2009-hamid et al-shear strength of unsaturated soil interfaces

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Shear strength of unsaturated soil interfaces
Tariq B. Hamid and Gerald A. Miller
Abstract: Unsaturated soil interfaces exist where unsaturated soil is in contact with structures such as foundations, retain-
ing walls, and buried pipes. The unsaturated soil interface can be defined as a layer of unsaturated soil through which
stresses are transferred from soil to structure and vice versa. In this paper, the shearing behavior of unsaturated soil interfa-
ces is examined using results of interface direct shear tests conducted on a low-plasticity fine-grained soil. A conventional
direct shear test device was modified to conduct direct shear interface tests using matric suction control. Further, the re-
sults were used to define failure envelopes for unsaturated soil interfaces having smooth and rough counterfaces. Results
of this study indicate that matric suction contributes to the peak shear strength of unsaturated interfaces; however, postpeak
shear strength did not appear to vary with changes in matric suction. Variations in net normal stress affected both peak
and postpeak shear strength. Failure envelopes developed using the soil-water characteristic curve (SWCC) appeared to
capture the nonlinear influence of matric suction on shear strength of soil and interfaces.
Key words: soil, unsaturated, interface, shear strength.
Résumé : Les interfaces de sol non saturés existent lorsque le sol non saturé est en contact avec des structures comme les
fondations, les murs de soutènement et les tuyaux enfouis. L’interface de sol saturé peut être définie comme une couche
de sol non saturé à travers laquelle les contraintes sont transférées du sol à la structure, et vice versa. Dans cet article, le
comportement en cisaillement des interfaces de sol non saturé est examiné à partir de résultats d’essais en cisaillement di-
rect sur des interfaces d’un sol fin à faible plasticité. Un appareil conventionnel d’essais de cisaillement direct a été modi-
fié afin d’effectuer des essais de cisaillement direct sur des interfaces en contrôlant la succion matricielle. De plus, les
résultats ont été utilisés pour définir l’enveloppe de fracture pour des interfaces de sol non saturé ayant des surfaces corres-
pondantes lisses et rugueuses. Les résultats de cette étude démontrent que la succion matricielle contribue à la résistance
au cisaillement de pic des interfaces non saturée; cependant la résistance au cisaillement dépassé le pic ne semblait pas va-
rier selon la succion matricielle. Les variations des contraintes normales nettes affectent autant la résistance au cisaillement
de pic et post-pic. Les enveloppes de fractures développées avec les courbes de rétention d’eau capturent l’influence non
linéaire de la succion matricielle sur la résistance au cisaillement des sols et des interfaces.
Mots-clés : sol, non saturé, interface, résistance au cisaillement.
[Traduit par la Rédaction]
Introduction
When structural elements are in contact with unsaturated
soil, there is transfer of stress between the two materials
through a contact zone referred to herein as an ‘‘unsaturated
interface.’’ The interaction of unsaturated soils with different
structures gives rise to many unsaturated interface problems
in civil engineering (e.g., unsaturated retaining wall backfill,
foundations in unsaturated soil). Analysis of some of these
problems is dominated by interface behavior, such as skin
friction along a pile or a retaining wall. Thus, proper charac-
terization of the interface behavior is crucial for accurate
performance predictions in these cases. This is especially
true with regard to interface strength properties used in
stability analyses.
During shearing to failure, the interface acts as a stress-
concentration zone subject to large strain variations due to
extreme displacement gradients (Navayogarajah et al.
1992). For this reason, among others, the mechanics of in-
terface behavior are complicated and difficult to model
mathematically. Thus, experimental observations of interface
behavior play a crucial role in advancing understanding of
this complex behavior. Several researchers have studied the
behavior of interfaces in sand (e.g., Yoshimi and Kishida
1981; Evgin and Fakharian 1996) and fine-grained soil
(e.g., Tsubakihara et al. 1993). However, the role of matric
suction in the behavior of interfaces in unsaturated soil has
received little attention. To design reliable and efficient geo-
technical structures, it is important to understand the me-
chanical behavior of unsaturated interfaces.
Research results presented and discussed in this paper
represent the first phase of ongoing research to address the
unsaturated interface problem. In particular, results of
suction-controlled direct shear tests conducted on interfaces
between an unsaturated low-plasticity fine-grained soil and
two stainless steel counterfaces, one rough and one smooth,
Received 20 September 2006. Accepted 6 January 2009. Published on the NRC Research Press Web site at cgj.nrc.ca on 7 May 2009.
T.B. Hamid1,2 and G.A. Miller. School of Civil Engineering and Environmental Science, University of Oklahoma, Norman, OK 73019,
USA.
1Corresponding author (e-mail: hamid_tariq@hotmail.com).
2Present address: GeoConcepts Engineering, Inc., 19955 Highland Vista Dr., Ste. 170, Ashburn, VA 20147, USA.
595
Can. Geotech. J. 46: 595–606 (2009) doi:10.1139/T09-002 Published by NRC Research Press
are presented and discussed. Results are used to define fail-
ure envelopes for the soil and interfaces, and possible ex-
planations for differences observed in the failure envelopes
are presented. Although the discussion focuses on strength,
shear-displacement and volume change behavior are pre-
sented and discussed to provide a complete description of
the shearing behavior.
Background
Modeling shear strength of interfaces in unsaturated soils
The strength of an interface in saturated soil under
drained shearing conditions, e.g., skin friction along a pile,
can be modeled using an equation of the following form
(e.g., Chandler 1968):
½1� tf ¼ s 0nf tan d0 þ c0a
where tf is the shear stress on the failure plane at failure or
shear strength, s 0nf is the normal effective stress to the failure
plane at failure (= snf – uwf, where snf is the total normal
stress to the failure plane at failure and uwf is the pore-water
pressure on the failure plane at failure), d’ is the interface
friction angle, and c0a is the effective adhesion intercept for
the interface.
One way to estimate the strength parameters in eq. [1] is
using drained interface direct shear tests. Equation [1] is of
the same form as the effective stress – strength equation for
saturated soil:
½2� tf ¼ s 0nf tan f0 þ c0
where f0 and c’ represent the effective stress friction angle
and cohesion intercept, respectively, such as might be ob-
tained from direct shear tests under drained loading condi-
tions on saturated soil.
For unsaturated soil, the constitutive behavior can be
modeled using two stress-state variables such as the net nor-
mal stress and matric suction. The following equation pre-
sented by Fredlund et al. (1978) is widely used (e.g.,
Escario and Saez 1986; Gan and Fredlund 1988; Oloo and
Fredlund 1996; Vanapalli et al. 1996) to model the shear
strength of unsaturated soil has the form:
½3� tf ¼ c0 þ ðsnf � uafÞtan f0 þ ðuaf � uwfÞtan fb
where uaf is the pore-air pressure on the failure plane at
failure, fb is the angle of friction with respect to matric
suction, snf – uaf is the net normal stress on the failure
plane at failure, and uaf – uwf is the matric suction on the
failure plane at failure.
The angle fb is approximately equal to f0 while the soil is
saturated; however, once the air-entry value is exceeded, fb
tends to decrease with an increase in matric suction. This is be-
cause the influence of matric suction on the intergranular
stress, and hence shear strength, depends on the interfacial
area among the air, water,and solid particles and the interfa-
cial area changes as matric suction is increased beyond the
air-entry value. The result is that the relationship between ma-
tric suction and shear stress becomes nonlinear, i.e., the angle
fb decreases as matric suction increases beyond the air-entry
value. To capture this behavior, Vanapalli et al. (1996) pro-
posed an equation to account for the variation of interfacial
area in the soil phases as matric suction is changed:
½4� tf ¼ c0 þ ðsnf � uafÞtan f0
þ ðuaf � uwfÞtan f0
q � qr
qs � qr
� �
where q is the current volumetric water content, qr is the re-
sidual volumetric water content from a soil-water character-
istic curve (SWCC), and qs is the saturated volumetric water
content from an SWCC.
Comparing eqs. [3] and [4], one can see that
tan fb ¼ tan f0½ðq � qrÞ=ðqs � qrÞ�. One very useful aspect of
eq. [4] is that, if the SWCC is available, the variation of shear-
ing resistance with matric suction can be predicted when f0
and c’ are known. Considerable experimental evidence (e.g.,
Fredlund and Rahardjo 1993) suggests that for many soils the
values of f0 and c’ are the same for both saturated and unsatu-
rated conditions. Thus, results from a saturated drained shear
test to determine f0 and c’ and from the SWCC test can be
used to predict the unsaturated shear strength without resort-
ing to the complex and time-consuming unsaturated shearing
tests. Of course, the predictions based on the SWCC will have
more uncertainty than direct determinations by unsaturated
shear strength testing. Furthermore, the SWCC selected will
have to account for the matric suction path followed in the
field (e.g., primary drainage, primary wetting).
Shear strength parameters in eqs. [3] and [4] have been
obtained using both direct shear and triaxial shear testing
equipment capable of controlling matric suction (e.g., Fred-
lund and Rahardjo 1993). It stands to reason, given eqs. [1]
and [2] are of a similar form, that the interface strength in
an unsaturated soil can be modeled using an equation simi-
lar to eqs. [3] and [4] and further that the interface shear
strength parameters can be defined using unsaturated inter-
face direct shear test results and the SWCC. For the current
study, the interface shear strength for an unsaturated soil is
modeled using the following two equations:
½5� tf ¼ c0a þ ðsnf � uafÞtan d0 þ ðuaf � uwfÞtan db
½6� tf ¼ c0a þ ðsnf � uafÞtan d0
þ ðuaf � uwfÞtan d0
q � qr
qs � qr
� �
where d’ is the interface friction angle with respect to net
normal stress, and db is the interface friction angle with re-
spect to matric suction.
The logical extension of eqs. [3] and [4] to eqs. [5] and
[6] is intuitive but, to the authors’ knowledge, its validity
has not been explored and, as mentioned previously, interfa-
ces in unsaturated soil have been investigated very little
(e.g., Gachet et al. 2003). Validation of eqs. [5] and [6]
through laboratory experimentation is the first step in ex-
tending their use to practical problems, such as the predic-
tion of skin friction along piles in unsaturated soils and
retaining walls with unsaturated backfill. This paper ex-
plores the use of eqs. [5] and [6] to model the shear strength
from a series of unsaturated direct shear tests and interface
direct shear tests conducted while controlling matric suction
and from the SWCC. Twenty seven unsaturated drained
596 Can. Geotech. J. Vol. 46, 2009
Published by NRC Research Press
shear tests were conducted for soil, with rough and smooth
interface conditions, and using three magnitudes of net nor-
mal stress and matric suction. In addition, one series of three
saturated tests was conducted for the rough interface for
comparison, and SWCC data were obtained. Although inves-
tigating a broader range of stress conditions would have
been desirable, as discussed at various points in this paper,
it was not possible given the duration of the project. How-
ever, as shown in this paper, sufficient results were obtained
to reasonably define the failure envelopes given by eqs. [3]–
[6] and gain valuable insight into the shear strength of inter-
faces.
The analysis of shear strength data would not be complete
without observations of the volume change behavior during
testing. Throughout the testing, the total volume change and
water volume change were determined and are presented in
this paper. Since the determination of volume change is
based on measurements at the top and bottom of the sam-
ples, there is some uncertainty regarding whether these
measurements are indicative of the localized behavior in the
zone of shearing. Nevertheless, these volume change deter-
minations lend valuable insight into the shearing mecha-
nisms occurring in the zone of shearing. It is postulated in
this study that, in the direct shear testing of soil and interfa-
ces, the volumetric behavior observed during shearing repre-
sents primarily the behavior of soil in the zone of shearing.
Consider, for example, that vertical deformation was meas-
ured at the top of the specimen (i.e., not at the interface)
and used to assess total volume change. It is possible that
volume change in the soil above the shearing zone will also
cause vertical deformation; however, it is assumed that vol-
ume changes above the shearing zone are small relative to
that in the shearing zone.
In this study, no attempt was made to directly measure the
thickness of the interface. However, a review of the litera-
ture (e.g., Hu and Pu 2003) indicates that the thickness of
the interface may be assumed as five times the diameter of
soil corresponding to 50% finer (i.e., 5D50), which is consis-
tent with the findings of Uesugi et al. (1988). In this study,
the test soil has a D50 of 0.05 mm, which would give an in-
terface thickness of approximately 0.25 mm according to the
Hu and Pu (2003) definition. A detailed discussion about the
thickness of interfaces can also be found in Desai et al.
(1985).
Unsaturated interface direct shear testing
Test soil
Direct shear and interface tests were performed using a
locally available soil from central Oklahoma known as
Minco Silt. The properties of Minco Silt are presented in
Table 1. The specimens were compacted to an initial target
dry unit weight of about 15.7 kN/m3 at a moisture content of
about 20%, giving a degree of compaction of about 89%
(based on standard Proctor energy) and degree of saturation
of approximately 80%.
In this study, 27 unsaturated test samples were prepared
using the same procedure. The initial dry unit weight of
these samples was in the range of 15.4–16.0 kN/m3, and the
initial moisture content was in the range of 19.3%–21.6%.
The maximum variations (percent difference) from the
mean values were 2.0% and 5.0% for the density and water
content, respectively. The three additional specimens for sa-
turated rough interface testing fell within these ranges as
well.
Soil-water characteristic curve (SWCC) for Minco Silt
An SWCC for Minco Silt during primary drainage was
obtained in an oedometer cell equipped with pore-air and
pore-water pressure control. The sample was prepared at an
initial void ratio (eo) of 0.67, which is similar to the initial
void ratio of the shear test samples, and was tested under
zero net normal stress. The Fredlund and Xing (1994) equa-
tion was used to model the resulting behavior shown in
Fig. 1:
½7� q ¼ qs 1� lnð1þ j=jrÞ
lnð1þ 106=jrÞ
� �
1
fln½eþ ðj=aÞn�gm
� �
where j is the matric suction; jr is the matric suction at
residual water content; e is the base of natural logarithm
(= 2.71828. . .); and a, m, and n are the fitting parameters
that describe the shape of the SWCC.
Also superimposed in Fig. 1 are the volumetric water con-
tent and corresponding matric suction for direct shear and
interface direct shear specimens prior to shearing. A primary
drainage curve was also fitted through the average of these
data using the Fredlund and Xing (1994) equation, as shown
in Fig. 1, and was used in conjunction with eqs. [4] and[6]
to model the influence of matric suction on shear strength.
The parameters for the Fredlund and Xing (1994) equations
are given in Table 2. Note there is some scatter of water
content data about the best-fit SWCC (curve 2) in Fig. 1.
This is attributed to experimental variations in water content
determinations and variations in net normal stress and inter-
face conditions during various tests. It is expected that dif-
ferences in the net normal stress and different interface
conditions would have some effect on the position of the
SWCC. However, for the purpose of this paper, the average
curve shown in Fig. 1 (curve 2) provided reasonable esti-
mates of shearing resistance when used in combination with
eqs. [4] and [6], as discussed later in the paper, so no at-
tempt was made to delineate separate SWCCs for different
net normal stresses and interface conditions.
Looking at the shear test data in Fig. 1, the range of ma-
tric suction used during testing appears around the air-entry
Table 1. Typical properties of Minco Silt.
Unified soil classification LL (%) PI (%) gdmax (kN/m3) wopt (%)
Percent passing
No. 200 sieve (%) G D50 (mm)
Lean clay, CL 28 8 17.7 12.8 73 2.674 0.05
Note: G, specific gravity; LL, liquid limit; PI, plasticity index; wopt, optimum moisture content from standard Proctor compaction test; gdmax,
maximum dry density.
Hamid and Miller 597
Published by NRC Research Press
value, which is estimated at 20–30 kPa. It would be desir-
able to have additional tests at matric suctions greater than
100 kPa; but this was not possible given the project dura-
tion. Based on the SWCC test at zero net normal stress
(curve 1 in Fig. 1), the range of matric suction selected for
the shear testing appears reasonable and covers a significant
range of water contents. However, the large reduction in
void ratio and saturated volumetric water content that ac-
companied compression during application of net normal
stress during shear testing had the effect of flattening out
the SWCC (curve 2 in Fig. 1), and thus the range of volu-
metric water content is not so great. Nevertheless, as shown
in subsequent discussions, the range of matric suction used
for direct shear testing did reveal a significant influence on
the shearing behavior.
Counterfaces
Two stainless steel plates (counterfaces) were fabricated
for this study. One steel plate was 25.5 mm thick and
102 mm in diameter with rough surface geometry. Another
steel plate with a polished surface was prepared with the
same height and diameter as that of the rough steel plate. Sur-
face roughness was defined based on the roughness profile.
The maximum peak-to-valley height (Rmax) was 0.38 mm for
the rough counterface and was estimated at 0.0025 mm for
the smooth counterface. Normalized surface roughness (Rn)
as proposed by Kishida and Uesugi (1987) is defined as
½8� Rn ¼ Rmax =D50
where D50 is the grain-size diameter corresponding to 50%
finer. Based on the grain-size analysis of Minco Silt (D50 =
0.05 mm), Rn is approximately 7.6 and 0.05 for rough and
smooth steel counterfaces, respectively.
Unsaturated interface direct shear apparatus
To determine the shearing behavior of unsaturated interfa-
ces, a conventional direct shear device was modified to con-
duct the unsaturated soil and interface direct shear tests.
This included the addition of an air-pressure chamber, new
testing cells, high air-entry porous disc (HAEPD), and a
pore-water pressure control system and other modifications.
The apparatus enables application of constant matric suction
and net normal stress and can be used to test both unsatu-
rated soils and interfaces.
The axis translation technique was used to control and
(or) apply the matric suction in the soil. An HAEPD was
used to control the water pressure in the soil specimen. For
unsaturated soil testing, the HAEPD was fixed in the bottom
half of the shear box (Fig. 2). The HAEPD was glued in a
brass ring, and an O-ring was placed around the brass ring
to seal it in the lower half of the shear box. Soil samples
were prepared in the direct shear box with the HAEPD be-
low the soil. For interface testing, the HAEPD was fixed in
the top platen and placed on the top of the soil (Fig. 3).
To control the pore-water pressure and pore-air pressure
for unsaturated direct shear testing of soil, water ports were
provided in the lower half of the direct shear box, as shown
in Fig. 2. For interface direct shear testing, two ports were
provided in the top platen that holds the HAEPD, as shown
in Fig. 3. One port was connected to the water pressure vol-
ume controller, and the other port to a pore pressure trans-
ducer or diffused air volume indicator (DAVI). During the
flushing of air from the pore-water control system, this port
can be connected to the DAVI. The pore-water pressure
controller can be used to control the volume of water (i.e.,
within ±1 mm3) or pore-water pressure (i.e., within ±1 kPa).
All drainage lines consist of 3 mm diameter high-pressure
polyvinylidene fluoride (PVDF) tubing with a wall thickness
of 0.8 mm.
Pore air diffuses through water if the axis translation tech-
nique is used for a long time. In this the study, axis transla-
tion was used to apply and (or) control the matric suction in
the soil. The DAVI was used for collecting accumulated air
flushed from the back of the HAEPD. The function of the
DAVI is explained in detail by Fredlund and Rahardjo
(1993). Matric suction used during testing (20, 50, and
100 kPa) was considerably lower than the air-entry value
(300 kPa) of the HAEPD. To achieve the desired matric suc-
tion, air pressure in the range of 70–120 kPa and water pres-
sure in the range of 20–50 kPa were used. Little to no
Fig. 1. Primary drainage SWCC data for Minco Silt modeled using
the Fredlund and Xing (1994) equation. eo, initial void ratio; ua,
pore-air pressure; uw, pore-water pressure; sn – ua, net normal stress
during testing; q, saturated volumetric water content.
Table 2. Fitting parameters for the Fredlund and Xing (1994) SWCCs for Minco Silt shown in Fig. 1.
Curvea sn–ua
b (kPa) eo qs qr jr
c (kPa) a (kPa) m n
1 0 0.67 0.400 0.129 300 52 0.7 2.5
2 105–210 0.41 0.290 0.157 700 70 0.45 1.3
Note: eo is the initial void ratio of the soil at saturation prior to drainage, and qr is the residual volumetric water content
used in eqs. [4] and [6] (for curve 2 only).
aCurve numbers given in Fig. 1.
bNet normal stress during testing; range of values for curve 2 corresponds to values used during the soil and interface direct
shear testing.
cjr was estimated; for the range of matric suction of interest, the shape of the curve was relatively insensitive to this value.
598 Can. Geotech. J. Vol. 46, 2009
Published by NRC Research Press
measurable air volume diffused into the water volume meas-
uring system for a typical test duration of about 5 days.
Testing procedure
A brief description of the test procedure is described in
the following section. Additional details of the apparatus,
sample preparation, and testing procedure are given in Ha-
mid (2005) and Miller and Hamid (2005).
Application of target stresses prior to shearing
The interface direct shear box was assembled by placing
the upper half of the shear box on the counterface. Two
screws were used to hold the counterface against the upper
half of the shear box. Soil was mixed to the desired water
content, stored in a humid chamber for 24 h, and then com-
pacted in the shear box to the required density. The compac-
tion was accomplished by tamping the soil in two layers. In
this study, all the samples were prepared at nominally the
same initial moisture content (about 20%) and dry density
(15.7 kN/m3). This is important to avoid differences in the
compacted sample fabric that can result from different com-
paction moisture contents.
Prior to applying target matric suction and net normal
stress, the specimen was compressed under a vertical stress
of 35 kPa, and the vertical deformation was recorded for ap-
proximately60 min, during which time the specimen height
became nearly constant. This step was necessary to generate
the lateral stress needed to maintain the position of the
upper half of the shear box when it was raised. When com-
pression under the initial vertical load was completed, the
screws holding the halves of the shear box together were
loosened and removed from the air pressure chamber using
a magnetic pick-up tool. The top half of the shear box was
raised by turning the four raising screws, which were then
reversed to eliminate contact between the screws and the
box. In this way, there was no contact between the upper
half and lower half of the shear box. A gap of approxi-
mately 0.6 mm was used, which is in the range of 10–20
times the median diameter of Minco Silt (D50 = 0.05 mm).
After initial soil compression and separation of the shear
box, the air chamber was sealed.
The target net normal stress was achieved by applying ad-
ditional air pressure and vertical load in increments of
35 kPa. Vertical strain associated with an increase in net
normal stress occurred fairly rapidly, with about 90% of the
vertical strain occurring within 5 min after application of the
net normal stress. Once the target net normal stress was
achieved, target matric suction (i.e., difference between the
target pore-water pressure and pore-air pressure) was applied
to the specimen by increasing the air and water pressures.
Note that since air pressure acts above and below the top
cap, an increase in air pressure does not affect the net nor-
Fig. 2. Cutaway cross-section view of the soil shear box (raising screws not shown).
Fig. 3. Cutaway cross-section view of the interface shear box (rough counterface shown).
Hamid and Miller 599
Published by NRC Research Press
mal stress except for a small correction needed to account
for the difference in air pressure above (outside the cham-
ber) and below (inside the chamber) the vertical load piston.
A period of equalization followed the application of target
suction prior to shearing. Application of the initial net nor-
mal stress increment of 35 kPa created significant compres-
sion of the sample, causing the degree of saturation to
increase to approximately 100%. During equalization, the
water content decreased due to an increase in matric suction,
starting from a nearly saturated condition. Thus, for the pur-
pose of analyzing results, the matric suction stress path was
assumed to follow the primary drainage path given by
SWCC curve 2 shown in Fig. 1. A separate specimen was
prepared for each combination of matric suction and net
normal stress used during the test program.
Prior to shearing, each sample was allowed to come to
equilibrium at the required net normal stress and matric suc-
tion. Equalization of the specimen was considered complete
when there was no appreciable change in the water content
or vertical strain. An appreciable change in water content
was defined as a change in water content greater than ap-
proximately 0.2% in about 24 h (i.e., Dw ‡ 0.2%, where w
is the water content). During equalization, the change in vol-
ume of water and the change in specimen height were re-
corded.
Figure 4 shows the variation of w and degree of saturation
(S) at different stages of testing and that all specimens were
prepared at approximately the same water content. During
initial compression under 35 kPa net normal stress, water
drained from the specimen through open pore-water drain-
age lines, and the thickness of the specimen decreased. It is
observed that computed value of S increased to about 100%
(Fig. 4) in almost all cases, and w decreased (Fig. 4) during
compression under the initial application of vertical load
(i.e., prior to application of target matric suction). Following
the application of target net normal stress and matric suc-
tion, w and S both decreased at the end of equalization con-
sistent with an increase in the target matric suction values.
Figure 4 also illustrates that w and S of specimens decreased
further during the drained shearing stage.
Shearing procedure
Shearing for both soil and interface testing was achieved
using a horizontal displacement rate of 0.005 mm/min.
Shearing was accomplished during a period of approxi-
mately 36 h. A slow rate was selected to avoid changes in
pore pressures during shearing. The shearing rate selected
falls within the range of rates used by other researchers for
soil types having greater plasticity. For example, Gan and
Fredlund (1988) reported that the value of peak shear stress
of a glacial till (liquid limit (LL) = 35.5; plasticity index
(PI) = 18.7%) was unaffected for a displacement rate less
than 0.0132 mm/min. For Madrid Clay (LL = 71%; PI =
35%), Escario (1980) and Escario and Saez (1986) used a
displacement rate of 0.0084 and 0.0017 mm/min, respec-
tively. Although no testing was performed to assess the in-
fluence of displacement rate on soil behavior, the value
selected is reasonable in light of previous research, espe-
Fig. 4. Evolution of water content (w) and degree of saturation (S)
during direct shear testing. ANS, apply additional net normal stress
and suction; BS, begin shearing; BT, beginning of test; ET, end of
test.
Fig. 5. Typical behavior observed during shearing of the soil for a
matric suction of 50 kPa. u, displacement; v/H0, vertical or volu-
metric strain; t, shear stress; tmax, peak shear stress; tpp, postpeak
shear stress; Dw, change in gravimetric water content.
600 Can. Geotech. J. Vol. 46, 2009
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cially given that the test soil (Minco Silt) contains about
27% sand and has low plasticity (LL = 28%; PI = 8%). Dur-
ing shearing, the horizontal load, horizontal displacement,
and vertical displacement were measured and recorded at
1 min intervals.
Consistent with drained testing, the pore-water pressure
was controlled and maintained constant during shearing,
and pore-water volume change was permitted. That pore
water flowed out of the specimens during shearing is an in-
dication that drainage was occurring and supports the pre-
sumption of fully drained tests. Air pressure was also
controlled and maintained constant during shearing. Shear-
ing generally continued to a displacement of about 10 mm
or until the post-peak behavior was clearly observed.
Results of shearing
Load–displacement and volume-change behavior during
shearing
Examples of typical shear stress (t) – displacement (u)
curves from soil direct shear tests are shown in Fig. 5 for a
matric suction of 50 kPa and three different net normal
stresses. Also shown in Fig. 5 are the vertical or volumetric
strain (v/H0, where v is the vertical displacement and H0 is
the specimen height) and change in gravimetric water con-
tent (Dw) during shearing. Similar data are shown in Fig. 6
from the soil tests for a net normal stress of 105 kPa for
three levels of matric suction. Data from the rough and
smooth interface direct shear tests are presented in Figs. 7–
10. Based on Figs. 5–10, which are fairly typical of soil and
interface behavior for all levels of matric suction and net
normal stress, some important observations are noted.
(1) During shearing of the rough interface and soil, a peak
shear stress (tmax) is achieved followed by a reduction
to a postpeak shear stress (tpp). For the smooth interface,
peak and postpeak shear strength are nearly the same.
(2) Peak shear stress increases with an increase in net nor-
mal stress and matric suction for soil and smooth and
rough interfaces.
(3) Postpeak shear strength of soil, and particularly for the
rough interface, appears to be little affected by matric
suction at a given net normal stress. However, postpeak
shear stress does increase with an increase in net normal
stress at a given level of matric suction. This observation
has practical implications where postpeak shearing con-
ditions exist in the field.
(4) The curves for smooth interface exhibit a stick-slip phe-
nomenon as evidenced by the jagged nature of the
curvesfollowing yielding. This is typical of laboratory
shearing along smooth interfaces (e.g., Fakharian 1996).
(5) Total volume change during shearing of rough interfaces
and soil shows similar behavior. As shearing begins,
Fig. 6. Typical behavior observed during shearing of the soil for a
net normal stress of 105 kPa.
Fig. 7. Typical behavior observed during shearing of the rough in-
terface for a matric suction of 50 kPa.
Hamid and Miller 601
Published by NRC Research Press
compression behavior is observed, followed by dilation
until the peak shear stress is reached. Generally, the
amount of compression increases and dilation decreases
as the net normal stress increases. The opposite effect is
observed when matric suction increases.
(6) For the smooth interface, only compression behavior is
observed during shearing. It is difficult to discern the in-
fluence of net normal stress and matric suction on the to-
tal volume change behavior during shearing of the
smooth interface, since the differences in volume change
behavior are small. It appears that a slightly greater
amount of compression may occur during shearing at
the lowest net normal stress and matric suction, which is
opposite to the results of soil and rough interface tests.
(7) Overall, trends in water content changes are less obvious
from test to test as compared with trends in total volume
change. In all cases, some water drained out of the speci-
men during shear. Changes in water content were in the
range of –0.1% to –1.4% (range of Dw). The amount of
drainage was greatest for the soil and least for the
smooth interface. Based on the observation of changes
in water content during shearing, it is postulated that re-
arrangement and the sliding of soil grains resulted in the
disruption and possibly the rupture of menisci between
soil grains and between soil and steel plates. The disrup-
tion of menisci caused a tendency for increasing pore-
water pressure and decreasing suction. Due to the ten-
dency for increasing pore-water pressure, the water flo-
wed from the sample and water volume decreased while
the specimen was shearing.
Failure envelopes for peak shear strength
Peak shear stress (tmax) from soil and rough and smooth
interface tests, respectively, is plotted against net normal
stress in Figs. 11, 12, and 13 and against matric suction in
Figs. 14, 15, and 16. The solid lines in Figs. 11, 12, and 13
represent the best-fit parallel lines and were used to deter-
mine values of f0 and d’. It was assumed that the change in
shear strength with respect to net normal stress was inde-
pendent of matric suction (i.e., f0 and d’ are constant). This
assumption is consistent with many published observations
with respect to f0, as discussed previously, and seems appro-
priate based on the test data obtained. Also shown in Fig. 12
are the results of saturated tests (ua – uw = 0) for the rough
interface. These results are consistent with those from tests
at increasing matric suction and generally support the as-
sumption that d’ is constant.
Results from some of the tests shown in Figs. 14–16
exhibit a nonlinear relationship between matric suction and
shear strength. Therefore, the Vanapalli et al. (1996) model
(eqs. [4] and [6]) was used to develop the nonlinear failure
envelopes shown in Figs. 14–16. This was done using the f0
Fig. 8. Typical behavior observed during shearing of the rough in-
terface for a net normal stress of 105 kPa.
Fig. 9. Typical behavior observed during shearing of the smooth
interface for a matric suction of 50 kPa.
602 Can. Geotech. J. Vol. 46, 2009
Published by NRC Research Press
and d’ values obtained from Figs. 11–13 in combination with
the SWCC (curve 2 in Fig. 1) and adjusting the values of c’
and c0a to achieve the best fit. Values of strength parameters
determined in this way are shown in Table 3. Also shown
for comparison are values obtained from using a linear
model (eqs. [3] and [5]), i.e., assuming fb is constant for
the range of matric suction used during the testing.
Based on the failure envelopes and the interpreted
strength parameters, several noteworthy observations are
made.
(1) The peak friction angle with respect to net normal stress
is similar for the soil and rough interface; however, the
corresponding friction angle for the smooth interface is
considerably lower. As in the case of soil, it appears
that the failure plane in the rough interface is dominated
by soil-to-soil shearing and gains significant strength
through dilation. In the case of the smooth interface, it
appears that the failure plane develops between the metal
counterface and soil, which has significantly lower
shearing resistance.
(2) Based on the linear model (eqs. [3] and [5]), the friction
angle with respect to matric suction is greatest for the
Fig. 10. Typical behavior observed during shearing of the smooth
interface for a net normal stress of 105 kPa.
Fig. 11. Peak failure envelope projections in the net normal stress –
shear stress plane from unsaturated soil direct shear tests. f0, effec-
tive stress friction angle.
Fig. 12. Peak failure envelope projections in the net normal stress –
shear stress plane from unsaturated interface direct shear tests with
a rough counterface. d’, interface friction angle.
Fig. 13. Peak failure envelope projections in the net normal stress –
shear stress plane from unsaturated interface direct shear tests with
a smooth counterface.
Hamid and Miller 603
Published by NRC Research Press
soil, followed by that for the rough interface and then by
that for the smooth interface, as shown in Table 3. For
the soil and rough interface, the shearing largely takes
place along a soil-to-soil shear plane. As shearing takes
place, the air–water menisci along the failure plane are
distorted and may reduce the effectiveness of the matric
suction contribution to strength. It appears that, at fail-
ure, this distortion and resulting change in local matric
suction along the failure plane are more severe in the
case of the rough interface, thus resulting in a lower fb
value. Another possibility is that strength was affected
by local variations in moisture content and fabric that re-
sulted when the soil was compacted for the soil and
rough interface tests.
(3) The nonlinear representation of the failure envelopes de-
veloped using eqs. [4] and [6] and the SWCC (curve 2)
shown in Fig. 1 seems to fit the data well. Additional
data at greater matric suction would help to validate the
model even further. For the range of matric suctions
used in the testing (20–100 kPa), either the linear model
or the nonlinear model would be reasonable for predict-
ing shear strength. The real advantage of the nonlinear
model would become apparent at matric suctions much
greater than the air-entry value, which appears to be in
the range of 20–30 kPa. The influence of matric suction
on shearing resistance was least pronounced for the
smooth interface. Assuming the failure plane developed
between the metal surface and soil particles, the contri-
bution of matric suction would result from menisci
formed between the smooth counterface and soil parti-
cles immediately above. It is possible that the smooth,
flat counterface allowed for menisci with larger radii to
develop, relative to menisci between particles. This may
have resulted in lower local matric suction along the in-
terface relative to internal soil.
(4) The value of c’ of soil is greater than c0a of the rough and
smooth interfaces. However, c0a is greater for the smooth
interface than for the rough interface. That c’ of soil is
greater than c0a of the rough interface, even though the
friction angles (f0 and d’) are the same for both, indi-
cates the presence of the interface causes a constant re-
duction in shearing resistance independent of stress
state. This might be partly explained by differences in
volume change behavior; soil shows consistently more
dilation than the rough interface during shearing under
similar stress conditions. Thatc0a of the smooth interface
is greater than that of the rough interface may also be
Fig. 14. Peak failure envelope projections in the matric suction –
shear stress plane from unsaturated soil direct shear tests. Open
diamonds represent intercepts at zero net normal stress in Fig. 11.
fb, angle of friction with respect to matric suction.
Fig. 15. Peak failure envelope projections in the matric suction –
shear stress plane from unsaturated interface direct shear tests with
a rough counterface. Open diamonds represent intercepts at zero net
normal stress in Fig. 12.
Fig. 16. Peak failure envelope projections in the matric suction –
shear stress plane from unsaturated interface direct shear tests with
a smooth counterface. Open diamonds represent intercepts at zero
net normal stress in Fig. 13.
604 Can. Geotech. J. Vol. 46, 2009
Published by NRC Research Press
due to the fact that yielding and failure occur nearly si-
multaneously for the smooth interface at a much lower
shear displacement than that for the rough interface. It
is possible some physical–chemical bonding is present
between the smooth steel counterface and soil and that
this component of shearing resistance is largely undis-
turbed at yielding, since displacements are relatively
small. Such bonding may be largely destroyed along the
failure plane in the rough interface due to slippage and
grain rearrangement that occurs after yielding before the
peak shear stress is reached. These explanations are
speculative and leave room for additional interpretation;
additional research is needed to look further into this be-
havior.
Failure envelopes for postpeak shear strength
The effect of matric suction on postpeak shear strength of
soil and rough interfaces is demonstrated in Figs. 17 and 18,
respectively. In the case of the smooth interface, there was
not much difference observed in peak and postpeak strength.
For the soil, the matric suction appeared to have some effect
on postpeak strength in some tests, whereas in others it did
not. This can be seen by the scatter in data points plotted in
Fig. 17. The scatter is random and suggests that matric suc-
tion, on average, does not impact postpeak strength. Further-
more, the rough interface data were most conclusive in
showing that matric suction had little or no effect on the
postpeak shear strength for a given net normal stress. This
is evidenced by the tight cluster of data points at each nor-
mal stress in Fig. 18 and by the postpeak behavior observed
in Fig. 6.
Collectively, the failure envelopes for postpeak shear
strength suggest that, unlike maximum shear strength, post-
peak shear strength does not change with a change in matric
suction at a given net normal stress (at least for the range of
matric suction investigated). A possible explanation for this
phenomenon is that, following the peak shear strength dur-
ing continued shearing, there is a complete disruption to the
air-water menisci along the failure surface. This disruption,
which may include the breaking of menisci, reduces the
influence of matric suction to a negligible level along the
failure plane. Hence, the postpeak strength is primarily de-
pendent on the frictional resistance resulting from the net
normal stress. This behavior has significant implications for
the stability of sliding soil masses under post-peak stress
conditions.
Conclusions
Based on direct shear testing of soil and rough and
smooth interfaces using compacted, low-plasticity clayey
silt, the following conclusions are presented:
(1) Matric suction and net normal stress influence the peak
shearing resistance of both smooth and rough interfaces.
For the range of matric suction investigated, both linear
and nonlinear failure envelopes provide a reasonable
model for peak shear strength of unsaturated soil and in-
terfaces.
(2) The angle of friction with respect to net normal stress
was similar for the soil and rough interface. Both of
these were considerably larger than the corresponding
friction angle for the smooth interface.
(3) Using the linear strength model, the angle of friction
with respect to matric suction was greatest for the soil,
followed by those for the rough and smooth interfaces.
Table 3. Failure envelope peak strength parameters for soil and rough and smooth interfaces.
Linear fit eqs. [3] and [5] Nonlinear fit eqs. [4] and [6]
Test type f0, d’ (8) fb, db (8) c’, c0a (kPa) c’, c0a (kPa)
Soil 34.5 26.6 12 12
Rough interface 34.5 18.6 3 0
Smooth interface 15.0 8.9 11 9
Fig. 17. Postpeak failure envelope projections in the net normal
stress – shear stress plane from unsaturated soil direct shear tests.
Fig. 18. Postpeak failure envelope projections in the net normal
stress – shear stress plane from unsaturated interface direct shear
tests with a rough counterface.
Hamid and Miller 605
Published by NRC Research Press
This may be due to local differences in matric suction
and soil fabric along the interface as well as differences
in the evolution of local matric suction during shearing
due to disruption to the air–water menisci along the fail-
ure plane.
(4) The cohesion intercept of the soil was greater than the
adhesion intercepts of the rough and smooth interfaces;
however, the value for the smooth interface was greater
than that for the rough interface. These differences
maybe due partly to differences in volume change beha-
vior and the physical–chemical interaction along the fail-
ures planes and near the counterface.
(5) Generally, it appears that at a given net normal stress,
the postpeak shear strength for soil and interfaces is lar-
gely unaffected by matric suction. The data were parti-
cularly conclusive in the case of the rough interface. It
appears that during shearing beyond the peak shear
stress, the air–water menisci are completely disrupted,
resulting in a negligible strength contribution due to ma-
tric suction.
Acknowledgements
This study was conducted at the University of Oklahoma
(OU), Norman, Okla., and was partly supported by the Na-
tional Science Foundation (NSF) under grants 0079785 and
0301457. The authors are grateful to the NSF for the finan-
cial support. T. Hamid would also like to acknowledge the
financial support provided by the School of Civil Engineer-
ing and Environmental Science throughout his study at OU.
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