Geotextiles and Geomembranes 29 (2011) 472e482
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Geotextiles and Geomembranes
journal homepage: www.elsevier.com/locate/geotexmem
A new procedure for measuring geosynthetic friction with an inclined plane
L. Briançon a, *, H. Girard b,1, J.P. Gourc c, 2
a
Cnam Paris, 2 rue Conté, 75141 Cedex 03, France
Cemagref, 50 avenue de Verdun, Cestas 33610, France
c
LTHE, University Joseph Fourier, 38041 GRENOBLE Cedex 9, France
b
a r t i c l e i n f o
a b s t r a c t
Article history:
Received 16 October 2010
Received in revised form
2 March 2011
Accepted 1 April 2011
Available online 13 May 2011
A method for the determination of the friction angle of geosynthetic interfaces (specifically those in
contact with soils at very low normal stresses) using an inclined plane is described by the European
Standard EN ISO 12957-2. Following this “Standard Displacement Procedure”, the friction angle of
a geosynthetic interface is determined using a displacement criterion between the tested geosynthetics.
However, the “Standard Displacement Procedure” seems to be poorly suited for many interfaces. Herein,
a new procedure is proposed, called the “Force Procedure”, which consists of measuring the force
required to restrain a box on top of the interface beyond a limiting value of sliding displacement. With
the “Force Procedure”, the friction is determined from the curve of friction mobilization versus planeinclination. The angle determined with the “Force Procedure” is not sensitive to the conditions of the test
and is more representative of real-world conditions, as it takes into account displacements observed in
the field. Based on the results of this study, it seems reasonable to suggest a revision of the EN ISO
12957-2 standard testing procedure.
Ó 2011 Elsevier Ltd. All rights reserved.
Keywords:
Inclined plane
Friction
Laboratory test
Standard
1. Introduction
Recent years have seen a large growth in engineering solutions
involving the implementation of geosynthetic materials. One of the
key issues concerning the mechanical characterization of geosynthetics is the friction at soil-geosynthetic and geosyntheticegeosynthetic interfaces. An estimation of this property is
very important in optimizing construction solutions such as slopeliner systems, which are very commonly used in landfills and
basins, for instance. Many failures of slope-liner systems have been
observed (Koerner and Soong, 2000), often due to a poor characterization of interfacial friction (Wu et al., 2008) or incorrect
choices in the construction sequence (Blight, 2007).
Liner systems used on slopes combine different components
such as geosynthetics and soil (Fig. 1). The liner system is designed
by taking into account the different functions and efficiencies of the
materials. These components are arranged to serve one or more
purposes, including water tightness (geomembranes, GMB),
drainage (geocomposites for drainage, GCD), reinforcement
* Corresponding author. Tel.: þ33 158 808 758; fax: þ33 140 272 428.
E-mail addresses: laurent.briancon@cnam.fr (L. Briançon), hugues.girard@
cemagref.fr (H. Girard), gourc@ujf-grenoble.fr (J.P. Gourc).
1
Tel.: þ33 575 890 800.
2
Tel.: þ33 687 860 873.
0266-1144/$ e see front matter Ó 2011 Elsevier Ltd. All rights reserved.
doi:10.1016/j.geotexmem.2011.04.002
(geotextiles, GTX or geogrids, GGR) and protection (cover soils or
geotextiles). Designing such systems for slopes requires a preliminary assessment of the friction angles between the different layers,
as the preferential critical sliding planes are generally located at the
interfaces between these materials.
Direct shear box and inclined plane experiments have been
applied in the definition of two standard tests (EN ISO 12957-1,
2005; EN ISO 12957-2, 2005) recommended for the characterization of interfacial friction behavior, each with its own specifications
and features. Several studies drawing a parallel between ‘‘inclined
plane’’ apparatus and shear boxes have shown that the inclined
plane is a more appropriate device for the characterization of
geosynthetic friction under normal stresses lower than 10 kPa,
whereas the direct shear box performs well under higher normal
stresses (Girard et al., 1990; Koutsourais et al., 1991; Izgin and
Wasti, 1998; Lala Rakotoson et al., 1999; Wasti and Ozduzgun,
2001; Palmeira et al., 2002; Palmeira, 2009; Reyes-Ramirez and
Gourc, 2003; Wu et al., 2008). However, a more detailed observation shows that the conditions when unrolling and laying geosynthetics and the method of placement of the cover soil can be
significantly different, causing variability in interfacial displacements; consequently, the sensitivity of the actual friction at the
interfaces to different field conditions must be considered.
The interface considered in this manuscript is between geomembrane and geotextile (or geocomposite) which is supposed to
be the critical interface of the system: the upper geotextile is
L. Briançon et al. / Geotextiles and Geomembranes 29 (2011) 472e482
473
Fig. 2. Free-body diagram for the “Standard Displacement Procedure”.
Fig. 1. Typical liner system on soil.
responsible for the stability of the cover soil and the geomembrane
the water tightness. The function of the geotextile (generally
reinforced) is to sustain the cover soil. In order to limit the tensile
mobilisation of the geomembrane, a low friction value between
geotextile and geomembrane is required.
2. Background
2.1. “Standard Displacement Procedure”
The standard EN ISO 12957-2 describes a method for determining the friction angle d of geosynthetic interfaces (geotextiles
and geotextile-related products) in contact with soils at low
normal stress using an inclined plane (called also a tilting-plane)
apparatus with specific variations for geosyntheticegeosynthetic
interfaces. This method has primarily been used as a performance
test for site-specific soils, but it may also be used as an index test.
Among the many points discussed, the most relevant ones are
discussed below.
In any friction method, the normal force to the interface,
W$cosb, must be evenly applied to obtain a regular distribution of
the normal stress over the entire surface of the specimen. EN ISO
12957-2 specified that the applied normal force must be such that
the initial normal stress (for b ¼ 0) is equal to 5.0 0.1 kPa. The
plane must be equipped with a mechanism for tilting the plane
slowly and at a constant rate, i.e., db/dt ¼ 3.0 0.5 /min. The
geosynthetic (lower layer) must be fixed to the inclined plane
apparatus to limit any relative movement between the layer and
the plane. The techniques used to fix the lower geosynthetic are
sewing or gluing, using a rough support to increase the coefficient
of friction, or anchoring the layer outside the contact area.
Regarding the dimensions of the apparatus, the standard
prescribes minimum dimensions for both the upper (length,
lu ¼ 0.3 m, and width, bu ¼ 0.3 m) and lower (ll ¼ 0.4 m,
bl ¼ 0.325 m) boxes. Any other test made on different sides of the
sample or in a different direction should be made using virgin
samples. The front and rear sides of the upper box are kept
parallel, and their inclination is predetermined to be close to the
vertical during the sliding phase.
Following the “Standard Displacement Procedure”, the friction
angle dstan of the geosyntheticegeosynthetic interface is determined by measuring the inclination angle, b50, of the apparatus at
which the upper box with attached geosynthetic slides to
a displacement of u ¼ 50 mm. The friction angle dstan is then
calculated by considering a static equilibrium (Fig. 2), as follows:
Ws ,sinb50 þ Frðb50 Þ N,tandstan ¼ 0
(1a)
Ws ,cosb50 ¼ N
(1b)
Here, N is the reactive force balancing the normal component of
the weight of the soil, WS, in the upper box with rollers; the normal
component of the weight of an empty upper box, Wb, is independently balanced by the reaction of the metallic frame. A calibration
is first performed with the empty upper box to assess the corresponding tangential friction force, Fb, as follows:
Wb ,sinb Fb ¼ FrðbÞ
(2)
where Fr (b) is the resulting force required to hold back the empty
upper box.
The value of the standard interface friction angle, dstan, is
obtained combining Eqs. (1a) and (1b) to yield the following:
tandstan ¼
Ws ,sinb50 þ Frðb50 Þ
Ws ,cosb50
(3)
Eqs. (1a) and (1b) are written regarding a static analysis, thus
allowing Eq. (3) to determine the value of the standard friction
angle, dstan, by taking into account the weight of the soil contained
in the upper box (Ws), the plane-inclination angle (b50) and the
force required to restrain the empty upper box Fr (b50) for
a displacement u of the upper box equal to 50 mm.
2.2. Analysis of sliding
Gourc and Reyes Ramirez (2004) modified a standard inclined
plane apparatus (Fig. 3) to study the behavior of geosynthetic layers
on slopes and through dynamic conditions. In this context, a few
modifications were implemented in the inclined plane apparatus.
For instance, the dimensions of the upper and lower boxes were
altered to increase the length of the sliding displacement in the
slope direction. The geosyntheticegeosynthetic interface setup was
also simplified. The upper box filled with soil was replaced by
a mobile-plate device. The mobile plate is composed of a geosynthetic sample glued onto a wooden plate (lu ¼ 0.18 m and
bu ¼ 0.7 m), a metallic plate with fixed lateral guides and three
different loads consisting of metallic plates. The length of the
wooden plate, lu, was shortened to allow for the observation of
sliding up to large displacements (u). Theoretically, the configurations of the lateral guides and the rolling contact enable a total
transmission of normal stress to the geosynthetic interface and
ensure an ideal displacement in relation to the slope; the guidance
system is also assumed to be frictionless (Fr (b) ¼ 0). The dimensions of the lower box are 1.3 m in length (ll) and 0.8 m in width (bl),
and the geosynthetic layer can be attached to it by anchoring grips
or with an adhesive. The tilting velocity of the plane db/dt can be
controlled and varies between 0.5 and 4.0 /min.
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Fig. 3. Modified inclined plane apparatus used to observe dynamic conditions.
From the results using this modified setup, Gourc and Reyes
Ramirez (2004) divided the upper box sliding behavior into three
characteristic phases (Fig. 4), as follows:
- Gradual sliding: displacement u increases with inclination b,
progressively increasing or displaying a stick-slip mode (jerky
sliding)
- Phase 1 (Static Phase): The upper box is practically motionless
(the displacement of the upper box equals zero) over the
inclined plane until a critical angle, b0, is reached.
- Phase 2 (Transitory Phase): With increasing inclination beyond
b0, the upper box moves gradually downward, and the acceleration g of the upper box increases.
- Phase 3 (Non-Stabilized-Sliding Phase): At b ¼ bs, the upper
box undergoes non-stabilized sliding at an increasing speed
(constant acceleration gc), even if the plane-inclination is held
constant at bS.
For many interfaces exhibiting a gradual sliding behavior, the
standard criterion seems to be poorly suited, in particular when
Phase 2 is very long, i.e., Phase 3 occurs for sliding-displacement
values greater than the standard value u ¼ 50 mm (Gourc and
Reyes Ramirez, 2004). These authors showed that, even for
sudden sliding, the standard method is unable to yield an accurate
value of the friction angle d50 corresponding to u ¼ 50 mm because
the standard recommends a static analysis (Eq. (3)) for conditions
that are actually dynamic. An accurate relation must take into
account the dynamic conditions (i.e., the constant acceleration gc in
Phase 3); thus, the standard relations (Eqs. 1a and 1b) should be
replaced with Eqs. (5a) and (5b):
Here, b0 is defined as the plane-inclination angle at the static
limit of equilibrium, and bS is the inclination angle for nonstabilized sliding.
The observation of many displacement (u) versus inclination (b)
diagrams (Fig. 5) highlights these different behaviors before
reaching the same value of inclination, bS, where, in general, for
a displacement u ¼ 50 mm and b50 ¼ bS; consequently, the same
value of the standard interface friction angle dstan is found for either
sudden sliding or gradual sliding (Eq. (4)), as follows:
tandstan ¼
Ws ,sinbS þ FrðbS Þ
Ws ,cosbS
(4)
where Fr (bS) ¼ 0 for this inclined plane.
As indicated by Pitanga et al. (2009), Phase 2 may be one of two
types (Fig. 5):
- Sudden sliding: abrupt displacement of the upper box under
non-stabilized sliding with a nearly nonexistent Phase 2
(b0 ¼ bS)
gc
Ws ,sinb50 N,tand50 ¼ Ws ,
g
Ws ,cosb50 ¼ N
(5a)
(5b)
The value of the actual friction angle d50 in place of dstan is
similarly obtained by combining Eqs. (5a) and (5b) to give:
tand50 ¼
Ws ,ðsinb50 gc =gÞ
sinb50 gc =g
¼
Ws ,cosb50
cosb50
(6)
where gc (m/s2) corresponds to the constant acceleration of the
upper geosynthetic component of the interface during the nonstabilized-sliding phase (Phase 3) and g (m/s2) corresponds to the
acceleration due to the gravity (g ¼ 9.8 m/s2). It is worth noting that
a comparison of Eq. (3) and Eq. (6) shows that d50 <dstan, therefore,
the “Standard Displacement Procedure” systematically overestimates the friction angle.
Fig. 4. Different phases of the upper box sliding process.
L. Briançon et al. / Geotextiles and Geomembranes 29 (2011) 472e482
a
475
b
Fig. 5. Different mechanisms of sliding: (a) sudden sliding; (b) gradual sliding.
3. A new “force procedure” for friction characterization:
device and methodology
As discussed in Section 2.2, the “Standard Displacement Procedure” is unsatisfactory for determining the friction angle; however,
the dynamic approach taking into account the acceleration is not
easy because monitoring the acceleration during the friction test is
difficult. Therefore, a new test procedure was developed. Briançon
et al. (2002) proposed a variant to the “Standard Displacement
Procedure” for determining interfacial friction angle with the
inclined plane apparatus by measuring the force required to
restrain the upper box above a limiting value of the sliding
displacement ulim. This method is called the “Force Procedure” to
distinguish it from the previous one, which is called the
“Displacement Procedure” because only displacements are monitored. When acceleration is not taken into account, this is the
“Standard Displacement Procedure”.
Since 2002, experiments have been performed on many interfaces using both the “Standard Displacement Procedure” and “Force
Procedure” tests. The “Force Procedure” has been modified to
improve the feasibility and the repeatability of the test. This section
presents the new developments in determining the friction at the
geosyntheticegeosynthetic interface with the “Force Procedure”
test. This procedure could also be applied to geosyntheticesoil
interfaces (Briançon et al., 2002), but these were not studied in the
present work.
3.1. Inclined plane device
The apparatus (Fig. 6) is composed of a lower box onto which is
fitted an upper box. The upper box can move along a system of wheels
on rails located on either side of the lower box. The upper box was
generally filled with a 30-cm thick layer of soil as a load. In the present
test, a rigid plate was fixed onto the lower box. The frictional interface
of 1 m2 (bu ¼ 1m, lu ¼ 1m, bl ¼ 1.2 m, ll ¼ 2 m) made it possible to
conduct tests on geosynthetic samples of large dimensions.
The geosynthetics were placed between the two boxes.
Depending on the interface to be tested, they were either attached
to the upper box or fixed to anchoring grips on the lower box. The
space between the two boxes is adjustable, thus enabling the
testing of Geosynthetic Liner Systems of varying thickness and
composed of one to four geosynthetics. A computer-controlled
Fig. 6. Inclined-plane apparatus used for the new procedure.
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L. Briançon et al. / Geotextiles and Geomembranes 29 (2011) 472e482
Fig. 7. Sketch of the different steps of the “Force Procedure” test.
motorized winch manages the tilting of the plane at variable
controlled lifting rates (db/dt ¼ 0.5e3.5 /min). The Standard
Procedure EN ISO 12957-2 can be applied with this inclined plane,
and other procedures have been developed for both dry and wet
conditions (Briançon et al., 2002).
3.2. Description of the “force procedure”
The upper box is linked to the inclined-plane frame by means of
a loose cable (Fig. 7), and a force sensor is connected between the
frame and the cable. Upon reaching a predetermined value, ulim, of
the upper box displacement corresponding to an inclination
b ¼ blim, the cable is stretched, and the force F (b) required to
restrain the upper box filled with soil is measured.
The test consisted of three steps (Fig. 7):
- Step 1 corresponds to the static state of the upper box with
respect to the lower plane during the tilting process (b < b0).
- Step 2 corresponds to the transitory state; the upper box slides,
gradually or suddenly, until the stretching of the cable corresponds to ulim (b0 b blim).
- Step 3 corresponds to the stretched condition of the cable after
the sliding; here, the variation of F is monitored during the
continuous tilting process (b > blim). The upper box can be
considered to be in a static state with respect with the lower
box if the elongation of the cable under the tensile force F is
neglected.
The analysis of the free-body diagram (Fig. 8) for the tested
interfaces during Step 1 (in which static conditions are checked)
and Step 3 (in which pseudo-static conditions are checked) leads to
the following equilibrium conditions:
Ws ,sinb þ FrðbÞ N,tand FðbÞ ¼ 0
(7a)
Ws ,cosb ¼ N
(7b)
tand ¼
Ws ,sinb þ FrðbÞ FðbÞ
Ws ,cosb
(8)
where Fr (b) is the force required to restrain the empty upper box in
relation to the plane angle, Ws the weight of soil contained in the
upper box and F (b) is the additional force required to restrain
the upper box filled with soil. For both static Steps 1 and 3, d is the
variable friction angle at the interface.
During the transitory Step 2, in which the upper box is sliding,
the analysis of the free-body diagram for the tested interfaces leads
to the following equilibrium conditions:
Ws ,sinb þ FrðbÞ N,tand FðbÞ ¼ Ws ,
g
(9a)
g
Ws ,cosb ¼ N
tand ¼
(9b)
Ws ,ðsinb g=gÞ þ FrðbÞ FðbÞ
Ws ,cosb
(10)
As the acceleration g of the upper geosynthetic component is
not measured, it is not possible to determine the value of the friction angle d even if the tensile force of the cable F (b) is monitored
continuously during the test.
3.3. Results with the new procedure
3.3.1. Presentation of the results
Several examples using different geotextileegeomembrane
interfaces (with the former generally in the upper position) are
presented in Section 3.3.7. As noted above, it is not possible to
calculate the variable friction angle d during Step 2, as the acceleration g is not monitored. For greater convenience, the friction is
represented as the value of l, which is plotted along the entire
friction test, as follows:
tanl ¼
Ws ,sinb þ FrðbÞ FðbÞ
Ws ,cosb
(11)
Table 1
Physical properties of the tested geosynthetics.
Geosynthetics
Characteristics
Composition
Thickness under
2 kN/m2
Mass per unit
area
Fig. 8. Free-body diagram for the “Force Procedure” test.
Geomembranes
Property
Thickness under
2 kN/m2
Surface
Unit
mm
g/m
2
Unit
mm
nwn(R)
nwn
þ PET
yarns
1.45
nwn(P1)
nwn endless
fibers
nwn(P2)
nwn
short fibers
nwh
nwh
2.5
2.8
0.59
260
400
300
220
PVC
1.5
HDPE
2
PP
1
EPDM
1.14
smooth
smooth
smooth
smooth
L. Briançon et al. / Geotextiles and Geomembranes 29 (2011) 472e482
477
Here, tan l is the only parameter that it is possible to evaluate
during the entire test.
During Steps 1 and 3; tanl ¼ tand
(12)
During Step 2; tanl ¼ tand þ g=ðg:cosbÞ
(13)
3.3.2. Geosynthetics used for the tests
The performance of the new procedure was validated on many
interfaces, including those between the following:
Fig. 9. Standard procedure applied on interfaces illustrating both sliding behavior.
- four smooth geomembranes: a polyvinyl chloride geomembrane (GMBPVC), a high-density polyethylene geomembrane (GMBHDPE), a polypropylene geomembrane
(GMBPP) and an ethylene/propylene/diene terpolymer geomembrane (GMBEPDM),
- four geosynthetics: a reinforced geocomposite consisting of
non-woven, needle-punched and knitted PET yarns on top
Fig. 10. a. Measurement during the “Force Procedure” test for sudden sliding. b. Graphic analysis of the “Force Procedure” test for sudden sliding (example of friction between
GMBHDPE and GTXnwn(R)).
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L. Briançon et al. / Geotextiles and Geomembranes 29 (2011) 472e482
Fig. 11. a. Measurement during the “Force Procedure” test for gradual sliding. b. Graphic analysis of the “Force Procedure” test for gradual sliding (example for friction between
GMBPP and GTXnwn(R)).
(GTXnwn(R)), two non-woven needle-punched geotextiles
GTXnwn(P1) and GTXnwn(P2) and a non-woven heated geotextile
GTXnwh. The physical properties of these geosynthetics are
given in Table 1.
Smooth geomembranes have been used for all tests since in the
landfill cover system it is usual to lay out a smooth geomembrane
under a reinforcement geotextile (or a geocomposite drain) to
obtain a maximal tensile force in the geotextile and to minimize the
tensile force in the geomembrane.
All the products are tested in the machine direction and for the
reinforced geocomposite GTXnwn(R), the side with PET yarns has
been tested.
All interfaces are tested with the standard procedure to compare
the result with the force procedure. Two interfaces are presented
(Fig. 9) to illustrate both sliding behaviors:
- gradual sliding with GMBPP/GTXnwn(R) interface,
- sudden sliding with GMBHDPE/GTXnwn(R) interface.
3.3.3. Analysis in the case of sudden sliding
Fig. 10 presents an example of sudden sliding (Fig. 5a) for an
interface between a GMBHDPE and a reinforced non-woven,
needle-punched fabric, GTXnwn(R). For the “Force Procedure”
test, the force F(b) and the displacement u of the upper box were
measured (Fig. 10a). From these measures, the parameter l,
calculated from (Eq. (11)), is plotted versus the plane-inclination
b (Fig. 10b). In this example (Fig. 10), the length of the cable was
adjusted to obtain ulim ¼ 100 mm. From (Eq. (11)) and (Eq. (12))
with F (b) ¼ 0, the variable friction angle d can be calculated
during all of Step 1.
3.3.3.1. Step 1. During Step 1, (b < b0) and the mobilization of
friction is partial; as the driving forces (Ws$sinb þ Fr (b)) are less
than the maximal resistant forces (Ws$cosb$tand), the value of l
increases to a peak corresponding to the beginning of the force
F (b) increase. It is possible to define a first friction angle d0
corresponding to the initialization of the sliding for b ¼ b0 as
follows:
L. Briançon et al. / Geotextiles and Geomembranes 29 (2011) 472e482
479
Fig. 12. Influence of the displacement ulim on dpeak (friction between GMBEPDM and GTXnwh).
Ws ,sinb0 þ Frðb0 Þ
tand0 ¼
Ws ,cosb0
(14)
In the case of “sudden sliding”, the end of Step 1 also corresponds to the maximum value, lpeak. The force F (b) increases
suddenly (Step 2) when the sliding displacement begins, here, for
b0 ¼ 11.5 corresponding to the end of the Step 1. Thus, in this
example, for b ¼ b, d0 ¼ 15.7. In the case of sudden sliding, l ¼ lpeak
obtained for b ¼ bpeak is such that bpeak ¼ b0.
3.3.3.2. Step 2. Step 2 is not used for the analysis and the shape of the
curve during this step depends on the interface tested, as highlighted
below. The value of l evaluated from (Eq. (11)) is no longer equal to the
value of d due to the dynamic mechanical conditions (Eq. (13)).
3.3.3.3. Step 3. At the end of the sliding step (b ¼ blim), Step 3
begins; the driving forces are higher than the friction-resistant
forces, and there is a full mobilization of the friction corresponding
to a displacement ulim. The force F (b) of the cable increases to
equilibrate the difference between the driving forces and the
friction-resistant forces (Fig. 10a), and a slight additional displacement (u > ulim) is observed corresponding to the elongation of the
cable: l versus b reaches a constant value (Fig. 10b). It is worth
noting that following Step 2, there is a stabilization of the friction
mobilization. Because (Eq. (12)) is still valid here, a second characteristic parameter can be determined on the plateau (dlim ¼ llim
for b > blim) after the stabilization of the system (Fig. 10b). Here, dlim
a
corresponds to the pseudo-static phase (Step 3) beyond the
displacement ulim of the upper box (Eq. (15)) as follows:
tandlim ¼
h
i
Ws ,sinb þFrðbÞFðbÞ
for b> blim plateauvalue : step3
Ws ,cosb
(15)
In this example (Fig. 10), dlim ¼ 11.4 .
Therefore, it is possible to determine two different friction angles
from the “Force Procedure” test: d0, corresponding to the initialization of the sliding, and dlim, corresponding to the plateau value. In
contrast, for sudden sliding, d0 ¼ dstan (Section 2). For the present
tests, a cable with relatively low tensile stiffness is used to absorb the
impact after the displacement of the upper box (noticeable in
particular for brittle interfaces) at the end of step 2. During the phase
3, there is a slight increase of the relative displacement due to the
tensile elongation of the cable, but the value of the angle dlim is
independent of the corresponding displacement.
3.3.4. Analysis in the case of gradual sliding
Fig. 11 presents an example of gradual sliding (Fig. 5b) for an
interface between a GMBPP and the same non-woven, needlepunched GTXnwn(R) used for the sudden sliding example (Section
3.3.1). In this example, the length of the cable is adjusted to obtain
ulim ¼ 60 mm. As for the previous example of sudden sliding, Step 2
is defined as b0 b blim. However, unlike the case of sudden
sliding, the force F (b) gradually increases during Step 2 from the
initiation of sliding at b ¼ b0.
b
Fig. 13. Influence of the displacement ulim on the llim determination: example of friction between (a) GMBHDPE-GTXnwn(P1) and (b) GMBPVC-GTXnwn(R).
480
L. Briançon et al. / Geotextiles and Geomembranes 29 (2011) 472e482
a
b
Fig. 14. Influence of the plane-inclination-rate on the llim determination: example of friction between (a) GMBEPDM-GTXnwh and (b) GMBHDPE-GTXnwn(P1).
3.3.4.1. Step 1. The angle b0 is more difficult to define in the case of
gradual sliding than in the case of sudden sliding; it could be chosen
as a displacement of u ¼ 1e2 mm. From (Eq. (14)), the friction angle
d0 can be calculated (Fig. 11) as follows: b0 ¼ 10.8 , d0 ¼ 14.9 .
behavior; the peak angle friction could be identified as d0. On the
other hand, the gradual sliding was associated to behavior without
peak and only a limit friction angle was considered for large
displacement. This is fully compatible with the results obtained by
the force procedure:
3.3.4.2. Step 2. As the displacement of the upper box is slow, the
cable is not immediately under tension, and the force begins to
increase for inclination b0; the cable is then stretched to the point
bpeak corresponding to lpeak (Fig. 11). Unlike in the sudden sliding
case, here b0 <bpeak <blim.
3.3.4.3. Step 3. As in the previous case of sudden sliding, it is
possible to determine a second characteristic parameter on the
plateau, dlim, after the stabilization of the system for an inclination
blim (Fig. 11b); from (Eq. (15)), dlim ¼ llim ¼ 14.5 .
3.3.5. Choice of the parameter to define the friction
Apart from the case of sudden sliding, it is difficult to determine the value of the friction angle d0 corresponding to the
initialization of the sliding and the plane-inclination b0, especially
when the gradual sliding is very slow. In addition, this angle
depends on the inclination rate and is therefore not truly an
intrinsic parameter of the interface. Finally, b0 does not fit with the
definition of a limiting slope, as it corresponds only to the initiation of the sliding and to a sliding displacement of zero. It was
therefore proposed to consider only the limit friction angle dlim,
which is the only intrinsic parameter common to the different
types of sliding.
Gourc and Reyes Ramirez (2004) highlighted that for brittle
interfaces the sudden sliding was associated to a peak-residual
a
- for sudden sliding, an initial friction angle d0 is identified and
for a relative displacement ulim a friction angle dlim d0 is
determined. This angle dlim could in this case be identified as
a residual value of the friction,
- for gradual sliding, the value of the angle d0 is difficult to
evaluate but clearly close to the friction angle value for large
displacement dlim. This is consistent with the behavior without
peak proposed by Gourc and Reyes Ramirez (2004).
3.3.6. Influence of the test conditions on the value of the friction
angle dlim
Hereinafter, only the diagrams of variation in l with angle b are
presented, as these curves provide enough information to determine the variable friction angle d during Steps 1 and 3.
3.3.6.1. Influence of the displacement ulim of the upper box. For tested
interfaces, for the two types of sliding, the displacement ulim has no
influence on the value of the friction angle dlim (Figs. 12 and 13), even
if Step 2 (b0 b blim) is longer when the value of ulim increases.
Consequently, it is better to choose a small displacement ulim:
- for sudden sliding, limiting the value of ulim allows a limitation
of the impact when the cable linked to the upper box (which
exhibits an increasing displacement rate) is being stretched
b
Fig. 15. Influence of successive tests on the determination of llim: example of friction between (a) GMBHDPE and GTXnwn(P2) and (b) GMBPP and GTXnwn(P1).
L. Briançon et al. / Geotextiles and Geomembranes 29 (2011) 472e482
Table 2
Examples of friction angles determined with the Standard Procedure (dstan) and with
the “Force Procedure” (dlim).
*
481
3.3.7. Comparison of limit and standard values of the friction angle
The results for the many geosynthetic interfaces tested by the
authors with the inclined plane apparatus show that the type of
GMB used, as shown below in Section 3.3.7, governs the sliding
pattern initially. Sudden sliding occurred preferentially at interfaces
with GMBHPDE, whereas gradual sliding was observed with GMBPP
and GMBEPDM. For GMBPVC, the sliding pattern combined both
gradual and sudden sliding, with a very slow displacement until 1 or
2 mm before exhibiting sudden sliding.
A comparison of the friction angles determined from the
Standard Procedure and those determined from the “Force
Procedure” (Table 2) shows that the “Force Procedure” gave values
lower than those found with the Standard Procedure for all tested
interfaces.
4. Conclusions
* the side with PET yarns has been tested
- for gradual sliding when the sliding-displacement rate of the
upper box is very slow, it’s a way to reduce the transitory stage
in which it is not possible to determine the friction angle.
Nevertheless, this limiting displacement must be sufficient to
allow full mobilization of the friction at the interface. The tests
presented on various (smooth) interfaces and for displacements
ulim until 121 mm showed that a 20-mm displacement is required
to ensure that the friction is fully mobilized,
Indeed the selection of the value of ulim is a key point, no
noticeable influence of ulim was observed for any tested interface.
This could mean that the selected limit displacement is sufficient to
mobilize the residual friction of the interface, but this value could
be modified for other interfaces yet untested.
Once ulim is reached, there is no further relative displacement
(apart for that caused by the stretching of the cable) and therefore
unless residual conditions are established for this displacement,
there will not be.
On the other hand, the influence of the cable stiffness was not
considered in the present set of tests, but it could be interesting to
consider different stiffnesses. Here the elongation of the cable
doesn’t exceed a few mm and there is no obvious influence of this
additional displacement on the value of the friction angle d.
3.3.6.2. Influence of the plane-inclination-rate. For each interface,
the tests were performed at four plane-inclination-rates (1.3 /
min, 1.9 /min, 2.6 /min and 3.2 /min). For both types of sliding,
the plane-inclination-rate had no significant influence on the
value of the friction angle dlim ¼ llim (Fig. 14). This observation
confirms that the friction angle dlim is an intrinsic parameter of the
interface.
3.3.6.3. Influence of the succession of tests. When the same interface was tested several times, even if the value of peak angle was
modified for sudden sliding (Fig. 15a) or gradual sliding (Fig. 15b),
the limit angle dlim ¼ llim was not sensitive to the succession of
tests, except in the case of damage of the geosynthetics at the
interface. An interface tested several times may be more representative of the conditions observed in the field: in fact, large
relative displacements at the different interfaces often occur
before the completion of the construction of a geosynthetic liner
system.
A comprehensive program of tests demonstrated that the friction parameter dstan measured with the “Standard Displacement
Procedure” test overestimated the friction angle, in particular for
gradual sliding (Table 2). Moreover, the analysis of the Standard
procedure is not rigorous because a static approach is proposed for
dynamic conditions. Due to the difficulties of implementing the
Standard Procedure in dynamic conditions, in particular for gradual
sliding with very slow displacements or for jerky sliding, the “Force
Procedure” test seems to be the best procedure with which to
assess the friction angle at geosynthetic interfaces with the inclined
plane with greater accuracy.
We proposed the selection of the residual angle dlim as the key
parameter in the “Force Procedure” test for many reasons:
- The experimental conditions of the test are simple to implement, and the monitoring is easy to perform.
- This angle is not sensitive to the conditions of testing.
- This angle is the only intrinsic parameter of the interface since
it is independent of the relative displacement at the interface
ulim from a minimum value of this displacement.
- Even if it’s not totally demonstrated, the “Force procedure” is
likely to provide a value of dlim close to the residual friction
angle dres, while d0 could be close to the peak friction angle
dpeak.
The choice of the limit angle of the “Force Procedure” was also
justified by the observations in the field: as noted, large relative
displacements at the different interfaces are known to occur during
the construction of geosynthetic liner systems. Thus, the limit value
is more representative of these displacements as observed in the
field.
Some questions related to this new method are still pending:
- one remaining important question is the appropriate selection
of a value for ulim, the sliding displacement corresponding to
the tensile mobilization of the cable linked to the upper box,
- cables of different tensile stiffness should be tested,
- the application of this “Force procedure” to a large range of
geosyntheticegeosynthetic and soil-geosynthetic interfaces
must be done in the next future.
With these considerations, it seems reasonable to suggest
a revision of the EN ISO 12957-2 standard methods to take into
account the results presented herein because it was shown that the
friction angle of geosynthetic interfaces under low normal stress
can be more accurately determined with an inclined plane apparatus using the “Force Procedure”.
482
L. Briançon et al. / Geotextiles and Geomembranes 29 (2011) 472e482
Nomenclature
bl
bu
g
ll
lu
F (b)
Fr (b)
GCD
GMB
GTX
N
Ws
b
blim
bpeak
bs
b0
b50
d
dlim
dstan
d0
d50
g
gc
l
llim
lpeak
lower box width
upper box width
acceleration due to the gravity (¼9.8 m/s2)
lower box length
upper box length
Force required restraining the upper box filled with soil
resulting force to hold back the empty upper box
geocomposite drain
geomembrane
geotextile
reactive force balancing the normal component of the
weight of the soil
weight of the soil inside the upper box
inclined plane-inclination
plane-inclination angle separating step 2 and step 3
plane-inclination angle corresponding to lpeak
plane-inclination angle for non-stabilized sliding
plane-inclination angle at the static limit of equilibrium
plane-inclination angle corresponding to a upper box
displacement equal to 50 mm
friction angle
friction angle determined in step 3 in force procedure
friction angle determined by the standard procedure
friction angle corresponding to the initialization of the
sliding in force procedure
friction angle determined by the displacement procedure
taking into account the dynamic conditions
acceleration of the upper box
constant acceleration of the upper box
parameter representing the friction plotted along the
entire friction test in force procedure
parameter representing the friction determined for b ¼ blim
parameter representing the friction determined for b ¼ bpeak
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