A Framework for Analyzing the Stability of Geosynthetic Reinforced Soil Walls under Unsaturated Conditions

Abstract

Suction stress is one of the most significant factors affecting the serviceability and stability of soil structures. This study presents a framework for analyzing the stability of geosynthetic reinforced soil (GRS) walls and slopes under unsaturated conditions. An analytical formulation of suction stress-based effective stress was implemented into a limit equilibrium solution, namely, the top-down procedure. The developed framework enables the prediction of the tensile load distribution and connection load between the reinforcement and wall face considering the pullout resistance of reinforcements in GRS walls backfilled with granular and marginal soils under unsaturated conditions. The applicability of the framework was demonstrated by providing an illustrative example followed by three series of parametric studies to understand the effects of pore size distribution, air entry pressure, and infiltration rate on the performance of an unsaturated GRS wall. The results quantify the impact of suction, showing that as it increases, the maximum tensile loads and connection loads decrease while pullout resistance increases. Mostly affected by the suction effect are upper reinforcement layers, where combined effects of reduced tensile load and increased pullout resistance decrease connection load and reinforcement length requirements. The current study strongly discourages counting on the contribution of suction for the design of new GRS walls. The suction value cannot be accurately and reliably determined for the entire lifespan of the GRS wall, and it may decrease or diminish in an uncontrolled and random manner under infiltration. However, by quantifying the effect of suction, the proposed framework in this study provides a valuable tool for analysis purposes, enabling a rigorous interpretation of field-measured reinforcement loads during wall service as well as evaluation of the forensics of failed GRS walls.

Full text

Technical Note
A Framework for Analyzing the Stability of Geosynthetic
Reinforced Soil Walls under Unsaturated Conditions
Ahmad Rajabian1; Farshid Vahedifard, F.ASCE2; and Dov Leshchinsky, M.ASCE3
Abstract: Suction stress is one of the most significant factors affecting the serviceability and stability of soil structures. This study presents a
framework for analyzing the stability of geosynthetic reinforced soil (GRS) walls and slopes under unsaturated conditions. An analytical
formulation of suction stress-based effective stress was implemented into a limit equilibrium solution, namely, the top-down procedure. The
developed framework enables the prediction of the tensile load distribution and connection load between the reinforcement and wall face
considering the pullout resistance of reinforcements in GRS walls backfilled with granular and marginal soils under unsaturated conditions.
The applicability of the framework was demonstrated by providing an illustrative example followed by three series of parametric studies to
understand the effects of pore size distribution, air entry pressure, and infiltration rate on the performance of an unsaturated GRS wall. The
results quantify the impact of suction, showing that as it increases, the maximum tensile loads and connection loads decrease while pullout
resistance increases. Mostly affected by the suction effect are upper reinforcement layers, where combined effects of reduced tensile load and
increased pullout resistance decrease connection load and reinforcement length requirements. The current study strongly discourages count-
ing on the contribution of suction for the design of new GRS walls. The suction value cannot be accurately and reliably determined for
the entire lifespan of the GRS wall, and it may decrease or diminish in an uncontrolled and random manner under infiltration. However,
by quantifying the effect of suction, the proposed framework in this study provides a valuable tool for analysis purposes, enabling a
rigorous interpretation of field-measured reinforcement loads during wall service as well as evaluation of the forensics of failed GRS walls.
DOI: 10.1061/JGGEFK.GTENG-12069.© 2024 American Society of Civil Engineers.
Author keywords: Geosynthetic reinforced soil (GRS) walls and slopes; Suction stress; Limit equilibrium; Unsaturated soil; Analysis;
Forensic analysis.
Introduction
Geosynthetic reinforced soil (GRS) walls and slopes are widely
used in practice as a cost-effective and effective alternative. The lit-
erature contains studies reporting field monitoring of such structures
acting as retaining walls (Benjamim et al. 2007), bridge abutments
(Saghebfar et al. 2017), and landslide rehabilitation (e.g., Rimoldi
et al. 2021). According to design guidelines [Eurocode 7 (CEN
2004); FHWA (Berg et al. 2009); AASHTO 2002], these structures
are recommended to be backfilled with select granular materials
due to their high permeability, which facilitates drainage and pos-
sesses reliable high shear resistance while being easily compacted.
However, because of the backfill cost, marginal soils containing
fines higher than 15% are frequently used for these structures,
especially in the private sector. Construction of marginal soils-
backfilled GRS walls necessitates an understanding of the field
performance of such structures. Unsaturated GRS walls backfilled
with marginal soils often exhibit good performance, likely due to
high matric suction, thus increasing the shear strength of soil and
soil-geosynthetic interface resistance (Portelinha et al. 2012;
Ehrlich et al. 1997;Riccio et al. 2014;Ling et al. 2012). This
phenomenon reflects the importance of including suction effects
in analyses to better understand structures typically deemed unac-
ceptable in the public sector.
Different design approaches, including lateral earth pressure
(AASHTO 2007), limit state [limit equilibrium (LE) and limit
analysis (LA)], the K-stiffness method (Allen et al. 2003;Bathurst
et al. 2006), and numerical methods are used for analysis and de-
sign of GRS walls. A review of these methods can be found in the
literature (Vahedifard et al. 2012;Leshchinsky et al. 2014). Han
and Leshchinsky (2006) developed an LE-based framework to de-
sign GRS slopes and walls considering a planar failure surface, ren-
dering the distribution of required tensile strength along each
reinforcement. Termed a top-down procedure, this method was
later extended by Leshchinsky et al. (2014) by considering a log
spiral failure surface instead of a planar one. Later, Leshchinsky
et al. (2017) modified the approach, modifying the Bishop analysis
so that complex geotechnical problems (e.g., layered soil) could be
considered. The main advantage of the method, which accommo-
dates the effects of short secondary reinforcements and facing
blocks into analysis, is producing a complete solution that yields
the minimum required wall-facing connection load as well as the
maximum tensile load considering the spacing of reinforcements
and their pullout capacity.
A concern associated with LE-based methods is a discrepancy
that has been observed between field performance and limit state-
based design predictions in terms of the tensile load mobilized in
1Assistant Professor, Dept. of Civil Engineering, Shiraz Branch, Islamic
Azad Univ., Shiraz 7198774731, Iran. ORCID: https://orcid.org/0000
-0002-4929-202X. Email: ahmadr2007@gmail.com
2Professor and Louis Berger Chair, Dept. of Civil and Environmental
Engineering, Tufts Univ., Medford, MA 02155 (corresponding author).
ORCID: https://orcid.org/0000-0001-8883-4533. Email: Farshid.vahedifard@
tufts.edu
3Emeritus Professor, Dept. of Civil and Environmental Engineering,
Univ. of Delaware, Newark, DE 19716; Partner, ADAMA Engineering,
12042 SE Sunnyside Rd., Clackamas, OR 97015. ORCID: https://orcid
.org/0009-0007-7800-983X. Email: dov@udel.edu
Note. This manuscript was submitted on June 29, 2023; approved on
January 19, 2024; published online on April 10, 2024. Discussion period
open until September 10, 2024; separate discussions must be submitted for
individual papers. This technical note is part of the Journal of Geotech-
nical and Geoenvironmental Engineering, © ASCE, ISSN 1090-0241.
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the reinforcements (Wu 1992). The main part of this discrepancy
has been attributed to rightfully neglecting the effect of suction,
along with a few other factors serving as implicit margins of safety
in the design procedure (Vahedifard et al. 2016). Suction has the
potential to increase the shear strength of backfill, especially in
marginal conditions, and this effect is often represented by apparent
cohesion (Vahedifard et al. 2015). A small amount of cohesion
(e.g., 5–10 kPa) can significantly decrease the lateral earth pressure
behind the wall, thereby necessitating a reduced contribution from
reinforcements (Vahedifard et al. 2014,2015). However, suction
can diminish or decrease rapidly under infiltration. Consequently,
its precise value may be challenging to determine and account
for over the entire lifespan of a wall. Therefore, it is recommended
to neglect the suction effect for design purposes. Nevertheless,
quantifying the impact of suction can be valuable for analysis pur-
poses, offering a better understanding of the in-service behavior of
GRS walls or aiding in the more accurate interpretation of field-
measured data.
Thus, incorporating the effect of suction stress into LE analyses
provides a better insight into the stability and reinforcement require-
ments, rendering more realistic results. In this regard, some inves-
tigations have attempted to incorporate the suction stress effect into
limit-state analyses of unsaturated GRS walls and slopes (Yang and
Chen 2019;Deng and Yang 2022).
Common LE-based analytical studies on the performance of
unsaturated GRS walls provide no information on the distribution
of tensile load along reinforcement layers and face connection load
required to produce an LE state. The present study aims to address
this gap by incorporating the influence of suction stress into the
top-down LE formulation. The proposed framework should be con-
sidered a tool for analysis (or back analysis), not for design pur-
poses. The solution is an extension of the top-down method by
Leshchinsky et al. (2017) that provides the distribution of tensile
load along each reinforcement as well as wall-face connection load
in consideration of pullout capacity under steady-state unsaturated
flow conditions for a GRS backfilled with cohesive-frictional soil.
Problem Definition
Fig. 1depicts a GRS wall with a batter of ωand height of H
reinforced with nlayers of reinforcements installed at an equal
spacing of SV. The top and bottom reinforcements are assumed
to be located at the depth of Htbelow the slope surface, and
Hbabove the toe level, respectively. Backfill is assumed to be
in unsaturated states with effective cohesion, internal friction angle,
and unit weight of c0,ϕ0, and γ, respectively. The GRS wall carries
an assumed surcharge of Qon its top and experiences a steady-state
infiltration rate of q. The water table level is taken to be constant at
a depth of z0below the toe elevation, as illustrated in Fig. 1.
As the problem is studied under unsaturated conditions, the ef-
fective stress is represented on the basis of suction stress. Lu and
Likos (2004) presented a unified expression that can be employed
for computing the effective stress under both saturated and unsatu-
rated situations as follows
σ0¼σ−ua−σsð1Þ
where σ0= effective stress; σ= total stress; ua= pore-air pressure;
and σs= suction stress. Unless stated otherwise, uais typically con-
sidered to be atmospheric pressure and treated as zero. Eq. (1) can
be readily incorporated into the Mohr-Coulomb failure criterion to
describe the shear strength of unsaturated soils, considering the
effect of suction stress. A closed-form equation for calculating the
suction stress under unsaturated conditions was proposed and
validated by Lu et al. (2010) as follows:
σs¼−
ðua−uwÞ
ð1þ½αðua−uwÞnÞðn−1Þ=nð2Þ
where uw= pore water pressure; (ua−uw) = matric suction; and α
and nare empirical fitting parameters of the soil water retention
curve (SWRC) model proposed by van Genuchten (1980). The first
parameter, α, is inversely related to the air entry pressure, and nis a
dimensionless pore size distribution number. These two parameters
are dependent on soil type and can be determined through labora-
tory tests, empirical relationships, or extracted from literature
values associated with various soil types (Lu and Likos 2004).
As reported by Lu et al. (2010), the values of αand nvary between
0.001–1ðkPa−1Þ, and 1.1–8.5, respectively, for various types of
soils. Statistical correlations between nand αmay exist (Phoon
et al. 2010;Shahrokhabadi and Vahedifard 2018), depending on
soil type, characteristics, and specific environmental conditions.
The statistical correlation between these two parameters can be
elucidated by examining the relationship with the physical factors
that govern them. The air entry value is intricately linked to the
characteristics of soil pore size distribution. This distribution,
in turn, relies on various factors, including particle size distribu-
tion, particle arrangement, and soil composition, among others
(Shahrokhabadi and Vahedifard 2018).
Incorporating Gardner’s hydraulic conductivity function (HCF)
(Gardner 1958) into Darcy’s law, Lu and Likos (2004) presented
the variation of matric suction versus the height above the water
table as follows:
ðua−uwÞ¼−
1
αln1þq
kse−γwαz−
q
ksð3Þ
where z= height above the water table; ks= saturated hydraulic
conductivity; and γw= unit weight of water. The parameter qrep-
resents the rate of vertical flow, which takes a positive and negative
value in the case of upward flow (evaporation) and downward flow
(infiltration), respectively. Combining Eqs. (2) and (3) yields the
profile of suction stress versus zunder vertical unsaturated seepage
conditions as
Fig. 1. Geometry of a typical GRS and notations.
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σs¼1
α
ln 1þq
kse−γwαz−
q
ks
1þ−ln 1þq
kse−γwαz−
q
ksnðn−1Þ=nð4Þ
The resulting Eq. (4) signifies the impact of unsaturated condi-
tions in extending the top-down method.
Extension of the Top-Down Method Considering
Suction Effects
Full details of the procedure of the top-down method can be found
elsewhere (Kang 2013;Leshchinsky et al. 2016). This section
presents a comprehensive derivation of the formulation compo-
nents that incorporate the influence of suction. To begin with,
the upper section of the slope with the height of H1(=HtþSv)
including one layer of reinforcement is analyzed using the log
spiral-based LE formulation to calculate the required tensile load
along the first reinforcement [Fig. 2(a)]. The log spiral failure sur-
face is considered rigorous in the sense that it implicitly satisfies all
LE equations. This has been demonstrated by Leshchinsky and
Reinschmidt (1985) for reinforced slopes where, for the critical
log spiral surface, all three equations of equilibrium, moment,
and two force equilibrium equation are satisfied. The validity of log
spiral failure surface has been reported in previous studies (Huang
and Avery 1976;Chen and Snitbhan 1975). The analysis proceeds
with dividing each reinforcement layer into a large number of seg-
ments as shown in Fig. 1. Then, for a selected segment located at
the distance of xfrom the wall face, stability analyses are performed
for several log spiral surfaces passing the segment. The starting
point of these slip surfaces is on the crest, and its ending point
is between the toe and the elevation of the reinforcement layer
[i.e., at a depth between Htand H1in Fig. 2(a)]. Note that the
stability analysis for a specific log spiral failure surface requires
satisfying moment equilibrium around the pole of the log spiral,
as depicted in Fig. 2(a).
In Fig. 2,c0dl and σsdl represent the elemental force due to ef-
fective cohesion and suction stress, respectively, acting along the
log spiral. It should be noted that the characteristic property of
the log spiral requires that the frictional component of soil (not
shown in Fig. 2) generates no moment about the pole; i.e., the result
of elemental force, representing normal force and its associated fric-
tional force, goes through the pole. It is important to note that the
trace of the log spiral is contingent on the soil friction angle. This
means that the moment arm of the force due to cohesion on any
points on the log spiral is a function of ϕ0. Consequently, the loca-
tion of the critical surface is influenced by both cohesion and
friction angle, ensuring equilibrium at a limit state. Therefore, the
absence of the frictional component in the moment equilibrium
equation does not negate its impact on achieving wedge equilib-
rium. Stability charts presented by Leshchinsky and Rendschmidt
(1985) and by Leshchinsky and Boedeker (1989) show a strong
dependence of the critical results (the reinforcement force corre-
sponding to the critical log spiral) on the soil friction angle.
The stability analysis of a log spiral slip surface intersecting the
reinforcement at the distance of xfrom the wall face yields the re-
quired tensile load, Treq−1ðxÞat the LE state. This representation
means that the tensile force developed in the reinforcement is a
function of x, where xis defined by the origin of the Cartesian co-
ordinate system that is the reinforcement-wall connection point for
each reinforcement. Satisfying the stability of the sliding mass aug-
mented by the wall face and the analyzed log spiral, this load can be
computed using Eq. (5)
Treq−1ðxÞ¼MwþMQ−Mc−Mσs
dð5Þ
where Mw,Mc,MQ, and Mσs= moments owing to the weight
of the sliding mass, cohesion, surcharge, and suction stress, respec-
tively, and d= moment arm of the tensile load, as depicted in
Fig. 2(a).
The suction stress affects the required tensile load through the
relevant resistive moment, reducing the required tensile load com-
pared to fully dry or saturated conditions where no suction stress
exists. The corresponding required tensile load is computed for
each assumed log spiral passing through the segment located at
a distance of xfrom the wall face. Then, the log spiral passing
through the segment that produces the maximum load is critical,
and the associated tensile load reflecting the minimum tensile load
required to provide LE state is considered the required value for
that segment. Repeating this process for all segments renders the
distribution of the required tensile load along the reinforcement
needed to produce an LE state.
In the second stage, the equilibrium of the upper portion with a
height of H2(¼H1þ2SV) considering two reinforcement layers is
satisfied [Fig. 2(b)]. Similar to the previous procedure, the second
reinforcement is first divided into a large number of segments, and
the moment equilibrium is satisfied for each log spiral. It should be
(a) (b)
e
Fig. 2. Free body diagram considered for analyses of stages 1 and 2.
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noted that while establishing the moment equilibrium, the required
tensile load is equally divided between two reinforcements. If, at a
given segment, the final required tensile load for the reinforcement
above is found to be smaller than the corresponding value achieved
from the previous stage, the obtained tensile load is increased to
the higher value, and accordingly, the required load for the lower
reinforcement is adjusted by resolving the moment equilibrium.
The procedure continues downward until the required tensile load
distributions for all reinforcement layers are found. Such tensile
load distributions ensure that all points of the GRS wall are at
an LE state.
The required load along the reinforcement obtained from the
LE-based stability analyses can be mobilized while not exceeding
pullout capacity. Alternatively stated, pullout capacity allows the
required load for stability to be developed. Thus, establishing
the pullout capacity along the reinforcement indicates whether the
reinforcement can mobilize the needed load to satisfy LE. This as-
pect is checked in the top-down procedure as it is essential for sta-
bility. If the pullout capacity at a specific point tends to be exceeded,
the load in other layers intersecting that slip surface is elevated
(i.e., load shedding) to a level that just mobilizes the pullout capac-
ity, not exceeding it. For unsaturated GRS walls, the effect of suc-
tion is required to be considered in the unsaturated pullout capacity
and incorporated into the formulation. It was found that pullout
capacity can be enhanced due to matric suction by increasing
the interfacial shear strength of soil reinforcement, particularly in
marginal soils (Hatami et al. 2013;Portelinha et al. 2018).
Fig. 3demonstrates a typical GRS wall with an assumed log
spiral failure surface intersecting the ith reinforcement with a
length of Lat a point located at a distance of xfrom the wall face.
At this typical point, the pullout resistance is either controlled by
the right part (rear end) pullout resistance or the left side (front end)
of the point, whichever is lesser. That is, the pullout resistance for a
point located at a distance of xfrom the front end of the reinforce-
ment, Pr, can be computed by the following relationship
Pr¼minfPr−E;Pr−Fgð6Þ
where Pr−Eand Pr−F= rear-end and front-end pullout resistance,
respectively, and can be calculated as
Pr−E¼ZL
x
2RcðCi−cc0þCi−ϕσ0tan ϕ0Þdx ð7Þ
Pr−F¼Zx
0
To−iþ2RcðCi−cc0þCi−ϕσ0tan ϕ0Þdx ð8Þ
where dx = elemental length of the reinforcement adopted at a dis-
tance of xfrom the face. Ci−cand Ci−ϕare interaction coefficients
relevant to cohesion and friction angle, respectively. These coeffi-
cients characterize the interfacial behavior between soil and geo-
synthetic, and can be determined through direct shear tests, such
as those outlined in ASTM D5321 (ASTM 2021), or as specified
by FHWA or AASHTO design guidelines. Rcrepresents coverage
ratio, which is typically taken as 1 in the case of geosynthetics, and
To−idenotes the wall-face connection load. The total stress (σ), for
a given point, is computed as σ¼γz, where zis the vertical dis-
tance of the soil surface to the point. This means that the slope angle
affects the overburden of the points along a reinforcement beneath a
sloping face. For slopes with horizontal backslope, the total stresses
for the points on the reinforcement layer located under the crest are
the same. As such, in general, total stress along the reinforcement
layer is a function of x. This means that effective stress varies with
x, as the suction stress remains unchanged along a reinforcement. It
is noted that the effective stress is not affected by xin GRS walls
with a zero batter and a backslope angle of zero. Also, when the
slope has a batter greater than zero, the effective stress in pullout
calculations would not be constant but rather dependent on x, de-
fining its location under the slope face.
The total normal stress, σ, in Eq. (1) is due to overburden pres-
sure, and as such, its distribution along a given reinforcement layer
depends on the batter of the slope. Consequently, for a nonzero
batter wall, one can expect the pullout capacity to vary nonlinearly
in the vicinity of the face (Fig. 3). Contrarily, for vertical walls, the
overburden stress poses a constant amount of γzfor a reinforce-
ment layer at a depth of zgenerating a linear distribution for
front-end pullout capacity. As defined, the prevailing pullout resis-
tance is the minimum of rear- and front-end pullout resistances at
each point. As can be viewed from Fig. 3, the pullout resistance in
the face equals the connection load (To-i), and it enables the needed
pullout capacity away from the face (Zhang et al. 2023). This
load is different from the tensile force, although shown by T.
Fig. 3. Pullout resistance along a reinforcement.
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The distribution of tensile load is determined with a combination of
the required tensile load for the stability and existing pullout resis-
tance along the reinforcement layer. Distribution of tensile load
along a given reinforcement provides direct information concerning
the type of internal instability and adequacy of reinforcement
length. It is worth mentioning that To−iis determined as a mini-
mum load required to prevent front pullout failure. Viewed differ-
ently, this load is the minimum load allowing the reinforcement to
mobilize the tensile load obtained from the stability analyses
around the front end and can be determined by shifting the front-
end pullout envelope to be tangent to the tensile load distribution
(Leshchinsky et al. 2014,2016)
Illustrative Example
Fig. 4depicts a GRS wall with a batter and height of 5° and 6 m,
respectively, including a backfill with the properties provided in
Table 1, adopted from Vahedifard et al. (2016). With a fines content
of 30%, this soil is classified as clayey sand (SC) based on USCS
and is regarded as marginal soil based on the design standards. It
should be noted that to better assess the influence of suction on the
results, particularly for upper layers where the overburden is low,
the cohesion of the soil was reduced to 2 kPa in the analyses. The
wall is reinforced with nine 4-m-long reinforcements (L=H¼
0.66) spaced at 0.6 m intervals. The interaction coefficients relevant
to cohesion (Ci−c) and friction angle (Ci−ϕ) are assumed to be the
same value of 0.8. The water level is taken to be constant at 1 m
below the toe level. The rate of vertical flow (q) is assumed to be
zero in the example, representing a no-flow condition.
Using the proposed framework, the distribution of tensile load
along each reinforcement under unsaturated conditions can be
obtained. More specifically, this example aims to qualitatively ex-
amine the effect of suction on the maximum tensile load developed
in reinforcements (Tmax), connection load (To), and pullout resis-
tive length of reinforcements.
To examine the influence of suction stress, the results of the
analyses, including and excluding suction stress, are also repre-
sented. Fig. 5provides a comparison of the distribution of tensile
load along each reinforcement with and without the suction effect.
In each subfigure of Fig. 5, the straight lines represent the pullout
capacity envelope around the front and rear end of the reinforce-
ment in the cases with and without considering suction. The pullout
capacity envelope around the front and rear end of each reinforce-
ment for two cases of suction included and excluded are also shown
in this figure. Further, the value of normalized suction stress
(σs=γH) for each reinforcement layer is shown. It should be noted
that the smoothness of the load distribution highly depends on the
size of segments adopted in the analysis process. While contribut-
ing to achieving a smoother distribution, reducing the segment size
increases the computational effort exponentially. Thus, the current
analyses were carried out by adopting an optimal segment size to
rationally meet both accuracy and smoothness requirements.
As expected, for all reinforcements, Tmax significantly drops in
the presence of suction stress. The top layer shows a notable dif-
ference between the inclinations of the pullout envelopes because
this layer carries the highest suction stress. The difference between
the inclinations diminishes with depth increase owing to a drop in
suction stress level. For the lower two layers, rear and front pullout
envelopes are nearly coincident for two cases. Although suction-
induced increased pullout resistance and reduced tensile loads
occur in the upper three layers under unsaturated conditions,
the development of tensile load is limited by rear-end pullout re-
sistance. This means that these layers are too short to mobilize the
required tensile load to provide internal stability. This is not sur-
prising when ϕ0is relatively small, typical of low-quality backfill.
However, suction notably reduces the relevant pullout resistive
length for these layers compared to the case in which the suction
effect is excluded. Note that the pullout resistive length denotes
the portion of a reinforcement in which the pullout governs the
development of tensile load. For example, the rear pullout resistive
length for the top layer was found to be 1.125 m (0.28 L), without
considering suction, reduced to 0.125 m (0.03 L) with considering
suction for the top layer. The reduction in the pullout resistive
length can be mainly attributed to the increase in pullout resistance
as well as the reduction in tensile load in the reinforcement upon
introducing suction. In fact, the suction effect enables the rein-
forcements to enhance their efficiency by reducing pullout resis-
tive lengths.
Some reinforcements have an unstressed portion (termed
dormant length hereafter) around their rear end, implying they
are longer than required for stability. In an unsaturated GRS wall,
this length appears in all layers except the upper three, while, in the
case of ignoring suction, only the lower two layers include dormant
length. That is, while selecting the 4-m-long reinforcements with the
layout adopted in this example is redundant only for the lower two
layers when ignoring suction, in an unsaturated GRS, this length
Fig. 4. Geometry and properties of a GRS wall considered for the
illustrative example.
Table 1. Properties of marginal soil adopted as backfill of GRS wall
Soil properties value
Unsaturated unit weight, γunsat (kN=m3)19
Saturated unit weight, γsat (kN=m3)20
aEffective internal friction angle, ϕ0(°) 25
Effective cohesion, c0(kPa) 13
USCS SC
n(dimensionless) 1.2
α(kPa−1) 0.15
Saturated permeability, ks(m=s) 5×10−7
Residual saturation, Sres 0.1
aResults from direct shear tests.
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of reinforcement is not needed for the lower six layers. The impact of
suction on the adequacy of reinforcement length depends on
the depth of layers. Generally, it can be concluded that ignoring suc-
tion results in shortening dormant lengths (i.e., requiring longer
reinforcement), and developing longer pullout resistive lengths.
For example, layers four through seven are excessively long
under unsaturated conditions but are too short when suction is
ignored.
Using the data extracted from Figs. 5,6compares Tmax and
Todeveloped in all reinforcement with and without introducing
suction. It is evident that all reinforcements under unsaturated con-
ditions experience the same Tmax of 2.93 kN=m while upon elimi-
nating suction, Tmax nonuniformly increases. This increase is the
highest (380%) for the lower four layers and the least (356%)
for the upper two layers. This considerable impact of suction stress
can compensate for any reduction in the load capacity of the
reinforcement due to creep, installation damage, and degradation.
The influence of suction on reducing connection load is also seen in
Fig. 6where owing to suction stress, all layers other than the bot-
tom need no connection load so that the required tensile load can be
mobilized. However, the connection load for the bottom layer is
negligible (0.6kN=m). This aspect can be explained by referring
to Fig. 5. As observed, regardless of the suction effect, the tensile
load close to the front end of the reinforcements is found to be
zero. Interestingly, when suction comes into play, this untensioned
portion gets longer. This phenomenon, combined with enhanced
pullout capacity, contributes to decreasing connection load for
unsaturated GRS walls. The unloaded portion shortens with depth
as it reduces from 1.425 m (0.35 L) at the top layer to 0.34 m
(0.08 L) at the bottom layer where a small connection load of
0.61 kN=m is needed to mobilize tensile load in the reinforcement.
Parametric Studies
Three sets of analyses were performed to study the impact of
suction stress-affecting parameters, namely n;α, and infiltration
rate (q), on the performance of the GRS wall whose geometry
and backfill are described in the illustrative example.
To capture the impact of n, a series of analyses were conducted
with n¼1.1, 2, 3, and 4. The results are depicted in Fig. 7. In all
these cases, α¼0.15 kPa−1and q¼0(no-flow conditions) are
(a) (b) (c)
(d) (e) (f)
(g) (h) (i)
Fig. 5. Distribution of tensile load along the reinforcements including and excluding suction. In each subfigure, the straight lines represent
the pullout capacity envelope around the front and rear end of the reinforcement in the cases with and without considering suction:
(a) top layer (σs=γH¼−0.347); (b) 2nd layer (σs=γH¼−0.321); (c) 3rd layer (σs=γH¼−0.293); (d) 4th layer (σs=γH¼−0.265); (e) 5th layer
(σs=γH¼−0.237); (f) 6th layer (σs=γH¼−0.207); (g) 7th layer (σs=γH¼−0.176); (h) 8th layer (σs=γH¼−0.144); and (i) bottom layer
(σs=γH¼−0.11).
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kept constant. The adopted values for nwere according to the
ranges of values reported by Lu et al. (2010) representing clayey
sand (n¼1.1,2) and silty sand (n¼3;4) as common marginal soil
used for backfill of GRS walls in practice. It is noted that the por-
tion of reinforcement along which the pullout resistance does not
restrict the development of tensile load is denoted as unaffected
length. It is seen in Fig. 7that in a GRS wall backfilled with soil
with n¼1.1(generating the highest level of suction stress) all
reinforcement layers are excessively long. With increasing n, cor-
responding to a reduction in suction stresses, dormant lengths de-
crease, and layers become shorter than required as rear resistive
pullout lengths play a role. As seen, the GRS wall with too long
layers and no connection load under n¼1.1becomes a wall whose
upper seven layers are too short, with the lower four layers requir-
ing connection load due to extending front resistive lengths when
increasing nto 4.
A set of analyses was conducted to investigate how the GRS
wall behaves when αvaries. The analyses were performed keeping
the value of n¼1.2and q¼0(no-flow conditions) unchanged and
(a) (b)
(c) (d)
Fig. 7. Impact of non the resistive and dormant lengths of reinforcements: (a) n¼1.1; (b) n¼2; (c) n¼3; and (d) n¼4.
Fig. 6. Variation of connection load and maximum load of reinforce-
ments considering suction.
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with four values of α¼0.05, 0.1, 0.25, and 0.5kPa−1, representing
clayey silt (α¼0.05,0.1kPa−1) and clayey sand (α¼0.25,
0.5kPa−1)(Lu et al. 2010). Fig. 8illustrates the variations in pullout
resistive and dormant lengths with a change in α. It can be seen that
for α¼0.05 kPa−1, other than the top layer having an ideal length,
the others are excessively long, with their dormant length increas-
ing with depth. As expected, with an increase in α, corresponding
to a decrease in the suction stress, the dormant lengths gradually
decrease or are eliminated in lower layers. However, in the upper
layers, the rear resistive length emerges and develops due to in-
creasing α. Once again, the impact of suction on reducing length
requirements is evident. For instance, the upper two layers, which
are shorter than required with α¼0.1kPa−1, become sufficient
(the top layer) and even excessively long (the second layer) with
the suction contribution.
The influence of infiltration under a steady-state situation with
the water level being constant was examined. Under such condi-
tions, the GRS remains unsaturated without generating any
positive pore water pressure due to infiltration. Fig. 9illustrates
the results of analyses performed on the GRS wall with three in-
filtration rates of q¼−3.14 ×10−8m=s, −1.15 ×10−8m=s, and
zero (no infiltration). The negative sign of qdenotes infiltration.
As expected, introducing a higher infiltration rate decreases the
absolute value of suction stress, shortening the dormant length
and extending the resistive length. For example, the upper three
layers are too short under no infiltration, while introducing infil-
tration causes the upper five layers to become shorter than re-
quired. Further, with an increased rate of infiltration, dormant
lengthsdecrease.Thiscanbeseeninthe6thlayer,whoselength
is excessive under a rate of q¼−1.15 ×10−8m=s, while being
adequate under q¼−3.14 ×10−8m=s.
Discussion
This study demonstrated that suction significantly contributes to the
internal stability of a GRS wall. However, when designing newly
(a) (b)
(c) (d)
Fig. 8. Influence of αon resistive and dormant lengths of reinforcements: (a) α¼0.05 kPa−1; (b) α¼0.1kPa−1; (c) α¼0.25 kPa−1; and
(d) α¼0.5kPa−1.
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constructed GRS walls, despite the potentially significant effects of
matric suction, the authors strongly recommend ignoring this factor
for safe design. The suction value cannot be accurately and reliably
determined for the lifespan of the GRS wall, and it may decrease or
diminish in an uncontrolled and random manner under infiltration.
This uncertainty arises from the large variation in matric suction
during the lifespan of the GRS wall, depending on the SWRC
parameters used in the analysis. Furthermore, accurately predicting
apparent cohesion due to matric suction under extreme conditions,
such as earthquakes, is challenging, representing the moment when
a given GRS wall would exhibit its lowest stability.
The proposed framework can advance the state of practice and
has two primary applications for analysis purposes:
•The proposed approach provides a robust tool for explaining
field-measured data and accurately interpreting observations of
reinforcement loads during wall service. Relying on measured
reinforcement loads under normal conditions, including back
analyses, to develop design methods can be misleading if
all contributing factors, including suction, are not properly
considered. Interpreting field data may be compromised by
attributing the impact of other factors, such as suction, to the
reinforcement contribution. For instance, AASHTO (2020)
employs empirical design for geosynthetic reinforced walls,
relying entirely on statistical analysis of measured reinforce-
ment loads under working load conditions. The proposed tool
offers an analytical perspective crucial for interpreting this
field data.
•The proposed framework offers a viable tool for evaluating the
forensics of failed GRS walls. Studies (Koerner and Koerner
2013;Valentine 2013) indicate that over 60% of failures and
poor performance of GRS walls result from internal or external
water. While some water-induced failures are due to poor drain-
age and subsequent saturation of the backfill, many failures are
reported in unsaturated GRSs under working stress conditions
and varying moisture content (Yoo and Jung 2006;Koerner and
Koerner 2013;Valentine 2013;McKelvey et al. 2015). Quanti-
fying the effect of suction allows more accurate forensic studies
of GRS walls.
The impact of positive or negative pore pressures on the stability
of GRS walls is well-recognized. Drainage systems are typically
integrated into GRS wall designs to mitigate positive pore pressure
in the soil. In traditional design approaches, negative pore water
(a) (b)
(c)
Fig. 9. Influence of infiltration rate (q) on resistive and dormant lengths of reinforcements (a) q¼0; (b) q¼1.15 ×10−8m=s; and
(c) 3.14 ×10−8m=s.
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pressure is overlooked and serves as an additional safety factor.
While effective drainage is crucial for dissipating positive pore
pressures, its correlation with stability analyses, considering the
beneficial effects of matric suction, is lacking. Consequently, suc-
tion should not be factored into design considerations. The poten-
tial loss of suction due to infiltration in marginal soils, coupled with
inadequate drainage, can result in significant issues such as tension
cracks, settlements, and potential wetting problems.
The current formulation does not consider tension cracks. Many
design guidelines restrict the use of backfill materials prone to ten-
sion cracks, necessitating extensive drainage and grading measures
for mitigation. Alternatively, guidelines may mandate treating the
fill with lime, cement, or another agent to prevent tension cracks
that could permit significant water infiltration into the backfill.
Despite such precautions, tension cracks and their associated con-
sequences remain crucial contributing factors in numerous GRS
wall failures (Koerner and Koerner 2013). When examining tension
cracks, the application of unsaturated soil mechanics can offer addi-
tional insights rooted in a sound theoretical foundation. This is
particularly relevant because tension cracks predominantly form
and propagate in GRS walls that are partially saturated. In the
unsaturated state, the presence of matric suction introduces two dis-
tinct influences on the stability of GRS walls. It can enhance
the soil shear strength by increasing the effective stress of the soil.
Conversely, the development of matric suction may induce tension
in a significant portion of the backfill soil, leading to deeper tension
cracks compared to saturated soil where no suction is present
(Abdollahi et al. 2021).
Conclusions
This study presents an analytical framework to quantify the con-
tribution of suction to the stability of unsaturated GRS walls. A
suction stress-based formulation was implemented into a previ-
ously developed framework methodology known as top-down to
predict the distribution of tensile load mobilized in the reinforce-
ments considering front and rear pullout resistance. The effect of
SWRC-controlling parameters and the rate of infiltration on the
performance of GRS walls were investigated. This proposed frame-
work offers a viable tool for analysis purposes to determine the
extent to which suction contributes to the internal stability of GRS
walls under working load conditions. Relying on suction contribu-
tion for design purposes is strongly discouraged due to its uncertain-
ties and variability over the lifespan of a GRS wall. However,
the proposed framework enables a robust interpretation of field-
measured reinforcement loads during the wall’s service and facili-
tates the assessment of the forensics of failed GRS walls.
The main consequence of an increase in suction is a decrease in
the maximum tensile load for all reinforcements. The suction stress
decreases the connection loads, primarily for upper layers where
required tensile loads decrease and increased pullout resistance in-
crease. The increased suction stress extends dormant, or unten-
sioned, length and shortens the resistive length. Upper layers are
highly influenced by suction stress as they experience the highest
level of suction stress, thus enhancing pullout resistance and de-
creasing length requirements. This can be impactful as upper layers
typically need longer to better utilize the reinforcement. From the
results obtained, it can be concluded that using marginal backfill
soil with lower values of pore size distribution, higher air entry
pressure, and maintaining the backfill from infiltration can produce
stable GRS walls meeting performance requirements. It is recog-
nized that low-quality backfills may have drawbacks in achieving
good construction with minimal post-construction settlements.
The proposed framework presents a practical tool for analyzing
the stability of GRS walls and slopes, considering the influence of
suction. This innovative approach provides valuable insights into
the actual behavior of unsaturated GRS structures throughout their
lifespan. The framework offers a comprehensive understanding of
system performance by quantifying the impact of suction on vari-
ous components, including tensile load distribution and connection
load between the reinforcement and wall face, while considering
the pullout resistance of reinforcements. The framework can be
applied in forensic investigations, enabling a thorough analysis
of observed behaviors and failure mechanisms. Furthermore, the
insights gained from this research can be utilized to verify or es-
tablish design methods, enhancing the reliability and effectiveness
of GRS structures in practical applications. The model can benefit
from validation against physical tests, which would be an interest-
ing topic to investigate in future studies.
Data Availability Statement
Some or all data, models, or code that support the findings of this
study are available from the corresponding author upon reasonable
request.
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