Designing Water Balance Covers (ET Covers) for Landfills and Waste Containment
by
Craig H. Benson, PhD, PE, DGE, NAE
Geological EngineeringUniversity of Wisconsin-MadisonMadison, Wisconsin 53706 USA
For more details, please see our book, which is available at
www.asce.org or amazon.com
Covers & Waste Containment
Waste
Groundwater
Native soil
Groundwater monitoring well
Gas vent or collection well
Leachate collection systemBarrier
system
Cover system
Cover Strategy - Conventional vs. Water Balance Covers
Conventional Cover Water Balance Cover
SurfaceLayer
Interim
ClayBarrier
GeomembraneStorageLayer
Interim
Capillary Break
Waste Waste
CapillaryBarrier
Monolithic Barrier
Coarse Soil
FineTextured
Soil
FineTextured
Soil
Monolithic barrier: thicker layer of engineered fine-textured soil – “storage layer.” Capillary barrier: fine-textured soil “storage layer” over coarse-grained capillary break.
Cover Profiles for Water Balance Covers
What Drives Interest: Cost Savings
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50,000
100,000
150,000
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300,000
SubDComposite
Monolithic1.2 m
Monolithic1.5 m
Cove
r C
ost
($
/ha
) in
20
00
For cost per acre, divide by 2.47 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
Precipitation
L “Sponge”
Infiltration
Percolation if S > Sc
Evapotranspiration
Water Balance Covers: How They Work
S = soil water storageSc = soil water storage
capacity
Natural water storage capacity of finer textured soils. Water removal by evaporation and transpiration.
Eva
potra
nspi
ratio
n (E
T) Soil W
ater Storage (S
)
S
ET
Sum
mer
Fall
Win
ter
Spr
ing
Fall
Win
ter
Spr
ing
Storage capacity of cover, Sc
The Balance in Water Balance Covers
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.
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Cu
mu
lativ
e P
reci
pita
tion
and
Eva
potr
ansp
iratio
n (
mm
) Soil W
ater S
tora
ge and C
umulative P
ercolation
and S
urface Run
off (mm
)
Precipitation
Soil WaterStorage, S
Evapotranspiration
Percolation
Surface Runoff (nil)
StorageCapacity, S
c
Available Storage, S
a
Annual Change in Storage, S
i
Real Data More Complex – But Predictable
Soil Water Retention In Unsaturated Soil
Field capacity
Wilting point
1
5
4
3
2
0
- +1
0
-+ 5
0
- +4
0
- +3
0
- +2 Volumetric Water Content, q
Su
ctio
n, y
As the soil becomes drier, the water filled pathways become narrower and more tortuous
Suction, y
Unsaturated Hydraulic Conductivity
10-20
10-18
10-16
10-14
10-12
10-10
10-8
10-6
0.00 0.10 0.20 0.30 0.40 0.50
Hyd
rau
lic C
on
duct
ivity
(cm
/s)
Volumetric Water Content
Silty ClayLoam
nand0;V
Vw
Water retreats into smaller pores as suction increases, causing water content (q) to diminish and hydraulic conductivity to drop.
Unsat. Hydraulic Conductivity & Suction
10-12
10-10
10-8
10-6
10-4
10-2
100
10-1 100 101 102 103 104
Matric Suction (cm)
Hyd
raul
ic C
ondu
ctiv
ity (
cm/s
)
Finer
Coarser
DRY SOIL
WETSOIL
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
Evaporation and Transpiration (ET)
PET = potential evapotranspiration = max ET for given meteorological condition
Potential Evapotranspiration (PET)
n s
9000.408 R G U e e
T 273PET
1 0.34U
FAO Penman-Monteith Reference Evaporation (PET) in mm/d
http://www.fao.org/docrep/x0490e/x0490e07.htm#solar%20radiation
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 = 0.408 mm/d water evaporation.
Design Process
1. Define performance goal (e.g., 3 mm/yr)
2. Evaluate local vegetation analog• Species distribution and phenology• Coverage• Leaf area index• Root depth and density
3. Evaluate candidate borrow sources• What types of soils?• How much volume?• Uniform?• Blending required or helpful?
Design Process - 24. Laboratory analysis on borrow source soil
• Particle size analysis• Saturated hydraulic conductivity• Soil water characteristic curve• Shrink-swell, wet-dry, pedogenesis
5. Preliminary design computations• Required storage• Available storage and required thickness
6. Water balance modeling• Typical performance• Worst-case performance• What if scenarios?
Design Process - 37. Final Design
• Geometric design• Surface water management• Gas management• Erosion control strategies• Specification preparation
8. Regulatory approval
9. Bid preparation & contractor selection
• 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
Design Questions for Step 5
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
Water Accumulation: When & How Much1. 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.
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AlbanyAltamontApple ValleyMarinaSacramento (thin)Sacramento (thick)
0 1 2 3 4 5 6Monthly P/PET during Fall-Winter (P/PET
m, FW) (mm)
(a) No Snow & Frozen Ground, Fall-Winter
Net
Mon
thly
Wat
er A
ccum
ula
tion
(S
r m
) (m
m)
Sr,m
= -2.324 (P/PET)m
2 + 39.189 (P/PET)m
- 13.174
R2 = 0.67
ClimateType
Season Threshold
No Snow & Frozen Ground
Fall-Winter P/PET > 0.34
Spring-Summer
P/PET > 0.97
Snow & Frozen Ground
Fall-Winter P/PET > 0.51
Spring-Summer
P/PET > 0.32
Thresholds for Water AccumulationExamined 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).
Fall-winter = September - FebruarySpring-summer = March - August
Water accumulates when P/PET threshold exceeded.
Example: Idaho Site (snow & frozen ground)
Mar-Aug:0.51
Sept-Feb0.32
Example: Texas Site (no snow & frozen grd.)
Mar-Aug:0.97
Sept-Feb0.34
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 – Λ4. Equation used to compute monthly accumulation of soil water
storage if P, PET, β, and Λ are known.
Parameters for Water Accumulation Equation
ClimateType Season β (-) Λ (mm)
No Snow&
Frozen Ground
Fall-Winter 0.30 27.1
Spring-Summer 1.00 167.8
Snow & Frozen Ground
Fall-Winter 0.37 -8.9
Spring-Summer 1.00 167.8
Δ S = P – β PET – Λ
Two sets of β and Λ parameters (fall-winter & spring-summer) for a given climate type.
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Monthly Computation of Required Storage
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.
Fall-WinterMonths
Spring-SummerMonths
6 6
r m r m m r mm 1 m 1FW SS
S h S h S
Computing Required Storage
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
If argument < 0, set = 0
6
r m m FW m FWm 1
S h P PET
6
m m SS m SSm 1
h P PETFall-Winter Months
Spring-Summer Months
Pm = monthly precipitation
PETm =monthly PET
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
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
Predicted and Measured Sr
Good agreement computed & measured required storage.
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Albany AltamontApple ValleyBoardman (thin)Boardman (thick)Cedar RapidsHelenaMarinaMonticelloOmaha (thin)Omaha (thick)PolsonSacramento (thin)Sacramento (thick)Underwood
Est
imat
ed
Req
uir
ed S
tora
ge (
mm
)
Measured Required Storage (mm)
Monthly P/PET
-100mm
+50mm
-50mm
Bias = 15.6 mmStandard Error = 43.1 mm
Monolithic Covers: Storage Capacity
What is the storage capacity (Sc)?
qc = water content when percolation transmitted.
· Coarse layer forces water to be stored in finer-grained layer
· Coarse layer can be used to wick drainage
StorageLayerL
z
c
Area
LzdS c
L
0
cc
Monolithic Covers: Storage Capacity
What is available
storage (Sa)?
LzdS minc
L
0
minca qmin = lowest water
content achieved consistently.
· Coarse layer forces water to be stored in finer-grained layer
· Coarse layer can be used to wick drainage
StorageLayerL
z
cmin
Area
r c minL S /a rS S
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 4000-6000 kPa. (use for qmin).
• qwp = qfc - qwp = unit storage capacity.
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10
100
1000
10000
0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35
Su
ctio
n (k
Pa
)
Volumetric Water Content
van Genuchtenequation
s = 0.33
r = 0.0
= 0.028 1/kPan = 1.72
fc = 0.26
wp = 0.01
qfc = 0.26, qwp = 0.01, qu = unit storage = 0.26-0.01 = 0.25
4000kPa
33kPa
Pedogenesis & Hysteresis
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n
r s r n
1
1 ( )
10-1
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102
103
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105
106
0 0.1 0.2 0.3 0.4
Soi
l Suc
tion
(kP
a)
Volumetric Water Content
Lab Drying Curve
Field Wetting Curve
fc
0.26
0.38
• 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
Compare: Field to Lab
11
n
r s r n
1
1 ( )
Create field SWCC by adjusting lab-measured SWCC:
• a adjustment • Plastic soils = 13x• Non-plastic soils =
none
• n = no adjustment
= More Plastic= Less Plastic
0.01
0.1
1
10
100
1000
Fie
ld-t
o-La
b R
atio
n
Median = 12.9 Median = 1.3 Median = 1.2 Median = 1.1
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.0
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600
800
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AlbanyAltamontApple ValleyCedar RapidsMarinaMonticelloOmaha (thin)Omaha (thick)Sacramento (thin)Sacramento (thick)
Com
pute
d S
tora
ge C
apa
city
(m
m)
Minimum Measured Storage Capacity (mm)
Design Step 6 – Water Balance Modeling
· Coarse layer forces water to be stored in finer-grained layer
· Coarse layer can be used to wick drainage
Finer-Grained Soil
Clean Coarse Soil
z
q
T E P
R
Pr
Sz
Kzz
K
t c
Webinar March 14
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)
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
Sample OutputPredictions for 2001-2003 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.
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Wat
er B
alan
ceQ
uant
ities
(mm
)
Mean Laboratory ParametersLEACHM Model
Precipitation ET
SWS
SROPercolation
Appendix
PET Calculations - 1Data 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
PET Calculations - 2x = 0.665x10-3 P where P is atmospheric pressure in kPa
P = 101.3 [(293-0.0065z)/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 = 0.6108exp[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
PET Calculations - 3Rns = net solar radiation = Rs (1-a)
a = albedo (fraction of solar energy reflected)
Rnl = net long wave radiation (emitted from earth)
max,K min,K
4 4
snl
so
T T RR 0.34 0.14 e 1.35 0.35
2 R
h = Stefan-Boltzman constant (4.903x10-9 MJ/K4-m2-d)
Tmin and Tmax in oK
Rso = clear-sky solar radiation
PET Calculations - 4
a r s s
118R d sin sin cos cos sin
with z in m above mean sea level 5so aR 0.75 2x10 z R
Ra = extraterrestrial radiation (MJ/m2-d):
1s sunset hour angle (rad) cos tan tan
J = Julian day (1-365 or 366)
r
2d inverse sun earth dis tance (m) 1 0.033cos J
365
latitiude (rads) latitude (degrees)180
2solar declination (rad) 0.409sin J 1.39
365
For latitude: http://www.bcca.org/misc/qiblih/latlong.html