Resolution - 2004 - 10 - Adopting Design Standards For Storm Drainage Facilities - 05/11/2004
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RESOLUTION NO. 04-10
A RESOLUTION OF THE EAGLE CITY COUNCIL, EAGLE, ADA COUNTY,
IDAHO ADOPTING DESIGN STANDARDS FOR STORM DRAINAGE FACILITIES;
AFFIRMING THAT PRESCRIBED NOTICE AND HEARING REQUIREMENTS
WERE MET IN ACCORDANCE WITH TITLE 67, CHAPTER 65, IDAHO CODE;
AND PROVIDING AN EFFECTIVE DATE.
WHEREAS, after providing legal notice, transmitting notice to other jurisdictions,
agencies, and entities, holding public hearings of the Planning and Zoning Commission
and City Council, the City Council, on April 13, 2004, unanimously voted to approve
ZOA-I-04 for a zoning ordinance amendment to adopt new design criteria to create the
basis for Design Standards for Storm Drainage Retention Facilities;
NOW THEREFORE, BE IT RESOLVED BY THE MAYOR AND COUNCIL OF THE
CITY OF EAGLE, IDAHO.
Section 1: The Eagle City Council hereby adopts the Design Standards for Storm Drainage
Retention Facilities, heard and adopted by the Council at its May 11, 2004, meeting.
Section 2: This Resolution shall be in full force and effect immediately upon its adoption
and approval.
ADOPTED by the Council of the City of Eagle, Idaho, this 11th day of May 2004.
CITY OF EAGLE
Ada County, Idaho
ATTEST:
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CITY OF EAGLE DESIGN STANDARD FOR STORM DRAINAGE
GENERAL PROVISIONS
1. Drainage facility designs for proposed subdivisions shall be included as part of construction plan
submittals to the Zoning Administrator. Drainage facility designs for construction projects on
individual sites that are already platted shall be submitted to the Building Inspector as part of plans
for review.
2. Drainage transmission facilities (pipes, orifices, intakes and the like) and drainage treatment facilities
(sand and grease traps, filter swales, turframps and the like) shall be sized based on peak flow rate
generated by the design storm. The design storm is defmed as a precipitation event delivering 1.1
inch of water, with precipitation intensity as described by the SCS Triangular Hydrograph with a
time-to-peak of one hour.
3. Retention facilities (seepage beds, basins, ponds, seepage swales, infiltration galleries and the like)
shall be sized based on design storm volume.
4. In submittal documents, drainage transmission, treatment and retention facilities shall be shown to
scale on a plan view of the development that also shows pre-development elevation contours and final
elevation contours. Plan shall also show, by outlines or shading, the areas characterized by each of
the runoff coefficients used in the runoffrate and volume calculations. Submittal documents shall
include:
a. Runoff volume and rate calculations,
b. Size design calculations for runoff transmission, treatment and retention facilities,
c. Structure detail drawings (showing dimensions, reinforcement, pipe sizes, inlet and outlet
invert elevations and the like) for treatment and retention facility structures, and line location
of any pipe, with notes giving pipe size, material, class, slope and inlet and outlet invert
elevations. Structure detail drawing views shall include at least plan view and two cross
sections in planes perpendicular to each other for each facility or structure built on site, or
manufacturer's drawings in like detail for manufactured or pre-cast elements.
d. Document of agreement with drainage receiver, if applicable.
5. Retention facilities:
a. If a seepage bed is chosen as the retention device, City of Eagle standard design calculation
form shall be completed and the dimensions so derived shall be minimum for the design.
b. If a grassy basin is chosen as the retention device, City of Eagle standard design calculation
form shall be completed and submitted as a part of design calculations, and basin size shall be
not less than the dimensions so derived.
c. If a wet pond is chosen as the retention facility, calculations shall be submitted to
demonstrate storage of the total runoff volume, with no credit allowed for percolation during
the event, plus not less than one foot freeboard, above design normal water level, along with
construction plans of the basin.
d. Storm runoff absorption time (time to virtually empty the bed or basin by percolation
following the event) for seepage beds or grassy basins shall be estimated at one-third of site's
percolation rate, or as 95% absorption by a falling-head analysis. If absorption time so
estimated is more than 72 hours, required storage shall be increased 50 percent as a safeguard
against subsequent storms.
e. Grassy basin design shall incorporate an absorption bed, either open-trench type or covered,
having a volume not less than one percent (I %) of the computed design runoff volume,
situated so that its inlet is at the lowest point of the basin, to prevent the occurrence of
Eagle Drainage Design Standard
Page-l
lingering puddling after storms. Base of any grassy retention basin shail be sloped not less
than one percent (1%), also to minimize puddling.
6. Rational Method shall be used as calculation basis for catchment areas up to 10 acres. Designer may
choose to use either Rational Method or NRCS TR-55 method for areas between 10 and 100 acres.
NRCS TR-55 shall be used if area exceeds 100 acres.
7. Runoff coefficients for designs shall be based on the following component values:
Roofs
Pavement and concrete
Graveled surfaces
Landscaped areas
Parks and lawns (uninterrupted turf)
Typical undeveloped
: 0.95
: 0.90
:0.40
: 0.20
: 0.10
: 0.15
Undeveloped areas:
Sandy and sandy loam
Sandy and sandy loam
Sandy and sandy loam
Clay - loam and clay
Clay - loam and clay
Clay - loam and clay
o - 2% slope
2 - 7% slope
> 7% slope
o - 2% slope
2 - 7% slope
> 7% slope
: 0.05
:0.10
:0.15
: 0.13
: 0.18
:0.25
Composite nmoff coefficients from tables shall not be used for design. Runoff quantity shall be
based on actual components proposed or maximum sizes of buildings and impervious surfaces
allowed by
zoning or by planned-unit development agreement. In cases where improvement design is not final,
maximum development allowed by zoning or by planned-unit development agreement shall be
assumed.
8. Calculation of concurrent infiltration during storms for design of all infiltrative systems, and of
storage capacity of native base materials for seepage beds and open-trench beds, shall be subject to
the following:
A. Porosity of 1.5" to 2" washed drain gravel shall be taken as 0.38. Value used for bed sizing shall
be reduced 15% from new-material value to account for silt accumulation as the bed ages.
B. Porosity of washed sand meeting ASTM C - 33 or ITD 703.02 may be taken as 0.35.
C. Porosity of fine-grained native strata shall be taken as 0.25 unless otherwise determined by
laboratory.
D. Appended tables of volume ratios and maximum depth during event are compiled by solving an
equation derived as a classical solution of a differential equation of the form (generalized) dV =
Qin - Qout. Copy of derivation may be viewed at the Planning and Zoning office. The values in
these tables shall be the values used in design of seepage beds and grassy basins for retention.
9. Minimum vertical separation between bottom of trench or bed excavation and maximum ground
water elevation shall be three (3) feet, subject to Health District requirements if more stringent.
Eagle Drainage Design Standard
page-2
10. Target recovery time after end of the design storm shall be seventy-two (72) hours to empty 95% of
the medium in the seepage bed.
11. Design shall provide for protection of groundwater from major episodes of microbial contamination
by including features to maintain unsaturated conditions in the native soils below the base elevation
and above the seasonal high water table (called the "foundation soils" in the following), or by
including special filtration provisions in lieu of assuring non-saturation.
A. If the pore volume of the fine-grained strata of the foundation soils totals more than twice the
during-storm seepage as calculated by 3.D foregoing, no special provisions are necessary. For
this provision, "fine-grained" means strata having a 10% or more passing the No. 60 sieve (grain
size less than 0.2 millimeter).
B. If the criterion of (a) is not met, foundation soils shall be over-excavated to a depth three feet
below design trench bottom and replaced with sand meeting ASlM C-33 or TIn 703.02. Such
replacement fill material shall not be counted as part of storm water storage volume.
12. For phased developments:
Each submittal for review shall be self-subsistent, containing all data, maps, and site-specific quantity
derivations employed in the drainage design for the facilities currently under review. If calculations
are presented in spreadsheet programming form, such spreadsheet programs shall be fully
documented, including all formulas and nomenclature. In the event that quantity values employed in
the design were developed at an earlier stage of a complex or phased development process,
calculations and data demonstrating such values shall be included with documentation, as reference
material in the submittal for staff review. Such previously reviewed materials shall be identified by
the submitter as previously reviewed and included for reference.
In the event that a previously reviewed phase is significantly changed after drainage design review,
and such change modifies the drainage volume received by the phase under consideration, such
changes in volume shall be quantified by the applicant, documentation shall be supplied to verify the
calculated volume change, and such changes in volume shall be accommodated by the facility being
designed for the current phase.
13. Alternative retention designs:
Designs for retention systems of styles other than seepage beds and retention basins shall be subiect to
technical review by City staff. Performance criteria to be met bv such alternative retention system
designs shall be:
A. Retention of 100-year storm runoff as herein defined. and reliable infiltration of the
retained runoff into 2foundwater. or defmite and workable provision for ultimate
disposal of the retained runoffby other means equallv protective of surface water, as
by evaporation (for instance).
B. Allowance for effects of degrading processes occurring over time upon the
performance capability of the system. by ( a) reduction of capacity rating. on a basis
plainly stated. to accommodate d~osition of particulates. growth of vegetation.
accumulation of plant and other organic debris, or such other time-related process as
de2fades performance of the alternative under consideration: or by (b) a defined
schedule of maintenance activities to be performed. with documentation clearly
setting forth what persons or organization shall perform such maintenance and what
institutional or organizational commitments there shall be to assure that such
maintenance will be performed.
Eagle Drainage Design Standard
page-3
C. Protection of groundwater from pathogenic organism and particulate contamination.
not less than the degree of protection afforded saturated infiltrative flow through a
three-foot layer of sand conforming to ASTM C-33 or lID 703.32.
D. fufiltration gallery systems: Desil!:I1 infiltration rate shall be not greater than 3.5
inches per hour. Provide storage volume as required by Table 3, plus a 15 percent
allowance for deposited particulates. Pretreatment to reduce sand and grease is
required as for other alternatives.
14. Conditions for exemption:
Residential subdivision development submittals conforming to either Criterion A or Criterion B,
as follows, shall not be required to provide retention facilities for stormwater directed onto back
yard turf areas, nor to submit stormwater retention design calculations to the City of Eagle, unless
the streets are private streets. This does not relieve developer from any requirement of the
highway authority that receives dedicated right of way as a part of the development process.
Criterion A: the subdivision is zoned A. A-R, or R-E.
Criterion B: impervious-surfaced area (roofs, concrete. pavement, decking, impermeable
landscaping membrane and comparable surfaces) is restricted to not more than twenty-five
pewrcent (25%) of lot area as defined I Eagle City Code 8-1-2 by a specific provision of a
development agreement between the developer and the City of Eagle, and roof drainage is
required to be directed onto back yard turf areas, rather than onto streets, by a specific provision
of such development agreement.
Eagle Drainage Design Standard
Page-4
SEEPAGE BED DESIGN PROCEDURE
1. Determine total area that will drain to the seepage bed.
2. Determine areas of roof, pavement and concrete, landscaping, turf, gravelled and
undeveloped. Check that the sum of partial areas is equal to the total.
3. Determine equivalent area A *, the sum of products of partial areas multiplied by the pertinent
runoff coefficients.
4. For total areas 10 acres or less, calculate design peak flow as 1.1 inches per hour multiplied
by equivalent area and design runoff volume as 1.1 inches multiplied by equivalent area. If
total area exceeds 10 acres, and is 100 acres or less, design runoff volume shall be the
equivalent area multiplied by 1.1 inches, but the design peak flow shall be as determined by
the ITD small-basin analysis method for 100-year storm and the equivalent area. For total
area greater than 100 acres, the NRCS TR-55 method shall be used for design peak flow, and
design runoff volume shall be based on 1.1 inches multiplied by the equivalent area.
5. Percolation rate K of the receiving soil shall be determined at the base of the bed by
percolation test or shall be based on the estimate stated in a written soils investigation report
by a soils scientist or geologist. Ifbased on a percolation test, the value ofK shall be the
equivalent rate in inches per hour; if reported in minutes per inch, the appropriate units
transformation calculation shall be made. K shall be defined as the percolation rate at a head
of one foot. If based upon a percolation test performed with two feet of standing water, K
shall be prorated to one-half the test percolation value. Ifbased on a percolation test
performed at 6 inches standing water, K shall be prorated to double the reported value.
6. IfK is less than 0.5 inch per hour, seepage beds may not be used. IfK is greater than 8
inches per hour, the upper three feet of receiving soils shall be removed and replaced with
washed sand conforming to ASTM C-33. Sand so placed for the purpose of modifying the
hydraulic conductivity shall not be credited as a storage medium in storage pore volume
calculations. Where sand is used to replace excessively pervious receiving soils, the original
percolation rate of the sand shall be taken as 8 inches per hour. For rock-filled bed design,
in-service percolation rate shall be taken as not greater than 2.0 inches per hour, based on
anticipated silt accumulation on the absorption interface, and also as not greater than the
value determined by soils investigation. For open basin design, in-service percolation rate
shall be taken as not less than 4.0 inches per hour, in recognition that the need for surface
maintenance will be visible if silt accumulation slows percolation at the absorptive interface.
7. Coefficients for design include:
a. porosity of I" to 2" washed drain rock : 0.38
b. runoff coefficient for roofs : 0.95
c. runoff coefficient for concrete slabs and pavement : 0.90
d. runoff coefficient for gravelled surfaces : 0.40
e. runoff coefficient for landscaped areas : 0.20
f. runoff coefficient for turf : 0.10
g. runoff coefficient for undeveloped areas : 0.15
8. Volume of storage gravel required shall be based on pore volume adequate for design storm
volume, plus one foot freeboard to top of rock, at porosity of 85% of the porosity of new
material, which equals 0.33 for washed drain gravel. Bed size shall be calculated as shown
on the appended design calculation form.
9. If the facility is a covered seepage bed, then sides of trench and top of rock shall be covered
with geotextile filter fabric not lighter than 6 ounce per square yard, and soil cover shall be
not less than 1.5 foot.
10. Ifthe facility is open-trench type, then sides of rock shall be separated from trench walls by
geotextile filter fabric not lighter than six ounces per square yard.
Eagle Drainage Design Standard
Page-5
11. If "pre-development drainage" is accepted by a drainage receiver (as duly documented by
instrument bearing signature of receiver), it shall be conducted to the receiving facility
through an overflow from the retention bed or basin, rather than through a by-pass.
12. Pre-treatment features (in most systems, sand and grease traps, but in some systems either
flow-through grassy swales, overland-flow turframps, or other solids removal approaches)
shall treat full storm runoff in all systems.
Eagle Drainage Design Standard
Page-6
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BASIC DIMENSIONS AND WAll. J
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SUBMIT STRUCTURAL DESIGN
CALCULATIONS OR DOCUMENT
SHOWING ACCEPTANCE AS
HS-20 BY HIGHWAY AUTHORITY.
GENERAL SAND & GREASE TRAP DETAIL
N.T.S.
CITY OF EAGLE
FOR PUBUC WORKS
CONSTRUCTION
CAPACITY: NOT LESS THAN 1 / 12 HOUR DESIGN
FLOW PER DRAINAGE CALCULATIONS. MEASURED TO
INVERTS OF INLET & OUlLET PIPES.
STORM DRAINAGE STANDARD
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BASE REPLACEMENT IS REQUIRED DUE TO
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LA YER. IF BASE REPLACEMENT IS REQUIRED,
FILTER SAND SHALL BE 3.0 FT.
SECTION B
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STANDARDS DRAWING
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Project:
Designer:
Date:
Site:
Calculated by:
RE: Eagle Drainage Standards Seepage Bed Design Form
(See reverse for defInitions of variables)
1. Percolation rate K, (attach soil column and investigation report):
(See Note 1): K = in/hr.
2. Equivalent watershed area:
Roof
Concrete
Pavement
Gravel
Landscaped
Turf
sq. ft. x 0.95 =
sq. ft. x 0.95 =
sq. ft. x 0.90 =
sq. ft. x 0.40 =
sq. ft. x 0.20 =
sq. ft. x 0.10 =
Aeq = Total Equivalent =
sq. ft.
sq. ft.
sq. ft.
sq. ft.
sq. ft.
sq. ft.
sq. ft.
3. Design storm volume = Aeq x 0.0917 ft
Vs = x 0.0917 = cu. ft.
4. Interpolate value of retention ratio, V N 5, corresponding to K, from table.
V Ns = . Vr = V Ns x Vs = x
cu. ft.
4a If developer has a right to discharge a pre-development volume V pd, then V d = V r - V ps =
cu. ft.
If not, then V d = Vr.
Note: Right to discharge, if claimed, must be verifIed by a signed and dated document from drainage
receiver granting permission, and by calculation or measurement of actual pre-development drainage
quantity.
5. Media bottom area Ab (chosen by designer) =
VJAb= / =
Max. height of stored water hmax =
sq. ft. (
ft. x
ft.)
/
ft. (from table)
6. Media depth (minimum) = hmax + 1.0 = Dm
= Vm=
cu. ft.
7. Ab X Dm =
x
Note 1: Percolation rate may be based on soil scientist's reported probable value, or on a value
determined by percolation test. If percolation test is used, value shall be expressed in inches per hour based
on one foot depth of water. Values determined at depths other than one foot shall be pro-rated based on
ratio of depths. Values reported in minutes per inch shall be converted to inches per hour.
Eagle Drainage Standards Seepage Bed Design Fonn
~sed September 24. 2003
\\Heco-2000\I\ENGR\EG\042203\Seepage Bed Design Fonn.doc
Project:
Designer:
Date:
Site:
Calculated by:
RE: Eagle Drainage Standards Seepage Bed Design Form
(See reverse for defInitions of variables)
1. Percolation rate K, (attach soil column and investigation report):
(See Note 1): K = inIhr.
2. Equivalent watershed area:
Roof
Concrete
Pavement
Gravel
Landscaped
Turf
sq. ft. x 0.95 =
sq. ft. x 0.95 =
sq. ft. x 0.90 =
sq. ft. x 0.40 =
sq. ft. x 0.20 =
sq. ft. x 0.10 =
Aeq = Total Equivalent =
sq. ft.
sq. ft.
sq. ft.
sq. ft.
sq. ft.
sq. ft.
sq. ft.
3. Design storm volume = Aeq x 0.0917 ft
Vs = x 0.0917 = cu. ft.
4. Interpolate value of retention ratio, V/Vs, corresponding to K, from table.
V /VS = . Vr = VrNs x Vs = x
cu. ft.
4a If developer has a right to discharge a pre-development volume V pd, then V d = V r - V ps =
cu. ft.
If not, then V d = Vr.
Note: Right to discharge, if claimed, must be verified by a signed and dated document from drainage
receiver granting permission, and by calculation or measurement of actual pre-development drainage
quantity.
5. Media bottom area Ab (chosen by designer) =
VJAb= / =
Max. height of stored water hmax =
sq. ft. (
ft. x
ft.)
/
ft. (from table)
6. Media depth (minimum) = hmax + 1.0 = Dm
7. Ab X Dm =
= Vm=
cu. ft.
x
Note 1: Percolation rate may be based on soil scientist's reported probable value, or on a value
determined by percolation test. If percolation test is used, value shall be expressed in inches per hour based
on one foot depth of water. Values determined at depths other than one foot shall be pro-rated based on
ratio of depths. Values reported in minutes per inch shall be converted to inches per hour.
.cagle Drainage Standards Seepage Bed Design Fonn
Revised September 24, 2003
\\Heco-2000\l\ENGR\EG\042203\Seepage Bed Design Fonn.doc
RE: Eagle Drainage Standards Seepage Bed Design Form
Variables:
K = Percolation Rate, in/hr
Ae = Equivalent drainage area
Vs = Volume of storm runoff, cu. ft.
Vr = "Volume retained" (at peak)in bed, cu. ft.
Vpd = "Pre-development" runoff volume, cu. ft.
Vd = "Design volume," cu. ft.
Ab = Base area, sq. ft.
hmax = Maximum water depths in bed, ft.
Dm = Depth of media
Vm = Volume of media
Eagle Drainage Standards Seepage Bed Design Form
Revised September 24. 2003
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Project:
Designer:
T)ate:
Site:
Calculated by:
~: Eagle Drainage Standards Grassy Retention Basin Design Form:
(See reverse for definitions of variables.)
1. Percolation rate K, inlhr
Note 1: Percolation rate may be based on soil scientist's reported probable value, or on a value determined by percolation test. If
percolation test is used, value shall be expressed in inches per hour based on one foot depth of water. Values determined at
depths other than one foot shall be pro~rated based on ratio of depths. Values reported in minutes per inch shall be converted to
inches per hour.
2. Equivalent watershed area:
Roofs
Concrete
Pavement
Gravel
Landscaped
Turf
sq. ft. x 0.95 =
sq. ft. x 0.95 =
sq. ft. x 0.90 =
sq. ft. x 0.40 =
sq. ft. x 0.20 =
sq. ft. x 0.10 =
sq. ft
sq. ft.
sq. ft.
sq. ft.
sq. ft.
sq. ft.
Aeq = Sum of CpAp =
sq. ft.
2. Design storm volume Vs =
x 0.0917 =
cu. ft.
3. Base area (mid depth)
Sq. ft.; Ratio V/Ab =
sq. ft.
5. Retained volume ratio from table V/Vs =
6. Required retained volume Vr = (V/Vs) x (V/A) =
cu. ft.
7. "Pre-development" discharge volume V pd = cu. ft. (Must be verified by a signed and dated document
from drainage receiver granting permission, and by calculation or measurement of actual pre-development drainage
quantity, or V pd = 0).
8. Design basin volume
Vd=Vr-Vpd
Vd=
cu. ft.
=
9. Select design water depth Dw and freeboard of basin. Design water depth Dw shall be not less than hmax as shown in
table for design K and Vs/Ab and not greater than 24K inches. Freeboard shall be not less than one foot and not less
than one-third of Dw. Dw = inches = ft.
Freeboard F = ft.
Total depth Db = Dw + F = ft.
10. Basin dimensions:
Show check calculations to demonstrate that basin volume up to depth Dw is greater than or equal to V d.
Notes:
a) Maximum slope of any part 4 horizontal to 1 vertical (includes freeboard).
b) Minimum width at top of any dike 8 feet.
c) Outer slope of any dike, unless supported by special structural provision, shall be not steeper than 4
horizontal to 1 vertical.
cagle Drainage Standards Grassy Retention Basin
Revised September 24, 2003
1:\ENGR\EG\042203\Drainage Standards.doc
Site:
Calculated by:
Project:
Designer:
late:
'{E: Eagle Drainage Standards Grassy Retention Basin Design Form:
(See reverse for definitions of variables.)
1. Percolation rate K, in/hr
Note 1: Percolation rate may be based on soil scientist's reported probable value, or on a value determined by percolation test. If
percolation test is used, value shall be expressed in inches per hour based on one foot depth of water. Values determined at
depths other than one foot shall be pro-rated based on ratio of depths. Values reported in minutes per inch shall be converted to
inches per hour.
2. Equivalent watershed area:
Roofs
Concrete
Pavement
Gravel
Landscaped
Turf
sq. ft. x 0.95 =
sq. ft. x 0.95 =
sq. ft. x 0.90 =
sq. ft. x 0.40 =
sq. ft. x 0.20 =
sq. ft. x 0.10 =
sq. ft
sq. ft.
sq. ft.
sq. ft.
sq. ft.
sq. ft.
Aeq = Sum of CpAp =
sq. ft.
2. Design storm volume Vs =
x 0.0917 =
cu. ft.
3. Base area (mid depth)
Sq. ft.; Ratio V JAb =
sq. ft.
'i. Retained volume ratio from table V/Vs =
6. Required retained volume Vr = (V/Vs) x (VJAr) =
cu. ft.
7. "Pre-development" discharge volume V pd = cu. ft. (Must be verified by a signed and dated document
from drainage receiver granting permission, and by calculation or measurement of actual pre-development drainage
quantity, or V pd = 0).
8. Design basin volume
Vd=Vr-Vpd
Vd=
=
cu. ft.
9. Select design water depth Dw and freeboard of basin. Design water depth Dw shall be not less than hmax as shown in
table for design K and Vs/Ab and not greater than 24K inches. Freeboard shall be not less than one foot and not less
than one-third of Dw. Dw = inches = ft.
Freeboard F = ft.
Total depth Db = Dw + F = ft.
10. Basin dimensions:
Show check calculations to demonstrate that basin volume up to depth Dw is greater than or equal to V d.
Notes:
a) Maximum slope of any part 4 horizontal to 1 vertical (includes freeboard).
b) Minimum width at top of any dike 8 feet.
c) Outer slope of any dike, unless supported by special structural provision, shall be not steeper than 4
horizontal to 1 vertical.
tag Ie Drainage Standards Grassy Retention Basin
Revised September 24, 2003
I:\ENGR\EG\042203\Drainage Standards. doc
RE: Eagle Drainage Standards Grassy Retention Basin Design Form
Variables:
K =
Aeq
Vs =
Vr =
Ab =
Vpd =
Vd =
Dw =
Db =
F =
Percolation rates, inlhr
Equivalent drainage area
Storm runoff volume, cu. ft. (for the design storm)
"Retained volume," cu. ft.
Equivalent base area, (at one-half design depth) sq. ft.
"Pre-development" runoff volume, cu. ft.
"Design volume," cu. ft.
Required water depth, ft; at peak
Total base depth, including freeboard, ft.
Freeboard, ft.
Eagle Drainage Standards Grassy Retention Basin
Revised Septembern24.2003
I:\ENGR\EG\042203\EG Drainage Standards Grassy Retention Variables.doc
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EAGLE DRAINAGE DESIGN STANDARD: APPENDIX A
City of Eagle
Storm Drainage Basin/Rock-Bed Design Derivation
9/18/03, SK
Define the Situation
This derivation is used to set the City of Eagle design standard for rock basins and open
ponds for storm drainage infiltration. The derivation is a classical solution based on
mathematical principles and the governing differential equation.
A visualization of the physical basis for the derivation is shown in the illustration below.
r ROCK -FIll/OR
~ OPEN POND
'~ ~/ SEEPAGE BASIN
I I
I I
BOTTOM AREA
Ab
Goals
- Develop the differential equation that governs the situation illustrated above.
- Derive the formula for water depth in the basin as a function of time.
- Derive the formula for maximum water depth in the basin.
Assumptions
- Percolation through trench walls is disregarded, based on anticipated bacterial blinding of
the interstices of the geotextile wrap.
- The influent flow rate to a storm water basin is governed by the SCS Triangular Hydrograph
shown in the illustration below.
- The governing law for percolation out of the pond/rock-bed bottom in this case is Darcy's
Law for saturated flow through a porous media.
q
Qp
Tp
t
~Tp
Variable Definitions
Refer to the sketches outlined above for dimensioned variable definitions.
h =
hmax =
Ab =
k =
P =
t =
Tp =
Qp =
q =
Vs =
L =
depth of water in the storm water seepage basin/or rock-bed (ft)
maximum depth of water in the storm water seepage basin/rock-bed (ft)
area of the base of the basinlrock-bed (ft2)
coefficient of permeability as defined by Darcy's law (ftlhr)
porosity of rock-fill in rock-filled bed (P = 1 for a basin)
time (hrs)
time of concentration as defined by the SCS Triangular Hydrograph (hrs)
peak flow rate as defined by the SCS Triangular Hydrograph (ft3/hr)
influent flow rate to a basin/rock-bed (ft3/hr)
total volume of surface runoff to the seepage basin/rock-bed (ft3)
depth of limiting soil layer at bottom of seepage basinlrock-bed (ft)
Solution
The governing differential equation:
dh qin h.k
-:=---
dt Ab'P L.P
The equations for influent flow rate are defined by the SCS Triangular Hydrograph:
Equation describing Interval 1 of the SCS Triangular Hydrograph:
Qp
ql:= -.t O<t<Tp
Tp
Equation describing Interval 2 of the SCS Triangular Hydrograph:
q2:= LQp.(s - 3.-.!...) T < t < !.T
5 Tp p 3 p
Darcy's Law:
Darcy's Law for saturated flow through a porous media is
h.k
v:= -
L
Adjustment of the general equation for porosity of a rock filled bed is included by dividing the
influent flow and seepage terms by P.
The total volume of stormwater from the design event:
4
Vs:= -.Qp.Tp
3
Solve for Qp:
3 Ys
Q .--.-
p.- 4 T
p
Substitute Qp in the 1st and 2nd interval equations for the influent flow rate:
Interval 1 :
Ys.t
ql := 0.75.-
T2
p
Interval 2:
1.2.Vs 0.45.t.Vs
q2:= --
T T2
P P
Solve The Differential Equation for Interval 1 (O<t<T p):
db qin b.k
dt:= Ab'P - L.P
Substitute the equation for q1 into the governing differential equation for qin'
db O.75.Ys b.k
dt:= T/-Ab'P.t - L.P
Define constants in the equation for simplification:
k O.75.Ys
a '- ---- a2:=
\.- L.P 2
Tp .Aj,.p
Substitute the constant definitions into the diffential equation:
db
-:= ary.t - a\.b
dt -
Rearange the equation in the general form of a 1sLorder, linear differential equation:
db
- + arb := a"t
dt -
Solve the differential equation:
Calculate the integrating factor
J aId!
p:= e
aj"t
p:= e
Multiply the general form of the differential equation by the integrating factor and
rearange the expression. The reader is referred to a standard textbook on
differential equations to show the intermediate steps for this manipulation.
(Reference: R.K. Nagle and E.B. Saft. Fundamentals of Differential Eauations. 4th
Ed. pp. 46-52.)
aj"t J at"!
e .b:= e .az.tdt + C
Solve the integral in the above expression (Reference: CRC Standard Math
Tables, 14th Ed. pp. 335, Equation 397.)
J [ art ~
eat"t.a2.tdt:= az. :/ .(a\.t-l)J
Substitue the solution to the integral into the expression
[ a!.( ~
al'( e
e .h:=a2' a/.(at.t-l) +C
Rea"ange the Equation
[ a(,( J
32' :/ .(at.t - l)J + C
h:=
at.t
e
Rearrange the Equation Again
h := (a2).t _ ~ + ~
a] 2 at,(
a] e
Apply a boundary condition to determine C
h=O @ t=O
a~
C := -=-
2
31
Solution to the 1 st interval (O<t<T ,)
h= (::) ~ ::' + '1::'"
Substitute the values for a 1 and a2 into the expression, rearrange, and write the
final form of the equation:
. [<O.75).Vs.L2.P] [( k ) 1]
h .= . -.t - 1 +
T 2 A k2 L.P ( k) -
. b' -.t
P L.P
e
forO<t<Tp
Solve The Differential Equation for Interval 2 (Tp< t < 8/3Tp):
db qin h.k
dt:= ~.p - L.P
Substitute the equation for q2 into the governing differential equation for qin'
( Vs Vs )
1.2'T - 0.45.2.t
dh p Tp h.k
dt:= Ab"P - L.P
Rearrange the equation.
dh 1.2.Vs 0.45.Ys h.k
-'- .t--
dt' Tp'~'P T/Ab'P L.P
Define constants in the equation for simplification:
1.2. Vs 0.45. Vs
a3:= a4:=
Tp'Ab'P T/-Ab-P
k
as:= -
L.P
Substitute the constant definitions into the diffential equation:
dh
- := a3 - a4.t - ayh
dt
Rearange the equation in the general form of a 1sLorder, linear differential equation:
dh
- + ayh := a3 - a4-t
dt
Solve the differential equation:
Calculate the integrating factor
I 3sdt
p:= e
U.li."t
p:= e'
Multiply the general form of the differential equation by the integrating factor and
rearange the expression. The reader is referred to a standard textbook on
differential equations to show the intermediate steps for this manipulation.
(Reference: R.K. Nagle and E.B. 8aft. Fundamentals of Differential Eauations. 4th
Ed. pp. 46-52.)
as'! J as-I ( )
e .h:= e. <13 - a40t dt + C
Rearrange the above expression
e ~.'. h ,= .,.J e".' dt +...J t.e .,.. dt
Solve the expression (Reference: CRC Standard Math Tables, 14th Ed. pp. 308 &
335, Equations 12 & 397.)
as'! as.!
as.! <13-e a4-e ( )
e .h:= - --. as.t-1 + C
as 2
as
Rearrange the Equation
a3 a4 C
h := - - --( as.t - 1) + -
as 2 as'!
as e
Rearrange the Equation Again
a3 a4 a4 C
h:= - --ot+- +-
as as 2 as'!
as e
Apply a boundary condition to determine C. h for the first interval is equal to h for
the second interval at t = Tp
. [(o.75).vs.L20P][( k ) 1]
h_= . - .Tp-1+
T 2.Ab.k2 L.P (~)'T
p L.P P
e
@
t = Tp
define the right-hand side of the equation as a constant to simplify the
expression _..
=z
Set h for the second interval equation equal to h from the first interval equation @ t =
Tp and solve for the constant of integration_
a3 a4 a4 C
z:= - - -.Tp+ - +-
as as 2 asoTp
as e
( a3 a4 a4J as.T
C:= Z--+--Tp--.e p
as as as2
Substitute the constant of integration into the equation for h for the 2nd interval and
solve
a3 a4 a4
h := - - -.t + - +
as as a/
as.T ( a3 a4 a4 J
e p. z--+-.Tp--
as as as2
as.t
e
for T p < t < 8/3*T p
Substitution of the values of a3. a4. a5. and z and expansion of the
equation is shown on the next page
Determine the equation for t where h is a maximum, This is the time at which the maximum
water depth in the basin occurs.
dh
-:=0
dt
This function determines the time value at maximum water depth.
Take the derivative of the function for h using the second interval equation
(Reference: eRe Standard Math Tables, 14th Ed. pp. 303 & 304, Equations 1, 2,
& 18)
dh -a4 as-T [ a3 (a4J a4] ( ) -as,t
- := - + e p. z - - + - .Tp - - . -as .e
dt as as as as2
Set dh := 0 and solve for t
dt
i-a4[ 1 ]]
1 -.
as as.T a3 14 a4
e 'f<Z) - " + (as }Tp - .,iJ.,
t '-
max'-
-as
To determine the value of hmax, substitute this equation for t into the equation for h
in the 2nd interval. The expanded equation for t is show on the last page.
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