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Engineering, Technology & Applied Science Research Vol. 12, No. 6, 2022, 9771-9778 9771
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Numerical Modeling of a Pile Group Subjected to
Seismic Loading Using the Hypoplasticity Model
Ahmed Salman Jawad
Civil Engineering Department
College of Engineering
University of Baghdad
Baghdad, Iraq
a.jawad1901p@coeng.uobaghdad.edu.iq
Bushra S. Albusoda
Civil Engineering Department
College of Engineering
University of Baghdad
Baghdad, Iraq
dr.bushra_albusoda@coeng.uobaghdad.edu.iq
Received: 21 September 2022 | Revised: 14 October 2022 | Accepted: 15 October 2022
Abstract-Various simple and complicated models have been
utilized to simulate the stress-strain behavior of the soil. These
models are used in Finite Element Modeling (FEM) for
geotechnical engineering applications and analysis of dynamic
soil-structure interaction problems. These models either can't
adequately describe some features, such as the strain-softening of
dense sand, or they require several parameters that are difficult
to gather by conventional laboratory testing. Furthermore, soils
are not completely linearly elastic and perfectly plastic for the
whole range of loads. Soil behavior is quite difficult to
comprehend and exhibits a variety of behaviors under various
circumstances. As a result, a more realistic constitutive model is
needed, one that can represent the key aspects of soil behavior
using simple parameters. In this regard, the powerful
hypoplasticity model is suggested in this paper. It is classified as a
non-linear model in which the stress increment is stated in a
tonsorial form as a function of strain increment, actual stress,
and void ratio. Eight material characteristics are needed for the
hypoplastic model. The hypoplastic model has a unique way to
keep the state variables and material parameters separated.
Because of this property, the model can implement the behavior
of soil under a variety of stresses and densities while using the
same set of material properties.
Keywords-constitutive modeling; hypoplasticity; pile; PLAXIS
3D; seismic loading
I. INTRODUCTION
Piles are an extensively utilized deep foundation type and
are usually adopted in heavy building constructions on weak
soils due to their large bearing capacity, low distortion, and
high reliability [1-3]. The behavior of piles under seismic stress
is a complicated soil–structure interaction phenomenon that can
compromise the stability of pile-supported structures to risk. In
seismically active places and during earthquakes, movements
go from stiffer to softer near-surface layers, they tend to
increase and pass to the superstructure via the piles. As a result,
structural vibrations develop in the superstructure, imposing
inertial pressure on the pile cap and pilings and if the inertial
load is big enough, the piles experience substantial lateral
displacement and bending moment and consequently piling
foundations may be severely damaged. So, in seismically
active locations, proper geotechnical and structural design
techniques for pile foundations are essential. The earthquake
usually creates an additional loading situation on the pile that
needs special attention [4-6].
Numerical modeling by FEM of experimental efforts is
comparatively advantageous, and is one of the preferred
approaches widely utilized for the modeling of the behavior of
piled foundations under earthquakes [7-8]. It has been noted
that FEM typically produces reliable findings that meet with
the experiments. In [9], a comparison of the shaking table test
and numerical model was performed to simulate the piled raft
foundation in a dry bed of deposited sand. The system was
subjected to a strong ground motion while the simulated model
was linear visco-elastic. The authors showed that the
experimental and numerical results match. The effect of pile
soil interaction on resistance and stiffness of pile with sandy
soil was investigated under centrifuge loading in [10]. The
study adopted finite element analysis to simulate the models.
The test results were compared with the analytical solution in
terms of bearing capacity. It was reported that the interaction
effect between raft and piles reduces the stiffness of the pile
group. At the same time, the increment in vertical and
horizontal stresses due to the presence of the raft on subsoil
causes an enhanced pile response. A three dimensional finite
element numerical analysis was performed using PLAXIS 3D
to investigate the behavior of pile-caps under seismic and time
history loading as settlement and load shearing between the
piles and foundation in [11] and the results were verified with
experimental work. The maximum amplitude of displacement
was decreased by burying the pile cap deeper into the ground
and increasing its thickness. Furthermore, reducing the
foundation's dynamic reaction was also accomplished by
increasing the separation between the foundation and the
relative density of the sand. 3D numerical finite element
simulation with ABAQUS was conducted to predicate single-
pile and pile-system behavior in soft, saturated kaolin clay
during various earthquakes in [12]. The results were verified
with the centrifuge results from [13]. The linear elastic model
was utilized for the piles and the nonlinear kinematic hardening
model with Von Misses failure criterion for the clay. The
Corresponding author: Ahmed Salman Jawad
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simulation results were in good agreement with the observed
acceleration and bending moment. Also, the distance between
piles in a pile group had a significant influence on the amount
of interaction, acceleration response, forces, and bending
moments. In [14], numerical analysis was conducted to
predicate the response of pile and soil-pile-stricture interaction
with ground improvement (cement mixing method) using
ABAQUS. A single pile model with superstructure was used to
examine soil-pile-structure interaction behavior with head
masses of 25, 100, and 160lbs. During the Loma Prieta
earthquake, the piles had a maximum horizontal acceleration of
0.16g. The simulation results agreed well with the acceleration
time history at the pile head of 160lbs mass.
The hypoplasticity model was first proposed in [15] and has
been in development since then. Due to the complicated
calculations of such a model, FEM is used via commercially
available FEM software, e.g. Plaxis, FEAT, and ABAQUS.
Some of these do not have hypoplasticity as a built-in model.
This problem is solved by using the subroutine UMAT with
PLAXIS 3D to provide the necessary tensor entries. PLAXIS
3D was used in this research due to the high capability of the
software to deal with the elastic-plastic, non-linear, and contact
problems [16]. This paper aims to use the hypoplasticity model
in soil structure interaction problems.
II. EXPERIMENTAL WORK
The hypoplastic model needs eight material parameters
(φ�, e��, e��, e��, n, hs, α, β). In order to obtain these model
parameters, a series of physical-mechanical tests was
performed on sand from Baghdad city, which was utilized in
this study. Its physical properties are summarized in Table I.
TABLE I. PHYSICAL PROPERTIES OF SAND SAMPLE
Test name Soil property Value
Specific Gravity Gs Specific gravity 2.64
Standard
Compaction Test
Maximum dry unit weight max
(kN/m
3
)
16.55
Minimum dry unit weight min
(kN/m
3
)
13.85
Maximum void ratio, emax 0.87
Minimum void ratio, emin 0.56
Grain size analysis
Coefficient of uniformity, Cu 3.33
Coefficient of curvature, Cc 0.83
Unified Soil Classification
System (USCS)
SP
III. HYPOPLASTICITY MODEL INPUT PARAMETERS
A. Void Ratio (e)
The void ratio is an essential factor in the calculation of the
parameter model. Three parameters are associated with the
void ratio. The relationships
�� ≈ �� ,
�� ≈ �� , and ���
����
= 1.2 [17] can be employed.
B. Critical Angle of Friction (c)
The critical angle of friction can be determined for loosely
dry sand (particle size greater than 0.1mm) by the conduction
angle of repose while for finer soil (particle size less than
0.1mm), the critical angle of friction can be determined by
classical mechanical soil tests [18].
C. Stiffness Parameters (n and hS)
The soil stiffness in the hypoplasticity model relies on the
hs and n parameters and is determined by the confined
compression test on loose dry sandy soil [19]. Cc (the
compression curve slope) describes the slope of the curve
derived from the confined compression test and displayed in
the ln vs. e plane:
c� =
∆�
∆��� (1)
The ko value along the normal consolidation line remains
constant throughout the proportional loading, and ko is
determined using Jacky's formula [19]:
k� = 1 − sin φ� (2)
Then, the value of ko is used to find the p by:
lnσ = ln ' ()*+,� p. = ln '
(
)*+,�
. + lnp (3)
Equation (4) used to get the value of n from the two values
of Cc shown in Figure 1 [20] for two distinct values of (ps):
n =
��'0122303221.
��'4341.
(4)
By applying (5), the hs can be calculated from the range of
p1 and p2:
ℎ6 = 38 '
��
�9
.
1
:
(5)
The compression curve is influenced by the stiffness
parameters (hs and n), where the former governs the curve's
overall slope and the latter its curvature [19].
Fig. 1. Confined compression test results are used to determine the hs and
n parameters [20].
Fig. 2. Confined compression test on loosely dry sample.
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Three confined compression tests were conducted on
loosely dry sand soil with an initial void ratio e of 0.82 and
800kPa maximal normal stress was applied to them. As part of
the sample preparation procedure, the sand was poured down a
zero-height funnel to create the loosest condition [20]. The
results from the confined compression test performed on
loosely sand sample are shown in Figure 2.
D. α and β Parameters
The α parameter is obtained from the triaxial Consolidated
Drained (CD) Test carried out on the dense sandy sample with
initial void ratio e = 0.62, corresponding with Relative Density
Dr = 80.6% and different confining pressures of 50, 100, and
200kPa as shown in Figures 3 and 4. From these tests, the α
parameter was found to be equal 0.136 while the hypoplasticity
model β can be set to 1 for natural [20]. The final values of the
hypoplasticity model are summarized in Table II.
Fig. 3. Deviatoric stress vs. axial strain of the triaxial CD test.
Fig. 4. Volumetric strain vs. axial strain of the triaxial CD test.
TABLE II. HYPOPLASTICITY MODEL PARAMETER VALUES USED IN
THIS RESEARCH
IV. VALIDATION PROBLEM
In order to validate the program's capabilities in modeling
the hypoplasticity problem, the findings from experimental,
numerical (Open Sees, SANI SAND model), and PLAXIS 3D
hypoplasticity analysis were compared. The problem involved
a comparison between the results obtained from the
experimental and numerical research performed by [22-24] and
the results obtained from PLAXIS 3D. The problem includes
conducting a number of centrifugal tests to assess the
interaction between the soil and the structure of layered
liquefiable soil deposits and the seismic site response. The total
depth of the soil profile was 18m, consisting of a 3 layered soil
of 2m coarse sand crust with a relative density Dr = 90%, a 6m
loose sand layer with Dr = 40%, and a 10m dense sand layer
with Dr = 90% at the bottom.
A. Finite Element Modeling
The geometry of the problem was modeled using finite
elements under PLAXIS 3D. It is similar to that adopted in the
experimental work as shown in Figure 5. A scaled version of
the recorded Kobe earthquake was applied at the base of the
model, which was referred to as the Kobe-L motion.
Fig. 5. The finite element model adopted in PLAXIS 3D.
B. Soil Modeling
The material behavior of sand in this study was modeled by
the hypoplasticity model and the parameters of its
implementation were determined by [21] as shown in Table III.
TABLE III. PARAMETERS OF THE HYPOPLASTICITY MODEL
Parameter Value
c 30
ed0, ec0, ei0 0.53, 0.82, 0.94
hs (MPa) 2000
n 0.22
0.25
1
C. Result Comparison
A comparison between the experimental test and PLAXIS
3D results is shown in Figures 6 and 7. It can be seen that the
results of maximum settlement are approximately compatible
with the results of finite element analysis with slightly
difference at 8m depth. The vertical settlement, however, is
evolving considerably more quickly according to the model
than what was actually seen during the experiment, even
though they are still in good agreement. The results of excess
pore water pressure show a good agreement between the
experimental results and numerical analysis. Finally, it can be
concluded that the proposed (hypoplasticity) model and
PLAXIS 3D software can manipulate the dynamic analysis
with good accuracy and are considered an appropriate tool for
studies of the soil pile interaction effects.
Parameter Value
Critical friction angle c 30
Minimum, maximum, and critical void ratio at
zero pressure ed0, ec0, ei0
0.56, 0.87,
1.044
Granular hardness hs (MPa) 4000
Exponent relating to sensitivity of granular
skeleton to changes of pressure n
0.419
Exponent describing the transition between peak
and critical stress
0.136
Exponent representing the change of stiffness at
current density
1
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(a)
(b)
(c)
Fig. 6. Experimentally measured, numerically computed (open sees)
settlement versus time after [23] and PLAXIS 3D results at depth (a) 0m, (b)
2m, and (c)=8m.
(a)
(b)
(c)
Fig. 7. Experimentally measured, numerically computed (open sees)
excess pore water pressure versus time after [23] and PLAXIS 3D results at
depth (a) 0m, (b) 2m, and (c) 8m.
V. PARAMETRIC STUDY
In this research, the behavior of the piled-raft system is
analyzed using PLAXIS 3D under varying seismic loading.
The analysis is focused on the pile response under seismic
loading. Three different elements are included in the model:
volume element for the soil, plate element for the raft, and
building and embedded beams for the piles as shown in Figure
8.
Fig. 8. 3D finite element model.
A. Material Properties
The properties of the sandy soil are shown in Table II. The
piles have been modeled as embedded circular massive beams
with 0.3m diameter.
B. Earthquake Data
Earthquake records data were utilized to study the effects of
acceleration characteristics within soil and pile. Two different
real acceleration records, namely Upland and Kobe
earthquakes were used (Table IV and Figure 9).
TABLE IV. INFORMATION REGARDING THE EARTHQUAKE DATA [25]
Earthquake Upland Kobe
Region
Los Angeles area,
Southern California, USA
Japan
Magnitude
(MW)
5.7 6.9
Date (UTC) 1990-02-28 23:43:36 1995-01-16 20:24:52
Shaking
duration (s)
20 48
Acceleration
direction
N-W N-S
Maximum
acceleration (g)
0.24 0.82
Epicenter depth
(km)
10 7.9
Station code CLMCV KIMA
Station distance
to the epicenter
(km)
120.3 1.0
Modified
Mercalli
intensity
(MMI)
VII –Very Strong VII –Very Strong
Reference [25]
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(a)
(b)
Fig. 9. Earthquake record.
C. Results and Discussion
1) Effect of Pile Length and Pile Spacing on Vertical
Settlement
The effect of pile spacing (2D, 3D, and 4D) on the response
of the piled raft subject to earthquake excitation is studied in
this section. Figures 10-14 show the time history of the soil
settlement measured in the middle of raft (A) and at the edge of
raft point (B) for both earthquake motions.
(a)
(b)
(c)
Fig. 10. Variation of the vertical settlement with time at point (A) during
the Kobe earthquake at S/D = (a) 2, (b) 3, (c) 4.
(a)
(b)
(c)
Fig. 11. Variation of the vertical settlement with time at point (B) during
the Kobe earthquake at S/D = (a) 2, (b) 3, (c) 4.
(a)
(b)
(c)
Fig. 12. Variation of the vertical settlement with time at point (A) during
the Upland earthquake at S/D = (a) 2, (b) 3, (c) 4.
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(a)
(b)
(c)
Fig. 13. Variation of the vertical settlement with time at point (B) during
the Upland earthquake at S/D = (a) 2, (b) 3, (c) 4.
It can be concluded that increasing the spacing among piles
to 3D and 4D from the basic 2D spacing increases the total
settlement. This behavior could be attributed to the decrease in
spacing between piles that applied additional lateral forces
between soil particles by holding them together and providing
confining media. This action resists the external forces thus
decreasing total settlement. This force affects the piles as well
as soil particles leading more friction forces at the pile surfaces
as the friction is a function of normal forces and the friction
coefficient, so increasing the skin friction leads to more
resistance in total settlement as a result. The decrease in
spacing between piles means that the piles are concentrated at
the middle of the raft which resists the dishing effect occurring
in the sand. This action leads to a decrease in probable total
settlement as the maximum settlement occurs in the middle of
the raft in the case of sand due to the dishing phenomenon.
Finally, it can be concluded that total settlement increases as
the pile spacing increases. Similar observation was noticed in
[26-27]. For increasing pile length, load transfer is affected by
the pile length. This factor is considered by selection of 3
different piles lengths (L/D) equal to 35, 45, and 55. Based on
numerical analysis, it is found that the increase of pile length
decreases the total settlement of piled foundation as shown in
Figures 10-14. This behavior can be attributed to the increase
of the pile length which absorbs more power applied from
earthquakes and dissipates the applied forces since the
settlement is a function of the applied load [26-32].
Earthquake excitation has a major influence on the piled
raft behavior. Piled raft foundation placed on loose dry soil and
subjected by Kobe and Upland earthquake motions was
modeled numerically to investigate the effect of the excitation
on the total settlement (Figures 10-14). From these Figures, it
can be concluded that the total settlement of pile raft increases
as the earthquake excitation increases. Higher excitation leads
to higher dynamic loading, which results in higher settlement,
as the settlement is a function of loading.
2) Effect of Pile Length and Pile Spacing on Maximum Pile
Bending Moment
Pile foundations can be divided into two categories based
on the ratio of the effective unsupported length (L) to the
average pile diameter (D), where L/D > 30 denotes a long pile
and L/D 20 denotes a short pile [28]. The effect of length to
pile diameter L/D (35, 45, and 55) and pile spacing S/D (2, 3,
and 4) on the response of piled raft subjected to two earthquake
excitations is illustrated in Figures 15-17. The following points
can be noted: The maximum bending moment occurred at the
connection between the piles and the raft and the zero moment
is located near the tip of the pile. Also, it can be concluded that
increasing the spacing among piles to 3D and 4D 2D increases
the bending moment along the pile shaft. This behavior can be
explained by the fact that higher excitation leads to higher
dynamic loading which results in higher bending moment.
(a)
(b)
Fig. 14. Variation of max. vertical settlement with S/D at point (A) for (a)
Kobe and (b) Upland earthquake.
The effectiveness of the constitutive models employed in
the modeling of the soil-pile interaction under the influence of
earthquake motion is a key factor in the precise simulation of
the numerical analysis in geotechnical engineering. There are
limited numerical investigations of the behavior of soil-pile
interaction using various constitutive models. Each of these
models has its own unique features and advantages, most fall
short of providing an adequate description of this behavior.
Due to this factor, the analysis of soil-pile-structure systems
subjected to seismic stress using an efficient model (the
hypoplasticity model) is the goal of this study. The
hypoplasticity constitutive model is implemented using the
UMAT subroutine, which is then incorporated as a dynamic
linked library (DLL) in the PLAXIS 3D finite element
program.
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(a)
(b)
(c)
Fig. 15. Variation of bending moment along pile (P11) at peak ground
acceleration during the Kobe earthquake at S/D = (a) 2, (b) 3, (c) 4.
(a)
(b)
(c)
Fig. 16. Variation of bending moment along pile (P11) at peak ground
acceleration during the Upland earthquake at S/D = (a) 2, (b) 3, (c) 4.
This model predicts with accuracy the soil response to
various soil densities, stress levels, and loading conditions. It
also requires several parameters that are easy to gather by
conventional laboratory testing. The model's ability in
modeling soil-pile interaction was validated with results from
experimental tests and also with findings from numerical
results conducted using the SANISAND constitutive model. A
numerical model of a 10-story building supported by pile
systems (soil-pile structure) was examined in order to look into
the effects of various interactional parameters. To examine the
impact of the excitation frequency, two seismic motions were
used. Additionally, the effects of various pile lengths and
spacings were examined.
(a)
(b)
Fig. 17. Variation of max. bending moment with S/D at pile (P11) at peak
ground acceleration for (a) Kobe and (b) Upland earthquake.
VI. CONCLUSION
The hypoplasticity constitutive model and the finite element
method were used in this study to investigate the dynamic soil
pile interaction. The soil parameters for this model were
obtained by laboratory tests and were calibrated according to
known relationships. The main conclusions from this study are:
The hypoplasticity constitutive model is quite satisfactory
in representing the behavior of the response of the pile
foundation under earthquake excitation.
Increasing in the length of piles decreases the settlement of
the piled raft system.
Increasing the spacing between piles increases the
settlement of the piled raft system.
Increasing the length and pile spacing increases the bending
moment.
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