Analysis of laterally loaded pile group in clay
T.Ilyas
Department of Civil Engineering, University of Indonesia, Indonesia
C.F Leung
Center for soft ground Engineering, Department of Civil Engineering, National University of Singapore,
Singapore
Y.K.Chow
Center for soft ground Engineering, Department of Civil Engineering, National University of Singapore,
Singapore
Abstract: Study on laterally loaded pile group in clay has been carried out using centrifuge modeling. The observed result will then be
back analyzed. Finite analysis program FLPIER and iterative method developed by NUS group are employed to predict the lateral response of the single pile, 2 x 1 , and 2x2 pile groups. The deflection and bending moment profile result will be discussed in this paper.
A good agreement has been observed between the analysis and observed results
1
INTRODUCTION
The response of single pile and pile group subject to lateral loads
in sand has been reported by several researcher ( McVay et al,
1998; Zhang et al, 1999). As clay characteristics are very different from those of sand, the analysis is conducted to study the performance of single and group pile in clay under lateral loading.
The result of Centrifuge model test for single pile and pile group
have been carried out at National University of Singapore. Details of the NUS Centrifuge are given in Lee et al. (1991). Both
normally consolidated (NC) and over consolidated (OC) clay
have been used as a media. Those observed result will be back
analyzed by three dimensional finite analysis program FLPIER
developed by Mc, Hoit et all 1996 ( to date the professional version is known as FBPIER) and iterative method developed by
Hong, 2000 (two dimensional analysis). In the FLPIER program,
both axial and lateral soil interactions are modeled by non linear
soil spring whose axial and lateral stiff nesses are obtained from
the p-y and t-z curves. The pile-soil-pile interaction is characterized through p-y multipliers which are input by row for describing shadowing effects. The pile’s axial response is characterized
by non linear vertical springs along its length (τ-Z curves) and its
tip (Q-Z curves). The FLPIER have designed for free and fix pile
cap condition. The fix pile cap condition is designed which can
be used over the surface so that the pile cap can rotate when lateral load applied. Hong’s program includes shadowing effect
which is developed through pile-soil-pile interaction using elastic theory in which Midlin solution is used to determine flexibility coefficients. The free and fix pile cap condition are offer to be
used for lateral load apply at the head. Hong’s program is firstly
introduced to be used for desk top personal computer. This paper
will report the detailed load versus deformation responses and
bending moment of single, 2x1, and 2x2 pile groups.
2. PILE - SOIL MODELS AND PARAMETERS
1
The soil parameter, undrained cohesion, is obtained from the Tbar test which is conducted in the National University of Singapore centrifuge. The T bar test conducted at the same G-level as
observed tests for both NC and OC clay. The T-bar test is firstly
introduced and developed by Stewart et al (1991) and followed
by Randolph et al (1998) at the University of Western Australia.
Cohesion undrained cu resulted from T-bar test is in the range of
0 -18 kN/m2 for NC clay and 10 - 25 kN/m2 for OC clay.
For lateral pile representations, the following soil parameter are
required for both NC and OC clay; angle of internal friction ǿ,
coefficient of lateral sub grade reaction nh, shear modulus G, Poison’s ratio ν, Young’s modulus E. Typically, a Poison’s ratio ν of
0.4 is used for both NC and OC clay (also recommended by
FLPIER software for soft clay). Angle of internal friction φ of
22-240 is used for both NC and OC clay. Young’s modulus E is
obtained from the relationship of E= α cu Coefficient α is in the
range of 150-300. For this analysis α is taken 150. The soil shear
modulus G is obtained from the formula G= E/2(1+ν). Limiting
soil pressure py of clay acting on the piles is determined using
Brom’s theory py= 2(1+z/d)cu ≤ 9 cu
To describe single pile behavior, FLPIER uses the p-y curve obtained from observed data done by Ilyas (2002).
3. PREDICTIONS
The model pile is made of hollow alumunium square tube
and instrumented with 10 pairs of strain gauges protected by a
thin layer of epoxy. The pile external width is 12 mm which
simulates a prototype width of 840 mm at centrifuge test of 70g.
The flexural rigidity EmIm of the model pile is 384 kNcm2 and the
prototype EpIp is 922 kNm2. The total model pile length is 260
mm with the lower 210 mm pile length to be inserted into the soil
sample. The prototype pile length is 18.2 m with an embedded
pile length of 14.7 m. The pile cap is designed in such a way that
the piles are tightly secured into respective openings by screws.
Although the piles are fixed to the pile cap, the pile cap itself is
allowed to rotate. The model pile cap is made of 20 mm thick
solid aluminum and place at 50 mm (3.5 m prototype scale)
above the ground level. The center-to-center pile spacing is three
pile width. The prototype lay out for single, 2x1 2x2 and 3x3
group pile is depicted in Fig.1
3.1 Single pile
In Fig 2a and 2b are presented lateral displacement – lateral load
relationship obtained from observed, predicted of FLPIER and
predicted of Hong. The comparison in NC and OC clay shows a
good consistency.
Lateral
load
Lateral
load
3.5m
It can be seen from Figure 2a and 2b at a small lateral displacement (less than 0.1D displacement) the predicted and observed
are shown almost coincide. Hong’s predicted is higher somewhat
of 5% and 14% for NC and OC clay, respectively. At larger displacement (more than 0.1D) the predicted both FLPIER’s and
Hong’s are larger than observed by 5% and 8% for NC clay and
22% and 25% for OC clay, respectively.
Bending moment, at 0.1D (8.4cm) pile head displacement, at any
depth of single pile in NC and OC clay is shown in Figure 3a and
3b, respectively. It was found the observed is slightly larger than
those predicted.
Even though for load-displacement relationship predicted is
somewhat higher than that of the observed for both NC and OC
clay, however for bending moment was obtained the observed is
slightly higher than the predicted.
0
14.7m
clay
Bending moment (kNm)
200
400
600
800
-5
a) NC clay
0
a)
Depth (m)
3d
b)
Figure 1 Lay out of single and pile group
5
10
15
Pred-FLPIER
Pred-Hong
500
a) NC clay
Observed
20
Lateral load (kN)
400
Bending moment (kNm)
300
0
-5
200
400
600
800
b) OC clay
0
Observed
100
200
Predicted (Hong)
0
20
40
60
80
Lateral Displacement (cm)
Depth (m)
Predicted_FLPIER
0
5
10
500
b) OC clay
15
Lateral Load (kN)
400
Observed
Pred-Hong
20
300
200
Figure 3 Bending moment-depth relationship of single pile
100
Observed
Predicted (HONG)
Predicted_FLPIER
0
0
20
40
60
80
Lateral Displacement (cm)
Figure 2 Lateral load-displacement relationship of single pile
2
Pred.FLPIER
In Figure 4 is depicted relationship between applied lateral
load and bending moment maximum for single pile in NC and
OC clay. The maximum bending moment/lateral load response,
observed and predicted, is found to be reasonably linear. Both
FLPIER and HONG’s predicted shown response of larger bending moment compare to the observed at the the same applied lateral load.
400
350
a) NC - 2pile
800
300
Lateral load (kN)
Lateral Load (kN)
1000
NC Clay
250
200
150
100
Observed
400
200
Pred-Hong
50
600
Observed
Pred-Hong
Pred-FLPIER
0
0
500
1000
1500
2000
Pred-FLPIER
0
2500
0
Maximum BM (kNm)
20
40
60
80
Lateral Displacement (cm)
1000
400
b) OC - 2pile
OC Clay
350
Lateral load (kN)
Lateral load (kN)
800
300
250
200
150
100
600
400
Observed
200
Observed
Pred-Hong
Pred-Hong
50
Pred-FLPIER
0
0
500
1000
1500
2000
2500
Pred-FLPIER
0
0
Maximum BM(kNm)
Figure 4 Maximum Bending Moment – Lateral load
of single pile
3.2 Two pile group
In order to better understand the analysis of behavior of pile
group, two pile group in OC and NC clay will be analyzed.
In Figure 5 is depicted lateral loads–displacement relation for 2
piles in NC and OC clay.
As shown in Figure 5a and 5b for 2-pile group the observed
slightly higher than that of FLPIER’s and Hong’s are predicted.
Bending moment FLPIER’s predicted is around 30% and 14%
less than observed for NC clay and OC clay, respectively.
Hong’s, 2000 made a comparison between computed and measured load deflection response of full scale field test (3x3 pile
group) in clay by Rollin et all 1998. He found the agreement of
computed and measured response of the single pile and the group
piles is reasonably good. As can be seen in the Figure 5 at small
displacement Hong’s predicted (less than 0.1D) almost coincide
with the observed. However at large displacement of pile head
the large different occurs. It might be caused due pile cap condition which originally Hong only consider fix pile cap condition
with no rotation.
3
20
40
60
80
Lateral Displacement (cm)
Figure 5 Lateral load – lateral displacement relationship of 2
pile group
In Figure 5a and 5b are also shown the observed is less than the
predicted. In the case of pile group in OC clay as shown in Fig 5b
the Hong’s predicted is higher than observed as well as FLPIER
predicted especially at displacement larger than 0.2D (16.8 cm).
The pile head condition significantly influenced result of lateral
load- displacement especially at pile group in OC clay as can be
seen in the Figure 5b.
3.3 Four pile group
In Figure 6a and 6b are shown lateral loads-displacement relation
for 2x2 pile groups. The FLPIER’s predicted for both in NC and
OC clay show a good agreement to the observed. However,
Hong’s predicted for both in NC and OC clay show over predicted by 30% and 50%, respectively at a displacement of pile
head larger than 0.1D. This condition has very much influenced
by pile cap condition deformed at a large pile head displacement.
Both the Hong’s and FLPIER’s at a small displacement (less than
0.1D) compare to the observed are very close to each other. The
FLPIER prediction show much better for a large displacement of
pile head condition in both NC and OC clay compare to the
Hong’s predicted.
2.The relationship between lateral load and maximum bending
moment response is found to be reasonably linear.
2500
3.For the observed and predicted results of the maximum
bending moment are obtained to be located at between 7 to
9.5 D below the ground surface
a) NC clay
Lateral load (kN)
2000
1500
ACKNOWLEDGMENTS
1000
500
Observed
Predicted(Hong)
Predicted(FLPIER)
This study is a research collaboration between the National University of Singapore and University of Indonesia. The Authors
would like to express their gratitude to the technical staffs at the
Geotechnical Centrifuge Laboratory of the National University
of Singapore
0
0
20
40
60
80
REFERENCES
Lateral Displacement (cm)
2500
b) OC clay
Lateral load (kN)
2000
1500
1000
500
Observed
Predicted(HONG)
Predicted(FLPIER)
0
0
20
40
60
80
Displacement (cm)
Figure 6 Lateral load – lateral displacement relationship
of 4 pile group
4. CONCLUSIONS
The analysis of single pile, two and four pile group have been
carried out. The following conclusions can be obtained bellow:
1.The observed versus the Hong’s and FLPIER’s predicted of
lateral load-displacement relationship as well as bending
moment-depth relationship show reasonably good agreement.
4
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