The design of stormwater management devices and permanent erosion and sediment control measures for a landfill’s final cover is not as straightforward as might be assumed. This is especially true when the final cover is steep and contains multiple layers including geosynthetics, so that drainage efficiency affects cover stability, and the consequences of erosion damage can be quite costly. Initial construction cost is also of concern, as is ease of construction, particularly where schedules are tight and final grades are limited by permit conditions.
To compound these challenges, there is limited design guidance available to landfill designers. Most conventional design approaches do not account for long, steep slopes or conveyances that are subject to potentially large subsidence, conditions that exacerbate erosion and bring durability of the stormwater conveyances to the top of the list of design criteria. Owners need to recognize the unique challenges brought about by these issues and establish clear design goals and realistic budgets for closure construction and postclosure maintenance. They also need to be selective when employing consultants to design these facilities, given the potentially serious consequences of a failure or repeated failures.
Erosion and sediment control is a critical factor in postclosure maintenance, and stricter enforcement of sedimentation laws and regulations is a national trend. Landfills face a particularly tough challenge in this regard given their large exposed areas, steep slopes, and generally hostile growing conditions, which make the establishment of vegetation and other stabilization methods very difficult.
Innovative designs and a heavier reliance on geosynthetic products for erosion control are almost certain to be needed to address this problem. Long-term cost-effectiveness and even initial cost savings are potential benefits of this increased effort to control stormwater and its effects, since construction and maintenance of a final cover and sedimentation facilities are costly line items in landfill closure and postclosure budgets.
This paper summarizes a design strategy developed by the author for stormwater drainage from a multi-layer geocomposite final cover on a steep (3:1 sideslopes) Subtitle D municipal solid waste landfill, though it is applicable to virtually all landfill types. The design approach emphasizes rigorous analysis of stormwater quantities and conveyances, stability of the final cover under saturated conditions, durability of the devices and structures employed, and aggressive erosion and sediment control.
A landfill final cover must perform several functions, most notably, (1) waste and waste byproducts containment, (2) rainfall infiltration barrier (or inhibitor), (3) landfill gas barrier (where vents or an active recovery system are employed), (4) odor and vector control, and (5) support acceptable aesthetics (“reclamation”). The consequences of final cover failure include costly cover damage (structural), erosion and sedimentation, releases of waste or waste byproducts to surface water and air, health and safety risks (vectors, fire, etc.), compromise of leachate collection and landfill gas systems, and increased postclosure maintenance costs.
In light of these concerns, the owner’s expectations should be clearly and thoughtfully defined. Major issues to clarify, in suggested order of importance, are (1) frequency of failure, (2) maintenance requirements, and (3) cost (construction and postclosure). It has been the author’s experience that owners’ expectations are normally poorly defined, and usually heavily weighted in favor of lower construction costs. Maintenance requirements are often only implied, and failure is usually considered unacceptable and improbable rather than a natural and unavoidable consequence of anything man-made, and thus a design variable.
Major design factors for landfill final covers include
- final configuration and postclosure use,
- removal of stormwater,
- erosion and sediment control,
- effect on waste filling,
In final cover design, the principle considerations with regard to managing stormwater include (1) removal of stormwater runoff, (2) cover stability, (3) erosion and sediment control, and (4) durability, constructability, and maintainability. This paper focuses on the first of these, with brief mention made of the others.
The current design guidance for stormwater drainage on landfills is very limited, with the presumption apparently being that conventional site development stormwater practices will suffice. Some notable deficiencies in the available design guidance include the following:
- How to handle long, steep slopes in general;
- Criteria for diversion channel design on sideslopes (longitudinal slope, spacing, freeboard, etc.);
- Design storm selection;
- Accommodation of differential settlement; and
- Failure criteria and replacement frequency.
The proposed design approach outlined below is intended to address most of these issues.
The proposed design approach tracks stormwater as it hits the landfill, working downstream to its discharge at perimeter ditches or into stormwater detention ponds. This is the logical sequence given the cumulative nature of runoff flows from contributing areas and sub-areas of the landfill cover. The steps are summarized as follows:
- Lay out the system and calculate stormwater runoff,
- Size diversion channels and berms,
- Select channel lining,
- Design downslope conveyances (slope drains, inlets, and conduits), and
- Adjust the layout as necessary.
Layout and Runoff Determination. The first step in the design is to lay out the diversion channels (berms) and downslope conveyances (slope drains are recommended). From experience gained from several iterations of trial layouts in the Piedmont Physiographic Province of North Carolina, where rainfall averages about 40 in. annually, a horizontal spacing of diversions of 90-120 ft. is recommended.
Closer spacing would result in a final cover crowded with stormwater conveyances, significantly raising costs and complicating construction and postclosure maintenance. Greater spacing would raise the risk of midslope erosion by increasing flow lengths, and would increase cumulative flows, possibly requiring inlet and/or slope drain conduit diameters that would be impractical for burial in the protective soil layer of the final cover. Of course, different climatic conditions dictate different optimum spacing and layout schemes.
The location of downslope conveyances is governed by topography and site constraints at the landfill perimeter, contributing drainage area (capacity of inlets and slope drains to be determined by trial and error) and landfill geometry. Landfill geometry is important because attention must be paid to changes in direction of flow and the directions of converging flows. The author has reviewed designs where channels turned 120-plus degrees abruptly around landfill corners, ran over 1,000 ft. without a downslope conveyance, then discharged against the flow of perimeter ditches. Water may “always run downhill,” but serious disruptions to flow and erosion should be avoided where possible. Landfill geometry also dictates the overall layout in fundamental ways, since more than one layout scheme is usually possible, but a “best fit” can usually be found from graphical trial and error.
To calculate runoff, and thus inflow from each contributing area, the Rational Formula is used since the sub-areas are small, typically less than 2 ac. The Rational Formula takes the following common form:
Q = CiA (cfs)
C = runoff coefficient (dimensionless)
i = rainfall intensity (in./hr.)
A = drainage area (ac.)
Runoff coefficients from old Soil Conservation Service guidelines, which are frequently used, range up to 0.6 for bare, compacted soils. Anecdotal evidence suggests that these values may be low, especially on steep landfill sideslopes with clayey cover soils. The use of higher coefficients is, of course, conservative for channel and downslope conveyance design. Slightly lower values may make sense for the top areas of the landfill where slopes of 5 to 10% are common.
Selecting the design storm is, in the author’s opinion, a crucial step with regard to frequency of failure from overtopping and erosion (flow velocity and tractive force). The Environmental Protection Agency’s Subtitle D design criteria suggest the 25-year, 24-hour storm as the minimum design storm for run-on and runoff. That is fine for volume-based designs, such as detention ponds, but it falls way short of predicting critical rainfall intensities that can occur during downpours from thunderstorms and the like.
From a quick examination of times of concentration on a steep landfill cover, and by selecting a storm duration that approximates the time of concentration, it becomes apparent that a very short storm duration, and thus a high rainfall intensity, should be considered. The author recommends comparing the result with site-specific rainfall records and/or anecdotal evidence of critical site rainfalls to calibrate the design to the anticipated “worst case” for the site. The author has used the 10-year, five-minute storm in most cases, resulting in design rainfall intensities of 6.5 to 8 in./hr.
Diversion Channels and Berms. Once the inflow from rainfall runoff is determined, the design of the diversion channels is straightforward. A V-ditch cross-section is recommended to conserve area, and it is the natural shape formed by the intersection of the landfill sideslope and the diversion berm. The channel/berm should be sized for the flow at the downstream end of the channel, i.e., at the inlet where the channel discharges. The flow can be calculated from Manning’s Equation and the Continuity Equation as follows:
Manning’s Equation V=1.486/n x R2/3 x S1/2 (fps)
Continuity Equation Q=AV (cfs)
For given degrees of sideslope, the two equations can be solved simultaneously for d = flow depth (ft.) and V (ft./sec.). An assumed value of Manning’s n is required. It is recommended that geosynthetic channel linings be used (“erosion control mats”); therefore, manufacturers’ suggested values of n are normally available for both the unvegetated and the vegetated conditions. The n value should be adjusted upward to allow for surface irregularities, cross-section variations, obstructions, etc.
The channel’s longitudinal slope (S) must be predetermined from the layout and used as an input variable in the solution. A slope in the range of 3-5% is recommended to allow for slope loss due to differential settlement of the landfill surface and sedimentation.
Once a design flow depth is selected, the berm height should be set to provide “freeboard,” or added height, to contain the flow and provide a factor of safety against sediment buildup and differential settlement. A minimum freeboard of 1 ft. is recommended, though a lesser value may be acceptable if berm height is becoming problematic from a design geometry standpoint.
An example diversion berm (and channel) cross-section is shown in Figure 1. Note the drainage outlet for the final cover drainage layer (a geonet composite), and that all earthwork construction takes place above the layered geosynthetics to facilitate construction.
Channel Lining. Though a grass lining alone may suffice during low flows, or even for the design flow in theory, relying on grass alone is a risky strategy, especially during the period of vegetation establishment. The variety of erosion control mats or, better yet, turf reinforcement mats (TRMs) currently available makes selection of a channel lining that provides both short- and long-term protection against erosion easier than ever and cost-effective. Several manufacturers produce multiple products that vary in materials and construction for short-term stabilization (biodegradable) or long-term turf reinforcement (nondegradable, synthetic). One manufacturer even produces a three-dimensional permanent erosion reinforcement matrix that can be substituted for riprap in most applications.
Selection usually is based on performance factors and cost. Manufacturers’ data usually exists on allowable velocity for both unvegetated and vegetated conditions. In addition to velocity, the allowable tractive force (actually shear stress) should also be checked, since it is a more reliable predictor of lining performance than velocity. The annual Geotechnical Fabrics Report Specifiers Guide, published by the Industrial Fabrics Association International, is a good comprehensive source of such data.
The tractive force, T, is calculated as follows:
T = y x d x S (psf)
y = unit weight of water (62.4 lb./ft.3)
d = flow depth (ft.)
S = channel slope (ft/ft.)
For long-term protection, the author recommends a composite mat of coconut fiber matrix in a synthetic mesh for low-velocity, low shear-stress conditions. For high-velocity, high shear-stress conditions, use a nondegradable TRM, either soil-filled or nonsoil-filled per the manufacturer’s recommendation. The designer must pay careful attention to the manufacturer’s suggested application and limitations and should consult with a manufacturer’s representative during design. In any event, the contractor must follow the manufacturer’s installation guidelines diligently in order to achieve optimum performance. Figure 1 shows the TRM channel lining in the diversion channel.
Slope Drains. Slope drains constructed from corrugated HDPE pipe with sewer-type, soil-tight connections are recommended for slope-drain construction. Some designers prefer open-channel “downchutes” lined with riprap or other hard armor, but the author has found them to be unreliable on steep, settling waste slopes and very costly to construct. The proposed slope drains come to the site ready to install and can be snapped together quickly and laid directly on the final cover geosynthetics prior to placing the final protective soil layer. Anchorage must usually be provided, especially where long runs are used, but considerable soil friction is developed with the corrugations. The resulting buried slope drain provides the added benefits of pleasing aesthetics and ease of slope maintenance.
For inlet design, a circular inlet constructed from the same corrugated HDPE pipe has proven successful. See Figure 2.
Again, the prefabricated inlet comes to the site ready to snap in place, speeding construction and thus reducing cost. Assume the inlet is a sharp-crested weir then solve for weir length using the weir equation (Francis Formula).
Q = 3.33 x L x H3/2 (cfs)
Q = cumulative inflow (cfs)
L = weir length (ft.)
H = head above crest = d + V2/2g (ft.)
d = depth of flow approaching weir (ft.)
V = velocity of flow (fps)
g = acceleration due to gravity (32.2 ft./sec2)
Solve for L based on flow from one direction. For a circular inlet, Lmax = 1.6 x D, where D = inlet diameter. Since flow is tangential to a portion of the inlet rim, the transverse projection of the rim represents a reasonable minimum value, thus, use Lmin = D. Select the inlet diameter such that D ³ Lmin. The author has found that 24-in. and 36-in. diameter inlets usually provide adequate capacity. A larger diameter would make the berm geometry difficult to construct, so a change in system layout would be recommended in that case.
Check to see if a hydraulic jump will occur where the channel widens at the inlet to make sure the berm won’t be overtopped. This occurs when flow goes from supercritical to subcritical, with the balance point known as critical depth. Thus, check critical depth, dc, to see if flow will go from supercritical to subcritical. Critical depth occurs when specific energy is at its minimum, and the following equation is satisfied:
A3/T = Q2/g or A/T = V2/g (because Q = A x V)
A = area of flow (ft.2)
T = width of channel at water surface (ft.)
Q = discharge (cfs)
g = acceleration due to gravity (32.2 ft./sec.2)
V = velocity of flow (fps)
For the triangular channel used, A/T = d/2, so the equation simplifies to:
dc = 2 x V2/g (ft.)
If d < dc, flow is supercritical. Assume a hydraulic jump will occur and calculate its depth. At a hydraulic jump,
(d1 x A1)/3 + (Q x V1)/g = (d2 x A2)/3 + (Q x V2)/g,
where subscripts 1 and 2 refer to before and after the jump. After making several substitutions, the equation can be simplified to:
d23 – d13 – (3 x Q x V1)/(C x g) x (1- d12/d22) = 0
C = 0.5 x T/d (dimensionless)
This must be solved by trial and error until d2 is found. The berm height can then be checked for adequate containment and freeboard at the hydraulic jump.
The next step in the design is to size the conduit exiting the inlet that forms the slope drain downslope conveyance. To assure nondestructive hydraulics under design flow conditions, and to analyze flow, the following stipulations/assumptions are suggested:
- The pipe should not flow full to avoid “slugging”
- Assume/assure the exit is “free” (unsubmerged)
- Assume/assure all flow is supercritical (pipe slope exceeds critical slope)
- Assume the entrance is submerged (orifice entrance condition)
The Orifice Equation is then used as follows:
Q = Cd x A x (2g x [h-a])1/2 (cfs)
Cd = coefficient of discharge (dimensionless)
A = area of orifice (ft.2)
g = acceleration due to gravity (32.2 ft./sec.2)
h = water depth at outlet (ft.)
a = one-half the outlet height (ft.)
Use Cd = 0.6 and get h from inlet design. Then solve for d by trial and error until the equation is satisfied. Finally, check the flow characteristics in the conduit using Manning’s Equation to confirm that the pipe is not flowing full, especially as flows accumulate from multiple inlets.
The author has had success with both 15-in. and 18-in. diameter conduits. Any greater diameter would create problems with soil cover thickness, and even 18 in. requires that the contractor reduce the intermediate cover soil layer thickness prior to the deployment of the final cover geosynthetics to provide additional depth for the conduit. A dual wall, smooth-wall interior pipe (versus single-wall corrugated), because of its superior hydraulic properties, can reduce pipe diameter. See Figure 3 for a slope drain cross-section as described.
Where multiple inlets discharge into one conduit from successive diversions parallel to the slope, converging flows could create disruptions to conduit flow that could hinder flow and cause destructive forces to develop. This would be especially true if inlets were merely put in series and the flows converged in the vertical plane. As such, an inlet configuration for all but the uppermost inlet was devised that lets the flows converge at a low, horizontal angle. See Figure 4 for a plan view of the slope drain at an intermediate inlet. The antivortex device incorporated into the inlet also shows in Figure 4.
Because most landfill sideslopes are steep, frequently 3:1 to maximize airspace, the flow velocity in the slope drain conduit can be quite high. Velocities as high as 40 fps have been calculated. This points out the need for robust energy dissipation and outlet protection at the outlet. Where site constraints exist at the toe of the landfill, a structural stilling basin may be needed.
Stormwater Drainage Effects on Veneer Stability. In their paper on geosynthetic landfill cover design, Thiel and Stewart (1993) discuss the effect of stormwater drainage on veneer stability. The analysis of final cover stability includes the destabilizing contribution of excess pore water pressure that results when the final cover soil profile becomes saturated. When the drainage layer reaches capacity and backs up, the resulting saturation of the full cover profile has a buoyant effect and can reduce the confining pressure to the point where interface friction will no longer keep the profile stable. A slide of the final cover can occur, sometimes with disastrous results.
Thiel and Stewart (1993) provide an analytical solution to calculate the maximum spacing of drainage outlets (diversion channels) required in order to keep saturation from occurring. Their equation takes the following form:
Lmax = k2/k1 x sinb x h2 (ft.)
k2, k1 = coefficients of permeability for drainage layer and protective cover soil layer, respectively (cm/sec.)
b = slope angle (degrees)
h2 = drainage layer thickness
Note that, for a given diversion spacing, L, the ratio of drainage layer permeability, k2, to cover soil permeability, k1, has a minimum value in order to maintain stability. This is a practical tool for specifying soil and drainage layer properties after the design has been finalized.
Erosion and Sediment Control. A key function of the stormwater management system is to minimize erosion and sedimentation from the landfill. This is especially crucial during the period right after construction when vegetation is not yet established. Careful and accurate grading during final cover construction is critical to performance of the stormwater conveyances. Proper maintenance is also crucial to satisfactory performance.
The design strategy outlined above incorporates and promotes the use of geosynthetic materials as a primary defense against erosion and sedimentation. It is recommended that all channels be lined with geosynthetic mats and that robust inlet and outlet protection be provided. Consideration should also be given to protecting the slopes between diversions with geosynthetic products, such as roving, netting, or even erosion control mats.
Careful attention should be paid to the vegetation specified for the landfill slopes and channels with regard to their ease of establishment, erosion resistance, impact on stormwater flow, survivability (especially drought resistance), and ease of maintenance.
Durability, Constructability, and Maintainability. Durability of the design elements should be a primary consideration in order to reduce postclosure maintenance frequency and cost. Durability of the soil cover relates directly to erosion and sediment control as described above, and geosynthetic products can provide much help in that regard by protecting the seedbed during vegetation establishment and reinforcing the roots of vegetation once established. For stormwater conveyances, flexibility is a must given the unavoidable differential settlement that results from decomposing waste. This suggests the avoidance of hard-armor solutions, and flexible “geopipes,” such as the slope drains proposed, become a logical choice.
Constructability is a design goal often underemphasized. Too often, landfill designers ask the landfill operator to achieve the desired final grades for stormwater management with waste placement. Benches and diversions are difficult if not impossible to grade with waste, and this leads to expensive regrading at closure time. The proposed design strategy allows the operator to grade uniform slopes, and then the geosynthetics installer to place materials on those same slopes. Only then are the undulating final contours for stormwater management created, and then with soil that is easy to place and shape.
The proposed slope drains are also easily constructed above uniform slopes protected with geosynthetics, virtually snapped together like toys with few tools and minimal labor and without complicated grading, alignment, and expensive on-site construction methods. The use of rolled erosion control products speeds construction and facilitates proper installation, usually with unskilled labor.
Maintainability refers to design features and construction quality assurance that provide for fewer failures and long-term maintenance cost savings. Smooth slopes created by buried stormwater conveyances mean easier access for mowing and erosion repairs. The liberal use of geosynthetic erosion control products, though more costly at the time of construction, can significantly reduce final cover repairs during the postclosure period and reduce the frequency of costly removal of sediment from ditches and ponds. Slope-drain inlets and grates that reduce clogging can help prevent diversion berm blowouts and reduce sedimentation.
Careful attention to construction layout and ample construction quality assurance testing and surveying can greatly reduce the number of problems that arise after the contractor has demobilized and been paid in full. After all, the design storm or one even more severe may not occur until well after the normal one-year warranty period.