Modeling Vertical Bearing Capacity of

Pile Foundation by Using ABAQUS

Yun-gang Zhan
School of Naval Architecture and Ocean Engineering, Jiangsu University of
Science and Technology, Zhenjiang, Jiangsu, China
Email: zygseastar@163.com
Hong Wang
School of Naval Architecture and Ocean Engineering, Jiangsu University of
Science and Technology, Zhenjiang, Jiangsu, China
Fu-chen Liu
Shandong Vocational Polytechnic College of Water Resources
Rizhao, Shandong, China

ABSTRACT
Pile foundations are widely used in weaker soil site to support superstructures. Study on the
predicting bearing capacity of pile foundations is still attracting interests of geotechnical
researchers. Besides laboratory or field tests, Finite element method is used increasingly to
deal with this problem. In this paper, some aspects for numerical analysis of vertical loading
pile foundation by using ABAQUS, such as self-weight stress field, Coulomb friction model,
shaft and base resistances, and selection of element type, were examined detailedly in order to
further clarify the establishing of numerical model and analysis procedures.
KEYWORDS: pile foundation; bearing capacity; finite element; contact behaviour.

INTRODUCTION
Pile foundations are often used in weaker soil to transfer the loads of superstructures to
underlying ground, aiming to increase the bearing capacity or lessen the settlement of
infrastructures. However, the load transfer mechanism and failure mode of pile foundations are
very complex and not fully understood yet (Johnson, et al., 2006; Salgado, et al., 2007). There are
no general equations to predict the bearing capacity and settlement for single pile or pile group
under different working conditions. Studies on this problem are still going on by using field or
laboratory tests (Buehler, 2004; Soldo, et al., 2005). Recently, with the rapid development of
computing technology, numerical analysis methods involving finite element method (FEM) are
widely used to understand the bearing capacity behavior of piles, especially for piles under
combined loading conditions (Lee, et al., 2002; Rajagopal and Karthigeyan, 2008;). The
advantage of numerical analysis method lies in its ability to address complex soil layer and the
interaction between soil and structure. In this paper, some aspects on numerical analysis of
vertical loading pile in homogeneous soil by using software package ABAQUS (Abaqus, 2010)
was examined in detail. Firstly the constitutive model for surrounding soil and the contact
behavior of pile-soil interface were discussed; then based on the established numerical model, the
methods for realizing self-weight stress state and the capability of Coulomb friction model to
describe the contact behavior were examined; lastly the deduced shaft resistance in terms of axial

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 Vol. 17 [2012], Bund. L 1856

forces and self-weight was compared with the direct result of numerical analysis, and based on
this comparison one can find the second-order 8-node biquadratic axisymmetric solid element is
not suit for predicting the shaft resistance.

CONSTITUTIVE MODEL OF SOIL

Lately, more and more comprehensive constitutive models are being developed to describe the
complex behavior of geomaterial under different loading conditions (Hashiguchi, 1989; Collins
and Kelly, 2002) which in turn leads to difficulties in numerical implementing and identifying
model parameters by means of standard material tests. Elasto-perfectly plastic model with Mohr-
Coulomb failure criterion, usually named as Mohr-Coulomb model, is widely used in finite
element analysis of geotechnical engineering, due to its simplicity and sufficiently accuracy
(Chen & Saleeb 1983). The failure envelope, being dependent on the major and minor principle
stresses ( σ 1 , σ 3 ) as shown in Fig. 1, is defined by cohesion, c and internal frictional angle, φ ,
1 1
(σ 1 -σ 3 ) + (σ 1 +σ 3 ) sin φ − c cos φ = 0 (1)
2 2

When extended into three-dimensional stress space, the failure envelope turns into irregular
hexagonal pyramid.

Mohr-Coulomb
failure envelope

τ φ

σ σ3 σ1
Figure 1: Mohr-Coulomb failure criterion

For Elasto-plastic constitutive model, the potential functions are usually taken as the same as
failure envelopes, with associated or non-associated flow rule. However, a flow potential, being
totally different from failure envelope, which has a hyperbolic shape in the meridional stress
plane and has no corners in the deviatoric stress spaces was adopted in ABAQUS, referenced to
Menétrey and Willam (1995). The merits of this non-associated flow potential lie in its complete
smoothness and unique definition of the direction of plastic flow.

CONTACT BEHAVIORS OF PILE-SOIL INTERFACE

The contact behaviors at the pile-soil surface include load transfer mechanisms both in the
normal and tangent direction. The normal force is transferred only when pile and soil are contact
tightly; otherwise, it becomes zero. This kind of normal contact behavior can be modeled by
“hard” contact option provided by ABAQUS. The tangent behavior can range from rough contact
with no relative sliding between soil and pile occurs to frictionless sliding conditions with no
friction develops along the shaft of the pile. For contact between these two ideal cases, Coulomb
frictional model built in ABAQUS can be selected to depict the interaction at the pile-soil
 Vol.
V 17 [201
12], Bund. L 185
57

face with a prrescribed fricttional coefficient, μ , as sshown in Fig.. 2. These two ideal contact
interfa
conditions can also o be realized through presscribing a higgher or a zeroo frictional cooefficients. Thhe
shear resistance off interface is always
a depen ndent on the ffrictional coeffficient and nnormal stress if
mit shear resistance is defiined (Fig.2b);; otherwise, iit keeps no chhange after it reach its lim
no lim mit
value (Fig. 2a). Thhe former is often
o used forr pile-undrain ed clay interaaction and thee latter is ofteen
used for pile-sand interaction. When the tan ngent shear sstress in pile--soil interfacee surpasses thhe
shear resistance, reelative slip beetween pile an
nd soil occurss.
Shear resistance

Shear resistance
Debonded
D
Debondedd
region
τ maax r
region

Bondded
μ Bonded
B μ region
n

1 reegion 1

Normal stresss Normmal stress

(a) Limit sheear resistance (b) N
No limit shear rresistance
Figure 2: Shear resistance versuus normal sttress

NUMERI
N ICAL MO
ODEL
The
T problem of vertical loaded l pile in
i homogeneeous soil is an axisymm metric one. So,
axisym mmetric num merical modeels can be built
b to analyyze the bearring capacityy behavior foor
simplicity. For thee purpose of clearness, a typical modeel with coarsse mesh is shhown in Fig 3.
Actuaally, refined meshes
m were utilized
u in anaalysis. The booundary condditions are deffined as show
wn
in Figg 3, which alllow vertical displacemen nt along both left side andd axis of sym mmetry and nno
displaacement in th he base of th
he mesh. In order
o to reducce the effect of boundaryy on numerical
resultt, a calculation
n domain withh 10.5D in width and (L+110D) in depthh is selected, w where D and L
is the diameter and length of pile
p with valu ues of 200mm m and 4m, seeparately. A kkind of 4-nodde
bilineear or 8-nodee biquadratic axisymmetriic solid elem ment was adoppted for this problem, annd
reduced integration n technique was
w used for soil element too overcome shhear locking.

Figure 3: Numerical m
model

The
T material of pile was simulated by
b using elaastic constituutive model with Young’s
modu n’s ratio, ν eequated to 0..2. The surroounding soil is
ulus, E equateed to 25GPaa and Poisson
 Vol. 17 [2012], Bund. L 1858

characterized by Mohr-Coulomb model described in the above section. For sandy soil, Young’s
modulus is 45MPa and Poisson’s ratio is 0.35. The internal frictional angle, φ is 30 and
dilatancy angle is taken as 2/3 of frictional angle. A small cohesion, 1kPa was set for sand to
avoid divergence in analysis. For clay under undrained conditions, the shear strength is 20kPa and
Young’s modulus is taken as 1000 times as many as undrained shear strength. A Poisson’s ratio
of 0.49 was set to model the undrained constant-volume response of the clay. The interaction
between pile and soil is established in terms of surrounding soil type.

NUMERICAL EXAMINING
Self-weight stress field
The weight of pile and soil was calculated utilizing a same value of density, 1.6 × 103 kg/m3 for
sandy soil and 1.8 × 103 kg/m3 for undrained clay, in order to obtain a balance state of self-weight
stress easily. The self-weight stress field can be established through two methods. One is using
the “geostatic” option provided by ABAQUS, which need to specify the coefficient of lateral
earth pressure, k0 . In the study, k0 was set as ν (1-ν ) , and ν is Poisson’s ratio of soil.
Specifically k0 is 0.538 and 0.96 for the two types of soil, separately. The other is to change the
soil into elastic material and set the material of pile as soil. Then the weight of pile and soil were
obtained through elastic analysis and the stresses in centroid of each element were output. The
initial self-weight stress field for the next analysis step of bearing capacity of pile was established
by inputting the centroid stresses. The self-weight stress field for pile in sandy soil is shown in
Fig. 4, and there is no essential difference between the results of these two methods. Fig. 5 shows
the vertical displacement field after the establishing of self-weight stress field. As can be seen, the
order of quantity of vertical displacement is 10-6 , which means an acceptable initial self-weight
stress state was obtained.

(a) “Geostatic” option (b) Elastic analysis method

Figure 4: Self-weight stress field
 Vol. 17 [2012], Bund. L 1859

(a) “Geostatic” option (b) Elastic analysis method

Figure 5: Initial vertical deformation field

NORMAL PRESSURE AND FRICION IN INTERFACE

The modelling of normal pressure in pile-soil contact surface is important for this kind of
problem because the shear resistance in interface is dependent on it. Fig. 6 shows the distribution
of lateral stress of soil within the range of depth of pile and the normal contact pressure in the
interface for pile in sandy soil when the balance state of self-weight stress was established. It can
be seen that there is only a little bit of difference between them, which perhaps was arisen by the
adjusting of contact of pile and soil. One can deduce that the shear resistance in the interface will
be fully mobilized, and this is confirmed by the friction and normal pressure along the shaft of
pile, shown in Fig. 7, after vertical displacement of 0.1m was exerted on pile top. The friction
varies with normal pressure strictly in terms of frictional coefficient, 0.42.

(a) Lateral stress (b) Normal pressure

Figure 6: Lateral stress and normal pressure
0.0
30
0.5
25
1.0
Normal pressure
1.5 20
Friction / kPa
Depth / m

2.0 15 0.42
1.0
2.5
10
3.0 Friction
5
3.5

4.0 0
0 20 40 60 80 0 10 20 30 40 50 60 70 80
Normal pressure (Friction) / kPa Normal pressure / kPa

(a) Normal pressure and friction (b) Friction versus normal pressure
Figure 7: Normal pressure and friction along shaft of pile in sandy soil
 Vol. 17 [2012], Bund. L 1860

Fig.8 shows the normal pressures along shaft of pile in undrained clay with vertical
displacement at pile top are 0.0m and 0.1m, separately. Obviously, the distribution of normal
stress is as alike as that of lateral soil pressure which increases with depth, when vertical
displacement of pile top is zero. A notable difference is observed for normal pressure near the tip
and top of pile due to external loading. However, the friction keeps no change with normal
pressure and equates to the prescribed limit shear resistance, 20kPa along the shaft of pile. This
means the Coulomb frictional model in conjugate with “hard” contact model is competent for
modeling the complex contact problem.

0.0

0.5
Normal pressure of v = 0.1m
1.0

1.5
Depth / m

2.0

2.5

3.0 Friction Normal pressure of v = 0.0m

3.5

4.0
0 20 40 60 80 100
Normal pressure (Friction) / kPa

Figure 8: Normal pressure and friction along shaft of pile in undrained clay
(v is vertical displacement of pile top)

Axial force, shaft resistance and base resistance

For a segment of pile, the relationship between shaft resistance (FS), self-weight (G), and
axial force (FAT, FAB) are shown in Fig. 9, which can be expressed as,
FS = FAT + G − FAB (2)
FAT

Fs Fs
G

FAB
Figure 9: External loads and internal forces of pile

If the axial forces in cross-sections of pile and self-weight of corresponding segment are
obtained, one can deduce the shaft resistance by using Equation (2). A simple case, pile in
undrained clay with frictionless contact between shaft and clay, was taken as example to examine
 Vol. 17 [2012], Bund. L 1861

the capability of contact modeling in ABAQUS. The axial forces of cross-section are output by
“section print” option of ABAQUS. As above-mentioned, the density of undrained clay and pile
is set as 1800 kg/m3.

From Table 1 one can see the extended shaft resistance for each segment is near the
theoretical value, zero, and the total shaft resistance is only 0.02kPa. The extended axial force at
pile-top is 8.41kN (in italic type in Tab. 1), which is almost equal to the bearing capacity, 8.40kN
shown in Fig. 10, when displacement equated to 0.5D. The extended axial force at pile-tip is
10.66kN (in italic type in Tab. 1), which is the base resistance provided by soil. Alternatively, one
can use the axial forces at the depth of 0.01m and (L-0.01) m to represent the bearing capacity
and base resistance, and obtain the total shaft resistance by substituting them into Equation 2.

If changing frictionless contact into rough one, the theoretical total shaft resistance is,
FS = π DLcu = 50.27kN (3)

The accumulated shaft resistant predicted by numerical analysis is presented in Fig. 10, which
is in accordance with the theoretical result. The bearing capacity should be 50.27+8.40=58.67kN
in theory and it also agrees well with the numerical result 58.44kN, shown in Fig. 11.
So this confirmed method can be used to predict shaft and base resistance and to study the effect
of shaft friction on the base resistance for pile in sandy soil by changing the frictional factors of
interface.

Table 1: Extended shaft resistance for Case 1

Self-weight of
Pile depth Axial force Shaft resistance
segment
(m) (kN) (kN)
(kN)
0.00 8.41
0.01 8.42 0.006
0.50 8.68 0.277 0.017
1.00 8.95 0.283 0.013
1.50 9.26 0.283 -0.027
2.00 9.52 0.283 0.023
2.50 9.80 0.283 0.003
3.00 10.09 0.283 -0.007
3.50 10.37 0.283 0.003
3.99 10.65 0.277 -0.003
4.00 10.66 0.006
∑=2.26 ∑=0.02
 Vol. 17 [2012], Bund. L 1862

Shaft resistant / kN
0 10 20 30 40 50 60
0.0

0.5

1.0

1.5 FEM predicted

Depth / m Theoretical result
2.0

2.5

3.0

3.5

4.0

Figure 10: Comparison of accumulated shaft resistant

Vertical load / kN
0 10 20 30 40 50 60
0

20
Vertical displacement / mm

40

Frictionless contact
60
Rough contact

80

100 58.44
8.40

Figure 11: Curve of vertical load-displacement for pile in undrained clay

Effect of element type on shaft resistance

In above sections, the element type is first-order element (CAX4) and good results were
obtained. It is known that some second-order element types provided by ABAQUS are not well-
suited for underlying the slave surface with the combination of a node-to-surface contact
formulation and strict enforcement of “hard” contact conditions, because of the ambiguous nature
of the nodal forces in second-order elements when a pressure acts on the face of the element. In
this section, analysis with calculation domain discretized by second-order element (CAX8) and
surface-to-surface contact was performed successfully. Fig. 12 presents the comparison of
vertical load-displacement curve obtained by first-order element (CAX4) and second-order
element (CAX8). It can be seen that the two curves agree well with each other and the difference
of bearing capacity at 0.5D displacement is 5.93kN. The shaft resistances deduced by Equation (2)
 Vol. 17 [2012], Bund. L 1863

for the two types of element are listed in Tab.2 and they are very close. However, there is a
dramatic difference between the accumulated shaft resistances reported by the numerical results,
shown in Fig.13. The numerical result for element CAX4 is 18.51Kn, which is close to the
deduced one. From what is analyzed above, one can draw a conclusion that, even using surface-
to-surface contact formulation, the second-order element CAX8 can only be used to predict the
bearing capacity of pile foundation, not be used to obtain the distribution of shaft resistance. The
alternative is using Equation (2) to deduce shaft resistance when using element CAX8.
Vertical load / kN
0 50 100 150 200 250 300 350
0
Vertical displacement / mm

20

CAX8
40
CAX4

60

80

100

Figure 12: Curve of vertical load-displacement for pile in sandy clay

Table 2: Shaft resistance for two types of element

Bearing Axial force (kN) Shaft
Element Self-weight
capacity resistance
type Depth=0.01m Depth=3.99m (kN)
(kN) (kN)
CAX4 306.62 306.5 290.1 2.0 18.4
CAX8 300.69 300.7 285.2 2.0 17.5

Shaft resistant / kN
0 5 10 15 20
0.0

0.5

1.0

1.5
Depth / m

CAX4
2.0 CAX8
2.5

3.0

3.5

4.0

Figure 13: Accumulated shaft resistant for two types of element

 Vol. 17 [2012], Bund. L 1864

CONCLUSION
Numerical analysis method, such as finite element method, is widely used to predict the
bearing capacity and settlement of pile foundation. ABAQUS, as a general-purpose finite element
analysis software package, is preferred in geotechnical engineering, due to its powerful capability
in non-linear analysis. In this paper, some aspects for numerical analysis of vertical loading pile
foundations by using ABAQUS were examined in order to further clarify the establishing of
numerical model. Conclusions can be drawn that:

(1) Coulomb frictional model in conjugate with “hard” contact model is capable of modelling
the pile-soil interactional mechanism;

(2) the confirmed relation between axial force, shaft resistance, self-weight of pile, base
resistance, and vertical bearing capacity can be used to study the mutual effects of shaft and base
resistance based on numerical result;

(3) Though the second-order element CAX8 is able to predict the bearing capacity of pile
foundation, it could not provide an accurate shaft resistance.

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