Development of geomembrane strains in waste containment facility liners with waste settlement

Geotextiles and Geomembranes 46 (2018) 226–242

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Development of geomembrane strains in waste containment facility liners with waste settlement☆

T

Yan Yu, R. Kerry Rowe∗ GeoEngineering Centre at Queen's−RMC, Department of Civil Engineering, Queen's University, Kingston, ON K7L 3N6, Canada

A R T I C L E I N F O

A B S T R A C T

Keywords: Geosynthetics Waste settlement Geomembrane strain Geosynthetic liner system Waste containment facility Numerical modelling FLAC

The development of tensile strains in geomembrane liners due to loading and waste settlement in waste containment facilities is examined using a numerical model. Two different constitutive models are used to simulate the waste: (a) a modified Cam-Clay model and (b) a Mohr-Coulomb model. The numerical analyses indicate the role of the slope inclination on the maximum geomembrane liner strains for both short-term loading (immediately post closure) and long-term waste settlement. A geosynthetic reinforcement layer over the geomembrane liner is shown to reduce the maximum geomembrane liner strains, but the strain level of the geosynthetic reinforcement itself may become an engineering concern on steeper slopes (i.e., greater than 3H:1V) for cases and conditions examined in this paper. The paper considers some factors (e.g., slope inclination, use of a high stiffness geosynthetic over the geomembrane liner) and notes others (e.g., the designer selection of interface characteristics below and above the geomembrane, use of a slip layer above the geomembrane) that warrant consideration and further investigation to ensure good long-term performance of geomembrane liners in waste containment facilities.

1. Introduction Barrier systems involving a geomembrane liner as part of a composite liner are widely used in the base of waste containment facilities to minimize contaminant escape to groundwater and surface water (Rowe et al., 2004; Rowe, 2005). The liner system is usually overlain by a leachate collection and removal system. Over the past decade, much work has been done on the design and behaviour of leachate collections systems (e.g., Cooke and Rowe, 2008a, 2008b; McIsaac and Rowe, 2006, 2008; Yu and Rowe, 2012, 2013; Rowe and Yu, 2012, 2013a, 2013b, 2013c). Also, there has been considerable work on the components of the composite liner such as the geomembrane (e.g., Abdelaal et al., 2014b; Saheli and Rowe, 2016; Jones and Rowe, 2016; Rowe et al., 2016b; Kavazanjian et al., 2017; Rowe and Shoaib, 2017a,b; Touze-Foltz et al. 2016a,b; Saheli et al., 2017; Yang et al., 2017; Koerner et al., 2017) and GCL (e.g., Bannour et al., 2016; Chai et al., 2016; Malusis and Daniyarov, 2016; Shackelford et al., 2016; Ali et al., 2016; Rouf et al. 2017a,b,c; Bouazza et al., 2017; Lu et al., 2017; Setz et al., 2017), as well as on the interface behaviour for composite liners (e.g., Fox and Stark, 2015; Tano et al., 2017), the field performance of liners (e.g., McWatters et al., 2016; Gallagher et al., 2016; Rentz et al., 2016; Rowe et al., 2016a, 2017; Touze-Foltz et al. 2016a,b), and the

interaction between the drainage layer and the geomembrane liner in terms of local strains induced by the drainage materials (e.g., Brachman and Gudina, 2008a, 2008b; Dickinson and Brachman, 2008; Brachman and Sabir, 2010, 2013; Hornsey and Wishaw, 2012; Sabir and Brachman, 2012; Rowe et al., 2013; Eldesouky and Brachman, 2018) for different geomembrane protection layers. It has been shown that tensile strains are critical to longevity of the geomembrane and should be kept below 5% by use of a suitable protection layer (e.g., Abdelaal et al., 2014a; Ewais et al., 2014). However, as important as local indentations are, they are only one potential source of tensile strain. Another key source is strains developed on slopes and at present there is very limited research regarding the performance evaluation and design of geosynthetic liner systems during waste filling and after closure of waste containment facilities. Snow et al. (1994) reported a field case using the geosynthetic liner system in the Lopez Canyon Landfill in Los Angeles, California, USA where a geonet was placed over the geomembrane resulting in an interface with a much lower interface friction than any interfaces below the geomembrane. The purpose of introducing this slip surface was to allow the interface between the geonet and geomembrane to slip when waste settles and thus to minimize the tensile strains (loads) generated in the geomembrane. The potential advantage of the use of a

☆ ∗

Dr. N. Dixon acted as Editor and organised the review process for this paper. Corresponding author. E-mail addresses: [email protected] (Y. Yu), [email protected] (R.K. Rowe).

https://doi.org/10.1016/j.geotexmem.2017.11.004 Received 2 October 2017; Received in revised form 22 November 2017; Accepted 24 November 2017 0266-1144/ © 2017 Elsevier Ltd. All rights reserved.

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Fig. 1. Base case landfill profile with a slope inclination of 1H:1V and two 4-m wide intermediate benches below the ground surface (average 1.2H:1V including benches).

Fig. 2. Example of numerical mesh for base case landfill profile on (a) left and (b) right side of the model.

strength of the geomembrane was exceeded causing liner failure which was associated with waste lateral displacements and surface depressions of as much as 10.7 m and 4.3 m, respectively (e.g., Seed et al., 1990; Mitchell et al., 1990; Byrne et al., 1992). This represents an extreme case of a slope stability failure. This risk is now well recognized and considered in good designs. However, slope stability failure is not the only cause for concern. A facility which is “safe” from a slope stability perspective, has the potential to fail in the long-term due to environmental stress cracking at strains well below the yield strain. Although geosynthetic liner systems are used in most modern waste containment facilities, reported field experiments associated with the performance of geosynthetic liner systems are limited (Villard et al., 1999; Zamara et al., 2014), and field performance data such as

preferential slip surface approach by providing an interface above the geomembrane with a shear strength less than any interface shear strength below the geomembrane has been recognized (e.g., Cowland et al., 2006; Thiel et al., 2014). Thiel et al. (2014) further proposed an enhanced method by using a veneer-reinforcement layer with enough tensile strength and stiffness above the primary geomembrane liner and below the slip layer to resist the downdrag shear force generated by waste settlement. However, the interaction between the veneer-reinforcement layer and geomembrane was not explicitly considered and the geomembrane strains were not evaluated by Thiel et al. (2014). The geosynthetic liner system can fail even during waste filling. A well documented example is the slope failure of the waste at the Kettleman Hills Landfill where the tear and/or multiaxial tensile break 227

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in design. The influence on geomembrane strains of the intermediate bench width, number of intermediate benches, side slope inclination, and use of a geosynthetic reinforcement over the geomembrane on a slope (with interaction between the geosynthetic reinforcement and geomembrane) is examined under both short- and long-term waste settlement. The numerical modelling was performed using the FDM program FLAC (Itasca, 2011).

Table 1 Municipal solid waste parameters. Parameters

Values Case 1

Unit weight, γ (kN/m3) Friction angle, ϕ (°) Poisson's ratio, ν (−)

10.7 33 a 0.33

Case 2

a

a

2. Problem definition and parameter values

Modified Cam-Clay Model Maximum elastic bulk modulus, Kmax (MPa) Frictional constant, M (−) Slope of normal consolidation line, λ (−) Slope of elastic swelling line, κ (−) Reference pressure, p1 (kPa) Pre-consolidation stress, pc (kPa) Initial void ratio, e0 (−)

0.086 a 0.0086 a

Mohr-Coulomb Model Young's modulus, E (MPa) Cohesion, c (kPa)

6

a

Common

4000 1.4 a

a

2.1. Problem definition 0.28 0.028

1 40 a 2.04

Augello et al. (1995) reported a case study at the geosynthetic-lined Chiquita Canyon landfill located at the western edge of the Santa Clara Valley in California where the slopes at the east-west orientated steepsided canyons typically approached 1H:1V (and were nearly vertical in some cases). Fig. 1 shows the two-dimensional base case geometry of half of a canyon waste containment facility examined herein. The foundation was competent rock. The 40 m high side slope had a 1H:1V inclination over a vertical distance of 13.3 m between two 4-m wide intermediate benches. The bench width, bench vertical spacing, side slope height, and slope inclination from the base case are the same as those from Wu (2013). In addition to the base case geometry, the influence of the 8-m wide benches (e.g., Brown et al., 1999), 2H:1V and 3H:1V slope inclination, four 4-m wide benches, and geosynthetic reinforcement over the geomembrane on geomembrane strains were also examined. For all cases, the 1-m thick final cover had two 4-m wide intermediate benches with an inclination of 3H:1V. To simplify the model, the cover material and the waste were separated by a layer of geomembrane only. Consideration is given to a geosynthetic base liner system including a geomembrane liner both with and without geosynthetic reinforcement over the geomembrane on side slope. Fig. 2 shows the example of numerical mesh for the base case geometry on the left and right sides of the model. The deformation of foundation rock in this investigation was negligible, thus only 4-m thick rock layer was modelled. The bottom of the foundation rock was fixed in both x- and y-direction. The left and right sides of the model were fixed in x-direction only. A total of 28,656 zones (elements) were used for the foundation rock, waste and final cover. The geomembrane (on side slope and flat base, and in the final cover) was modelled by 770 beam elements. For the case where a geosynthetic reinforcement layer was used over the geomembrane liner, the geosynthetic reinforcement was only on side slope where it was modelled by 198 beam elements. The FLAC model reported in this paper did not consider the geometric irregularity (e.g., Mitchell et al., 2016) and geomembrane seams (e.g., Fowmes et al., 2008b; Kavazanjian et al., 2017; Rowe and Shoaib, 2017a,b) on benches and side slopes, which may have an influence on the interaction along interfaces and the geomembrane tensile strains.

a

2 5

Based on Wu (2013).

Table 2 Geomembrane and geotextile parameter values using FLAC beam elements. Beam element parameters

Value

HDPE Geomembrane Axial stiffness, Jgm (kN/m) Moment of inertia, Igm (m4) Young's modulus b, Egm (MPa) Cross-sectional area c, Agm (m2/m)

726 a 0 484 1.5 × 10−3

PET Geotextile Axial stiffness, Jgt (kN/m) Moment of inertia, Igt (m4) Young's modulus f, Egt (MPa) Cross-sectional area g, Agt (m2/m)

4200 d (8000 e) 0 2100 (4000) 2 × 10−3

a

Axial stiffness value from Wu (2013). Egm = Jgm/Agm. Based on 1.5-mm thick product per meter out-of-plane direction. d Axial stiffness value from Thiel et al. (2014). e Axial stiffness value from Liu and Rowe (2016). f Egt = Jgt/Agt. g Based on 2-mm thick product per meter out-of-plane direction. b c

measurement of geomembrane strains under waste settlement are still scarce. Centrifuge tests have been performed in order to understand the behaviour of the geomembrane liner subject to waste settlement (Thusyanthan et al., 2007; Kavazanjian and Gutierrez, 2017). The physical performance data from the centrifuge models are valuable in terms of understanding the fundamental working and failure mechanisms associated with the geosynthetic liner systems, but high quality physical data from these centrifuge tests are also very limited. An alternative approach to improve the understanding of performance of geosynthetic liner systems under waste settlement is the use of numerical experiments with the finite element method – FEM (e.g., Villard et al., 1999; Filz et al., 2001) and finite difference method – FDM (e.g., Jones and Dixon, 2005; Fowmes, 2007; Fowmes et al., 2008a; Arab, 2011; Sia and Dixon, 2012; Wu, 2013; and Zamara et al., 2014). The numerical modelling of geosynthetic liner systems (cited above) has provided valuable information to improve the design of geosynthetic liner systems. However, more research is needed in order to advance the understanding of generation and distribution of geomembrane tensile strains after the short- and long-term waste settlement. The objectives of this paper are to numerically examine the performance of geosynthetic liner systems under waste settlement in the waste containment facilities and to discuss potential design options that could reduce the maximum geomembrane strain to an acceptable level

2.2. Parameters The waste was divided into 27 layers (lifts) each with an average thickness of about 3 m following general practice. Two different constitutive models were used to simulate the waste settlement: (a) a modified Cam-Clay model and (b) a Mohr-Coulomb model. For each constitutive model, two sets of parameter values were considered (Table 1). The parameter values from Case 1 were used to simulate the short-term waste settlement, while those from Case 2 were for the longterm waste settlement. The differences between Case 1 and Case 2 were the slopes of the normal consolidation line and elastic swelling line from the modified Cam-Clay model, and the Young's modulus from the Mohr-Coulomb model. For the modified Cam-Clay model, Case 1 parameter values were taken from Wu (2013), and in Case 2 the slopes of normal consolidation line and elastic swelling line (Table 1) are such that they generate the similar maximum geomembrane strain as Wu (2013) after the long-term waste settlement. Stark et al. (2009) 228

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Fig. 3. Interfaces between dissimilar materials (a) without and (b) with geosynthetic reinforcement overlying geomembrane on side slope.

Clay model; this was important since it is the maximum geomembrane strain that is of most practical concern. The cover material properties were not reported by Wu (2013). In this investigation, the cover material was modelled by a Mohr-Coulomb model with a unit weight = 17.3 kN/m3, Young's modulus = 20 MPa, Poisson's ratio = 0.3, friction angle = 30°, dilation angle = 0, and cohesion = 5 kPa. However, the differences in the calculated geomembrane strains before and after installing the final cover were negligible for all cases reported in this paper. The foundation rock was modelled as elastic material with a unit weight = 16.5 kN/m3 and Poisson's ratio = 0.25 (Arab, 2011). The Young's modulus was not reported by Arab (2011) and Wu (2013), and was set to 500 MPa in this paper. The use of a higher Young's modulus based on the shear wave velocities from Arab (2011) and Wu (2013) had negligible influence on the calculated geomembrane strains. The geomembrane and geotextile beam elements were assigned constitutive parameters (Table 2) based on published sources where possible. In particular, a comparison was initially made with the case examined by Wu (2013) and Thiel et al. (2014) since these were the only published work addressing a similar issue to this paper and then the effect of other parameters (i.e., variations from the base case) were considered. The high-density polyethylene (HDPE) geomembrane was 1.5 mm thick with an axial tensile stiffness Jgm = 726 kN/m (Wu, 2013). The axial tensile stiffness of the woven polyester (PET) geotextile was Jgt = 4200 kN/m (Thiel et al., 2014). A higher stiffness

Table 3 Interfaces and corresponding parameter values (see also Fig. 3). Interface and parameters

Value

Normal stiffness, kn (MPa/m) Shear stiffness, ks (MPa/m) Dilation angle, ψi (°) Cohesion, ci (kPa)

100 1 0 0

Geomembrane-LCS under waste and geomembrane-subgrade over waste Friction angle, ϕgmw (°) 20 Geomembrane-GCL over foundation Friction angle, ϕgmf (°)

10

Geomembrane-cover soil Friction angle, ϕgmc (°)

20

Geosynthetic reinforcement-LCS under waste Friction angle, ϕgtw (°)

30

Geosynthetic reinforcement-geomembrane Friction angle, ϕgtgm (°)

10

summarized the effective cohesion of the waste reported in the literature ranging from 0 to 67 kPa. Thus for the Mohr-Coulomb model the cohesion of the waste was taken to be 5 kPa. The Young's modulus was set to 6 MPa for Case 1 and 2 MPa for Case 2. These parameters generated a similar maximum geomembrane strain as the modified Cam229

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reinforcement and LCS under the waste, and ϕgtgm = 10° (Thiel et al., 2014) between the geosynthetic reinforcement and geomembrane (Fig. 3). Unlike Thiel et al. (2014), the geomembane and geomembraneGCL over foundation interface were explicitly modelled in this study. Table 3 summarizes the parameter values for all interfaces. 2.3. Modelling of waste filling The numerical simulation was initiated by activating the foundation rock and establishing initial force equilibrium. The geomembrane liner and interface elements between the geomembrane liner and the foundation were then added to the model up to the end of the first bench (i.e., effectively simulating the placing of the liner to this level in the early stages of the analysis and the progressively placing liner as the waste level rose). The waste and associated interface elements between the geomembrane and the waste was then activated in 3-m lifts, layer by layer, up to the first bench with force equilibrium being established at each step. Once the waste reached the first bench, the geomembrane liner beam elements and interface elements between the geomembrane liner and the foundation up to the end of the second bench were activated. The process of placing the waste and interface elements between the geomembrane and the waste in 3-m lifts was then repeated to the second bench. When the waste reached the second bench, the geomembrane liner beam elements and interface elements between the geomembrane liner and the foundation up to the anchor trench were activated. The process of placing the waste and interface elements between the geomembrane and the waste in 3-m lifts was repeated to the top of the side slope. After the base geomembrane and waste had been placed to the ground surface, the remainder of the waste above this level was placed in 3-m lifts. Once the final waste layer (i.e., the twenty-seventh layer) was in place, the cover system including a geomembrane (with interface elements between the geomembrane and waste and between the geomembrane and cover soil; Fig. 3) were put into place. For cases where the geosynthetic reinforcement was used over the geomembrane liner the geosynthetic reinforcement beam nodes were added to the model immediately after the geomembrane liner beam nodes (with interface elements between the geosynthetic reinforcement and geomembrane; Fig. 3). The above modelling process was followed for Case 1 and Case 2 parameter values. The simulation was performed in FLAC large-strain mode.

Fig. 4. Example of the distribution of geomembrane tensile strains from base case landfill profile with a slope inclination of 1H:1V and two 4-m wide intermediate benches below the ground surface (using modified Cam-Clay model and Case 1 waste parameter values).

(Jgt = 8000 kN/m; Liu and Rowe, 2016) of the woven PET geotextile was also considered to examine the influence of the tensile stiffness of the geosynthetic reinforcement on geomembrane strains. The thickness of the geosynthetic reinforcement was assumed to be 2 mm. It should be noted that the thickness of the geosynthetic reinforcement and geomembrane in the numerical model has no influence on the final results reported in this paper. It is the stiffness of the geosynthetic reinforcement and geomembrane that matters. Yielding and rupture of the geosynthetic reinforcement and geomembrane under the tension was not modelled. The geosynthetic reinforcement and geomembrane were assumed to have no compressive stiffness and consequently no stress in compression. The interaction between the dissimilar materials was modelled using zero-thickness interface elements (Fig. 3). The interface normal and shear stiffness values were set to kn = 100 MPa/m and ks = 1 MPa/ m, respectively (Yu and Bathurst, 2017). No dilation and cohesion was considered for all interfaces (ψi = 0 and ci = 0; Wu, 2013). Based on Wu (2013), the interface friction angle between the geomembrane and geosynthetic clay liner (GCL) resting on the foundation was ϕgmf = 10° and between the geomembrane and leachate collection system (LCS) under the waste was ϕgmw = 20° (a same interface friction angle was also used between the geomembrane and subgrade above the waste in the final cover). The use of ϕgmf = 10° for the geomembrane lower interface was a conservative assumption for a single composite design. If the design called for a geomembrane with a textured lower surface and either a smooth or textured upper surface (depending on the design) the tensile strains may be smaller. The use of a higher lower interface friction angle (ϕgmf > 10°) was not pursued in this paper but will be considered in a subsequent paper (Rowe and Yu, 2018). Wu (2013) did not use an interface between the geomembrane and overlying material while in this study the interface between the geomembrane and overlying material was explicitly modelled with joint elements having a friction angle ϕgmc = 20° (Fig. 3). However, the differences in the calculated geomembrane strains were negligible between whether or not this interface was explicitly modelled in this case. When geosynthetic reinforcement was placed over the geomembrane, the interface friction angle was ϕgtw = 30° between the geosynthetic

3. Results 3.1. Base case with modified Cam-Clay model (average side slope 1.2H:1V including benches) The base case has 1H:1V slopes between benches which corresponds to an overall top to bottom slope of 1.2H:1V once benches are considered although it is the 1H:1V slope that controls the geomembrane strain and, when used, geosynthetic reinforcement strain. For this case the geomembrane strain distribution (Fig. 4) for the base case landfill profile (Fig. 1) shows that the maximum strain occurs on the slope very close to the bench. Tensile strains extended about 25% of the way down the slope from the bench and, at much smaller level, across the bench itself. The maximum tensile strain at the end of filling (immediately after final closure; Fig. 5a) was 8.7% at the crest of the slope near the first (bottom-most) intermediate bench. A similar maximum geomembrane tensile strain (i.e., 8.3%) was reported by Wu (2013) at the end of waste placement for the same landfill profile and parameters. With long-term waste settlement, the maximum geomembrane tensile strain increased to 19.2% (Fig. 5b) which was similar to 19.3% reported by Wu (2013). A comparison was made here only for the maximum

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Fig. 5. Calculated geomembrane tensile strains from base case landfill profile with a slope inclination of 1H:1V and two 4-m wide intermediate benches below the ground surface using modified Cam-Clay model and waste parameter values from: (a) Case 1 and (b) Case 2.

With the 1H:1V slope, the tensile strains calculated for the base case are excessive even for the short-term waste settlement (i.e., immediately after final closure; Case 1) and are more than twice as high in the longer-term (Case 2). If identified in the design of the geomembrane liner, the engineer would be seeking a means of reducing the calculated maximum geomembrane tensile strains. Assuming the waste, geomembrane, and interface properties remain the same, three potential design options were considered in this paper to reduce the maximum geomembrane tensile strains including: (a) changing the landfill profile to reduce the differential settlement between the waste and the geomembrane, (b) adding a geosynthetic reinforcement layer over the geomembrane on side slope to carry most of the downdrag load from the waste so that it is not transferred to the geomembrane, and (c) combining both methods of (a) and (b). The following sections examine these options.

geomembrane strain because it is the maximum geomembrane tensile strain that is of practical concern in term of the design of a geomembrane liner. 3.2. Base case landfill profile with Mohr-Coulomb model (1.2H:1V including benches) The same base case as examined above using the Cam-Clay model for the waste was also modelled using the Mohr-Coulomb waste model. The calculated maximum geomembrane tensile strain was 8.6% immediately after final closure (Case 1; Fig. 6a) and 19.8% after long-term settlement (Fig. 6b). The numerical results obtained using the MohrCoulomb model (Fig. 6) were in good agreement with those from the modified Cam-Clay model (Fig. 5 and Wu, 2013). Thus only results from the Mohr-Coulomb model are reported for the rest of this paper. 231

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Fig. 6. Calculated geomembrane tensile strains for base case landfill profile with a slope inclination of 1H:1V and two 4-m wide intermediate benches below the ground surface using Mohr-Coulomb model and waste parameter values from: (a) Case 1 and (b) Case 2.

Fig. 7. Landfill profile with a slope inclination of 1H:1V and two 8m wide intermediate benches below the ground surface (average 1.2H:1V including benches).

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Fig. 8. Calculated geomembrane tensile strains for landfill profile with a slope inclination of 1H:1V and two 8-m wide intermediate benches below the ground surface using Mohr-Coulomb model and waste parameter values from: (a) Case 1 and (b) Case 2.

Fig. 9. Landfill profile with a slope inclination of 1H:1V and four 4m wide intermediate benches below the ground surface (average 1.2H:1V including benches).

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Fig. 10. Calculated geomembrane tensile strains for landfill profile with a slope inclination of 1H:1V and four 4-m wide intermediate benches below the ground surface using Mohr-Coulomb model and waste parameter values from: (a) Case 1 and (b) Case 2.

Fig. 11. Landfill profile with a slope inclination of 2H:1V and two 4-m wide intermediate benches below the ground surface (average 2.2H:1V including benches).

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Fig. 12. Calculated geomembrane tensile strains for landfill profile with a slope inclination of 2H:1V and two 4-m wide intermediate benches below the ground surface using Mohr-Coulomb model and waste parameter values from: (a) Case 1 and (b) Case 2.

Fig. 13. Landfill profile with a slope inclination of 3H:1V and two 4-m wide intermediate benches below the ground surface (average 3.2H:1V including benches).

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Fig. 14. Calculated geomembrane tensile strains for landfill profile with a slope inclination of 3H:1V and two 4-m wide intermediate benches below the ground surface using Mohr-Coulomb model and waste parameter values from: (a) Case 1 and (b) Case 2.

3.4. Influence of number of intermediate benches (1.4H:1V including benches)

3.3. Influence of bench width (1.4H:1V including benches) Consider a landfill profile with a slope inclination of 1H:1V and two 8-m wide benches (reducing the average top to bottom slope to 1.4H:1V; Fig. 7), rather than 4-m wide intermediate benches (average top to bottom slope to 1.2H:1V; Fig. 1) considered in the base case. With the two 8-m wide benches, the maximum geomembrane strain remained essentially the same at 8.4% immediately after final closure (Fig. 8a; Case 1) compared to 8.6% in the base case (Fig. 6a) and the long-term settlement strain was 20.0% (Fig. 8b) versus 19.8% for two 4m wide benches (Fig. 6b). Thus reducing the average slope by increasing the intermediate bench width from 4 to 8 m had negligible influence on the maximum geomembrane strains.

The effect of doubling the number of benches (Fig. 9) was examined with the same 1H:1V slope between benches and the same top to bottom slope of 1.4H:1V as in the previous section (Fig. 7). Despite having the same average slope as in the previous case, the increase in the number of intermediate benches resulted in a notable decrease in maximum geomembrane strain immediately after final closure to 6.0% (Case 1; Fig. 10a) compared to 8.6% (Case 1; Fig. 6a) and after longterm settlement to 15.3% (Case 2; Fig. 10b) compared to 19.8% (Case 2; Fig. 6b) with two 4-m wide intermediate benches. The explanation for the better performance here than with earlier 1H:1V cases arises from the fact that the vertical displacements of the waste on each bench was near zero because of high modulus of the rock foundation. Thus four 4236

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Fig. 15. Calculated geomembrane and geotextile (Jgt = 4200 kN/ m) tensile strains for landfill profile with a slope inclination of 1H:1V and two 4-m wide intermediate benches below the ground surface using Mohr-Coulomb model and waste parameter values from: (a) Case 1 and (b) Case 2.

m wide benches can reduce the bench vertical distance and thus the differential settlement between the geomembrane and the waste on the side slope (therefore the maximum geomembrane strain) when compared to two 4-m benches (other conditions being the same). Nevertheless, while there is a notable benefit in terms of reduced strains, the benefit of using four 4-m wide intermediate benches instead of two was limited because the maximum geomembrane strains were still too large to be accepted.

Fig. 12a) compared to 8.6% for 1H:1V slope in Fig. 6a. While this may be acceptable, once the long-term settlement was considered the maximum strain increased to 10.7% (Case 2; Fig. 12b) compared to 19.8% (base case; Fig. 6b). While better, a tensile strain of 10.7% in the longterm is still not acceptable for HDPE.

3.5. Influence of changing slope inclination to 2H:1V (average 2.2H:1V including benches)

Changing the slope inclination from 1H:1V to 2H:1V had a positive effect in reducing the maximum geomembrane strains. However, a further decrease in the slope inclination was needed to reduce the maximum geomembrane strains to acceptable levels under long-term waste settlement. With a 3H:1V slope above and below the two 4-m wide intermediate benches (Fig. 13), the maximum geomembrane strain was reduced to 2.0% immediately after final closure (Case 1;

3.6. Influence of changing slope inclination to 3H:1V (average 3.2H:1V including benches)

Since adjusting the average slope using benches did not result in an acceptable situation, here the slope between benches is changed to 2H:1V (Fig. 11). This resulted in a decrease in the maximum geomembrane strain immediately after final closure to 4.4% (Case 1: 237

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Fig. 16. Calculated geomembrane and geotextile (Jgt = 8000 kN/ m) tensile strains for landfill profile with a slope inclination of 1H:1V and two 4-m wide intermediate benches below the ground surface using Mohr-Coulomb model and waste parameter values from: (a) Case 1 and (b) Case 2.

force of 240 kN/m for 1H:1V slope inclination resulting in a maximum geotextile tensile strain of 240/4200 = 5.7%) by assuming that the lower geomembrane interface would have peak interface shear strength greater than the upper geomembrane interface and no geomembrane tensile force/strain would be generated. The present numerical analysis indicated that the maximum geomembrane strains (Fig. 15) were less than 2% for both immediately after final closure (Case 1) and after long-term settlement (Case 2). Thus, the geotextile over the geomembrane was very effective in reducing the maximum geomembrane strains. However, the geotextile itself provided a quasi-preferential slip surface and sustained most of downdrag force induced by waste settlement resulting in a maximum geotextile strain of 5.0% immediately after final closure (Case 1) and of 9.1% for long-term settlement (Case 2). The latter strain is very close to the nominal break strain of the reinforcement (about 10%).

Fig. 14a) and only 2.1% after long-term settlement (Case 2; Fig. 14b). Based on currently available information, these now represent acceptable design strains for the conditions examined. 3.7. Influence of geosynthetic reinforcement over geomembrane (1.2H:1V including benches) The use of a high stiffness geosynthetic reinforcement over the geomembrane with a relative low interface shear strength between the geosynthetic reinforcement and geomembrane represents a possible alternative to flattening the slope. An initial analysis was performed for the use of a woven polyester (PET) geotextile with an axial tensile stiffness Jgt = 4200 kN/m (Thiel et al., 2014) as reinforcement for the base case landfill profile (Fig. 1). Thiel et al. (2014) only estimated geotextile tensile forces after long-term settlement (with a maximum 238

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Fig. 17. Calculated geomembrane and geotextile (Jgt = 8000 kN/ m) tensile strains for landfill profile with a slope inclination of 2H:1V and two 4-m wide intermediate benches below the ground surface using Mohr-Coulomb model and waste parameter values from: (a) Case 1 and (b) Case 2.

3.8. Influence of slope inclination and geosynthetic protection layer over geomembrane

To reduce the geosynthetic reinforcement strains, a woven PET geotextile with an axial tensile stiffness Jgt = 8000 kN/m available on the market was used for the base case landfill profile (Fig. 1). The maximum geomembrane strains were less than an acceptable 2% for both immediately after final closure (Case 1) and after long-term settlement (Case 2). The maximum geotextile strains were 3.7% (Fig. 16a; versus 5.0% in Fig. 15a) immediately after final closure (Case 1) and 6.1% (Fig. 16b; versus 9.1% in Fig. 15b) after long-term settlement (Case 2). Given a typical failure strain in the high strength reinforcement of about 10% this may be acceptable but considering that these are long-term sustained strains, 6.1% is still quite high and of potential concern when allowance is made for time dependant degradation of properties. This suggests that a 1H:1V slope is still potentially problematic even with very stiff/strong reinforcement, although the strength demand on the reinforcement layer can be greatly reduced if a sacrificial slip layer is placed immediately above the reinforcement.

In the previous section, the landfill profile with a slope inclination of 1H:1V and two 4-m intermediate benches below the ground surface (base case; Fig. 1) was a very challenging design option even when using a high stiffness/strength geosynthetic reinforcement over the geomembrane liner. Reducing the side slope inclination of 2H:1V with two 4-m wide intermediate benches and again using the 8000 kN/m high stiffness woven PET geotextile reinforcement, the maximum geomembrane strains were 1.0% (Fig. 17a) and 1.5% (Fig. 17b) for immediately after final closure (Case 1) and after long-term settlement (Case 2), respectively. The maximum strain in the geotextile reinforcement was 2.5% (Fig. 17a) for immediately after final closure (Case 1) and 3.7% (Fig. 17b) for Case 2 both of which are considered more reasonable. Thus changing the slope inclination of 1H:1V to 239

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reinforcement tensile strains to less than 4% immediately after final closure and after long-term settlement.

2H:1V together with a geosynthetic reinforcement (Jgt = 8000 kN/m) over the geomembrane would limit both the maximum geomembrane and geosynthetic reinforcement strains to acceptable levels for cases and conditions examined.

While the strains given above are specific to the cases analyzed, the magnitude of the geomembrane strains and, when used, reinforcement strains for slopes steeper than 3H:1V, and especially for slopes steeper than 2H:1V, are sufficient to highlight the need for careful analysis of the potential impact of downdrag on both the geomembrane and reinforcement (if used) when using geomembranes in waste containment faculties with slopes steeper than 3H:1V. However, the results reported herein also suggest that an optimum design solution can be achieved by the proper selection of the slope inclination, strategic design of friction at interfaces above and below the geomembrane (e.g., textured lower and smooth upper geomembrane surface with a sacrificial slip layer), and strength/stiffness and location of the geosynthetic reinforcement over the geomembrane liner. Although the real design case is likely to be more complicated than the cases examined in this paper the current modelling was conservative and is a starting point for more designspecific modelling. A good designer may take advantage of a number of strategies not examined herein to better accommodate waste settlement and reduce induced geomembrane tensions. For example, they may incorporate not just reinforcement, but also a complete slip layer on slopes steeper than 3H:1V and while not considered in this paper these strategies deserve future investigation.

4. Conclusions When a geomembrane is used in the base of a landfill, tensile strains can be expected to develop in the geomembrane due to downdrag both (i) as the overlying cover layers and waste are placed, and (ii) as the waste continues to settle after the closure of the facility. If the waste containment facility is not properly designed, this downdrag may induce excessive tensile strains in the geomembrane, which can compromise the intended performance of geosynthetic liner system. The finite difference method program FLAC (Itasca, 2011) was used to calculate the tensile strains in the geomembrane liner due to waste settlement for a hypothetical waste containment facility and a range of cases considering both short-term (immediately after final closure; Case 1) and long-term (post-closure; Case 2) waste settlement. Cases were considered both with and without geosynthetic reinforcement over the geomembrane liner. Interface elements were used between the dissimilar materials. The following conclusions were reached for the specific cases and conditions examined:

• The maximum tensile strain was developed close to but below the intermediate benches and the top of slope. • For a slope inclination of 1H:1V with two 4-m intermediate benches

• • •

• •

•

Acknowledgements The work reported in this paper was supported by a grant (A1007) from the Natural Sciences and Engineering Research Council of Canada. The authors are extremely grateful to the two anonymous reviewers for their insightful comments and suggestions which greatly helped improve the paper.

and a geomembrane directly exposed to friction from the overlying soil (i.e., no slip layer), the calculated maximum geomembrane tensile strain was large (> 8%) immediately after final closure and very large (> 19%) after long-term settlement; both are considered unacceptable. Increasing the intermediate bench width from 4 to 8 m had negligible influence on the maximum geomembrane tensile strains when other conditions were same. When replacing the two 4-m wide benches with four 4-m wide benches thereby cutting the slope distance between benches in half, the maximum geomembrane tensile strain decreased to 6% immediately after final closure and about 15% after long-term settlement; both are considered unacceptable. A decrease in the slope inclination from 1H:1V to 2H:1V to 3H:1V reduced the maximum geomembrane strain from 8.6% (1H:1V) to 4.4% (2H:1V) to 2.0% (3H:1V) immediately after final closure, and from 19.8% (1H:1V) to 10.7% (2H:1V) to 2.1% (3H:1V) after longterm settlement. Thus without geosynthetic reinforcement the slopes greater than (3H:1V) gave problematic long-term strains, while the 3H:1V slopes had acceptable strains. The length of slope, slope inclination, loading and settlement, and relative interface shear strengths above and below the geomembrane all influenced the maximum geomembrane tensile strain. A geosynthetic reinforcement layer with an axial stiffness, Jgt ≥ 4000 kN/m over the geomembrane liner reduced the maximum geomembrane tensile strains to less than 2% (likely acceptable) with the 1H:1V slopes. However, with the 1H:1V slopes, the strains (forces) in geosynthetic reinforcement itself may be an engineering concern. For the woven PET geotextile the calculated strains developed after long-term settlement were 9.1% for Jgt = 4200 kN/m and 6.1% for Jgt = 8000 kN/m (both likely unacceptable high) for the 1H:1V slopes. Changing the slope inclination from 1H:1V to 2H:1V and using a woven PET geotextile reinforcement with Jgt = 8000 kN/m over the geomembrane liner reduced the maximum geomembrane tensile strains to less than 2% and the maximum geosynthetic

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