Download Soil-Limiting Flow from Subsurface Emitters

Guo, James C.Y. (2010)“Preservation of Watershed Regime for Low Impact Development
using Detention”, ASCE J. of Engineering Hydrology, Vol 15, No 1., January, 2010
Guo, James C.Y., Kocman, S and Ramaswami, A (2009) “Design of Two-layered Porous
Landscaping Detention Basin,”, ASCE J. of Environ Engineering, Vol 145, Vol 12,
December.
_________________________________________________________________________________________________________
OPTIMAL DESIGN FOR POROUS LANDSCAPING DETENTION BASIN
1.
2.
Guo, J. C.Y.1 , Kocman, S. M.2, Ramaswami A.3
Professor, Civil Engineering, U of Colorado at Denver, Colorado. Email: [email protected]
Graduate Student, Civil Engineering, U of Colorado at Denver, Colorado.
Professor, Civil Engineering, U of Colorado at Denver/HSC, Colorado.
3.
___________________________________________________________________________________
Abstract
Under the mandate of the Federal Clean Water Act, porous landscaping detention (PLD) has been widely
used to increase on-site infiltration. A PLD system consists of a surface storage basin and subsurface
filtering layers. The major design parameters for a PLD system are the infiltration rate on the land surface
and the seepage rate through the subsurface medium. A low infiltration rate leads to a sizable storage
basin while a high infiltration rate results in standing water if the subsurface seepage does not sustain the
surface loading. In this study, the design procedure of a PLD basin is revised to take both detention flow
hydrology and seepage flow hydraulics into consideration. The design procedure begins with the basin
sizing according to the on-site water quality control volume. The ratio of design infiltration rate to sand-mix
hydraulic conductivity is the key factor to select the thickness of sand-mix layer underneath a porous bed.
The total filtering thickness for both sand-mix and gravel layers is found to be related to the drain time and
infiltration rate. The recommended sand-mix and granite gravel layers underneath a PLD basin are
reproduced in the laboratory for infiltration tests. The empirical decay curve for sand-mix infiltration rate
was derived from the laboratory data and then used to maximize the hydraulic efficiency through the
subsurface filtering layers. In this study, it is recommended that a PLD system be designed with the
optimal performance to consume the hydraulic head available and then evaluated using the prolonged
drain time for potential standing water problems under various clogging conditions.
Keywords: Porous landscaping basin, infiltration, seepage, porous pavement, stormwater detention, LID,
and BMP
INTRODUCTION
A porous landscaping detention basin (PLDB) in Figure 1 reduces on-site stormwater runoff volume and
peak discharge using subsurface infiltration. Beneath the porous basin bottom is an aggregate sub-base
that is typically divided into an upper filtering layer comprised of fine aggregate, and a lower reservoir
layer comprised of larger aggregate. The geotextile fabric provides the separation between these two
layers. Stormwater that is intercepted by the surface basin will be infiltrated into the subsurface reservoir
where the seepage flow is filtered, stored, and gradually released into the perforated pipes that are tied
into the downstream storm sewer manhole. The water detention process is usually assumed to begin with
dry subsurface layers. During an event, all the aggregate voids are filled up with water before the
seepage flow can be fully developed through the saturated medium.
The infiltrating rate on the basin bottom represents the inflow to the PLD system while the seepage rate
through the subsurface medium represents the outflow. The operation of a PLDB is controlled by either
the infiltrating rate or the seepage rate, whichever is smaller (Guo 1998). If the subsurface seepage flow
cannot sustain the infiltrating flow, the water mounding will be built up to balance the inflow and outflow
rates. This phenomenon is manifested by standing water often observed in many water quality
enhancement basins (Guo 2001). The similar phenomena were also observed in the subsurface drip
1
irrigation system that has become a common method for the irrigation of field crops, trees, and
landscaping. When the pre-determined discharge of the emitter is larger than the soil infiltration capacity,
water pressure at the dripper outlet increases and can become built up. This pressure buildup in the soil
decreases the pressure difference across the dripper and, subsequently, decreases the trickle flow (Shani
et al. 1996). Therefore, it is advisable that the subsurface geometry beneath the PLDB sustains the
continuity of flow.
Figure 1 Layout of Porous Landscaping Basin
The design of a PLD system is to seek the balance between the surface and sub-surface flows under the
available hydraulic head and required water quality control storage volume. This study presents an
attempt to integrate the surface and subsurface hydrology and hydraulic processes together to design a
PLDB.
SURFACE STORAGE BASIN
A PLDB is designed as an on-site storm water disposal facility. The storage volume of a PLDB is often
sized for the water quality control volume (WQCV) or equivalent to the flush volume. From previous
studies, WQCV is approximately equal to 3- to 4-month event (Guo and Urbonas 1996). For convenience,
WQCV is directly related to the local rainfall distribution. There are many recommended probabilistic
distributions derived for complete rainfall data series, such as exponential distribution (Bedient and
Huber, 1992), one-parameter Poisson distribution (Wanielista and Yousef, 1993), and two-parameter
model of Gamma distribution (Woolhiser and Pegram, 1979). In this study, the one-parameter exponential
distribution is adopted to fit the frequency distribution of rainfall event depths (Guo 2002). The exponential
distribution is described as:
−p
1 Pm
f ( p) =
e
Pm
(1)
in which f(p) = frequency distribution for local rainfall depth, p. Integrating Eq 1 yields the cumulative
probability distribution as:
F (0 ≤ p ≤ P ) = 1 − e
−P
Pm
(2)
2
in which F(0≤p≤ P) = non-exceedance probability for rainfall depth to be less than or equal to the design
rainfall depth, P. Considering surface depression, a runoff-producing rainfall depth can be converted into
its runoff volume as:
Po = C ( P − Pi )
(3)
in which Po = WQCV in mm per watershed, C= runoff coefficient used in the Rational method, and Pi =
incipient runoff depth. As recommended, an incipient runoff depth of 2.5 mm is introduced to filter out
extremely small rainfall events (Guo and Urbonas in 1996, Driscoll et al. in 1989). Normalizing Eq 3 yields
P
P
P
= o + i
Pm CPm Pm
(4)
in which Pm = local average rainfall event-depth that can be found elsewhere (EPA 1986). Substituting Eq
4 into Eq 2 yields
F (0 ≤ p ≤ Po ) = 1 − e
−(
Pi
P
+ o )
Pm CPm
(5)
in which F(0≤ p≤Po) = probability to have an event that can be completely captured by the design water
control volume, i.e. Po. In this study, Eq 5 is termed the synthetic runoff capture curve that is normalized
by local average rainfall event-depth, runoff coefficient, and runoff incipient depth. Re-arranging Eq 5
yields:
Cv = 1 − α e
α =e
− Po
CPm
(6)
− Pi
Pm
(7)
In which Cv = runoff volume capture rate between zero and unity, and α = constant determined by
incipient runoff depth. The value of α represents the watershed natural depression capacity. Figure 2
presents a set of normalized runoff capture curves produced using Eq 6 with runoff coefficients of 0.4,
0.6, 0.8, 0.9 and 1.0. It is noticed that the curvature of runoff capture curve increases when the runoff
coefficient decreases. This tendency reflects the fact that the higher the imperviousness in a watershed,
the less the surface depression and detention. As a result, the response of a watershed to rainfall is quick
and direct.
For a selected runoff volume capture rate, Figure 2 provides the required WQCV for a PLD basin as:
Vo = Po A
(8)
where Vo = WQCV in m3 and A = catchment area tributary to basin. Safety is always a concern when
designing a PLDB. Often the water depth in a PLDB is set to be 15 to 30 cm (6 to 12 inches). With a
selected basin depth, the basin cross sectional area is determined as:
Ao =
Vo
Y
(9)
where Ao = average cross section area, and Y= basin depth. To enhance the infiltrating process, the
basin bottom shall be on a flat to mild slope.
3
1.00
0.90
Runoff Capture Rate
0.80
0.70
0.60
0.50
0.40
0.30
0.20
0.10
0.00
0.00
C=0.40
0.50
C=0.60
C=0.80
1.00
C=0.90
1.50
C=1.0
2.00
2.50
3.00
Po/Pm (Basin Size/Average Rainfall Depth)
Figure 2 Stormwater Quality Control Volume for Porous Landscaping Basin Design
SUBSURFACE FILTERING SYSTEM
Drain time is critically important to the operation of a PLDB because it controls the sediment removal rate.
Based on the urban pollutant characteristics, a drain time for the PLDB is usually set to be between from
12 to 24 hours (USWDCM 2001). Figure 3 illustrates the flow through the two filtering layers including
sand-mix and then gravel. Under a constant head, the steady flow condition is derived as:
f = V1 = V2
(10)
In which f = infiltrating rate, and V= seepage flow velocity through each layer, The subscriptions “1” and “2”
represent the variables associated with the sand-mix and gravel layers, respectively. A saturated
seepage flow through a medium is proportional to the energy gradient as:
V1 = K1
dH 1
H1
(11)
V2 = K 2
dH 2
H2
(12)
Where K = hydraulic conductivity, H = energy head, and dH = energy loss.
4
Figure 3 Illustration of Infiltrometer Operation
In practice, the design infiltrating rate depends on the drainage nature of the selected sand-mix. With a
pre-selected design infiltrating rate, the total filtering thickness for the two filtering layers is calculated as:
D = f Td
(13)
Where D= total thickness for two filtering layers, f = infiltration rate, and Td = PLD drain time. The
fundamental challenge in PLDB design is how to divide the total thickness between the two filtering layers
because the layer thickness is directly related to the hydraulic gradients for seepage flow through the
system.
D = H1 + H 2
(14)
where H1 = sand-mix thickness and H2 = gravel layer thickness. As illustrated in Figure 3, the available
hydraulic head for the PLD system is
H =Y +D
(15)
where Y = water loading depth in PLDB. In this study, the optimal performance of a PLDB is defined by
the infiltration flow and the subsurface thickness that allow the seepage flow to consume the hydraulic
head available as:
H = dH 1 + dH 2
(16)
Aided by Eq’s 10, 11,and 12, the head losses through the two filtering layers are:
dH 1 =
f
H1
K1
(17)
dH 2 =
f
H2
K2
(18)
Aided by Eq’s 15, 16, 17 and 18, the optimal performance of a PLDB is described as:
5
H1
+
D
(
f
Y
− 1) −
K1
D
=1
f
f
(
−
)
K1 K 2
in which f/K1 >1, and K2>K1
(19)
H 2 = D − H1
(20)
Eq 19 is valid when f/K1 >1 and K2>K1. In other words, the infiltration rate is greater than the seepage rate
and the sand-mix layer is above the gravel layer. Eq’s 19 and 20 are derived to be the guidance to divide
the total required filtering thickness into two layers.
OPERATION OF POROUS LANDSCAPING BASIN
The operation of a PLDB is subject to clogging due to sedimentation in the basin. The pollutant deposit is
often accumulated on top of the basin bottom and then diffused into the top layer of the sand-mix medium.
When the infiltration rate decays on the basin bottom, the friction losses are reduced accordingly. Namely,
dH 1 =
f s H1
K1
(21)
dH 2 =
fsH2
K2
(22)
In which fs = reduced infiltrating rate due to clogging effect. Clogging to a PLD system generally occurs as
a thin, hard “cake” layer (0.2 to 0.5 cm) of sediment on the basin bottom. As reported, migration of solids
only diffuses into the top 5 to10 cm of the sand-mix layer while the hydraulic conductivity in the sand-mix
layer remains unchanged (Li and Davis 2008a and 2008b; Mays 2005). As illustrated in Figure 3, the
reduced infiltration flow under a clogging condition may not completely consume the hydraulic head
available. As a result, the residual pressure in the system, is calculated as:
H t = Y + D − dH 1 − dH 2
(23)
where Ht = residual pressure head. If the cake layer presents an additional friction loss, the value of Ht will
decrease; otherwise it represents the pressure built up in the filtering layers. The reduced infiltrating rate
implies a prolonged drain time, or a period of standing water in the PLDB, as:
Tw =
D
− Td
fs
(24)
in which Tw = increased drain time or period of standing water. As the basin bottom is gradually clogged,
the infiltration flow rate continues to decrease and the hydrostatic head, Ht, in the medium continues to
build up. When the hydrostatic head in the filtering medium is close to the available head, the system is
about to cease functioning because the medium layers are almost plugged.
LABORATORY TESTS
Previous reports recommended that a sand-mix thickness of 30 to 60 cm (or 12-24 inches) can effectively
remove pollutants in stormwater (Hunt 2001, Hunt 2006, NCDENR 2007, Sun 2004, Toronto and Region
Conservation Authority 2007). As reported, metals are removed in the top 20 to 45 cm (8 to 18 inches) of
sand-mix layer (Davis et al. 2003; Sun 2004; Winogradoff 2001). In practice, the sand-mix layer
thickness is recommended to be 45 cm (18 inches) to allow for both adequate pollutant removal and root
zone for vegetation. In the laboratory, a 38-cm (15-inch) circular infiltrometer in Figures 4 and 5 was
6
utilized to represent a section of the PLDB . Sand-mix sample columns were prepared to mimic the field
conditions as closely as possible. As illustrated in Figure 5, the sample column in the infiltrometer is built
with an upper layer of sand-mix, a lower layer of gravel, and a perforated bottom drain. The1.9 cm (¾ inch) crushed granite was spread in the bottom. ASTM C33 washed sand and Canadian peat were
combined at the ratio of 85% sand and 15% peat by volume for the sand-mix layer. Table 1 presents the
compaction and density of the sand-mix samples prepared for infiltrometer tests. For this study, the
filtering layers were structured with an upper 45-cm (18-inch) sand-mix layer and a bottom layer of 20-cm
(8-inch) gravel. As illustrated in Figure 5, the total thickness of a sample column is set to be 65 cm (26
inches). With a constant head of 30 cm (12 inch), the total head applied to the infiltrating flow is 95 cm (38
inches) as shown in Table 2. To evaluate the effect of the geotextile on the infiltration rates, Sample
Column I had a geotextile layer separating the sand-mix layer from the aggregate layer; and sample
Columns J and F were constructed and tested without the geotextile. Manometers were installed on the
infiltrometer wall at 4 stations to measure the variation of static heads. The locations of manometers are
expressed by the vertical distances above the bottom of the sample column as shown in Table 2.
Soil Column
15” diameter
38”
12 inches of
water capacity
26”
24”
Manometers
Entry Layer
18 inches
soil mix
18”
11”
9”
8”
Exit Layer
8 inches coarse
aggregate
Geotextile
0”
Figure 4 infiltrometers built in Laboratory.
Drain line
and valve
Figure 5 Sample Column for Infiltration Tests
Table 1 Compaction and Density of Sand-mix Sample
Material
Sand
Peat
85% Sand and 15% Peat
Sand-mix Sample Density
grams per cubic centimeter
(pounds per cubic foot)
Loose Sand-mix
Compacted Sand-mix
1.39 (86.79)
1.76 (109.65)
0.42 (26.05)
0.84 (52.43)
1.16 (72.31)
1.75 (109.22)
7
Compaction
Ratio
1.26
2.01
1.51
Test Flow Rates Over Time
flow rate (cm/hr)
60
Column I
50
Column F
40
Column J
30
Horton's
Estimate
20
10
0
0:00:00
24:00:00
48:00:00
72:00:00
hours:min:sec
Figure 6 Variation of Infiltration Rates for Sample Columns
Table 2 Variation of Hydraulic Heads Measured at 5 Stations
Column
Sample
ID
Infiltrating
Rate
cm /hr
Col F without geotex
Col I with geotex
Col J without geotex
22.9
24.3
25.9
Locations of manometers above ground in cm
66.0
61.0
27.9
22.9
entrance
upper
lower
geotextile
sand layer
sand layer
sand layer
layer
Reading in manometers above ground in cm
97.8
95.3
31.1
22.9
96.5
94.0
29.2
22.9
96.5
94.6
48.6
22.9
Col F without geotex
8.8
97.8
96.2
27.9
Col I with geotex
12.4
96.5
94.6
27.9
Col J without geotex
13.5
96.5
95.3
30.5
Note: Col F without geotex = Soil Column F without geotextile measured after 72 hr.
22.9
22.9
22.9
Table 3 Hydraulic Conductivity in Soil Layer at 72 hours
Column Sample ID
Col F without geotex
Col I with geotex
Col J without geotex
Infiltration Rate
cm/hr
8.8
12.4
13.5
Hydraulic Conductivity for Sand-mix
cm/hr
4.9
6.1
7.3
8
The sample columns were tested with the “wet” initial condition by filling each column to 30.5 cm (12
inches) of water and soaking the sample column overnight with the drain valves closed. The next
morning the valve was opened and outflow measurements were recorded. The outflow rates from
sample columns were recorded for 72 hours continuously. Figure 6 is the plot of the decayed infiltration
rate through the sand mix layer over 72 hours. The best fitted Horton’s infiltration equation for the sandmix tested is (Horton 1933):
f t = 9.8 + 37.2e −0.144 t
(25)
Where ft = infiltration rate in cm/hr at elapsed time t in hours. Eq 25 has a correlation coefficient, r2 = 0.85.
The differences in the infiltration decay among sample columns are attributed to sample preparations,
compaction condition, and test operations. Sand-mix compaction alone can have a significant impact on
infiltration rates in sandy soils (Pitt et al. 1999). Although the impact of the geotextile fabric on the flow
rate was not measurable through the sample columns, the sand-mix particles were found to migrate into
the gravel layer (Haliburton and Wood, 1982). Based on three sannd-mix column tests, the average final
infiltration rate is found to be 11.6 cm/hr (or 4.6 inch/hr). The hydraulic conductivity coefficients were
found to be 6.1 cm/hr (or 2.4 inch/hr) for sand-mix and 64.0 cm/hr (or 25.2 inch/hr) for gravel. As listed in
Table 3, these values are within the range reported before (Schwartz and Zhang, 2003).
DESIGN EXAMPLE AND SCHEMATICS
The PLD basin located in the City of Denver, Colorado is employed as an example to illustrate the design
procedure. The catchment draining into this basin has a tributary area of 1.0 hectare (2.5 acre) and runoff
coefficient of 0.60. As reported, the average event depth for the Denver metropolitan area is 1.0 cm (or
0.41 inch) (EPA 1986). With a runoff volume capture rate of 80%, the WQCV for this basin is calculated
as:
α =e
− Pi
Pm
=
Cv = 1 − α e
−0.25
e 1 .0
− Po
CPm
= 0.79
= 1 − 0.79
− Po
0
.
60
e ×1.0
= 0.8 or Po = 0.86 cm
Vo = Po A = 0.86 cm × 1.0 ha = 86 m 3
From the laboratory test, f = 11.6 cm/hr (or 4.6 inch/hr), K1 = 6.1 cm/hr (or 2.4 inch/hr) for sand mix and K2
= 64.0 cm/hr (or 25.2 inch/hr) for gravel. Consider a drain time of 6 hours. The required dimension for the
subsurface filtering system is calculated as:
D = f Td = 11.6 × 6 = 69.6 cm
H = Y + D = 30.5 + 69.6 = 100.1 cm
f
Y
11 . 6
30 . 5
(
− 1) −
(
− 1) −
H1
K1
D
6
.
1
69
. 6 = 0 . 73 or H1 = 51.0 cm and H2 = 18.6 cm
= 1−
=1−
f
f
11 . 6 11 . 6
D
(
−
)
−
)
(
K1 K 2
6 .1
64 . 0
Substituting the above dimension into Eq’s 17 and 18 yields
9
dH 1 =
11.6
f
H1 =
× 51.0 = 97.0 cm
6.1
K1
dH 2 =
f
11.6
H2 =
× 18.6 = 3.1 cm
K2
64.0
As expected, the total friction losses for the seepage flow through the two layers satisfy Eq 15. This is the
optimal performance for this PLD basin, according to Eq 19. In practice, the infiltration rate at the site is
estimated with uncertainties. Secondly, the infiltration rate is subject to the clogging effect. For
comparison, the performance of this PLDB is further assessed for the condition that the infiltration rate is
reduced to 7.5 cm/hr. The corresponding head losses are calculated as:
dH 1 =
f s H 1 7.5 × 51.0
=
= 62.7 cm
K1
6.1
dH 2 =
f s H 2 7.5 × 18.6
=
= 2.2 cm
K2
64.0
H t = H − dH 1 − dH 2 = 100.1 − 62.7 − 2.2 = 35.2 cm
Tw =
D
69.6
− Td =
− 6.0 = 3.3 hr -- an extended period of standing water.
fs
7.5
Under the clogging condition, this PLDB drains slowly. After the design drain time of 6 hours, standing
water is developed in the basin. The residual pressure head, Ht, is either dissipated through the cake
layer or built up in the sand medium.
The above analysis was repeated for the bio-retention medium studies (Li and Davis 2008a and 2008b).
In the laboratory, the clean sand column was used as the subsurface medium to filter the solids in storm
water. After several loading cycles of stormwater, a 0.1 to 0.6-cm cake layer was formed on the basin
bottom. The deposited solids were also diffused into the top layer of the sand medium up to 3 to 7 cm.
Table 4 summarizes the laboratory measurements and observed data. The clean sand medium started
with a hydraulic conductivity of 45 cm/hr. After the top layer is clogged, the equivalent hydraulic
conductivity coefficients for the sand medium were measured as listed in Table 4.
Table 4 Observed Case Studies for Bi-Retention Medium (Li and Davis 2008a and 2008b)
Infiltrating
Flow
Rate
f
cm/h
4.8
4.9
9.5
19.8
19.7
Laboratory Dimension
Filtering
Bottom
Media
Conductivity
Thickness
Coeff
D
K2
cm
cm/h
5.5
45.0
10.5
45.0
10.5
45.0
5.5
45.0
10.5
45.0
Equivalent
Conductivity
Coeff
Ke
cm
3.0
3.0
3.0
5.0
6.0
Calibrated Parameters
Water
Upper
Depth
Conductivity
in Basin
Coeff
Y
K1
cm
cm/h
3.3
2.0
6.6
2.0
22.5
2.0
16.3
3.5
24.0
3.5
10
Upper
Clogged
Layer
H1
cm
3.5
7.0
7.4
3.7
6.7
Observed Thickness
Bottom
Cake
Clean
Layer
Layer
H2
cm
cm
2.0
0 - 0.3
3.5
0 - 0.4
3.1
0 - 0.1
1.8
0 - 0.3
3.8
0 - 0.6
0.80
Predicted Thickness Ratio
0.70
0.60
0.50
0.40
0.30
0.20
0.10
0.00
0.00
0.10
0.20
0.30
0.40
0.50
0.60
0.70
0.80
Observed Thickness Ratio
H1/H -Top Layer
H2/H - Bottom Layer
Figure 7 Comparison between Observed and Calculated Filtering Thickness
Consider that the clogged top layer is equivalent to a sand-mix layer and the bottom clean layer is
equivalent to a gravel layer. Eq 19 was applied to 5 case studies to predict the thickness ratio between
the top and bottom layers. Figure 7 presents good comparison between the calculated and observed
thickness ratios.
CONCLUSION
1. A PLDB shall be designed using the concept of hydrologic system to take both the surface and
sub-surface flows into consideration. In this study, it is recommended that the PLDB be sized for
the on-site storm water quality control volume according to the selected drain time and target
pollutant removal rate. The total filtering thickness underneath the PLDB shall be determined by
the selected drain time and infiltration rate.
2. The filtering layers beneath a PLDB shall be structured to completely consume the hydraulic head
available in the system. The optimal dimension of the sub-base medium is found to be closely
related to the design infiltrating and seepage rates. In this study, Eq 19 was derived to provide the
optimal thickness ratio between the sand-mix and gravel layers. The optimal sub-base dimension
delivers the highest seepage flow rate for the unclogged condition.
3. Eq 19 is numerically sensitive to f/K1, but not to f/K2 because the hydraulic conductivity coefficient
of granite gravel is usually much higher than the infiltrating rate or the ratio, f/K2, numerically
close to zero. For simplicity, the thickness for the sand-mix layer is approximated as:
H 1 = (1 −
K
K1
)D + 1 Y
f
f
(26)
In practice, it is critically important that the ratio, f/K1, is properly selected to avoid undesirable
prolonged standing water in the PLDB.
4. In this study, the infiltration rate for the sand-mix layer varies from 50 to 7.5 cm/hr (20 to 3 inch/hr).
The final infiltration rate is approximately 7.5 to 12.5 cm/hr (3 to 5 inch/hr) after an operation of 72
11
hours . The hydraulic conductivity coefficient was varied within a small range through the sandmix column. All these uncertainties are attributed to the residual pressure in the PLD system. As
a common practice, perforated pipes are installed in the subsurface system. A sub-drain pipe
creates an accelerated hydraulic gradient to collect the excessive water and to alleviate the buildup pressure.
5. This study is a research project supported by the Urban Drainage and Flood Control District,
Denver, Colorado and the Urban Watersheds Research Institute. The detailed construction plan
and drawings to design a porous landscaping detention basin can be found elsewhere
(USWDCM 2001).
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NOTATIONS
A = catchment area tributary to basin
Ao = average cross section area
C= runoff coefficient
Cv = runoff volume capture rate between zero and unity.
D= total filtering thickness
f = infiltrating rate, design infiltrating rate defined by land surface
fs = reduced infiltrating rate due to clogging effect
ft = infiltration rate at time t
f(p) = frequency of rainfall event-depth
F(0≤p≤Po) = non-exceedance probability for runoff volume
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F(0≤p≤ P) = probability to have complete runoff volume capture
dH = energy loss
H = energy head or total head
H1 = sand-mix thickness
H2 = gravel layer thickness
Ht = residual pressure head
K = hydraulic conductivity
Po = WQCV in mm per watershed
Pi = incipient runoff depth
p = rainfall event depth
P = design rainfall depth
Pm = average rainfall event-depth
Td = drain time
Tw = increased drain time or period of standing water
V = seepage flow velocity through each layer
Vo = WQCV in m3
Y= water loading depth in basin
α = constant determined by incipient runoff depth
The subscriptions “1” and “2” represent the variables associated with the two layers of medium
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