2d and 3d numerical simulations of reinforced embankments on soft ground

7/28/2019 2D and 3D Numerical Simulations of Reinforced Embankments on Soft Ground

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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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D.T. Bergado, C. Teerawattanasuk / Geotextiles and Geomembranes 26 (2008) 395540


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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.

ARTICLE IN PRESS

Fig. 1. Schematic plan view and cross-section indicating instrumentation points in steel grid reinforced embankment. (a) Plan view and (b) cross-section.

D.T. Bergado, C. Teerawattanasuk / Geotextiles and Geomembranes 26 (2008) 3955 41


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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

ARTICLE IN PRESS

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.

ARTICLE IN PRESS

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)


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.


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.


In numerical simulation of the steel grid reinforced

embankment, the stages of construction applied in 3D

ARTICLE IN PRESS

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)


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.


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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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)


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



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).



12/17

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)


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)


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).



13/17


14/17


15/17

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 (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.



16/17

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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