1
Predicting Deformations when Designing
MSE Walls with Synthetic Inclusions
Anthony Vasile, Class of 2010,
Major:
Civil Engineering
Mentor:
Huabai Liu
,
Professor
,
Civil Engineering
ABSTRACT
:
With increases in vehicle miles traveled the trend in transportation, the development of
new highways to
carry the load
seems likely. Often with the development of highways, a system of retaining walls is
necessary. Mechanically stabilized ear
th walls represent an alternate system to accomplish the purposes
of traditional concrete gravity
retaining
walls. MSE walls as they are commonly referred provide a much
more cost effective alternative as well as
provide for
other
benefits
. However, no m
ethod currently exists
to predict the lateral facial movement that will occur. In order to predict lateral facial deformations, this
report assumes that
an
accurate prediction of maximum ten
sion in a layer of reinforcement can be made
and
that deformation
s can be predicted
using that information
.
Findings
ha
ve
shown
that lateral
deformation is calculated accurately when integrating the tension in reinforcements with the stiffness of
the reinforcement along the length of each inclusion.
KEYWORDS
:
Mechanically Stabilized Earth Walls, K

Stiffness Method, Tension
INTRODUCTION
The use of mechanically stabilized earth walls in
substitution of traditional concrete gravity walls has
been used extensively in highway construction to
reduce development costs. A mechanically stabilized
earth wall acts by binding a large soil mass toge
ther
through the use of reinforcement inclusion layers.
Figure 1 below displays a typical MSE (Mechanically
Stabilized Earth) wall. Choosing to build an MSE
wall as opposed to a traditional concrete gravity wall
for the purpose of retaining soil offers g
reat benefits.
Costs are reduced with quicker build times,
with
elimination of large foundations, and with the use of
less expensive materials. In addition, MSE walls
perform better under seismic loading than do rigid
walls because of their inherent fle
xibility. Finally, a
MSE wall can compensate for settlement better than
a rigid wall again due to its greater flexibility.
However, failure of MSE walls is still possible.
Hence, checking for pullout failure and inclusion
rupture as well as checking for
deep seated failure
and global sliding is still required as with traditional
concrete gravity walls.
Re
inforcement inclusions are typically either
of steel or of geosynthetic material.
The
effectiveness
of an MSE wall will depend on both the
soil fill c
hosen and on the type of reinforcement
selected. Generally, granular soil is used to allow for
drainage and as well as for a larger friction angle.
MSE walls implemented with steel inclusions are
much stiffer than MSE walls designed with
geosynthetic in
clusions. It is expected that a much
larger facial deformations will occur when
geosynthetic reinforcement is used as opposed to
when steel reinforcing is used. However, the use of
geosynthetic reinforcement as opposed to steel
reinforcement does ensure
warning in the form of
deformation before failure as opposed to a sudden
bond failure between the soils and steel reinforcing.
Costs for using geosynthetic reinforcements are also
less prohibitive than when using steel reinforcing.
The facing element o
f a MSE wall is
variable. Typical elements include geosynthetic
wrapping, masonry block units, and precast panels.
The serviceability of a MSE wall is often measured
by the amount of facial deformation occurring. Large
strains could compromise the facing
elements or
interact with
existing structures. Also
,
large
strain
leads to a sense of discomfort for pedestrians.
According to The USDOT (Ellias et al.
2001, p 36), “No method is presently available to
definitively predict lateral displacements.” It is
specified that the amount of horizontal or lateral
2
deformations will depend on compaction effects,
reinforcement type, reinforcement length, and details
of the facing system.
Determining with better accuracy the
horizontal displacement expected after co
nstructing
an MSE wall would facilitate a greater use of this
type of retaining system. In this paper, a method
was proposed to estimate the lateral facing
displacement of MSE walls with geosynthetic
reinforcements and concrete

block facing constructed
o
n sound foundations. The predictions of the method
were then compared to the measured results in field
tests.
Methodology
Lateral facing displacement is predicted in
this paper under the assumption that the lateral facing
displacement is equal
to
the reinforcement
Figure
1: example of a typical MSE wall
elongation. Three things must be true in order for
this assumption to be valid. First, the soil and
reinforcement must be compatible to ensure that the
reinforcing does not experie
nce pull out failure.
Generally, while under working stress condition, soil
compatibility exists for MSE walls. Secondly, the
MSE wall must have a stable toe so that sliding does
not occur. Most MSE walls satisfy this condition
since they are generally b
uilt on sound foundations.
Finally, the reinforcement must be sufficiently long
so that the lateral deformation at the back of the
reinforced soil block is negligible. USDOT
guidelines (Ellias et al. 2001) have suggested that
MSE walls be constructed at
a width equal to 0.7
times the height in part to ensure that the MSE soil
block is large enough to resist back pressure. Thus,
given the stated conditions, the third assumption is
also considered to be valid.
Reinforcement elongation is calculated
using
the known reinforcement stiffness and the
calculated tension at intervals along a reinforcing
layer. The load

strain relationship of geosynthetic
inclusions is modeled by the following hyperbolic
function:
(
)
T=tension
ε=strain
Where a and b can be obtained from the secant
stiffness of geosynthetics at different strains. In this
paper, the secant strains at 1% and at 2% are used to
obtain parameters a and b for the hyperbolic model.
In order to predict the strain experie
nced b
y
an inclusion from the a
model
(1)
,
an assumption for
the value of tension is required. It is known that
toward the rear end of reinforcement, the
reinforcement
does not experience tension since the
layer is not anchored. Meanwhile, it is also known
tha
t the front of a reinforcing layer, where the front of
a layer refers to the connection at the facing end,
would hold some tension since it is anchored to
concrete panels or modular blocks. Finally, MSE
walls traditionally assume a Rankine failure plane f
or
internal failure. A Rankine failure plane is defined as
follows:
(
2
).
It is also known that if failure is to occur along this
plane, then the tension in the reinfor
cement at
locations which cross the failure plane are relative
maximum. It has been proposed that
the
value of
relative maximum tension for a reinforcement layer
can be found using the K

stiffness Method under
working stress condition (Bathurst et al. 200
8). The
k

stiffness method is implemented by the following
equation:
(
)
(3)
T
max
=maximum tension
K=horizontal earth pressure coefficient
γ=soil weight
H=height of wall
S=height of soil surcharge
S
v
=height of spacing beteen a layers
D
tmax
=distribution correction factor
Φ
g
=global stability correction factor
Φ
local
=local stability correction factor
Φ
fs
=facing stiffness correction factor
Φ
fb
=facing batter correction factor
Φ
c
=cohesion correction facto
r
TYPICAL REINFORCEMENT
LAYER
SMALL TOE
FOUNDATION
RETAINED
SOIL
TYPICAL MODULAR
BLOCK OR PANEL
FACING
MECHANICALLY
STABILIZED
EARTH SOIL MASS
3
The method makes use of the horizontal earth
pressure coefficient at rest (K=1

sin
) as well as the
use of many additional reduction factors all of which
appea
r in (
3
)
. The meaning of these parameters can
be found in Bathurst et al. (2008).
Tension
at different points along a reinforcement
layer is then assumed to follow a continuous
distribution. Deformations were calculated and
compared to actual measured deformations in test
walls. The distribution of tension along a layer of
reinforcement was a
ssumed as being either constant
along the layer towards the facing, that the tension
was distributed as a linear function along a layer
towards the facing, and finally that tensioned was
distributed as a parabolic function along a layer
toward the facing.
This is illustrated below through
figures 2 and 3.
Using the load distribution as displayed in
figure 3 and the cal
culation of Tmax from equation 3
,
the strain at increments along each layer of
reinforcement was dete
rmined following from (1)
.
The stain
along each layer is integrated to obtain the
total lateral displacement at the facing.
T
his
methodology was repeated for each of the
distributions described in figure 3.
Figure 2: This is a typical illustration of an
MSEW. The failure is Rankine’s activ
e failure
surface
Results
This paper uses data from several sources to test the
proposed methodology. Data from three test walls
built by the Louisiana Research Transportation
Center and published under Farrag et al. in 2004 is
used. The test walls are
simply called Section 1,
Section 2, and Section 3. Additional data is used
from a test wall built by Barry Rodney Christopher
for his doctoral dissertation and published in 1993.
Christopher’s wall is called GW8. Finally, a third
source of data was est
ablished from 4 test walls built
by Dave L. Walters for his doctoral dissertation
Figure 3: Assumed Tensile Force Distribution
along Reinforcement Layers
which was published in 2004. Those walls are
simply labeled as wall 1, 2, 3, and 5. Each of th
ose
eight test walls was built by those referenced housing
much instrumentation. Strain gages were fixed along
the length of inclusions. Actual values of tension
along the length of the reinforcement were calculated
using the measured strain values and the known
reinforcement stiffness. Also, the test walls carried
additional instrumentation which measured the facial
deformations. Additional information can be fo
und
by following up and finding the full citations to these
references.
Reinforcement
layers
Rankine Failure Plane
Facing
1.
Tmax is constant throughout
forward section
and regresses
linearly to zero in the section
beyond the failure plane
2.
linear from
1
2
Tmax up
Tmax and down to zero
3
.
parabolical from zero up
to Tmax and down to zero
4
.
parabolical from
1
3
Tmax up
to Tmax and down to zero
5
.
parabolical from
1
2
Tmax up
to Tmax and down to zero
6
.
parabolicall from
2
3
Tmax up
to Tmax and down to zero
Location of the reinforcement
layer at the failure plane.
Tmax
4
For the methodology of this paper, the k

stiffness method (Bathurst et al., 2008) was employed
to determine the value
of maximum tension for a
layer of reinforcement. However, there has been
evidence to show that maximum tension predictions
are not always accurate. Figure 4 below shows how
large that the difference in maximum tension can b
e.
Figure 4 shows data for test
wall section 2 built by
th
e Louisiana Transport Resear
ch Center (Farrag et
al. 2004)
Figure 4: LRTC Section 2 Wall
.
Comparison of Maximum Tension as published
from measurement by the LRTC and as
calculated in this paper using K

stiffness
approach
The soil used in Farrag’s research was clayey silt
instead of clean granular soil and thus relied more
heavily on the reinforcement for support. This
inconsistency points out a limitation using the k

stiffness method. The k

stiffness approach assumes
the
use of granular soil fill. When granular soil fill is
not used, the k

stiffness approach overestimates the
inherent stability of the soil itself. Section 1 and
section 3 of the LRTC wall although not cited also
show a similar inconsistency with this pap
ers
calculated maximum tension. In order to use these
walls to predict lateral deformations, the value of
tension as calculated by the k

stiffness method was
adjusted by
increasing the soil weight in (3
). This
adjustment for wall 2 is also displayed in f
igure 4 and
labeled as adjusted values.
On the other hand, a remarkable consistency
between measured maximum tension and calculated
maximum tension is demonstrated in the other test
walls studied. Those walls employed the use of
granular soil.
Using the maximum tension values
calculated by k

stiffness method and the approach as
outlined above, lateral deformations were predicted
using each of the distributions as show
n in figure 3
earlier. Figure 5
below compares each of the
predictions
as cal
culated for
Walter’s wall 1.
Figure
5
: Calculated and measured deformation
for Walter’s Wall 1 (2004)
.
D
istributions refer
to the distributions detailed in figure 3
.
Although the range of calculated lateral deformation
does not vary by a significant am
ount between each
figure, by visual inspection the closest agreement to
the actual measured deformation occurs when
assuming distribution 2. This comparison was made
on each of the eight test wall, ending with the same
observation
.
Distribution 2 always produced the
closest prediction to actual measured deformation.
.
Assuming only distribution 2,
Figure 6 on the next
page
shows the comparison between the calculated
facial deformation using the methodology detailed in
this report a
nd the field data from
LRTC wall 2
(
Farrag et.
a
l 2004)
and
Christopher’s
GW8
(1993).
The figure illustrates the accuracy of this
methodology given compatible soil and a valid
approximation of T
max
.
Overall,
the predicted and measured lateral facing
disp
lacements after construction are very
close
. This
demonstrates that the proposed approach is valid for
predicting lateral facing displacement.
0
5
10
15
20
0
500
1000
elevation (ft)
Tmax (lb/ft)
This Report using Equation 3
reported values as measured in the field
This Report adjusted values
0
1
2
3
4
0
5
10
elevation (m)
deformation (mm)
Wall 1
reported as measured in the field
Distribution 1
Distribution 2
Distribution 4
Distribution 5
Distribution 6
5
Conclusion
This paper concludes research conducted in order to
detail the methodology required to predict
lateral
deformation of mechanically stabilized earth walls of
geosynthetic reinforcing. The research is based on
the precept that the maximum tension along the
length of an inclusion is predicted using the k

stiffness method and that the location of this
behavior
occurs at a point which can be determined from a
Rankine failure plane. Tension is assumed to vary
along a length of reinforcement. Several different
distributions were assumed to represent this variation.
The methodology was put to trial on ei
ght existing
test walls from previous research.
Figure 6: Comparison between calculated
deformation and measured deformation
occurring on the test walls. (Farrag et al
2004),(Christopher 1993).
It has been shown that when accurate calculations of
maximum
tension are generated, a strong agreement
between the measured and calculated later facing
displacements also exists. In fact, selecting
distribution 2 from figure 3 of this paper provides the
most accurate calculation. The research in this paper
can be s
ummarized by 2 main points:
1.
The k

stiffness method works well if the
backfill soil is granular. However, it does not
work well if the backfill soil is cohesive or soft
soil.
2.
Given modular block facing, given that the
MSE wall is sufficiently deep enough to
neglect the effect of back pressure, and given
that a strong
toe
foundation exists, then the
approach outlined in the methodology with
load distribution 2
can be used to pre
dict the
lateral facing displacement of MSE walls
provided that T
max
in each reinforcement layer
can be approximately estimated.
Acknowledgements
This study was conducted with a support from the
Professional Staff Congress of City University of
New York
(PSC

CUNY). The support is gratefully
acknowledged.
References
[1]
Allen, T.M. & Bathurst, R.J. (2006). Design and
performance of an 11

m high block

faced geogrid
wall.
Procedings of the 8
th
International Conference
on Geosynthetics
, Yokohama,
Japan, September
2006, 953

956.
[2]
Allen, T.M., Bathurst, Richard J., Holtz, Robert
D., Walters, D., & Lee, Wel F. (2003). A new
working stress method for prediction of
reinforcement loads in geosynthetic walls.
Canada
Geotech. J. 14,
976

994.
[3]
Bathurs
t, R. J., Miyata, Y., Nernheim, A. and
Allen, A. M. (2008). Refinement of K

stiffness
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Christopher, Barry Rodney. (1993). Deformation
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[6]
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Farsakh, Murad & Morvant,
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[7]
Farrag, Khalid & Morvant, Mark. (2004).
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in Cohesive Soils ( FHWA/LA.03/379). Baton
Rouge, LA: Louisian
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Center.
[8]
Miyata, Yoshihisa & Bathurst, Richard J. (2007).
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stiffness method for
geosynthetic reinforced soil walls constructed with c

ϕ
soils.
Canada
Geotech J. 44,
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1416.
[9]
Walters, Dave L. (2004). Behaviour of
Reinforced Soil Retaining Walls Under Uniform
Surcharge Loading (Doctoral Disertation, Queen’s
University; Kingston, Ontario, Canada; 2004).
0
2
4
6
0
10
20
30
elevation (m)
deformation (mm)
Christopher's
GW8 Wall
deformation, measured
deformation, calculated
0
5
10
15
20
0.00
0.05
0.10
elevation (ft)
deformation (ft)
LRTC section 2
measured deformatin
calculated deformation
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