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Geotextiles and Geomembranes 26 (2008) 3955
2D and 3D numerical simulations of reinforced embankments
on soft ground
Dennes T. Bergadoa,, Chairat Teerawattanasukb
aSchool of Engineering and Technology, Asian Institute of Technology, P.O. Box 4, Klong Luang, Pathumthani 10120, ThailandbDepartment of Civil and Environmental Engineering Technology, King Mongkuts Institute of Technology North Bangkok, Bangkok 10800, Thailand
Received 22 April 2006; received in revised form 14 February 2007; accepted 21 March 2007
Available online 30 May 2007
Abstract
Utilizing the same constitutive models and properties of foundation soils as published by previous researchers, two full-scale test
embankments, namely steel grid embankment having longer plan dimensions with length-to-width ratio of 3.0 (long embankment) and
hexagonal wire mesh reinforced embankment having shorter plan dimensions with length-to-width ratio of 1.0 (short embankment), were
investigated using numerical simulation in two-dimensional (2D) and three-dimensional (3D) explicit finite-difference programs,
FLAC2D and FLAC3D, respectively. The 2D numerical analysis simulated the overall behavior of the steel grid reinforced long
embankment with very reasonable agreement between the field measurements and the calculated values. On the other hand, the 3D
numerical analysis simulated the overall behavior of the hexagonal wire mesh reinforced short embankment. Furthermore, the
simulation results from the FLAC3D used in the 2D analysis agreed with the measured settlement data in the long embankment as
well as the 2D predictions from FLAC2D. The 2D and 3D numerical analyses should be considered important factors that may affect the
numerical simulation results which are consistent with the current settlement predictions with SkemptonBjerrum corrections.
r 2007 Elsevier Ltd. All rights reserved.
Keywords: Reinforced embankment; Numerical simulation; Soft ground; Full-scale test
1. Introduction
Issues related to the design and factors affecting the
performance of reinforced soil have been addressed by
many researches in recent times (e.g. Bathurst et al., 2005;
Kazimierowicz-Frankowska, 2005; Park and Tan, 2005;
Skinner and Rowe, 2005; Varsuo et al., 2005; Al Hattamleh
and Muhunthan, 2006; Hufenus et al., 2006; Nouri et al.,
2006). Also, the behavior of reinforced earth structures has
been comprehensively studied through field observation offull-scale physical model, laboratory model testing, and
numerical simulation. However, the cost of constructing
and monitoring full-scale reinforced test embankments is
quite high. An alternative method such as a numerical
experiment or simulation by means of appropriate
methods such as finite-element (FE) or finite-difference
(FD) techniques (e.g. Ho and Rowe, 1994) is essentially
required. In general, two-dimensional (2D) analysis can be
categorized into two types: (1) 2D plane stress which is
usually applied for stress analysis of thin plate structure by
assuming the stress in the direction perpendicular to the
plate is equal to zero and (2) 2D plane strain which is
defined as the strain state in the direction perpendicular to
the plane is equal to zero. Most researches assumed plane
strain condition for numerical simulations of reinforced
earth structures (Chai, 1992, Chai and Bergado, 1993a, b;Bergado et al., 1995, 2003; Karpurapu and Bathurst, 1995;
Alfaro et al., 1997; Chai et al., 1997; Rowe and Ho, 1998;
Rowe and Li, 2002; Zdravkovic et al., 2002; Hinchberger
and Rowe, 2003).
Many studies attempted to conduct 3D FE analyses
while investigating the behavior of embankments (e.g.
Smith and Su, 1997; Briaud and Lim, 1999; Auvinet and
Gonzalez, 2000). Smith and Su (1997) summarized that the
3D FE analysis can be used to model the reinforced soil
embankment under service loading and at collapse
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www.elsevier.com/locate/geotexmem
0266-1144/$ - see front matterr 2007 Elsevier Ltd. All rights reserved.
doi:10.1016/j.geotexmem.2007.03.003
Corresponding author. Tel.: +662 524 5512; fax: +662 524 6050.
E-mail addresses: [email protected] (D.T. Bergado),
[email protected] (C. Teerawattanasuk).
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successfully. Briaud and Lim (1999) utilized three-dimen-
sional (3D) nonlinear FE analysis to study the influence
factors on the tieback walls. In addition, Auvinet and
Gonzalez (2000) recommended that a 3D analysis must be
considered under the following conditions: (a) in the case
of short slopes of which boundary conditions cannot be
ignored, such as earth dams built in a narrow valley orembankment at the bridge approach, (b) when soil
properties vary significantly along the longitudinal direc-
tion of the slope or embankment, (c) when the slope is
subjected to concentrated loading and (d) when the
potential failure is irregular.
Two full-scale test embankments were constructed on
Bangkok clay deposit with different types of reinforcement
and backfill soil: steel grid reinforced long embankment
having longer plan dimensions with length-to-width ratio
of 3.0 (Shivashankar, 1991) and hexagonal wire mesh
reinforced short embankment having shorter plan
dimensions with length-to-width ratio of 1.0 (Voottipruex,
2000). These two embankments have been fully instrumen-
ted with piezometers, settlement gauges, inclinometer
casings and strain gauges (on reinforcements). High-
quality field monitoring data have been obtained. Based
on the work of Teerawattanasuk (2004), the numerical
simulations of these two embankment systems were
realized by means of FD method using 2D and 3D explicit
FD programs, FLAC2D (ITASCA and FLAC2D Version
3.4, 1998) and FLAC3D (ITASCA and FLAC3D Version
2.0, 1997), respectively. The aim of this study is to
investigate the influence of geometric configurations using
2D and 3D numerical simulations of the two full-scale tests
(i.e. class C1 prediction, Lambe, 1973). Particular attentionis given to the settlements, excess pore-water pressures,
horizontal displacements, and tensile forces in the reinfor-
cements. Subsequently, comparisons are made between the
findings of 2D and 3D numerical simulations and those
from the actual measured field data of the two full-scale
test embankments.
2. Description of the two full-scale test embankments
2.1. Wall embankment system with steel grid reinforcement
The reinforced long embankment with steel grid
reinforcement (Fig. 1) was constructed on the campus of
the Asian Institute of Technology (AIT) having a length-
to-width ratio of 15/5 3.0 (Shivashankar, 1991). The
embankment was constructed over a period of 30 days (see
Fig. 6). The long embankment was divided into three
sections along its length with three different backfill
materials, namely clayey sand, lateritic soil, and weathered
clay. The embankment is 5.70 m high above the existing
ground surface, with 5.64 m width and 14.64 m length at
the top, and about 26.0m length at the base. This
embankment has three sloping faces with 1:1 slope and
one vertical wall facing.
2.2. Wall embankment system with hexagonal wire mesh
reinforcement
On the AIT campus nearby, a fully instrumented short
embankment with hexagonal wire mesh as the reinforce-
ment also was constructed. It had a length-to-width ratio
of 6/6 1.0 (Voottipruex, 2000). This embankment wasconstructed within 60 days. This short embankment is
6.0 m in height with 6.0 m wide, and 6.0 m long at the top,
and 18.0 m long at the base as shown in Fig. 2. After 405
days of construction, the top of the embankment was
raised up by 1 m of additional fill to investigate its behavior
(see Fig. 6). The embankment was divided into two parts
along its length with zinc-coated and PVC-coated hexago-
nal wire mesh reinforcements backfilled with Ayutthaya
sand. The gabion facing of the embankment was built with
101 inclination from the vertical alignment. The side slopes
and back slope have 1:1 inclination.
3. Model parameters
3.1. Foundation soils
Referring to Bergado et al. (1995), the typical subsoil
profile, together with the general soil properties at site, is
illustrated in Fig. 3. Similar foundation soil was used for
2D and 3D numerical simulation of the two full-scale test
embankments. According to the existing database
of geotechnical properties of the foundation subsoils
at the site (Balasubramaniam et al., 1978), the
linear elasticperfectly plastic model parameters (Mohr
Coulomb failure criteria) were used for the topmost heavilyoverconsolidated clay. The modified Cam clay model
parameters were adopted for the other underlying four
layers together with the estimated value of permeability
(Bergado et al., 1995). For the fluid properties adopted in
the FLAC2D and FLAC3D analyses, the Biots modulus
was applied equal to one for the incompressible grains
condition. The level of groundwater was designated at 2 m
depth below the ground surface. The input model para-
meters of foundation soils used in FLAC2D and FLAC3D
analyses are tabulated in Table 1 together with the
permeability coefficients and porosities for each layer of
the foundation subsoils.
3.2. Backfill soils
3.2.1. Lateritic backfill material
The lateritic backfill soil was utilized in the middle
portion of the steel grid reinforced embankment and was
used as its representative backfill soil. Theoretically, the
lateritic soil is a complex engineering material which has
nonlinear and nonhomogeneous properties. Many consti-
tutive soil models were developed to represent its compli-
cated soil behavior. However, in this study, the commonly
used nonlinear elastic model with MohrCoulomb failure
criteria was selected to represent the stressstrain behavior
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of this backfill material because the MohrCoulomb failure
criteria can represent the failure behavior of soils having an
apparent cohesion and obtaining the model parameters is
also simple (Zienkiewicz et al., 1975). Bergado et al. (1993)
obtained the parameters of the lateritic backfill materials
from the large-scale direct shear tests as tabulated in Table
1 for the MohrCoulomb model used in FLAC2D and
FLAC3D analyses.
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Fig. 1. Schematic plan view and cross-section indicating instrumentation points in steel grid reinforced embankment. (a) Plan view and (b) cross-section.
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linear elastic material with Youngs modulus of
2.0 1011 Pa and Poissons ratio of 0.33 (Bergado
et al., 1995). The reinforcement was represented by linear
elastic structural shell elements. The properties required
for the reinforcement were density, Youngs
modulus, Poissons ratio, and thickness, which were
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12 14 16 18 20
Unit Weight (kN/m2)
2.0 2.5 3.0
Specific Gravity
20 40 60 80 100 120
Preconsolidation Pressure (kPa)
Plastic limitLiquid limitNatural watercontent
PL & LL & Water Content (%)
0 10 20 30 40
Undrained Shear Strength (kN/m2)
0 50 100 150 200
From Oedometer
Test
P'oP'max
0 2 4 6 8 10
OCR
OCR
11
10
9
8
7
6
5
4
3
2
1
0
Depth(m)
Lightlyoverconsolidated
weathered clay
Heavily
overconsolidatedweathered clay
Very soft clay
Medium stiff clay
Stiff clay
Fig. 3. General soil profile and properties of the subsoil at Asian Institute of Technology (AIT) (Chai, 1992; Bergado et al., 1995).
Table 1
Selected parameters for steel grid reinforced embankment adopted in 2D and 3D finite-difference analyses
Parameters Symbol Soil layer Wall face Backfill
1 2 3 4 5
Depth (m): 01 12 26 68 812
Soil model MCa MCCb Elastic MCa
Slope of elastic swelling line k 0.04 0.11 0.07 0.04
Slope of normal consolation line l 0.18 0.51 0.31 0.18
Frictional constant M 1.1 0.9 0.95 1.1
Specific volume at reference pressure (1 Pa) Vl 4.256 8.879 5.996 4.168
Reference pressure (1 Pa) P1 1 1 1 1
Poissons ratio n 0.25 0.25 0.3 0.3 0.25
Maximum elastic bulk modulus ( 107 Pa) kmax 12.5 2.88 4.86 9.6
Preconsolidation pressure ( 104 Pa) pco 14.3 7.55 9.30 10.7
Elastic bulk modulus ( 106 Pa) K 2.67 463,000 79.80
Elastic shear modulus ( 106 Pa) G 1.6 70,000 28.98Friction angle (deg) f0 29 32
Cohesion ( 103 Pa) C0 29 60
Total unit weight (kg/m3) rt 1750 1750 1500 1650 1750 2400 2000
Dry unit weight (kg/m3) rd 1750 1750 803 1050 1226 2400 2000
Porosity N 0.545 0.545 0.697 0.600 0.524
Permeability ( 1012 m2/(Pa s)) 25.0kv 17.8 17.8 2.65 2.65 17.8
aElasticperfectly plastic MohrCoulomb model.bModified Cam clay model.
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back-calculated by matching the EI in addition to EA
values as demonstrated by Teerawattanasuk et al. (2003).
The input parameters of the reinforcement as structural
shell element are tabulated in Table 3.
In FLAC2D, the linear elastic material properties
assigned to the reinforcements were the same as those
applied in FLAC3D
. The steel grid reinforcementwas modeled using linear elastic structural cable elements
with Youngs modulus of 2.0 1011 Pa, and cross-sectional
area of longitudinal bar per meter width of 180 mm2
(Bergado et al., 1995). The input parameters of steel grid
reinforcement as the structural cable elements are listed in
Table 4.
3.3.2. Hexagonal wire mesh
In FLAC3D, the linear elastic structural shell
elements were adopted in the numerical simulation of the
hexagonal wire mesh reinforcements. The linear axial
stiffnesses, EA, were determined from the in-air tensile
tests conducted by Wongsawanon (1998). The axial
stiffness of the reinforcement, EA, was similar to that in
the numerical simulation of laboratory in-soil pullout tests
(Teerawattanasuk et al. (2003)). The input parameters of
hexagonal wire mesh reinforcement as structural shell
element applied in FLAC3D program are tabulated in
Table 3. For the numerical simulation using FLAC2D, the
hexagonal wire mesh reinforcements were represented by
the structural cable elements (ITASCA and FLAC3D
Version 2.0, 1997). The input parameters of hexagonal
reinforcement as the structural cable elements are tabulated
in Table 4.
3.4. Wall face
3.4.1. Steel grid wall-facing system
In both FLAC2D and FLAC3D programs, the steel grid
wall-facing system was represented by the solid elements
which were similar to the elements applied in the backfill
soil material. The wall-facing system was treated as linear
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Table 2
Selected parameters for hexagonal wire mesh reinforced embankment adopted in 2D and 3D finite-difference analyses
Parameters Symbol Soil layer Wall face Backfill
1 2 3 4 5
Depth (m): 1 12 26 68 812
Soil model MCa MCCb MCa MCa
Slope of elastic swellingline k 0.04 0.11 0.07 0.04
Slope of normal consolation line l 0.18 0.51 0.31 0.18
Friction constant M 1.1 0.9 0.95 1.1
Specific volume at reference pressure (1 Pa) Vl 4.256 8.879 5.996 4.168
Refrence pressure (1 Pa) P1 1 1 1 1
Possion ratio n 0.25 0.25 0.3 0.3 0.25
Maximum elastic bulk modulus ( 107 Pa) kmax 112.5 2.88 4.86 9.6
Preconsolidation pressure ( 104 Pa) pco 114.3 7.55 9.30 10.7
Elastic bulk modulus ( 106 Pa) K 2.67 5.88 5.00
Elastic shear modulus ( 106 Pa) G 1.6 2.69 2.31
Friction angle (deg) f0 29 45 30
Cohesion ( 103 Pa) c0 29 20 10
Total unit weight (kg/m3) rt 1750 1750 1500 1650 1750 1800 1800
Dry unit weight (kg/m3) rd 1750 1750 803 10,500 1226 1800 1800
Porosity N 0.545 0.545 0.697 0.600 0.524
Permeability ( 1012 m2/(Pa s)) 25.0kv 17.8 17.8 2.65 2.65 17.8
aElasticperfectly plastic MohrCoulomb model.bModified Cam clay model.
Table 3
Selected parameters for structural shell element applied in FLAC3D
Parameters Steel grid
reinforcement
Hexagonal wire mesh
reinforcement
Youngs modulus, E
(Pa)
2 1011 5.4 108
Poissons ratio 0.33 0.33
Thickness (m) 0.006 0.003
Density (kg/m3) 2500 2500
Table 4
Selected parameters for structural cable element applied in FLAC 2D
Parameters Steel grid
reinforcement
Hexagonal wire
mesh reinforcement
Bond friction angle of grout
(deg)
32.5 27.5
Bond strength of grout (N/m) 6 104 9 103
Youngs modulus, E (Pa) 2 1011
5.4 108
Tensile yield strength (Pa) 6 108 6 10
8
Cross sectional area (m2) 180 106 156 106
Grout shear stiffness (N/m) 1.5 107 7.764 107
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elastic material with bulk modulus of 1.56 1011 Pa and
shear modulus of 7.01010 Pa (Bergado et al., 1995). The
input parameters adopted in the numerical simulation
using FLAC2D and FLAC3D analyses are listed in Table 1.
3.4.2. Hexagonal wall-facing system
The hexagonal wall-facing system was made from largerectangular wire mesh baskets joined together and filled
with crushed rock (Bergado et al., 2000). Similar to the case
of steel grid wall-facing system, the hexagonal wall-facing
system was also modeled using solid elements. However,
the linear elasticperfectly plastic, MohrCoulomb model
was used to simulate the hexagonal wall-facing system
based on the study of Bergado et al. (2000b). The
parameters required for FLAC2D and FLAC3D analyses
are tabulated in Table 2.
3.5. Soilreinforcement interface
In the simulation of the soilreinforcement interface, two
interaction modes were considered: namely, direct shear
and pullout modes. However, for the steel grid and
hexagonal wire mesh, only the pullout mode is applicable.
In FLAC3D, the interface element where sliding or
separation occurred, is characterized by Coulomb sliding
having the properties of friction, cohesion, dilation, normal
stiffness and shear stiffness (ITASCA and FLAC3D
Version 2.0, 1997). The interface elements are utilized to
provide the sliding plane for the soilreinforcement inter-
face. The interface resistance can be determined in terms of
the interaction coefficient, R, as explained in the study ofBergado et al. (2000b). For 2D and 3D numerical analyses,
the adopted interaction coefficients were 1.0 for steel grid
reinforcement (Bergado et al., 1995) and 0.9 for the
hexagonal wire mesh reinforcement (Teerawattanasuk
et al. (2003)). The properties of soilreinforcement inter-
face element used in the numerical simulation of steel grid
and hexagonal wire mesh reinforced embankments with
FLAC3D program are listed in Table 5. For FLAC2D, the
applied soilreinforcement interface has been combined
with the structural cable element as described previously.
The input interface parameters adopted in FLAC2D
program for steel grid and hexagonal wire mesh reinforce-
ments as structural cable elements are tabulated in Table 4.
4. Numerical simulations
Comparing the length-to-width ratio (L/B) of the two
embankments, the L/Bfor the steel grid embankment is 3.0
(15/5) as indicated in Figs. 1 and 7, which is about 3.0 times
greater than the hexagonal wire mesh embankment (Figs. 2
and 8) where L/B 1 (6/6). Using numerical simulationsunder 2D and 3D conditions, this study was carried out to
investigate the influence of geometric configurations on the
calculated results such as settlements, excess pore-water
pressures, and horizontal displacements, as well as tensile
forces in the reinforcements. Using the same constitutive
models and properties of the foundation soils utilized by
Bergado et al. (1995) and Alfaro (1996), numerical
simulations were conducted using 2D and 3D explicit FD
programs, FLAC2D and FLAC3D, respectively. The
coupled analyses were carried out in the consecutive steps.
A summary of various numerical simulations that were
performed on these two full-scale test embankments is
tabulated in Table 6.
The materials applied in the numerical simulation of the
reinforced structure were classified into four types, namely
(a) soil (solid brick-shaped element), (b) reinforcement
(structural shell or cable element), (c) soilstructure
interaction (interface element) and (d) wall-facing structure
(solid brick-shaped element). The interface elements were
attached to provide the sliding plane for the reinforcement
and surrounding soil.
5. 2D numerical simulations of steel grid reinforcedembankment (Analyses 1 and 2)
5.1. 2D FD grid discretization
For 2D or plane strain condition analysis (refer to
Analysis 1 in Table 6), FLAC3D was used to simulate the
long steel grid reinforced embankment (refer to Fig. 1)
by restricting the planes perpendicular to the side of the
embankment: e.g. fixed only the longitudinal directions.
The materials applied in FLAC3D were presented by 3D
grid elements. The FD grid discretization used in FLAC3D
analysis is shown in Fig. 4. Similarly, the FD grid
discretization corresponding to FLAC2D program (Analy-
sis 2 in Table 6) is presented in Fig. 5. The x-, y-, and z-
dimensions of the foundation soil were 43, 1, and 12 m,
respectively (see Fig. 5). Similar soil profile was utilized for
the foundation soils (refer to Table 1).
The uniform vertical spacing of steel grid reinforcement
in the reinforced embankment was 0.45 m with a length of
5 m. In the 2D numerical simulation using FLAC3D
program, the structural shell element with 5 m length, 1 m
width, and 0.006 m thickness was adopted to simulate the
steel grid reinforcement. As noted earlier, in FLAC2D
program, the structural cable elements were used to
simulate the steel grid reinforcement.
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Table 5
Interface parameters adopted in finite-difference analysis with FLAC3D
Parameters Values
Types of reinforcement Steel grid Hexagonal
wire mesh
Cohesion of interface element, ci (kPa) 60 9
Friction angle of interface element, d (deg) 32 27.5
Interface shear stiffness, ks* (kPa/m) 1.5104 7.682 104
Interface normal stiffness, kn*
(kPa/m) 5.0106 3.028 10
5
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equivalent period of 30 days (Fig. 6). The procedure in
numerical simulation for the steel grid reinforced embank-
ment was done by placing the backfill material and
inserting the reinforcement at an interval of 0.45 m vertical
spacing per stage until the completion at the full height of
the embankment. During the placement of the backfill
materials and inserting the reinforcement, a coupled
analysis was undertaken but without pore pressure
dissipation. Pore pressure dissipation was then permitted
after the construction phase (about 2 days for every stage).
6. 2D numerical simulations of hexagonal wire mesh
reinforced embankment (Analyses 3 and 4)
6.1. 2D FD discretization
With the same numerical procedures, the hexagonal wire
mesh reinforced embankment (refer to Fig. 2) was
subsequently analyzed using FLAC3D and FLAC2D (refer
to Analyses 3 and 4 in Table 6), respectively. The
dimensions of the foundation soil were as follows 42 m
length, 1 m width, and 12 m depth which were x-, y-, and z-
axes, respectively. The foundation soil was divided into five
layers (see in Table 2). The reinforcement was representedby structural shell elements that were 4 m long, 1 m wide,
and 0.003 m thick. The inclined wall-facing system of the
hexagonal wire mesh reinforced embankment was repre-
sented by the brick-shaped elements 1.0 m long, 1.0 m wide,
and 6.0 m high.
6.2. Boundary and initial conditions
In the 2D numerical analyses of hexagonal wire mesh
reinforced embankment using FLAC2D and FLAC3D,
similar procedures were employed for assigning the
boundary and initial conditions.
6.3. Stages of construction
Referring to Fig. 6, the construction sequence of the
hexagonal wire mesh reinforced soil embankment was
divided into 12 stages with a total duration of 60 days. The
procedure in numerical simulation for the hexagonal wire
mesh reinforced soil embankment was done by placing thebackfill material and inserting the hexagonal reinforcement
at an interval of 0.5 m vertical spacing per stage until the
completion of full height embankment. The coupled
analysis, undrained and consolidation analysis, was also
taken into account in the numerical simulation. After 405
days, the traction of 16.7 kN/m2 was added on the top of
the embankment.
7. 3D numerical simulations of steel grid reinforced
embankment (Analysis 5)
7.1. 3D FD discretization
The numerical simulation by FLAC3D has the advantages
in obtaining the exact full-scale test procedures. The 3D FD
discretization is illustrated in Fig. 7. Because of the
symmetry of the embankment structure, only the half
section of the reinforced embankment and the foundation
soil were simulated to reduce the numbers of the degrees of
freedom, which is time consuming in the calculation steps.
The dimensions of the foundation soil were as follows 43 m
long, 28 m wide, and 12 m depth which correspond to the x-,
y-, and z-axes respectively. The dimensions of wall facing
with respect to x-, y-, and z-axes, were 0.2 m long, 7.5 m
wide, and 5.70 m high, respectively. The reinforcement wasmodeled using structural shell elements in the embankment
that were 5 m long, 7.5 m wide, and 0.006 m thick.
7.2. Boundary and initial conditions
The boundary condition used in the numerical simula-
tion of the embankment was assigned by the fixed velocity
boundary in x-, y-, and z-directions at the bottom of the
foundation soil. The horizontal fixed velocities of grid
points in x-direction were attached to two vertical planes of
the foundation soil (at x 0 and 43). The horizontal fixed
velocities in y-directions were attached to four vertical
planes of the foundation soil that cross the x- and y-axes,
respectively, as shown in Fig. 7. For 3D numerical model,
the velocities in y-direction along the symmetry plane of
the reinforced embankment were assigned to be zero while
the velocity boundaries in x-, y-, and z-direction for the
other sides of the embankment were set to be free velocity
boundaries to allow the occurrence of free displacements in
all directions.
7.3. Stages of construction
In numerical simulation of the steel grid reinforced
embankment, the stages of construction applied in 3D
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0 50 100 150 200 250 300 350 400 450 500 550
0
1
2
3
4
5
6
7
8
405days
30days
60days
Steel grid reinforced embankment(5.70 m high with 13 incremental layers )Hexagonal wire mesh reinforced embankment(6.0 m high with 12 incremental layers)
AdditionalSurcharge16.7 kPa
Embankmen
tHeight(m)
Time (days)
Fig. 6. Construction sequence of AIT full-scale test reinforced embank-
ments.
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numerical analyses were parallel to the construction
applied in 2D numerical analyses.
8. 3D numerical simulation of hexagonal wire mesh
reinforced embankment (Analysis 6)
8.1. 3D FD discretization
Fig. 8 presents the 3D FD discretization of geometry
used for the hexagonal wire mesh reinforced embankment.
The dimensions of the foundation soil were the following:
42 m long, 24 m wide, and 12 m depth which correspond to
the x-, y-, and z-axes, respectively. The gabion facing
structures were comprised of brick-shaped elements with
dimensions 3.0 m width, 1.0 m length, and 6.0 m height.
The uniform vertical spacing of hexagonal wire mesh
reinforcement in reinforced embankment was 0.5 m. The
reinforcement was modeled using the structural shell
elements in the embankment that were 4 m long, 3 m wide,
and 0.003 m thick.
8.2. Boundary and initial conditions
In the 3D numerical simulation of the hexagonal wire
mesh reinforced embankment using FLAC3D, procedures
similar to those described in Section 7.2 were employed for
assigning the boundary and initial conditions.
ARTICLE IN PRESS
15.8m 0.2
m
5m7m
15m
43m
14.5 m
2.5 m
5 m
6 m
12
m
5.7
0m
x (+)
y (+)
z (+)
12
m
Fig. 7. 3D finite-difference grid discretization for steel grid reinforced embankment FLAC3D (Analysis 5).
12
m
15m
12m
15m
15m
6m
3m
6 m
x (+)y (+)
z (+)
Fig. 8. 3D finite-difference grid discretization for hexagonal wire mesh reinforced embankment with FLAC3D (Analysis 6).
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8.3. Stages of construction
In numerical simulation of the hexagonal wire mesh
reinforced embankment, the stages of construction applied
in 3D numerical analyses were similar to those applied in
2D numerical analyses.
9. Results and discussions
9.1. Steel grid reinforced embankment
To investigate the influence of geometric configurations,
the steel grid reinforced embankments have been simulated
by 2D and 3D numerical analyses (refer to Analyses 1, 2
and 5 in Table 6) by means of FD technique using FLAC2D
and FLAC3D programs. The comparisons between the
measured field data and the calculated results (e.g. vertical
settlements, excess pore-water pressures, lateral displace-
ments, and tension force distribution) are discussed in the
following sections.
9.1.1. Settlement
The calculated and measured surface settlement (0.45 m
depth below the original ground surface, refer to settlement
plate S5) and subsurface settlement (3.0 m depth below the
original ground surface, refer to settlement plate SS8) are
compared in Figs. 9 and 10, respectively. The calculated
values of surface and subsurface settlements obtained from
2D numerical analyses (refer to Analyses 1 and 2 listed in
Table 6) were in agreement with the measured data as well
as the FE results using CRISP program (Bergado et al.,
1995; Chai, 1992). However, the calculated values for bothsurface and subsurface settlements attained from 3D
numerical analysis (refer to Analysis 5 listed in Table 6)
significantly underestimated the measured field data,
possibly because of the three 3D loading condition and
geometric effects which are significant influence factors on
numerical simulation (Auvinet and Gonzalez, 2000). In
addition, for the steel grid reinforced embankment, the
measured settlement pattern is closer to 2D numerical
analysis, than for 3D numerical analysis because of its
longer plan dimensions.
9.1.2. Excess pore-water pressure
As shown in Fig. 11, at the end of construction (i.e., after
an elapsed time of 30 days), the calculated maximum excess
pore-water pressures at the locations HP5 and HP6
obtained from 2D numerical analyses (refer to Analyses 1
and 2 in Table 6) overestimated the measured field data
while the calculated values from 3D analysis (Analysis 5 in
Table 6) yielded satisfactory agreement. After the end of
construction, the dissipation of pore-water pressures
among three analysis schemes (Analyses 1, 2, and 5) have
higher dissipation rate, than the measured field data.
However, referring to Analysis 1 using FLAC3D considered
as 2D numerical analysis, the calculated values yielded a
better agreement. Therefore, using the permeability value
equal to 25 times of kv, the results also could not predict
the variation of measured pore-water pressure changes
with time.
9.1.3. Lateral displacement
Fig. 12 shows the comparison of lateral displacement
profiles of the steel grid reinforced embankment 7 monthsafter the end of construction (or at the elapsed time of 240
days). The measured field data only reached down to 3 m
depth because the inclinometer probe could not be inserted
into the deformed casing below 3 m depth (Bergado et al.,
1995). In the embankment zone, the calculated results from
FLAC2D (refer to Analysis 2 in Table 6) agreed well with
the calculated results using CRISP program conducted by
Chai (1992), but underestimated the measured field data.
For the foundation soil zone, the results calculated from
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0 50 100 150 200 250 300 350 400 450
1200
1100
1000
900
800
700
600
500
400
300
200
100
0
S5
Emb.
Measured field dataFEM CRISP 25kv (Chai, 1992)
FDM FLAC2D 25kv
FDM FLAC3D 25kv (2D analysis)
FDM FLAC3D 25kv (3D analysis)
End of Construction
VerticalDisplacement(mm)
Elapsed Time (days)
Fig. 9. Comparison of measured and predicted surface settlement of steel
grid reinforced soil embankment, under 2D and 3D analyses at settlement
plate S5 (0.45 m depth at the middle).
0 50 100 150 200 250 300 350 400 450
900
800
700
600
500
400
300
200
100
0
Measured field dataFEM CRISP 25kv (Chai, 1992)
FDM FLAC2D 25kv
FDM FLAC3D 25kv (2D analysis)
FDM FLAC3D 25kv (3D analysis)
SS8
Emb.
End of ConstructionVerticalDisplacement(mm)
Elapsed Time (days)
Fig. 10. Comparison of measured and predicted subsurface settlement of
steel grid reinforced soil embankment, under 2D and 3D analyses at
settlement plate SS8 (3 m depth at the middle).
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FLAC2D overestimated the measured field data. In analysis
1 (FLAC3D under 2D numerical analysis, see Table 6), the
calculated results underestimated the measured field data.
Thus, the measured field data beneath the reinforced
embankment are in between the calculated results obtained
from Analyses 1 and 2 (under 2D numerical analysis).
9.1.4. Tension force in reinforcement
For a reinforced soil wall constructed on rigid founda-
tion with high stiffness reinforcement, the maximum
tension force in the reinforcement is close to the value
calculated by at-rest earth pressure coefficient (Adib et al.,
1990; Rowe and Ho, 1997). However, for a reinforced soil
wall constructed on soft ground, under embankment
loading, the soft foundation soil tends to squeeze out of
the base of the reinforced embankment that caused large
relative horizontal movement between the soil and the
reinforcement. Moreover, the settlement pattern may form
a concave shape at the base of the reinforced embankment.
Therefore, large tension forces can be developed in the
bottom reinforcements of the embankment (Bergado et al.,
1995). Fig. 13 compared the calculated tension forcedistribution along the reinforcement length obtained from
2D and 3D numerical analyses immediately after construc-
tion (at the elapsed time of 30 days) and the measured field
data obtained from strain gauges as well as the calculated
results using CRISP program (Chai, 1992). The maximum
tension forces in Mat 1 occurred at 4 m from the wall face.
This might be attributed to the bending effect in the
reinforced embankment due to differential settlements of
foundation soil between the front and rear of the reinforced
embankment. These results are similar to the previous
results reported by Chai (1992) and Alfaro et al. (1997).
Moreover, the calculated tension force distribution from
2D and 3D numerical simulation (Analysis 1, 2, and 5)
consistently shows logical results in which the tension
forces of 2D numerical analysis are larger than that of 3D
analysis because of higher calculated settlements of the
former compared to the latter (see Figs. 9 and 10).
9.2. Hexagonal wire mesh reinforced embankment
The hexagonal wire mesh reinforced embankment which
has a shorter plan dimensions (length-to-width ratio,
6/6 1.0), is compared with the steel grid reinforced
embankment. For the sake of comparison, 2D and 3D
numerical simulations of hexagonal wire mesh reinforcedembankment (refer to Analyses 3, 4 and 6 in Table 6) were
also studied using the same procedure as discussed in the
previous section. Similar foundation soil parameters and
permeability values of foundation soils (k 25 kv) were
applied in the numerical analyses. Comparisons between
the findings of 2D and 3D numerical results and the
measured field data (e.g. settlements, excess pore-water
pressures, lateral displacements, and tension force distribu-
tion) are also discussed in the following sections.
9.2.1. Settlement
Referring to Figs. 14 and 15, we see the calculated values
of surface settlements obtained from 3D numerical
analyses (Analysis 6, refer to Table 6) are closer and they
slightly overestimated the measured data than the calcu-
lated results obtained from 2D numerical analyses. As
shown in Fig. 16, the calculated subsurface settlements
(SS2) from 3D analysis (Analysis 6 in Table 6) were slightly
less than the measured field data. The measured field data
at the settlement plate SS2 were higher than the calculated
results. However, the actual settlement patterns for this
embankment agreed more closely with the 3D analyses.
The use of the 2D numerical simulation for the hexagonal
wire mesh reinforced embankment case could not predict
the actual surface and subsurface settlements. Therefore,
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0 50 100 150 200 250 300 350 400 450 500 550
-12
-10
-8
-6
-4
-2
0
2
4
6
8
Ground surface EL. = 0.0
Measured field data at 240 days
FEM CRISP 25 kv
at 240 days
FDM FLAC2D 25 kv at 240 days
FDM FLAC3D 25 kv at 240 days (2D analysis)
FDM FLAC3D 25 kv at 240 days (3D analysis)
Depth/Height(m)
Lateral Displacement (mm)
Fig. 12. Comparison of measured and predicted lateral displacement
profiles of steel grid reinforced soil embankment, under 2D and 3D
analyses.
0 50 100 150 200 250 300 350 400 450
0
10
20
30
40
50
60End of Const ruct ion Measured field data
FEM CRISP 25kv (Chai, 1992)
FDM FLAC2D 25kv
FDM FLAC3D 25kv (2Danalysis)
FDM FLAC3D 25kv (3D analysis)
HP5
Emb.
ExcessPore
Pressure,
kPa
Elapsed Time (days)
Fig. 11. Comparison of measured and predicted excess pore-water
pressure of steel grid reinforced soil embankment, under 2D and 3D
analyses at piezometric point HP5 (under lateritic Section 7 depth at the
middle).
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9.2.4. Tension force in reinforcement
Fig. 19 shows the comparisons between 2D and 3D
calculated tension force distribution along the reinforce-
ment length at 7 months after construction (elapsed time
equal to 240 days), as well as the measured field data.
Similar to 2D and 3D numerical simulation of the steel grid
reinforced embankment, the calculated tension force
distribution (refer to Analyses 3, 4, and 6 in Table 6) also
shows consistent results in which the tension forces of 2D
numerical analysis are greater than that of 3D numerical
analysis due to overestimated settlements of the former
compared to the latter (see Figs. 1416). However, thecalculated results from 3D numerical analysis yielded
values closer to the measured field data than the 2D
numerical analysis because the calculated settlement and
lateral movement from 2D numerical analysis predomi-
nantly overestimated the measured field data. Considering
the tension force distribution in Mat 1, the maximum
tension force occurred at 3 m from the wall face similar to
the steel grid reinforced embankment case which may be
due to the differential settlements of the soft foundation
soil at the base of the reinforced embankment.
9.3. Results summary
The aforementioned simulation results of the long and
short embankments corresponding to 2D and 3D
conditions, respectively, are quite consistent with 2D/3D
settlement predictions of embankments on soft ground.
According to Skempton and Bjerrum (1957), the 3D
settlement predictions are consistently low than 2D
settlement predictions mainly due to lower pore pressures
and lower lateral deformations in the 3D conditions.
Consequently, Skempton and Bjerrum (1957) proposed a
settlement correction factor (usually less than one)
depending on the geometry of the problem as well as the
pore pressures. Similarly, as shown in Figs. 11 and 17, the
3D pore pressures were consistently low than the 2D pore
pressures. Moreover, the 3D lateral deformations were
consistently low than the lateral deformations as
demonstrated in Figs. 12 and 18, and the trends of the
results are reflected in the predicted tensions in the
reinforcements (see Figs. 13 and 19). Finally, the simula-
tion results from the FLAC3D used in 2D analysis agreed
with the measured settlement data in the long embank-
ment as well as the respective 2D settlement predictions
from FLAC2D and the 2D FEM CRISP of Chai (1992) as
shown in Figs. 9 and 10.
10. Conclusions
Utilizing the constitutive models and properties of
foundation soils published by previous researchers, numer-
ical simulations were conducted using 2D and 3D explicit
FD programs, FLAC2D and FLAC3D, respectively. The
2D and 3D numerical simulations have been done to
investigate the influence of the embankment geometry.
Two full-scale test embankments, namely steel grid
reinforced long embankment with plan dimensions
(length-to-width ratio, 15/5 3.0) and hexagonal
ARTICLE IN PRESS
100500 150 200 250 300 350 400 450 500 550
-12
-10
-8
-6
-4
-2
0
2
4
6
8
10
Measured field data at 490 days
FDM FLAC2D 25 kv at 490 days
FDM FLAC3D 25 kv at 490 days (2D analysis)
FDM FLAC3D 25 kv
at 490 days (3D analysis)
Ground surface EL. = 0.0
Additional sandbags1 m high were added
Depth/Height(m)
Lateral Displacement (mm)
Fig. 18. Comparison of measured and predicted lateral displacement
profiles of hexagonal wire mesh reinforced soil embankment, under 2D
and 3D analyses.
0
5
10
15
20
45+/2 El. = 0.0 m
Force(kN/m)
Distance from embankment face (m)
Legend:
Measured field data 240 days
FDM FLAC2D 240 days 25kv
FDM FLAC3D 240 days 25kv (2D analysis)
FDM FLAC3D 240 days 25kv (3D analysis)
0
5
10
15
El. = 2.0 mMat. 2
Mat. 1
Coherent gravityfailure plane
0
5
10
15
El. = 4.0 m Mat. 3
0
0 1 2 3 4
0 1 2 3 4
0 1 2 3 4
2
4
6
0.3*H =1.8 m
Tie-back wedgefailure plane
Wallheight(m)
Fig. 19. Comparison of measured and predicted tension force in the
reinforcement of hexagonal wire mesh reinforced soil embankment, under
2D and 3D analyses.
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wire mesh reinforced short embankment with plan
dimensions (length-to-width ratio, 6/6 1.0), were studied.
The calculated results were compared to the measured field
data with particular attention to settlements, excess pore-
water pressures, lateral displacements, and tension force
distributions in the reinforcement. The actual behavior of
the steel grid reinforced long embankment correspondedmore closely to the results of the 2D numerical simulations.
Furthermore, the actual behavior of the hexagonal wire
mesh reinforced short embankment corresponded more
closely to the results of the 3D numerical simulations.
Moreover, the simulation results from FLAC3D used in 2D
analysis agreed with the measured settlement data in the
long embankment as well as the 2D predictions from
FLAC2D. Therefore, the geometric effects should be
considered as important factors that can affect the results
of the numerical simulations, which are consistent with the
current settlement predictions with Skempton and Bjerrum
corrections.
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