DESIGN OF LANDFILL DAILY CELLS TO REDUCE COVER SOIL USE

Waste Management & Research (1997) 15, 585–592

DESIGN OF LANDFILL DAILY CELLS TO REDUCE COVER SOIL USE Mark W. Milke Department of Civil Engineering, University of Canterbury, Private Bag 4800, Christchurch, New Zealand (Received 29 January 1996, accepted 8 July 1996) Daily cell design for a landfill is analysed from the viewpoint of minimizing the use of daily cover soil. The landfill’s daily cell is idealized to be in the shape of a parallelopiped. To minimize cover soil use and for fixed values of the working face length, volume of refuse, and slope of compaction, the optimal ratio of length to height for the daily cell is found to be the slope gradient (horizontal to vertical). For this optimum ratio, an equation is provided relating the soil-to-refuse ratio to daily cell design parameters. For situations away from the optimum length-to-height ratio, an equation is provided to estimate the excess soil required. These equations can help designers evaluate tradeoffs when a designer attempts to minimize cover soil use.  1997 ISWA Key Words—Landfill design, daily cells, cover soil, optimization.

1. Introduction The use of cover soil in landfills, although important in protecting health and the environment, leads to less landfill volume available for compacted waste. The more cover soil used in landfills, the quicker the landfill will become full. If landfills receive revenue based on the amount of waste received, then a greater use of cover soil means less income during the life of the landfill. As a result of these concerns, there is great interest in ways to minimize the amount of cover soil used in landfills. For example, there is interest in using less spacedemanding geotextiles (Querio & Lundell 1992) and foams (Carson 1992) in place of cover soil. In spite of this interest, there is little documented advice on ways to minimize daily cover soil use in more typical landfill operations. Landfills are constructed as a sequence of cells, where each cell typically constitutes one day’s compacted refuse plus a covering of soil (Bagchi 1990; Tchobanoglous et al. 1993; McBean et al. 1995). A typical daily cell is shown schematically in Fig. 1. The solid figure is a parallelopiped, i.e. a box that has been pushed in one top corner to give two pairs of parallel, sloping sides. A simple engineering description of the daily cell would use the variables shown in Fig. 1: Vr, the volume of refuse; Vs, the volume of cover soil; W, the length of the working face along which refuse is disposed and compacted; H, the height of the compacted refuse; T, the thickness of the daily cover soil; L, the length of the cell; and G, the gradient (horizontal to vertical) of the sloping faces. At any particular landfill, the gradient, G, the cover thickness, T, and the working face length, W, are generally fixed by operational or equipment limitations. Before or 0734–242X/97/060585+08 $25.00/0

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 1997 ISWA

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GT Vs

W H

T G Vr

L GT

Fig. 1. Schematic of the daily landfill cell idealized as a parallelopiped.

during a landfill’s lifetime there may be interest in exploring the advantages and disadvantages of changes in any of the variables key to daily cell design. For both of these situations the landfill engineer would want to know how design choices affect the requirements for cover soil. This paper intends to help meet that need. 2. Theoretical optimization of cell height and length to minimize cover soil The volume of refuse and cover soil for the daily cell shown in Figure 1 can be expressed in terms of the distances, H, L, W, and T and the gradient, G. The volume of refuse is the volume of the parallelopiped with dimensions, H, L, and W: Vr=H×L×W

[1]

The total volume of refuse plus soil is given by the product of the total height, total length, and total width. With the addition of soil, the total height is T+H. The total length increases from L to L+GT to reflect the additional length needed to cover the corner of the parallelopiped in soil to a depth of T. Similarly, the width increases from W to W+GT. As a result, the volume of refuse plus soil is given by: Vr+Vs=(H+T)(L+GT)(W+GT)

[2]

Since the volume of refuse is often a more important design parameter than the length or height of the daily cell, [1] can be solved for H and substituted into [2] to give: Vs=TGVr/W+TGVr/L+T2G2Vr/WL+TWL+T2GL+T2GW+T3G2

[3]

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A landfill operator would be interested in minimizing Vs but is likely to be under many design constraints. These would tend to fix T, G, Vr, and W, leaving only L to be varied. Taking the partial derivative of [3] with respect to L, and setting that equal to zero should give the value of L that minimizes Vs. The resulting equation is: ∂Vs/∂L=−TGVr/L2−T2G2Vr/WL2+TW+T2G=0

[4]

Solving for L in [4] gives: L=JGVr/W

[5]

Substituting [5] into [1] gives the resulting optimum height: H=JVr/WG

[6]

By combining [5] and [6], this optimum condition can also be represented as: G=L/H

[7]

3. Theoretical soil requirements at optimum L/H ratio To see the implications of [7], consider the volumetric ratio of the soil needed to the refuse filled, Vs/Vr, at the optimum ratio. Rearranging [2] and dividing by Vr gives: Vs/Vr=(H+T)(L+GT)(W+GT)/Vr −1

[8]

Using [1] to substitute for Vr gives: Vs/Vr=(1+T/H)(1+GT/L)(1+GT/W)−1

[9]

Using [6] and [7] to substitute for L and H in [9] and rearranging gives the minimum Vs/Vr: Vs/Vr min=(1+T/W×JG×JW3/Vr)2×(1+T/W×G)−1

[10]

This gives the minimum soil-to-refuse ratio in terms of four common design variables: the thickness of the cover soil, the length of the working face, the daily compacted volume of refuse and the slope gradient. In [10] these four variables are clustered into three dimensionless groups: G, T/W,

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and W3/Vr. In Fig. 2, contours of the minimum soil-to-refuse ratio at three specific values of G are plotted for various values of T/W and W3/Vr. Independently of W and Vr, as either the gradient, G, or the cover thickness, T, increases, so does the minimum soil-to-refuse ratio. 4. Theoretical excess soil requirements away from optimum L/H ratio A landfill designer would only consider using the optimum L/H ratio described above when the consequences of not using the optimum became too great. It is important then to describe the penalty one pays, in terms of excess soil use, when one uses an L/ H ratio away from the optimum. To analyse this issue, one can compare the soil required for a non-optimum cell with that required for the optimally-designed cell. Define the excess soil-to-refuse ratio, ESR, to be the Vs/Vr given in [9] minus that given in [10], or: ESR=(1+T/H)(1+GT/L)(1+GT/W)−1−

[11]

{(1+T/W×JG×JW /Vr) ×(1+GT/W)−1} 3

2

Algebraic manipulation of [11] with [1] gives:

ESR=(1+GT/W)×T×JGW/Vr)×

GJ

NJ

L/H +1 G

L/H −2 G

H

[12]

L/H Figure 3 is a plot of [12] with ESR as a function of for a series of values for G L/H becomes greater than the optimum T×J(GW/Vr) and assuming that TG/Wp1. As G value of 1, the landfill cell becomes squatter, requiring excess soil on its top face, while L/H as becomes less than one, the landfill cell becomes tall and thin, requiring excess G soil to cover the working face. These two cases are shown in Fig. 4 and can be contrasted L/H is closer to one. with the schematic in Fig. 1 where G 5. Sample application Applying these results with practical values demonstrates their utility and limitations. Consider the following case: (i) after compaction, the refuse received is 1000 m3 day−1; (ii) the working face length required for the incoming vehicles is 30 m; (iii) the thickness of the daily cover averages 200 mm; and (iv) the site operates at a slope gradient of 3 horizontal to 1 vertical. For this situation, one might want to answer the following questions: (1) what are the preferred cell dimensions to minimize cover soil use? (2) how much cover soil would be used daily for the preferred cell dimensions? (3) how much extra cover soil would be used if the operator made the cell higher or lower than the preferred dimensions?

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Design of landfill daily cells 0.1 (a) log10(Vs /Vr) 0.0 0.01 –0.5

–2.0 0.001 0.1

1

–1.0

–1.5

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100

1000

0.1 (b)

log10(Vs /Vr) T/W

0.0 0.01 –0.5

–1.5

–2.0 0.001 0.1

1

10

–1.0

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1000

0.1 (c)

log10(Vs /Vr) 0.0 0.01 –0.5

–2.0 0.001 0.1

–1.5 1

10 W 3/ Vr

–1.0 100

1000

Fig. 2. Calculated values of minimum soil-to-refuse ratio for the idealized landfill cell. Contours are of equal values of minimum soil-to-refuse ratio. (a) G=2, (b) G=3, (c) G=4.

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ESR

T GW/Vr

0.05

0

0.20 0.10 0.05 0.02 0.01

0.20 0.10 0.05 0.02 0.01

1.0

2.0

3.0

L/H G Fig. 3. Calculated values of the excess soil requirement for the idealized landfill cell as a function of two dimensionless groups.

(4) how much less cover soil would be used if the working face width could be reduced? (5) how much less cover soil would be used over the life of the facility if the daily incoming waste were to increase? Use of the equations developed in this paper can aid in answering these questions. In response to question (1), equation [5] can be used. For G=3, Vr=3, Vr=1000 m3 d−1, and W=30 m, L=10 m. In addition, by equation [7], H=3.3 m. Thus, the preferred cell from the viewpoint of minimizing cover soil use would have dimensions of 30 m by 10 m at the base, and a height of 3.3 m. In response to question (2), the values of H and L above can be used in equation [2] to give Vs=146 m3 soil day−1. In this case, Vs/Vr would be 0.146, and cover soil would be 13% of the total volume. Analysis of questions like (3) can be approached with equation [12]. Take the cases where a daily cell is 1 m higher and 1 m lower than the preferred height of 3.3 m. For L/H =0.6. In this example, the case of H=4.3 m, by (1), L=7.7 m. As a result G T×J(GW/Vr)=0.06, and GT/W=0.02. Note that in this case GT/W p1 and the first term in [12] can be dropped and the results in Fig. 3 are appropriate. With these dimensionless values, the excess soil ratio, ESR, is 0.0042. The excess soil needed is Vr×ESR, or 4.2 m3 day−1. For the case where H=2.3 m, one would calculate L= L/H 14.3 m, =2.0, and ESR=0.0079. So, for the case of the short cell, the soil needed G is 146+8=154 m3 day−1. This small 5% increase in the daily soil needs could be significant over the life of a large landfill project where either cover may be scarce or revenue may be lost through soil use lessening waste volumes. Question (4) can be approached by changing the initial example to one where W= 20 m. Following the calculations in questions (1) and (2), L=12.2 m, H=4.1 m, and

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(a)

(b)

Fig. 4. Schematics of deviations from the optimum shape for a landfill cell. (a) An overly squat cell, [

L/H >2.0] G

L/H >0.5]. G Note: Same notation as Fig. 1. (b) an overly tall cell, [

Vs=133 m3 day−1. This implies a reduction in cover soil with the decrease in the length of the working face. The decrease from 30 m to 20 m, implies in this case a 9% reduction in daily soil needs. This estimate could in turn allow a site engineer to decide whether the advantages of reducing the working face would exceed the disadvantages. Question (5) can be approached in a similar manner to question (4). For example, consider a 50% increase in the compacted waste volume to 1500 m3 day−1. Assume that W remains at 30 m. As in the approach above, the cell becomes one where L=12.2 m, H=4.1 m, and Vs=183 m3 day−1. Although the soil used per day increases in this case, the soil-to-refuse ratio, Vs /Vr , has decreased from 0.146 to 0.122, meaning that 24 m3 less soil is needed per 1000 m3 refuse.

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6. Discussion The utility of theoretical equations developed in this paper will be limited because of their imperfect ability to describe in-field conditions. All edges of landfills must slope inwards and cannot be parallel, and so not all landfill daily cells can be of the parallelopiped form shown in Fig. 1. In addition, the vagaries of day-to-day operations may preclude the construction of solid forms very similar to the parallelopiped assumed here. For example, the compacted slope may not be constant, or the cover thickness not uniform. Those who use these equations will need to consider how far their daily cells differ from the idealized form presented here, and then consider how appropriate these equations might be. The assumption of the parallelopiped and the equations that result from the assumption should serve as a useful starting point for such analyses. The equations developed here give insight into the cell design appropriate when one wants to minimize the cover soil needed. The equations show that slight deviations from the optimum design are unlikely to lead to major changes in the cover soil required. Only when the lift height is 0.5 m or more from the optimum height is significant excess soil usage likely. The equations can help in assessing the optimum height of a landfill cell, but they are likely to be more useful in evaluating changes in daily cell designs and the resulting effects on soil usage. Changes in the compacted density, waste mass, cover thickness, slope gradient and working face length all have an effect on the amount of cover soil used. These equations provide a benchmark for comparisons of different designs in terms of their cover soil requirements. The current analysis assumes that the compacted density and the slope gradient can be specified by the designer. In some situations both of these variables are controlled by the degree of compaction. The result would be that a steep slope (low value of G) could lead to less cover soil, as shown by equation [10], but it would also likely lead to poorer compaction and so an increase in Vr, thereby increasing the soil needs. This interrelationship of Vr and G is not included in the equations presented here. On the other hand, for deeper landfills, the compaction on the day of waste placement may be less important than the total weight of refuse above, thereby lessening this interrelationship. This issue merits further analysis. Minimizing the use of cover soil is not the only factor to be considered in designing a landfill’s daily cell. Safety concerns might limit the height of the cells. High wind might lead a designer to have lesser slopes near the top of a landfill, or more slope on one facing of the cell than on the other. Still, it is useful to have idealized forms with calculable properties. The parallelopiped is such a volume, and calculations based on this shape should serve as a useful benchmark for daily cell designs. References Bagchi, A. (1990) Design, Construction, and Monitoring of Sanitary Landfill. New York, U.S.A.: John Wiley. Carson, D. A. (1992) Municipal solid waste landfill daily cover alternatives. Geotextiles and Geomembranes 11, 629–635. McBean, E. A., Rovers, F. A. & Farquhar, G. J. (1995) Solid Waste Landfill Engineering and Design. New Jersey, U.S.A.: Prentice Hall. Querio, A. J. & Lundell, C. M. (1992) Geosynthetic use a daily cover. Geotextiles and Geomembranes 11, 621–627. Tchobanoglous, G., Theisen, H. & Vigil, S. A. (1993) Integrated Solid Waste Management. New York, U.S.A.: McGraw-Hill.