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Resilient modulus and plastic deformation of soilconfined in a geocell
M. Mengelt1, T. B. Edil2 and C. H. Benson3
1Project Engineer, Ramboll Finland Ltd, PO Box 3, Piispanmaentie 5, 02241 Espoo, Finland,
Telephone: +358 20 755 6511, Telefax: +358 20 755 6201, E-mail: michael.mengelt@ramboll.fi,2Professor, Geological Engineering Program, University of Wisconsin-Madison, 2228 Engineering Hall,
1415 Engineering Dr., Madison, WI 53706, USA, Telephone: +1 608 262 3225,
Telefax: +1 608 263 2453, E-mail: edil@engr.wisc.edu3Professor, Geological Engineering Program, University of Wisconsin-Madison, 2228 Engineering Hall,
1415 Engineering Dr., Madison, WI 53706, USA, Telephone: +1 608 262 7242,
Telefax: +1 608 263 2453, E-mail: benson@engr.wisc.edu
Received 29 January 2006, revised 19 June 2006, accepted 13 July 2006
ABSTRACT: Resilient modulus tests were conducted on two coarse-grained soils (gravel and sand)
and a fine-grained soil (lean silty clay) in a large-size cell with and without confinement in a
geocell. The effect of the geocell on resilient modulus depended on the infill (soil in the geocell).
Resilient modulus increased by only 1.4–3.2% when the infill was coarse-grained, but increased by
16.5–17.9% when the infill was fine-grained. The effect on resilient modulus was larger when the
fine-grained infill was compacted wet of optimum water content. Larger deformations occurred in
the tests on the fine-grained soil, which most likely contributed to the greater increase in resilient
modulus when confined in a geocell. Tests with the coarse-grained soils indicated that the rate of
long-term strain accumulation in the sand and gravel under constant cyclic loading decreased by
approximately 2% when they were confined in geocells.
KEYWORDS: Geosynthetics, Geocell, Pavement, Resilient modulus, Permanent strain, Cellular
confinement
REFERENCE: Mengelt, M., Edil, T. B. & Benson, C. H. (2006). Resilient modulus and plastic
deformation of soil confined in a geocell. Geosynthetics International, 13, No. 5, 195–205
1. INTRODUCTION
Soft subgrades in the upper Midwestern United States
generally are removed and replaced prior to construction of
highway pavements. The soft soil is replaced with a layer of
crushed rock 0.3–0.9 m thick to provide a strong working
platform for construction and a firm layer to support the
overlying pavement during its service life (Edil et al. 2002).
This ‘cut-and-replace’ method adds significant cost to
construction of the pavement structure. Consequently, alter-
native construction techniques are being explored, includ-
ing methods that employ geosynthetics (Kim et al. 2006).
One type of reinforcement being considered is cellular
confinement using geocells, which were originally devel-
oped by the US Army Corps of Engineers for stabilizing
beaches and deserts where rapid deployment of materials
and personnel was required (Webster 1981; Koerner
1997). Geocells are three-dimensional mats of polymeric
material that are shipped to the job site in a collapsed
configuration. They are expanded in an accordion-like
fashion and filled with soil to form a three-dimensional
mat consisting of a honeycomb of interconnected cells
(Figure 1). In a pavement system, a mat of soil-filled
geocells is believed to distribute loads and reduce sub-
grade pressure, thereby minimizing deformation and dif-
ferential settlement of pavements constructed on soft
subgrades (Bathurst and Jarrett 1988; Al-Qadi and Hughes
2000). Geocells are also used for constructing embank-
ments and other earthen structures over soft soils (e.g.
Bush et al. 1990; Cowland and Wong 1993).
The objective of this study was to evaluate how confine-
ment in a single geocell affects the resilient modulus and
plastic deformation of the infill soil. Group effects are
investigated in a companion study (Lau et al. 2001). To
meet this objective, a laboratory testing program was
conducted using a large-size triaxial cell equipped for the
cyclic loading sequence used in resilient modulus testing.
The results of this test program are described in this paper.
2. BACKGROUND
Failure of flexible pavements is normally caused by rutting
and/or cracking. Rutting is caused by excessive permanent
Geosynthetics International, 2006, 13, No. 5
1951072-6349 # 2006 Thomas Telford Ltd
(plastic) deformation of pavement components (plastic
flow of the hot mix asphalt or the subgrade) during
repeated sub-failure loading and is often associated with
lateral deformation of the base, subbase, and subgrade
layers. Cracking is caused primarily by fatigue in pave-
ment components and volume changes caused by thermal
effects (Huang 1993).
Fatigue cracking is caused by repetitive loading of the
asphalt surface layer, which induces tensile strains at the
base of the asphalt. The number of loading cycles (N) that
will produce failure depends on the stiffness of the
pavement structural components. This stiffness typically is
characterized by the resilient modulus (Huang 1993).
Pavement layers having higher resilient modulus generally
experience smaller strains during loading.
The resilient modulus is measured in a cyclic loading
test (AASHTO T 294-94) that consists of a conditioning
phase (1000 loading cycles) and a loading phase (1500
cycles). During the loading phase, the confining pressure
and deviator stress are varied to simulate the range of
stresses common in pavement systems. The resilient
modulus (Mr):
M r ¼�d
�r(1)
is computed for each stress state from deviator stresses
(�d) and elastic strains (�r, also referred to as the ‘resilient
strain’) measured at the end of the loading sequence for
the stress state (Thompson and Robnett 1979).
State of stress has a significant effect on the resilient
modulus of soils (Tanyu et al. 2003). For granular soils,
the resilient modulus generally is expressed relative to the
bulk total stress (�b):
�b ¼ �d þ 3�c (2)
where �c is the total confining stress. For cohesive soils,
the resilient modulus is typically expressed relative to the
deviator stress. The resilient modulus of granular soils
generally increases monotonically with increasing bulk
stress, whereas the resilient modulus decreases monotoni-
cally with increasing deviator stress for cohesive soils
(Thompson and Robnett 1979).
Confinement in a geocell is analogous to confinement
in a stiff membrane. Laboratory studies have indicated
that lateral confinement provided by a membrane can
increase the shear strength and resilient modulus of soils.
The classic work by Henkel and Gilbert (1952) used
elastic theory to quantify the additional confinement
provided by a triaxial membrane and the effect that the
additional confinement has on shear strength. The effect
on resilient modulus was demonstrated by Edil and
Bosscher (1994) with data from tests using a PVC
membrane that was much stiffer than a conventional latex
membrane. An increase in resilient modulus of approxi-
mately 7% was attributed to the additional stiffness of the
PVC membrane.
Bathurst and Karpurapu (1993) used a triaxial test to
evaluate how confinement in a geocell affected the shear
strength of a silica sand and a limestone gravel. Confine-
ment in a geocell increased the shear strength between
42% and 66%. A strain-hardening response was also
observed when the soils were confined in geocells. The
increase in shear strength was attributed to increased
confinement provided by the geocells. Predictions of
increases in strength using the elastic theory developed by
Henkel and Gilbert (1952) were in close agreement with
the increases in strength that were measured.
Tests on panels of geocells (i.e. as would be used in the
field) with sand and gravel infill have been conducted by
Rajagopal et al. (1999). They found that the shear strength
of panels of geocells was 1.4 times higher than that of one
sand-filled geocell. However, for axial strains less than
2%, the stiffness was no different for tests conducted with
one geocell or a group of geocells.
Al-Qadi and Hughes (2000) describe a case history in
Pennsylvania, USA, where a combination of a nonwoven
geotextile, high-strength geogrids, and a gravel-filled mat
of geocells was used to support a pavement structure on
top of a very soft subgrade. Back-analysis of deflection
data from tests conducted with a falling weight deflect-
ometer (FWD) indicated that the geotextile–geogrid–
geocell combination increased the resilient modulus of the
gravel by a factor of two.
Lau et al. (2001) evaluated deformation of prototype
pavements that included a layer of gravel-filled geocells
underlain by simulated layer of soft clay. Inclusion of
Figure 1. (a) Close-up of geocells filled with crushed rock;
(b) installation of geocells for subgrade stabilization at the
field site in Wisconsin described in Edil et al. (2002)
196 Mengelt et al.
Geosynthetics International, 2006, 13, No. 5
geocells reduced plastic deflection of the prototype pave-
ments by 50–70%. Prototype tests conducted by Dash et
al. (2004) in a large steel tank showed that footings on
sand exhibit reduced settlement and greater bearing
capacity when the sand was confined in geocells.
Edil et al. (2002) constructed a highway test section
that incorporated a 150 mm-thick layer of geocells filled
with granular foundry slag. The geocell layer was under-
lain by a soft fine-grained subgrade and overlain by a
granular base course and an asphalt pavement. One half of
the test section was constructed with geocells 260 mm in
diameter and the other half with geocells 320 mm in
diameter. Tests conducted with a falling-weight deflect-
ometer indicated that the geocell test section had similar
stiffness as an adjacent control section where a 840 mm-
thick layer of crushed rock was used between the fine-
grained subgrade and the base course. No difference in
stiffness was observed between the test sections con-
structed with different size geocells.
3. MATERIALS
3.1. Soils
Three soils were used as infill (i.e. the soil filling the
geocell) in this study: Grade 2 gravel, Rodefeld sand, and
Antigo silt loam. Index properties, particle size fractions,
and compaction characteristics of these soils are sum-
marized in Table 1. Grade 2 gravel is a crushed limestone/
dolomite aggregate that is used as base course in Wiscon-
sin highway construction and classifies as GP-GM in the
Unified Soil Classification System (USCS). Rodefeld sand
is silty sand from glacial outwash that classifies as SM in
the USCS. Antigo silt loam is a lean silty clay of
glaciolacustrine origin that classifies as CL-ML in the
USCS. Although the Grade 2 gravel and Rodefeld sand
classify as coarse-grained soils in the USCS, both have a
sufficient amount of fines to yield typical bell-shaped
compaction curves using standard Proctor compaction
(Mengelt et al. 2000).
3.2. Geocells
GeowebTM geocells produced by Presto Products, Inc. of
Appleton, Wisconsin, USA were used in this study.* The
geocells are comprised of strips of high-density polyethy-
lene (1 mm thick and 254 mm wide) welded together at
305 mm intervals. When expanded, the cells form 2.5 m
3 18 m panels, with each expanded geocell having a
diameter of 250 mm and depth of 200 mm.
The material and structure of the geocells were char-
acterized using tensile tests conducted following the
procedure described in ASTM D 4885 and ASTM D
4437. Tests were conducted on the bulk material (a section
of HDPE without welds) using ASTM D 4885 and on
welded material using ASTM D 4437. In all cases, speci-
mens having ‘wide-strip’ dimensions (200 mm 3 200 mm)
were used. Tests on the welded material were conducted in
peel and shear modes. A tensile test of the bulk material
containing a weld at the center was also conducted to
assess the influence of discontinuities at the center of the
specimen on the tensile strength of the geocell material.
Three replicate tests of each type were conducted.
A summary of the test results is provided in Table 2.
Nearly identical results were obtained from the replicate
tests (Mengelt et al. 2000). Thus only averages are
reported in Table 2. Note that the stiffness was highest for
the bulk material and slightly lower (5%) for the bulk
material with a weld.
Table 1. Index properties for the soils used in this study.
Soil USCS
Classification
Liquid
limit
Plasticity
index
% Gravel(a) % Sand(a) % Fines(a) Optimum water
content(b) (%)
Maximum dry
unit weight(b)
(kN/m3)
Grade 2 Gravel GP-GM – – 70 22 8 10 22.2
Rodefeld Sand SM – – 4 83 13 11 19.1
Antigo Silt Loam CL-ML 32 12 0 22 78 14 18.3
(a)Particle sizes based on Unified Soil Classification System per ASTM D 2487.(b)Standard Proctor per ASTM D 698.
Table 2. Tensile properties of bulk geocell and seamed geocell
Tensile test type Ultimate load
(kN/m)
Ultimate displacement
(mm)
Stiffness
(kN/m-m)
Bulk materiala 21 15 49
Bulk material with weld(a) 22 20 43
Seam: peel(b) 13 28 –
Seam: shear(b) 21 13 –
(a)Per ASTM D 4885.(b)Per ASTM D 4437.
* Mention of trade names and manufacturers is forinformation only, and does not constitute endorsement.
Resilient modulus and plastic deformation of soil confined in a geocell 197
Geosynthetics International, 2006, 13, No. 5
4. RESILIENT MODULUS TESTING
4.1. Test cell and loading apparatus
The resilient modulus of the soils and soil-filled geocells
was measured using the method in AASHTO T 294-94 for
unbound soil materials. Because the expanded geocells
have a much larger diameter than the conventional speci-
mens used for resilient modulus testing, a large-size
resilient modulus test cell was developed. A photograph of
the cell is shown in Figure 2. The new cell and the
modifications to the test procedure were evaluated for
equivalence with the conventional-size test cell and proce-
dure (Mengelt et al. 2000). The test cell is essentially the
same as cells used for specimens of conventional size
(diameter < 102 mm), but is large enough to accommo-
date specimens up to 250 mm in diameter and 500 mm
tall. The only significant modification to the cell design is
that the end plates include a recess so that the geocells
float when the piston applies load to the infill. A detailed
description of the cell design can be found in Mengelt et
al. (2000).
A load frame used specifically for resilient modulus
testing and meeting the criteria in AASHTO T 294-94 was
used for loading (Mengelt et al. 2000). A 1 Hz haversine
load pulse (specified by AASHTO T 294-94) was used,
with the load applied for 0.1 s at the beginning of each
cycle followed by a rest period of 0.9 s. Cell pressure was
monitored and controlled using an electronic pressure
regulator, and vertical deformation was measured using
two diametrically opposed linear variable displacement
transducers (LVDTs) mounted outside the test cell. Defor-
mations measured with the LVDTs, which differed by less
than 1%, were averaged when calculating the elastic and
permanent strains. The cross-sectional area used in the
calculations was corrected for permanent deformation
following the procedure in AASHTO T 294-94.
Tests were conducted to determine whether resilient
moduli obtained with the large-diameter resilient modulus
cell were comparable to resilient moduli obtained using a
conventional cell. A cylindrical block of urethane was
used for the comparison to eliminate any differences due
to variations in sample preparation. The resilient modulus
data from both cells were compared using a paired t-test
at significance level of 0.05 (Berthouex and Brown 2002).
No statistically significant difference was found between
the resilient moduli obtained from both cells (t ¼ 0.246 ,
tcr ¼ 1.761).
4.2. Aspect ratio
Geocells typically have an aspect ratio (height/diameter)
near unity (the geocells used in this study have an aspect
ratio of 0.8). Thus the conventional aspect ratio of 2 used
in resilient modulus testing of earthen materials cannot be
used when testing soil confined in a single geocell.
Testing conducted by the National Cooperative Highway
Research Program for Large Stone Asphalt Mixes
(NCHRP 1997) has indicated that aspect ratio does not
influence the resilient modulus of hot-mix asphalt. How-
ever, aspect ratio is known to influence the shear strength
of soil measured in triaxial compression (Bishop and
Figure 2. Large-scale resilient modulus cell: (a) side view of assembled cell; (b) top view of unassembled cell with specimen
confined in geocell. Scale has units of inches (1 inch = 25.4 mm)
198 Mengelt et al.
Geosynthetics International, 2006, 13, No. 5
Green 1965), and its effect on the resilient modulus of
soils has not been documented. Thus resilient modulus
tests were conducted at aspect ratios of 0.8 and 2.0 using
specimens of Grade 2 gravel prepared at 95% relative
compaction (based on standard Proctor) and 5% water
content. Each specimen had a diameter of 250 mm (i.e.
the same diameter as a filled geocell).
Resilient modulus is shown against bulk stress in Figure
3 for the tests conducted at both aspect ratios. The data
points shown in Figure 3 are averages obtained from the
three tests at each aspect ratio (the variation in resilient
modulus from test to test was less than 3% at a given bulk
stress). The resilient modulus curves obtained at both
aspect ratios appear essentially the same. A paired t-test
conducted at a significance level of 0.05 also indicated
that the resilient moduli for the two aspect ratios are not
statistically different (t ¼ 0.895 , tcr ¼ 1.697). Compari-
son of the deformation data also indicated that plastic
strain (�p) accumulated at the same rate for specimens
prepared at both aspect ratios (Mengelt et al. 2000). Based
on these findings, resilient moduli obtained from tests
conducted in this study with an aspect ratio of 0.8 were
considered comparable to those from a conventional test
conducted with an aspect ratio of 2.0.
4.3. Preparation of test specimens
Test specimens were prepared at 95% of the maximum
dry unit weight obtained from a standard Proctor compac-
tion test (ASTM D 698). Specimens prepared with Grade
2 gravel and Rodefeld sand were compacted 2% dry of
optimum water content to simulate typical placement
conditions in the field. Specimens of Antigo silt loam
were prepared 6% wet of optimum water content to
simulate the in situ water content typical of non-plastic
subgrade soils in Wisconsin (Edil et al. 2002; Bin-
Shafique et al. 2004). Specimens of the silt loam were
also prepared 2% dry of optimum water content to
simulate the condition where the soil would be dried and
compacted.
Soil was compacted directly in the geocells for tests
conducted to evaluate the effect of geocell confinement. A
photograph of a specimen compacted in a geocell is
shown in Figure 2b. Steel bands were wrapped around the
geocells to prevent excessive deformation, and to provide
the lateral confinement during compaction as would be
provided by adjacent geocells in the field. After compac-
tion, the bands were removed and two latex membranes
were placed around the specimen to prevent leakage of the
confining fluid during the resilient modulus test. The
additional confinement provided by the latex membranes
is believed to be negligible compared with that provided
by the geocell, because the HDPE used for the geocell is
much stiffer than latex. Specimens for testing without
geocells were prepared in a steel split mold and tested
with a latex membrane.
4.4. Loading sequence
The loading schedule for Type I (granular) materials in
AASHTO T 294-94 was followed when testing the Grade
2 gravel and Rodefeld sand. For Antigo silt loam, the
loading schedule for Type II (cohesive) materials was
used. Similar tests using the Type I loading schedule were
not completed on specimens of Antigo silt loam prepared
wet of optimum water content without a geocell because
the material was too weak to withstand the deviator
stresses applied during Type I loading.
Both the Type I and II procedures (referred to herein as
‘conventional loading schedules’) apply 1000 load cycles
for conditioning and 1500 load cycles for testing. In the
field, many more cycles typically are applied during the
service life of a pavement. To evaluate effects that might
occur over longer time periods, additional tests were
conducted where the AASHTO T 294-94 loading sequence
was repeated five times (referred to herein as the extended
loading schedule).
5. RESILIENT MODULUS
5.1. Coarse-grained soils
5.1.1. Conventional loading schedule
Resilient moduli for the coarse-grained materials (Rode-
feld sand and Grade 2 gravel) are shown in Figure 4 as a
function of bulk stress. For both materials, the resilient
moduli with and without geocell confinement differ by
only a small amount. Over the range of bulk stresses that
were applied, the resilient modulus of Rodefeld sand in a
geocell is 1.4% higher, on average, than the resilient
modulus of Rodefeld sand without a geocell (Figure 4a).
Similarly, the resilient modulus of Grade 2 gravel in a
geocell is 3.2% higher, on average, than the resilient
modulus of Grade 2 gravel without a geocell (Figure 4b).
The similarity in the resilient moduli is consistent with
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Figure 3. Resilient modulus of Grade 2 gravel at aspect
ratios of 0.8 and 2.0. Specimens were compacted to 95% of
maximum dry unit weight and 5% water content. All
specimens had a diameter of 250 mm. Three specimens were
tested at each aspect ratio. Symbol represents the average
resilient modulus for each bulk stress. Dashed line is least-
squares regression through data from tests with an aspect
ratio of 2; solid line is for aspect ratio of 0.9
Resilient modulus and plastic deformation of soil confined in a geocell 199
Geosynthetics International, 2006, 13, No. 5
the small permanent axial strains (0.9% for Rodefeld sand
and 0.8% for Grade 2 gravel) and circumferential defor-
mations (the diameter of the specimens increased by 1–
2 mm) that were recorded for the specimens in geocells.
These strains and deformations are small, and are unlikely
to result in appreciable additional confinement by the
geocell. To evaluate this hypothesis, the additional con-
finement provided by a geocell was estimated using the
elastic theory described in Henkel and Gilbert (1952) and
the modulus of the geocell measured from the wide-strip
tests on specimens with welds. The permanent axial strain
measured at the end of the test was used to compute the
circumferential strain. These calculations indicated that
the geocell provided approximately 2 kPa of additional
confinement, which is too small to cause an appreciable
increase in resilient modulus. This additional confinement
is much smaller than that reported by Bathurst and
Karpurapu (1993) (150–180 kPa in some cases) for
triaxial shear tests on soil confined in geocells. However,
the axial strains in their triaxial tests were large (10% or
more) compared with the strains in the resilient modulus
tests. Consequently, the additional confinement observed
by Bathurst and Karpurapu (1993) is expected to be much
larger than observed in the resilient modulus tests.
Additional tests were conducted with Rodefeld sand in
a geocell without cell pressure to provide another assess-
ment of the confinement provided by the geocell. A test
on Rodefeld sand was also conducted without a geocell
and without cell pressure, which was possible because the
fines in the sand provided sufficient cohesion. The tests
were conducted using four cyclic deviator stresses (25, 50,
75, and 100 kPa) and four confining pressures (21, 34, 69,
and 103 kPa) (when cell pressure was used). Confining
stress afforded by the geocell was determined by inter-
polation from graphs of resilient modulus against confin-
ing pressure for each deviator stress obtained from tests
conducted on Rodefeld sand tested with cell pressure, but
without a geocell (see Mengelt et al. 2000 for more
information). The effective confining pressures are sum-
marized in Table 3, along with confining pressures
computed with Henkel and Gilbert’s theory. Plastic defor-
mations from the tests without cell pressure are shown in
Figure 5.
The effective confining stresses determined by interpo-
lation ranged between 0 and 11 kPa, and are comparable
to those computed from Henkel and Gilbert’s theory
(Table 3). Thus the confining pressure provided by the
geocell is low. However, the plastic deformation data
indicate that the confinement provided by the geocell is
not negligible (Figure 5). The test conducted with Rode-
feld sand and without a geocell or confining pressure had
to be terminated after 128 cycles owing to excessive
plastic strain (9.8%). In contrast, when Rodefeld sand was
in a geocell, but no cell pressure was applied, the entire
load sequence (1500 cycles) was completed and the final
plastic strain was 3.9%.
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Figure 4. Resilient modulus plotted against bulk stress, with
and without a geocell: (a) Rodefeld sand; (b) Grade 2 gravel.
Dashed lines are least-squares regressions through data from
tests with a geocell; solid lines are for tests without a geocell
Table 3. Apparent and predicted confining pressures applied to Rodefeld sand by a
geocell (�gc). Predicted confining pressures were computed using Henkel and Gilbert’s
(1952) theory.
Deviator stress
(kPa)
Axial strain
(%)
Circumferential strain
(%)
Apparent �gc(kPa)
Predicted �gc(kPa)
5 – – 6.0 –
10 – – 6.9 –
25 2.6 1.3 6.9 7.1
50 3.0 1.6 8.1 8.6
75 3.3 1.7 10.0 9.4
100 3.9 2.0 10.0 11.2
200 Mengelt et al.
Geosynthetics International, 2006, 13, No. 5
5.1.2. Extended loading schedule
Resilient moduli for Grade 2 gravel and Rodefeld sand are
shown in Figure 6 from the conventional (2500 cycles)
and extended (12,500 cycles) loading schedules. Compari-
son of the moduli after completion of each loading
schedule (not shown) indicated that the resilient modulus
did not change after the third application of the conven-
tional loading schedule. Thus the resilient moduli shown
in Figure 6 for the ‘extended’ schedule are representative
of conditions after the third loading sequence.
For both the Rodefeld sand and the Grade 2 gravel,
higher resilient moduli were obtained after the extended
loading schedule, particularly at higher bulk stresses.
Confinement in a geocell had no apparent effect on this
increase in resilient modulus for the Rodefeld sand (Figure
6a). However, the resilient modulus of the Grade 2 gravel
increased more when confined in a geocell, at least for
higher bulk stresses (. 300 kPa) (Figure 6b).
5.2. Fine-grained soil
5.2.1. Conventional loading schedule
Resilient moduli of the Antigo silt loam are shown in
Figure 7. Resilient moduli of fine-grained soils typically
are expressed relative to the deviator stress. However, the
resilient modulus of Antigo silt loam was found to be
weakly related to the deviator stress and more strongly
related to confining pressure, perhaps because of the low
plasticity and high silt fraction of the soil (Moosazedh and
Witczak 1981). Thus the resilient modulus is plotted
against confining pressure in Figure 7.
Results of the tests on Antigo silt loam indicate that the
resilient modulus increases appreciably when the soil is
confined in geocells (Figure 7) for water contents dry and
wet of optimum water content. For specimens compacted
2% dry of optimum water content, the resilient modulus
was 16.5% higher on average when the soil was confined
in a geocell, with the increase in resilient modulus more
pronounced at higher confining pressures (12 MPa when
the confining pressure was 40 kPa). Similarly, 6% wet of
optimum water content, confinement in a geocell caused
an increase in resilient modulus of 17.9%, on average,
with greater increases in resilient modulus at higher
confining stresses.
The increase in resilient modulus shown in Figure 7
cannot be explained based solely on increased confining
pressure provided by the geocell using elastic theory. For
example, the permanent axial strain was 0.5% for Antigo
silt loam compacted dry of optimum water content, which
corresponds to an additional confining pressure of
1.2 kPa. The increase in modulus is attributed to densifi-
cation, as discussed subsequently.
5.2.2. Extended loading schedule
Extended loading tests were also attempted on specimens
of Antigo silt loam in a geocell that were compacted 2%
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Figure 5. Plastic strain plotted against number of loading
cycles for resilient modulus tests conducted on Rodefeld sand
with and without a geocell and no pressure applied in the test
cell
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Figure 6. Resilient modulus plotted against bulk stress from
conventional and extended loading schedules: (a) Rodefeld
sand; (b) Grade 2 gravel. Lines are least-squares regressions
through data from tests with a geocell
Resilient modulus and plastic deformation of soil confined in a geocell 201
Geosynthetics International, 2006, 13, No. 5
dry of optimum and 6% wet of optimum water content.
For the specimens compacted 6% wet of optimum water
content, the limits of the testing machine were reached
because of excessive plastic strain shortly after the second
loading schedule began, precluding determination of resi-
lient moduli under extended loading. However, all five
loading schedules were completed for Antigo silt loam
compacted 2% dry of optimum water content. Resilient
moduli for these specimens are shown in Figure 8. The
extended loading schedule had a pronounced effect on the
Antigo silt loam in a geocell (the resilient moduli in-
creased by 9%, on average, during extended loading).
Without geocells, the resilient moduli are essentially the
same for the conventional and extended loading schedules.
The increase in resilient modulus obtained with geocell
confinement is attributed to an increase in dry density
during loading. Without a geocell, the infill did not
densify during loading (i.e. lateral deformation in conjunc-
tion with axial deformation resulted in negligible volume
change). In contrast, when a geocell was present, lateral
deformation was limited, and axial compression of the
infill occurred, causing the dry density to increase by 9%.
6. PERMANENT STRAINS ANDRUTTING POTENTIAL
Permanent strains measured during a resilient modulus test
are indicative of the rutting potential for a particular
material (i.e. larger permanent strains correspond to
materials with a greater propensity to rut during their
service life; Huang 1993). Permanent strains recorded
during tests on Grade 2 gravel and Rodefeld sand with
and without geocells are shown in Figure 9 as a function
of the step in the loading schedule. These data are from
specimens subjected to two consecutive applications of the
Type I loading schedule.
Permanent strain accumulated at essentially the same
rate in the Grade 2 gravel regardless of the presence of the
geocell. Only slight differences exist between the plastic
strains obtained from the two specimens. For Rodefeld
sand, however, greater accumulation of permanent strain
occurs for the specimen without a geocell. The largest
differences in permanent strain in the Rodefeld sand with
and without geocells occurred during loading sequences
where the ratio of deviator stress to confining stress was
largest (Mengelt et al. 2000). By the end of the first
loading schedule, the cumulative plastic strain of the
specimen confined in a geocell was 2.3 times smaller than
that of the specimen without a geocell. Similarly, at the
end of the second loading schedule, confinement in a
geocell resulted in 2.9 times less permanent strain.
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Figure 7. Resilient modulus of Antigo silt loam plotted
against confining stress for specimens: (a) compacted 2% dry
of optimum water content; (b) compacted 6% wet of
optimum water content. Lines are least-squares regressions
through data from tests
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Figure 8. Resilient modulus of Antigo silt loam compacted
2% dry of optimum water content plotted against confining
stress with and without geocells after conventional and
extended loading schedules. Dashed lines are least-squares
regressions through data from tests with a geocell
202 Mengelt et al.
Geosynthetics International, 2006, 13, No. 5
Accumulation of permanent strain was also evaluated by
conducting cyclic loading tests on Grade 2 gravel and
Rodefeld sand. A constant cyclic deviator stress (103 kPa)
was applied with a constant confining pressure of 103 kPa
for 1000 cycles. The VESYS rut-depth power function
(FHWA 1978) was fitted to the permanent strain accumu-
lated during the conditioning phase. This power function is
log �pcð Þ ¼ I þ S log Nr (3)
where �pc is the cumulative permanent strain, S is a
dimensionless measure of the rate of increase in permanent
strain as a function of the number of load repetitions (Nr),
and I is the initial offset (also dimensionless), considered to
be due to initial densification due to the first pass of traffic.
Results of the analysis are shown in Table 4. The
VESYS rut-depth power function is normally applied to
data sets consisting of many more cycles than applied
during the conditioning phase of the resilient modulus test.
Moreover, Equation 3 conventionally is used to compute
permanent strain for primary rutting, whereas in this study
Equation 3 was used as a parametric method to character-
ize accumulation of plastic strain of soil confined in a
geocell. Thus the parameters in Table 4 should not be
directly compared with other data in the literature. Never-
theless, comparison of I and S from the tests with and
without geocells provides an indication of the effect that
geocells are likely to have on the accumulation of plastic
strain in soils under constant cyclic loading.
A similar effect on the parameters S and I was obtained
for Grade 2 gravel and Rodefeld sand. Confinement in a
geocell resulted in a reduction in I (immediate deforma-
tion) of 1.8 times and a reduction in S (the rate of strain
accumulation) of 2.3% for both materials. Thus less
permanent strain should accumulate in granular materials
in geocells, which should result in less rutting.
7. SUMMARY AND CONCLUSIONS
The objective of this study was to evaluate how resilient
modulus and permanent strain are affected by confining
soil in a single geocell. Resilient modulus tests were
conducted in a specially constructed large-size cell with
and without geocells using three soils representative of
earthen materials normally encountered during construc-
tion of highways in Wisconsin (Grade 2 gravel, Rodefeld
sand, and Antigo silt loam).
Results of the resilient modulus tests indicate that the
effect of geocells depends on the infill (soil in the geocell)
that is used. The resilient modulus of the granular infills
improved by a minor amount (1.4–3.2%) by addition of
geocell reinforcement, whereas the resilient modulus of
the fine-grained low-plasticity infills increased by 16.5–
17.9% when confined by a geocell. The effect on resilient
modulus of the fine-grained infill was larger when the
infill was compacted wet of optimum water content (i.e.
the infill material was softer). Larger deformations oc-
curred in the tests on the fine-grained soil, which most
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Figure 9. Permanent strain with and without a geocell during
two consecutive applications of the Type I loading schedule:
(a) Grade 2 gravel; (b) Rodefeld sand
Table 4. Rutting parameters with and without geocell confinement for Rodefeld sand
and Grade 2 gravel
Soil Confinement S I
Grade 2 Gravel No geocell 0.227 1.2 3 10–3
Geocell 0.222 7.0 3 10–4
Rodefeld Sand No geocell 0.166 1.6 3 10–3
Geocell 0.162 9.0 3 10–4
Note: S and I are dimensionless
Resilient modulus and plastic deformation of soil confined in a geocell 203
Geosynthetics International, 2006, 13, No. 5
likely contributed to the greater effect of the geocell.
Greater effects on resilient modulus were obtained by
extended loading (12,500 cycles as opposed to 2500
cycles) for specimens confined in a geocell. This effect
was more pronounced for the fine-grained soil, but was
also evident at higher bulk stresses for the sand.
Analysis of permanent strains during resilient modulus
tests on the gravel and sand indicated that confinement in
a geocell reduces the accumulated plastic deformation of
coarse-grained materials. This effect may be significant
over the lifespan of a pavement.
These findings suggest that confinement of pavement
soils in geocells may not have an appreciable effect on the
elastic behavior of flexible pavements. However, long-term
permanent strains will likely be lower when geocells are
used to confine base or subbase soils, which should result
in reduced rutting. However, because only a single geocell
was tested, group effects provided by a three-dimensional
mattress of geocells are not considered. Thus the results of
these tests are expected to be conservative (i.e. the
modulus may be lower than that existing in the field, and
plastic strains may be larger than those in the field).
ACKNOWLEDGMENTS
Financial support for the study described in this paper was
provided by the University of Wisconsin Industrial and
Economic Development Research Fund and Presto Pro-
ducts, Inc. of Appleton, Wisconsin. D. Senf of Presto
Products provided valuable input to the study. The find-
ings reported in this paper are those solely of the authors,
and do not necessarily represent the policies or opinions
of the University of Wisconsin Industrial and Economic
Development Research Fund or Presto Products.
NOTATIONS
Basic SI units are given in parentheses.
Mr resilient modulus (Pa)
S dimensionless measure of rate of increase in
permanent strain (dimensionless)
Nr number of load repetitions (dimensionless)
I initial offset of increase in permanent strain
(dimensionless)
t t-statistic (dimensionless)
tcr critical t-statistic (dimensionless)
�p plastic strain (dimensionless)
�r resilient or elastic strain (dimensionless)
�pc cumulative permanent strain (dimensionless)
�b bulk stress (Pa)
�c confining stress (Pa)
�d deviator stress (Pa)
�gc confining stress applied by a geocell (Pa)
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The Editors welcome discussion on all papers published in Geosynthetics International. Please email your contribution to
discussion@geosynthetics-international.com by 15 April 2007.
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