Load-Carrying Capacity and Required Reinforcement Strength of Closely Spaced Soil-Geosynthetic Composites

Abstract

In current design methods for reinforced soil walls, it has been tacitly assumed that reinforcement strength and reinforcement spacing play an equal role. This fundamental design assumption has led to the use of larger reinforcement spacing (0.3-1.0 m) in conjunction with stronger reinforcement to reduce construction time. Recent studies, however, have clearly indicated that the role of reinforcement spacing is much more significant than that of reinforcement strength. With closely spaced (reinforcement spacing <= 0.3 m) reinforcement, the beneficial effects of geosynthetic inclusion is significantly enhanced, and the load-deformation behavior can be characterized as that of a composite material. A reinforced soil mass with closely spaced geosynthetic reinforcement is referred to as geosynthetic-reinforced soil (GRS). In this study, an analytical model is developed for predicting the ultimate load-carrying capacity and required reinforcement strength of a GRS mass. The model was developed based on a semiempirical equation that reflects the relative roles of reinforcement spacing and reinforcement strength in a GRS mass. Using measured data from field-scale experiments available to date, it is shown that the analytical model is capable of predicting the ultimate load-carrying capacity and required reinforcement strength of a GRS mass with good accuracy. (C) 2013 American Society of Civil Engineers.

Full text

Load-Carrying Capacity and Required Reinforcement Strength
of Closely Spaced Soil-Geosynthetic Composites
Jonathan T. H. Wu
1
and Thang Q. Pham
2
Abstract: In current design methods for reinforced soil walls, it has been tacitly assumed that reinforcement strength and reinforcement spac-
ing play an equal role. This fundamental design assumption has led to the use of larger reinforcement spacing (0.3–1.0 m) in conjunction with
stronger reinforcement to reduce construction time. Recent studies, however, have clearly indicated that the role of reinforcement spacing is
much more significant than that of reinforcement strength. With closely spaced (reinforcement spacing #0:3 m) reinforcement, the beneficial
effects of geosynthetic inclusion is significantly enhanced, and the load-deformation behavior can be characterized as that of a composite
material. A reinforced soil mass with closely spaced geosynthetic reinforcement is referred to as geosynthetic-reinforced soil (GRS). In this
study, an analytical model is developed for predicting the ultimate load-carrying capacity and required reinforcement strength of a GRS mass.
The model was developed based on a semiempirical equation that reflects the relative roles of reinforcement spacing and reinforcement strength
in a GRS mass. Using measured data from field-scale experiments available to date, it is shown that the analytical model is capable of predicting
the ultimate load-carrying capacity and required reinforcement strength of a GRS mass with good accuracy. DOI: 10.1061/(ASCE)GT.1943-
5606.0000885.©2013 American Society of Civil Engineers.
CE Database subject headings: Soil stabilization; Geosynthetics; Load bearing capacity.
Author keywords: Reinforced soil; Geosynthetics; Reinforcement strength; Composite; Load-carrying capacity.
Introduction
Over the last two decades, the concept of incorporating layers of
geosynthetic sheets to improve the performance and stability of
compacted fills has been used with increasing popularity in the
construction of many types of earth structures, including retaining
walls, bridge abutments, embankments, slopes, and shallow foun-
dations. In actual construction, soil walls reinforced with layers of
geosynthetics have demonstrated many distinct advantages over
their conventional counterparts. Soil walls reinforced with geo-
synthetics are typically more ductile, more flexible (hence more
tolerant to differential settlement), more adaptable to low quality
backfill, easier to construct, require less overexcavation, and more
economical (Wu 1994;Holtz et al. 1997;Bathurst et al. 1997).
Even though reinforcement spacing of 0.3–1.0 m has commonly
been used in the construction of reinforced soil walls, the benefitof
closely spaced reinforcement has been recognized and demonstrated
through full-scale experiments (Wu 2001;Adams et al. 2002;Wu
et al. 2011). When reinforcement spacing is kept small (#0:3 m), the
reinforcement has been shown to offer added beneficial effects (in
addition to being a tensile resistance member), and its behavior can
be characterized as that of a composite. A soil-geosynthetic com-
posite with closely spaced reinforcement (reinforcement spacing
#0:3 m) is referred to as geosynthetic-reinforced soil (GRS). The
schematic cross section of a typical GRS wall with segmental facing
is shown in Fig. 1.
GRS walls bear a strong resemblance to mechanically stabilized
earth (MSE) walls. The two systems, however, are quite different
in fundamental design concepts. A GRS wall incorporates closely
spaced geosynthetic reinforcement in a soil mass to improve the
engineering behavior of the soil mass, hence the term reinforced in
GRS, whereas a MSE wall uses reinforcement as tiebacks, i.e., as
a tension resistance member to help holding a potential failure
wedge (assumed to be formed between a critical slip plane and wall
face) in place and preventing it from reaching a failure condition,
hence the term stabilized in MSE.
The mechanism by which geosynthetic reinforcement contrib-
utes to the increase in shear strength of a soil-geosynthetic composite
has been explained in many ways (Schlosser and Long 1972; Yang
1972;Hausmann 1976;Bassett and Last 1978;Ingold 1982;Gray
and Ohashi 1983;Maher and Woods 1990;Athanasopoulos 1993;
Elton and Patawaran 2004;Pham 2009). Among the reinforcing
mechanisms that have been proposed, two mechanisms involve
quantitative evaluation of the reinforcing effect. In one mechanism
proposed by Schlosser and Long (1972), the presence of geo-
synthetic reinforcement is said to give the soil an added anisotropic
cohesion and result in apparent cohesion. The second mechanism
proposed by Yang (1972) considers that the geosynthetic rein-
forcement increases effective confinement of the soil, commonly
referred to as apparent confining pressure. Fig. 2illustrates the
concepts of apparent cohesion and apparent confining pressure.
Using Fig. 2, the apparent cohesion cR(the sum of cohesion of
soil and added cohesion from reinforcement) can be expressed as
cR¼Ds3Rffiffiffiffiffiffi
KP
p
2þc(1)
where cR5apparent cohesion of a soil-geosynthetic composite
mass; c5cohesion of soil; Kp5coefficient of Rankine passive earth
1
Professor, Dept. of Civil Engineering, Univ. of Colorado, Denver,
CO 80217 (corresponding author). E-mail: jonathan.wu@ucdenver.edu
2
Ph.D. Researcher, Institute of Geotechnical Engineering (IGE/IBST),
Ministry of Construction, 81 Tran Cung, Cau Giay, Hanoi, Vietnam.
E-mail: phamthangibst@gmail.com
Note. This manuscript was submitted on May 8, 2012; approved on
January 2, 2013; published online on January 12, 2013. Discussion period
open until February 1, 2014; separate discussions must be submitted for
individual papers. This paper is part of the Journal of Geotechnical and
Geoenvironmental Engineering, Vol. 139, No. 9, September 1, 2013.
©ASCE, ISSN 1090-0241/2013/9-1468–1476/$25.00.
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pressure; and Ds3R5apparent confining pressure of a soil-
geosynthetic composite mass. The apparent confining pressure
can be evaluated by an equation proposed by Yang (1972)as
Ds3¼Tf
Sv
(2)
Substituting Eq. (2) into Eq. (1) yields
cR¼Tfffiffiffiffiffiffi
KP
p
2Svþc(3)
Eq. (2) implies that an increase in reinforcement strength (Tf) has the
same effect as a proportional decrease in reinforcement spacing (Sv).
The ultimate load-carrying capacity of a soil-geosynthetic composite
mass, basedon Schlosser and Long (1972) and Yang (1972), becomes
qult ¼s1R¼s3Kpþ2cRffiffiffiffiffiffi
Kp
p¼scþTf
SvKpþ2cffiffiffiffiffiffi
Kp
p(4)
where sc(or s3)5actual confining pressure of soil mass and not the
enhanced confining pressure.
It is important to note that the assumption of an equal role of
reinforcement strength and reinforcement spacing has also been
used as a fundamental assumption made in current design methods
of reinforced soil walls, where the required minimum reinforcement
strength, Trequired, is determined by
Trequired ¼shSvFs(5)
in which Trequired 5required minimum strength for reinforcement at
depth z;sh5average horizontal stress in a reinforced soil structure
at depth z;Sv5vertical spacing of reinforcement at depth z; and
F5safety factor.
Eq. (5) implies that the reinforcement in a reinforced soil structure
should possess a minimum strength value that is equal to the lateral
stress developed in the soil mass multiplied by the reinforcement
spacing and a proper safety factor. The equation appears to be quite
reasonable (after all, that is what force equilibrium is all about).
However, if the values of shand Fsremain unchanged with re-
inforcement spacing (as has always been the case for the design of
reinforced soil walls and abutments), Trequired becomes linearly
proportion to Sv, i.e., the ratio Trequired=Sv5constant. This again
implies that larger reinforcement spacing can be fully compensated
by employing reinforcement of proportionally higher strength. For
example, if the reinforcement spacing is doubled, the same per-
formance can be achieved by using reinforcement of twice the
strength. This basic design assumption has encouraged the use of
large reinforcement spacing along with high strength reinforcement,
because the combination will typically reduce construction time.
Many laboratory and field experiments have, however, shown
that Eq. (2), as well as all equations derived from Eq. (2), is far from
being correct. Reinforcement spacing has been found to play a far
more important role than reinforcement strength (Adams et al. 2002,
2007;Elton and Patawaran 2004;Ziegler et al. 2008;Wu et al. 2011).
Fig. 1. Schematic cross section of a typical GRS wall with segmental facing
Fig. 2. Concepts of apparent cohesion and apparent confining pressure
of a soil-geosynthetic composite
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This paper presents an analytical model for predicting the ulti-
mate load-carrying capacity and required reinforcement strength
of a GRS mass. The analytical model is based on a semiempirical
equation that reflects the relative roles of reinforcement spacing and
reinforcement strength in a soil-geosynthetic composite. Measured
data from field-scale experiments available to date were used to
verify the analytical model in terms of its capability to predict the
ultimate load-carrying capacity and required reinforcement strength
in those soil-geosynthetic composites.
Analytical Model for Ultimate Load-Carrying Capacity
The analytical model assumes that the apparent confining pressure
caused by closely spaced reinforcement in a GRS mass can be ex-
pressed as
Dsc¼WTf
Sv(6)
in which the parameter, W(referred to as the Wfactor), is a function
of reinforcement spacing and assumes the following form
W¼mðSv=SrefÞ(7)
where Tf5extensile strength of reinforcement; m5a di-
mensionless parameter describing the fraction of mobilized strength
in reinforcement; Sv5vertical spacing of reinforcement; and Sref 5
reference spacing. The parameters mand Sref are described below.
The parameter mis regarded as the ratio of the average force and
maximum force in reinforcement. To determine the value of pa-
rameter min Eq. (7), the concept of average stresses proposed by
Ketchart and Wu (2001) was used, except the average stress was
replaced by average force.
Ketchart and Wu (2001) proposed a concept of average stress for
investigation of soil-geosynthetic composite behavior based on a
load-transfer mechanism. Based on a simplified preloading-reloading
(SPR) model for a representative soil-geosynthetic composite pro-
posed by Hermann and Al-Yassin (1978), as shown in Fig. 3(a),the
equations for calculation of stresses and displacements of a GRS
mass were derived by considering an idealized plane-strain soil-
geosynthetic composite mass shown in Fig. 3(b).Usingtheequi-
librium equations, the forces in the reinforcement and the maximum
force can be written as (Ketchart and Wu 2001)
Fx¼ArEr ns
12nsPv2Ph12n2
s
Es12b
a2
12coshðaxÞ
coshðaLÞ(8)
and
Fmax ¼ArEr ns
12nsPv2Ph12n2
s
Es12b
a2
121
coshðaLÞ(9)
where Fx5force in reinforcement at distance xfrom the origin;
Fmax 5maximum force in reinforcement; vs5Poisson ratio of
soil; Ar5cross-sectional area of reinforcement; Er5tensile modulus
of reinforcement; Es5compressive modulus of soil; L5length
of reinforcement; Pv5vertical pressure; Ph5horizontal pres-
sure; a25kipf½1=ðArErÞ1½ð12n2
sÞ=ðEsAsÞg and b5½ð12n2
sÞ
=ðEsAsÞkipin the expressions of aand b,p5perimeter of rein-
forcement in contact with soil; ki5stiffness of soil-geosynthetic in-
terface; and As5cross-sectional area of soil under consideration.
The average force in reinforcement, F, can be calculated as
F¼ð
L
0
Fxdx
L(10)
Substituting Eq. (8) into Eq. (10) leads to
F¼ArEr
Lð
L
0 ns
12nsPv2Ph 12n2
s
Es!12b
a2
12coshðaxÞ
coshðaLÞdx (11)
or
F¼ArEr
L ns
12nsPv2Ph 12n2
s
Es!12b
a2
L2sinhðaxÞ
acoshðaLÞ(12)
With parameter m5F=Fmax and from Eqs. (9) and (12), the value
of mcan be expressed as
Fig. 3. (a) Idealized plane-strain GRS mass for the SPR model; (b) equi-
librium of differential soil and reinforcement elements (Ketchart and Wu 2001)
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m¼aLcoshðaLÞ2sinhðaLÞ
aL½coshðaLÞ21(13)
Using the data from calculation examples for the SPR model used
by Ketchart and Wu (2001), the values of parameter mfor different
applied pressures and reinforcement lengths can be determined as
shown in Table 1.
As seen in Table 1, the average reinforcement forces are about
70% of the respective maximum reinforcement forces. Thus, the W
factor in Eq. (7) becomes
W¼0:7ðSv=SrefÞ(14)
Substituting Eq. (14) into Eq. (6), the apparent confining pressure of
a soil-geosynthetic composite becomes
Dsc¼WTf
Sv¼h0:7ðSv=SrefÞiTf
Sv(15)
The apparent cohesion, cR, of a soil-geosynthetic composite thus
becomes
cR¼Dsc
2ffiffiffiffiffiffi
Kp
pþc¼0:7ðSv=SrefÞTf
2Svffiffiffiffiffiffi
Kp
pþc(16)
where c5cohesion of soil; Kp5coefficient of passive earth
pressure; Tf5tensile strength of reinforcement; Sv5vertical spacing
of reinforcement; and Sref 5reference reinforcement spacing. The
reference reinforcement spacing Sref may be regarded as the min-
imum distance between vertically adjacent reinforcement layers of
which the composite behavior will not be significant effected by
the grain size of the soil. Based on the authors’experiences with
behavior of the soil-geosynthetic composites and the significance
of aggregate particle sizes, it was found that the reference re-
inforcement spacing, Sref can be approximated by an empirical
equation: Sref 56dmax, where dmax 5maximum particle size of the
soil. It follows that the ultimate load-carrying capacity of a soil-
geosynthetic composite, qult, can be expressed as
qult ¼s1R¼scþ0:7ðSv=6dmaxÞTf
SvKpþ2cffiffiffiffiffiffi
Kp
p(17)
The parameter scin Eq. (17) represents the external confining
pressure exerted on the GRS mass. If a sieve analysis is performed on
the fill material, an alternative expression of Sref 520D85 may be
used in place of Sref 56dmax, where D85 is the equivalent grain
diameter for which 85% of the soil by weight is finer. The alternative
expression, however, requires further verification. For a GRS wall
with dry-stacked modular block facing, the value of sccan be es-
timated by sc5gbDtand, where gb5bulk unit weight of facing
block, D5depth of facing block unit (in the direction perpendicular
to wall face), and d5friction angle between adjacent facing blocks
(or between geosynthetic reinforcement and facing block, if geo-
synthetic is sandwiched between adjacent blocks). The value of scis
typically very small for dry-stacked modular block facing without
cast-in lips or mechanical connection units and can be conservatively
assumed to be zero.
Verification of Analytical Model for Ultimate
Load-Carrying Capacity
Verification of the analytical model [Eq. (17)] for predicting the
load-carrying capacity of a GRS composite is carried out by com-
paring the model calculation results with measured data from (1)
a series of generic soil-geosynthetic composite (GSGC) tests (Pham
2009;Wu et al. 2011,2012), (2) unconfined compression tests (Elton
and Patawaran 2004), and (3) available field-scale tests (as of 2011).
The soils involved in the comparisons described previously range
from uniform fine sand to crushes gravel, the geosynthetic rein-
forcement varies from lightweight nonwoven to heavyweight woven
geotextiles, and the reinforcement spacing ranges from 0.15 to 0.3 m.
For each of the previous cases, the wide-width tensile strength
obtained from ASTM D4595 (ASTM 1986) was used for Tf.The
soil friction angle fwas obtained from triaxial compression tests.
Comparison between the Analytical Model and Generic
Soil-Geosynthetic Composite Tests
Pham (2009) and Wu et al. (2011) conducted a series of tests on field-
scale GRS mass, known as the GSGC tests. The soil-geosynthetic
composite specimens in the tests were 2.0 m high and 1.4 m wide and
in a plane-strain condition. The soil was diabase crushed gravel
having a maximum particle size of 33 mm. Large-size triaxial tests
(specimen diameter 5150 mm and height 5300 mm) reveal that
the soil has an internal friction angle, f550°, and cohesion,
c570 kPa, in the stress range of interest for the GSGC tests. The soil
was reinforced with a woven geotextile of wide-width strengths of
70 and 140 kN=m at vertical spacing of 0.2 and 0.4 m. The geotextile
with Tf5140 kN=m was obtained by gluing two sheets of the same
geotextile with Tf570 kN=m. Uniaxial tension tests were con-
ducted to verify the tensile strengths. The test results are shown in
Fig. 4. Table 2shows the conditions of the GSGC tests. If Test 2 is
regarded as the baseline, Test 4 has twice the reinforcement spacing
of the baseline, and Test 3 has twice the reinforcement spacing and
twice the reinforcement stiffness/strength of the baseline (while
maintaining the same interface properties). Comparisons of calcu-
lated ultimate capacity from the analytical model and measured data
from the GSGC tests are also shown in Table 2. The deviatoric
stresses at failure as calculated from the analytical model [Eq. (17)]
are seen to be in very good agreement with the measured data of
GSGC tests. The differences between the two are between 4 and 9%.
For reference purposes, comparisons of the results between the
model proposed by Schlosser and Long (1972) and Yang (1972) and
the GSGC tests are presented in Table 3. The deviatoric stresses at
failure calculated from the model proposed by Schlosser-Long and
Yang are between 20 and 86% compared with 4–9% for the ana-
lytical model.
Comparison between the Analytical Model and
Elton-Patawaran’s Tests
Elton and Patawaran (2004) presented seven large-size unconfined
compression tests on soil-geosynthetic composites with dimensions
of 1.5 m in height and 0.75 m in diameter. The properties of the tests
are given as follows.
Table 1. Values of Parameter mfor Different Applied Pressures and
Reinforcement Lengths
Increment of vertical
pressure, Pv(kPa)
Reinforcement
length, L(m) Am5F=Fmax
9.0 0.127 13.875 0.698
18.0 0.127 14.616 0.701
9.0 0.225 6.851 0.691
18.0 0.225 6.966 0.692
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Backfill
The soil used in the tests was a poorly graded sand with maximum dry
unit weight ðgdry Þ519:0kN=m3, optimum moisture content ðwoptÞ5
9:3%, internal friction ðfÞ540°, and cohesion ðcÞ527:6kPa. The
maximum particle size of the backfill was dmax 512:5mm.
Reinforcement
Six types of reinforcement, designated as TG500, TG600, TG 700,
TG800, TG1000, and TG028, were used, with reinforcement spacing
of 0.15 and 0.3 m. The reinforcement strength Tfand reinforcement
spacing Svof each test are listed in Table 4.
The measured stress-strain relationships of the unconfined com-
pression tests are shown in Fig. 5. Comparisons of Elton-Patawaran’s
tests results with the analytical model and with the Schlosser-Long
and Yang model are presented in Tables 4and 5, respectively. The
deviatoric stresses at failure as calculated by the analytical model are
found to be 0–18% higher than the measured values. The calculated
values by the Schlosser-Long and Yang model, on the other hand, are
between 69 and 97% higher than the measured values.
Comparison between the Analytical Model and Available
Field-Scale Tests
The Federal Highway Administration (FHwA) recently conducted
an independent study to examine the validity of the analytical model.
In the FHwA Synthesis Report of Geosynthetic-Reinforced Soil
Integrated Bridge System (GRS-IBS) manual (Adams et al. 2011),
comparisons between measured ultimate load-carrying capacities of
field-scale experiments of GRS masses and the analytical model are
given. The comparisons include all available (as of 2011) field-scale
experiments that had been loaded to failure. A total of 15 cases were
included in the comparisons performed by the FHwA, including (1)
two loading experiments of a 4.65-m-high segmental GRS bridge
abutment with different backfills, referred to as the NCHRP bridge
abutment experiments (Wu et al. 2006,2008); (2) five unconfined
compression tests of 1.5-m-high soil-geosynthetic composites with
different reinforcement strengths and spacings (Elton and Patawaran
2004); (3) four plane-strain compression tests of soil-geosynthetic
composites with different reinforcement strengths, reinforcement
spacing, and confining pressures, referred to as GSGC tests (Wu
et al. 2011;Pham 2009); (4) two 1.94-m-high FHwA performance
tests with different reinforcement strengths, referred to as the De-
fiance County pier (Adams et al. 2007); (5) a 2.4-m-high soil-
geosynthetic composite pier with modular block facing, referred
to as the Vegas Mini Pier (Adams et al. 2002); and (6) a 4.3-m-high
soil-geosynthetic composite pier with segmental facing, referred to
as the UMass pier (Michael Adams, unpublished data, 2000).
The comparison between load-carrying capacity of the analytical
model and measured values of the field-scale experiments in the
FHwA manual is reproduced in Fig. 6. It is seen that the analytical
model agrees very well with the measured values. The data analyzed
by the FHwA are for reinforcement spacing up to 0.3 m, except one
case with 0.4 m. All the data are for GRS with flexible facing.
Analytical Equation for Required Reinforcement
Strength and Verification
Using the analytical model developed for ultimate load-carrying
of a soil-geosynthetic composite as described in section Analytical
Model for Ultimate Load-Carrying Capacity, an analytical equation
for evaluation of required tensile strength of reinforcement in a GRS
mass can readily be obtained. The derivation and verification of the
analytical equation for required reinforcement strength are presented
as follows.
Analytical Equation for Required
Reinforcement Strength
In current design methods for reinforced soil walls, Eq. (5) has been
used to determine the required reinforcement strength, Trequired ,of
Fig. 4. Global stress-strain relationships of GSGC tests (Wu et al. 2011;
reprinted with permission from Maney Publishing)
Table 2. Comparison of Results between the Analytical Model and GSGC
Tests
Parameter Test 2 Test 3 Test 4
Reinforcement strength, Tf(kN/m) 70 140 70
Reinforcement spacing, Sv(m) 0.2 0.4 0.4
Ds3ðkN=m2Þ, calculated 245 172 86
cRðkN=m2Þ, calculated 407 305 188
ðs1R2s3ÞðkN=m2Þ, measured 2,700 1,750 1,300
ðs1R2s3ÞðkN=m2Þ, calculated 2,460 1,900 1,250
Difference between calculated and
measured values (percentage)
291824
Note: Mohr-Coulomb strength parameters of soil: internal friction angle,
w550°, and cohesion, c570 kPa.
Table 3. Comparison of Results between Schlosser-Long and Yang Model
and GSGC Tests
Parameter Test 2 Test 3 Test 4
Reinforcement strength, Tf(kN/m) 70 140 70
Reinforcement spacing, Sv(m) 0.2 0.4 0.4
Ds3ðkN=m2Þ, calculated 350 350 175
cRðkN=m2Þ, calculated 550 550 310
ðs1R2s3ÞðkN=m2Þ, measured 2,700 1,750 1,300
ðs1R2s3ÞðkN=m2Þ, calculated 3,250 3,250 1,930
Difference between Schlosser-Long and
Yang model and measured data (percentage)
120 186 148
Note: Mohr-Coulomb strength parameters: internal friction angle, w550°,
and cohesion, c570 kPa.
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a GRS structure. For Fs51, it leads to Trequired 5Tf(ultimate
strength of reinforcement), and Eq. (5) becomes
Tf
Sv¼sh(18)
The deficiency of Eq. (18) has been discussed earlier in the In-
troduction. Using the expression that can reflect more accurately
the roles of Tfand Sv[Eq. (15)], an analytical equation to determine
required reinforcement strength of a GRS mass can be obtained as
subsequently described.
For a granular fill (c50), Eq. (17) becomes
s1R¼scþ0:7ðSv=6dmaxÞTf
SvKp(19)
or
s1RKa¼scþ0:7ðSv=6dmaxÞTf
Sv(20)
where Ka5coefficient of active earth pressure. Setting s1R as
svðmaxÞ5maximum vertical stress, Eq. (20) becomes
Table 4. Comparisons of the Results between the Analytical Model and Elton and Patawaran’s Tests
Parameter
Reinforcement type
TG 500 TG 500 TG 600 TG 700 TG 800 TG 1000 TG 028
Reinforcement strength, Tf(kN/m) 9 9 14 15 19 20 25
Reinforcement spacing, Sv(m) 0.15 0.30 0.15 0.15 0.15 0.15 0.15
Ds3ðkN=m2Þ, calculated 30 8 47 48 62 67 83
cRðkN=m2Þ, calculated 60 36 78 79 94 99 116
ðs1R2s3ÞðkN=m2Þ, measured 230 129 306 292 402 397 459
ðs1R2s3ÞðkN=m2Þ, calculated 256 153 333 341 402 426 498
Difference between calculated and measured values (percentage) 11 18 9 17 0 7 8
Note: Internal friction angle of soil, w540°; cohesion of soil, c527:6 kPa.
Fig. 5. Stress-strain relationships of soil-geosynthetic composites in unconfined compression tests (from Elton and Patawaran 2004; Figure 4, p. 84.
© National Academy of Sciences, Washington, DC, 2004; reproduced with permission of the Transportation Research Board)
Table 5. Comparisons of Results between Schlosser-Long and Yang Model and Elton and Patawaran’s Tests
Parameter
Reinforcement type
TG 500 TG 500 TG 600 TG 700 TG 800 TG 1000 TG 028
Reinforcement strength, Tf(kN/m) 9 9 14 15 19 20 25
Reinforcement spacing, Sv(m) 0.15 0.30 0.15 0.15 0.15 0.15 0.15
Ds3ðkN=m2Þ, calculated 59 30 92 95 122 132 163
cRðkN=m2Þ, calculated 91 59 126 130 158 169 202
ðs1R2s3ÞðkN=m2Þ, measured 230 129 306 292 402 397 459
ðs1R2s3ÞðkN=m2Þ, calculated 390 254 541 557 678 726 868
Difference between calculated and measured values (percentage) 70 97 77 91 69 83 89
Note: Internal friction angle of soil, w540°; cohesion of soil, c527:6 kPa.
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svðmaxÞKa¼scþ0:7ðSv=6dmaxÞTf
Sv(21)
or
Tf
Sv¼svðmaxÞKa2sc
0:7ðSv=6dmaxÞ(22)
For a GRS wall with level crest, the required tensile strength of the
reinforcement in a design, therefore, is
Trequired ¼svðmaxÞKa2sc
0:7ðSv=6dmaxÞSvFs(23)
For Fs51
Tmax ¼svðmaxÞKa2sc
0:7ðSv=6dmaxÞSv(24)
Eq. (24) is applicable to the condition where a soil-geosynthetic
composite reaches a failure state. As has been described in section
Analytical Model for Ultimate Load-Carrying Capacity, for a GRS
wall with modular block wall with dry-stacked facing, sccan be
estimated by sc5gbDtandand can generally be conservatively
ignored because the value of scis typically very small without cast-
in lips or mechanical connection units.
Fig. 7, plotted based on Eq. (24), shows the relationships be-
tween Tmax and Svfor GRS walls of different heights, with soil unit
weight 518.9 kPa, sc50, dmax 525 mm, and an internal friction
angle of 37°. The nonlinear relationship between Tmax and Svis
evident from Fig. 7.
Verification of Analytical Equation for Required
Reinforcement Strength
Because the analytical equation for required reinforcement strength
addresses the limiting state, only soil-geosynthetic composites that
have been loaded to failure can be used for the verification. To this
end, the same cases described in section Verification of Analytical
Model for Ultimate Load-Carrying Capacity are used, i.e., (1) a
series of field-scaleGSGC tests (Pham 2009;Wu et al. 2011), (2) field-
scale unconfined compression tests by Elton and Patawaran (2004),
and (3) all field-scale tests examined by the FHwA. For comparison
purposes, the reinforcement loads determined by the model proposed
by Schlosser and Long (1972) and Yang (1972) are also presented.
Table 6shows a comparison of the maximum reinforcement
loads obtained from Eq. (24) and inferred reinforcement loads from
the GSGC tests described in section Comparison between the
Analytical Model and GSGC Tests. The largest difference in re-
inforcement loads between the two is 16%, whereas it is 47% be-
tween the values calculated by Schlosser-Long and Yang models
and the inferred reinforcement loads.
Fig. 6. Comparison of calculated load-carrying capacities with mea-
sured field-scale tests values (Adams et al. 2011)
Fig. 7. Relationships between maximum reinforcement load, Tmax, and
reinforcement spacing, Sv, for GRS walls of different heights
Table 6. Comparison of Reinforcement Loads between Eq. (24) and
Inferred Values from GSGC Tests and between the Schlosser-Long-Yang
Equation and Inferred Values from GSGC Tests
Parameter Test 2 Test 3 Test 4 Test 5
Reinforcement force at failure,
Tf(kN/m)
70 140 70 70
Reinforcement spacing, Sv(m) 0.2 0.4 0.4 0.2
Applied surcharge pressure at
failure (kPa)
2,700 1,750 1,300 1,900
Lateral constraint pressure, s3(kPa) 34 34 34 0
Calculated maximum reinforcement
force (kN/m) by Schlosser-Long
and Yang equation
62.4 74.4 50.5 41.2
Difference between Schlosser-
Long-Yang equation and
reinforcement force at failure
(percentage)
211 247 228 241
Calculated maximum reinforcement
force (kN/m) by Eq. (24)
79.4 124.1 75.4 58.8
Difference between Eq. (24) and
reinforcement force at failure
(percentage)
13 211 8 216
Note: Soil properties: internal friction angle w550°; cohesion c570 kPa;
unit weight gbackfill 524 kN=m3; maximum grain size dmax 533 mm.
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A comparison of the maximum reinforcement loads between
Eq. (24) and Elton and Patawaran’s tests results (2004) is shown in
Table 7. In four of seven tests, the calculated loads agreed nearly
exactly with the tests results. The largest difference between cal-
culated and test results is 13%, whereas it is 74% for the Schlosser-
Long and Yang models.
Fig. 8shows a comparison between maximum reinforcement
loads calculated by Eq. (24) and the values inferred from the field-
scale tests described in section Comparison between the Analyti-
cal Model and Available Field-Scale Tests, as given in the FHwA
manual for GRS-IBS. It is seen that the agreement between the two is
again very good.
The evidence presented previously suggests that Eq. (24) appears
to be a valid tool for evaluation of required reinforcement strength in
a soil-geosynthetic composite. It is clear that the analytical equation
gives a much improved tool over the equation proposed by
Schlosser-Long and Yang for evaluation of required reinforcement
strength in a GRS mass.
Summary and Concluding Remarks
A soil mass with closely spaced geosynthetic reinforcement (re-
inforcement spacing #0:3 m) is referred to as GRS. GRS differs
from MSE in the fundamental design concept. In the latter, the re-
inforcement is considered to act as a tieback member, i.e., a tension
member to resist tensile force in the soil mass, whereas in the former,
the reinforcement is considered to act as an inclusion to improve the
stiffness and strength of the soil-geosynthetic composite. Current
analysis and design equations fail to properly account for the relative
roles of reinforcement spacing and reinforcement strength in a GRS
mass. An analytical model for predicting the ultimate load-carrying
capacity and required reinforcement strength of a GRS mass is
developed. In the analytical model, failure of a soil-geosynthetic
composite is assumed to be governed by rupture of reinforcement.
This assumption appears to be supported by the agreement between
analytical model and available field-scale experiments of GRS mass
that have been loaded to failure. The GRS mass is assumed to situate
over a competent foundation where there is little postconstruction
settlement, and soil-geosynthetic interface is assumed to be fully
bonded. Fully bonded interface has been observed in the GSGC tests
that are loaded to failure. Whether the assumption is true in ge-
neral may need to be further investigated. The analytical model
is based on a semiempirical equation that reflects the relative roles
of reinforcement spacing and reinforcement strength in a soil-
geosynthetic composite subject to vertical loads. Using measured
data from 15 field-scale experiments available to date, it is shown
that the analytical model provides a much improved tool for
predicting the ultimate load-carrying capacity and required rein-
forcement strength of a soil-geosynthetic composite. Although the
analytical model was developed for a GRS mass under a plane-strain
condition, errors from applications of the model to axisymmetric
conditions appear to be quite small, as suggested by the agreement
of results with measured data given previously, of which many are
in a near-axisymmetric condition.
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