京 都 大 学 防 災 研 究 所 年 報 第48号 B 平成17年4月
Annuals of Disas. Prev. Res. Inst., Kyoto Univ., No. 48 B, 2005

Dynamic Behavior of Group Pile Under Lateral Spreading

Tetsuo TOBITA, Susumu IAI, Kenji NAKAYAMA*,
Masato NAKAMICHI**, Kikuo HIRATA***Graduate school of Civil and Earth Resources Engineering, Kyoto University, Japan* Kinki Regional Development Bureau, Ministry of Land, Infrastructure and Transport, Japan
Synopsis
Results of a series of centrifuge experiments to study the dynamic response of pilefoundations under lateral spreading were compared to the results of numerical analysis.
Experiments were carried out under the centrifugal acceleration of 40 G. Piles in the model
foundation were lined up 3 by 3 pattern with a spacing of three pile diameter, and both pile headand bottom were rotation fixed. Piles were placed in the inclined ground of saturated sands andapplied lateral loads due to the ground deformation. The effective stress finite element analysis was
conducted to simulate these experiments. Computed time histories of pile head acceleration anddisplacement were consistent with those obtained from experiments. However, much smaller
surface ground deformation in simulation might cause small amplitude of bending moments. Some
calibration in the numerical modeling may be required to have more consistent results on bending
moments.
Keywords: Pile foundation, Centrifuge experiments, Numerical simulation, Liquefaction

1.

Introduction

Many waterfront structures are built on deep
foundations which are vulnerable to lateral loads
especially due to the ground deformation during and afterlarge earthquakes. Liquefaction-induced lateral spreadingis one of the major causes of that ground deformation.
(e.g., Mizuno 1987; Matsui and Oda 1996; Hamada andO'Rourke 1992; O'Rourke and Hamada 1992; Tokimatsu
and Asaka 1998). Pile foundations not only support theinertial loads of the superstructures but also suffer thelateral loads due to the ground deformation. Therefore,
the dynamic behavior of soil-pile system have been
intensively studied for the last decade. Dynamic behaviorof pile foundations is highly nonlinear and influenced bynumbers of parameters, such as material of a pile and soil,

pile diameter and spacing, natural period ofsuperstructures and soil-pile system. To study such acomplicated phenomena, full scale experiment, althoughcases are limited, have been conducted (e.g., Brown et al.
1988; Peterson and Rollins 1996; Ashford and Rollins
2002). Brown et al. (1987) conducted large-scale tests forgroup pile subjected lateral load and proposed thep-multiplier concept to reshape the p-y curve of single
pile to take into account the group effect. Rollins et al.
(2005ab) conducted lateral loading tests with a full-scale
pile group under blast-induced liquefaction anddeveloped p-y curve for liquefied ground.
Instead of carrying out those full scale experiments,
numerous small scale model tests have been employedusing shaking tables or the geotechnical centrifuge (e.g.
Tobita et al. 2004). Abdoun et al. (2003), for example,

2.

Centrifuge modeling for group pile behavior
under lateral spreading

Experiments were carried out with the geotechnicalcentrifuge at the Disaster Prevention Research Institute,
Kyoto University (DPRI-KU). The centrifuge with

Table 1 Soma-Silica sand No. 5.

emax
1.105

emin
0.685

D50(mm)
0.38

Uc
1.5

100

Percent finer byweight(%)

conducted centrifuge experiments with a slightly inclined
laminar box to study pile response under lateral spreadsof 0.7 to 0.9 m. One of their results is consistent with theobservation that the maximum permanent bending
moments occurred at the boundaries between liquefied
and non-liquefied ground.
Numerical simulation is also widely used to simulate
the dynamic response of pile foundations (e.g. Reese etal. 1996; Kitade et al. 2004). Most of two dimensionalmodel uses p-y curve concept, or soil-pile interaction
spring, that is required to simulate the three dimensional
effects, such as slippage of soils near a pile surface.
Therefore, it is important to properly determine thesoil-pile interaction spring for a reasonable estimate ofpile response. In the present study, the interaction springobtained by the method proposed by Ozutsumi et al.
(2003) is used to simulate those afore mentioned three
dimensional effects observed in centrifuge experiments,
and that is of prime objective of this paper.

80
60
40
20
0
0.01

0.1
1
Grain size (mm)10Fig. 1 Particle size distribution curve for Soma-Silica
sand No.5.
rotation radius of 2.5 m has dual swing platforms at bothends of arms. The maximum capacity is 24 G-tons with amaximum centrifugal acceleration of 200 G. A shake
table unidirectionally driven by a servo hydraulicactuator is attached to a platform and it is controlled
through a personal computer (PC) on the centrifuge arm.
All the equipment necessary for shake table control is put
together on the arm. The PC is accessible during flightfrom a PC in the control room through wireless LAN and

Fig. 2 Cross section of centrifuge model.

“Remote Desktop Environment” of WindowsXP(Microsoft, 2003). Capacity of the shake table is 15 kN,
10G and ±5 mm in maximum force, acceleration anddisplacement, respectively. Base excitation was given toa rigid soil box.
The uniform model ground was made of Soma-Silica
sand No. 5 having the physical properties shown in Table
1 and the particle size distribution curve shown in Fig. 1.
To study the behavior of pile foundations under lateral
spreading, the model ground surface was inclined withthe target inclination of 26.6° to the horizontal(vertical/horizontal=1/2) as shown in Fig. 2 and Photo 1,
thus simulating rather steep slope which might beencountered in port facilities. The ground had flat part indownstream to simulate the sea floor. Sands were slowly
sprinkled over the soil box filled with a viscous fluid.
The target relative density of the ground was set to be
40 %. However, slightly lower values were obtained for
all the cases as shown in Table 3. During the preparationof inclined ground, some fraction of surface soils were
slowly moved downward due to the gravitational force,that might caused a development of the loose surface
deposit.
A viscous fluid made of Metolose (Type: SM-25
Shin-Etsu Chemical Co.) was used to properly simulatepore water pressure dissipation during and after shaking.
Metolose is water-soluble cellulose made of organic
material. After preparing in the room temperature, thefluid was tested using a viscometer to achieve thespecified viscosity (40cSt for 40g centrifugal
acceleration) before pouring sands. There might be slightdifference between the room temperature and thetemperature in the centrifuge pit during flight but theeffects of the difference was considered negligible
because the duration of flight is about 20 to 30 min
before the dynamic loads were applied.
A pile with a 7 mm diameter brass tube simulated a
prototype diameter pile of 0.28 m at 40 G. Other
dimensions and mechanical properties of a model pile
are shown in Table 2. As shown in Fig. 2, group piles
were lined up 3 by 3 with a spacing of 3 times a pile
diameter. Both the pile top and bottom were set inrotation fixed condition. To achieve the fixity conditionat the pile head, each pile in group was squeezed into ahole on an aluminum plate of 2 mm thickness, then amass of 2.7 kg was placed on top and tied up with theplate. The weight of mass was determined so that thenatural period of soil-pile system becomes about one

Photo 1 Side view of the model ground.
Table 2 Model pile properties.

LengthOuter diamter (D)Wall thickness
Young's modulus (E)Moment of inertia of area (I)Bending stiffness (EI)

Model
0.25
7
0.9
101
82
8.2

Prototype
Uni
10
m
280
mm
36
mm
101
Gpa
2.1x108mm
8
2.1x10
MN-m

Table 3 Experimental condition.

CS1
CS2
CS3
CS8

Input
Dr (%)
Sin
35.4
Near Field
36.0
Plate Boundary 35.5
Plate Boundary 40.5

second. The bottom of each pile was plugged into a holeon a bottom plate.
In a series of model tests, 6 accelerations, 2
displacements and 15 strain gage readings of a pile, and4 pore water pressures were measured as shown in Fig. 2.
A laser displacement sensor was used to measure pilehead displacement. Accelerometers of strain gage type
and pore pressure transducers of semi-conductor typewere used. Total four cases are presented in this study aslisted in Table 3, CS1: sinusoidal input with 40 Hz, CS2:
synthesized near-field earthquake, CS3: synthesized plateboundary earthquake, and CS8: duplicated test of CS3.
Input accelerations measured at the base of soil box are
shown in Fig. 3. In what follows, units are all in
prototype, unless otherwise noticed.
2.1 Ground Deformation After Shaking
Tracing the shape of the ground surface before andafter shaking, and vertical markers attached on the insideof soil box, the ground deformation pattern is drawn as

Fig. 4 Ground deformation after shaking.
CS3.

Fig. 3 Input acceleration in centrifuge experiments.
shown in Fig. 4. Large ground deformation of 2 to 4 m
was occurred after shaking. It is clear that duration of
shaking, i.e., 10, 60, and 100 seconds for CS1, CS2 andCS3/CS8, and the magnitude of surface displacement
proportionally increase, and as duration becomes longer
the ground surface tends to become flat. For CS1,
compared with other cases the ground at deeper depth
was mobilized and the surface displacement is about 3 m.
While for CS2 and CS3/CS8, the surface displacements
are, respectively, about 2 and 6 m, and the ground atshallower depth was mobilized. The pattern of theground deformation of CS8 is consistent with the one of

2.2 Pile Head Acceleration, Pile Head Displacementand Excess Pore Water Pressure
Results of a series of centrifuge experiments, CS1, CS2,
and CS3, are shown in Fig. 5. Piles had no permanent
deformation after experiments and therefore were within
an elastic range. Initial vertical effective stress drawn in
Fig. 5 is computed based on the vertical depth of thesensors (P1) from the ground surface. Comments foreach case are as follows:• CS1: Compared with the input acceleration shown in
Fig. 3, the peak of measured pile head acceleration in
Fig. 5 seems to be reduced with the development ofexcess pore water pressure. The pile head is shifted
downward about 400 mm after about 5 seconds andthe residual displacement of 300 mm is measured.
• CS2: Compared with the input acceleration shown in
Fig. 3 (b), pile head acceleration is amplified about
100 %, even after the soil is liquefied. The pile head is
moved downward with the maximum displacement of
600mm, and the residual displacement of about 80
mm is observed.
• CS3: The pile head acceleration is amplified similarly
to CS2. Maximum displacement is 600 mm indownstream, and residual displacement is about 80
mm. Compared to the ground deformation of about 6
m as shown in Fig. 4, the residual displacement issmall. This is because liquefied soil is soft enough topass through the space between the piles.

Fig. 5 Time histories of pile head acceleration (a) and pile head displacement (b) and excess pore water pressure (c).
0.6
CS1

300

#7 Silica sand: Dr=40%
Ground slope: 26.6 (deg.)

250
200
150

CS8

100

CS2

50

N=5

0.5
0.4
0.3
0.2
0.1

CS3

0

0
0

50

100

150

Duration of liquefaction (sec)Fig. 6 Duration of shaking and pile head displacement
The relation between the duration of liquefaction andthe pile head displacement obtained from a series of theexperiments is summarized in Fig. 6. It is clearly shownthat the residual pile head displacement becomes smaller
as duration of liquefaction becomes longer, although, asmentioned earlier, the ground deformation contrary
becomes larger. This is because liquefied soils are softenough to pass through the space between piles. From
the residual displacement of CS2 and CS3, the resistanceforce of pile and lateral force of the deformed ground
may be in equilibrium at the pile head displacement of
80 mm.
3.

Stress ratio (τ/σ o')Pile head displacement
(mm)

350

Numerical simulation

Two dimensional effective stress finite element
analysis, FLIP (Iai et al. 1992), is employed. Research isstill on going and therefore results of CS2 only arepresented. Physical properties of soil corresponding to
the SPT value of 5 were assumed because of the lack ofexperimental results of the soil used in the centrifuge
tests. Soil is modeled as having the multi-shear

0

5

10

Number of cyclic loads

Fig. 7 Liquefaction strength curve.
mechanism and piles are modeled with elastic beam
elements. No joint elements but soil-pile interaction
springs are implemented between soil and pile elements.
The liquefaction strength curve in simulation is shown in
Fig. 7. The meshes before and after the shaking areshown in Fig. 8. Compared to the one shown in Fig. 2,
the pattern of ground deformation is similar but themagnitude of deformation is computed small. Pile headacceleration and displacement are compared in Fig. 9.
The shape and amplitudes of both acceleration anddisplacement are consistent with the results of theexperiment, except high spikes on the measured
acceleration, and the amplitude of displacement which iscomputed smaller than the measured when piles moved
downward.
Time histories of excess pore water pressure of P1 andP2 shown in Fig. 10 agree with experiments, however,for those of P4 and P5, simulation gives build up ofpressure about one to two seconds earlier. Simulated
pore pressure adjacent to piles may depend strongly on
the response of piles. The elements to plot P4 and P5 areadjacent to the pile and therefore they may be subject toFig. 8 Mesh and deformation after shaking: CS2

Fig. 9 Comparison of pile head acceleration and displacement: CS2.

Fig. 10 Comparison of excess pore water pressure: CS2.
large shear compared to the elements of P1 and P4
surrounded by soil elements.
Time histories of bending moment for the downstream
pile (GD1, GD3, and GD5) are plotted in Fig. 11.
Computed bending moments from GD1 and GD3 areconsistent with measured in terms of their amplitude andphase. As shown in Fig. 2, however, those are locatedabove the ground surface. For the bending moments
located under ground, GD5, computation gives smaller
amplitude after 8 seconds than the ones measured in theexperiment, This may be attributed to the small grounddeformation in simulation, and require some calibrationin the numerical model. Bending moments in depth isplotted in Fig. 12 for the time of 5.6 sec (a) and 41.8 sec(b). In Fig. 12(a) at t=5.6 sec, the trend of the curve issimilar each other, however, at time 41.8 sec shown in
Fig. 12(b) piles above the ground surface were mostly
bent in computation.
4.

Conclusions

Fig. 11 Comparison of time history of bending moment of downstream pile: CS2.

Bending moment (kN m)

Bending moment (kN m

-50

-200

0

50

0

20

0

Depth (m)1References2
3
4

ground surface with a reasonable degree of accuracy.
However, the ground deformation and the bending
moments of piles under ground were simulated to besmall compared to the one in the experiments. Further
calibration is required numerical model.

MeasuredComputed

5(a) t=5.6s(b) t=41.8s

Fig. 12 Comparison of bending moment in depth: CS2.

To study the dynamic response of pile foundations
under liquefaction-induced lateral spreading, centrifuge
experiments are conducted with inclined ground surface.
Experimental results show that the duration ofliquefaction is inversely proportional to the residual pilehead displacements because liquefied soils are softenough to flow between piles and give less lateral force
and enough time for piles to be unloaded. This may
possibly be observed in pile supported waterfront
structures. However, the piles have to survive large
lateral force that gives the maximum pile headdisplacement.
Numerical analysis based on the effective stressanalysis, FLIP, properly simulated pile head acceleration,
pile head displacement, and bending moment above theAbdoun, T., Dobry, R., O'Rourke, T.D., and Goh, S.H.
(2003): Pile response to lateral spreads: Centrifuge
modeling, Journal of Geotechnical and Environmental
Engineering, , ACSE, Vol. 129, No. 10, pp. 869-878.
Ashford, S.A., and Rollins, K. M. (2002): TILT: The
Treasure Island liquefaction test, Final Report No.
SSRP 2001/17, Department of Structural Engineering,
University of California, San Diego.
Brown, D.A., Reese, L.C., and O'Neill, M.W. (1987):
Cyclic lateral loading of a large-scale pile group,
Journal of Geotechnical Engineering, ASCE, Vol. 113
No. 11, pp. 1326-1343.
Brown, D.A., Morrison, C., and Reese, L.C. (1988):
Lateral load behavior of pile group in sand, Journal of
Geotechnical Engineering, ASCE, Vol. 114, No. 11, pp.
1261-1276.
Hamada, M., and O'Rourke, T.D. (1992): Case histories
of liquefaction and lifeline performance during pastearthquakes, Technical Report NCEER-92-0001,
National Center for Earthquake Engineering Research,
State University of New York, Buffalo, 2 vols.
Iai, S., Matsunaga, Y., and Kameoka, T. (1992): Strain
space plasticity model for cyclic mobility, Soils andFoundations, Japanese Society of Soil Mechanics andFoundation Engineering, Vol. 32, No. 2, pp. 1- 15.
Kitade, T., Kawamata, K., Ichii, K., and Iai, S. (2004):
Analysis of laterally loaded pile groups using 2-D FEM,
The 11th International Conference on Soil Dynamics &Earthquake Engineering, The 3rd International
Conference on Earthquake Geotechnical Engineering,pp. 850-856.
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Geotechnical Aspects of the January 17 1995
Hyogoken-Nambu Earthquake, pp. 189-200.
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Co., One Microsoft Way, Redmond, WA 98052-6399,
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National Center for Earthquake Engineering Research,
State University of New York, Buffalo, 2 vols.
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Peterson, K.T., and Rollins, K.M. (1996): Static anddynamic lateral load testing of a full-scale pile group in
clay, Civil Engineering Department Research Report,
CEG. 96-02, Brigham Young University, Provo, Utah.
Reese, L.C., Wang, S.T., Arrellaga, J.A., and Hendrix, J.
(1996): Computer program GROUP for windows,
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S.A. (2005a): Lateral resistance of a full-scale pilegroup in liquefied sand, Journal of Geotechnical andEnvironmental Engineering, ASCE, Vol. 131, No. 1, pp.
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Measured and computed lateral response of a pilegroup in sand, Journal of Geotechnical andEnvironmental Engineering, ASCE, Vol. 131, No. 1, pp.
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側方流動を受ける群杭基礎の動的挙動
飛田哲男・井合進・仲山賢司*・中道正人**・平田喜久男***

京都大学社会基盤工学専攻
国土交通省近畿地方整備局神戸港湾空港技術調査事務所**

要旨
液状化による側方流動地盤中の杭基礎の挙動について、遠心模型実験および数値解析により考察した。模型実験は40分の1の縮尺で、用いた杭の配置は3x3の9本群杭、杭間隔は杭径の3倍である。杭の上下端は固定とした。杭基礎を配置した飽和地盤表面に傾斜30度を設け、地震波を入力し液状化による流動を発生させた。
実験より、流動初期には杭頭の変位は地表面の変位に追随しているが、最終的な杭頭の変位は地表面変位よりも小さくなった。これは杭の剛性が高く杭間を土がすり抜けるためである。この実験結果より2次元有効応力解析法の妥当性について検討したところ、地盤ばねを適切に評価することで、すり抜けの効果を再現することができた。
キーワード:杭基礎，遠心模型実験，数値解析，液状化