ELSEVIER

Compurers and Geotechnics 17 (1995) 441411 0 1995 Elsevier Science Limited

Printed in Great Britain. All rights reserved 0266-352X195/$9.50

FE ANALYSIS OF GRID REINFORCED EMBANKMENT SYSTEM ON SOFT BANGdOK CLAY

D.T. Bergado Associate Professor of Geotechnical Engineering

School of Civil Engineering, Asian Institute of Technology P.O. Box 2754, Bangkok 10501 Thailand

J.C. Chai Research Engineer, Kiso-Jiban Consultants Co. Ltd. l-11-15 Kudan-Kita, Chiyoda-Ku, Tokyo 102, Japan

N. Miura Director, Institute of Lowland Technology

Dept. of Civil Engineering Saga University, Saga 840, Japan

ABSTRACT

The behavior of a reinforced embankment on soft Bangkok clay has been analyzed by plane strain finite element method. The finite element analysis considers the selection of proper soil/reinforcement properties according to the relative displacement pattern of upper and lower interface elements. The large deformation phenomenon is simulated by updating the node coordinates, including those of the embankment elements above the current construction level, which ensures that the applied fill thickness simulates the actual field value. A full scale test reinforced embankment with a vertical face (wall) on Bangkok clay has been analyzed by the proposed finite element method, and the numerical results are compared with the field data. The response of a reinforced embankment on soft ground is principally controlled by the interaction between the reinforced soil mass and soft ground and the interaction between the grid reinforcement and the backfill soil. The tension in reinforcement and lateral displacement of the wall face varied during consolidation of foundation soil. The maximum tension force occurred in the reinforcement layer placed at the base of reinforced mass, due to bending of the reinforced mass resulting from differential settlements. It is considered necessary to account for the permeability variation of the soft ground foundation in the finite element analysis.

INTRODUCTION

To analyze the behavior of reinforced earth structure on soft ground,

it is necessary to consider the , elasto-plastic behavior of soil,

soil/r2inforcement interaction, and soft.ground consolidation systematically

and simultaneously. To solve this type of complex problem, the numerical

technique, such as finite element has been used by several investigators

[1.2,3,41.

The properties of soil/reinforcement interface are usually determined

by direct shear or pullout tests. However, for grid reinforcement, the

different soil/reinforcement interaction mode yields different interface

properties, i.e. for strip reinforcement, usually, direct shear interaction

mode gives higher interface strength than the pullout interaction mode [21.

To properly simulate the soil/reinforcement interaction behavior in numerical

analysis, it is necessary to use different interface properties for different

interaction modes.

447

448

In finite element analysis, the large deformation problem is

approximately considered by updating qthe node coordinates during the

incremental analysis. However, most computer programs used for analyzing the

reinforced wall or embankment, e.g. REA Program by Herrmann 151, do not

consider that each new layer of soil elements must be placed on soil elements

which already undergone certain displacements. For reinforced wall on rigid

foundation, the errors introduced by ignoring the coordinate change of the

elements above the current construction level are relatively small. But for

reinforced embankment on soft ground, ignoring the change in coordinates would

lead to soil lift thickness greater than the actually applied lift thickness.

For reinforced earth structure on soft ground due to large deformation,

the interaction between the soft ground and reinforced mass might be different

from that of the rigid foundation case. It is necessary to investigate the

interaction behavior between the reinforced mass and soft foundation as well

as the related influence factors.

In this paper. the concepts of considering the different

soil/reinforcement interaction modes and large deformation problem in finite

element modelling [61 have been applied to analysis of a full scale test

reinforced embankment with a vertical face (wall). The effect of large

deformation on the results of the analyses has been discussed and

subsequently, the finite element results are compared with the field data.

Finally, the influence of soil/reinforcement interaction mode on the response

of the system and the interaction between reinforced mass and soft ground are

investigated.

MODELLING SOIL/REINFORCEMENT INTERFACE BEHAVIOR

Two soil/reinforcement interaction modes can be expected: pullout of

reinforcement from soil and soil sliding over the reinforcement (direct

shear). For grid reinforcement, the' interface resistance mobilization

mechanisms for these two different modes are different. In modelling the

soil/reinforcement interface behavior, two models are used for pullout and

direct shear modes [61. The hyperbolic shear stress/displacement model [71

is used to represent direct shear interaction mode. The pullout of grid

reinforcement from the soil represents a three-dimensional situat,ion and can

only approximately modelled in a two-dimensional analysis. The idea is to

convert the pullout skin friction and bearing resistances to total

soil/reinforcement interface. Therefore, the pullout interface tangential

shear stiffness, k,, consists of a skin friction resistance component,k,,, and

a passive bearing resistance component, k,,, respectively. The total

equivalent tangential shear stiffness k, is the sum of k,, and k,,.

449

Detailed expressions for k,, and k,, were given by Chai and Bergado [61.

In finite element analysis, the signs of the shear stress in the

interface elements above and below the reinforcement are compared to determine

whether the direct shear mode (same sign) or the pullout mode (different sign)

is the acting mode. The interface elements above and below reinforcement are

treated as pair elements, and the numbers of pair elements are noted and

maintained throughout the analysis. Suppose the shear stresses of pair

elements are T, and r2, if 1 T,I + 1~~1 equals 1 T, + ~~1, that means rI and T,

have the same sign and direct shear mode is applicable. Otherwise, pullout

mode is used. For both direct shear and pullout interaction modes, when the

normal stress at the interface is in tension, a very small (e.g. 100 kN/m')

normal and shear stiffness are assigned to allow the opening and slippage at

interface.

The concept of selecting proper soil/reinforcement properties according

to the relative displacement pattern of upper and lower interface elements was

applied to analyze a base reinforced embankment on soft ground [Gl. Finite

element results showed that both pullout and direct shear interaction modes

yield practically the same results. The problem investigated in this study

is a reinforced embankment on soft ground with multi-layer reinforcements and

a vertical face (wall) . It will be discussed in detail later that

soil/reinforcement interaction mode does have significant influence on the

behavior of this reinforced embankment (wall).

OTHER ASPECTS OF NUMERICAL MODELLING

Correction of Node Coordinates During Incremental Analysis

The reinforced embankment on soft' ground, usually will cause large

settlement. Conventional stress/strain relationship is developed based on

infinitesimal deformation assumption, and it is not suitable for analyzing

large deformation problem. In finite element analysis, if the deformation

does not cause serious rotation of soil elements, the large deformation

phenomenon can be approximately treated by updating the nodal coordinates.

The approach was checked against the rigorous large deformation analysis given

by Carter et al (81 and was found to provide good results for the embankment

on soft foundation problem [91. Therefore, the large deformation phenomenon

is considered by updating the node coordinates in this study. Note, for

simulating the actual construction procedure and ensuring that the applied

fill thickness is the same as the field value, the coordinates of the node

above current construction top surface should also be updated. Otherwise, the

applied fill thickness will be more than the prescribed value [61 _ For the

analyzed embankment, the effectiveness of large deformation analysis is

450

checked by comparing with small deformation analysis (not updating the

coordinates)

Variation of Permeability

The formula proposed by Taylor [lo] and verified by the Tavenas et al

[ill for several natural clays has been used to represent the variation of the

permeability of soft clay during consolidation.

La -aI ‘-+I

k - k&o (2)

where e, is the initial void ratio; e is the void ratio at the condition under

consideration; k is the permeability; k, is the initial permeability; and C,

is constant, which is equal to O.Se, according to Tavenas et al [ll]. The

above modelling technique is incorporated in CRISP computer program (121, and

the program is renamed as CRISP-AIT. The numerical procedure used was the

same as original CRISP computer program, and its validity has been checked by

comparing with classical solution [13]. The standard formulations have been

used for newly included bar and beam elements and checked with theoretical

solution. For soil/reinforcement interface element, the formulation used is

essentially the same as used by Hird and Kwok [l].

ANALYSIS OF AIT TEST REINFORCED EMBANKMENT ON SOFT GRODND

A full scale welded steel grid reinforced test wall with a vertical face

was constructed inside the campus of Asian Institute of Technology (AIT). The

embankment system has been analyzed by finite element program CRISP-AIT. The

main purpose of this analysis is to investigate the capability of the finite

element method to predict the response of the reinforced embankment on soft

ground, to test the interaction model formulated between the grid

reinforcement and backfill soil, and investigate the interaction behavior

between the reinforced mass and the soft,foundation soil.

Reinforced Test Embankment

The reinforced test embankment was reported by Bergado et al [14, 151

in detail. The embankment is 5.8 m (19.5 feet) above the existing ground

surface with about 26.0 m (87 feet) base length. It has three sloping faces

with 1:l slope and one vertical front face (wall). The embankment was

constructed in one month period with an average rate of fill thickness

increase of 0.19 m/day. The welded wire mats used in the test embankment

system consisted of galvanized welded steel wire mesh with 152 mm x 228 mm

grid openings in the longitudinal and transverse directions, respectively.

The diameters are 5.4 mm for transverse bars and 6.1 mm for longitudinal bars.

The total length of reinforcement was 5.7 m including the bent-up portion of

about 0.7 m. The bent-up portion eventually formed part of the facing. The

vertical spacing between the reinforcements was 0.45 m. The embankment was

451

divided into three sections along its length corresponding to three different

backfill materials, namely: clayey sand, lateritic soil, and weathered clay

that were used in each section. The instrumentation program included the

measurement of strains, and therefore, tension forces in the longitudinal

wires, surface and subsurface settlements, pore pressures, vertical pressures

at the base of the wall, and lateral movements of the wall face. The strain

was measured by electric wire resistance strain gages bonded on both the top

and the bottom faces of the longitudinal wire.

Model Parameters

A typical subsoil profile together with the general soil properties at

the site is depicted in Figure 1. For the purpose of numerical modelling, the

foundation soil was divided into 5 layers to represent the weathered crust,

soft clay, firm-to-stiff clay and the transition zones. The linear elastic-

perfect plastic model parameters for the topmost weathered clay layer and

modified Cam clay parameters for other layers are shown in Table 1. In Table

1. the Poisson's ratio of all soils and Young's modulus for the top 1.0 m

thick weathered clay were determined empirically. Other Cam clay parameters

were determined based on laboratory test data [16, 171 following the method

suggested by Britto and Gunn [121. The permeability of clays is one of the

most difficult parameters to determine. The test data show that the

horizontal permeability was approximately 2 times the vertical value (181.

However, for Bangkok clay deposit, back analysis of embankment settlement by

Bergado et al 1191 showed that the laboratory test underestimated permeability

significantly. Based on the preceding information, 3 sets of permeabilities

were used in the analysis, namely: high, middle, and low permeabilities as

indicated in Table 1. The top 2 m weathered clay is heavily overconsolidated

with an average overconsolidation ratio (OCR) of 5 and the underlying soft

clay layer are slightly overconsolidated with an average OCR of 1.2.

The backfill material in the middle section consisting of lateritic soil

was considered in finite element analysis: The lateritic soil has 18% passing

sieve no. 200 (0.75 mm) with D,, of 3.0 mm and D,, of 0.002 mm. Standard

Proctor compaction test yielded the optimum water content of 11.5% and maximum

dry density of 19.3 kN/m'. During the embankment construction, the backfill

material was compacted to about 95 degree of compaction at near optimum water

content corresponding to a saturation of about 70%. The triaxial

unconsolidated undrained (UU) test results of corresponding backfill materials

were used to determine the hyperbolic, non-linear elastic soil model

parameters by the method proposed by Duncan et al [201 and the values are

tabulated in Table 2.

The interface hyperbolic direct shear model parameters are given in

Table 3 which were determined from laboratory direct shear test results of

corresponding backfill material (211 and follows the method proposed by Clough

SOIL

LA

YERS

BRO

WN

TO R

EDDI

SH

3 4 DA

RK

GRA

Y SO

FT

CLAY

6

_ O

FTEN

W

ITH

DECO

MPO

SE

D wo

oD

AND

SAND

Y SE

AMS

E 6-

r ; l-

i B-

9-l

Fig.

1

ATTE

RBER

G

LIM

ITS

AND

UNIT

W

EIG

HT

IATU

RAL

WAT

ER

CONT

ENT

(O/o

(

kN/m

’ )

20

40

60

60

100

I,5

tp

‘7

0 0

0 0

0 0

0 0

o-

0

0 0

0 0

0 0

0 0

oe

i)

‘L

W”

LL

0 =

Q

VANE

SH

EAR

STRE

NGTH

kPa

20

30

40 I

o TE

ST

NO. I

A

TEST

NO

. 2

q

TEST

NO

. 3

CONE

RE

SIST

ANCE

kPa

2000

40

00

6000

60

0

Inde

x Pr

oper

ties,

V

ane

Stre

ngth

an

d D

utch

C

one

Res

ista

nce

of B

angk

ok

Cla

y at

AIT

Cam

pus

Table 1. Soil Parameters of Bangkok Clay

Parameter

Low k., 6.9

NOTE: High: = 50 times of estimated average test value; Middle: $ = 25 times of estimated average test value; Low: ” = 10 times of estimated average test value.

Horizontal permeability is always 2 times of the vertical value.

454

and Duncan [71. The backfill soil parameters for pullout bearing resistance

model are the same as the values tabulated in Table 2. Additional pullout

bearing resistance and skin friction model parameters are indicated in Table

4. The adhesion, c,, and skin friction angle, 6, between reinforcement

frictional surface and the lateritic soil as well as the displacement, d,,, for

mobilizing the maximum skin friction were determined from the laboratory

pullout test results using steel bars with corresponding backfill soils 1221.

The values of R,,, R,,, and nr are already discussed previously. Other

parameters in Table 4 are calculated from the geometry of grid reinforcement,

except for determining I,, wherein the Young's modulus of steel bar is needed.

For both direct shear and pullout models, the normal stiffness of the

interface was defined as 10' kN/m' for compression case and 10' kN/m' for

tension case.

The welded wire reinforcement and wall face were considered to be linear

elastic material with Young's modulus of 2.0 x 10' kPa. The cross-sectional

area of longitudinal bar per meter width was 180 mm2. For the steel bar, the

yielding stress is 6.0 x 10' kPa. For the wall face, the shear modulus is 8.3

x 10' kPa, and the moment of inertia of cross-sectional area was 45 mm' which

was the sum of the moment of inertia of individual bars within 1.0 m width.

The shear and normal stiffness for nodal link were assigned as 1.5 x 10' kN/m

and 5.0 x lo6 kN/m, respectively, for the current problem. The nodal link

connects two nodes above and below the free end of reinforcement. Physically,

its stiffness represents the stiffness contributed to the nodes from two

elements just beside the free end of reinforcement that contains these two

nodes, respectively. Therefore, these values should be adjusted according to

soil stiffness and size of elements adjacent to the free end of reinforcement.

Finite Element Analysis

The finite element mesh used for analyzing the AIT test reinforced full

scale embankment is shown in Figure 2: The simulated fill thickness/time

curve is also indicated in Figure 2. The bar and beam elements are indicated

by darker solid line. For clarity, the interface elements are not shown in

the mesh. The mesh was drawn up considering the use of fine mesh at high

stress gradient area and also referred to the finite element mesh used by

other investigators for analyzing similar problem [3, 231. The embankment

above the ground surface was simulated by 13 incremental layers. For each

layer, the self-weight load was applied by two increments. All analyses are

consolidation analyses. Besides the selected foundation permeability values

in Table 1, varied permeability analyses were also conducted with initial

value of middle permeability and varied with void ratio according to Equation

10.

455

Table 2. Hyperbolic Soil Parameters Used for Later& Backfill Material

Para- Cohesion Friction Modulus Modulus Failure Bulk Bulk unit meter Angle Number Exponent Ratio Modulus Modulus Weight

Number Exponent

c, &Pa) 0, (“1 k n RI k, m y&N/n?)

Value 60 32.5 1078 0.24 0.96 1050 0.24 20.0

Table 3. Parameters for Direct Shear Interaction Mode

Parameter

Value

Cohesion

c, (Ha)

60

Friction Angle

w”)

32.5

Shear Shear. Stiffness Stiffness Number Exponent

k, nl

10500 0.72

Failure Ratio

Rn

0.85

Stiffness Number for Reloading

41

1300

Table 4. Additional Parameters for Pullout Interaction Mode 1

Parameter C, 6 R, &

nr I, S D d, AJA, &Pa) (“1 (mm) (mm) (mm>

Value 50.0 9.0 0.1 250 0.75 28 225.0 5.4 2.0 0.06

,O

I

Fill

thic

knes

s

5m

I

Fig.

2

Fini

te

Ele

men

t M

esh

Use

d fo

r A

IT

Tes

t R

einf

orce

d E

mba

nkm

ent

457

FINITE ELEMENT RESULTS ANLl CDNPARISQN WITH FIELD DATA

One analysis was conducted by not updating the node coordinates (smaller

deformation analysis). During actual construction process, a new soil layer

is placed on a deformed system, and during consolidation process, if the

deformation is large, the drainage length may be changed. However, small

deformation analyses cannot consider these effects. Comparing the results of

analysis for this embankment, it was shown that: (1) small deformation

analysis yields 90 mm less wall face lateral deformation, in which, 55 mm

occurred during consolidation; (2) higher excess pore pressure is built up at

the end of construction with a smaller dissipation rate later; and (3)

smaller deformation analysis results in about 10 mm less maximum settlement

at end of construction and 10 mm larger maximum settlement at 1 year after

construction. For small deformation analysis, during construction, the wall

face lateral deformation of a newly constructed layer has been corrected by

adding the lateral deformation of the previous layer before constructing the

next new layer. For piezometer point HP5 (7 m below the ground surface), at

the end of construction, the calculated excess pore pressure is built up at

end of construction, and the calculated excess pore pressure at small

deformation analysis of 54 kPa reduces to 14kPa at 1 year after construction.

For large deformation analysis, the corresponding values are 44 kPa and a

kPa, respectively. In the case of small deformation analysis, the maximum

settlement point is closer to the centerline of the reinforced mass than that

of large deformation analysis. From the comparison, it can be seen that the

large deformation analysis used in this study is effective. Thus, only large

deformation analysis results are presented.

The presentation of finite element results and the comparison with the

field data are made in this section. The data included excess pore pressures,

vertical settlements, wall face and subsoil lateral displacements, and tension

forces in the reinforcements.

Excess Pore Pressure

Figure 3 shows the typical calculated excess pore pressure variations

with time together with the field data at piezometer point 7 m below the

ground surface. The excess pore pressures are strongly influenced by the

foundation soil permeability. The high permeability analysis yields better

prediction at end of construction but the excess pore pressure dissipation

rate after construction was too fast. The low permeability analysis predicts

higher value during construction. The middle permeability analysis fits the

field data better from overall point of view. However, none of the analyses

predicted the whole process of excess pore pressure build-up and dissipation

well.

458

In finite element analysis, for making a precise simulation of pore

pressure, correctly determining the values and the variation of the

permeability of the soils and drainage boundary conditions are essential.

However, as pointed out by Tavenas and Lerouil 1241, there are no satisfactory

methods to solve these problems. The variation of permeability during loading

and consolidation is still under research. For permeability, if possible, the

values derived from back analysis of existing case histories should be

preferred. Of course, for back analysis, the parameter and the calculation

method are related.

Settlement

Calculated and measured surface settlements under the center point of

reinforced mass are compared in Figure 4. The locations of settlement plate

is also shown by the key sketch in the figure. It can be seen that the

calculated values using middle permeability have remarkable agreement with

measured data. At other settlement plate locations, the agreement is also

good with maximum difference of only 10%.

Considering the comparison for both excess pore pressures and

settlements, it appears that the middle permeability, i.e. k, is 25 times of

estimated average test values, can be considered to be the representative

value for this case. The finite element results reported in the following

sections, unless otherwise indicated, are all from middle permeability

analysis.

In consolidation analysis, the excess pore pressure and settlement are

related factors. The discrepancy between the agreement of excess pore

pressure and settlement prediction might be the limitations of the soil model

used. Although Cam clay model is a simple and effective model for normal to

slightly overconsolidated clay, several factors, such as the effect of

different stress path, and creep have not been considered. If checked

carefully, the analysis with middle permeability matched field data very well

up to the time of about 250 days, but slightly underestimated the final

settlement. Further increase of field data might be due to creep of the soil.

Another point is that settlement is an integrated value of the deformation of

the soils below a measurement plate, while pore pressure is a point value.

Lateral Displacement

Figure 5 shows the comparison of lateral displacement profiles for both

end of construction and 7 months after construction cases. For lateral

displacements in the foundation soils, the measured data up to 7 months after

construction only reach down to 3 m depth because the inclinometer probe could

not be inserted into the deformed casing below 3 m depth. At the end of

construction and at 7 months after construction, the calculated wall face

lateral displacements agreed well with the measured data. However, the

459

60

- D40 OF CONSTRUCTION _ MIDDLE PERMEAEIIUM SS- f\ -- VARIED PERMEAEIUM 52-

'1 -_- ' \

LOW PERMEABIul-Y ______ HIGH PERMEABILITY )~a,* MEASURED

Fig. 3 Typical Calculated and Measured Excess Pore Pressure Variation

_ MIDDLE PERME4EKi-iY -- LOW PERME4BILllY _____ HIGH PERMEABlLfTf 1.8.. MEASURED

IOOO- = i END OF CONSlRUCTlON

. .

,IlW ,,:,,,,,, ,,,,,,,,, ,,

0 1M ,,,,,,,,,,,,,,,,,,,,,,,'

404 500

Fig. 4 Typical Calculated and Measured Settlement Curves

ELEV

ATIO

N RE

LATI

VE

TO

ORI

GIN

AL

GRO

UND

SURF

ACE,

r-n

r

pl R

@

I J

461

calculated subsoil lateral displacements qre nearly twice as large as that of

measured data. At the top of the wall face, the calculated values are less

than the col-responding measured ones.

The time-lateral displacement relationship is shown in Figure 6 for two

points, namely: (a) top of the wall face and (b) 3 m below the original ground

surface. For the top of the wall face, the discrepancy between the calculated

and the measured values appears at 3 months after the construction. At that

time, the measured data showed an increased rate of lateral displacements.

It was probably due to the occurrence of heavy rainfall because there was a

sudden total water level increase at that time [141. For the point under the

wall face and 3 m below original ground surface, the discrepancy between the

calculated and the measured lateral displacements mostly occurred during the

construction period. After construction, both the calculated and the measured

lateral displacements show small increment rate. There are two reasons for

the differences obtained between the measured lateral displacements and those

calculated by the finite element analyses, namely: (1) the deficiency of the

analytical method as pointed out by Poulos 1251; and (2) the influence of

inclinometer casing stiffness which may result in relative displacements

between the soil and the casing, especially for this case wherein the casing

deformed to an "S" shape.

Tension Force in Reinforcement

The maximum tension forces in reinforcements immediately after

construction and 1 year after construction are shown in Figure 7, together

with the data deduced from the measured strain in reinforcement immediately

after construction. Also shown is at-rest earth pressure lines. The data

deduced from the measured strain at 1 year after construction is not included

because of too much scatter. The data are presented in terms of per meter

width and per reinforcement layer (0.45 m vertical spacing). The data show

that for reinforced embankment on soft greund at the end of construction, the

maximum tension forces in the reinforcements at the top half of the wall are

much larger than k, line. At the middle height of wall, the data are close to

k, line. At the bottom of the wall, the data are much higher than k, line'.

In a reinforced wall structure, the horizontal earth pressure developed

in soil mass need to be balanced by tension force in the reinforcements. The

value of the horizontal earth pressure depends on the deformation status of

soil. If there is no occurrence of horizontal displacement at-rest earth

pressure will be developed. The active and passive earth pressure will be

induced by active (minus strain) and passive (positive strain) displacement,

respectively. For a reinforced wall constructed on rigid foundation with

stiff reinforcement, the maximum tension force in the reinforcement is close

to the value calculated by at-rest earth pressure coefficient [41. For

reinforced wall on soft ground, however, under the wall loading, the soft soil

462

TOP OF ME WALL

<3360-

&?.0-

I5 - Ok-

4 1 CL =a v-l __---- _--- --- sm- 3 m BELOW THE ORIGINAL -I .d 1cJJ-

GROUND SURFACE

END OF CONSRUCTION VUBMEWJRDJ 3 m DWIH _ CA_CULATEfI TOP -- aLcuwEll3 m OEmH ,,,,,,,,,,,,,,,,,,,,~,,1, ,,,l,,,,r,,,,,r,,r~~

0

Fig. 6 Maximum Lateral Displacement Curves

Fig. 7 Maximum Reinforcement Tension Force Profiles

463

tends to squeeze out of the base of the -reinforced mass which causes large

relative movement between the reinforcement and the soil. Therefore, large

tension force is developed in the reinforcements placed at bottom.

The large and differential settlement of the ground also can change the

stress/strain condition within the reinforced mass. Following the convex

shapes settlement, certain amount of bending effect can be induced on

reinforced mass, which tends to increase the tension force at bottom and

reduce the tension force at upper part of the wall. For this embankment, at

top of the wall, the maximum tension force occurred very close to the wall

face (Figure 10) and the large lateral deformation of the wall face is one of

the reasons for the higher tension force at top of the wall.

The maximum tension forces in the reinforcements increased during the

foundation soil consolidation process because the consolidation induced

further differential settlement and lateral wall face deformation. At the top

half of the wall, the maximum reinforcement tension forces at 1 year after

construction are twice as large as those immediately after construction due

to the large lateral displacement of the wall face. In the bottom half of the

wall, the absolute amount of increments are slightly lower than those of the

top half, and the percentage increments are much smaller.

The tension force distributions along the reinforcement immediately

after construction are shown in Figure 8. For other .times, the tendency is

the same. Generally speaking, the agreement between the finite element

results (direct shear/pullout interface mode) and the data deduced from

measured strains is fair. Figure 10 also shows that the soil/reinforcement

interaction mode has strong influence on reinforcement tension force

distribution. The pullout interaction mode has weaker interface stiffness and

yields larger tension force and longer length of the reinforcement in tension

in the lower half of the reinforced wall. The difference between direct

shear/pullout interaction mode and direct shear interaction mode is not

evident because for this particular reinforced earth structure, the

soil/reinforcement pullout interaction mode zones are small and located near

the wall face and at the bottom of the reinforced mass as shown in Figure 9.

Figure 10 shows the contour of stress levels within the embankment from

the results of finite element analysis at end of construction condition.

There is no clearly defined potential failure line. The highest stress level

(ratio between shear stress and shear strength) occurs at the toe of the wall

and the highest value is 0.8. At the zone inside the embankment where pullout

soil/reinforcement interaction mode occurs (Figure 91, the value of stress

level is relatively high, about 0.4, and above this zone, the gradient of

stress level is high. The bending effect on the embankment also can be

observed from the contour of stress level with high value of stress level at

464

- DIRECT SHEAR/PULLOUT MODE -- DIRECT SHEAR MODE ____ PUUOUT MODE

. . . . . MWURal

. . . . . 0-e

. . l .

WT 7 ik*OSm

40-

2 m-_-__ _ WE . -- x:\ O

_ -___ - - _ .

-__?-A_____ l .

UAT.4 aL?nm

UAT 3 a: ,J!l n

NJ- Eko.um KAr 2

w- .

10 - . . . --. . l -----______ ,,,,,,,,,,,1,11,,11,111111111,,,,,,,,,,,,,,,,,llt

0 1 7. 3 4

DISTANCE FROM ME WALL FACE, m

Fiu 0 2’ Reinforcement Tension Force Distribution

465

n DIRECT SHEAR MOOE

m PULLOUT MODE

REINFORCEME

Fig. 9 Pullout and Direct Shear Soil/Reinforcement Interaction Zone

Fig. 10 Contours of Stxss Level within Embankment

466

the bottom of the embankment and low stress level (less than 0.05) in a convex

shaped zone at top of the embankment.

INTERACTION BETWEEN REINFORCED MASS AND SOFT GROUND

The response of the soft foundation soil under a reinforced embankment

load can be classified into two extremes, namely: (1) the same as that of

under rigid footing, and (21 the same as that under flexible surface loading.

Any factor tending to increase the rigidity of the reinforced mass will result

in larger settlement under the toe of the reinforced wall and smaller lateral

spreading of the foundation soil. Figure 11 shows the influence of the

different soil/reinforcement interaction modes on the foundation deformation

pattern. Although it is not significant, the difference between the

settlement profiles of using direct shear and pullout interaction modes is

evident. The direct shear interaction mode has a stronger tangent shear

stiffness, and the whole reinforced mass deformed more like a rigid body

resulting in larger settlement occurring nearly under the wall face. On the

other hand, the pullout interaction mode has a weaker tangent stiffness making

the soil under the embankment to squeeze out easier, resulting in less

settlement under the wall face and more settlement at the centerline of the

reinforced mass. As discussed previously, due to the interaction between the

soft ground and r-einforced soil mass, different foundation settlement patterns

also influence the stress/strain state in the reinforced soil mass.

Generally, more compressible foundation soil means more foundation

lateral displacement, more wall face lateral displacement and more tension

force in the reinforcement at the lower part of the reinforced wall. The

foundation soil consolidation rate also influence the interaction behavior

between the reinforced mass and soft ground by influencing the deformation

pattern. The higher the foundation permeability, the smaller the lateral

displacement [ll

CONCLUSIONS

:11 The finite element method has been used to simulate the behavior of a

reinforced embankment on soft ground. The modelling exercise

demonstrates that the soil/reinforcement interaction properties can be

properly selected according to the relative displacement pattern between

soil and reinforcement (direct shear or pullout), and the construction

process can be most closely simulated.

2) Embankment loading will cause large total and differential settlement,

which will induce the bending effect on the reinforced soil mass. The

maximum tension force may occur at the reinforcement layer placed at the

base of reinforced mass. For design purposes, the smaller vertical

spacing or stronger reinforcement should be used at this location to

467

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-100 -I

‘- A 1w 7.W-

300-

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EOQ-

7w-

dM-

Qoo-

lccu-

11001

14x-z-z ‘Dl$&W&WJ_oUT L400E

OlRfCT SHE43 WOE 1%X-=UMUREI, MO OF COHSR”C,,ON

-I-.U YQ.SURED 1 tuR AFrGl CONSRUCI’ION 1.%x ,,,,,,,,,,,,,,,,,,, ,,(,,,,,, , , I,, I-

O IO 7.0 30 4a

HORIZONTAL DISTANCE, m

Fig. 11 Comparison of Settlement Patterns

(31

(4)

468

restrict the lateral spreading of backfill and squeezing out of soft

foundation soil, and also to avoid the yielding of high stiffness

reinforcement.

The response of the reinforced embankment on soft ground is varied

during the consolidation process of the foundation soil. Both tension

forces in reinforcements and lateral wall face displacements are

increased when the degree of consolidation increased.

Comparison of the predicted and measured data indicate that the

performance of the reinforced embankment on soft ground can be predicted

by finite element method through proper selection of the foundation

permeability based on back analyzed values from case histories. It has

been found that the predicted foundation settlements and wall face

lateral displacements agreed reasonably well with the field data, and

the agreement between predicted excess pore pressures, tension forces

in reinforcements, and foundation lateral displacements are quite fair.

ACKNOWLEDGEMENTS

The test reinforced embankment was part of a research project sponsored

by the U.S. Agency for International Development (USAID), Bangkok, Thailand,

conducted at the Asian Institute of Technology (AIT). The financial support

provided by the USAID, Bangkok, Thailand and the facilities provided by AIT

are gratefully acknowledged. Hilfiker Co. of the U.S.A. donated the

galvanized welded-steel grid reinforcements.

a

9

4

b

c,

ct

d

D

d Cr

d,

E

S,

B,P

e,

I

1,

Appendix: NOTATIONS

The following notations are used in this paper:

constant

friction area of grid reinforcement,

interface area provide shear resistance

constant

adhesion

constant for permeability variation with void ratio relationship

unit length

thickness of grid reinforcement transverse member

critical displacement for mobilizing maximum skin friction resistance

normalized pullout displacement

Young's modulus of the reinforcement

initial tangent modulus

initial slope of pullout bearing resistance/normalized displacement

curve

initial void ratio

moment of inertia

bearing member deflection rigidity index

469

k horizontal earth pressure coefficient

k, at-rest earth pressure coefficient

k, shear stiffness of interface

k ,( skin friction component of interface shear stiffness

k 'P bearing resistance component of interface shear stiffness

k, vertical permeability

L span of the two ends fixed beam

m bulk modulus exponent

N, bearing capacity factor for cohesion resistance

N, bearing capacity factor for overburden resistance

nr exponent in bearing resistance ratio and space ratio relationship

P, atmospheric pressure

R bearing resistance ratio

Rf, failure ratio for pullout bearing resistance

RI initial slope ration between pullout and triaxial test

RI0 initial slope ratio for rigid bearing member

R, stiffness ratio

R IC critical stiffness ratio

S space between two neighboring transverse members

S/B bearing member space ratio

S/D rough sheet space ratio

S,/B free interference space ratio

S" vertical reinforcement spacing

B angle of rotation failure zone for bearing capacity problem

Y unit weight

d angle of skin friction

Ub bearing resistance on grid reinforcement bearing member

abn maximum pullout bearing resistance

O'h effective horizontal stress

0" effective normal stress

T shear stress

4 friction angle

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Received 27 April 1994; revised version received 24 June 1994; accepted 29 June 1994