1. Designing Water Balance Covers (ET Covers) for Landfills and Waste Containment by
Craig H. Benson, PhD, PE, DGE, NAE
Geological Engineering
University of Wisconsin-Madison
Madison, Wisconsin USA   

2. For more details, please see our book, which is available at www. asce
For more details, please see our book, which is available at or amazon.com

3. Covers & Waste Containment
Cover system
Gas vent or collection well
Groundwater monitoring well
Waste
Native soil
Groundwater
Leachate collection system
Barrier system

4. Cover Strategy - Conventional vs. Water Balance Covers
Conventional Cover
Water Balance Cover

5. Cover Profiles for Water Balance Covers
Monolithic barrier: thicker layer of engineered fine-textured soil – “storage layer.”
Capillary barrier: fine-textured soil “storage layer” over coarse-grained capillary break.

6. What Drives Interest: Cost Savings
Subtitle D composite at site: 450 mm fine-grained soil < 10-5 cm/s, 1-mm geo-membrane, drainage layer, and 300 mm surface layer.
> 64% cost savings with water balance cover

7. Water Balance Covers: How They Work
Precipitation
Evapotranspiration
Infiltration
“Sponge” L
S = soil water storage
Sc = soil water storage capacity
Percolation if S > Sc

8. The Balance in Water Balance Covers
Storage capacity of cover, Sc
Natural water storage capacity of finer textured soils.
Water removal by evaporation and transpiration.
Key: Design for sufficient storage capacity to retain water accumulating during periods with low ET with limited or desired percolation. Need to know required storage, Sr.

9. Real Data More Complex – But Predictable

10. Soil Water Retention In Unsaturated Soil
Suction, y - + 5 1 5 4 3 2
Wilting point
Suction, y - + 4
Field capacity - + 3 - + 2
Volumetric Water Content, q
As the soil becomes drier, the water filled pathways become narrower and more tortuous - + 1

11. Unsaturated Hydraulic Conductivity
Water retreats into smaller pores as suction increases, causing water content (q) to diminish and hydraulic conductivity to drop.

12. Unsat. Hydraulic Conductivity & Suction
Water retreats into smaller pores as suction increases, causing water content (q) to diminish and hydraulic conductivity to drop.
Coarser soil becomes less permeable than drier soil when suction is high enough
WET
SOIL
DRY SOIL

13. Evaporation and Transpiration (ET)
PET = potential evapotranspiration = max ET for given meteorological condition

14. Potential Evapotranspiration (PET)
FAO Penman-Monteith Reference Evaporation (PET) in mm/d
e = atmospheric vapor pressure at 2 m (= saturated vapor pressure x relative humidity), [kPa]
es = saturated vapor pressure [kPa] of air at 2 m at air temperature Ta [oC]
U = wind velocity at 2 m above ground surface [m/s]
x = psychometric constant [kPa/oC]
D = slope of curve relating es and T [kPa/oC]
Rn = net radiation [MJ/m2-d] = net solar radiation (Rns) – long wave radiation (Rnl)
G = soil heat flux [MJ/m2-d]
T = atmospheric temperature (oC)
1 MJ/m2-d of energy = mm/d water evaporation.

15. Design Process Define performance goal (e.g., 3 mm/yr)
Evaluate local vegetation analog
Species distribution and phenology
Coverage
Leaf area index
Root depth and density
Evaluate candidate borrow sources
What types of soils?
How much volume?
Uniform?
Blending required or helpful?

16. Design Process - 2 Laboratory analysis on borrow source soil
Particle size analysis
Saturated hydraulic conductivity
Soil water characteristic curve
Shrink-swell, wet-dry, pedogenesis
Preliminary design computations
Required storage
Available storage and required thickness
Water balance modeling
Typical performance
Worst-case performance
What if scenarios?

17. Design Process - 3 Final Design Geometric design
Surface water management
Gas management
Erosion control strategies
Specification preparation
Regulatory approval
Bid preparation & contractor selection

18. Design Questions for Step 5
How much water needs to be stored?
Identify critical meteorological years
Define precipitation to be stored
How much water can be stored?
Define the storage capacity
Compute required thickness
Can water can be removed?
Define wilting point
Determine available capacity

19. Required Storage: Design Year
Typical Design Scenarios:
Wettest year on record
95th percentile wettest year
Typical year
Wettest 10 yr period
Entire record
Year with highest P/PET
Snowiest winter
Combinations

20. Water Accumulation: When & How Much
1. Determine when water accumulates. 2. Define how much water accumulates.
Example: for fall-winter months at sites without snow, water accumulates in the cover when monthly P/PET exceeds 0.34.

21. Thresholds for Water Accumulation
Examined P, P/PET, and P-PET as indicators of water accumulation and found P/PET threshold works best.
Data segregated into two climate types (with & without snow and frozen ground) and two periods in each year (fall-winter and spring-summer).
Water accumulates when P/PET threshold exceeded.
Climate
Type
Season
Threshold
No Snow & Frozen Ground
Fall-Winter
P/PET > 0.34
Spring-Summer
P/PET > 0.97
Snow & Frozen Ground
P/PET > 0.51
P/PET > 0.32
Fall-winter = September - February
Spring-summer = March - August

22. Example: Idaho Site (snow & frozen ground)
Mar-Aug:
0.51
Sept-Feb
0.32

23. Example: Texas Site (no snow & frozen grd.)
Mar-Aug:
0.97
Sept-Feb
0.34

24. How Much Water Accumulates?
1. Use water balance approach: ΔS = P – R – ET – L – Pr
Δ S = change in soil water storage
R = runoff
P = precipitation
ET = evapotranspiration
L = lateral internal drainage (assume = 0)
Pr = percolation
2. ET is unknown, but is a fraction (β) of PET: ET = β PET
3. R, L, and Pr can be lumped into losses (Λ)
Simplify to obtain: ΔS = P – β PET – Λ
4. Equation used to compute monthly accumulation of soil water storage if P, PET, β, and Λ are known.

25. Parameters for Water Accumulation Equation
Δ S = P – β PET – Λ
Climate
Type
Season
β (-)
Λ (mm)
No Snow
&
Frozen Ground
Fall-Winter
0.30
27.1
Spring-Summer
1.00
167.8
Snow &
0.37
-8.9
Two sets of β and Λ parameters (fall-winter & spring-summer) for a given climate type.

26. Monthly Computation of Required Storage
Fall-Winter
Months
Spring-Summer
Months
Sr = required storage
Δ Sr m = monthly water accumulation
hm = monthly index for threshold (0 = below, 1 = above)
If Δ Sr m < 0, set Δ Sr m = 0.

27. Computing Required Storage
Fall-Winter Months
Spring-Summer Months
If argument < 0, set = 0
βFW = ET/PET in fall-winter
βSS = ET/PET in spring-summer
ΛFW = runoff & other losses in fall-winter
ΛSS = runoff & other losses in spring-summer
Pm = monthly precipitation
PETm = monthly PET

28. Example: Idaho Site (snow & frozen ground)
For months below threshold, set ΔS = 0
Δ S = P – 0.37*PET
(Fall-Winter)
β = 0.37, Λ = 0
Store 97 mm for typical year, 230 mm for wettest year

29. Example: Texas Site (no snow & frozen ground)
For months below threshold, set ΔS = 0
ΔS = (P – 0.37*PET)-27
(Fall-Winter)
β = 0.3, Λ = 27
Store 188 mm for 95th percentile year,
548 mm for wettest year

30. Predicted and Measured Sr
Good agreement computed & measured required storage.

31. Monolithic Covers: Storage Capacity
What is the storage capacity (Sc)?
Area
qc = water content when percolation transmitted.

32. Monolithic Covers: Storage Capacity
What is available storage (Sa)?
qmin = lowest water content achieved consistently.
Area

33. Soil Water Characteristic Curve (SWCC)
qfc = field capacity water content, qfc at 33 kPa suction (use for qc).
qwp = wilting point water content, q at 1500 kPa. Arid regions kPa. (use for qmin).
qwp = qfc - qwp = unit storage capacity.
4000
kPa 33
kPa
qfc = 0.26, qwp = 0.01, qu = unit storage = = 0.25

34. Pedogenesis & Hysteresis
Lab curve on small compacted specimen, typically ASTM D6836
Field curve has lower air entry suction and steeper slope.
qs = saturated q
qr = residual q
a = shape parameter controlling air entry suction
n = shape parameter controlling slope

35. Compare: Field to Lab
Create field SWCC by adjusting lab-measured SWCC:
a adjustment
Plastic soils = 13x
Non-plastic soils = none
n = no adjustment

36. Compare Field-Measured & Computed Storage Capacities from ACAP
Good agreement between computed and field-measured storage capacities.
Need to account for effect of pedogenesis on soil properties.

37. Design Step 6 – Water Balance Modeling
Webinar March 14 T E P R q Pr z

38. Why model water balance covers?
Predict performance relative to a design criterion and/or refine design
Sensitivity analysis to determine key design parameters
Comparison between conventional and alternative designs.
“What if?” questions.
For these purposes, model MUST capture physical and biological processes controlling behavior (e.g., unsaturated flow, root uptake)

39. Output: Water Balance Quantities
Precipitation: water applied to the surface from the atmosphere (unfrozen and frozen)
Evaporation: water discharged from surface of cover to atmosphere due to gradient in vapor pressure (humidity)
Transpiration: water transmitted to atmosphere from the soil via plant root water uptake
Evapotranspiration: evaporation + transpiration
Infiltration: water flowing into soil across the surface

40. Predictions for 2001-2003 for a site in Altamont, CA using LEACHM
Sample Output
Predictions for for a site in Altamont, CA using LEACHM
Predictions appear realistic, but are not real. All models are mathematical abstractions of reality. Apply appropriate skepticism to predictions.

41. Appendix

42. PET Calculations - 1 Data for Input:
Air temperature at 2 m (daily minimum, Tmin, and maximum, Tmax), oC
Solar Radiation, Rs (MJ/m2-d)
Daily average wind velocity, U, at 2 m (m/s)
Daily average relative humidity, RH (%)
Soil heat flux, G ~ assume = 0

43. PET Calculations - 2
x = 0.665x10-3 P where P is atmospheric pressure in kPa
P = [( z)/293]5.26 , P in kPa and z in m above mean sea level
T = mean daily air temperature (oC) at 2 m, [Tmin+Tmax/2]
es = exp[17.27 T/(T+237.3)] in kPa and T in oC
{compute as average of es determined for Tmin and for Tmax}
e = es(RH/100), in kPa, where RH is relative humidity in %
D = 4098{0.6108exp[17.27 T/(T+237.3)]}/(T+237.3)2 , kPa/oC

44. PET Calculations - 3 Rns = net solar radiation = Rs (1-a)
a = albedo (fraction of solar energy reflected)
Rnl = net long wave radiation (emitted from earth)
h = Stefan-Boltzman constant (4.903x10-9 MJ/K4-m2-d)
Tmin and Tmax in oK
Rso = clear-sky solar radiation

45. For latitude: http://www.bcca.org/misc/qiblih/latlong.html
PET Calculations - 4
with z in m above mean sea level
Ra = extraterrestrial radiation (MJ/m2-d):
J = Julian day (1-365 or 366)
For latitude: