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Study The Behavior of Pile Group Under Torsional and Horizontal Load
To cite this article: Abdulameer Qasim Hasan and Rafi M. Qasim 2021 J. Phys.: Conf. Ser. 1773 012032

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ISC-AET 2020 IOP Publishing
Journal of Physics: Conference Series 1773 (2021) 012032 doi:10.1088/1742-6596/1773/1/012032

Study The Behavior of Pile Group Under Torsional and

Horizontal Load

*Abdulameer Qasim Hasana1, Rafi M. Qasima2

a
Basra Engineering Technical College, Southern Technical University, Basra, Iraq.
1
a.almubarak@stu.edu.iq, 2 rafi.mohammed@stu.edu.iq

Abstract. Many structures are subjected to torsional and horizontal loads in addition to vertical load
lead that the foundation of these structures may be collapsed. The proposed model for pile groups
consists of an elastic beam-column that represents the pile, rigid cap and nonlinear spring to simulate
the soil. In the horizontal direction, the p-y curve method is used to calculate the subgrade reaction
of soil while the τ-θ curve method and the load transfer method are used in the vertical direction. The
effect of pile group and load coupling is considered by the p multiplier method in the pile head. A
parametric study is carried out under the combined action for horizontal and torsional loads. The
study shows that unequal shear force distribution in the head of piles is very significant. The axial
force variation in each pile with different length is obtained. The study is very important to take into
account the design pile group under combined loads.

1. Introduction
Some engineering structures such as offshore oil platforms, cross-sea bridges, towers, and trans-sea
transmission towers are subjected to horizontal loads by water waves, ship impacts, and wind forces. These
forces are transmitted to the foundation in the form of eccentricities loads and cause torsion and complex
structural responses. Many Bridges have been subjected to ship collision accidents, and the foundations of
these Bridges have been collapsed [1]. Many researchers have carried out theoretical and experimental
studies on a pile or pile groups under horizontal loads [2-6], but there are few studies on the effects of pile
groups under horizontal and torsional loads. Hu et al. [7] study the experimental behaviour of a single pile
subjected to torsion load, the result of the test shows the torsion is reducing the horizontal capacity by 30%
to 50%. Abdulameer Q. [8] studied the experimental behaviour of a single pile subjected to pure torsion
load for different piles section and different soil type, the result of the tests show the pile section and sand
soil is very sensitive to torsion load. Konj et al. [9] carried out many experimental studies and theoretical
models on pile groups under twisting load. He was found that the strong coupling effect directly between
torsional and horizontal degrees of freedom of all piles, the torsion has little influence on the lateral capacity
of the pile, and there are significantly improve in torsional capacity when the pile is trusted. The present
work used a calculation method to study the behavior of pile groups under torsional and horizontal loads
and discusses the force law of pile groups under combined loads.

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ISC-AET 2020 IOP Publishing
Journal of Physics: Conference Series 1773 (2021) 012032 doi:10.1088/1742-6596/1773/1/012032

2. Calculation Method

2.1. Theoretical Model

Under the torsional and horizontal loads, the pile's cap is subjected to horizontal displacement and rotation,
and the piles are subjected to complex forces and moments. The displacements, forces, and moments on the
piles will be not the same. Figure 1 shows the piles cap under torsional and horizontal loads.

A-Horizontal Load B-Torsional load C-Horizontal and Torsional load

Figure 1. The pile's cap under torsional and horizontal loads.
This study presents a new model to calculate the behavior of pile group as shown in Figure (2). The new
model assumed the following: Piles are assumed elastic beams, the pile's cap is regarded as rigid and has a
large thickness, and the soil action is replaced by nonlinear springs. Horizontal spring (p–y curve), torsion
spring (τ–θ curve) and friction vertical spring (τ–z curve) are used in the side of the pile, vertical springs
(q–z curves) and torsion springs (Tt –θ curves) are used in the pile end. The p-y curve method depended on
the lateral loading at the pile head, and the spring is in the same plane of the pile body. However, the p-y
curves method not applicable under horizontal and torsional loads, because the forces and moments are
applied in different planes. To solve the above problem, vertical and horizontal springs are used at each
node in the pile.

(a) Cap coordinate (b) Base model (c) Pile model

Figure 2. Group pile Model.

2.2. Cap Forces and Displacements

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Journal of Physics: Conference Series 1773 (2021) 012032 doi:10.1088/1742-6596/1773/1/012032

The total coordinate system of the model at the center of the cap for calculation, the total coordinate system
is translated to the top of the pile to form the local coordinate system for each pile. Single pile calculations
are done according to the local coordinate system; each coordinate system is defined in the basic physical
quantity as shown in Figure (2) [10].
Cap center displacement vector s  = [S S S θ θ θ ]
External load vector F  = [F F F M M M ]

Pile foundation displacement vector s  = S S S θ θ θ
 
Back pile force vector s = F F F M M M
Where s is the displacement, the rotation angle, F is the force, and M is the bending moment.

2.2.1. Equations of Equilibrium force

The cap is subjected to the external load and the reaction force of each pile is taken to the center of the cap
(origin), the balance forces expression is as follows;
F = ∑ F
⎫
F = ∑ F
⎪
⎪
F = ∑ F
M = ∑(−F Z + F y + M )⎬ Where is F = ∏(S) = ∑(A F  ) (1)
M = ∑(F Z − F x + M ) ⎪⎪
M = ∑(−F y + F x + M ) ⎭

Among them, Π(S) is the total reaction force of each test pile head, and Ai is the i-th pile conversion [10].

1 0 0 0 0 0
⎡ 0 1 0 0 0 0⎤
⎢ ⎥
0 0 1 0 0 0⎥
matrix, A = ⎢ 0 −z y
⎢ 1 0 0⎥
⎢ z 0 −x 0 1 0⎥
⎣−y x 0 0 0 1⎦

2.2.2. Displacement equations at each pile head

In the rigid cap, after the displacement of the cap is determined, the displacement of each pile head can be
derived through the displacement of the cap, which has the following relationship [10]:

S = S + z θ − y θ
⎫
S = S − z θ − x θ ⎪
⎪
S = S + y θ − x θ 
Where S  = A S (2)
θ = θ ⎬
θ = θ ⎪
⎪
θ = θ ⎭

2.3. Stiffness Matrix Definition

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ISC-AET 2020 IOP Publishing
Journal of Physics: Conference Series 1773 (2021) 012032 doi:10.1088/1742-6596/1773/1/012032

The total reaction force Π(S) at each pile head is regarding the displacement of the cap [10],
  ∑   !"  ∑  # !" #
= = (3)
  # 
by substitute equation 2, one can obtain
# 

= A (4)
by substitute equation 4 in equation 1 yields to,
 ∑  # !"   #
= ∑ A (5)
# #
the i-th pile head stiffness matrix:
  #
K = (6)
#
The simultaneous equations (4) to (6) define the total stiffness matrix K:
 
K= = ∑ A K  A

(7)

2.4. Solving of The Equation

2.4.1. Newton Iteration Method

Newton iterative method has quadratic convergence characteristics, which brings good convergence speed
and is more suitable for nonlinear calculation. According to the load balance equation (1) [7].
Φ(S) = Π(S) − F = 0 (8)
Using the Newton iteration method, In the case where the n-th approximate solution S(n) is obtained,
Φ(S(n+1)) can be expressed as a Taylor expansion in which only the linear term is retained near S(n), that
is,
-
Φ S (&'*) ≡ Φ S (&) + # . (/) ∆ S (&) = 0 (9)

Introducing the total stiffness matrix (7), gives
- (()3) 
. (/) =
# 
. (/) = ∑ A K  A . (/)
#
(10)
 
Based on,
 3*
∆ S (&) = ∑ A K  A . (/)
" [Π(S) − F] (11)

(&'*) (&) (&)
S = S +∆S (12)

2.4.2. Flow Chart

To analyze the nonlinear behaviour of pile group under the horizontal and torsional loads based on the above
calculation model, MATLAB program is used to simulate the calculation model. The calculation process is
shown in Figure 3.

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ISC-AET 2020 IOP Publishing
Journal of Physics: Conference Series 1773 (2021) 012032 doi:10.1088/1742-6596/1773/1/012032

Figure 3. Flow chart of calculation.

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ISC-AET 2020 IOP Publishing
Journal of Physics: Conference Series 1773 (2021) 012032 doi:10.1088/1742-6596/1773/1/012032

3. Verification Model
Che et al. [10] conducted a large-scale model test on the horizontal and torsional load of a 3×3 pile group.
The test pile is made of steel pipe pile; the pile diameter D is 114 mm, the wall thickness is 4.5 mm, the pile
length is 5.95 m, and the length above the mud surface is 2.54 m, and the pile end is a cone-shaped pile tip.
The cap is a cast-in-place reinforced concrete with dimensions 1026 × 1026 mm and 300 mm thick, and the
pile spacing is 3D, as shown in Figure 4. The test soil sample was sand, soil parameters: K=23464 kN/m3,
internal friction angle 30°, floating weight = 8.8 kN/m3, ultimate side friction = 8 kPa, ultimate end
resistance = 1200 kPa. Two different eccentric loadings were used in the test, 6D, and 11D respectively. In
the test, the maximum torsion is 21.8 kN.m, and the maximum force is 31.9 and 17.4 kN in two directions.
This paper verifies the eccentricity as a 6D test. In the model, the horizontal reaction force and the stiffness
calculation of the sand p–y curve proposed by Reese et al. [11]; the vertical reaction force and stiffness
calculation are based on the load transfer curve of the sand pile side and pile end proposed by Coyle et al.
[12 ], the ultimate resistance reduction coefficient of the lateral soil of the pile is 0.5; the torsional reaction
force and stiffness are calculated by torsional load calculation method and the load transfer curve is proposed
by Kong [13]. the torsional reaction force and stiffness are calculated by the above-mentioned method; the
load transfer curve is proposed by Kong [13]. The calculation parameters of the load transfer curve are
calculated in the test, the results of a single pile torsion test were obtained, A=4.5×107
N/m2㸪B=8800×0.23z N/m2㸪At=1090 N/m㸪Bt = 52 N/m㸪β=2.0ࠋ
In this paper, the torsional frictional resistance of the pile side varies linearly with the depth z. The elastic
modulus of the pile is E=2.06 MPa, and the shear modulus G=7.9 MPa, see Figure 4.

Figure 4. (3×3) Pile group test under combined loads.

It can be seen from the analysis that the calculation results of the horizontal load-displacement curve and
the torsion-angle curve of the pile cap are in good agreement with the measured results, which reflects the
behaviour of the pile group under horizontal and torsional loads, as shown in Figure 5.

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ISC-AET 2020 IOP Publishing
Journal of Physics: Conference Series 1773 (2021) 012032 doi:10.1088/1742-6596/1773/1/012032

Exp. Result Model Result Exp. Result Model Result

35 25
Horizontal Load, kN

30
20

Torsion, kN.m
25
20 15
15
10
10
5 5
0
0 50 100 150 0
0 5 10
Y-Displacement, mm
Twist Angle, deg.
(a) Horizontal-Displacement Curve (b) Torsion-Twist Angle Curve

Exp. Result Model Result

35
30
Horizontal Load, kN

25
20
15
10
5
0
0 0.5 1 1.5 2 2.5 3
Angle of Inclination, deg.
(c) Horizontal Load-Angle of Inclination,Curve

Figure 5. Load, Displacement, and Angles curves of cap center.

Under the horizontal loads, the piles in the front of the pile group are the most stressed, also when the piles
are subjected to torsional loads all the piles have the same force state. In Figure 6 (T indicates that the
internal force of the pile head is obtained by the test, and S indicates that the internal force of the pile head
is calculated; the numbers represent different horizontal force load values). Under the combined action of
horizontal and torsional loads, the internal force distribution in each pile head combines the characteristics
of the two alone and is more complicated. The maximum internal force in the pile head appears in the corner
pile. Among them, the total bending moment and total shearing force of the pile 7 are the largest. The
calculation results and measured results are reflecting this fact. Pile 5 has the smallest bending moment and
pile 6 head has the smallest shearing force.

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ISC-AET 2020 IOP Publishing
Journal of Physics: Conference Series 1773 (2021) 012032 doi:10.1088/1742-6596/1773/1/012032

16 T-10.82 T-22.51 T-31.87

14 S-9.57 S-22.33 S-31.9
Bending Moment, kN.m

12
10
8
6
4
2
0
1 2 3 4 5 6 7 8 9
Pile Number
(a) Pile Head Bending Moment Distribution

T-10.82 T-22.51 T-31.87

10 S-9.57 S-22.33 S-31.9

8
Shear Force, kN

0
1 2 3 4 5 6 7 8 9
Pile Number
(b) Pile Head Shear Force Distribution

Figure (6) Distribution of Bending Moment and Shear Force on Pile Head

4. Parameter Study

4.1. Influence of Pile Spacing on Shear Force.

when the pile spacing increases, the force arm of each pile to the center of the cap increases also the
horizontal force in the pile head which resists the torsion is reduced so that the total shear force of the pile
head is reduced. For smaller spacing, the internal force distribution in the pile head is more significant. The
pile 7 in the front row is the most sheared, and the maximum shear force in the pile head is about 1.6 to 2.4
times the nominal average shear force in the pile 1, the non-corner pile 4 and pile 8 are also subject to a
large shearing force, as shown in Figure 7. The load change has little effect on the total shear force
distribution in the pile head, mainly because the horizontal stiffness of the pile has little change within the
horizontal load range.

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ISC-AET 2020 IOP Publishing
Journal of Physics: Conference Series 1773 (2021) 012032 doi:10.1088/1742-6596/1773/1/012032

Pile spacing 3d Pile spacing 4d Pile spacing 3d Pile spacing 4d

Pile spacing 5d Pile spacing 6d Pile spacing 5d Pile spacing 6d
3

Single Pile T.SF \ normal A.SF

2.5
Single Pile T.SF \ normal A.SF

2.5
2
2
1.5
1.5
1 1

0.5 0.5

0 0
1 2 3 4 5 6 7 8 9 1 2 3 4 5 6 7 8 9
Pile Number Pile Number
(a) 30% of Horizontal Load (b) 100 % of Horizontal Load

Figure 7. Shear Force Distribution on the pile head with different spacing between piles.

4.2. Influence of Pile Cap Thickness on Axial Force.

For small pile cap thickness, Horizontal and vertical stiffness for pile become greater, and the
inclination of the cup is smaller, when pile cup height 2.6, 2.0, 1.3, 0.7 m the y-direction inclination is 2.9°,
1.9°, 1.0°, 0.4°. When the pile group are affected by the horizontal and torsional loads, the front piles are
pressed and the rear piles are taken 30% of the total horizontal force. For increase the cup thickness the axial
force becomes greater (upper/lower pressure). Figure (8) show the ultimate pile capacity of the piles under
different cap thickness. The change in the cap thickness will not effect on the vertical ultimate bearing
capacity of the pile, Therefore, when the horizontal force of the pile is large, the axial force of each pile is
the same. In the calculation of the fails of the pile group, the back row reaches the ultimate bearing capacity.
Therefore, when analyzing the pile group foundation subjected to complex loads, it must be attention pile
pullout performance.

H1=2.6 m H1=2.0 m
10 H1=2.6 m H1=2.0 m
H1=1.3 m H1=0.7 m 15 H1=1.3 m H1=0.7 m

10
Axial Force, kN
Axial Force, kN

5
5

0
0 1 2 3 4 5 6 7 8 9
1 2 3 4 5 6 7 8 9
-5

-5 -10
Pile Number Pile Number
(a) 30 % of Horizontal Load (b) 100 % of Horizontal Load

Figure 8. Variation of axial force of pile head in 3×3 pile group with different free lengths.

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ISC-AET 2020 IOP Publishing
Journal of Physics: Conference Series 1773 (2021) 012032 doi:10.1088/1742-6596/1773/1/012032

5. Conclusion
In this paper, a nonlinear proposal model of group piles has been established under the action of horizontal
and torsion. The following are the summarized conclusions of the present proposal model:

a. The method proposed in this paper is mainly for the analysis of the pile group under horizontal and
torsional loads.
b. The proposed model gave very acceptable results with test result for group piles under combined
horizontal and torsional loads.
c. Under the combined action of horizontal and torsional loads, the shear force distribution of each
pile in the pile group is very complicated, and when a small spacing between the pile the shear force
is more uneven in the distribution.
d. The axial force of each pile in the pile group is change with the applied horizontal force and the
thickness of the pile cup.
e. When applied combined load on pile groups, it should be attention to the pile pull resistance.
f. The spacing between the pile can improve the mechanical properties of pile groups.

6. Reference

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Geomechanics (eds. J.W. Bull), Spon Press (Taylor & Francis Group Ltd), Oxford, Chapter 10, pp.
278-315.
[2] Gue, W.D., and Randolph, M.F. 1996. The torsional response of piles in non-homogeneous media.
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[3] Fine, W.D.L. 2005. A study of piles during earthquakes: issues of design and analysis. Bulletin of
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[4] Hady, S. and Obrien, A.S. 2006. Non-linear analysis of large pile groups for the new Wembley stadium.
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[5] Konj, L.G. 2006. Behaviour of pile groups subjected to torsion. PhD Thesis, The Hong Kong University
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[8] Abdulameer Qasim Hasan. Analytical and Experimental Response of Single Pile to Pure Torsion,
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[9] Kong L G, Zhang L M. Experimental study of interaction and coupling effects in pile groups subjected
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[10] Che Ren-peng, Wang Sho-hang, Konj Ling-gang, et al. Test investigation on distribution of internal
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[11] Reese L C, Cox W R, Koup F D. Analysis of laterally loaded piles in sand[C]// Proceeding, Fifth
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[12] Cuyle H M, Sulaman I H. Skin friction for steel piles in sand[J]. Journal of Soil Mechanics &
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