For Review Purposes Only/Aux fins d'examen seulement
Analyses of water diversion along inclined covers with capillary barrier effects
M. Aubertin1,3,*, E. Cifuentes1, S. Apithy1, B. Bussière2,3, J. Molson1, and R.P. Chapuis1
1
Department of Civil, Geological and Mining Engineering
École Polytechnique de Montréal
C.P. 6079, Centre-ville
Montréal, QC, Canada, H3C-3A7.
2
Department of Applied Sciences
Université du Québec en Abitibi-Témiscamingue
445 boul. de l'Université
Rouyn-Noranda, QC, Canada, J9X 5E4
3
Industrial NSERC Polytechnique-UQAT Chair on Environment and Mine Wastes Management
*
Corresponding author: phone 514-3404711 #4046; fax 514-3404477;
e-mail: [email protected]
Manuscript submitted to the Canadian Geotechnical Journal
February 2008
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Analyses of water diversion along inclined covers with capillary barrier effects
M. Aubertin*, E. Cifuentes, S. Apithy, B. Bussière, J. Molson, and R.P. Chapuis
Abstract: Various types of cover systems can be used to control water infiltration into waste
disposal sites. In this regard, an interesting option is to combine different types of soil to create a
layered cover with capillary barrier effects (CCBE). A CCBE basically involves the placement of
layers that include a relatively fine-grained soil, such as silt, over a coarser material. The
difference in unsaturated hydrogeological properties between these two soils serves to impede
water percolation downward across the interface, as moisture is preferentially retained in the top
soil layer. The stored moisture can later be released by evaporation during dry spells. In sloping
areas, the CCBE also acts to promote lateral water diversion. Inclined CCBEs, however, are
relatively complex as their behaviour is influenced by numerous factors. In this paper, the authors
present the main results ensuing from a numerical investigation into the response of steeply
inclined CCBEs where the moisture retaining layer is made of silty materials. The study
evaluates the behaviour of two types of covers: one that pertains to dry climates where short term
recharge events typically control the cover performance, and one that more commonly relates to a
relatively humid climate where the analysis must encompass a longer term evaluation of moisture
distribution and flow. After a review of the physical processes and background studies, the paper
presents the results from a series of simulations which demonstrate the effect of key factors on
the diversion length of covers, including layer thicknesses, material properties and recharge rates.
The paper ends with a discussion on the practical implications and limitations of these results.
Key words: cover, capillary barrier, unsaturated flow, water infiltration, diversion length, waste
rock piles, tailings dams, silt, acid mine drainage
*
Corresponding author: phone 514-3404711 #4046; fax 514-3404477; e-mail: [email protected]
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Résumé: Divers systèmes de recouvrement peuvent être utilisés pour contrôler l’infiltration de
l’eau dans les sites d’entreposage de rejets. A cet égard, il peut s’avérer intéressant de combiner
différents types de sol afin de créer une couverture avec effets de barrières capillaires (CEBC).
Une CEBC consiste à superposer des couches qui incluent un sol à grains fins, tel un silt, sur un
matériau plus grossier. La différence des propriétés hydrogéologiques non saturées entre ces deux
sols peut alors servir à restreindre la percolation de l’eau à travers l’interface, car celle-ci est
retenue préférentiellement dans la couche supérieure. L’humidité ainsi emmagasinée peut être
libérée ultérieurement par évaporation durant les périodes sèches. Lorsque placée sur une pente,
la CEBC peut aussi favoriser la diversion latérale de l’eau. Les CEBC inclinées sont toutefois
relativement complexes car leur comportement est influencé par plusieurs facteurs. Dans cet
article, les auteurs présentent les principaux résultats d’une investigation numérique portant sur la
réponse de CCBE installées sur des pentes prononcées dans lesquelles la couche de rétention
d’eau est formée de matériaux silteux. L’étude évalue spécifiquement le comportement de deux
types de couverture: un type qui est associé principalement aux climats secs, là où des recharges
ponctuelles à court terme contrôlent usuellement leur performance, et un autre type qui touche
habituellement les climats relativement humides, avec une évaluation à plus long terme de la
distribution et du mouvement de l’eau. Après une revue des processus physiques impliqués et de
certaines études antérieures, l’article présente les résultats d’une série de simulations qui
démontrent l’effet de facteurs clé sur la longueur de diversion des couvertures, incluant
l’épaisseur des couches, les propriétés ces matériaux, et le taux de recharge. Le papier inclus
aussi une discussion des implications pratiques et les limitations des résultats obtenus.
Mots-clés: couverture, barrière capillaire, écoulement non saturés, infiltrations d'eau, longueur de
diversion, piles de stérile, digues en résidus miniers, silt, drainage minier acide
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Introduction
Cover systems are a practical means for controlling the exchange of water and/or gas at the
surface of waste disposal sites. Many different cover configurations and materials have been
considered and applied over the past 25 years, depending on their specific purpose and
environmental setting (e.g., Oakley 1987; Lutton 1987; EPA 1989; Aubertin and Chapuis 1991;
Aubertin et al. 1995; Dunn and Singh 1995; Koerner and Daniel 1997; MEND 2004, 2007). In
this regard, one of the most interesting cover designs uses a combination of various soils having
different grain size. Such layered systems, typically located above the water table under
unsaturated conditions, may induce a capillary barrier effect when a relatively fine-grained
material (such as a silty or clayey soil) overlies a coarser soil (e.g., Corey and Horton 1969;
Rançon 1972; Hill and Parlange 1972; Gillham 1984; Rasmuson and Eriksson 1986; MorelSeytoux 1992, 1994; Schackelford et al. 1994). The difference in unsaturated hydraulic properties
between the layered soils then tends to limit the downward flow of water at their interface
because the coarse-grained material is easily drained and thus typically shows a much lower
unsaturated hydraulic conductivity ku than the finer material located above it (which has more
pronounced water retention capabilities). In addition to its function in engineered covers, the
capillary barrier phenomenon is important for other practical situations, including issues that
pertain to irrigation and infiltration in natural soil strata (e.g., Iwata et al. 1988; Zaradny 1993)
and moisture distribution in stratified media such as waste rock dumps (e.g., Lefebvre et al. 2001;
Fala et al. 2005, 2006).
The authors have been using the term “cover with capillary barrier effects”, or CCBE, to
identify this type of layered cover system (Aubertin et al. 1997a; Aachib et al. 1998; Bussière et
al. 1998). CCBEs are raising considerable interest as they often represent an advantageous
alternative to other types of covers, particularly those that rely on materials having a low
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saturated hydraulic conductivity. For example, the construction of a CCBE is relatively simple
(Ricard et al. 1997), durability can be excellent particularly when built with low plasticity
materials (Aubertin and Chapuis 1991; Dagenais 2005; Bussière et al. 2007a), and the costs
involved may be substantially lower than those of other types of layered cover systems
(McMullen et al. 1997; Ricard et al. 1999; Aubertin et al. 1999). Furthermore, the ability of a
CCBE to control water influx can be comparable to, and sometimes even exceed, that of a low
saturated hydraulic conductivity cover (Wing and Gee 1994; Morris and Stormont 1997). Finally,
a CCBE may efficiently reduce gas flux at the surface, particularly under a relatively wet climate
when the moisture retaining layer can remain at a high degree of saturation (e.g., Collin 1987,
Nicholson et al. 1989; Yanful 1993). This latter aspect has been the main focus of the authors’
earlier investigations on CCBEs, which aimed at assessing the behaviour of various
configurations and materials in order to create an effective oxygen barrier for applications on
acid-generating tailings (e.g., Aachib et al. 1993, 1994, 1998; Aubertin et al. 1994, 1995). Results
have shown that hindering oxygen penetration into reactive mine wastes is an effective control
method, particularly on relatively flat areas. However, the geometry encountered on some mine
sites, such as large tailings dykes and waste rock dumps, makes it more difficult to maintain an
effective oxygen barrier along the entire sloping area because of local desaturation of the
moisture retaining layer (Aubertin et al. 1997b; Bussière et al. 1998, 2000a; 2003a). In such
cases, it may be necessary to design the cover primarily to minimize water infiltration.
This paper deals with the use of inclined CCBEs to control infiltration of water into waste
disposal sites. The main situations targeted by the analyses presented here would typically
involve waste rock piles and large tailings dykes encountered on many mine sites, and other
geometrically similar waste disposal facilities. The moisture retaining layer is made of materials
having the hydraulic properties of low plasticity silty soils, which have been shown to be
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advantageous in many ways when used in layered cover systems (Aubertin et al. 1993, 1994,
1995, 1999). The results presented below have been obtained from a series of more than 120
numerical simulations conducted to assess the behaviour of unsaturated flow in and below cover
systems. The study focuses on specific factors which can affect the diversion length of CCBEs,
including climatic conditions and precipitation rate, hydraulic properties of the materials and
cover configuration. The paper discusses the basic concepts involved in the analysis of inclined
covers, presents some of the means available to predict the behaviour of CCBEs, and includes a
summary of the main results from the numerical simulations.
Basic concepts and background studies
Water storage and diversion in covers
Various studies have shown that a CCBE can be quite effective for controlling water infiltration,
particularly under arid and semi-arid climatic conditions. In such cases, the cover is able to store
water in the fine-grained soil layer because of its high retention capacity (reflected by a relatively
large air entry value, or AEV). This soil should also have a relatively low residual water content
qr to maximise its storage and transfer capacity. The moisture accumulated in this soil layer,
following wetting events, can later be released by evaporation (or evapotranspiration) during dry
spells. Various terms, such as “store-and-release”, “alternative”, "water balance", and
"evapotranspirative" (or “evapotranspiration”), are used to identify this type of cover, which has
been investigated fairly extensively in recent years (e.g., Fayer et al. 1992; Khire et al. 1995,
2000; Williams et al. 1997; Morris and Stormont 1997, 2000; Zhan et al. 2000, 2006; Benson et
al. 2001; Fourrie and Moonsammy 2002; Scanlon et al. 2005; Shackelford and Benson 2006; also
see Session on Cover Systems in Miller et al. 2006).
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Water retention in a CCBE is mainly associated with capillary forces, which are typically
more pronounced in unsaturated soils with a finer pore structure. In a layered cover, the upper
fine-grained soil layer, located above a coarser material that easily desaturates (due to a low
retention capacity), tends to store moisture coming from the surface as it does not easily move
downward into the underlying material due to its low hydraulic conductivity at the reduced
degree of saturation. The water then accumulates above the interface until the local negative
pressure (suction) approaches the water entry value WEV (or water entry pressure) of the coarsegrained material. The WEV corresponds, on the water retention curve (WRC), to the suction y at
which water starts to penetrate significantly into the material on a wetting path; this suction is
reached at the residual water content qr of the coarse grained material (see Fig. 1). Once water
moves across the interface, it progressively increases the degree of saturation and hydraulic
conductivity of the coarser material, hence dissipating the capillary barrier effect.
The behaviour of horizontal CCBEs is quite well understood as they have been studied at
length over many years using 1D analytical solutions (e.g., Morel-Seytoux 1992), physical
models (e.g.,Yanful and Aubé 1993; Aachib et al. 1994; 1998; Aubertin et al. 1994; 1995, 1997a;
Choo and Yanful 2000; Yang et al. 2004), in situ test plots (Yanful 1993; Aubertin et al. 1997c,
1999; Scanlon et al. 2005), and 1D numerical simulations (e.g., Akindunni et al. 1991; Crespo
1994; Bussière et al. 1995; Khire et al. 1995; Aubertin et al. 1996; Aachib 1997; Simms and
Yanful 1999; Khire et al. 2000; Mohamed and Shooshpasha 2004; Shackelford and Benson
2006). Inclined layered covers have not yet been assessed with as much emphasis, therefore their
response is not as well defined. Previous studies have nonetheless indicated that dipping covers
show a more complex response (e.g., Zaslavsky and Sinai 1981; Odenberg and Pruess 1993;
Khire et al. 1995; Bouchenttouf 1996; Stormont, 1996; Aubertin et al. 1997b; Kämpf et al. 2003;
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Alfnes et al. 2004; Tami et al. 2004), which is influenced by many factors that affect their ability
to control water infiltration and/or gas flux (Bussière 1999; Bussière et al. 1998, 2000a, 2003a,
2003b).
A tilted CCBE, used as a means to control water infiltration, may take advantage of the
unsaturated soil properties to favour lateral drainage during and after wetting periods. This
drainage will complement moisture release by evaporation from the cover. In this case, the
moisture that builds up in the fine-grained material above the contact with the coarser material
tends to flow along the inclined interface (as shown schematically in Fig. 2). When there is a
significant inflow of water from the top (for example, following a large precipitation event),
moisture accumulation in the fine-grained soil layer may render it wet enough so that, at a certain
point downdip, the pressure at the interface reaches the WEV of the coarse-grained material (see
Fig. 1). Water infiltration into the latter then becomes significant at this location, where the
capillary barrier effect disappears. The location of this “point” along the slope, which is actually a
zone, is sometimes called the Down Dip Limit or DDL point (Ross 1990). The distance between
the top of the slope and the DDL point (Fig. 2) is referred to as the diversion (or effective) length
(LD) of the capillary barrier.
In inclined cover systems, which are sometimes referred to as Store-Divert-and-Release (SDR)
covers (e.g., Zhan et al. 2001a; Bussière et al. 2003b), moisture is not evenly distributed along
the slope length, which makes such CCBEs somewhat more complex to analyse. One must then
pay attention to water accumulation in specific parts of the cover system. Depending on the
intensity and duration of the precipitation, the cover system may need to manage a large amount
of water that can exceed its diversion capacity (Bussière et al. 2003b; Kampf et al. 2003;
Aubertin et al. 2006; Zhan et al. 2006). This can occur after an intense event (which may become
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the critical condition for relatively dry climates) or after a prolonged wetting sequence (which is
more typical of relatively humid climatic conditions).
Ross (1990) proposed an analytical solution to estimate the diversion length (and
corresponding diversion flow capacity) of an idealised sloping cover. Ross’ solution was
followed by a few others (e.g., Steenhuis et al. 1991; Morel-Seytoux 1994; Warrick et al. 1997;
Webb 1997; Lu and Likos 2004), which have mostly been developed from the same assumptions,
including a steady-state condition with a constant pressure (or suction) along the slope (except for
Morel-Seytoux 1994), an infinitely thick coarse-grained material layer at the base, and a deep
phreatic surface. These assumptions may, however, be unrealistic for actual field situations;
furthermore, the adopted suction distribution is not supported by other evidence obtained from
numerical and experimental results (Aubertin et al. 1997b; Bussière 1999; Bussière et al. 2007b).
The behaviour of a CCBE should also be analysed under transient conditions as steady-state is
seldom attained in actual situations (Aubertin et al. 1996; Morris and Stormont 2000; Aubertin
and Bussière 2001). Because of such limitations, specific analyses have shown that these
analytical solutions have a limited applicability in practice (e.g., Bussière et al. 1998, 2003b,
2007b). Hence, further investigation was deemed necessary with more flexible techniques to
better define the response of inclined CCBEs used to store, divert and release water.
Previous work on CCBEs
The authors and their collaborators have been conducting theoretical and experimental studies on
the behaviour and design of CCBEs for over fifteen years. The main emphasis of the initial work
was placed on the use of silty materials to create a moisture retaining layer that acts as an oxygen
barrier to limit the production of acid mine drainage (e.g., Aubertin et al. 1993, 1994, 1995;
Aachib et al. 1993, 1994; Bussière et al. 2003a, 2004).
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Additional laboratory tests were also performed with a specially developed large-scale
physical model composed of a transparent instrumented box with a rain simulator. The model
was used to investigate the diversion length of layered systems at different slope angles and for a
range of precipitation rates (Bussière et al. 1998, 2002, 2003b). The tests performed with the
inclined box showed that the capillary barrier effect along the interface between a fine sand and a
coarse gravel disappears progressively downdip, rather than at a pin-point location. The data
obtained from these tests were well correlated to unsaturated flow modelling results obtained
with SEEP/W (from Geoslope Inc). The numerical simulations predicted the diversion length
more precisely than analytical solutions for these inclined capillary barriers (Bussière 1999). The
results also indicated that the precipitation rate has a large influence on the location of the DDL
point (or zone). Such laboratory tests using physical models can be quite useful to better
understand the behaviour of inclined CCBEs (e.g., Bussière et al. 1998, 2002; see also Kämpf et
al. 2003; Tami et al. 2004), and to validate modelling tools (Bussière 1999). However, as in
column tests, they provide limited insight into the practical solutions of actual field problems
involving steeply inclined CCBEs.
The laboratory studies and corresponding numerical simulations were complemented by in
situ data obtained from instrumented sites (Aubertin et al. 1997a, c, 1999; Bussière and Aubertin
1999; Zhan et al. 2001a, b; Bussière et al. 2003a, 2006, 2007a; Molson et al. 2008). The field
results generally agreed with the numerical calculations which showed that the actual behaviour
of steeply inclined CCBEs can be quite different than that of horizontal covers. The observed
response is affected by many factors such as material properties, cover configuration and climatic
conditions (see also Alfnes et al. 2004). The large-scale field data also confirmed the slope effect
on the cover behaviour with the existence of a DDL zone, where the capillary barrier effect is
progressively reduced and where the CCBE becomes less effective for limiting water infiltration.
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The results from these investigations also highlighted the need for further (and more elaborate)
studies to optimise the design of inclined CCBEs, particularly those that aim at reducing water
infiltration. In this regard, the background studies mentioned above have shown that numerical
modelling is a very convenient tool to investigate the unsaturated flow behaviour of a CCBE
under a variety of situations.
Numerical simulations
The following sections present the main results obtained from a series of numerical analyses,
inspired by typical field cases from existing mine sites. The simulations were performed to
investigate the effect of different parameters on the performance of CCBEs used to limit
infiltration. Two distinct situations are considered in the next section. First, the study focuses on
the case of a cover installed on a waste rock pile under dry (semi-arid) conditions, and is loosely
based on a mine site located in northern Nevada, as described by Zhan et al. (2001a, b). This
series of simulations investigates the cover response following relatively short term events, which
are expected to control the design under such climates. The second situation pertains to a cover
placed on a steep slope exposed to a relatively humid climate. This case is related to an
uncovered waste rock pile constructed at a mine site located in Abitibi (Quebec, Canada), which
has also been studied for its hydrogeological properties, internal structure and general behaviour
(e.g., Aubertin et al. 2005; Fala et al. 2005, 2006; Molson et al. 2005; Anterrieu et al. 2007). A
longer term (yearly) response of the covered pile is simulated for this situation.
All simulations in this paper were completed using the commercial finite element code
SEEP/W developed by GEOSLOPE International (2002). This program uses Richards’ (1931)
equation to simulate problems in two dimensions, including variably saturated flow for steady11
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state and transient conditions. SEEP/W has been previously used by the authors for several
studies on layered covers and other similar unsaturated soil systems (e.g., Chapuis et al. 1993,
2001; Bussière et al. 1995, 2003a, 2003b; Aubertin et al. 1996; Martin et al. 2005). Other codes
have also been used for simulating related problems involving mine waste contamination and
management (Aachib et al. 1998; Molson et al. 2005, 2008; Fala et al. 2005, 2006; Abdelghani et
al. 2007), including validation of results obtained with SEEP/W.
Short term analyses
The efficiency of a CCBE under arid and semi-arid conditions is essentially controlled by the
occasional precipitation events which may exceed the storage or diversion capacity of the cover.
Since the long-term water balance for such climates is largely negative, evapotranspiration is
quite sufficient to dispose of accumulated water that is stored near the surface following the
occasional showers (e.g., Zhan et al. 2000). In this case, the critical situation that may initiate an
infiltration breakthrough is typically caused by a large storm when the accumulated amount of
precipitation that infiltrates the surface (i.e. recharge) exceeds the storage and diversion capacity
of a SDR cover (Zhan et al. 2001a). Hence, for these types of conditions, the evaluation of cover
performance should focus on these large recharge events that may exceed the short-term storage
capacity of the cover. This may be assessed by establishing the diversion length of the CCBE.
The conceptual model represents a circular, axisymmetric waste rock pile. Its height is 24.5 m,
with a base radius of 50 m and a slope angle of 40° (Fig. 3). The model and the corresponding
boundary conditions are loosely based on various piles that have been studied by the authors and
their collaborators (Aubertin et al. 2002; Apithy 2003). The mesh contains over 3200 elements,
with the mesh density adapted to improve the solution accuracy in critical zones, particularly
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where the gradients were most pronounced. Convergence and numerical stability was established
according to the procedure described by Chapuis et al. (2001).
The model contains three different materials: a homogeneous waste rock that has the
properties of a gravely soil, a silty cover material (with a thickness of 0.5 or 0.25 m, depending
on the simulation), and a 6 cm layer of drainage/runoff material. The latter is a “virtual” layer
(which would not necessarily exist in reality), introduced because SEEP/W does not consider
water accumulation on the surface; this layer was used to allow the flow of water as runoff at the
surface of the cover. In this particular case, the cover is made of only one silty material layer,
with the waste rock creating the necessary capillary barrier effect at the interface with the silty
soil (as was done with the actual cover built on the reference site; Zhan et al. 2001a, b). The
thickness of the cover layer is selected to be relatively small as this creates more critical
conditions for water storage (by reducing the void space available for moisture accumulation). A
toe drain is placed at the base of the pile which is simulated by applying a boundary pressure
equal to atmospheric pressure at the bottom of the slope (in the cover at x = 55 m and z = 0.5 m).
The water table was placed near the base of the grid (z = 0.5 m). The initial pressure head at each
node, required for transient calculations, was obtained from a steady-state simulation for which a
recharge rate R (= P – ET) of 1 mm/day was applied on top of the cover. During the transient
analyses, the top boundary condition R = P (i.e. ET = 0) ranged from 0.5 to 30 cm/day. More
details on these calculations can be found in Apithy (2003).
The water retention curve and unsaturated hydraulic conductivity function used for the waste
rock (Material 1), the silty cover materials (Materials 2a-2d), and the virtual surface layer
material (Material 3) are shown in Fig. 4. The main parameters are given in Table 1. As can be
seen, the air entry value (AEV or y a) of the waste rock is about 0.5 m of water and its saturated
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hydraulic conductivity ksat is 10-3 cm/s, and its porosity n is 0.39 (which is equal to the saturated
volumetric water content qs). On the water retention curve, it has been determined that the
residual volumetric water content, qr, is 0.06, attained at a suction (WEV) of about 8.5 m of
water. Four silty materials were considered in the analyses (Materials 2a, b, c, d) which have
saturated hydraulic conductivities ksat varying from 10-3 to 10-6 cm/s. The virtual layer material
(Material 3) has a high hydraulic conductivity at all water contents, but its ability to retain water
is very limited (with an AEV that is almost nil); this makes Material 3 very efficient for
conveying water flow, and does not tend to retain water once the flux has passed. In the
simulations, the precipitation (recharge) was applied for 5 days and the system was then allowed
to drain for 23 days. Different precipitation rates P (cm/s) were used: 5.79´10-6, 1.16´10-5,
2.31´10-5, 5.78´10-5, 1.16´10-4, 2.31´10-4, 3.47´10-4 (corresponding to 0.5, 1, 2, 5, 10, 20, and
30 cm/day, respectively, for average to very extreme events). Also, for precipitation rates of
1.16´10-4 and 2.31´10-4 cm/s, and for a cover material with a ksat of 10-4 cm/s, two cover
thicknesses were considered: 25 and 50 cm. Nearly 100 different simulations were performed in
this part of the study (Apithy 2003).
Much of the emphasis of this investigation was placed on identifying the position of the DDL
point along the slope (and identifying the corresponding diversion length LD), as it represents a
means to evaluate whether or not the cover will be able to prevent deep percolation of water into
the underlying waste (Bussière et al. 1998, 2003b). As explained above, the DDL point can be
seen as the theoretical location where the capillary barrier effect begins to disappear due to water
accumulation above the interface, and thus where water begins to infiltrate significantly below
the moisture retaining layer. The DDL location corresponds here to the point where the pressure
near the interface between the fine- and coarse-grained materials becomes equal to the WEV of
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the latter (i.e. about 85 kPa in this case). This relatively high WEV was identified conservatively
on the water retention curve of the waste rock (tested in the lab and in the field – e.g., GamacheRochette 2004; Aubertin et al. 2005) which contained a significant amount of fine-grained
particles. A high WEV implies that it is somewhat easier for suction to become lower than this
critical value, hence providing a “worst-case” scenario (with a shorter diversion length) of the
DDL location (Aubertin et al. 2006). Other possible means to define the DDL point have also
been used (Bussière 1999; Apithy 2003; Bussière et al. 2003b), but will not be presented here.
Figure 5 shows key results from the simulations, which, when extracted and treated, indicate
how the precipitation rate P influences the diversion length LD (or position of the DDL) over
time, when Silt A is used for the cover material. As can be seen, the value of LD varies between
18.2 and 23.8 m (from the top of the pile), with the greatest length corresponding to the lowest P.
The results also indicate there is a critical precipitation rate above which the DDL point starts to
move upward along the slope. In this series of calculations, the critical recharge rate R (= P) was
between 2 and 5 cm/day. When the recharge rate is less than this critical value, the cover is able
to divert water along the slope, corresponding to the maximum length as determined by the
position of the water table and by material properties. As the precipitation rate (and volume) is
increased, the water starts to infiltrate below the cover at (or near) the DDL point, so that the
diversion length LD diminishes as P increases. For P values exceeding about 5 cm/day, the
system does not reach a steady-state condition after 5 days of precipitation, and the diversion
length continues to decrease for a few days.
The evolution of the diversion length is related to the change in suction y near the surface of
the covered pile. This change in y is illustrated in Fig. 6, which shows the suction along a
vertical profile located near mid-height of the slope (only the top portion close to the cover is
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presented). This figure illustrates how the suction progressively changes near the surface during
the precipitation period of 5 days (for P = 10 cm/day). At this location, the suction in the waste
rock below the cover does not reach the WEV (= 85 kPa) so water infiltration remains negligible.
Another series of simulations revealed the influence of the saturated hydraulic conductivity of
the silty material (ksat) on the cover’s ability to limit water infiltration (Fig. 7). Four different ksat
values were used (see Table 1). The results, which present the DDL location as a function of the
cumulative precipitation (i.e. P for 5 days), show that for materials having a ksat less than (or
equal to) 10-5 cm/s, the position of the DDL point does not appear to vary with P (= R). However,
the diversion length is affected if the hydraulic conductivity is higher than this threshold value
(ksat of 10-5 cm/s). These results highlight the potential influence of ksat on the diversion capacity
of this type of inclined CCBE.
Figure 8 shows the numerical results from two cover thicknesses (25 and 50 cm of Silt B), and
with two high recharge rates R (= P of 10 and 20 cm/day) applied as boundary conditions. As can
be seen, the reduction of the diversion length (over time) is more pronounced with the thinner
cover layer. Again, shorter diversion lengths are obtained for higher P values. As expected, the
results confirm that increasing the cover thickness is a means to reduce water infiltration; this
feature is discussed further below.
Long-term analyses
The simulations presented above represent typical cases which can be used to assess limiting
situations for the application of a SDR cover under a relatively dry climate, where occasional (but
extreme) events, of fairly short duration, would control the overall efficiency and the
corresponding design.
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For a humid climate, the use of an inclined CCBE to prevent water infiltration into the waste is
less obvious, and this possibility has not been investigated much in the past. For conditions where
there is an excess of precipitation in the water budget, it can be anticipated that the diversion
capacity may be exceeded following the longer term accumulation of moisture in the cover (in
part due to the shorter duration of the dry spells). Hence, the analysis should focus on the long
term (annual) climatic regime of the site, rather than on occasional events (as was done above). In
this part of the study, various SDR cover scenarios have been analysed for climatic conditions
typical of the Abitibi-Temiscamingue region (Quebec, Canada). The climatic data introduced in
the calculations are shown in Fig. 8; somewhat similar data have also been used in other
simulations that focussed on the behaviour of a CCBE on a tailings impoundment (Dagenais et al.
2005a, b) and on internal flow and contaminant transport within unsaturated waste rock piles
(Fala et al. 2005, 2006; Molson et al. 2005; Fala 2008). The annual regime of precipitation and
evaporation given in Fig. 9 includes alternate days of positive (infiltration) and negative
(moisture loss) surface fluxes based on mean monthly climatic data. Note that there is no surface
flux during the winter months, because the surface soils are frozen.
The model represents a circular waste rock pile (or dump) with a height of 25 m, and a base
diameter of 110 m (see Fig. 10). The top surface of the pile is slightly inclined, at an angle of
about 5° (to promote runoff), while the main external slope angle is 37°. The waste rock in the
dump is considered homogeneous; its hydraulic properties have been defined from in situ tests at
a reference site, and from laboratory tests of the same material (Aubertin et al. 2005; Anterrieu et
al. 2007). The waste rock hydraulic conductivity ksat is 4.3´10-4 cm/s, its AEV is about 10 cm of
water, and its WEV is about 60 cm of water (the porosity is 0.23). The cover is made of a single
layer of silt placed at the surface of the waste rock, with a layer of coarse sandy soil added on top
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For Review Purposes Only/Aux fins d'examen seulement
to promote runoff and control erosion. The properties for the silt and the coarse sand (with
variable thickness in both cases) are, respectively: ksat = 5.0´10-5 cm/s and 9.9´10-2 cm/s; AEV @
200 cm and 10 cm of water (porosities are 0.44 and 0.36, respectively). Figure 11 shows the
water retention curves and hydraulic conductivity functions for these three materials (again with
imposed minimum conductivity values – see Ebrahimi et al. 2004, Mbonimpa et al. 2006); the
corresponding parameters are given in Table 2.
The simulations represent various scenarios and help assess the effect of changing cover
characteristics on the diversion length. Typical calculation results are shown in Fig. 12 which
illustrates how the numerical data were extracted to evaluate the observed trends. This figure
shows how the suction value just below the cover evolves over time during the year (for the base
case shown in Fig. 10, with a cover made of 1 m of sand above 1 m of silt). These suction
profiles are used to identify the DDL location (as a point), which is taken as the intersection
between the two tangents, representing the location of a sudden change of suction, as shown in
Fig. 12. This point corresponds to the DDL (distance measured from the top of the slope), where
water starts entering the coarse grained material below the silt layer. The diversion length was
also determined from preset values of the suction along the profile (corresponding to the WEV of
the coarse grained material); the two types of method gave almost similar values for LD
(Cifuentes 2006), so only the former approach is used here.
Figure 13 shows, for the base case, how the diversion length changes during the year (using
the results from Fig. 12). The results indicate that LD is progressively reduced as water from
precipitation accumulates in the cover layers. This tendency is quite different than that observed
for a dry climate (preceding section), and it confirms that the analysis of a SDR cover in a
relatively humid climate must involve a longer term evaluation.
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For Review Purposes Only/Aux fins d'examen seulement
Figure 14 shows how the diversion length is affected by the silt layer thickness (for a sand
layer thickness of 1 m), based on the calculation results at the end of the one-year climatic cycle
(i.e. in December, at the onset of winter when infiltration stops for about 4 months due to
freezing). This figure shows that a minimum thickness (of about 0.6 m in this case) is required to
divert water along the inclined CCBE. The diversion length increases with the silt layer thickness
in a non-linear manner. A quasi-plateau is reached at a thickness of about 2 m; beyond which LD
is little influenced by the silt layer thickness. For such cases, the value of LD is less than the total
length of the slope (about 39 m), which means that in parts of the inclined CCBE, some water
would percolate below the cover.
Other calculations have been conducted to assess the effect of the sand layer thickness (for a
constant silt layer thickness of 1 m), which also promotes lateral flow when there is surface
infiltration. The results are shown in Fig. 15. As can be seen, a thicker sand layer can also
augment the value of LD. In this case, there is an increase in the diversion length up to a thickness
of about 1.5 m. Again, for the situations analysed here, the diversion length would be less than
the total slope length.
Other cover characteristics have also been evaluated in the parametric study, including the
material properties, cover geometry and climatic regimes (Cifuentes 2006). The results (not
presented in detail here) show that for a humid climate, the saturated hydraulic conductivity of
the moisture retaining layer (silty soils) does not have a major impact on the value of the
diversion length. A lower ksat still favours lateral flow (as was the case in the short term analysis)
but this effect is offset by the slower drainage of the moisture retention layer, which then tends to
accumulate more water down-dip. This additional moisture storage reduces the suction at the
interface, which tends to reduce the value of LD. For instance, reducing the hydraulic conductivity
of the silt from 7´10-5 cm/s to 10-6 cm/s (and increasing its AEV by a factor of about 2, typically
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For Review Purposes Only/Aux fins d'examen seulement
reduces the value of LD by 1 to 3 m for the cases shown in Fig. 14 (i.e. a variation of less than
10% in most instances).
The additional calculations, conducted for short term and long term conditions also indicated
that the diversion length is typically shorter when the slope is less steep. A minimum inclination
angle, which depends on the material properties, pile height, and precipitation regime, is usually
required to obtain a significant diversion length. However, other factors (in addition to LD), such
as slope stability and surface erosion, would play a major role in defining the slope angle during
construction and upon closure of the pile.
Wetter years (with more precipitation) typically tend to reduce the value of LD at the end of the
calculation period (December). This indicates that analysis for the final design of a CCBE should
not only consider average climatic conditions, but also more extreme situations when more
surface water would have to be handled by the cover.
Additional results and discussion
The main results presented above indicate that a properly designed (and constructed) CCBE
can be very effective as a SDR cover to prevent percolation of water into a waste rock pile under
a relatively dry climate. There is, however, a limit to their efficiency, which is controlled by the
amount of precipitation required to significantly reduce the diversion length.
The calculation results also suggest that for the physical and climatic conditions considered
here, a two-layer cover (sand on silt) placed on a waste rock pile under a humid climate typical of
eastern Canada would not be able to totally prevent water infiltration.
The limitations imposed on the diversion length of a SDR cover do not imply, however, that a
CCBE could not play a positive role on seepage and water quality. A closer look at how water
flow occurs in covered piles indicates that deep infiltration, when it occurs, is mainly
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For Review Purposes Only/Aux fins d'examen seulement
concentrated near its external boundary, beyond the DDL point that is often close to the base of
the slope. This means that only a fraction of the total waste rock volume would be affected by
internal seepage. Also, the presence of the SDR cover, which favours lateral diversion, can
significantly reduce the total amount of water inflow. For instance, when the base case used for
the long term analyses (Fig. 10) is examined more closely, it is seen that the presence of a cover
made of 1 m of silt and 1 m of sand reduces the amount of infiltration by about 75% for one year
(when compared to the pile without a cover). In the case of thicker cover layers, this reduction is
even more pronounced and can exceed 90%. This is important because it would diminish the
amount of potentially contaminated water to be collected and treated. Furthermore, as the
infiltration can be limited to the lower part of the slope, contamination could be reduced (or even
eliminated) by reducing the quantity of reactive waste rock in the external areas of the pile
affected by deep percolation; this disposal scheme has been proposed as a prevention method to
control leachate contamination (Aubertin et al. 2002; Fala et al. 2005; Molson et al. 2005). Thus,
a CCBE may still be a viable option in such cases, for both dry and humid climates, as part of a
global strategy to control leachate quality. This is particularly relevant because other types of
covers (with geomembranes or CGLs, for instance) cannot easily be placed (and remain stable)
on the steeply inclined surfaces of many waste rock piles.
This investigation has also included simulations with other, less conventional, cover
configurations to evaluate if alternate designs could better handle the most demanding situations,
with high precipitation. This additional work included the study of different ways to increase the
diversion length (e.g., Bussière 1999; Martin et al. 2005; Cifuentes 2006); somewhat similar
work was also performed by others, including Pease and Stormont (2003). In the case of a dry
climate, where short term events are considered critical, simulations were performed on an
alternative cover configuration in which the coarse-grained material is sandwiched between two
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For Review Purposes Only/Aux fins d'examen seulement
layers of finer materials. This SDR cover configuration was conceived to promote runoff and
internal diversion at the interfaces between the various layers, thus favouring a longer diversion
length along the sloping system. The results have shown that this type of SDR cover can better
handle very high precipitation rates of short duration (a few hours to a few days) by increasing LD
(Martin et al. 2005; Aubertin et al. 2006). For humid climatic conditions, this alternate cover
geometry does not appear to be a major improvement compared to the two layer (sand on silt)
cover analysed in the previous section (Cifuentes 2006). Nonetheless, additional work is required
on this aspect before a definite conclusion can be reached.
Previous work on CCBEs used as oxygen barriers has shown that the risk of cover
desaturation in the upper parts of a sloping cover can be mitigated by adding suction breaks
(Aubertin et al. 1997a; Bussière et al. 2000b). This concept was used to develop a new type of
cut-off in the moisture retaining layer that promotes a localized accumulation of water and helps
control the magnitude of the suction in the upper parts of the cover (Maqsoud et al. 2005). A
somewhat similar concept can be used to reduce water accumulation at the interface to increase
the diversion length. This option, called a diversion trench barrier (DTB), which was also
analysed during the current project (Cifuentes 2006), would involve installing an impervious
membrane (like a geomembrane or a GCL) in the moisture retaining layer to induce upward
water flow (from the silt to the sand) at critical locations along the slope (at or upstream of the
DDL). The preliminary results obtained to date on such DTBs are encouraging, as they indicate
that such additions to the cover can increase its diversion length. However, it is too early to
conclude at this point and more work is also needed on this aspect.
The above preliminary results ensuing from the numerical simulations indicate that it can be
worthwhile to investigate less conventional cover configurations in order to maximise the amount
of water that can be diverted along a sloping CCBE. They also highlight the usefulness of
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For Review Purposes Only/Aux fins d'examen seulement
modelling for improving the conceptual design of a cover (or many other types of geotechnical
structures). As was noted by Barbour and Krahn (2004), numerical modelling should not be first
seen as a prediction tool, but rather as a means to better understand how complex systems behave
under various situations. In many cases, the actual predictive capabilities of the simulations will
be limited, because real situations often involve many different levels of complexity (in terms of
material heterogeneity, material behaviour, and boundary conditions) that are difficult to identify
and integrate into numerical models. This natural complexity may explain why the accuracy of
unsaturated flow models can vary widely when compared to monitored cover behaviour, as
mentioned by various groups in recent years (e.g., Shackelford and Benson 2006; Young et al.
2006). Nonetheless, the simulations can be quite revealing when it comes to comparing various
options and to evaluate the relative effects of specific factors. Furthermore, when the design and
construction processes are guided by numerical analyses that are well conceived and understood,
field behaviour can be fairly close to that envisioned at the design stage of a CCBE (e.g.,
Dagenais et al. 2005a,b; Bussière et al. 2006).
It should also be pointed out that some factors that may be important in particular cases have
not been taken into account in the analyses presented here. These include, for example, the effect
of hysteresis in the WRC (Maqsoud et al. 2004, 2006; Yang et al. 2004), temperature (Kampf et
al. 1995; Mohamed and Shooshpasha 2004) and chemistry (Henry 2007) on fluid properties,
localised flow (with possible fingering) at the fine-coarse material interfaces (e.g., Fala et al.
2005, 2006), time required for capillary barrier recovery after water breakthrough (Porro et al.
2001), uncertainty and variability of material properties (Young et al. 2006; Fala, 2008), and
desiccation and cracking (or freezing and cracking) of the cover material (e.g., Dagenais 2005;
Fredlund and Wilson 2006; Albright et al. 2006; Benson et al. 2007) with possible fracture
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For Review Purposes Only/Aux fins d'examen seulement
healing observed for low plasticity silts and highly swelling clays (e.g., Aubertin and Chapuis
1991; Eigenbrod 2003) .
The effect of evaporation (Wilson et al. 1997; Blight 2002; Yanful et al. 2003; Weeks and
Wilson 2005) was also not taken into account in a realistic manner. In the case of short term
analyses (for dry climates), evaporation was completely neglected (ET = 0, so P = R) as it was
considered conservative (and often realistic) to neglect evaporation during and just after large
precipitation events when the upward surface flux is insignificant. In the case of the longer term
calculations, evaporation was indirectly considered in the numerical analyses as part of the
precipitation sequence introduced in the model as recharge (given in Fig. 9). However, it is
recognised that a more detailed evaluation of the cover behaviour should involve the introduction
of evaporative fluxes as part of the calculation (rather than as an input), using the recently
developed numerical tools that are available; this approach was adopted in other parts of this
broad investigation (Dagenais 2005), and will be included in ongoing studies.
By the same token, the effect of vegetation should also be taken into account (Zhan et al.
2006). Vegetation can influence many facets of cover behaviour, due to its effects on soil
structure, pore pressure (suction) distribution, and surface flux (in terms of evapotranspiration,
albedo, temperature, etc.). In many situations, some vegetation may be required to help stabilize a
surface (particularly to resist erosion), which will certainly affect how a cover behaves. The
presence of micro-organisms in the CCBE could also affect its behaviour (Lehman et al. 2004).
Also, the effect of interface irregularities and of localised flow have not been included here,
but these aspects have been treated elsewhere (e.g., Fala et al. 2005, Fala 2008; see also Tsutsumi
et al. 2005). The effect of variable material properties (defined using a probability distribution
function) have also been evaluated elsewhere (Fala 2008; see also Young et al. 2006); such
factors may be important because other studies have shown that anisotropy of the hydraulic
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For Review Purposes Only/Aux fins d'examen seulement
properties may play a significant role on water diversion (Alfnes et al. 2004). Other aspects that
have been addressed in complementary analyses include longer term calculations (e.g. multi-year
cases by Fala et al. 2006; see also Fayer and Gee 2006), and the hydrogeochemical response of
exposed and covered reactive mines wastes when some internal seepage occurs (Molson et al.
2005, 2008).
Finally, it should be emphasized that cover performance is highly dependent on the installation
process (Ricard et al. 1997, 1999). Its efficiency may be jeopardized when the quality of
construction is not fully controlled (e.g., Adu-Wusu and Yanful 2007).
Conclusion
The results presented above illustrate how simulations can be used to investigate the response
of inclined covers with capillary barrier effects (CCBEs) which are designed to limit water
infiltration under various climatic conditions. For this purpose, the authors have used the location
of the DDL point to determine the diversion length LD of the covers. This point is identified from
the calculation results as the location where the suction in the coarse grained material, acting as
the capillary break below the moisture retaining layer, reaches its water entry value (WEV) at the
interface with the overlying layer. The results presented here show how the diversion length of a
Store-Divert-and-Release (SDR) type of layered cover is influenced by factors such as layer
thickness (which generally has a positive effect on LD), climatic conditions (LD is reduced when
recharge increases), soil properties (LD depends on both the hydraulic conductivity and water
retention capacity), and slope geometry (a more pronounced inclination angle tends to increase
LD). The results also indicate that such types of covers must be assessed in 2D and in terms of
their transient behaviour, as steady state analyses are not representative of how they actually
behave. This type of parametric study can be quite useful to evaluate the possible use of a CCBE
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For Review Purposes Only/Aux fins d'examen seulement
to prevent water infiltration into a waste disposal site. This paper relates the calculation results to
the main physical processes which govern the behaviour of sloping CCBEs and indicates how
covers can be optimised with the help of numerical simulations.
Acknowledgements
Funding for this work was provided by the Industrial NSERC Polytechnique-UQAT Chair on
Environment and Mine Wastes Management (http://www.enviro-geremi.polymtl.ca/). The
authors also thank Dr Li Li for his help in preparing the manuscript.
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40
For Review Purposes Only/Aux fins d'examen seulement
List of tables
Table 1. Main hydraulic properties of the materials used in the numerical calculations conducted
with the model shown in Fig. 4 (after Apithy 2003).
Table 2. Main hydraulic properties of the materials used in the numerical calculations
conducted with the model shown in Fig. 10 (after Cifuentes 2006).
41
For Review Purposes Only/Aux fins d'examen seulement
List of figures
Figure 1.
Water retention curves of two soils used to create a layered cover with capillary
barrier effects; when placed below the fine-grained soil 2 (with the largest air entry
value y a2), the coarse-grained soil 1 serves to limit the downward flow of water until
the suction at the interface reaches its water entry value (y r1 in this case).
Figure 2.
Schematic representation of water movement in an inclined layered cover made of
silt and sand layers, placed on a coarse-grained material (rock waste in this case).
Following a precipitation event, the water flows along the cover and breaks through
the coarse material at the DDL point where the suction reaches its WEV; this gives
the diversion length LD (adapted from Bussière 1999).
Figure 3.
Basic model of the simulated pile exposed to various surface precipitation rates.
Figure 4.
Water retention curves (a) and unsaturated conductivity functions used for the
different materials (b).
Figure 5.
Variation of the diversion length LD as a function of the precipitation (recharge) rate
(a) for different times, and evolution of LD over time for various surface recharge
fluxes (b); the simulations include 5 days of precipitation followed by a drainage
period of 23 days.
Figure 6.
Suction profiles at mid-height of the slope
Figure 7.
Evolution of the DDL point location during the 28-day simulation for different
precipitation rates (adapted from Apithy 2003).
Figure 8.
Evolution of the diversion length over time, for two cover thicknesses (25 and 50 cm)
and for two precipitation rates (10 and 20 cm/day).
Figure 9.
Distribution of precipitation and evaporation during the modelled year.
42
For Review Purposes Only/Aux fins d'examen seulement
Figure 10. Representation of the base model used for the numerical simulations; different silt
and sand layer thicknesses were considered in the calculations. The position of the
water table corresponds to the top of the toe drain.
Figure 11. Water retention curves (a) and hydraulic conductivity functions (b) for the materials
considered in the long-term simulations of CCBE behaviour.
Figure 12. Evolution of the calculated suction profiles along the slope, just below the cover
(base case: 1 m of sand above 1 m of silt). The DDL point is located by the tangent
method, which corresponds to the location where the suction is approximately equal
to the WEV of the coarse waste rock (the distance is then equal to LD).
Figure 13. Evolution of the diversion length during the year, as obtained from the DDL point
location calculated using the tangent method shown in Fig. 12.
Figure 14. Effect of the silt layer thickness on the diversion length of a sand-on-silt cover placed
on the slope of the waste rock pile (at the end of the year); the diversion length LD is
shown here for a DDL point location determined according to the tangent method
(Fig. 12).
Figure 15. Effect of the sand layer thickness on the diversion length of a sand-on-silt cover placed
on the slope of the waste rock pile (at the end of the year); the DDL point is
determined according to the tangent method (Fig. 12).
43
For Review Purposes Only/Aux fins d'examen seulement
Figure 1. Water retention curves of two soils used to create a layered cover with capillary barrier
effects; when placed below the fine-grained soil 2 (with the largest air entry value y a2), the
coarse-grained soil 1 serves to limit the downward flow of water until the suction at the interface
ψ a2
ψ a1
θs2
θ s1
ψ r2 ψ r 1
Log matrix suction ψ
(kPa)
F1
Volumetric water content θ
reaches its water entry value (y r1 in this case).
For Review Purposes Only/Aux fins d'examen seulement
Figure 2. Schematic representation of water movement in an inclined layered cover made of silt
and sand layers, placed on a coarse-grained material (rock waste in this case). Following a
precipitation event, the water flows along the cover and breaks through the coarse material at the
DDL point where the suction reaches its WEV; this gives the diversion length LD (adapted from
Bussière 1999).
Sand
and gravel
= DDL Point
Silt
Mine
waste
Ld
grossiers
F2
For Review Purposes Only/Aux fins d'examen seulement
Figure 3. Basic model of the simulated pile exposed to various surface precipitation rates.
q = Variable precipitation rate
z
q
24
21
Élévation z (m)
x
y
Draining Material #1
(Sand) 6.25 cm
Diversion length LD
Material #2
(Silt) 50 cm Z Toe drain
h =X 0.5 m
Material #3 : Waste rock
Y
at
z = 0.5 m
Observation line
18
15
12
9
6
3
0
-3
0
5
10
15
20
25
30
Distance x (m)
F3
35
40
45
50
55
For Review Purposes Only/Aux fins d'examen seulement
Figure 4. Water retention curves (a) and unsaturated conductivity functions used for the different
materials (b).
0.45
Volumetric water contentθ
0.40
0.35
Drainage/Runoff
Material
Silty Soil
0.30
0.25
0.20
Sand
0.15
0.10
0.05
0.00
1.00E-02 1.00E-01 1.00E+00 1.00E+01 1.00E+02 1.00E+03
Matrix suction ψ (kPa)
(a)
Hydraulic conductivity k (m/s)
1.00E-02
Draining Material #1
1.00E-03
1.00E-04
Silt Cover - Material #2
1.00E-05
1.00E-06
Silt Cover - Material #2b;
ks = 1e10-6 m/s
1.00E-07
1.00E-08
Silt Cover - Material #2c;
ks = 1e10-7 m/s
1.00E-09
1.00E-10
1.00E-11
Silt Cover - Material #2d;
ks = 1e10-8 m/s
1.00E-12
Sand - waste rock
1.00E-13
1.00E+00
(b)
1.00E+01
1.00E+02
Matrix suction (kPa)
F4
1.00E+03
For Review Purposes Only/Aux fins d'examen seulement
Figure 5. Variation of the diversion length LD as a function of the precipitation (recharge) rate (a)
for different times, and evolution of LD over time for various surface recharge fluxes (b); the
simulations include 5 days of precipitation followed by a drainage period of 23 days.
Diversion length LD
24
23
22
21
20
19
18
0
5
10
15
20
25
30
Initial Time
1 hr
1 Day
2 Days
3 Days
4 Days
5 Days
6 Days
7 Days
14 Days
28 Days
Precipitation rate (cm/day)
(a)
Diversion length LD (m)
24.0
q = 0,5 cm/day
23.0
q = 1 cm/day
22.0
q = 2 cm/day
21.0
q = 5 cm/day
20.0
q = 10 cm/day
q = 20 cm/day
19.0
q = 30 cm/day
18.0
0
(b)
5
10
15
20
Time (days)
F5
25
30
For Review Purposes Only/Aux fins d'examen seulement
Figure 6. Suction profiles at mid-height of the slope.
Elevation z (m)
12.0
11.6
11.2
10.8
10.4
10.0
-110
a)
1h
6h
12 h
18 h
Day 1
Day 2
Day 3
Day 4
Day 5
-105
-100
-95
Matrix suction ψ (kPa)
F6
-90
For Review Purposes Only/Aux fins d'examen seulement
Figure 7. Evolution of the DDL point location during the 28-day simulation for different
precipitation rates (adapted from Apithy 2003).
Diversion length LD(m)
24.0
23.5
23.0
Ks = 1e-5 m/s
Ks = 1e-6 m/s
Ks = 1e-7 m/s
Ks = 1e-8 m/s
22.5
22.0
21.5
21.0
20.5
0
25
50
75
100
Precipitation (cm)
F7
125
150
For Review Purposes Only/Aux fins d'examen seulement
Figure 8. Evolution of the diversion length over time, for two cover thicknesses (25 and 50 cm)
and for two precipitation rates (10 and 20 cm/day).
Diversion Length LD(m)
24.0
10 cm/day
25 cm Silt
23.0
10 cm/day
50 cm Silt
22.0
21.0
20 cm/day
25 cm Silt
20.0
20 cm/day
50 cm Silt
19.0
0
4
8
12
16
20
Time (days)
F8
24
28
Unit flux q (1x 10-9 m/s)
-20
0
5
10
15
20
25
40
Time in seconds (1x 10+6)
30
F9
20
9.5
0
Precipitation periods
Periods with negative unit flux -q (evapotranspiration)
60
40
20
0
Time in seconds (1x10+6)
10.0
10.5
Evapotranspiration Precipitation periods
April 28
April 29
9.0
April 25
April 26
8.5
April 22
April 23
8.0
April 19
April 20
-20
April 16
April 17
60
April 13
April 14
80
April 10
April 11
100
April 30
April 27
April 24
April 21
April 18
April 15
April 12
April 09
April 06
April 03
80
April 07
April 08
April 01
April 02
120
Unit flux q (1x 10-9)
December
November
October
September
August
July
June
May
April
March
February
January
For Review Purposes Only/Aux fins d'examen seulement
Figure 9. Distribution of precipitation and evaporation during the modelled year.
For Review Purposes Only/Aux fins d'examen seulement
Figure 10. Representation of the base model used for the numerical simulations; different silt and
sand layer thicknesses were considered in the calculations. The position of the water table
corresponds to the top of the toe drain.
Elevation
z (m)
(m)
Élévation z
25.0
25.0
22.5
22.5
Sable/Gravier SBL = 1.0 m
20.0
Sand SBL = 1.0 m
17.5
17.5
15.0
12.5
12.5
10.0
Do = Longueur de diversion
Diversion Length
Ld Pt.= DDL
7.5
7.5
Silt MRN
MRN ==1.01.0
m
Silt
5.0
2.5
2.5
00.0
-2.5
-2.5
Drain
Toe
de
pied
drainage
0
0
55
10
10
15
15
20
20
25
25
30
30
35
35
Distance x
x (m)
Distance
(m)
F10
40
40
45
45
50
50
55
55
For Review Purposes Only/Aux fins d'examen seulement
Figure 11. Water retention curves (a) and hydraulic conductivity functions (b) for the materials
Volumetric water content
θ
considered in the long-term simulations of CCBE behaviour.
0.45
0.40
0.35
0.30
0.25
0.20
0.15
0.10
0.05
0.00
Waste rock
Silt MRN
Silt SLV
Sable SBL
1.00E-02
1.00E+00
1.00E+02
1.00E+04
Matrix suction ψ (kPa)
Hydraulic conductivity
k (m/s)
(a)
1.00E-03
1.00E-04
1.00E-05
1.00E-06
1.00E-07
1.00E-08
1.00E-09
1.00E-10
1.00E-11
1.00E-12
1.00E-13
1.00E-14
Waste
Rock
Silt
MRN
Sand
SBL
1.0E-01 1.0E+00 1.0E+01 1.0E+02 1.0E+03
(b)
Matrix suction ψ (kPa)
F11
For Review Purposes Only/Aux fins d'examen seulement
Figure 12. Evolution of the calculated suction profiles along the slope, just below the cover (base
case: 1 m of sand above 1 m of silt). The DDL point is located by the tangent method, which
corresponds to the location where the suction is approximately equal to the WEV of the coarse
waste rock (the distance is then equal to LD).
Ld (Tangent Method) = 11.6 m
Soil matric suction y (kPa)
0
Day 90
Day 120
-40
Day 150
Day 180
-80
Day 210
Day 240
-120
Day 270
-160
Day 300
Day 330
-200
Day 360
0
5
10
15
20
Distance (m)
F12
25
30
35
For Review Purposes Only/Aux fins d'examen seulement
Figure 13. Evolution of the diversion length during the year, as obtained from the DDL point
Diversion length Ld (m)
location calculated using the tangent method shown in Fig. 12.
38
34
30
Simulation
26
1.0 m SBL +
1.0 m MRN
22
18
14
10
90 120 150 180 210 240 270 300 330 360
Time (days)
F13
For Review Purposes Only/Aux fins d'examen seulement
Figure 14. Effect of the silt layer thickness on the diversion length of a sand-on-silt cover placed
on the slope of the waste rock pile (at the end of the year); the diversion length LD is shown here
Diversion length Ld (m)
for a DDL point location determined according to the tangent method (Fig. 12).
30.0
25.0
20.0
15.0
Ld Tangent
Method
10.0
5.0
0.0
0.0
0.5
1.0
1.5
2.0
2.5
3.0
Thickness of the silt layer in the two layer cover (m)
F14
For Review Purposes Only/Aux fins d'examen seulement
Figure 15. Effect of the sand layer thickness on the diversion length of a sand-on-silt cover placed
on the slope of the waste rock pile (at the end of the year); the DDL point is determined
Diversion length Ld (m) .
according to the tangent method (Fig. 12).
18.0
16.0
14.0
12.0
10.0
Ld Tangent
method
8.0
6.0
4.0
2.0
0.0
0.0
0.5
1.0
1.5
2.0
2.5
Thickness of the sand layer in the two layer cover (m)
F15
For Review Purposes Only/Aux fins d'examen seulement
Table 1. Main hydraulic properties of the materials used in the numerical calculations conducted
with the model shown in Fig. 4 (after Apithy 2003).
Material
surface
Silt A
Silt B
Silt C
Silt D
Waste rock
y a (m of water)
0.5
1.5
1.5
1.5
1.5
»0
qs (or n)
0.39
0.38
0.38
0.38
0.38
0.3
ksat (cm/s)
1´10-3
1´10-3
1´10-4
1´10-5
1´10-6
1´10-0
qr
0.06
0.06
0.06
0.06
0.06
0.005
WEV (m of water)
8.5
10.0
10.0
10.0
10.0
<1
Table 2. Main hydraulic properties of the materials used in the numerical calculations conducted
with the model shown in Fig. 10 (after Cifuentes 2006).
Material
Silt MNR
Silt SLV
Sand SBL
Waste rock
y a (m of water)
1.00
3.50
0.08
0.10
qs (or n)
0.44
0.43
0.06
0.231
ksat (cm/s)
5x10-5
1x10-6
9.92x10-2
4.25x10-4
qr
0.054
0.150
0.063
0.012
WEV (m of water)
70.0
100.0
2.0
0.7