slìzMi` - Peoria County

APPENDIX K.3
LEACHATE HEAD
A
slìzMi'
Page:
1\
haut
rH
" ShaW EnvirOnmental, lnC.
Glient:
Peoria Gity/County Landfill, lnc.
Project:
PCCLExpansion
Proi.
#:
1 oÍ
4
137618
By:
Checked By:
Galculated
DJR
RDS
Date:
Date:
4118111
4123111
TITLE: LEACHATE HEAD (LEAGHATE COLLECTION DESIGN)
Problem Statement:
Determine the leachate head on the landfill liner system for the expansion design. The leachate
collection system is designed to maintain a maximum one (1) foot of head of leachate on the liner.
Given:
1.
Richardson, G., Design of Waste Containment and Final Closure Sysfems. ASCE
Publication, April 2001. (Please see attached pages.)
2.
Landfill cellular designs presented in the design drawings.
Assumptions:
L
Giroud's Approximate Numerical Solution used to calculate leachate head on a liner.
t**
Where:
tno* = leachate head on landfill liner (ft)
B:
slope angle (degrees)
q,, : leachate generation rate (ft / yr)
k : hydraulic conductivity of drainage material (ft / yr)
L : maximum horizontal drainage distance (ft)
j: numerical modiffing factor given as:
j : r-rrr".r{
[.{H]-l
TlProjects\2oog\1 37618 - PDC\Design\Leachate\Final
}
Leachãte Calculat¡ons - STAND ALONE ÞESIGN\K.03 Leachate Hêâd 4.1 3.201'1.wpd
Page:
.A
haw '
Shaw EnVirOnmental, lnC.
Glient:
Peoria City/County Landfill, lnc.
Project:
PCGLExpansion
Proj.
#:
4
137618
By: DJR
By: RDS
Galculated
Ghecked
2 ol
Date:
Date:
4118111
4123111
TITLE: LEACHATE HEAD (LEACHATE COLLECTION DESIGN)
3,
The leachate collection system was analyzed as follows:
The maximum flow length (L) to a leachate collection pipe is 431 feet in Cell 3.
The hydraulic conductivity of the granular drainage media is 0.02 cm/s.
k
=(
\
9r2!!.\(',
sec
t_\lsq4gqrelfrg¡4ry1 _ 20,6s3ft
)\2.54cil\l2in)\ day /\ yeor ) year
\(
The slope of the liner is 2.0o/o, therefore, tan(p) = 0.020.
4.
= 17.38 gal/acre-day = 0.02 fVyr during steady-state conditions (Refer to Appendix
K.10).
Qr
5.
q, = 0.02 fllyr = Rate of groundwater seepage through the composite liner system (see
Appendix K.2).
6.
TlPrcjects\2009\'1 376'1
Qn
I
= Qr * Q" = 0.02 + 0.02 = 0.04 fyyr.
- PDC\Design\Leachate\Final
Leachate Calculations - STAND ALONE DESIGN\K.03 Leachate Head 4.1 3.201 '1.wpd
Page:
3 of
4
Landrirr' rnc
::ï:,,
Shaw Environmental, lnc, Proj. #:
/\,,
ShW'
::iJr.r"*untY
137618
By:
Checked By:
Galculated
DJR
RDS
TITLE: LEACHATE HEAD (LEACHATE COLLECTION DESIGN)
Galculations:
j =l-rtr.-r{-
lr(+)l
"1-r,.",,r,,J
s/8
j = l-rt,
".rl-
f-[#-)
ogl
s(o.o2o)'
I -
:,rl
'r-
zcos(Þ)
t@-oo2ol
'L
t no* = (0.979)l
-nìâx
'
}
2
cos(tan-r(o.o2o))
l(431)'
]'
tn
^
=0.040ft
T:\Prcjectsuo09\'1376'18
- PDC\Design\Leachate\Final
Leachate Calculations - STAND ALONE DESIGN\K.03 Leachate Hæd 4.'13.201 l.wpd
Date:
Date:
4118111
4123111
Page:
aW'
Shaw Environmental, lnc.
Glient:
Peoria Gity/County Landfill, Inc.
Project:
PGGLExpansion
Proj.
#:
4 of
137618
By:
By:
Calculated
DJR
Ghecked
RDS
Date:
Date:
4118111
4123111
TITLE: LEACHATE HEAD (LEACHATE COLLECTION DESIGN)
Results:
Head (ft)
Maximum Flow Length, L (ft)
Maximum Flow Length
(CELL 3)
431
0.040
Gonclusion:
The leachate drainage and collection system has been designed to maintain less than one (1)
foot of head above the liner during steady state conditions,
TlPrcjects\2oog\'137618
- PDC\Design\Leachate\Final
Leachate Calculal¡ons - STAND ALONE DESIGN\K.03 Læchate Head 4.13.201 l.wpd
4
Design of Lateral Drainuge Sysrems for Landfills
h,^
l'
*
- LS(^. /tS + n"' ¡''' Ll/o äiä
-_-
,R(1-2Rçl 211(5l"s-i;
".nt¡:znsX
I
-1{.,.','''
For R <1/4
^
t)
l-or
L
_
R:1/4
^
lz*" is the maximum head over ilre liner, ,11: rl(ksin2 p), S : slope of liner : tanor, l: ( l4IÐr/2, ß : (4R7)t't, ,: design rate of fluitl supply, /r: coeflìcient of petmeability of the drainage layer, TLe sawtooth liner
geometry assruned in McEr¡¡oe's solution is shown in Figure 5.3. McEruoe evaluatecl tlrree impingement
where
conditions:
Casel -r/ksin2þ>0.25-theslope/transmissivitycapacityoftheclrainagelayercontrolsthernor¡¡rdingheiglrt
as is appropriate for flatter slopes,
Case
II - r/ksintþ: 0.25 - a balance conditions exists between tl:e clesign rate of fluid supply
ancl thc
slope/transmissivity capacity of the drainage layer , and
Case
III - r/ksinz B < 0.25
- the clesign rate of
fluìd supply controls the mounding heiglrt
as is appropriate
for
typìcal side slopes.
Ths three cascs ar€ shown in Figure 5.3, Note that Cases tr and III can also be used to moclel the condition of
liner on an infinite slope rvith collector pipes uniformly spaced down the slope- Case I conditions for the
infinitc slope condition require the slope length to tre taken as the actual <listance between the pipes, 2L,. A
rnore tlrorough discussion of McEnroe's analysis is given by Mcllean et al, (1995).
lmpinçeirl*ñt, r
r¡
Y
ry
v
*ass
¡i
rIl
F
5. 2.
ìgune 5"3 Sawtooth-limer geonmetry f'o¡'
2 Giroucl's Approximate Numeric al S oluti on
52
ft4fl
cEmroe' s sE¡lu tions
a
Ðesign of Lateral Drainage Systems
for I'øndJills
While McEnroe's solution is "exact", it is difficult to use and may be very sensitive to ilre number of
signilicant digits used- An altcrnative solution based on sirnplifying assunrptions and numedcal lneilr<lds was
fnst presented by Giroud et al. (1992) and is discussed in Giroud ef al. (2000). 'l'he maximum heacl on the
liner, terrned t,*" by Giroucl, is given by the l'ollowing equation:
=j
t,,,,
lu*'ß +4q,,lk __'
-tan
Zcos þ
ß
8q.5.7
L
where r7r, ìs the de sign rate rate of liquid supply over'a horizontal surface in temrs of an ec¡uivalent velocity,
is the slope ang7e, L is the drainage length of the lateral drain, and fr is tlie permeability of the lateral drain.
'Ihe j term is a numerical rnodifying factor given by the following:
o,2exp{-['"'[r,
j -l-_
$
Eq.5-B
I]']
Table 5-i shows that values of the maximum liquid thickness calculated using Giroud's equation are within 1%
of the McEnroe results for q/k Iess than I x 10-1, which is the case in virlually all practical applications. Note
also that the a¡;terisked McEnroe values in Table 5.x could not be calculated usirtg a Ilewlett Packard FIP 15 C
calculator, although it uses lû digits (see the discussion nea¡the end of Example 1). The calculation had to be
done using Microsoft Excel, which uses I5 digits. The double asteriskcd valucs could not be calculated with
Microsoft Excel, although it uses 15 digits- For example, the value 3.16x10-e was obtained using Equation 5-x
as follows: (q¡lk)/su,þ: 1xl0--e / sin[tarl'(t/3)] : 3,16x10'e. Ironically, in this particular case, tlre
"approximate" Giroud equation gives an accurate value wlrereas McEnroe's equatìon, even when used with
Microsoft Excel, cloes not.
.{'anile
5.1 Com¡lanisor¡ befweem
NfcEmroe's equa$ñoms"
Q¡
lk
0-r
fanþ
0.02
vrùånn€s
ol t^JÍ,
ohtainecl numericatly usimg Gínoud's eqnaatioms ancÌ
Giroud's
McErnoe's
equation
Eq. 5.xx
equations
fbr rloo: cosp
5.00x10-8*
X 0-8
5-00x 0-8
5-00x 0*7
X 0-7
4-99x 0-6
4.99x104
X 0-6
493x
0-5
X 0-5
X
X 0-4
X 0-3
X
0-
X 0-I
0-e
X 0-8
X 0-7
x
0-6
X 0-5
0-4
0.3333
tanþ
0.5
Giroud's
McEnroe's
equation
equations
Eq.5.xx
for rlon: cosp
2.24x1}-e
2.24x1c.e +*
2.24x10-8
2-24x10-8 +
4.94x10-s
2.24x10-r
2.24x104
4.61x 0-4
3.68x 0-l
4.65x10+
2.24x10-5
3.6Bxl0-3
2-0Bx 0-2
8.65x 0-2
3.04x 0-r
2.09x104
B.67xl0¿
2.23x104
2. I 9xl 0-3
2.24x10-7+
2-24x10-6*
2.73x10-5
2.23x10-a
2.19x10-3
2.0lxl0-2
2.Olx|0-2
6x
3 6x
3 6x
3 6x
3 6x
3 4x
3
5-00x I 0-7*
0-v
3-16x10-r
3.16x10-v*+
0-8
3.16x10-8+
0"7
0-5
6x10-7*
3.t6x10-6
lì- 1 6x l0-5
0-4
3. 1 4x1 0-a
0-,6
3. I
53
IO
l.51xl0-'
1.4lxl0-'
I -4txl0-B
L41xI0-7
t.4lxl0-r
1.52x10-t
I"4lx10-e*+
].41x10-8*
l-4lxl0-7"
I.41xl0-5
l.4lx10-6*
l.4lx10-s
l.4lx10=a
1.41xl0-a
I)esign of Latero-l Drainage S),stems for Landfills
lx10'3
3.03x10-3
1xl0-2
lxl o-I
2.65x10-2
1,77x1tr1
3.05x10-3
2..66x10-2
l.40xl0l.35xl0-2
l.41xl0-3
I -4lxl0-2
l.B5><10-r
l.l7xl0t_
1.41x10-I
fhe total flow rate through the collecter, p, is equal lo q¡L per unit width of the clrainage layer. For
geocornposite lateral drains, Giroud (2000) has shown that Eq. 5.7 can be simplified clue to the slnall flow
fhickncss to thc following:
/,*
=
QnL
Iìq. 5.9
ksin {)
Tliis greatly sirrrplifìed equation is appropriate when the thickness of the geocomposite is less than 20 mrn over
the range of slopes conÌnon to nrost lanclfills, This equation should not be uscd with thicker natural drainage
layers. 'Ihis allorvs the required transn¡jssivity for a geocomposite drain to be clirectly solved for as follor¡'s
0
Iiq.5.10
(sina) I L
Solutions based on Gir-oud's numerical solution will be conservative and less than 5o/" in error. Again, the
simplifìed solution is applicable to geocornposile drainagc systems only.
5-2.3 EPA's Published Equation
IISEPA (1989) also published ille following equation, comrnonly referred to
the maximum head over the liner:
as Moore's equation, to calculate
It**: Lrt''sino4-!:- 4-l- ,S, (S2 +rsin' æ\'''I
rsln-d rstn" u,
Eq.5.l1
The derivation of fhis equation has never been presented and its validity is questioned, Giroud (2000)Iìor a 25"/" slope, the EPA equation over-estimate s the head over the hner at low r, while at r greater than 0.1 ,
the EPA equation g:dqr-q$rmqjgq the head. Tløe øø¿$øors str{tvgly recornwewd tke wse af Girowd's eEøaøtiords
for
L¡e
tlae corn¡twtøÍioea af tlee keød i¡a løterøt drøÊrøøge sJ,stewøs" l'n-ior ec¡uatioms pnesemted hy USEI,,A shqlt¡Ïd
with cawúia¡rn si¡¡ee thein qlenivatioxr [nas r¡even heem pnesemôed a¡¡d the equafioms are sus¡rect.
used
5.2.4 Desigrr Rate of Liquid Supply, q¡
t
he most significant unknown for the designer to evaluate is tle rate of liquid supply vertically entedng the
lateral drainage layer. Forthe design rate of fluid supply of liquid vertically entering the lateral drainage layer
over the liner system, we must estimate tle rate that leachate is draining from the waste. Two methods exist
for making this estimate: l) use EPA's IIELP model, or 2) use errpir-ical rates based on historic leachate
generation rates. The IfELF rnodel is limited in that it does not readily allow the operationaVpost-closure
transition life of a landfill to be modeled,
the geomefy of the tandfill model ¡emains the same through the
entire evaluation analysis. Because of this".g,,
limjtation, empir-ical rates are commonly used to evaluate the tþ¡ee
key phases in the iife of the lateral drainage layer. Irese phases are 1) during active placement of the waste, 2)
-14