Material selection for the design of inclined covers with capillary barrier effect Serge-Étienne Parent1 and Alexandre Cabral2* 1
Ph.D. candidate, Dept. Civil Eng., Univ. de Sherbrooke, Quebec, Canada,
[email protected] 2 Professor, Dept. Civil Eng., Univ. de Sherbrooke, Sherbrooke, Quebec, Canada,
[email protected] * Author to whom all correspondence should be sent: Département de génie civil, Faculté de génie, Université de Sherbrooke. 2500, boul. de l’Université, Sherbrooke, Québec, Canada J1K 2R1 Tel.: 819-821-7906; Fax: 819-821-7974 Abstract. The capillary effect is created by superposing a relatively fine pore material over a coarser one. The upper material retains water into its fine pores, while the bottom layer may be kept relatively dry. An inclined cover with capillary barrier effect (CCBE) results in the drainage of infiltrating water into the upper layer. CCBEs are widely used for the final top cover of landfills in order to limit water infiltrations through municipal wastes disposals. A design procedure is proposed to select materials for inclined CCBEs. Keywords. Capillary barrier, Lateral diversion, Landfill cover, Unsaturated flow. 1. Introduction Covers with capillary barrier effect (CCBE) are used as final capping systems after the closure of municipal waste facilities for their low cost, long term stability and effective alternatives (Barth and Wohnlich 1999; Stormont and Anderson 1999; von Der Hude et al. 1999). The capillary barrier effect is created when a relatively fine pore material overlies a coarser one. The textural contrast between the upper layer material (called moisture retention layer, MRL) and the bottom layer material (called capillary break layer, CBL) controls vertical infiltration through the barrier by capillary forces. In humid regions, evapotranspiration may not be sufficient to remove moisture stored into the capping system, which may eventually result in a reduction in the capillary forces, thus in greater infiltration through the cover system. In order to minimize percolation, the materials and the dip angle of the capillary barrier must be carefully determined so that infiltrating waters are diverted laterally (downslope) through the MRL. However, water accumulation is inevitable, leading to a decrease in suction. At a certain point downslope, the level of saturation is such that capillary forces no longer retain water, which results in a significant increase in infiltration. This point is called the breakthrough, whereas the distance between the top of the slope and the breakthrough is called the diversion length. The latter can be calculated using the Ross (1990) model, by calculating the maximal horizontal flow that the MRL can retain, called the diversion capacity. This paper proposes a procedure based on the Ross (1990) model for selecting materials that constitute an inclined CCBE, in order to maximize the diversion length.
2. The Ross (1990) model Ross (1990) developed an analytical relationship to calculate the steady-state diversion capacity of a capillary barrier submitted to a constant infiltration rate. Ross (1990) assumed four hypothesis: (1) the water table lies far below the MRL-CBL interface; (2) both layers are very thick; (3) the interface is inclined and much longer than the diversion length; (4) a vertical infiltration rate is applied uniformly to the top of the MRL. The general form of the Ross model (1990) is the following: c _ MRL
Qmax k sat tan
c _ CBL
k r d
[1]
where Qmax is the diversion capacity (m²/s), ksat is the saturated hydraulic conductivity of the porous medium (m/s), kr() is the relative permeability function, is the slope of the interface, c_CBL and c_MRL are the maximal suction values that can be found for the given infiltration rate (q) under unit gradient into, respectively, the CBL and the MRL. The diversion length (L) is obtained using Equation 2. Q L max q
[2]
3. Materials and methods Three materials were selected to illustration the proposed selection method: a sand (SRsand), a gravel (C-gravel) and a well-graded loam (WG-loam). The hydraulic conductivity functions (k-function) of the three materials are presented in Figure 1. Numerical computations needed to solve the Ross (1990) model were performed using Matlab. 1E-02
Hydraulic conductivity (m/s)
1E-03
SR-sand C-gravel WG-loam
1E-04 1E-05 1E-06 1E-07 1E-08 1E-09 1E-10 1E-11 1E-12 0.01
0.1
1
10
100
1000
Suction (kPa)
Figure 1. Hydraulic conductivity functions of the SR-sand, C-gravel and WG-loam
4. Material selection for an optimal design Equations [1] and [2] show that the diversion length is proportional to the area under the k-function of the material constituting the MRL, between the limits c_CBL and c_MRL. This renders the k-function, hence material selection, an important input in capillary barrier design. As shown in Figure 2, the area under the MRL k-function can be maximized by selecting the most appropriate materials for the construction of a capillary barrier, using the following four criteria (numbered 1 to 4 in Figure 2): (1) for an infiltration rate q, the maximal suction existing in the CBL (c_CBL) should be as low as possible; (2) for the infiltration rate q, the maximal suction existing in the MRL (c_MRL) should be as high as possible; (3) and (4) the hydraulic conductivities in the MRL corresponding to c_CBL and to c_MRL should be as high as possible. All in all, an ideal inclined capillary barrier should include a CBL within which capillarity forces are as weak as possible for the infiltration rate q, and a MRL capable to develop capillarity forces as strong as possible, for the same infiltration rate. In addition, the MRL must be as permeable as possible for suctions between c_CBL and c_MRL, so that water is efficiently drained downslope.
Figure 2. Hydraulic conductivity functions showing how to choose the best materials to constitute the CCBE for a given infiltration rate As shown in Figure 3, different material combinations give different outputs from the Ross (1990) model, in terms of diversion length. It is shown that a combination of coarse materials is more efficient than superposing a fine-grained material over a much coarser one. For an infiltration rate of 1×10-8 m/s, water will be diverted over 15 m if the CCBE is a WG-loam over SR-sand, and over 178 m if the CCBE is a SR-sand over C-gravel.
1E-03
WG-loam / SR-Sand
1E-04
SR-sand / C-gravel
Infiltration rate, q (m/s)
1E-05 1E-06 1E-07 q = 1×10-8 m/s
1E-08 1E-09 1E-10 1E-11 L = 15 m
1E-12 0
1
10 100 Diversion length, L (m)
L = 178 m
1 000
10 000
Figure 3. Diversion length for different infiltration rates, using different material combinations 5. Conclusions The procedure presented above allows for the optimization capillary barriers in terms of material selection in order to limit water infiltrations, based on maximizing the area under the k-function of the moisture retaining layer between the suction values found in the two materials under unit gradient for a specific infiltration rate. It was shown that coarse materials are more efficient than fine materials in the constitution of capillary barriers. This analysis does not take into account that coarse materials are susceptible to fingering (preferential flow) over a large range of infiltration rates. References Barth, C., and Wohnlich, S. "Proof of effectiveness of a capillary barrier as surface sealing of sanitary landfill." 7th international waste management and landfill symposium, Sardina, 389-392. Geo-slope. (2002). SEEP/W for finite element seepage analysis, version 5: User's guide, Geo-slope International Ltd., Calgary. Parent, S.-É. (2003). "Étude des couvertures avec effet de barrière capillaire: applications à l'utilisation des résidus de désencrage comme matériau de recouvrement de sites de résidus miniers et de lieux d'enfouissement sanitaire," Masters thesis, Université de Sherbrooke, Sherbrooke. Ross, B. (1990). "The Diversion Capacity of Capillary Barriers." Water Resources Research, 26(10), 2625-2629. Stormont, J. C., and Anderson, C. E. (1999). "Capillary barrier effect from underlying coarser soil layer." Journal of Geotechnical and Geoenvironmental Engineering, 125(8), 641-648. von Der Hude, N., Melchior, S., and Möckel, S. "Construction of a capillary barrier in the cover of the Breinermoor landfill." Seventh International Waste Management and Landfill Symposium, Sardinia, 393-402.
