Research ArticleHorizontal Loading Tests on Disconnected Piled Rafts anda Simplified Method to Evaluate the Horizontal Bearing Capacity

Xiao-jun Zhu ,1,2 Kang Fei ,1 and Sheng-wei Wang 1

1College of Civil Science and Engineering, Yangzhou University, Yangzhou 225127, Jiangsu, China2School of Civil Engineering, Southeast University, Nanjing 210096, Jiangsu, China

Correspondence should be addressed to Xiao-jun Zhu; zhuxiaojun@yzu.edu.cn

Received 24 April 2018; Revised 21 June 2018; Accepted 14 August 2018; Published 16 September 2018

Academic Editor: Chiara Bedon

Copyright © 2018 Xiao-jun Zhu et al. *is is an open access article distributed under the Creative Commons Attribution License,which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Disconnected piled raft (DPR) foundations have been widely adopted as an effective foundation system where the piles areseparated from the raft by a granular layer, which can limit the shear forces and moments transmitted between the raft and thepiles. *us, DPR foundations may avoid the problem of horizontal forces, such as those from an earthquake or dynamic loads,which damage the structural connection between the pile head and raft. A series of static horizontal loading tests were carried outon three types of foundation models, i.e., piled raft, disconnected piled raft, and raft alone models, on fine sand using a geo-technical model in a 1 g field. In this paper, the influences of vertical loading and interposed layer thickness were presented anddiscussed.*e results showed that most of the horizontal force was carried by raft/interposed layer friction in the DPR foundationtype, and the shear force and moment of the piles were greatly reduced due to the gap between the raft and the heads of the piles.*e tested foundations were simulated using a simplified method with theoretical equations derived by making several ap-proximations and assumptions. *e simulated results agreed well with the test results.

1. Introduction

In situations where a raft foundation alone does not satisfythe design requirements, it may be possible to enhance theperformance of a raft by adding piles, producing what iscalled a piled raft [1–3]. In seismically active zones, if thepiles are structurally connected to the raft, high lateralshear forces and moments may develop at the connectionbetween the piles and raft due to cyclic or dynamic hori-zontal loads. Meanwhile, the bearing capacity of the pilemay be governed by their structural capacity rather than bytheir geotechnical capacity. *erefore, the concept ofa disconnected piled raft has been discussed, where thepiles are separated from the raft with an interposedgranular load distribution layer [4, 5]. In such a founda-tion, the interposed layer prohibits loads that resultfrom the superstructure in a direct manner, the discon-nected piles are regarded as the ground reinforcementrather than pure structural members, and the factor ofsafety against structural failure can be significantly re-duced. In addition, the disconnected piled raft avoids the

problem of horizontal forces, such as those from earth-quakes or dynamic loads, that can damage the structuralconnection between the pile head and raft since such forcescan normally be resisted by the friction mobilized along thegranular layer/raft contact, as shown in Figure 1.

Compared with the concept of piled raft foundationswith connected piles, the disconnected piled raft alternativehas been much less investigated. Some guidance was givenby [4]. An analytical design method has been developed inthe French research programme ASIRI. In addition, somepiled footing projects have employed disconnected piledrafts. Among others, the Rion–Antirion Bridge in Greece[6, 7] and the ICEDA nuclear waste storage facility [8] werefounded on clay reinforcement by settlement-reducing pileswith an interposed granular load distribution layer, whichcan limit the shear forces and moments transmitted betweenthe raft and the subsoil. However, the behaviour of the DPRunder a seismic load has not been well clarified, which ispartly due to the uncertainty in the complicated behaviour ofthe disconnected piled raft when it is subjected to seismicand lateral loads.

HindawiAdvances in Civil EngineeringVolume 2018, Article ID 3956509, 12 pageshttps://doi.org/10.1155/2018/3956509

To clarify the complicated behaviours of the discon-nected piled raft, understanding the observed data underseismic and lateral loading is crucial. However, whencomparing the studies of vertically loaded disconnectedpiled rafts, research on the behaviour of laterally loadedDPRs is relatively limited. Fatahi et al. [9, 10] found that thecushion could modify the dynamic structural characteristicsand the load transfer mechanism and proved the seismicperformance of the DPR foundation system using numericalsoftware FLAC3D. In particular, the �eld data on discon-nected piled raft foundations subjected to seismic and lateralloading are very limited. �e behaviours of piled raftfoundations recorded at the Paci�c coast during the Tohokuearthquake [11] and the 2015 Nepal earthquake [12] are veryrare case records. It was found that there was little change inthe foundation settlement and the load sharing between theraft and the piles before and after the earthquake. But thehorizontal accelerations of the superstructure were reducedto approximately 30% of those of the ground near theground surface by the input losses due to the kinematic soil-foundation interaction in addition to the base isolationsystem [11].

Since it is di�cult to record the actual �eld data of thepiled raft foundation during an earthquake, physical modelscan play an important role in the study of connected ordisconnected piled raft foundations under seismic or hor-izontal loading. Table 1 summarizes the research on piledraft models subjected to a static lateral load. A series ofhorizontal loading tests on piled raft models was conductedby [20]; in which a horizontal load was applied to theconnected piled raft to discuss the pile bending moment andthe shear force of the raft. Hamada et al. [13, 14] carried outstatic cyclic lateral loading tests on large-scale piled raftfoundations and found that most of the lateral force wascarried by raft friction when there was large contact earthpressure beneath the raft, and piles experienced pullingforces from the raft, behaving like anchors at large de-formations. Sawada et al. [15] carried out a series of statichorizontal loading tests by using a geotechnical centrifugeand found that the horizontal resistance of the pile part inthe piled raft is higher than those observed in the pile groupdue to the raft base contact pressure. In their study, the pileswere rigidly �xed to the raft.

In the above research, the in�uences of the connec-tion between the pile head and raft were not considered.

Matsumoto et al. [17, 18] carried out static and dynamichorizontal loading tests on a connected model piled raft toprove that the resonant frequency of superstructure de-creases when the connection between the raft and the piles ishinged. Horikoshi et al. [19, 21] found that the horizontalsti�ness of the piled raft with the hinged pile head con-nection was smaller than that of the piled raft with the rigidpile head connection, and the inclination of the piled raftduring shaking was much smaller than that of the pile groupdue to the contribution of the soil resistance beneath the raft.Nakai et al. [16] focused on the connection conditionsbetween the raft and piles subjected to dynamic loads byperforming a centrifuge mode test and found that the dy-namic response of a structure was reduced considerably bydisconnecting the raft and pile. However, the detailed be-haviour of disconnected piled raft foundations subjected tohorizontal loads has yet to be clari�ed. �is lack of clari-�cation is partially because disconnected piled raft foun-dations are considered a raft foundation in the currentdesign practice. Since the behaviour of a disconnected piledraft foundation subjected to horizontal or dynamic loads isconsidered fairly complex due to the interaction mecha-nisms among the raft, the granular layer, piles, and soil, thedesign procedure should include the e�ect of these mech-anisms in an appropriate manner.

�is paper examines the horizontal resistance of dis-connected piled rafts. A series of static horizontal loading testswere conducted for a disconnected piled raft foundation toinvestigate the in�uence of vertical loading and the interposedlayer thickness on the sectional forces on the piles. �e mostimportant issues in developing a seismic design concept fordisconnected piled rafts are evaluating the sectional force onthe piles and the lateral bearing capacity of the raft.

2. Horizontal Loading Tests

Static horizontal loading tests of raft foundations, piled raftfoundations, and disconnected piled raft foundations wereconducted in a 1 g �eld.

2.1. Testing Devices and Measuring Devices. �e tests wereconducted using a container indoors. �e test arrangementfor the disconnected piled raft foundation is shown inFigure 2. �e container was 1.5m long, 1.5m wide, and1.2m high, and a piece of 20mm thick transparent temperedglass existed on the front of the container, while theremaining four sides consisted of 10mm thick steel plates.�e horizontal load was applied using a �xed pulley devicewith a counterweight. �e vertical load of the raft was ap-plied by a jack over a tailor-made loading platform with steelballs to ensure that the raft was free to slide horizontally, andthe footing was restrained from a rigid frame. To overcomethe rigid ferrule e�ect on the soil container walls on soil,25mm thick foamed plastic was placed on the inner wall ofthe container to remove the soil level limit. During the testprocess, a layer of lubricating oil was applied to the innerwall of the tempered glass to reduce the friction between thetest soil, half piles, and the box wall.

Horizontal load

Friction force beneath raft

Pile-pileinteraction

Shear force at pile head

Soil displacement caused by raft friction

Horizontal load is carried by interposed layer and

raft friction

Raft-layer-pile interaction

Figure 1: Horizontal load distribution within the disconnectedpiled raft foundations under a horizontal load.

2 Advances in Civil Engineering

*e test device is mainly composed of a soil container,loading device, and measuring system. *e measuring systemconsists of strain gauges, load cells, a data acquisition in-strument, a linear displacement transducer (LDT), and a digitalcamera.*e axial loads and bendingmoments on the piles weremeasured using strain gauges. Earth pressures beneath the raftand on top of the piles weremeasured using earth pressure cells.

2.2. Test Model Overview. Figure 2 shows the test setupincluding the model piled raft, model ground, and loadingapparatus. Figure 3 shows the setup of the model piles priorto preparing the model ground and footing. *e footingconsisted of a high-strength steel plate that was 0.3m long(Br), 0.3m wide, and 0.05m deep placed on 9 piles including3 half piles reinforced in the ground for disconnected piledraft foundations. *e elasticity modulus of the raft footingwas 3.2×105MPa and can be considered as rigid because theraft-soil stiffness ratio is sufficiently high. *e piles weredisconnected from the steel footing. *e piles were madefrom an aluminium pipe with a 20mm outer diameter,0.8mm-thick wall, Young’s modulus of 60000MPa, anda second moment of area of 1.7×10−9m4. *e piles weremade not to be rigid and were 0.4m long, which was longerthan the footing width. *e external layers of the piles andraft were specially treated via mechanical turning to ensurethat the relative roughness of the pile-soil and raft-soil wasgreater than 0.1 so that the ultimate shear resistance did notdepend on the raft surface roughness [22]. Both the lengthand the materials of the piles were selected based on thestiffness of the model sand. Strain gauges were attachedinside the pile to measure the axial load along the pile. Pairsof shear strain gauges were attached to the opposite sides ofthe outer surface of each pile, which were wrapped bya silicone package to measure the bending moment andshear force. *e half piles were affixed to the inside of thetempered glass as needed to take digital photographs, whilepiles P1, P2, P3, and P4 were regarded as the test piles.

2.3. Model Ground. *e test soil samples are dry fine sandwith 0.075–0.25m size particles, and the interposed granularlayer adopts gravel sand with a particle size between 0.5mmand 5mm. *e particle size distributions of the soil samplesand interposed layer are shown in Figure 4, and the physicalproperties of the model sand are summarized in Table 2. *e

internal friction angle estimated from consolidated drainedtests was 32 degrees at a relative density of 60%.When fillingin the sand, dry fine sand was poured in 10 cm thick layersinto the container from a height of 2.2m above the modelground surface. *e sand weight from each layer can becalculated from the sand density and the volume of eachlayer. Stratified compaction was carried out until the soilreached the design height.*e samples were not moved afterlaying the sand for 12 hours to ensure the consistency of thedensity under the pressure of gravity.

2.4. Test Series. *e test cases were conducted in the orderlisted in Table 3.*e piles were penetrated at a rate of 0.3mm/suntil the raft base reached the ground surface for the piled raft.With these installation processes, the piles in the piled raft andthe disconnected piled raft foundations can be regarded asdisplacement piles.*e test cases were focused on the thicknessof the interposed layer and the vertical load to find the factorsaffecting the horizontal load transfer mechanism of the dis-connected piled raft, while R1 and PR2 were used as referencetests. In the test, a vertical load was first exerted on the raftmodel, and a horizontal load was imposed later through thefixed pulley and counterweight after settling. In the trial test,when the vertical load applied on the raft was 800N, thehorizontal ultimate load of the raft reached 350N; thus, thevalue of each loading step was taken as 50N. For each loadingstage, the static load was kept constant for 10mins, and thendata including the raft horizontal displacement record, thestrain data of the pile shaft, and the Earth pressure load weregathered. Digital photographs were taken to record the soildeformation observation points and the soil displacement field.

3. Test Results and Analysis

Piles P1, P2, P3, and P4 were selected as the test piles. Bymeasuring the tensile strain ε+ and the compressive strain ε−at each cross section of the pile shaft, the bending momentscan be calculated by the following equation:

M �EpIpΔε

b0, (1)

where M is the bendingmoment, Ep is the elastic modulus ofthe pile, Ip is the inertia moment of the pile section, b0 is the

Table 1: Summary of previous studies on piled raft foundations subjected to a static horizontal load and this study.

Loadingcondition Condition between raft and pile head Pile length (mm) RVLP (%) Foundation type tested

Hamada et al. [13] Vertical load Rigidly connected 700 45–82 R, PR, PGHamada et al. [14] Vertical load Rigidly connected 700 58–82 R, SP, PR, PGSawada et al. [15] Vertical load Rigidly connected 160 27 R, PR, PGNakai et al. [16] Dynamic load Connected and disconnected 180 0–100 PG, PR, DPRMatsumoto et al. [17–18] Vertical load Hinged and rigidly connected 170 9.6–42.8 PRHorikoshi et al. [19] Vertical load Hinged and rigidly connected 180 60 R, PR, SPPastsakorn et al. [20] Vertical load Rigidly connected 200 8.7–42.4 PR, PG*is study Horizontal load Disconnected 400 72–100 R, DPRNote. RVLP is the proportion of the vertical load carried by the raft; R is the raft; PR is the piled raft; PG is the pile group; SP is the single pile; DPR is thedisconnected piled raft.

Advances in Civil Engineering 3

space between the tensile strain and compressive strain, andΔε � ε+ − ε− is the bending strain of the pile section.

�en, dividing the di�erence between the two sectionalmoments by the distance between the two sections, the shearforce of the piles can be obtained through the following equation:

Q �dM

dz, (2)

where Q is the shear force of the piles and z is the depth ofthe pile section.

3.1. Raft Load-Displacement Curve. To study the behaviourof disconnected piled raft foundations under a lateral load,analyses of the raft and piled raft under a lateral load wereperformed as references. �e total vertical load was pro-portional to themaximum lateral load of the raft foundation,as shown in Figure 5. �e evaluated coe�cient of frictionwas 0.44, calculated as the maximum horizontal load versusthe vertical load in Figure 5.

Figure 6 shows the in�uence of the vertical loads andinterposed layer thickness on the lateral response of the DPR

Fixed pulley

Counter weight

Fine sand

Rigid frameLDTLDT

LDT

Br = 300

5Br = 1500

25D

=50

0L

=40

0

Hc

Loading platform

Raft

Hydraulic jackProving ring

50

Strain gauge

Load cell

Pile

Granular layer

60

D = 202.0Br = 600

Foamed plastic Foamed plastic

Unit: mm

(a)

120

120

120

60

300

1500

P3 P2 P1

P4

120 3030

Unit: mm

PileEarth pressure cell

Half pile

300

(b)

60

60

60

60

60

60

400

Strain gauge

20

60

60

60

60

60

60

2030

400

20 Piled raftDisconnected pile

Unit: mm

(c)

Figure 2: Sketch map of the test model. (a) Side view. (b) Top view. (c) Attached strain gauge arrangement.

4 Advances in Civil Engineering

foundations in sandy soil. It can be illustrated that the lateralcapacity of the DPR is a�ected by the presence of the verticalload but slightly a�ected by the thickness of the interposedlayer. However, the largest displacement distance of the raftincreased with the thickness of the interpose layer in DPRfoundations. Compared to the DPR foundation, the dis-placement distance was restrained in the raft of PR2 and DPR6due to the rigid connection of the pile-raft and vertical load.

3.2. Pile Bending Moment. Figure 7 illustrates the e�ects ofthe interposed layer on the bending moments of the piles.�e bending moments have similar distributions along thepiles. However, compared to the piled raft foundation, thede�ection and themaximummoment of the piles of the DPRfoundations are lower by 56–82% than those in PR2 due tothe interposed layer. Meanwhile, the bending moment de-creases with an increase in the interposed layer thickness.

Figure 8 examines the synergistic e�ects of a horizontalforce and a vertical load applied simultaneously on the raftfoundation.�ree di�erent vertical loads of 400N, 800N, and1600N are considered in this �gure. �e e�ect of the verticalload on the lateral responses of the pile is revealed in Figure 8.Compared with the 400N vertical load, when the load in-creases to 800N and 1600N, the bending moment risesapproximately 70% and 166%, respectively, which means thebending moment, particularly within its upper part, increaseswith the vertical load. �is increase is because the greater thevertical load is, the greater the contact pressure between thebottom of the raft and the soil is, leading to greater frictionaland horizontal forces delivered to the soil.

3.3. Pile Shear Force. Figure 9 exhibits the pile shear forcedistribution considering the interposed layer thickness, wherePR2 is a reference. It can be seen that the maximum pile shearforce appears at the top of the pile and gradually decreases withan increase in the depth. At a distance of 140mm from the piletop (about seven times that of the pile diameter), the pile shearforce becomes 0; if the distance is larger than 140mm, then thereverse shear force comes out, which is the result of the soilround pile resistance on the piles. When the interposed layerthicknesses are 20mm and 40mm, the maximum shear forcesat the pile top are 5.6N and 11.3N, respectively. However, themaximum shear force at pile top in PR2 is 52.1N, so we can geta conclusion that the shear force at the pile top can be reducedsigni�cantly by the interposed layer between the pile head andraft. Otherwise, the shear force at the pile top decreases with thethickness of the interposed layer.

�e e�ect of the vertical load on the lateral responses ofthe pile shear force is revealed in Figure 10. �e resultsindicate that the shear force at the pile top increases with anincrease in the vertical load. �is law is consistent with theabovementioned law that the pile bending moment changeswith vertical loading, as shown in Figure 8.

Based on the e�ect of the interposed layer thickness andthe vertical load on the shear force at the pile top, as shownin Figure 11, it can be seen that the shear force decreases withthe thickness of the interposed layer, while the shear forceincreases with an increase in the vertical load. In otherwords, the interposed layer can adjust the horizontal loadsharing between the pile and soil through the mobility of thesoil particles and shear deformation.

4. Soil Displacement Field

�e soil displacement process during the horizontal loadingtests was captured by a high-resolution camera. �e analysisgrid could be superimposed onto the photographs. �e

Half pile

P1P2P3

P4

Figure 3: Sketch map of the piles.

10 1 0.1 0.01

10 1 0.1 0.01

0

20

40

60

80

100

Perc

enta

ge p

assin

g

Soil particle size (mm)

Gravel sandFine sand

Figure 4: Particle-size distributions of soil in the model test.

Table 2: Physical properties of the model sand.

Sand types Fine sand Gravel sand50 percent diameter D50 (mm) 0.12 2.37Maximum density (g·cm−3) 1.67 1.72Minimum density (g·cm−3) 1.42 1.38Uniformity coe�cient, Cu 2.81 2.13Speci�c gravity of the soil particles 2.64 2.66Relative density 0.6 0.67Internal friction angle, φ (o) 32.23 34.14Cohesion, c (kPa) 1.8 0.6Compression modulus, Es (MPa) 22 36

Advances in Civil Engineering 5

images have a resolution of 7.9 pixels per millimetre. �en,using MATLAB’s toolbox for digital image correlation [23],it is possible to track the movement of the soil and computethe strain �eld that occurs in the soil mass.

4.1. Horizontal Displacement Field. �e soil displacement�eld obtained from the digital image correlation (DIC)technique is shown in Figure 12. To visualize thesoil displacement more easily, colour changes are de�nedin the colour bar. �e interval for DPR6 was 0 <displacement value < 4.0. �e unit of the coordinates ismillimeter. During the initial loading, the displacementis mainly concentrated on the right region of the in-terposed layer, and there is a rather small displacementfrom the left side of the raft. With an increase in thehorizontal load, the soil displacement �eld from the rightside of the raft also increases continuously. Afterwards,the displacement �eld from the right region spreadsalong the lower right direction and forms a local dis-placement concentration area under the right side of raft,as shown in Figure 12(b).

Six characteristic particles (M1∼M6) from the bottomof the raft are tracked based on the soil displacementnephogram, and the horizontal displacement curve isshown in Figure 13. In Figure 13, the dotted line is thehorizontal displacement of measuring points M4, M5, and

M6 under di�erent horizontal loads; the solid line is thehorizontal displacement of measuring points M1, M2, andM3. It can be seen that the horizontal displacement de-creases with the depth of the measuring points. Mean-while, the horizontal displacement from the right side ofthe raft is larger than that from the middle position.Additionally, the larger the horizontal load is, the moreobvious the di�erence value is.

As the raft moves to the right, the soil from the left side,which was squeezed by the raft, losses the support from theraft blade and collapses, leading to the result that thereexists a rather small horizontal displacement regarding thesoil particles on the left side of the raft. In comparison, thesoil particles on the right side of the raft experience weresqueezed and displaced on the right, meaning that thereexists a larger horizontal displacement for soil particlesfrom the right bottom of the raft than that from the leftbottom.

It is revealed that soil particles near the left side of the raftedge angle mainly generate a clockwise rotation, while thosenear the right side of the edge angle are rotated in thecounterclockwise direction due to the pushing of raft, asshown in Figure 14. �ere exists an interface that connectsthe positive and negative corners in the particle movementsystem, where the particles rotate clockwise and counter-clockwise alternatively and �nally form a thorough soil shearzone.

4.2. Soil Shear Failure Band. Figure 15 presents the soil shearband diagram of the DPR foundations under a horizontalload when the vertical load is 1600N and the thickness ofinterposed layer is 40mm. It can be found that when thehorizontal load is small, a number of independent shearbands start to form on the right side of the raft but do notbecome scalable; thus, the interposed layer still has a certainstability. As the horizontal load increases, the shear anddeformation �elds continue to develop, producing localshear zones that �nally interpenetrate with each other toform complete shear bands.

5. Calculation Method of the HorizontalBearing Capacity for the DPR Foundations

5.1. Simpli�ed CalculationModel. Figure 16 is the load pathdiagram of the DPR foundations under both vertical andhorizontal loads. Subjected to both vertical and horizontal

Table 3: Test arrangement.

Case Foundation type Pile diameter,D (mm)

Pile space/pilediameter, S/D

Pile length,L (mm)

Interposed layer thickness,Hc (mm)

Vertical load,P (N) Initial RVLP (%)

R1 Raft — — — — 800 100PR2 Piled raft 20 6 400 — 800 72DPR3 Disconnected piled raft 20 6 400 20 800 100DPR4 Disconnected piled raft 20 6 400 40 800 100DPR5 Disconnected piled raft 20 6 400 40 400 100DPR6 Disconnected piled raft 20 6 400 40 1600 100

0 400 800 1200 16000

100

200

300

400

500

600

700

800

Max

imum

late

ral l

oad

(N)

Vertical load on raft (N)

0.44

Figure 5: Load-displacement curve of the raft.

6 Advances in Civil Engineering

loads on the raft, the raft will �rst transfer the load down tothe interposed layer and the surrounding soil of the raft, andthen later, the load will be passed to the pile and the soilbetween the piles.

According to the horizontal force transfer mechanismof DPR foundations, if the pressure distributed on thebottom of the raft is uniform and experiences vertical andhorizontal load, then its horizontal bearing capacity iscomposed of the bearing capacity of the raft structure, the

interposed layer, the interface between the raft and in-terposed layer, and the interface between the interposedlayer and pile-soil ground. �e minimum horizontalbearing capacity in each part can exert control over theDPR foundations, which means the calculation method forhorizontal bearing capacity of the DPR foundations can belisted as

Q � min QR, QI, QR−I, QZ( ), (3)

where Q is the horizontal bearing capacity of the DPRfoundations, QR is the horizontal ultimate bearing capacity

0 5 10 150

100

200

300

400

500

600H

oriz

onta

l loa

d (N

)

Horizontal displacement (mm)

R1PR2

DPR3, Hc = 20 mmDPR4, Hc = 40 mm

(a)

0 5 10 15 20 250

100

200

300

400

500

600

Hor

izon

tal l

oad

(N)

Horizontal displacement (mm)

DPR4, P = 800NDPR5, P = 400NDPR6, P = 1600N

(b)

Figure 6: Horizontal load versus horizontal displacement of the raft foundations. (a)�e in�uence of the connection condition between theraft and piles. (b) �e in�uence of the vertical load on the DPR.

–300 0 300 600 900 1200 1500

400

300

200

100

Dep

th (m

m)

Pile-bending moments (N·mm)

PR2-P2DPR3-P2, Hc = 20mmDPR4-P2, Hc = 40mm

Figure 7: In�uence of the interposed layer on the responses of thepile bending moments under a 300N horizontal force.

–400 –200 0 200 400 600 800 1000

400

300

200

100

Dep

th (m

m)

Pile-bending moments (N·mm)

DPR4-P3, 800NDPR5-P3, 400NDPR6-P3, 1600N

Figure 8: In�uence of vertical loading on the lateral responses ofthe pile bending moments under a 300N horizontal force.

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of the raft structure, QI is the horizontal ultimate shearbearing capacity of the interposed layer, QR−I is the hori-zontal bearing capacity of the interface between the raft andinterposed layer, andQZ is the horizontal bearing capacity of

the interface between the interposed layer and pile-soilground.

5.2. �eoretical Analysis of Horizontal Bearing Capacity

(1) �e horizontal ultimate bearing capacity of the raftstructure is decided by its own strength. Because theraft in this test is an absolute rigid body, its bearingcapacity is considered large.

(2) Subjected to vertical and horizontal loads, the in-terposed layer appears as horizontal shear failure.Figure 17 shows the interposed layer cell form anypoints for analysis.�e major and minor principal stress is

σ1,3 �σx + σy

2±

�������������σx − σy

2( )

2+ τ2x

√

, (4)

where σ1 is the major principal stress, σ3 is the minorprincipal stress, σx is the x-stress, σy is the y-stress,and τx is the x-shear stress.�e angle between the principal stress plane and thehorizontal plane is

2α0 � arctan−2τxσx − σy( ), (5)

where α0 is the angle between the principal stressplane and the horizontal plane.�e angle between the failure surface and the majorprincipal stress plane is

θf � 45 +φ2, (6)

where θf is the angle between the failure surface andthe major principal stress plane and φ is the internalfriction angle of the interposed layer.�en, the angle between the failure surface and thehorizontal plane is

–20 0 20 40 60

400

300

200

100

0

Dep

th (m

m)

Pile’s shear force (N)

PR2-P2DPR3-P2, Hc = 20 mmDPR4-P2, Hc = 40 mm

Figure 9: In�uence of the interposed layer on responses of the pileshear force under a 300N horizontal force.

–4 –2 0 2 4 6 8 10

Dep

th (m

m)

Pile′s shear force (N)

DPR4-P3, 800NDPR5-P3, 400NDPR6-P3, 1600N

400

300

200

100

0

Figure 10: In�uence of the interposed layer on the responses of thepile shear force under a 300N horizontal force.

3 6 9 12

400

800

1200

1600

Ver

tical

load

(N)

Shear force at pile top (N)

20

40Interposed layerthickness

Vertical load

DPR5 Thic

knes

s of i

nter

pose

d la

yer (

mm

)

DPR3

DPR4

DPR4

DPR6

Figure 11: Shear force at the pile top versus interposed layerthickness and vertical load.

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θ � 45 +φ2+arctan σx − σy( )−(sinφ + 2c · cosφ)2[ ]

2,

(7)

where θ is the angle between the failure surfaceand the horizontal plane and c is the cohesion ofthe soil.If shear failure occurs to the interposed layer, then

σ1 � σ3 ·1 + sinφ1− sinφ

+ 2c ·cosφ

1− sinφ. (8)

From Equations (3) and (7), the maximum hori-zontal shear stress can be listed as

τmax �

����������������������������������σx + σy( )sinφ + 2c · cosφ[ ]

2− σx − σy( )

2√

2,

(9)

where τmax is the maximum horizontal shear stress; cis the cohesion of the interposed layer; σy is thevertical stress of the soil from the top of the in-terposed layer; and σx � (]/1− ]) · σy is the hori-zontal stress of the soil from the top of the interposedlayer, in which ] is referred to as Poisson’s ratio of theinterposed layer.�e horizontal ultimate shear bearing capacity of theinterposed layer is

QI � τmax · S, (10)

where S is the contact area of the raft with an in-terposed layer.

(3) �e horizontal bearing capacity at the interfacebetween the raft and interposed layer is mainly thefrictional force generated between the raft bottomand the interposed layer under the in�uence of thehorizontal sliding trend. Additionally, with passiveearth pressure from the horizontal load direction, the

Y (m

m)

1.0

0.5

Raft

Horizontal load

M1M2M3

M4M5M6

240

192

144

96

48

00 96 192 288 384 480

X (mm)0.00 2.00 4.00

(a)

Y (m

m)

Raft

3.51.8

1.51.0

Horizontal load

0

240

192

144

96

48

0 96 192 288 384 480

X (mm)0.00 2.00 4.00

(b)

Figure 12: Soil displacement nephogram: horizontal load of (a) 100N and (b) 500N.

0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5

40

30

20

10

0

M6

M5

M4

M3

M2

M1

Horizontal displacement (mm)

Dep

th o

f mea

surin

g po

ints

(mm

)

150N200N250N

200N250N100N

M4,M5,M6M1,M2,M3100N150N

Figure 13: Horizontal displacement path of the characteristicparticles.

0 60 120 180 240 300 360 420 4800

40

80

120

160

200

240Raft

Horizontal load

Y (m

m)

X (mm)

Figure 14: Vector diagram of soil particles in the displacement �eld.

Advances in Civil Engineering 9

calculation method of the horizontal bearing ca-pacity is

QR−I � μR−I · P +WR( ) + Ep,

Ep �12· cH2Kp + 2c ·H

���Kp

√,

(11)

where μR−I is the static friction coe�cient betweenthe raft and the interposed layer, c is the soil unitweight, P is the vertical load undertaken by the raft,

WR is the weight of the raft, Ep is the passive earthpressure, Kp is the coe�cient of the passive soilpressure, and H is the buried depth of the raft.

(4) �e bearing capacity of interface between theinterposed layer and pile-soil ground mainly in-cludes the horizontal bearing capacity between theinterposed layer and pile head and the capacity atthe interface between the interposed layer andpile-soil, of which the calculation method can belisted as

QZ � QP + QS,

QP � μI−P · Pp � μI−P ·P · n ·m

1 +m(n− 1),

QS � μI−S · PS � μI−S ·P · (1−m)1 +m(n− 1)

,

(12)

where QP is the horizontal bearing capacity betweenthe interposed layer and pile head, QS is the hori-zontal bearing capacity between the interposed layerand soil, μI−P is the static friction coe�cient betweenthe interposed layer and pile head, μI−S � tan((2/3) ·ϕ) is the static friction coe�cient between the in-terposed layer and soil (the external frictional angleis taken 1/2∼2/3 of the internal frictional angle basedon the empirical value), φ is the soil internal frictionangle, n is the pile-soil stress ratio, and m is the pilereplacement ratio.

5.3. Comparison of the �eoretical Calculation and TestResults. �e theoretical calculation method proposed in thispaper is used to calculate the horizontal bearing capacity ofthe tests DPR4 and DPR6. �e calculated results werecompared with the model test results to verify the appli-cability of the calculation method. �e test parameters arelisted as follows: self-weight of the raft, WR � 167N; basearea, S� 0.09m2; buried depth of the raft, H� 0.01m; re-placement rate, m � 0.01; pile-soil stress ratio, n � 3.56;static friction coe�cient between the raft and the interposed

σy

σx

τy

τx

Figure 17: Model of the interposed layer cell.

ps pp ps

Passive soil pressureRaft

z

Interposed layer

Pile

0

PQ

x

Figure 16: Horizontal force transfer mechanism of DPRfoundations.

Y (m

m)

X (mm)

Raft

Horizontal load

0.01 0.06 0.11

240

192

144

96

48

00 96 192 288 384 480

(a)

Raft

Y (m

m)

X (mm)

Horizontal load

0.01 0.06 0.11

240

192

144

96

48

00 96 192 288 384 480

(b)

Figure 15: Soil shear band nephogram: horizontal load of (a) 100N and (b) 500N.

10 Advances in Civil Engineering

layer, μR−I � 0.42; static friction coefficient between theinterposed layer and the pile head, μI−P � 0.42; and the staticfriction coefficient between the interposed layer and soil,μI−S � 0.39. Other parameters are shown in Table 3. Table 4presents the theoretical calculation results for the horizontalbearing capacity of the DPR foundations compared with thetest data.

It can be concluded from Table 4 that when the verticalload is 800N, the DPR’s horizontal bearing capacity iscontrolled by the bearing capacity of the interface betweenthe raft and interposed layer. However, the bearing capacityof the DPR foundations is controlled by the interposedlayer’s horizontal bearing capacity when the vertical load is1600N, which is consistent with the conclusion thatfoundation failure occurs at the interposed layer in themodel test, as shown in Figure 15. When the thickness of theinterposed layer is 40mm, the vertical loads are 800N and1600N, and the corresponding theoretical calculation resultsof the horizontal bearing capacity for the DPR foundationsare Q � min(QR, QI, QR−I, QZ) � 324N and 483.7N, re-spectively. Meanwhile, the measuring data in the model testare 350N and 500N with the relative error rates of 7.4% and3.3%, respectively. In this sense, the calculation method putforward in this paper appears to be of some usefulness fortheoretical calculations regarding the horizontal bearingcapacities of DPR foundations.

6. Conclusions

In this paper, an experimental and theoretical study of thehorizontal bearing capacity of DPR foundations was pre-sented based on six laboratory tests. *e focus of the studywas on the thickness of the interposed layer and vertical loadon the raft. *emain conclusions of this study are as follows:

(1) Compared to the piled raft foundation, the deflectionand the maximum moment of the pile of the DPRfoundations are lower by 56–82% than those of PR2due to the interposed layer.

(2) *e pile shear force decreases with the thickness ofthe interposed layer, while the force increases with anincrease in the vertical load. In other words, theinterposed layer can adjust the horizontal loadsharing between the pile and soil through the mo-bility of soil particles and shear deformation.

(3) *e soil shear and deformation fields were repro-duced by using the DIC technique. It was seen that

a number of independent shear bands began to formon the right side of the raft but do not becomescalable during the initiation of loading. *en, thelocal shear zones finally interpenetrated with eachother to form complete shear bands at the later stageof the loading.

(4) A calculation method for horizontal bearing capacityof the DPR foundations was put forward, which iscompared with the model test results to prove itscorrectness.

Data Availability

*e data used to support the findings of this study areavailable from the corresponding author upon request.

Conflicts of Interest

*e authors declare that they have no conflicts of interest.

Acknowledgments

*is study was supported by the Natural Science Foundationof Jiangsu Province of China (Project nos. BK20170509 andBK20170501), the National Natural Science Foundation ofChina (Project no. 51778557), and the Natural Science ofFoundation for Colleges and Universities in Jiangsu Prov-ince (Project no. 15KJB580013).

References

[1] H. G. Poulos, “Piled raft foundations: design and applica-tions,” Geotechnique, vol. 51, no. 2, pp. 95–113, 2001.

[2] O. Reul and M. F. Randolph, “Piled rafts in overconsolidatedclay: comparison of in situ measurements and numericalanalyses,” Geotechnique, vol. 53, no. 3, pp. 301–315, 2003.

[3] A. Mandolini, G. Russo, and C. Viggiani, “Pile foundations:experimental investigations, analysis and design,” in Pro-ceedings of the 16th ICSMGE, pp. 177–213, Osaka, Japan,September 2005.

[4] H. Wong, M. F. Chang, and X. D. Cao, “Raft foundations withdisconnected settlement-reducing piles. *omas Telford,” inDesign Application of Raft Foundations, J. A. Hemsley, Ed.,pp. 469–486, *omas Telford, London, UK, 2000.

[5] V. Fioravante, “Load transfer from a raft to a pile with aninterposed layer,” Geotechnique, vol. 61, no. 2, pp. 121–132,2011.

[6] J. Garnier and A. Pecker, “Use of centrifuge tests for thevalidation of innovative concepts in foundation engineering,”

Table. 4: Comparison of the calculation and test results on the horizontal bearing capacity of the DPR foundations.

Horizontal bearing capacity of the piledraft foundation with a cushion

Vertical load 800N (DPR4) Vertical load 1600N (DPR6)Test result

(N)Calculationresult (N)

Relative error(%)

Test result(N)

Calculationresult (N)

Relative error(%)

Raft, QR 350 — — 500 — —Granular layer, QI 350 406.2 16.1 500 483.7 3.3Interface between the raft and granularlayer, QR−I

350 324.0 7.4 500 574.3 14.9

Interface between interposed layer andpile-soil ground, QZ

350 378.2 8.1 500 534.6 7.0

Advances in Civil Engineering 11

in Proceedings of the 2nd International Conference of Earth-quake Geotechnical Engineering, pp. 431–439, Lisboa, Por-tugal, June 1999.

[7] A. Pecker, “Design and construction of the rion antirionbridge,” in Proceedings of Geotechnical Engineering forTransportation Projects, pp. 216–240, Los Angeles, CA, USA,July 2004.

[8] N. Mattsson, A. Menoret, C. Simon, and M. Ray, “Case studyof a full-scale load test of a piled raft with an interposed layerfor a nuclear storage facility,” Geotechnique, vol. 63, no. 11,pp. 965–976, 2013.

[9] B Fatahi, S Basack, P Ryan et al., “Performance of laterallyloaded piles considering soil and interface parameters,”Geomechanics and Engineering, vol. 7, no. 5, pp. 495–524,2014.

[10] R Xu and B Fatahi, “Geosynthetic-reinforced cushioned pileswith controlled rocking for seismic safeguarding,” Geo-synthetics International, pp. 1–78, 2018.

[11] K. Yamashita, “Field measurements on piled raft foundationsin Japan,” in Proceedings of the 9th International Conferenceon Testing and Design Methods for Deep Foundations (IS-Kanazawa), pp. 79–94, Kanazawa, Japan, December 2012.

[12] P. Badry and N. Satyam, “Seismic soil structure interactionanalysis for asymmetrical buildings supported on piled raft forthe 2015 Nepal earthquake,” Journal of Asian Earth Sciences,vol. 133, no. 1, pp. 102–113, 2017.

[13] J. Hamada, T. Tsuchiya, T. Tanikawa, and K. Yamashita,“Lateral loading tests on piled rafts and simplified method toevaluate sectional forces of piles,” Geotechnical EngineeringJournal of the SEAGS and AGSSEA, vol. 46, no. 2, pp. 29–42,2015.

[14] J. Hamada, N. Aso, A. Hanai, and K. Yamashita, “Stress ofpiles and lateral load sharing ratio between piles and raftevaluated from seismic observation on piled raft foundation,”Journal of Structural and Construction Engineering, vol. 77,no. 680, pp. 1537–1544, 2012.

[15] K. Sawada and J. Takemura, “Centrifuge model tests on piledraft foundation in sand subjected to lateral and momentloads,” Soils and Foundations, vol. 54, no. 2, pp. 126–140, 2014.

[16] S. Nakai, H. Kato, R. Ishida et al., “Load bearing mechanism ofpiled raft foundation during earthquake,” in Proceedings of the3rd UJNR Workshop on Soil-structure Interaction, pp. 29-30,Menlo Park, CA, USA, March 2004.

[17] T. Matsumoto, K. Fukumura, P. Kitiyodom, K. Horikoshi,and A. Oki, “Experimental and analytical study on behaviourof model piled rafts in sand subjected to horizontal andmoment loading,” International Journal of Physical Modellingin Geotechnics, vol. 4, no. 3, pp. 1–19, 2004.

[18] T. Matsumoto, K. Fukumura, K. Horikoshi, and A. Oki,“Shaking table tests on model piled rafts in sand consideringinfluence of superstructures,” International Journal of PhysicalModelling in Geotechnics, vol. 4, no. 3, pp. 21–38, 2004.

[19] K. Horikoshi, T. Matsumoto, Y. Hashizume, T. Watanable,and H. Fukuyama, “Performance of piled raft foundationssubjected to static horizontal loads,” International Journal ofPhysical Modelling in Geotechnics, vol. 3, no. 2, pp. 37–50,2003.

[20] K. Pastsakorn, Y. Hashizume, and T. Matsumoto, “Lateralload tests on model pile groups and piled raft foundations insand,” in Proceedings of International Conference PhysicalModelling in Geotechnics, pp. 709–714, St John’s, Canada, July2002.

[21] K. Horikoshi, T. Matsumoto, Y. Hashizume, and T.Watanable,“Performance of piled raft foundations subjected to dynamic

loading,” International Journal of Physical Modelling in Geo-technics, vol. 3, no. 2, pp. 51–62, 2003.

[22] V Fioravante, “On the shaft friction modelling of non-displacement piles in sand,” Journal of the Japaness Geo-technical Society Soils and Foundation, vol. 42, no. 2,pp. 23–33, 2002.

[23] E. Christoph, T. Robert, and G. Daniel, Digital Image Cor-relation and Tracking with Matlab, 2006.

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