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

  chbenson@wisc.edu

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

200,000

250,000

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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6/30/00 6/30/01 6/30/02 7/1/03

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.

-300

-200

-100

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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.

0

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.

1

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

11

n

r s r n

1

1 ( )

10-1

100

101

102

103

104

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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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