Resilient modulus and plastic deformation of soil confined ...chbenson.engr.wisc.edu/images/stories/pdfs/Geo_Syn/Mengelt et al 06... · Resilient modulus and plastic deformation of

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: [email protected],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: [email protected], 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: [email protected]

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.


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


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.


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



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.


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



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.


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



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

[email protected] by 15 April 2007.



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