_Cliffside Unit 5 CBE - Appendix C1_20200107

Duke Energy Coal Combustion Residuals Management Program December 18, 2019
Cliffside Steam Station— Inactive Unit 5 Ash Basin CAMA Closure Plan (Closure by Excavation)
Revision 0
Wood E&IS Project No. 7812190194
APPENDIX C: ENGINEERING EVALUATIONS AND
ANALYSES
wood.

Duke Energy Coal Combustion Residuals Management Program December 18, 2019
Cliffside Steam Station— Inactive Unit 5 Ash Basin CAMA Closure Plan (Closure by Excavation)
Revision 0
Wood E&IS Project No. 7812190194
APPENDIX Cl: STORMWATER
wood.

Channel and Dam Breach Calculation
Duke Energy — Rogers Energy Complex
Inactive Unit 5 Ash Basin Closure Plan
Calculation Title:
Channel and Dam Breach Calculation
Summary:
The channels for the Inactive Unit 5 Ash Basin final closure were designed to have adequate capacity
and stability for the 25-year, 24-hour design storm event.
The breach of the Main Dam (RUTHE-070) was designed to have adequate capacity and stability for the
100-year, 24-hour design storm event. All channels were evaluated for the 100-year, 24-hour design
storm event.
Notes:
Revision Log:
No.
Description
Originator
Verifier
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a y�caI Reviewer
0
Permit Submittal
67 f L:I(s�Za�4
Kevin Ferry
Jos6iv&
BeJI
0a Bell
4Qs
:v0' . GINS
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.,�
" 0,
Wood E&IS Project No. 7812-19-0194 1 of 7 wood.
10/1 /2019

Channel and Dam Breach Calculation
Duke Energy — Rogers Energy Complex
OBJECTIVE:
Inactive Unit 5 Ash Basin Closure Plan
The objective of this calculation is to support the design of stormwater conveyance measures for
the Inactive Ash Basin based on long-term conditions following closure by removal of the basin and
decommissioning of the Main Dam (RUTHE-070)
METHOD
Stormwater flow rates were calculated using the SCS method. The hydraulic capacity and stability
of proposed channels was evaluated using Manning's equation and HydroCAD software [Ref. 1].
DEFINITION OF VARIABLES:
T =
shear;
A =
area;
b =
bottom width;
CN =
curve number;
d =
flow depth;
D =
channel depth;
L =
length;
n =
Manning's n;
P =
wetted perimeter;
Q =
flow;
R =
hydraulic radius;
S =
longitudinal slope;
t =
time
T =
top width;
Tc =
time of concentration;
V =
velocity; and
Z =
channel side slope.
CALCULATIONS:
1.0 Channel Design
1.1 Estimate Drainage Areas
Drainage area delineation was based on the proposed final conditions after closure of the Inactive
Ash Basin. Outside of the basin footprint, existing topography was used for delineation. Within the
basin footprint, a combination of estimated bottom of ash and proposed channel grades was used
for delineation.
Wood E&IS Project No. 7812-19-0194 2 of 7 wood.
10/1 /2019

Channel and Dam Breach Calculation Inactive Unit 5 Ash Basin Closure Plan
Duke Energy — Rogers Energy Complex
Table 1: Drainage Area Summary
Drainage
Curve
Drainage
Area
Soil Class
Number
Area ID
(A)
(CN)
(ac)
DA-1
33.17
B/C
70
DA-2
9.73
B/C
70
DA-3
97.80
B/C
82
DA-4
28.11
B/C
76
1.2 Describe Land Use Conditions
Land use conditions were determined based on the proposed final conditions after closure of the
Inactive Ash Basin. Areas within the basin footprint are anticipated to be grass in fair condition (50-
75% cover) and areas outside of the basin footprint consist of wooded and grassed areas. Site soils
information shows that the drainage areas are comprised of hydrologic soil group B and C soils
[Ref. 3]. Based on the following land use conditions and soils data, composite CN values were
assigned to the drainage areas as shown in Table 1.
1.3 Calculate Time -of -Concentration
The time -of -concentration (Tc) is the amount of time needed for water to travel from the
hydrologically most distant point in a drainage area to the drainage area outlet. The estimated time
of concentration for each drainage area is shown in Figure 1.
The total time -of -concentration for a catchment generally consists of the following three
components: sheet flow, shallow concentrated flow, and channel flow. Sheet flow was assumed to
be no longer than the first 100 feet of the flow path, followed by shallow concentrated flow and
channel flow.
Table 2: Time of Concentration from Sheet Flow
Time of
Flow Length
Concentration
Manning No.
Land Slope
Drainage Area ID
{L}
Surface Description
{T }
c,sheet
{n}
(ft/ft)
(ft.)
(min)
[Ref. 2]
Woods: Light
DA-1
100
0.400
0.0255
17.9
Underbrush
DA-2
100
Range
0.130
0.0870
4.5
DA-3
100
Range
0.130
0.0160
8.8
DA-4
100
Range
0.130
0.0530
5.4
Table 3: Time of Concentration from Shallow Concentrated Flow
Time of
Flow Length
Concentration
Land Slope
Drainage Area ID
{L}
Surface Description
(T
(ft.)
(min)
[Ref. 2]
DA-1
1,239
Unpaved
0.0958
5.1
DA-2
673
Unpaved
0.1734
1.7
DA-3
2,295
Unpaved
0.0403
11.5
DA-4
1,416
Unpaved
0.0450
6.9
Wood E&IS Project No. 7812-19-0194 3 of 7 wood.
10/1 /2019

Channel and Dam Breach Calculation
Duke Energy - Rogers Energy Complex
Inactive Unit 5 Ash Basin Closure Plan
Table 4: Time of Concentration from Channel Flow
Time of
Flow Length
Concentration
Drainage Area ID
(L)
{Tc,channel}
(ft.)
(min)
[Ref. 2]
DA-1
512
1.1
DA-2
433
1.9
DA-3
1,295
3.8
DA-4
329
1.2
Table 5: Total Time of Concentration
Shallow
Total Time of
Selected Time of
Sheet Flow
Concentrated
Channel Flow
Concentration
Concentration
{Tcshee[ )
Flow
{Tc,channel}
Drainage Area ID
{TC,totai}
{TJ
(min)
{Tqs.f}
(min)
(min)
(min)
[Ref.2]
min
(min)
[Ref.2]
[Ref.2]
[Ref.2]
[Ref. 21
DA-1
17.9
5.1
1.1
24.1
24.1
DA-2
4.5
1.7
1.9
8.1
8.1
DA-3
8.8
11.5
3.8
24.1
24.1
DA-4
5.4
6.9
1.2
13.5
13.5
1.4 Peak Flows
HydroCAD software was used to estimate stormwater flows from each drainage area for the 25-
year, 24-hour and 100-year, 24-hour storm events based on the SCS method. The 25-year storm
depth is 6.52 inches, and the 100-year storm depth is 8.21 inches. A type II 24-hr rainfall storm
distribution was selected [Ref. 4]. Table 6 summarizes the peak flow for each drainage area:
Table 6: Peak Flow
Peak
Peak
Flow
Flow
Drainage Area ID
{Q25)
(Qloa)
(cfs)
(cfs)
[Ref.1]
[Ref.1]
DA-1
105.57
153.16
DA-2
51.16
73.24
DA-3
430.85
587.52
DA-4
145.06
200.72
1.5 Channel Capacity and Stability
The proposed trapezoidal channels were designed to tie into the bottom of ash of the Inactive Ash
Basin. In areas where channels will be constructed on fill material, the channel side slopes are
10H:1V. In areas where the channel will be constructed by cut below estimated bottom of ash, the
channel side slopes are 3H:1 V. A total of four (4) channels were designed and analyzed for
capacity and stability. Channel dimensions are summarized in the following table:
Wood E&IS Project No. 7812-19-0194 4 of 7 wood.
10/1 /2019

Channel and Dam Breach Calculation Inactive Unit 5 Ash Basin Closure Plan
Duke Energy — Rogers Energy Complex
Table 7: Channel Dimensions
Min.
Max.
Bottom
Min.
Left Side
Right Side
Length
Longitudinal
Longitudinal
Width
Depth
Channel ID
Slope
Slope
(L)
Slope
Slope
(b)
(D)
{Z,H:V)
{ZZH:V)
(ft)
(S)
(S)
(ft)
(ft)
(ft/ft)
(ft/ft)
1R
20
3.0
3
3
512
0.0625
0.0625
2R
20
3.0
3
3
562
0.0107
0.0122
311
20
4.0
3
3
1363
0.0308
0.0308
411
10
3.0
3
3
314
0.0700
0.0700
For the purpose of this analysis, the channel reaches were modeled with the corresponding cut side
slopes of 3:1 as this is more conservative and results in a smaller cross -sectional flow area. Due to
the irregular cross -sectional geometry of the channel, channels were first modeled as trapezoidal
channels using Manning's equation to iteratively determine an approximate Manning's n value. This
Manning's n value was then input into HydroCAD and the channels were modeled for capacity and
stability using the determined Manning's n.
The capacity of the proposed stormwater channel was evaluated using Manning's equation
presented as:
V _ 1.49 R2/3S1/2 [Ref. 5]
n
and
Q = AV [Ref. 5]
For the Manning's equation spreadsheet analysis, the flow area "A" and wetted perimeter "P" were
calculated using the following relationships based on the geometry of a trapezoidal channel with a
flow depth "d", bottom width "b", left side slope "21", and right side slope "72":
A = bd + 0.5Z1d2 + 0.5Z2d2
P = b + [(Z1d) 22 + d2] + [(Z2d) 22 + d2]
For the capacity and stability analysis in HydroCAD, the flow area "A" and wetted perimeter "P"
were calculated based on coordinate inputs into HydroCAD that represent the actual channel cross-
section.
The stormwater channel capacities were evaluated using HydroCAD. The minimum longitudinal
slope of each diversion was used for the capacity analysis. All channels will be stabilized by grouted
riprap for permanent conditions due to the high velocity anticipated as result of their longitudinal
slopes. Results from the channel capacity analysis are summarized in the following table:
Wood E&IS Project No. 7812-19-0194 5 of 7 wood.
10/1 /2019

Channel and Dam Breach Calculation
Duke Energy - Rogers Energy Complex
Inactive Unit 5 Ash Basin Closure Plan
Table 8: Channel Capacity
Peak
Min.
Storm
Manning's n
Normal
Runoff
Logitudinal
Freeboard
Channel ID
Recurrence
Channel Lining
{n}
Depth
(Q)
Slope
(in)
Interval
(ft)
(cfs)
(ft/ft)
1R
25
250.63
Grouted Riprap
0.0625
0.036
1.05
23
2R
1 25
1482.01,
Grouted Riprap
0.0107
0.028
2.25
9
3R
1 25
1430.851
Grouted Riprap
0.0308
0.031
1.66
28
4R
1 25
1 145.061
Grouted Riprap
0.0700
0.035
1.09
23
Stability of the proposed channel reaches was also analyzed using HydroCAD. Stability analysis
was based on the maximum effective longitudinal slope of each channel. Although permissible
values for shear and velocity are not provided for Grouted Riprap linings, the shear force for each
channel was calculated using the following equation:
T = Ywater dS
Results from the channel stability analysis are summarized in the following table:
[Ref. 5]
Table 9: Channel Stability
Max.
Permissible
Calculated
Permissible
Calculated
Storm
Peak Runoff
Longitudinal
Manning's n
Velocity
Velocity
Shear
Shear Stress
Channel ID
Recurrence
{Q}
Slope
Channel Lining
{n}
Safe
{V}
{V}
{'sperm}
{'r}
Interval
(cfs)
{S}
(ft/s)
(ft/s)
(psf)
(psf)
(ft/ft)
1R
25
250.63
0.0625
Grouted Riprap
0.036
N/A
10.26
N/A
4.44
Yes
2R
25
482.01
0.0122
Grouted Riprap
0.028
N/A
8.02
N/A
1.50
Yes
3R
25
430.85
0.0308
Grouted Riprap
0.031
N/A
10.42
N/A
3.18
Yes
4R
25
145.06
0.0700
Grouted Riprap
0.035
N/A
10.06
N/A
4.75
Yes
1.6 Dam Breach Capacity and Stability
Channel 1 R and 2R passes through the Main Dam (RUTHE-070) proposed breach opening and
discharges into the Broad river. As a result, the capacity and stability of the channels were re-
analyzed for the 100-year, 24-hour storm event. The results of the analysis are summarized in the
tables below:
Table 10: Channel Capacity
Peak
Min.
Storm
Manning's n
Normal
Runoff
Logitudinal
Freeboard
Channel ID
Recurrence
Channel Lining
{n}
Depth
{Q}
Slope
(in)
Interval
(ft)
(cfs)
(ft/ft)
1R
100
353.88
Grouted Riprap
0.0625
0.034
1.28
20.7
2R
100
651.76
Grouted Riprap
0.0107
0.028
2.65
4.2
3R
100
578.52
Grouted Riprap
0.0308
0.029
1.89
25.4
4R
100
200.72
Grouted Riprap
0.0700
0.034
1.27
20.8
Table 11: Channel Stability
Max.
Permissible
Calculated
Permissible
Calculated
Storm
Peak Runoff
Longitudinal
Manning's n
Velocity
Velocity
Shear
Shear Stress
Channel ID
Recurrence
{Q}
Slope
Channel Lining
{n}
{V}(VI
{
{'Cperm}
{T}
Interval
(cfs)
{$}
(ft/s)
(ft/s)
(psf)
(psf)
(ft/ft)
1R
100
353.88
0.0625
Grouted Riprap
0.034
N/A
11.63
N/A
4.98
2R
100
651.76
0.0107
Grouted Riprap
0.028
N/A
8.79
N/A
1.77
3R
100
578.52
0.0308
Grouted Riprap
0.029
N/A
11.94
N/A
3.63
4R
100
200.72
0.0700
Grouted Riprap
0.034
N/A
11.44
N/A
5.55
Wood E&IS Project No. 7812-19-0194 6 of 7 wood.
10/1 /2019

Channel and Dam Breach Calculation
Duke Energy — Rogers Energy Complex
DISCUSSION:
Inactive Unit 5 Ash Basin Closure Plan
The results from the analyses above show that the proposed channels for the Inactive Basin final
closure have storage capacity and stability to convey runoff from the 25-year, 24-hour storm event.
The flow velocities were all above the permissible velocity of 4.5 feet per second for grass lined
open channels; therefore, all channels will be stabilized with grouted riprap.
The Main Dam (RUTHE-070) breach opening was designed to have storage capacity and lining
stability for the 100-year, 24-hour storm event. In the final condition, Channel 1 R and 2R conveys
stormwater runoff through the Dam breach opening. Therefore, the channels were re-evaluated for
the 100-year, 24-hour storm. The results of that analysis show that the channels both have
adequate storage capacity and maintain stability with the proposed grouted riprap lining.
FIGURES:
Figure 1 — Drainage Area Map
REFERENCES:
1. HydroCAD 10.00 (build 24), HydroCAD Software Solutions LLC, 2018.
2. United States Department of Agriculture, "Urban Hydrology for Small Watersheds", Technical
Release 55, June 1986.
3. United States Department of Agriculture, "Web Soil Survey", obtained June 20, 2019.
4. Bonnin, G.M. et. al., "NOAA Atlas 14, Volume 2, Version 3, Point Precipitation Frequency
Estimates", NOAA National Weather Service, obtained May 16, 2019.
5. North Carolina Department of Environment and Natural Resources, "Erosion and Sediment
Control Planning and Design Manual", Revised May 2013.
6. Manning's Equation Calculation Results, prepared June 20, 2019.
Wood E&IS Project No. 7812-19-0194 7 of 7 wood.
10/1 /2019

FIGURE 1
REV. 0
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ptn
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Table 1: Drainage Area Summary
Time of
Drainage
Peak Flow
Peak Flow
Curve
Concentration
Drainage
Area
{Q25}
{Q50}
Soil Class
Number
{Tc,total}
Area ID
{A}
(cfs)
(cfs)
(CN)
(min)
(ac)
DA-1
33.17
B/C
70
23
105.57
128.54
DA-2
9.73
B/C
70
8.1
51.16
61.91
DA-3
97.80
B/C
82
24.1
430.85
503.35
DA-4
28.11
B/C
76
18
145.06
172.29
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Plotted By: Ojaruega, Vona Sheet Set: New Sheet Set (3) Layout: FIGURE 1 October 01, 2019 12: 10: 50pm P:\7812 Duke EEOC\Projects\2019\7812-19-0194 Cliffside Closure Plan\Calculations\Inactive Basin Storm water\References\Unit 5 Inactive Drainage Map FG.dwg
DESCRIPTION
10

6/3/2019 Precipitation Frequency Data Server
NOAA Atlas 14, Volume 2, Version 3"
' Location name: Mooresboro, North Latitude: 3 2147 , Longitude: 81rUSA*
7666°
Elevation: 767.52 ft**
source: ESRI Maps "ky
" source: USGS
POINT PRECIPITATION FREQUENCY ESTIMATES
G.M. Bonnin, D. Martin, B. Lin, T. Parzybok, M.Yekta, and D. Riley
NOAA, National Weather Service, Silver Spring, Maryland
PF tabular I PF graphical I Maps & aerials
PF tabular
PDS-based point precipitation frequency estimates with 90% confidence intervals (in inches)1
Average
recurrence interval (years)
Duration ����������
1 2
5
10
25
50
100
200
500
1000
5-min 0.399 0.474
(0.363-0.439) (0.432-0.521)
0.560
(0.509-0.616)
0.626
(0.568-0.687)
0.711
(0.642-0.779)
0.773
(0.694-0.848)
0.837
(0.748-0.918)
0.900
(0.798-0.989)
0.981
(0.861-1.08)
1.05
(0.910-1.16)
10-min 0.637 0.758
(0.580-0.701) (0.691-0.833)
0.898
(0.816-0.986)
1.00
1 (0.909-1.10)
1.13
1 (1.02-1.24)
1.33
1 (1.19-1.46)
1.43
(1.26-1.57)
1.55
(1.36-1.71
1.65
1 (1.43-1.83)
1.14
1 (1.03-1.25)
1.27
1 (1.15-1.39)
1.44
1 (1.30-1.57)
1.56
(1.40-1.71)
1.68 1.80
1 (1.50-1.84) 1 (1.60-1.98)
1.95
(1.72-2.16)
F 2.07
(1.80-2.29)
15-min 0.797 0.953
(0.725-0.876) (0.869-1.05)
(1.4751177
1.67--2401
1.92 2333)
(2.91 3572
30-min 0.994-11.20) (1. 0--31245)
(2.121 2558
2. 0 2783 2. 8--3008)
F�273 3 43)
2.07
(1.88-2.27)
2.39
(2.17-2.62)
2.83
(2.56-3.11)
3.18
(2.86-3.49)
4.46 )
(3.92-4.92
4.89
( 4.25-5.42)
60-min 1.36 1.65
(1.24-1.50) 5.51-1.81)
3.55 3.93
(3.17-3.89) (3.48-4.32)
2.43
1 (2.22-2.67) 11
2.83
(2.57-3.10)
3.39
1 (3.06-3.72)
3.85
(3.46-4.22)
4.35 4.89 5.67
1 (3.88-4.77) 1 (4.33-5.37) (4.96-6.25)
4.79 .44 6.40
(4.24-5.29) [(4:77-6.02) (5.54-7.11)
6.33
(5.48-7.00)
2-hr 1.59 1.93
(1.45-1.75) 1 (1.77-2.13)
3-hr
1.71 2.06
(1.55-1.89) (1.88-2.29)
2.59
(2.36-2.87)
3.03
(2.74-3.35)
3.67
(3.29-4.05)
4.21
(3.76-4.64)
7.23
(6.18-8.05)
6-hr
2.13 2.57
(1.96-2.34) F(2.35-2.82)
2.62 =(2.83.46)
(2.40-2.87)
3.13 3.78
(2.91-3.39) (3.51-4.09)
3.20
1 (2.92-3.51)
3.93
(3.59-4.31)
3.73
1 (3.40-4.09)
4.51
(4.08-4.94)
5.50
(4.97-6.02)
5.18
(4.65-5.68) 11
6.29
(5.66-6.89)
5.92 6.74 7.97
(5.26-6.49 1 (5.93-7.40) (6.90-8.77)
7.15 8.09 9.50
(6.37-7.82) (7.14-8.87) (8.26-10.4)
8.23 9.11 10.3
1 (7.54-8.86) 1 (8.32-9.82) (9.39-11.1)
F 9.54 F 10.5 11.9
1 (8.77-10.3) 1 (9.67-11.4) (10.9-12.9)
9.04
(7.72-9.98)
12-hr
4.57
(4.16-5.01)
10.7
(9.21-11.8)
24-hr
4.74
1 (4.40-5.12)
5.49
1 (5.09-5.93)
6.44
5.98-6.93
6.54
i (6.03-7.05)
7.62
7.06-8.20)
7.37
1 (6.78-7.94
11.3
(10.2-12.2)
13.0
(11.8-14.0
2-day
3.72
3.46-4.01
4.48
4.17-4.83
5.57
5.18-6.01
F 8.57
1 (7.91-9.22)
3-day
3.95
(3.68-4.25)
4.75
5.87
1 (5.47-6.31)
6.76
(6.29-7.26)
7.97
8.94
1 (8.27-9.59)
9.92 I 10.9 12.4
1 (9.15-10.7) 1 (10.1-11.8) (11.3-13.3)
13.5
(12.3-14.5)
4-day
4.18
(3.91-4.49)
5.01
(4.69-5.38)
6.17
(5.76-6.61)
7.08
1 (6.59-7.58)
8.32
1 (7.73-8.90)
F 9.30
(8.62-9.96)
10.3 11.3 12.8
1 (9.54-11.0) (10.5-12.2) (11.7-13.7)
13.9
(12.7-14.9)
7-day
4.88
(4 .57-5.21)
5.82
(5.45-6.21)
7.07
(6.62-7.54)
8.08
(7.56-8.61)
9.45
(8.81-10.1)
10.5
(9.80-11.2)
11.7 12.8 ) 14.4
( 10.8-12.4) (11.8-13.6 ( 13.2-15.3)
15.6
( 14.3-16.7)
10-day
5.235591
6.2257002
(7.45 8?42
8.42 9552
9.7 0131.0
10.7- 2.2
11 �13.3 E121:74.6) (14 15 6.2
15 2- 7.5
20-day
10.3
(9.76-10.9)
11.5
1 (10.9-12.2)
13.2
1 (12.4-13.9)
14.5
15.8 F 18.8
1 (14.8-16.7) (16.0-18.0) (17.5-19.9)
20.2
(18.7-21.4)
7.42
(7.03-7.83)
8.76
(8.29-9.24)
30-day
9.07
(8.63-9.54)
10.7
(10.1-11.2)
12.4
1 (11.8-13.0)
13.7
1 (13.0-14.4)
15.5
1 (14.6-16.2) 11
16.8
(15.9-17.6) 11
18.1 19.4 21.2
(17.1-19.0) (18.3-20.4 11 (19.8-22.3 11
22.5
(21.0-23.7)
45-day
11.5
(11.0-12.0)
13.7
(13.1-14.3)
13.4
(12.8-14.0)
15.3
(14.6-16.0)
16.7
(15.9-17.5)
18.6
(17.7-19.4)
20.0
(19.0-20.9)
21.3 22.7 24.4
(20.2-22.3) (21.5-23.7) (23.0-25.6)
24.5 25.8 27�
(23.3-25.6) (24.6-27.0) (26.2-29.0)
25.7
(24.2-26.9)
60-day
15.9
(15.2-16.6)
18.0
(17.2-18.8)
19.5
(18.7-20.4)
21.5
(20.6-22.5)
23.0
(22.0-24.0)
29.0
(27.5-30.4)
1 Precipitation frequency (PF) estimates in this table are based on frequency analysis of partial duration series (PDS).
Numbers in parenthesis are PF estimates at lower and upper bounds of the 90% confidence interval. The probability that precipitation frequency estimates (for
a given duration and average recurrence interval) will be greater than the upper bound (or less than the lower bound) is 5%. Estimates at upper bounds are
not checked against probable maximum precipitation (PMP) estimates and may be higher than currently valid PMP values.
Please refer to NOAA Atlas 14 document for more information.
Back to Top
PF graphical
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6/3/2019 Precipitation Frequency Data Server
PD5-based depth -duration -frequency {DDT} curves
Latitude: 35.2147a, Longitude:-31.7666'
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Back to Top
Maps & aerials
Small scale terrain
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— 64-min —
1O-day
— 2fir —
20-day
— 3-hr —
30-day
— "r —
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— 12-hr —
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https://hdsc.nws.noaa.gov/hdsc/pfds/pfds_printpage.html?lat=35.2147&Ion=-81.7666&data=depth&units=english&series=pds 2/4

6/3/2019 Precipitation Frequency Data Server
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Chapter 3
Time of Concentration and
'Navel Time
Travel time ( Tt ) is the time it takes water to travel
from one location to another in a watershed. Tt is a
component of time of concentration ( T, ), which is
the time for runoff to travel from the hydraulically
most distant point of the watershed to a point of
interest within the watershed. T, is computed by
summing all the travel times for consecutive compo-
nents of the drainage conveyance system.
T, influences the shape and peak of the runoff
hydrograph. Urbanization usually decreases T,,
thereby increasing the peak discharge. But T, can be
increased as a result of (a) ponding behind small or
inadequate drainage systems, including storm drain
inlets and road culverts, or (b) reduction of land slope
through grading.
Factors affecting time of concen-
tration and travel time
Surface roughness
One of the most significant effects of urban develop-
ment on flow velocity is less retardance to flow. That
is, undeveloped areas with very slow and shallow
overland flow through vegetation become modified by
urban development: the flow is then delivered to
streets, gutters, and storm sewers that transport runoff
downstream more rapidly. Travel time through the
watershed is generally decreased.
Channel shape and flow patterns
In small non -urban watersheds, much of the travel
time results from overland flow in upstream areas.
Typically, urbanization reduces overland flow lengths
by conveying storm runoff into a channel as soon as
possible. Since channel designs have efficient hydrau-
lic characteristics, runoff flow velocity increases and
travel time decreases.
Slope
Slopes may be increased or decreased by urbanization,
depending on the extent of site grading or the extent
to which storm sewers and street ditches are used in
the design of the water management system. Slope will
tend to increase when channels are straightened and
decrease when overland flow is directed through
storm sewers, street gutters, and diversions.
Computation of travel time and
time of concentration
Water moves through a watershed as sheet flow,
shallow concentrated flow, open channel flow, or
some combination of these. The type that occurs is a
function of the conveyance system and is best deter-
mined by field inspection.
Travel time ( Tt ) is the ratio of flow length to flow
velocity:
Tt ❑ L [eq. 3-1]
3600V
where:
Tt = travel time (hr)
L = flow length (ft)
V = average velocity (ft/s)
3600 = conversion factor from seconds to hours.
Time of concentration ( T, ) is the sum of Tt values for
the various consecutive flow segments:
Tc ❑Tt1 ❑Tt2 ❑... Ttm
where:
T, = time of concentration (hr)
in = number of flow segments
[eq. 3-2]
(210-VI-TR-55, Second Ed., June 1986)
3-1

Chapter 3 Time of Concentration and Travel Time Technical Release 55
Urban Hydrology for Small Watersheds
Figure 3-1 Average velocities for estimating travel time for shallow concentrated flow
.50
.20
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.02
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3-2 (210-VI-TR-55, Second Ed., June 1986)

Chapter 3
Sheet flow
Time of Concentration and Travel Time Technical Release 55
Urban Hydrology for Small Watersheds
Sheet flow is flow over plane surfaces. It usually
occurs in the headwater of streams. With sheet flow,
the friction value (Manning's n) is an effective rough-
ness coefficient that includes the effect of raindrop
impact; drag over the plane surface; obstacles such as
litter, crop ridges, and rocks; and erosion and trans-
portation of sediment. These n values are for very
shallow flow depths of about 0.1 foot or so. Table 3-1
gives Manning's n values for sheet flow for various
surface conditions.
Table 3-1 Roughness coefficients (Manning's n) for
sheet flow
Surface description n 1/
Smooth surfaces (concrete, asphalt,
gravel, or bare soil) ..........................................
0.011
Fallow (no residue) ..................................................
0.05
Cultivated soils:
Residue cover E200/o .........................................
0.06
Residue cover >20%.........................................
0.17
Grass:
Short grass prairie ............................................
0.15
Dense grasses 2/................................................
0.24
Bermudagrass..................................................
0.41
Range (natural).........................................................
0.13
Woods:3/
Light underbrush ..............................................
0.40
Dense underbrush ............................................
0.80
1 The n values are a composite of information compiled by Engman
(1986).
2 Includes species such as weeping lvegrass, bluegrass, buffalo
grass, blue grama grass, and native grass mixtures.
3 When selecting n , consider cover to a height of about 0.1 ft. This
is the only part of the plant cover that will obstruct sheet flow.
For sheet flow of less than 300 feet, use Manning's
kinematic solution (Overtop and Meadows 1976) to
compute Tt:
0.0071k f.s
Tt ❑ � �-5S0.4 [eq. 3-3]
2
where:
Tt = travel time (hr),
n = Manning's roughness coefficient (table 3-1)
L = flow length (ft)
P2 = 2-year, 24-hour rainfall (in)
s = slope of hydraulic grade line
(land slope, ft/ft)
This simplified form of the Manning's kinematic solu-
tion is based on the following: (1) shallow steady
uniform flow, (2) constant intensity of rainfall excess
(that part of a rain available for runoff), (3) rainfall
duration of 24 hours, and (4) minor effect of infiltra-
tion on travel time. Rainfall depth can be obtained
from appendix B.
Shallow concentrated flow
After a maximum of 300 feet, sheet flow usually be-
comes shallow concentrated flow. The average veloc-
ity for this flow can be determined from figure 3-1, in
which average velocity is a function of watercourse
slope and type of channel. For slopes less than 0.005
ft/ft, use equations given in appendix F for figure 3-1.
Tillage can affect the direction of shallow concen-
trated flow. Flow may not always be directly down the
watershed slope if tillage runs across the slope.
After determining average velocity in figure 3-1, use
equation 3-1 to estimate travel time for the shallow
concentrated flow segment.
Open channels
Open channels are assumed to begin where surveyed
cross section information has been obtained, where
channels are visible on aerial photographs, or where
blue lines (indicating streams) appear on United States
Geological Survey (USGS) quadrangle sheets.
Manning's equation or water surface profile informa-
tion can be used to estimate average flow velocity.
Average flow velocity is usually determined for bank -
full elevation.
(210-VI-TR-55, Second Ed., June 1986)
3-3

Chapter 3
Manning's equation is:
2 1
V ❑1.49r3s2
n
where:
Time of Concentration and Travel Time Technical Release 55
Urban Hydrology for Small Watersheds
• A culvert or bridge can act as a reservoir outlet if
there is significant storage behind it. The proce-
dures in TR-55 can be used to determine the peak
[eq. 3-4] flow upstream of the culvert. Detailed storage
routing procedures should be used to determine
the outflow through the culvert.
V = average velocity (ft/s)
r = hydraulic radius (ft) and is equal to a/pw
a = cross sectional flow area (ft2)
pW = wetted perimeter (ft)
s = slope of the hydraulic grade line (channel
slope, ft/ft)
n = Manning's roughness coefficient for open
channel flow.
Manning's n values for open channel flow can be
obtained from standard textbooks such as Chow
(1959) or Linsley et al. (1982). After average velocity is
computed using equation 3-4, Tt for the channel seg-
ment can be estimated using equation 3-1.
Reservoirs or lakes
Sometimes it is necessary to estimate the velocity of
flow through a reservoir or lake at the outlet of a
watershed. This travel time is normally very small and
can be assumed as zero.
Limitations
• Manning's kinematic solution should not be used
for sheet flow longer than 300 feet. Equation 3-3
was developed for use with the four standard
rainfall intensity -duration relationships.
In watersheds with storm sewers, carefully identify
the appropriate hydraulic flow path to estimate T,.
Storm sewers generally handle only a small portion
of a large event. The rest of the peak flow travels
by streets, lawns, and so on, to the outlet. Consult a
standard hydraulics textbook to determine average
velocity in pipes for either pressure or nonpressure
flow.
• The minimum T, used in TR-55 is 0.1 hour.
Example 3-1
The sketch below shows a watershed in Dyer County,
northwestern Tennessee. The problem is to compute
T, at the outlet of the watershed (point D). The 2-year
24-hour rainfall depth is 3.6 inches. All three types of
flow occur from the hydraulically most distant point
(A) to the point of interest (D). To compute T,, first
determine Tt for each segment from the following
information:
Segment AB: Sheet flow; dense grass; slope (s) = 0.01
ft/ft; and length (L) = 100 ft. Segment BC: Shallow
concentrated flow; unpaved; s = 0.01 ft/ft; and
L = 1,400 ft. Segment CD: Channel flow; Manning's
n = .05; flow area (a) = 27 ft2; wetted perimeter
(pw) = 28.2 ft; s = 0.005 ft/ft; and L = 7,300 ft.
See figure 3-2 for the computations made on
worksheet 3.
�100 ft• 1,400 ft 7,300 ft
(Not to scale)
X
3-4 (210-VI-TR-55, Second Ed., June 1986)

3
m
431000
35' 13' 18" N
35' 12' 4" N
431000 431200 431400 431600 431800 432000
3
m
Map Scale: 1:11,100 if printed on A portrait (8.5" x 11") sheet.
Meters
m N 0 150 300 600 900
Feet
0 500 1000 2000 3000
Map projection: Web Mercator Comer coordinates: WGS84 Edge tics: UTM Zone 17N WGS84
U}DA Natural Resources Web Soil Survey
Conservation Service National Cooperative Soil Survey
Soil Map —Cleveland County, North Carolina
(Active Ash Basin - Soils Map)
431200 431400 431600 431800 432000 43=
432400
432200 4324W
N
432600
35° 13' 18" N
35' 12' 4" N
432600
3
N
6/20/2019
Page 1 of 3

MAP LEGEND
Area of Interest (AOI)
0
Area of Interest (AOI)
Soils
0
Soil Map Unit Polygons
rwr
Soil Map Unit Lines
0
Soil Map Unit Points
Special
Point Features
Vo
Blowout
Borrow Pit
Clay Spot
Closed Depression
Gravel Pit
.14
Gravelly Spot
0
Landfill
Lava Flow
Marsh or swamp
+
Mine or Quarry
Miscellaneous Water
Perennial Water
Rock Outcrop
Saline Spot
4
Sandy Spot
Severely Eroded Spot
Sinkhole
Slide or Slip
oa
Sodic Spot
Soil Map —Cleveland County, North Carolina
(Active Ash Basin - Soils Map)
MAP INFORMATION
Spoil Area
The soil surveys that comprise your AOI were mapped at
1:24,000.
Stony Spot
Very Stony Spot
Warning: Soil Map may not be valid at this scale.
Wet Spot
Enlargement of maps beyond the scale of mapping can cause
misunderstanding of the detail of mapping and accuracy of soil
Other
line placement. The maps do not show the small areas of
.-
Special Line Features
contrasting soils that could have been shown at a more detailed
scale.
Water Features
Streams and Canals
Please rely on the bar scale on each map sheet for map
measurements.
Transportation
Rails
Source of Map: Natural Resources Conservation Service
Web Soil Survey URL:
rwr
Interstate Highways
Coordinate System: Web Mercator (EPSG:3857)
US Routes
Maps from the Web Soil Survey are based on the Web Mercator
L
Major Roads
projection, which preserves direction and shape but distorts
distance and area. A projection that preserves area, such as the
Local Roads
Albers equal-area conic projection, should be used if more
accurate calculations of distance or area are required.
Background
.
Aerial Photography
This product is generated from the USDA-NRCS certified data as
of the version date(s) listed below.
Soil Survey Area: Cleveland County, North Carolina
Survey Area Data: Version 21, Sep 10, 2018
Soil map units are labeled (as space allows) for map scales
1:50,000 or larger.
Date(s) aerial images were photographed: Apr 23, 2014—Oct
18, 2017
The orthophoto or other base map on which the soil lines were
compiled and digitized probably differs from the background
imagery displayed on these maps. As a result, some minor
shifting of map unit boundaries may be evident.
USDA Natural Resources Web Soil Survey 6/20/2019
Conservation Service National Cooperative Soil Survey Page 2 of 3

Soil Map —Cleveland County, North Carolina
Active Ash Basin - Soils Map
Map Unit Legend
Map Unit Symbol
Map Unit Name
Acres in AOI
Percent of AOI
BuB
Buncombe loamy sand, 1 to 5
16.8
2.6%
percent slopes, rarely
flooded
CaB2
Cecil sandy clay loam, 2 to 8
0.7
0.1 %
percent slopes, moderately
eroded
ChA
Chewacla loam, 0 to 2 percent
10.3
1.6%
slopes, frequently flooded
DAM
Dam
3.9
0.6%
PaD2
Pacolet sandy clay loam, 15 to
3.5
0.5%
25 percent slopes,
moderately eroded
PbB2
Pacolet-Bethlehem complex, 2
144.6
22.3%
to 8 percent slopes,
moderately eroded
PbC2
Pacolet-Bethlehem complex, 8
196.4
30.3%
to 15 percent slopes,
moderately eroded
PbD2
Pacolet-Bethlehem complex,
58.8
9.1 %
15 to 25 percent slopes,
moderately eroded
PeD
Pacolet-Bethlehem complex,
3.8
0.6%
15 to 25 percent slopes,
stony
PtD
Pacolet-Saw complex, 15 to 25
2.9
0.5%
percent slopes, stony
RaE
Rion -Ashlar complex, 25 to 60
8.7
1.3%
percent slopes, rocky
RnE
Rion-Cliffside complex, 25 to
23.4
3.6%
60 percent slopes, very
stony
UdC
Udorthents, loamy, 0 to 15
119.3
18.4%
percent slopes
W
Water
55.0
8.5%
Totals for Area of Interest
648.1
100.0%
usDA Natural Resources Web Soil Survey 6/20/2019
Conservation Service National Cooperative Soil Survey Page 3 of 3

5/16/2019 Precipitation Frequency Data Server
NOAA Atlas 14, Volume 2, Version 3
Location name: Mooresboro, North Carolina, USA*-
Latitude: 35.2146°, Longitude:-81.7479.
Elevation: 761.42 ft**
* source: ESRI Maps ,, , m y�
** source: USGS
POINT PRECIPITATION FREQUENCY ESTIMATES
G.M. Bonnin, D. Martin, B. Lin, T. Parzybok, M.Yekta, and D. Riley
NOAA, National Weather Service, Silver Spring, Maryland
PF tabular I PF graphical I Maps & aerials
PF tabular
PDS-based point precipitation frequency estimates with 90% confidence intervals (in inches)1
Average recurrence interval (years)
1
2 5
10
25
50
100
200
500F
1000
0.399
0.474 0.560
0.626
0.711
0.773
0.836
0.898
0.979
1.05
5-mm
(0.364-0.439)
(0.433-0.521) (0.510-0.616)
(0.568-0.687)
(0.642-0.779)
(0.694-0.847)
(0.747-0.917)
(0.797-0.988)
(0.860-1.08)
(0.909-1.16)
0.638
0.758 0.898
1.00
1.13
1.23
1.33
1.42
1.55
1.65
1 0-min
(0.581-0.701)
(0.692-0.833) (0.816-0.986)
(0.909-1.10)
1 (1.02-1.24) 11
(1.11-1.35)
1 (1.19-1.46)
1 (1.26-1.57)
(1.36-1.71)
(1.43-1.82)
0.797
0.953 1.14
1.27
1.44
1.56
1.68
1.80
1.95
2.07
1 5-min
(0.726-0.876)
(0.870-1.05) 1 (1.03-1.25)
1 (1.30-1.57) 11
(1.40-1.71)
1 (1.50-1.84)
1 (1.59-1.98)
(1.71-2.15)
(1.80-2.29)
1.09
1.32 1.61
1.84
2.13
2.35
2.57
2.80
3.10
3.35
30-min
(0.995-1.20)
(1.20-1.45) (1.47-1.77)
(1.67-2.01)
(1.92-2.33)
(2.11-2.57)
(2.30-2.82)
(2.48-3.08)
(2.73-3.42)
(2.91-3.71)
1.65
2.07
2.39
2.83
3.18
3.54
3.92
4.45
4.88
C1.36
60-min
(1.24-1.50)
(1.51-1.81)
(1.88-2.27)
(2.17-2.62)
(2.56-3.10)
(2.86-3.49)
(3.17-3.89
(3.48-4.31)
(3.91-4.91)
( 4.25-5.41)
1.59
1.94
2.43
2.83
3.39
3.85
4.35
4.887F
5.667F
6.31
2-hr
(1.46-1.75)
(1.77-2.13)
(2.22-2.67)
(2.57-3.10)
(3.06-3.71)
(3.46-4.22)
(3.88-4.77)
(4.32-5.36)
(4.95-6.24)
(5.47-6.98)
1.71
2.06
2.60
3.03
3.67 -IF-4-21--ll
4.79
5.44
6.39
7.22
3-hr
(1.55-1.89)
1 (1.88-2.29)
1 (2.36-2.87)
1 (2.74-3.35)
1 (3.29-4.05) 11
(3.76-4.64)
1 (4.24-5.29)
(4.77-6.01)
(5.53-7.09)
(6.17-8.03)
2.13 2.56 3.20 3.73 4.51 5.18 5.91 6.73 7.95
9.01
6-hr (1.95-2.34) 1 (2.35-2.82) 1 (2.92-3.51) 1 (4.07-4.94) 1 (4.64-5.67) 1 (5.26-6.48) 1 (5.92-7.39) (6.88-8.75)
(7.70-9.94)
2.61 3.14 3.92 4.56 5.49 6.28 7.14 8.08 9.49
10.7
12-hr (2 .39-2.86) (2.88-3.45) (3.58-4.30) (4.15-5.00) (4.97-6.01) (5.65-6.87) (6.36-7.81) 11 (7.13-8.85) (8.25-10.4)
(9.19-11.8)
3.13 3.77 4.72 5.48 6.52 7.35 8.21 9.10 10.3
11 .3
24-hr (2.90-3.38) (3.50-4.08) (4.39-5.11) (5.08-5.92) (6.02-7.03) (6.76-7.92) (7.53-8.85) (8.31-9.80) (9.38-11.1)
( 10.2-12.2)
3.71 4.46 5.56 6.42 7.61 8.55 9.52 10.5 11.9
13.0
2-day (3.45-4.00) (4.15-4.82) (5.17-6.00) (5.96-6.92) (7.04-8.19) (7.89-9.21) (8.76-10.2) 1 (9.66-11.3) (10.9-12.8)
(11.8-14.0)
3.94 4.73 5.85 6.74 7.95 8.92 9.90 10.9 12.3
13.4
3-day (3.67-4.24) 1 (4.41-5.09) 1 (5.45-6.30) 1 (6.27-7.24) 1 (7.38-8.54) 11 (8.25-9.57) 1 (9.13-10.6) 1 (10.0-11.7) (11.3-13.3)
(12.2-14.5)
4.17 5.00 6.15 7.06 8.30 9.28 10.3 11.3 12.7
13.9
4-day (3.90-4.48) 11 (4.68-5.37) 1 (5.74-6.60) 1 (6.58-7.57) (7.71-8.88) (8.60-9.94) (9.51-11.0) 1 (10.4-12.1) (11.7-13.7)
(12.7-14.9)
4.86 5.80 7.05 8.06 9.42 F 10.5 F 11.6 12.8 44.3
15.6
7-day (4.56-5.19) (5.44-6.19) (6.61-7.52) (7.53 8.58) (8.78-10.0) (9.77-11.2) (10.8-12.4) (11.8-13.6) ( 13.2-15.3)
(14.3-16.6)
5.53
6.58
7.89 8.93 10.3 11.4
12.5 13.6 15.2
16.3
10-day (5.22-5.89)
(6.20-7.00)
(7.43-8.39) 1 (8.39-9.48) 1 (9.67-11.0) 1 (10.7-12.1)
1 (11.7-13.3) 1 (12.7-14.5) (14.1-16.1)
(15.1-17.4)
7.39
10.3 F 13.1 F 14.4
15.7 17.0 F 18.8
8.72
20.1
20-day (7.00-7.80)
(8.26-9.20)
(9.73-10.8) (10.912.1) (12.4-13.9) 1 (13.6-15.2)
1 (14.7-16.6) (15.9-18.0) (17.5-19.9)
(18.7-21.3)
9.03
12.3 F 15.4 16.7
18.0 19.4 21.1
10.6
22.4
30-day (8.60-9.50)
(10.1-11.2)
1 (11.7-13.0) (13.014.3) (14.6-16.2) 1 (15.8-17.6)
1 (17.0-19.0) (18.2-20.4) (19.8-22.2)
(21.0-23.6)
11.4
15.2 16.7 18.5 19.9
21.3 22.6 24.3
25.6
13.4
45-day 109-12.0)
(
(12.8-14.0)
(14.5-15.9) (15.917.4) (17.6-19.4) (18.9-20.8)
(20.2-22.2) ( 21.4-23.6) (23.0-25.5)
(24.1-26.8)
13.6
15 .9
17.9 19.4 21.4 22.9
24.4 25.8 27.6
28.9
60-day 13.0-14.2)
(
(15.2-16.6)
(17.1-18.7) (18.6-20.3) (20.5-22.4) (21.9-24.0)
(23.2-25.5 24.5-27.0 26.2-28.9)
) ( ) (
(27.4-30.3)
1 Precipitation frequency (PF) estimates in this table are based on frequency analysis of partial duration series (PDS).
Numbers in parenthesis are PF estimates at lower and upper bounds of the 90% confidence interval. The probability that precipitation frequency estimates
(for a given duration and average recurrence interval) will be greater than the upper bound (or less than the lower bound) is 5%. Estimates at upper bounds
are not checked against probable maximum precipitation (PMP) estimates and may be higher than currently valid PMP values.
Please refer to NOAA Atlas 14 document for more information.
Back to Top
https:Hhdsc.nws. noaa.gov/hdsc/pfds/pfds_printpage.htmI?lat=35.2146&Ion=-81.7479&data=depth&units=engIish&series=pds 1 /4

5/16/2019 Precipitation Frequency Data Server
PF graphical
PDS-based depth -duration -frequency (DDF) curves
Latitude: 35.2146 Longitude:-31.74791
30
25
C
t 20
N
d
di
U
O 15
49
CL
V 10
FU
ill
0
-Y -Y -Y -Y
OO OO u'i OO
ri ri rn LO ri N rn V ID
Duration
30
25
e
20
C
CL
m
15
,9
CL
10
a
5
O F --t-- TI I I I I I I
1 2 5 10 25 50 100 200 500 1000
Average recurrence interval (years)
NDAAAtlas 14, Volume 2, Version 3 Created {GMT}: Thu May 16 18:50:29 2019
Back to Top
Maps & aerials
Small scale terrain
Average recurrence
inlenral
{years)
— t
2
— 5
— 10
25
50
100
200
500
1000
Duration
— 5-min —
2-day
— 1 d-min —
3-day
15-min —
4-day
— 30-min —
7-day
— 8D-min —
10-day
— 2fir —
20-(Jay
— "r —
30-(Jay
— 6-1r —
45-day
— 12-hr —
6d-eay
- 24-hr
https:Hhdsc.nws.noaa.gov/hdsc/pfds/pfds_printpage.htmI?lat=35.2146&Ion=-81.7479&data=depth&units=engIish&series=pds 2/4

5/16/2019 Precipitation Frequency Data Server
nennettia
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2mi 5�
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https:Hhdsc.nws.noaa.gov/hdsc/pfds/pfds_printpage.htmI?lat=35.2146&Ion=-81.7479&data=depth&units=engIish&series=pds 3/4

5/16/2019
Precipitation Frequency Data Server
Back to Top
US Department of Commerce
National Oceanic and Atmospheric Administration
National Weather Service
National Water Center
1325 East West Highway
Silver Spring, MD 20910
Questions?: [e-mail]
Disclaimer
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Appendices
This section addresses the design of stable conveyance channels and
diversions using flexible linings. A stable channel is defined as a channel
which is nonsilting and nonscouring. To minimize silting in the channel, flow
velocities should remain constant or increase slightly throughout the channel
length. This is especially important in designing diversion channels and can
be accomplished by adjusting channel grade. Procedures presented in this
section address the problems of erosion and scour. More advanced procedures
for permanent, unlined channels may be found elsewhere. (References: Garde
and Ranga Raju, 1980)
Diversions are channels usually with a supporting ridge on the lower side.
They are generally located to divert flows across a slope and are designed
following the same procedures as other channels. Design tables for vegetated
diversions and waterways are included at the end of this section.
Flexible channel linings are generally preferred to rigid linings from an
erosion control standpoint because they conform to changes in channel shape
without failure and are less susceptible to damage from frost heaving, soil
swelling and shrinking, and excessive soil pore water pressure from lack of
drainage. Flexible linings also are generally less expensive to construct, and
when vegetated, are more natural in appearance. On the other hand, flexible
linings generally have higher roughness and require a larger cross section for
the same discharge.
EROSION CONTROL CRITERIA
The minimum design criteria for conveyance channels require that two
primary conditions be satisfied: the channel system must have capacity for
the peak flow expected from the 10-year storm and the channel lining must be
resistant to erosion for the design velocity. In some cases, out -of -bank flow
may be considered a functional part of the channel system. In these cases,
flow capacities and design velocities should be considered separately for out -
of -bank flows and channel flows.
Both the capacity of the channel and the velocity of flow are functions of the
channel lining, cross -sectional area and slope. The channel system must carry
the design flow, fit site conditions, and be stable.
STABLE CHANNEL DESIGN METHODS
Two accepted procedures for designing stable channels with flexible linings
are: (1) the permissible velocity approach; and (2) the tractive force approach.
Under the permissible velocity approach, the channel is considered stable if the
design, mean velocity is lower than the maximum permissible velocity. Under
the tractive force approach, erosive stress evaluated at the boundary between
flowing water and lining materials must be less than the minimum unit tractive
force that will cause serious erosion of material from a level channel bed.
8.05.1

0
The permissible velocity procedure is recommended for the design of vegetative
channels because of common usage and the availability of reliable design
tables. The tractive force approach is recommended for design of channels
with temporary synthetic liners or riprap liners. The tractive force procedure
is described in full in the U.S. Department of Transportation, Federal Highway
Administration Bulletin, Design of Roadside Channels with Flexible Linings.
Permissible Velocity The permissible velocity procedure uses two equations to calculate flow:
Procedure Manning's equation,
V = 1.49 R2/3 S1/2
n
where:
V = average velocity in the channel in ft/sec.
n = Manning's roughness coefficient, based upon the lining of the
channel
R = hydraulic radius, wetted cross -sectional area/wetted perimeter
in ft
S = slope of the channel in ft/ft
and the continuity equation,
Q = AV
where:
Q = flow in the channel in cfs
A = cross -sectional area of flow within the channel in ftz
V = average velocity in the channel in ft/sec.
Manning's equation and the continuity equation are used together to determine
channel capacity and flow velocity. A nomograph for solving Manning's
equation is given in Figure 8.05a.
Selecting Permanent Channel lining materials include such flexible materials as grass, riprap and
Channel Lining gabions, as well as rigid materials such as paving blocks, flag stone, gunite,
asphalt, and concrete. The design of concrete and similar rigid linings
is generally not restricted by flow velocities. However, flexible channel
linings do have maximum permissible flow velocities beyond which they are
susceptible to erosion. The designer should select the type of liner that best
fits site conditions.
Table 8.05a lists maximum permissible velocities for established grass linings
and soil conditions. Before grass is established, permissible velocity is
determined by the choice of temporary liner. Permissible velocities for riprap
linings are higher than for grass and depend on the stone size selected.
8.05.2

0
60
50
40
30
20
10
5 0.0001
4 0.0002
3
0.0005
2
U)
0.001
0
m
0.002
0.005
1.0
D
CCD
0.01 �Qp
CD
0.02
0
0
10.5
(n
0.05
- 0.4
0.1
- 0.3
0.2
0.3
- 0.2
- 0.1
Figure 8.05a Nomograph for solution of Manning equation.
Appendices
50
40
30
20
0
Oh i
0.01A/ m
/ 5
/ m
4
m
/ 0
Q 3
O/ c <
j 0.05
o,
n 0.1
0
co
cD
a
r.
0
0.5
4
1.0
0.5
8.05.3

0
Table 8.05a
Maximum Allowable Design Velocities'
for Vegetated Channels
Typical
Soil
Grass Lining
Permissible Velocity'
Channel
Slope Characteristics'
for Established Grass
Application
Lining (ft/sec)
0-5%
Easily Erodible
Bermudagrass
5.0
Non -plastic
Tall fescue
4.5
(Sands & Silts)
Bahiagrass
4.5
Kentucky bluegrass
4.5
Grass -legume mixture
3.5
Erosion Resistant
Bermudagrass
6.0
Plastic
Tall fescue
5.5
(Clay mixes)
Bahiagrass
5.5
Kentucky bluegrass
5.5
Grass -legume mixture
4.5
5-10%
Easily Erodible
Bermudagrass
4.5
Non -plastic
Tall fescue
4.0
(Sands & Silts)
Bahiagrass
4.0
Kentucky bluegrass
4.0
Grass -legume mixture
3.0
Erosion Resistant
Bermudagrass
5.5
Plastic
Tall fescue
5.0
(Clay mixes)
Bahiagrass
5.0
Kentucky bluegrass
5.0
Grass -legume mixture
3.5
>10%
Easily Erodible
Bermudagrass
3.5
Non -plastic
Tall fescue
2.5
(Sands & Silts)
Bahiagrass
2.5
Kentucky bluegrass
2.5
Erosion Resistant
Bermudagrass
4.5
Plastic
Tall fescue
3.5
(Clay mixes)
Bahiagrass
3.5
Kentucky bluegrass
3.5
Source:
USDA-SCS Modified
NOTE:
'Permissible Velocity based on 10-year
storm peak runoff
2SoiI erodibility based on resistance to soil movement from concentrated
flowing water.
'Before grass is established, permissible velocity is determined by the
type of temporary liner used.
Selecting Channel To calculate the required size of an open channel, assume the design flow is
uniform and does not vary with time. Since actual flow conditions change
Cross -Section throughout the length of a channel, subdivide the channel into design reaches,
Geometry and design each reach to carry the appropriate capacity.
The three most commonly used channel cross -sections are "V"-shaped,
parabolic, and trapezoidal. Figure 8.05b gives mathematical formulas for the
area, hydraulic radius and top width of each of these shapes.
8.05.4

Appendices
Cross -Sectional Area (A) = Zd2
Top Width (T) = 2dZ
Hydraulic Radius (R) = Zedd
2 Z� `+ 1
V-Shape
T
Z _ e
is e
Parabolic Shape
T
Cross -Sectional Area (A) = 2 Td
Top Width (T) = 1.5 A
d
Hydraulic Radius = T2d
1 .5T2 + 4d2
I
Trapezoidal Shape
T
�— b 1. e
Cross -Sectional Area (A) = bd + Zd2
Top Width (T) = b + 2dZ
Hydraulic Radius = bd + Zd2
b + 2d 4Z2+ 1
Figure 8.05b Channel geometries for v-shaped, parabolic and trapezoidal channels.
Z_e
_d
8.05.5

0
Design Procedure- The following is a step-by-step procedure for designing a runoff conveyance
Permissible Velocity channel using Manning's equation and the continuity equation:
Table 8.05b
Manning's n for Structural
Channel Linings
Step 1. Determine the required flow capacity, Q, by estimating peak runoff
rate for the design storm (Appendix 8.03).
Step 2. Determine the slope and select channel geometry and lining.
Step 3. Determine the permissible velocity for the lining selected, or the
desired velocity, if paved. (see Table 8.05a, page 8.05.4)
Step 4. Make an initial estimate of channel size —divide the required Q by the
permissible velocity to reach a "first try" estimate of channel flow area. Then
select a geometry, depth, and top width to fit site conditions.
Step 5. Calculate the hydraulic radius, R, from channel geometry (Figure
8.05b, page 8.05.5).
Step 6. Determine roughness coefficient n.
Structural Linings —see Table 8.05b, page 8.05.6.
Grass Lining:
a. Determine retardance class for vegetation from Table 8.05c, page
8.05.8. To meet stability requirement, use retardance for newly
mowed condition (generally C or D). To determine channel capacity,
use at least one retardance class higher.
b. Determine n from Figure 8.05c, page 8.05.7.
Step 7. Calculate the actual channel velocity, V, using Manning's equation
(Figure 8.05a, pg. 8.05.3), and calculate channel capacity, Q, using the
continuity equation.
Step 8. Check results against permissible velocity and required design
capacity to determine if design is acceptable.
Step 9. If design is not acceptable, alter channel dimensions as appropriate.
For trapezoidal channels, this adjustment is usually made by changing the
bottom width.
Recommended
Channel Lining n values
Asphaltic concrete, machine placed
0.014
Asphalt, exposed prefabricated
0.015
Concrete
0.015
Metal, corrugated
0.024
Plastic
0.013
Shotcrete
0.017
Gabion
0.030
Earth
0.020
Source: American Society of Civil Engineers (modified)
8.05.6 Rev. 12/93

Appendices
5
4
3
2
Z
_U)
0)
.08
CZ
.06
04
.02
Step 10. For grass -lined channels once the appropriate channel dimensions
have been selected for low retardance conditions, repeat steps 6 through 8
using a higher retardance class, corresponding to tall grass. Adjust capacity of
the channel by varying depth where site conditions permit.
NOTE 1: If design velocity is greater than 2.0 ft/sec., a temporary lining
may be required to stabilize the channel until vegetation is established.
The temporary liner may be designed for peak flow from the 2-year storm.
If a channel requires a temporary lining, the designer should analyze
shear stresses in the channel to select the liner that provides protection
and promotes establishment of vegetation. For the design of temporary
liners, use tractive force procedure.
NOTE 2: Design Tables —Vegetated Channels and Diversions at the end
of this section may be used to design grass -lined channels with parabolic
cross -sections.
Step 11. Check outlet for carrying capacity and stability. If discharge
velocities exceed allowable velocities for the receiving stream, an outlet
protection structure will be required (Table 8.05d, page 8.05.9).
Sample Problem 8.05a illustrates the design of a grass -lined channel.
MIN
Longer than 30"
Less than 2"
IN
2 .4 .6 .8 1.0 2 4 6 8 10 20
VR, Product of Velocity and Hydraulic Radius
Figure 8.05c Manning's n related to velocity, hydraulic radius, and vegetal retardance.
Note: From Sample Problem 8.05a multiply Vp x Hydralulic Radius (4.5x0.54=2.43), then enter the product of VR and extend a
straight line up to Retardance class "D", next project a straight line to the left to determine a trial manning's n.
Rev. 12/93 8.05.7

0
Table 8.05c
Retardance Classification for Vegetal Covers
Retardance
Cover
Condition
A
Reed canarygrass
Excellent stand, tall (average 36")
Weeping lovegrass
Excellent stand, tall (average 30")
B
Tall fescue
Good stand, uncut, (average 18")
Bermudagrass
Good stand, tall (average 12")
Grass -legume mixture
(tall fescue,red
fescue, sericea
lespedeza)
Good stand, uncut
Grass mixture
(timothy, smooth
bromegrass or
orchardgrass)
Good stand, uncut (average 20")
Sericea lespedeza
Good stand, not woody, tall (average 19")
Reed canarygrass
Good stand, cut, (average 12-15")
Alfalfa
Good stand, uncut (average 11 ")
C
Tall fescue
Good stand (8-12")
Bermudagrass
Good stand, cut (average 6")
Bahiagrass
Good stand, uncut (6-8")
Grass -legume mixture --
summer (orchardgrass,
redtop and annual
Good stand, uncut (6-8")
lespedeza)
Centipedegrass
Very dense cover (average 6")
Kentucky bluegrass
Good stand, headed (6-12")
Redtop
Good stand, uncut (15-20")
D
Tall fescue
Good stand, cut (3-4")
Bermudagrass
Good stand, cut (2.5")
Bahiagrass
Good stand, cut (3-4")
Grass -legume mixture --
fall -spring (orchardgrass,
redtop, and
annual lespedeza)
Good stand, uncut (4-5")
Red fescue
Good stand, uncut (12-18")
Centipedegrass
Good stand, cut (3-4")
Kentucky bluegrass
Good stand, cut (3-4")
E
Bermudagrass
Good stand, cut (1.5")
Bermudagrass
Burned stubble
Modified from:
USDA-SCS, 1969. Engineering Field Manual.
8.05.8

Appendices
Table 8.05d
Maximum Permissible
Velocities for Unprotected
Soils in Existing Channels.
Sample Problem 8.05a
Design of a
Grass -lined Channel.
Materials
Fine Sand (noncolloidal)
Sand Loam (noncolloidal)
Silt Loam (noncolloidal)
Ordinary Firm Loam
Fine Gravel
Stiff Clay (very colloidal)
Graded, Loam to Cobbles (noncolloidal)
Graded, Silt to Cobbles (colloidal)
Alluvial Silts (noncolloidal)
Alluvial Silts (colloidal)
Coarse Gravel (noncolloidal)
Cobbles and Shingles
Maximum Permissible
Velocities (fps)
2.5
2.5
3.0
3.5
5.0
5.0
5.0
5.5
3.5
5.0
6.0
5.5
Given:
Design Q10 = 16.6 cfs
Proposed channel grade = 2%
Proposed vegetation: Tall fescue
Soil: Creedmoor (easily erodible)
Permissible velocity, VP = 4.5 ft/s (Table 8.05a)
Retardance class: "B" uncut, "D" cut (Table 8.05c).
Trapezoidal channel dimensions:
designing for low retardance condition (retardance class D)
design to meet VP.
Find:
Channel dimensions
Solution:
Make an initial estimate of channel size
A = Q/V, 16.6 cfs/4.5 ft/sec = 3.69 ftz
Try bottom width = 3.0 ft w/side slopes of 3:1
Z=3
A = bd + Zdz
P=b+2d Z2+1
R = AP
An iterative solution using Figure 8.05a to relate flow depth to Manning's n
proceeds as follows: Manning's equation is used to check velocities.
*From Fig. 8.05c, pg. 8.05.7, Retardance Class d (VR=4.5x0.54=2.43)
d (ft) A (ftz) R (ft) *n Vt (fps) Q (cfs) Comments
0.8 4.32 0.54 0.043 3.25 14.0 V<V OK,
Q<dio
(too small, try deeper channel)
0.9 5.13 0.59 0.042 3.53 18.10 V<VP, OK,
Q>Qto, OK
Now design for high retardance (class B):
For the ease of construction and maintenance assume and
try d = 1.5 ft and trial velocity V, = 3.0 ft/sec
d (ft) A (ft2) R (ft) Vt (fps) n
V (fps)
Q (cfs)
Comments
1.5 11.25 0.90 3.0 0.08
2.5
28
reduce V,
2.0 0.11
1.8
20
reduce Vt
1.6 0.12
1.6
18
**1.5 0.13
1.5
17
Q>Qja OK
** These assumptions = actual V (fps.) (chart continued
on next page)
8.05.9

0
(continued)
Sample Problem 8.05a
Design of a
Grass -lined Channel.
Tractive Force
Procedure
Table 8.05e
Manning's Roughness
Coefficients for Temporary
Lining Materials
Channel summary:
Trapezoidal shape, Z = 3, b = 3 ft, d = 1.5 ft, grade = 2%
Note: In Sample Problem 8.05a the "n-value" is first chosen based on a
permissible velocity and not a design velocity criteria. Therefore, the use of
Table 8.05c may not be as accurate as individual retardance class charts when
a design velocity is the determining factor.
The design of riprap-lined channels and temporary channel linings is based on
analysis of tractive force.
NOTE: This procedure is for uniform flow in channels and is not to be
used for design of deenergizing devices and may not be valid for larger
channels.
To calculate the required size of an open channel, assume the design flow is
uniform and does not vary with time. Since actual flow conditions change
through the length of a channel, subdivide the channel into design reaches as
appropriate.
PERMISSIBLE SHEAR STRESS
The permissible shear stress, Td, is the force required to initiate movement of
the lining material. Permissible shear stress for the liner is not related to the
erodibility of the underlying soil. However, if the lining is eroded or broken,
the bed material will be exposed to the erosive force of the flow.
COMPUTING NORMAL DEPTH
The first step in selecting an appropriate lining is to compute the design
flow depth (the normal depth) and determine the shear stress.
Normal depths can be calculated by Manning's equation as shown for
trapezoidal channels in Figure 8.05d. Values of the Manning's roughness
coefficient for different ranges of depth are provided in Table 8.05e for
temporary linings and Table 8.05f for riprap. The coefficient of roughness
generally decreases with increasing flow depth.
n value for Depth Ranges*
0-0.5 ft
0.5-2.0 ft
>2.0 ft
Lining Type
Woven Paper Net
0.016
0.015
0.015
Jute Net
0.028
0.022
0.019
Fiberglass Roving
0.028
0.021
0.019
Straw with Net
0.065
0.033
0.025
Curled Wood Mat
0.066
0.035
0.028
Synthetic Mat
0.036
0.025
0.021
* Adapted from: FHWA-HEC 15, Pg. 37 - April 1988
8.05.10 Rev.12/93

Appendices
S (ft/ft)
0.1
0.08
0.06
0.05
0.04
10.03
0.02
NOTE: Project horizontal frog
d 1 to obtain values for Z
z
B I
Qn
(Ft3/S)
r-20
•10
8.0
6.0
5.0
4.0
We
MCI
0.01
0.008
0.006 \\ 1.0
♦ 0.8
0.005 �\
\ 0.6
0.004 \ 0.5
\\ 0.4
0.003 \
0.002
0.2 \
0.1
-0.001 0.08
0.06
0.05
0.04
0.03
0.02
Figure 8.05d Solution of Manning's equation for trape
Adapted from: FH WA-HEC. 15, Pg 40 -
N
c
J
0)
c
.E
H
r
d (ft)
CD B (ft)
of
N N
.01
/ Example:
Given: Find: Solution:
S=0.01 ft/ft d Qn = 0.3
Q = 10 ft3/S d/B = 0.14
n = 0.03 d = 0.14(4) = 0.56 ft
B=4ft
Z = 4
Manning's equation: Q=11.49 A R2/3 Sll 8 V = 11.n 99 R2/3 S112 f
zoidal channels of various side slopes.
April 1988
.02
.03
.04
.05
.06
.08
.1
IE
1.3
1.4
1.5
1.6
,.8
.0
Rev.12/93 8.05.11

0
Table 8.05f Manning's Roughness Coefficient
Lining Category
Lining Type
n - value
n value for Depth Ranges
0-0.5 ft 0.5-2.0 ft 2.0 ft
(0-15 cm) (15-60 cm) (>60 cm)
Rigid
Concrete
0.015
0.013
0.013
Grouted Riprap
0.040
0.030
0.028
Stone Masonry
0.042
0.032
0.030
Soil Cement
0.025
0.022
0.020
Asphalt
0.018
0.016
0.016
Unlined
Bare Soil
0.023
0.020
0.020
Rock Cut
0.045
0.035
0.025
Gravel Riprap
1-inch (2.5-cm) D50
0.044
0.033
0.030
2-inch (5-cm) D50
0.066
0.041
0.034
Rock Riprap
6-inch (15-cm) D50
0.104
0.069
0.035
12-inch (30-cm) D50
--
0.078
0.040
Note: Values listed are representative values for the respective depth ranges. Manning's roughness coefficients, n, vary with the flow depth.
DETERMINING SHEAR STRESS
Shear stress, T, at normal depth is computed for the lining by the following
equation:
T=yds
Td = Permissible shear stress
where:
T = shear stress in lb/ft2
y = unit weight of water, 62.4 lb/ft'
d = flow depth in ft
s = channel gradient in ft/ft
If the permissible shear stress, Td, given in Table 8.05g is greater than the
computed shear stress, the riprap or temporary lining is considered acceptable.
If a lining is unacceptable, select a lining with a higher permissible shear stress
and repeat the calculations for normal depth and shear stress. In some cases it
may be necessary to alter channel dimensions to reduce the shear stress.
Computing tractive force around a channel bend requires special considerations
because the change in flow direction imposes higher shear stress on the channel
bottom and banks. The maximum shear stress in a bend, Tb, is given by the
following equation:
Tb = K b T
where:
Tb = bend shear stress in lb/ft2
kb = bend factor
T = computed stress for straight channel in lb/ft2
The value of kb is related to the radius of curvature of the channel at its center
line, Rc, and the bottom width of the channel, B, Figure 8.05e. The length of
channel requiring protection downstream from a bend, LP, is a function of the
roughness of the lining material and the hydraulic radius as shown in Figure
8.05ff,
8.05.12 Rev.12/93

Appendices
Table 8.05g
Permissible Shear Stresses
for Riprap and Temporary
Liners
Permissible Unit Shear Stress, Td
Lining Category
Lining Type
(lb/ft2)
Temporary
Woven Paper Net
0.15
Jute Net
0.45
Fiberglass Roving:
Single
0.60
Double
0.85
Straw with Net
1.45
Curled Wood mat
1.55
Synthetic Mat
2.00
d50 Stone Size (inches)
Gravel Riprap
1
0.33
2
0.67
Rock Riprap
6
2.00
9
3.00
12
4.00
15
5.00
18
6.00
21
7.80
24
8.00
Adapted From: FHWA, HEC-15, April 1983, pgs. 17 & 37.
Design Procedure- The following is a step-by-step procedure for designing a temporary liner for
Temporary Liners
a channel. Because temporary liners have a short period of service, the design
Q may be reduced. For liners that are needed for six months or less, the 2-year
frequency storm is recommended.
Step 1. Select a liner material suitable for site conditions and application.
Determine roughness coefficient from manufacturer's specifications or Table
8.05e, page 8.05.10.
Step 2. Calculate the normal flow depth using Manning's equation (Figure
8.05d). Check to see that depth is consistent with that assumed for selection of
Manning's n in Figure 8.05d, page 8.05.11. For smaller runoffs Figure 8.05d
is not as clearly defined. Recommended solutions can be determined by using
the Manning equation.
Step 3. Calculate shear stress at normal depth.
Step 4. Compare computed shear stress with the permissible shear stress for
the liner.
Step 5. If computed shear is greater than permissible shear, adjust channel
dimensions to reduce shear, or select a more resistant lining and repeat steps
1 through 4.
Design of a channel with temporary lining is illustrated in Sample Problem
8.05b, page 8.05.14.
Rev.12/93 8.05.13

0
Sample Problem 8.05b
Design of a Temporary Liner
for a Vegetated Channel
Given:
Qz = 16.6 cfs
Bottom width = 3.0 ft
Z=3
n = 0.02 (Use basic n value for channels cut in earth (Table 8.05b)
Vp = 2.0 ft/sec maximum allowable velocity for bare soil (pg. 6.30.1)
Channel gradient = 2%
Find:
Suitable temporary liner material
Solution:
Using Manning's equation:
b(ft) d(ft) A(ft2) R(ft) V(fps) Q(cfs) Comments
3.0 0.59 2.82 0.42 5.88 16.60 V>Vp,
(needs protection)
Q>_Q2, OK
Velocity >2.0 fps channel requires temporary liner:*
Calculate channel design with straw with net as temporary liner.
n = 0.033 (Table 8.05e). Td = 1.45 (Table 8.05g, pg. 8.05.13)
b(ft) d(ft) A(ftz) R(ft) V(fps) Q(cfs) Comments
3.0 0.76 4.05 1.94 4.10 16.60 V<Td, OK
Calculate shear stress for QZ conditions:
T = yds where: y = unit weight of water (62.4 Ib/ft3)
d = flow depth in ft
s = channel gradient in ft/ft
T = (62.4)(0.76)(0.02) = 0.95 T<Td, OK
Temporary liner: straw with net.
*In some cases the solution is not as clearly defined; the use of a more conservative material is
recommended.
DESIGN OF RIPRAP LINING -MILD GRADIENT
The mild gradient channel procedure is applicable for channel grades less than
10%. The method assumes that the channel cross section has been designed
properly, including undercut and that the remaining problem is to provide a
stable riprap lining.
Side slope stability. As the angle of the side slope approaches the angle of
repose of the channel lining, the lining material becomes less stable. The
stability of a side slope is given by the tractive force ratio, Kz, a function of the
side slope and the angle of repose of the rock lining material.
The rock size to be used for the channel lining can be determined by comparing
the tractive force ratio, an indicator of side slope stability, to the shear stress
on the sides and shear stress on the bottom of the channel. The angle of
repose for different rock shapes and sized is shown in Figure 8.05g. The
required rock size (mean diameter of the gradation, d50) for the side slopes is
determined from the following equation:
K1
d50 (sides) — K d50 (bottom)
2
where:
Kt = ratio of shear stress on the sides, Ts, and bottom, T, of a
trapezoidal channel (Figure 8.05h),
Kz = tractive force ratio (Figure 8.05i)
8.05.14 Rev. 12/93

Appendices
2.0
1.9
1.8
1.7
1.6
Kb 1.5
1.4
1.3
1.2
1.1
1.01 1 ' 1 I 1
0 1 2 3 4 5
Rc
B
Figure 8.05e Kb factor for maximum shear stress on channel bends.
Adapted from: FH WA-HEC 15, Pg. 47 - April 1988
Tb = Kb Td
g 7 8 9 10
Rev.12/93 8.05.15

nb
0.5
0.1
DR•1-i
0.01
0
Lp/R = 0.604 ((R")/nb)
9
.0°o
'0
0
.j
i
1.0 5.0 10.0 20.0 30.0
Lp/ R
Figure 8.05f Protection length, LP, downstream from a channel bend.
nb = Manning Roughness of the lining material in the bend and the depth of flow (see tables 8.05e and f).
R = Hydraulic Radius = Area/wetted perimeter
Adapted from: FH WA-HEC 15, pg 48 - April 1988
50.0
8.05.16 Rev. 12/93

Appendices
43
41
39
a�
Q 37
cc
0 35
m
Q 33
31
Mean Stone Size d50, ft
ooti Z1313?L2
/()Y
(�/ "</.
Emil
NONNI
.000
low
051111EWMIEU@1
Mean Stone Size, d50, mm
Figure 8.05g Angle of repose for different rock shapes and sizes.
Adapted from: FH WA, HEC-15, pg. 49 - April 1988
Selection of riprap gradation and thickness. Rpprap gradation should
have a smooth size distribution curve. The largest stone size in the
gradation should not exceed 1.5 times the d50 size. The most important
criterion is that interstices formed by larger stones be filled with smaller sizes
in an interlocking fashion, preventing the formation of open pockets. These
gradation requirements apply regardless of the type of filter design used.
In general, riprap constructed with angular stone performs best. Round stones
are acceptable as riprap provided they are not placed on side slopes steeper than
3:1. Flat, slab -like stones should be avoided since they are easily dislodged by
the flow. An approximate guide to stone shape is that neither the breadth nor
the thickness of a single stone be less than one-third its length.
The thickness of a riprap lining should equal 1.5 times the diameter of the
largest rock size in the gradation.
Filter design: When rock riprap is used, an appropriate underlying filter
material must be selected. The filter material may be either a granular, gravel
or sand filter blanket, or a geotextile fabric.
Rev.12/93 8.05.17

0
For a granular filter blanket, the following criteria must be met:
d15 filter
<5
d85 base
d filter
5 < 15
< 40
d15 base
d50 filter
< 40
d50 base
Where "filter" refers to the overlying riprap or gravel and "base" refers to
the underlying soil, sand or gravel. The relationship must hold between the
filter blanket and base material and between the riprap and filter blanket.
The minimum thickness for a filter blanket should not be less than 6
inches.
In selecting a filter fabric, the fabric should have a permeability at least
equal to the soil and a pore structure that will hold back the base soil. The
following properties are essential to assure performance under riprap:
• For filter fabric covering a base with granular particles containing 50
percent or less (by weight) of fine particles (less than U.S. Standard
Sieve No. 200):
a. d85 base (mm)/EOS* filter cloth (mm) > 1.
b. Total open area of filter is less than 36%.
- Filter fabric covering other soils:
a. EOS less than U.S. Standard Sieve No. 70.
b. Total open area of filter less than 10%.
*EOS - Equivalent Opening Size to a U.S. Standard Sieve Size
Design Procedure- The following is a step-by-step procedure for designing a riprap channel
lining with mild gradients. This procedure is designed for smaller channels
R i p ra p Lining, Mild that are generally used as erosion control measures, and is not intended for
Gradient conveyance channels.
Additional design information for lined channels may be obtained from the
National Technical Information Services (NTIS) by obtaining a copy of the
National Cooperative Highway Research Program Report No. 108, titled
"Tentative Design Procedure for Riprap - Lined Channels".
Step 1. Select a riprap size, and look up the Manning's n value (Table 8.05f)
and permissible shear stress, Td (Table 8.05g).
Step 2. Calculate the normal flow depth in the channel, using Manning's
equation (Figure 8.05d). Check that the n value for the calculated normal
depth is consistent with that determined in step 1.
Step 3. Calculate shear stress at normal depth.
8.05.18 Rev.12/93

Channel and Dam Breach Calculation Prepared By: Vona Ojaruega Inactive Ash Basin Closure Plan
Duke Energy - Rogers Energy Complex Checked By: Josh Bell
METHOD
This spreadsheet calculates flow characteristics for an open channel based on channel geometry,
channel lining, and peak flow parameters provided by the user. The spreadsheet uses an iterative
calculation process to determine the flow depth and the corresponding Manning's n value.
Additionally, flow velocity and shear stress are computed and compared against allowable values to
determine the stability of the channel's lining.
DEFINITION OF VARIABLES
A - area (ft2)
b - bottom width (ft)
C, - retardance curve index
d - flow depth (ft)
d50 - midrange riprap diameter (ft)
m, - left side slope (H:V)
m2 - right side slope (H:V)
n - Manning's roughness coefficient
P - wetted perimeter (ft)
Q - flow (ft3/s)
R - hydraulic radius (ft)
S - longitudinal slope (ft/ft)
V - flow velocity (ft/s)
T - shear stress (ft2/s)
Ywater - specific weight of water (62.4 Ibf/ft3)
CALCULATIONS
Channels are evaluated using Manning's equation presented as:
V = 1.49 Rz/3S1/z
and Q = VA [Ref. 1 ]
n
The flow area "A", wetted perimeter "P", and hydraulic radius "R" were calculated using the following
relationships based on the geometry of a trapezoidal channel with a flow depth "d", bottom width "b",
left side slope "21", and right side slope "Z2":
1 1 A
A=bd+2Z1dz+2Z2dz P=b+d�Z12++1d Z2+1 and R=P [Ref. 1]
The shear stress "T" was calculated using the following equation where "Ywatw" is the specific weight of
water, "d" is the flow depth, and "S" is the longitudinal slope:
T = YwaterdS
[Ref. 1 ]
Permissible shear stress and permissible velocity values for channel linings were taken from the
NCDEQ "Erosion and Sediment Control Planning and Design Manual" [Ref. 1] and from the North
American Green "RollMax Product Selection Chart" [Ref. 41.
The Manning's n value for grass lined channels was calculated using the following equation where
"Cl" is the retardance curve index, "V" is the channel velocity, and "R" is the hydraulic radius:
n = e[CI(0.0133[(ln(VR)]Z-0.0954[ln(VR)]+0.297)-4.16]
[Ref. 2]
The retardance curve index "Cl" for each SCS retardance class is presented in the following table:
SCS Retardance Class
Retardance Curve Index
A
10.0
B
7.64
C
5.60
D
4.44
E
2.88
Wood E&IS Project No. 7812-19-0194 wood.
9/30/2019 Page 1 of 5

Channel and Dam Breach Calculation Prepared By: Vona Ojaruega Inactive Ash Basin Closure Plan
Duke Energy - Rogers Energy Complex Checked By: Josh Bell
The Manning's n value for riprap lined channels was calculated using the following equation where "d"
is the flow depth and "d50" is the midrange riprap diameter:
n=
d1/6
21.6 X 1og10 V-0) + 14.0
[Ref. 3]
The Manning's n value for all other channel linings was calculated based on minimum (nm;n) and
maximum (nmaX) n values provided for a given lining option. nm;n corresponds to the Manning's n value
at a flow depth of 2.0-feet or greater. nmaX corresponds to the Manning's n value at a flow depth of 0.5-
feet or less. For flow depths in between 0.5-feet and 2.0-feet, the Manning's n value was linearly
interpolated using the following equation:
n = nmin — nmax X (d — 0.5) + nmax
2.0 ft — 0.5 ft
REFERENCES
1. North Carolina Department of Environmental Quality, "Erosion and Sediment Control Planning and
Design Manual", Revised May 2013.
2. Temple, D.M. et. al., "Stability Design of Grass -Lined Open Channels", United States Department
of Agriculture: Agriculture Research Service, September 1987.
3. Pennsylvania Department of Environmental Protection, "Erosion and Sediment Pollution Control
Program Manual", Revised March 2012.
4. North American Green, "RollMax Product Selection Chart", Obtained February 13, 2019.
Wood E&IS Project No. 7812-19-0194 wood.
9/30/2019 Page 2 of 5

Channel and Dam Breach Calculation Prepared By: Vona Ojaruega
Duke Energy - Rogers Energy Complex Checked By: Josh Bell
Inactive Ash Basin Closure Plan
Wood E&IS Project No. 7812-19-0194
9/30/2019 Page 3 of 5
wood.

Channel and Dam Breach Calculation Prepared By: Vona Ojaruega Inactive Ash Basin Closure Plan
Duke Energy - Rogers Energy Complex Checked By: Amarachi Eze
Channel Input Parameters
Channel
ID
Storm
Event
(yrs)
Peak
Flow
{Q}
cfs
( )
Soil Type
(Grass and Soil -Lined
Channels Only)
Grass Type
(Grass -Lined
Channels Only)
Channel
Lining
Bottom
Width
{b}
ft
( )
Channel
Depth
{D}
ft
( )
Left
Side
Slope
{Z,H:V }
Right
Side
Slope
Z H:V
{ z }
Channel
Slope
{S}
ft/ft
( )
1 R
25
250.63
N/A
N/A
Grouted Riprap
20.0
3.00
3.0
3.0
0.0674
2R
25
482.01
N/A
N/A
Grouted Riprap
20.0
3.00
3.0
3.0
0.0107
3R
25
430.85
N/A
N/A
Grouted Riprap
20.0
4.00
3.0
3.0
0.0308
4R
25
145.06
N/A
N/A
Grouted Riprap
10.0
3.00
3.0
3.0
0.0700
1 R
50
300.83
N/A
N/A
Grouted Riprap
20.0
3.00
3.0
3.0
0.0309
2R
50
565.26
N/A
N/A
Grouted Riprap
20.0
3.00
3.0
3.0
0.0107
3R
50
503.35
N/A
N/A
Grouted Riprap
20.0
3.00
3.0
3.0
0.0308
4R
50
172.29
N/A
N/A
Grouted Riprap
10.0
3.00
3.0
3.0
0.0700
1 R
100
353.88
N/A
N/A
Grouted Riprap
20.0
3.00
3.0
3.0
0.0625
2R
100
651.76
N/A
N/A
Grouted Riprap
20.0
3.00
3.0
3.0
0.0107
3R
100
578.52
N/A
N/A
Grouted Riprap
20.0
4.00
3.0
3.0
0.0308
4R
100
200.72
N/A
N/A
Grouted Riprap
10.0
3.00
3.0
3.0
0.0700
Wood EMS Project No. 7812-19-0194 g wood.
9/30/2019 Pa e 1 of 5

Channel and Dam Breach Calculation Prepared By: Vona Ojaruega Inactive Ash Basin Closure Plan
Duke Energy - Rogers Energy Complex Checked By: Amarachi Eze
Channel Capacity Analysis
Channel Stability Analysis
Channel
ID
Manning's
n
{n}
Area
{A}
(ftz)
Wetted
Perimeter
{P}
(ft)
Hydraulic
Radius
{R}
(ft)
Normal
Depth
(ft)
Calculated
Flow Rate
{Qca�c}
(cfs)
Freeboard
(in)
Safe?
Permissible
Velocity
{V}
(ft/s)
Calculated
Velocity
{V}
(ft/s)
Permissible
Shear
Stress
{Tperm}
(psf)
Calculated
Shear
Stress
{T}
(psf)
Safe?
1 R
0.036
24.43
26.67
0.92
1.05
250.63
23.3
Yes
N/A
10.26
N/A
4.44
Yes
2R
0.028
60.13
34.22
1.76
2.25
482.01
9.0
Yes
N/A
8.02
N/A
1.50
Yes
3R
0.031
41.34
30.47
1.36
1.66
430.85
28.1
Yes
N/A
10.42
N/A
3.18
Yes
4R
0.035
14.42
16.88
0.85
1.09
145.06
22.9
Yes
N/A
10.06
N/A
4.75
Yes
1 R
0.033
33.86
28.85
1.17
1.40
300.83
19.2
Yes
N/A
8.88
N/A
2.70
Yes
2R
0.028
67.16
35.52
1.89
2.45
565.26
6.5
Yes
N/A
8.42
N/A
1.64
Yes
3R
0.030
44.97
31.23
1.44
1.78
503.35
14.7
Yes
N/A
11.19
N/A
3.41
Yes
4R
0.035
16.01
17.47
0.92
1.18
172.29
21.8
Yes
N/A
10.76
N/A
5.16
Yes
1 R
0.034
30.42
28.07
1.08
1.28
353.88
20.7
Yes
N/A
11.63
N/A
4.98
Yes
2R
0.028
74.18
36.78
2.02
2.65
651.76
4.2
Yes
N/A
8.79
N/A
1.77
Yes
3R
0.0289003
48.44
31.94
1.52
1.89
578.52
25.350477
Yes
N/A
11.94381
N/A
3.6275475
Yes
4R
0.0338365
17.55
18.03
0.97
1.27
200.72
20.754719
Yes
N/A
11.4393
N/A
5.5492826
Yes
Wood E&IS Project No. 7812-19-0194 g wood.
9/30/2019 Pa e 2 of 5