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-
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dM-
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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
Anpendix-REFERENCES
1. Hird, C.C. and Kwok, C.M., Prediction for the Stanstead Abbotts trial embankment, based on the finite element method. Proc. of the Prediction Svm~. on Reinforced Embankment on Soft Ground, Strand, London (19861.
2. Rowe, R.K. and Mylleville, B.L.J., The analysis of steel reinforced embankment on soft clay foundation. Proc. 6th Intl. Conf. on Numerical Methods in Geotechnics, Innsbruck (1988) 1273-1278.
3. Schaefer, U.R. and Duncan, J.M.. Finite element analyses of the St. Alban test embankments, ASCE Geotech. Special Publication No. 18, (1988), 158-177.
4. Adib. M., Mitchell, J.K. and Christopher, B., Finite element modelling of reinforced soil walls and embankments. Desisn and Performance of Earth Retaining Structure, ASCE Geotech. Special Publication, No. 25 (1990) 409-423.
5.
6.
7.
8
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
21.
470
Herrmann, L.R., User's Manual for REA (general two dimensional soils and reinforced earth analysis program). Univ. of California, Davis, California, U.S.A. (1978).
Chai, J.C. and Bergado, D.T., Performance of reinforced embankment on Muar clay deposit. Soils and Foundations, 33(4).
Clough, G.W. and Duncan, J.M., Finite element analysis of retaining wall behavior. J. of Soil Mech. and Found. Enq'q. Div., ASCE, 97(12) (1971) 1657-1673.
Carter, J.P., Booker, J.R. and Small, J.C., The analysis of finite elasto-plastic consolidation. Intl. J. for Numerical and Analvtical Method in Geomechanics, 3(2) (1979) 107-130.
Rowe, R.K., Reinforced embankments, analysis and design. J. of Geotech. Enq. Div., ASCE, llO(2) (1984) 231-246.
Taylor, D.W., Fundamentals of Soil Mechanics. John Wiley & Sons Inc. New
York (1948).
Tavenas, F., Jean, P., Leblond, P., and Leroueil, S., The permeability of natural soft clays, part II, permeability characteristics. Can. Geotech. J. 20 (1983) 645-660.
Britto, A.M. and Gunn, M.J., Critical State Soil Mechanics via Finite Elements. Ellis Horwood (1987).
Hird, C.C., Pyrah, I.C. and Rusell, D., Finite element analysis of the collapse of reinforced embankment on soft ground. Geotechnique, 40(4) (1990) 633-640.
Bergado, D.T., Sampaco, C.L., Shivashankar, R., Alfaro, M.C., Anderson, L.R. and Balasubramaniam, A.S., Performance of a welded wire wall with poor quality backfills on soft clay. Proc. ASCE Geotech. Enq'q. Concress at Boulder, Colorado, U.S.A., ASCE Geotech. Special Publication No. 27 (1991a) 909-922.
Bergado, D.T., Shivashankar, R., Sampaco, C.L., Alfaro, M.C. and Anderson, L.R., Behavior of a welded wire wall with poor quality, cohesive-frictional backfills on soft Bangkok clay (a case study). Can. Geotech. J. 20(6) (1991b) 860-880.
Balasubramaniam, A.S., Hwanq, Z.M.. Uddin, W., Chaudhry, A.R. and Li. Y.G., Critical state parameters and peak stress envelopes for Bangkok clays. 9.5. Enq'q. Geol., 11 (1978)' 219-232.
Asakami, H., The smear effect of vertical band drains. M. Enq'c. Thesis. No. GT-88-8, Asian Institute of Technology, Bangkok, Thailand (1989‘).
Ahmed, M.M., Determination of permeability profile of soft Rangsit clay by field and laboratory tests. M. Enq'q. Thesis, No. 1002, Asian Institute of Technology, Bangkok, Thailand (1977).
Bergado, D.T.. Ahmed, S., Sampaco, C.L., Balasubramaniam, A.S., Settlements of Banqna-Bangpakong Highway on soft Bangkok clay. J. of Geotech. Enq'q. Div.. ASCE, 116(l) (1990) 136-155.
Duncan, J.M., Byrne, Wong, K.S. and Mabry, P., Strength, stress-strain and bulk modulus parameters for finite element analysis of stresses and movements in soil, Geotech. Enq'q. Research Reoort No. UCB/GT/BO-01, Dept. of Civil Eng'g., Univ. of California, Berkeley (1980).
Macatol, K.C., Interaction of lateritic backfill and steel grid reinforcements at high vertical stress using pullout test. M. Enq'q Thesis, GT-89-12, Asian Institute of Technology, Bangkok, Thailand (1990).
471
22.
23.
24.
25.
Shivashankar, R., Behavior of a mechanically stabilized earth (MSE) embankment with poor quality backfills on soft clay deposits, including a study of the pullout resistances. D. Eno'q. Dissertation, Asian Institute of Technology, Bangkok, Thailand (1991).
Schmertmann, G.R., Chew, S.H. and Mitchell, J.K., Finite element modelling of reinforced soil wall behavior. Geotech. Enq'q. Reoort, No. UCB/GT/89-01, Dept. of Civil Eng'g. Univ. of California, Berkeley (1989).
Tavenas, F. and Leroueil, S., The behavior of embankments on clay foundations. Canadian Geotech. J., 17 (1980), 236-260.
Poulos, H.G., Difficulties in prediction of horizontal deformation in foundations. J. of Soil Mech. and Found. Eno's. Div., ASCE, 98(B) (1972) 843-848.
Received 27 April 1994; revised version received 24 June 1994; accepted 29 June 1994