 69 112 23 45 56 78 89 14 47 25 58 36 69 1

15 24 26 35 48 57 59 68 2

17 28 39 13 46 79 3

18 27 29 38 16 34 49 67 4

19 37 5




13/22

Now we write eq. [10] three times, once for each of the three piletypes (a, b, and c), keeping in mind that the settlement of each isequal to the settlementwgof the pile group. Any three piles, one ofeach type, will suffice. We take piles 1, 4, and 5. For pile 1

[22] w1 wg j

1

n

ij

Qj

Ktj

Qa/Kta 21Qb/Ktb 2Qc/Ktc 23Qa/Kta 24Qb/Ktb 5Qa/Kta

whereKta,Ktb, andKtcare the pile head stiffness of the singlepile of type a, b, and c with the same length as the piles in thegroup. Likewise, for piles 4 and 5

[23] w4 wg j1

n

ij

Qj

Ktj

Qb/Ktb 21Qa/Kta 1Qc/Ktc 22Qb/Ktb 3Qb/Ktb 24Qa/Kta

[24] w5 wg j1

n

ijQj

Ktj Qc/Ktc 41Qb/Ktb

42Qa/Kta

In this case, we have five unknowns and three equations.

Using eq. [11], we can write four additional equations that can

be used for the ratios of interaction coefficients.

[25]1

2 1.10,

2

3 1.12,

3

4 1.04,

4

5 1.09

In Appendix A, we discuss how to obtain the interactioncoefficients using these equations by linear optimization.

Resulting influence coefficientsEach loadsettlement data point from the load test can be

used to calculate one influence coefficient. The influence co-efficient can then be expressed in terms of settlement for thedifferent pile groups, as shown inFig. 13.In general, with theincrease of group settlement, the interaction coefficient in-creases, with an inflection point for small settlements (markingthe transition from minimal interaction for small settlements toa higher level of interaction) and later a tendency of stabili-zation at large settlements, which is consistent with moreintense localization of shear strain around the piles at large

settlements, leading to a reduction in the interaction for incre-mental settlement. The results for the two-pile groups QZ2 areinconsistent with the other results, with the interaction coef-ficient being practically zero. This may be because of spatialvariability of the soil or other variability in the pile installationor pile cap. For the four-pile groups, the pile spacing has alarger effect on interaction than pile length, which is to beexpected. The interaction coefficient in group QZ4 with sp 2.5B and L 20 m is on average larger than that of groupQZ4L with sp 3.0Band L 24 m. For the nine-pile group,the interaction coefficients are distributed proportionally topile center-to-center spacing. As shown inFig. 13, the inter-action coefficients for the piles in the four-pile group are larger

than comparable coefficients (at the same spacing) for thenine-pile group. The presence of additional piles around in-teracting piles likely interferes with load or settlement trans-mission between the interacting piles. Although the resultscannot be used at this time to propose any relationship forinteraction coefficients, they do show clearly (i) the depen-dence of these factors on settlement (which means that factors

derived from elasticity theory must be used with proper judg-ment) and (ii) the dependence of these factors on the size ofthe group (because of interference of additional piles on howpiles interact). Research on clarifying and quantifying theseeffects is needed.

Summary and conclusions

A field pile load testing program was carried out on isolatedbored piles and bored pile groups installed in a soil profile withmixed layers of clay and silt in Nanjing, China. The programincluded two single instrumented piles and six types of pilegroups with two, four, and nine piles with different pilelengths and pile spacing. Based on the analysis of the field test

results, the following conclusions can be reached:

1. Using the conventional definition of ultimate load as theload causing a settlement of 10% of the pile diameter, thetwo single piles DZ1 (L/B 50) and DZ1L (L/B 60)mobilized essentially only shaft resistance, with loadsmeasured at the strain gauge level closest to the pile baseaccounting for only 2.2% of the total load for the 20 m longpile and 4% of the total load for the 24 m long pile.

2. The general response of an individual pile in the two-pilegroups was observed to be very close to that of the corre-sponding single pile. This is evidenced, for example, bythe values of limit unit shaft resistance of piles in thetwo-pile group being approximately the same as those for

the corresponding single pile. This means that interactionbetween piles in the two-pile groups was relatively small.This was not observed in the 4-and 9-pile groups, in whichsubstantial interaction and group effect was observed.

3. In general, values of Rs of both the four- and nine-pilegroups tended to increase with settlement. The single pilesettlement was observed to be generally smaller thanthe corresponding pile group settlement at the same aver-age load per pile when the load was relatively large.

4. For the four- and nine-pile groups, group effect was morepronounced for QZ4 than for QZ4L and about the same forQZ9L and QZ9, showing that the impact of the pile spac-ing is greater than that of the pile length on group load.

5. Based on the analysis of the load distribution between thegroup piles in the nine-pile groups, the load at the top ofthe corner piles was observed to be the largest, followed byside piles and then center piles. However, the load differenceswere not large, particularly for side versus corner piles.

6. Based on the results of the load tests, the individual valuesof the interaction coefficients of each pile in the group wereback-calculated. The interaction coefficient was seen to bea function of settlement and the size of the group. With theincrease of group settlement, the interaction coefficientwas observed to increase.

7. A method of determining interaction coefficients from pilegroup load test results was proposed.

Dai et al. 1305



14/22

Acknowledgements

This research was supported by the National Natural Sci-ence Foundation of China (Grant No. 50908048) and a projectfunded by the Priority Academic Program Development ofJiangsu Higher Education Institutions (PAPD).

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Fig. 13. Interaction coefficients versus settlement for each pile group: (a) two-pile group with L 20 m; (b) two-pile group withL 24 m;

(c) four-pile group with L 20 m; (d) four-pile group withL 24 m; (e) nine-pile group withL 20 m; (f) nine-pile group withL 24 m.

0.0

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0.60.7

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Appendix A. Determination of interaction

coefficients for a nine-pile group

As seen earlier from eqs. [22] to [25], repeated here as eqs.[A1] to [A4], respectively, the available equations for a nine-pilegroup are

[A1] w1 wg j1

n

ij

Qj

Ktj

Qa/Kta 21Qb/Ktb 2Qc/Ktc 23Qa/Kta 24Qb/Ktb 5Qa/Kta

[A2] w4 wg j1

n

ij

Qj

Ktj

Qb/Ktb 21Qa/Kta 1Qc/Ktc 22Qb/Ktb 23Qb/Ktb 4Qa/Kta

[A3] w5 wg j1

n

ij

Qj

Ktj

Qc/Ktc 41Qb/Ktb 42Qa/Kta

[A4]1

2 1.10,

2

3 1.12,

3

4 1.04,

4

5 1.09

where these ratios of interaction coefficients are specific tothe pile group geometry and conditions considered in thispaper.

Dai et al. 1307

http://dx.doi.org/10.1680/geot.1970.20.1.94http://dx.doi.org/10.1680/geot.1970.20.1.94http://dx.doi.org/10.1680/geot.1971.21.1.43http://dx.doi.org/10.1061/(ASCE)0733-9410(1991)117%3A11(1655)http://dx.doi.org/10.1680/geot.1980.30.2.97http://dx.doi.org/10.1680/geot.1963.13.4.334http://dx.doi.org/10.1061/(ASCE)1090-0241(2001)127%3A9(766)http://dx.doi.org/10.1061/(ASCE)1090-0241(2001)127%3A9(766)http://dx.doi.org/10.1061/(ASCE)0733-9410(1993)119%3A9(1449)http://dx.doi.org/10.1061/(ASCE)0733-9410(1993)119%3A6(984)http://dx.doi.org/10.1061/(ASCE)GT.1943-5606.0000392http://dx.doi.org/10.1680/geot.2008.58.4.283http://dx.doi.org/10.1680/geot.1997.47.4.791http://dx.doi.org/10.1680/geot.1998.48.1.55http://dx.doi.org/10.1680/geot.1989.39.3.365http://dx.doi.org/10.1061/(ASCE)0733-9410(1983)109%3A3(355)http://dx.doi.org/10.1680/geot.2003.53.10.847http://dx.doi.org/10.1680/geot.2003.53.10.847http://dx.doi.org/10.1680/geot.1979.29.4.423http://dx.doi.org/10.1061/(ASCE)1532-3641(2007)7%3A4(251)http://dx.doi.org/10.1061/(ASCE)1532-3641(2007)7%3A4(251)http://dx.doi.org/10.1680/geot.1957.7.4.147http://dx.doi.org/10.1680/geot.2006.56.5.349http://dx.doi.org/10.1680/geot.2006.56.5.349http://dx.doi.org/10.1680/geot.1957.7.4.147http://dx.doi.org/10.1061/(ASCE)1532-3641(2007)7%3A4(251)http://dx.doi.org/10.1061/(ASCE)1532-3641(2007)7%3A4(251)http://dx.doi.org/10.1680/geot.1979.29.4.423http://dx.doi.org/10.1680/geot.2003.53.10.847http://dx.doi.org/10.1680/geot.2003.53.10.847http://dx.doi.org/10.1061/(ASCE)0733-9410(1983)109%3A3(355)http://dx.doi.org/10.1680/geot.1989.39.3.365http://dx.doi.org/10.1680/geot.1998.48.1.55http://dx.doi.org/10.1680/geot.1997.47.4.791http://dx.doi.org/10.1680/geot.2008.58.4.283http://dx.doi.org/10.1061/(ASCE)GT.1943-5606.0000392http://dx.doi.org/10.1061/(ASCE)0733-9410(1993)119%3A6(984)http://dx.doi.org/10.1061/(ASCE)0733-9410(1993)119%3A9(1449)http://dx.doi.org/10.1061/(ASCE)1090-0241(2001)127%3A9(766)http://dx.doi.org/10.1061/(ASCE)1090-0241(2001)127%3A9(766)http://dx.doi.org/10.1680/geot.1963.13.4.334http://dx.doi.org/10.1680/geot.1980.30.2.97http://dx.doi.org/10.1061/(ASCE)0733-9410(1991)117%3A11(1655)http://dx.doi.org/10.1680/geot.1971.21.1.43http://dx.doi.org/10.1680/geot.1970.20.1.94http://dx.doi.org/10.1680/geot.1970.20.1.94


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The residual form of eqs. [A1] to [A3] can be expressed as

[A5] r(ij)i wg j1

n

ij

Qj

Ktj

This residual r(ij)i, which is a function of the interaction

coefficients, is the difference between the measured and cal-culated pile top settlement for pile type i. The coefficient ofinteraction vector is defined as {1, 2, 3, 4, 5}. Apossible objective function is the sum of the settlement differ-ences, represented by the Frobenius norm r2 of the residualvector r {r1, r2, r3, r4, r5}. The optimization problem cannow be expressed as finding the minimum ofr2.

The solution to this optimization problem is obtained byfinding the optimal interaction coefficients optimumat whichthe minimum residual r2,min is obtained. We can obtain the

optimal values of the interaction coefficients using the Sim-plex method. The algorithm for this is summarized as follows;

1. START with an assumed very small initial value of5, and thencalculate 1to 4through the constraint eq. [A4].

2. LOOP with the constraint that i 1 for i 1, 2,. . .,5.3. INCREMENT5 by a small amount to obtain its current

value 5,current

and calculate new values 1,current

to4,current of the other interaction coefficients through theconstraint eq. [A4].

4. COMPUTE the Frobenius norm of residual r2,current forcurrent values currentof the interaction coefficients.

5. IF r2,current r2,min. this means the current interactioncoefficient vector is a better solution, so update the solu-tion by settingr2,min r2,current, and optimum current.

6. ENDLOOP.7. END with optimal interaction coefficient vector optimum

and r2,min.




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DISCUSSION

Discussion of Load tests on full-scale bored pile groups1

Bengt H. Fellenius

The authors are correct in stating for static loading tests thatthere are few full-scale pile group load tests reported in theliterature. I agree. However, a few more references are availablethan those listed by the authors, e.g., O'Neill et al. (1982a,1982b),Phung (1993),and O'Neill and Reese (1999).Figure D1shows theloadmovement measured byPhung (1993)in comparing the re-sponse of a single pile to a group of five piles driven at a center-to-center spacing (c/c) of 5.7 pile diameters in a fine sand. Thecenter pile (pile #1) was installed and tested as a single pile beforethe other piles were installed and connected by a rigid cap. Theloadmovement response of the five piles was different, but thedifference was limited to the development during the initialloading. Beyond the first about 4 mm of movement, the loadmovement curves were essentially parallel. Measurements of loaddistribution showed that the difference was mostly due to thedifference in shaft resistance the toe resistances were essen-tially equal for the five piles and no correlation to locationwithin the group could be discerned. The differences are consid-ered caused by unsystematic compaction of the sand with noapparent effect of the driving sequence or other driving effect. Amain observation was that the response in the loading of thecenter pile as a part of the group in effect was a reloading of thepile. The response at first loading of the pile as a single pile wasconsiderably less stiff.

Similar to the authors' work, the references mentioned aboveinvolve pile groups that at most consist of nine piles. A group ofjust a few piles and nine piles is a very small number, wherepile groups are concerned

will show minimal interaction and

variation between the piles in supporting a structure. For a smallpile group, the difference in load response between the piles in apiled foundation subjected to working load from the supportedstructure will be more affected by load variations, such as loadcenter, load inclinations, and lateral loads, as opposed to whensubjected to astatic loading teston the group.

Very few well-documented case histories are available in theliterature with regard to full-scale studies of the performance oflarge pile groups under working load. However, a few are; forexample,Golder and Osler (1968),Badellas et al. (1988),Goossensand Van Impe (1991), and Savvaidis (2003).The case histories showbeyond doubt that the capacity and the load distribution of anindividual pile in a large group of piles is of little relevance to theresponse of the piled foundation. Instead, the response of a piled

foundation made up of a good-size pile group constitutes a settle-ment problem, and the capacity and load distribution of either anindividual pile or thegroup is notthe governingissuefor a design.

Despite that the authors (as do so many others) imply that thestatic loading test measures pile settlement, what is measured ina loading test isa movement response to a series of applied loads, not

settlement. The authors' paper presents the movement response toapplied load for a single pile and a few very small pile groups, not

the settlement. Of course, settlement assessment reliesvery muchon the results of a static loading test; in particular, on the re-sponse of the pile toe. However, the actual settlement of a piledfoundation due to a working load, whether composed of a singlepile, a few piles, or a large group of piles, is a very different issue.

The authors present the loadmovement response of two singlepiles and state the capacity criterion that the capacity of the pilesis based on the traditional 10% relative settlement criterion.Although the criterion is used less often these days, it does keepappearing in the literature. A couple of years ago, I searched anassortment of successively older papers, textbooks, and standardsthat essentially stated the same criterion sometimes with aslight modification away from the 10% value. Many did not givereference to the source, but some did, and I found the originalsource. The criterion has its origin in a mistaken quotation of anow70 year oldstatement byTerzaghi (1942).Terzaghi wrote: thefailure load is not reached unless the penetration of the pile is atleast equal to 10% of the diameter at the tip (toe) of the pile. (Forfull quotation and context, seeLikins et al. 2011). Note, Terzaghidid not define the capacity as the load generating a movementequal to 10% of the pile diameter, he emphatically stated thatwhatever definition of capacity or ultimate resistance used, itmust not be applied until thepile toehas moved at least a distancecorresponding to 10% of the pile toe diameter. (The pile head willthen have moved an additional distance equal to the pile shorten-ing.) Most certainly, Terzaghi did not suggest that a fixed move-ment value, however determined, could serve as a definition ofcapacity.

Figure D2shows the loadmovement plot of the authors' staticloading test on pile DZ1L. The usually very conservative definitioncalled offset limit, or Davisson limit, indicates a lower-boundvalue of 1400 kN. It is here offered for reference. I do not suggestthat the offset limit would be the pile capacity, but it does showthe load for which the ultimate shaft resistance would have beenreached. The Hansen 80-percent method results in an interpretedcapacity of 1700 kN, coincidentally the maximum load applied inthe test the pile seems to be plunging. The ChinKondner andDecourt extrapolation methods indicate 1850 kN. Thus, coinciden-tally,the 1540 kN capacity perthe authors' traditionaldefinitionhappens to be a reasonable value to choose from the loadmovement curve. For full definitions and description of themethods for determining the capacity from the pile-head load

movement response, seeFellenius (1975,2012).Figure D3 shows the authors' load distributions as evaluated

from the strain-gage measurements in pile DZ1L up to a load of1440 kN. The authors did not include the distribution for themaximum applied load (1700 kN). I have supplemented the figurewith the authors' q

cdiagram from the sounding pushed nearest

the test pile, soil descriptions, and layer boundaries. I have alsoadded a distribution determined by means of both total stress and

Received 22 January 2013. Accepted 24 January 2013.

B.H. Fellenius.Bengt Fellenius Consultants Inc., 1905 Alexander Street SE, Calgary, AB T2G 4J3, Canada.

E-mail for correspondence:[email protected] in the Canadian Geotechnical Journal,49(11): 12931308.[doi:10.1139/t2012-087].

451

Can. Geotech. J.50: 451453 (2013)dx.doi.org/10.1139/cgj-2013-0027 Published at www.nrcresearchpress.com/cgj on 5 April 2013.
mailto:[email protected]://dx.doi.org/10.1139/t2012-087http://dx.doi.org/10.1139/t2012-087http://dx.doi.org/10.1139/t2012-087http://dx.doi.org/10.1139/cgj-2013-0027http://dx.doi.org/10.1139/cgj-2013-0027http://dx.doi.org/10.1139/t2012-087mailto:[email protected]


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effective stress calculations back-calculated to fit the distribution

at the 1540 kN applied load. The total stress values of the average

unit shaft resistance, rs, and the -coefficients I used to achieve

the fitareshownto the leftof the qc

diagram. For the calculations,

I used the UniPile program (Goudreault and Fellenius 1998).

The authors differentiated the loads determined at the strain-gage levels and determined the average unit shaft resistances be-tween the gage levels. This method requires that the strainmeasurements be accurate, which seems to have been the case forthis test. When the accuracy is less good, the inaccuracies will beenlarged by the differentiation. The alternative of evaluating theshaft resistance by fitting calculations to a load distributionmakes for results less dependenton inaccuracies.Moreover, whenthe gage levels are not at the layer boundaries, as is the case at the16.1 m boundary level and 17.5 m gage level, and the shaft resis-tances in the layers are different, the differentiation method willbe somewhat distorted. By evaluating the shaft resistance be-tween the layer boundaries as opposed to between thegage levels,the potentialdistortion is avoided.

Figure D4 compiles the authors' unit shaft resistance valuesobtained by differentiation and those I have obtained from thetotal stress calculation fitted to the measured distribution. The

values of unit shaft resistance by the two methods agree quite wellwhere layer boundaries and gage levels are at the same depth, butthey deviate where the gage levels and boundaries are not.

The authors discuss the interaction between piles in a pilegroup by comparing the loadmovement results of a single pile tothat of the piles in the group (where the pile head loads weremeasured individually). The authors state that the pile caps werecast and rested on the ground. If indeed the pile caps were incontact with the ground during the tests on the pile groups, thiswould have added some resistance and stiffness to the group tests.I wonder if the contact stress was measured and, if so, how large itwas.

Moreover, there does not seem to have been any measurementof the compression of the clay below the pile toe level. The two9-pile groups have a footprint area of about 10 m2 and the stress

produced by themaximum applied load distributed over that areawas therefore about 1500 kPa. The applied test load produces shaftresistance that is transmitted downward through the soil, andalthough it would be somewhat dispersed laterally, a good por-tion of it will reach the pile toe level together with the toe stress(which was small). Although the authors do not provide details ofthe clay, I would expect that the measured pile head movementfor the pile group will have experienced some additional move-ment due compression of the clay below the pile toe level. Thiswould have appeared as a reduced stiffness for the group piles asopposed to the single pile even for the case of shaft and toe resis-tances and toe movement being equal for a group pileand a singlepile. And it would, therefore, explain part of the authors' observedstiffness differences between single piles and group of piles.

Fig. D1. Loadmovement response of a five-pile group (data from

Phung 1993).b, pile diameter.

0

2

4

6

8

10

12

14

16

0 5 10 15 20 25 30 35 40 45 50

MOVEMENT OF PILE HEAD (mm)

LOAD/PILE(kN)

Average

#2

#5

#4

#3

#1

#1

2.3 m

340 mm

#2

#3 #4

#5

680 mm

c/c = 5.7 b

#1 as single

sq60 mm

Fig. D2. Loadmovement curve of test on pile DZ1L. Ru, ultimate

resistance.

0

200

400

600

800

1,000

1,200

1,400

1,600

1,800

2,000

0 10 20 30 40 50 60 70 80

MOVEMENT (mm)

LOAD

(kN)

Pile DZ1L

Hyperbolic and

80-% methods load-

movement curves

fitted to the test data

Chin-Kondner and Decourt: Ru= 1,850 kN

Hansen 80-% method: Ru= 1,700 kN

Offset: 4 mm + b/120 = 7.3 mm

Ru-range: 1,400 kN

to 1,700 kN

Offset limit: Ru= 1,400 kN

1,540 kN

1,700 kN

Fig. D3. Pile DZ1L load distribution. GW, groundwater level;rs, unit

shaft resistance;qc, cone stress.

0

5

10

15

20

25

0 400 800 1,200 1,600 2,000

LOAD (kN)

DEPTH(m)

rs= 33 KPa or = 1.2

rs= 85 KPa or = 1.5

rs= 63 KPa or = 0.6

= 0.6

rs= 65 KPa

= 0.3

rs= 25 KPa or = 0.1

qc

Pile DZ1L

?

Distributions by - and

methods fitted to the

measured load

distribution for the

1,540 kN load

Clay

Fill

Silt

Silt

Clay

GW

Fig. D4. Evaluated distributions of unit shaft resistance for pile

DZ1L.

0

5

10

15

20

25

0 20 40 60 80 100

UNIT SHAFT RESISTANCE, rs (KPa)

DEPTH(m)

Pile DZ1L

Authors' evaluation

using differentiation

Evaluation using

total stress

calculation fitted

to measured

distribution




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The loadmovement response of a shaft bearing pile group isnot just governed by the soil shear strength. (The test piles at thesubject site were essentially shaft bearing and the test on pileDZ1L showed a mobilized shaft resistance of about 1400 kN.) Thebuoyant weight of the soil in between the piles has a moderatinginfluence on the pile stiffness response, dependingon the spacingbetween the piles. Once the buoyant weight of the soil betweenthe piles placed in a group is smaller than the shaft resistance for

a single pile, the amount of shaft resistance available to a pileinside the group becomes correspondingly limited. The centerpileof the 24 m 9-pilegroup has a share of the soil weight equal tothe square of the spacing minus the cross section of the pile timesthe effective stress at the pile toe. The effective stress at the 24 mpile toe level was about 240 kPa. Thus, the share of soil weight fora 400 mm diameter pile inside the group of piles spaced c/c 3.0diameters is about 300 kN. That is, at such spacings, when theshaft resistance demand becomes larger than 300 kN, there willbe interference between the piles, resulting in a softer shaft re-sponse for the interior piles in the group as opposed to that of asingle pile.Hadthe spacing been about twice larger, as for thecaseshown in Fig. D1, this buoyant weight influence would havebeen minimal.

References

Badellas, A., Savvaidis, P., and Tsotos, S. 1988. Settlement measurement of aliquid storagetank founded on 112long bored piles.In Proceedingsof SecondInternational Conference on Field Measurements in Geomechanics, Kobe,

Japan. Balkema Rotterdam. pp. 435 442.Fellenius, B.H. 1975. Test loading of piles. Methods, interpretation, and new

prooftesting procedure. ASCE Journal of GeotechnicalEngineeringDivision,101(GT9): 855869.

Fellenius, B.H. 2012. Basics of foundation design. Electronic ed. Available at

www.Fellenius.net.

Golder, H.Q., and Osler, J.C. 1968. Settlement of a furnace foundation, Sorel,

Quebec. Canadian Geotechnical Journal,5(1): 4656. doi:10.1139/t68-004.

Goossens, D., and Van Impe, W.F. 1991. Long-term settlement of a pile group

foundation in sand, overlying a clayey layer. InProceedings of the 10th Euro-

pean Conference on Soil Mechanics and Foundation Engineering, Firenze,

2630 May. Vol. I, pp. 425428.

Goudreault, P.A., and Fellenius, B.H. 1998. UniPile Version 4.0 User Manual.

UniSoft Ltd., Ottawa, Ont. Available at www.UniSoftLtd.com.

Likins, G.E., Fellenius, B.H., andHoltz, R.D. 2011. Piledrivingformulas

past and

present. In Proceedings of the ASCE GeoInstitute Geo-Congress, Full-scale

Testing in Foundation Design, State of the Art and Practice in Geotechnical

Engineering, Oakland, 25 29 March 2012. Geotechnical Special Publication

227.Edited by M.H.Hussein,K.R. Massarsch,G.E. Likins, andR.D. Holtz.ASCE,

Reston, Va. pp. 737753.

O'Neill, M.W., and Reese, L.C. 1999. Drilled shaft construction procedures and

designmethods. Federal HighwayAdministration, Washington, D.C. Techni-

cal Report FHWA-IF-99-025.

O'Neill, M.W., Hawkins, R.A., and Audibert, J.M.E. 1982a. Installation of pile

group in overconsolidated clay. Journal of the Geotechnical Engineering

Division, ASCE,108(11): 13691386.

O'Neill, M.W., Hawkins, R.A., andMahar, L.J. 1982b. Load transfermechanisms in

piles and pile groups. Journal of Geotechnical Engineering Division, ASCE,

108(12): 16051623.

Phung, L.D. 1993. Footings with settlement-reducing piles in non-cohesive soil.

Ph.D. thesis, Department of Geotechnical Engineering, Chalmers University

of Technology, Swedish Geotechnical Institute, Goteborg. Report 43.Savvaidis, P. 2003. Long term geodetic monitoring of deformation of a liquid

storage tank founded on piles.In Proceedings,11th FIGSymposium on Defor-

mation Measurements, Santorini, Greece.

Terzaghi, K. 1942. Discussions on the progress report of the committee on the

bearing value of pile foundations.In Proceedings of the American Society of

Civil Engineers,68: 311323.

Fellenius 453

http://dx.doi.org/10.1139/t68-004http://dx.doi.org/10.1139/t68-004http://dx.doi.org/10.1139/t68-004http://dx.doi.org/10.1139/t68-004


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DISCUSSION

Reply to the discussion by Fellenius on Load tests on full-scale

bored pile groups1

Rodrigo Salgado, Yanbei Zhang, Guoliang Dai, and Weiming Gong

We thank Dr. Fellenius for his discussion of our paper.The discussion suggests that we have left out four references on

load tests on pile groups (O'Neill et al. 1982a,1982b;Phung 1993;O'Neill and Reese 1999). Our paper focused on instrumented fieldload tests on bored piles, with a clear focus on pile groups. Thereferences mentioned in the discussion, while of interest, are notdirectly applicable in the present case. The Ph.D. thesis ofPhung(1993)focuses on model, steel pipe piles driven in sand. O'Neilland Reese (1999)discuss load tests on instrumented single boredpiles, but not on pile groups. The papers byO'Neill et al. (1982a,1982b)focus on instrumented driven pile groups.

The discussion appears to argue that the position of the pilewithin the group (i.e., whether a corner, side or central pile) wouldhave no effect on load response. Our tests show otherwise. Thepile spacing in the data reported by Phung (1993), as shown inFig. 1 of the discussion, is of the order of 10 times the equivalentdiameter of the piles, while the pile spacing is 2.5 and 3 times thepile diameter in our tests. The focus ofPhung (1993)was on pilesas settlement-reducing elements (i.e, piled mats or rafts); ourwork, in contrast, focused on spacings that would be more typicalin a traditional pile group, for which spacings are kept relativelysmall so that pile cap costs do not increase. The different spacingobviously has an impact on pile interaction and on the influenceof pile position on pile response. The extent of the effect of pileposition also depends on other factors, chiefly the relative stiff-nesses of the various components of the foundation system (pilecap, individual piles, and soil), and could be obscured by randomvariation of soil properties around the pile group or, particularlyin the case of driven piles, by variability related to installationprocedure and sequence. Another issue with model pile testing isthe scale effects, which become quite significant as shear strainbegins to localize next to the pile (see, for example,Foray et al.(1998); Lehane et al. (2005); Loukidis and Salgado (2008)). Thesescale effects may distort results significantly.

The next point raised refers to the use of the termsettlementbythe geotechnical engineering profession. It is useful in issuesrelated to notation to refer back to the underlying science:mechanics in this case. In mechanics, the pertinent quantity isdisplacement. In the context of the present paper, we are dealing

with vertical displacements, routinely referred to as settlement infoundation engineering.The term has of course been used univer-sally (e.g.,Poulos 1989;Briaud et al. 2000;Lehane and Randolph2002; Randolph 2003; de Sanctis and Mandolini2006; McCabe andLehane 2006;Xu and Zhang 2007; Salgado 2008) and is appropriateto describe the results of our tests.

Another question raised regards the use of the traditional 10%relative settlement criterionfor estimation of the ultimate load of

an individual pile. It is a criterion that is indeed widely usedinternationally both in design and in the interpretation of loadtests (e.g., Skempton 1959; Lee and Salgado 1999; Briaud et al.2000; Paik and Salgado 2003; Paik et al. 2003; Randolph 2003;Jardine et al. 2005;de Sanctis and Mandolini 2006;McCabe andLehane 2006; Salgado 2008;Xu et al. 2008; Fleming et al.2009; Kimet al. 2009;Seo et al. 2009). The reason for its widespread use isthat it does work well for a range of design situations. As pointedout bySalgado et al. (2011),deviations would occur, for example,for piles bearing in rock (when a smaller relative settlementwould be appropriate) or for piles in very weak clay (when a limitor plunging load would be reached before a relative settlement of10% could develop). The notion of arelativesettlement (in contrastto aset valueof settlement) is useful in designing foundations forframe structures in that the pile diameter has some correlationwith span, which, in turn, correlates with tolerable differentialsettlement(Salgado 2008). The correlation weakens as we movefrom one pile per column to multiple piles per column, but it stillexists. In any case, relative settlement is typically used to definean ultimate load for an individual pile. Many authors (e.g., LeeandSalgado 1999; Lehaneand Randolph 2002; Fleming et al.2009) alsoexplicitly use or refer to use of the relative settlement of the base,not of the top of the pile, which would specifically separate outthe contribution of pile compression to total settlement at thepile head.

In summary, if the range of applicability of the criterion isproperly considered, the 10% relative settlement criterion has arole in piledesign. Itis no worsethan any method inthe literatureand definitely superior to the so-called graphical methods thatattempt to arrive at an ultimate load based on the appearance ofthe loadsettlement curve, without any reference to the fact thatthe foundation element is supporting a structural load and has asits primary function minimization of the chances of the structurereaching a limit state. Ideally, an engineer would be able to usemuch more specific criteria, applicable to a given structure andcircumstances, and definition of an ultimate load for an individ-ual pile, much less for a pile group, would not even be required insuch a case.

Now we turn to some specific clarifications regarding the test

results. With respect to the last applied load (equal to 1680 kN) onpile DZ1L, this was a plunging load. As it could not reach equilib-rium, we must assume that plunging would have occurred be-tween the 1540 and 1680 kN loads. Details were provided only forthe 1540 kN load.

With respect to load transfer plot estimation, taking the loca-tion of layer interfaces, if accurately known, into account wouldlead to an improved estimation of these plots and therefore of the

Received 11 March 2013. Accepted 11 March 2013.

R. Salgado and Y. Zhang. School of Civil Engineering, Purdue University, 550 Stadium Mall Drive, West Lafayette, IN 47907, USA.G. Dai and W. Gong. School of Civil Engineering, Southeast University, No.2 Sipailou, Nanjing, Jiangsu, 210096, China.

Corresponding author:Rodrigo Salgado (e-mail:[email protected]).1Appears in the Canadian Geotechnical Journal,50(X): XXXXXX[doi:10.1139/cgj-2013-0027].

454

Can. Geotech. J.50: 454455 (2013)dx.doi.org/10.1139/cgj-2013-0096 Published at www.nrcresearchpress.com/cgj on 5 April 2013.
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This article has been cited by:

1. D. Basu, Rodrigo Salgado. 2014. Closure to Load and Resistance Factor Design of Drilled Shafts in Sand by D. Basu andRodrigo Salgado.Journal of Geotechnical and Geoenvironmental Engineering07014002. [CrossRef]
http://dx.doi.org/10.1061/(ASCE)GT.1943-5606.0001055

Documents

Load Test on Full Scale Bored Piles Groups _ Salgado 2012