Sensitivity of Hydraulic Models to Manning s n in Computing WSEL

Transcription

Creating Value …
… Delivering Solutions
Sensitivity of Hydraulic Models to Manning’s n in Computing WSEL
with Different Stream Sizes
M. Saleem Ashraf, Ph.D. P.E. and Rashed Farid, P.E., CFM
Michael Baker Jr. Inc. Alexandria, Virginia
MSFSM 8th Annual Conference, Linthicum, MD
October 25, 2012
Objectives of Presentation
 Describe the significance of roughness coefficient, Manning’s n, in
computations of Water Surface Profiles in one-dimensional hydraulic
models, and relate it with the theory of hydraulics.
 Describe the procedure for conducting the sensitivity analyses for
this study.
 Provide some examples for sensitivity of roughness coefficient to
computed water surface profiles for different size streams.
 Provide guidelines for the appropriate selection of roughness
coefficient for use in the one-dimensional hydraulic models.
2
Roughness Coefficient in 1-D Hydraulic Models
 Baker as the PTS Contractor for Risk MAP receives a large number of
hydraulic studies for review to process map revision requests
 The ultimate objective of the flood hazard studies is to compute Base
Flood Elevations (BFEs) along the reaches of the stream.
 It has been observed that Roughness coefficient is very sensitive for
some streams, which can affect the BFEs.
 A small change in the Manning’s n can affect the BFE, and thus raise the
issues of (a) appropriate selection of Manning’s n, and (b) accuracy of
computed WSEL for NFIP studies and water resources planning and
mitigation studies
Theory of Hydraulics - Assumptions
 Steady flow
 Gradually varied flow
 Small channel slope
 Frictional slope constant between two adjacent cross sections
 Rigid channel boundaries
Energy Balance at Two Cross Sections
α2v22
α1V12
Y2 + Z2 +  = Y1+ Z1 +  + he
2g
2g
(1)
Energy Losses
he = Friction loss + transitional Loss
he = L Sf + C [ ΔVh]
(2)
L = Discharge weighted reach length
Sf = Friction slope
ΔVh = Absolute differences in the velocity
head
C = Contraction and expansion loss coefficients
Energy Losses
L Sf = Friction loss
Q
= K Sf1/2
Sf = (Q/K)2
where K = (1.49/n) A R2/3
Accuracy of Computations of WSEL
 WSEL = f (slope, velocity, friction losses, transitional losses)
 Any deviations from the assumption made regarding energy balance
and head loss equations may cause instability in the computation of
energy losses, and potential inaccuracy in computed water surface
elevation (WSEL).
 When the program can not balance the energy equation at a cross
section, it is usually caused by an inadequate number of cross sections
or bad cross section data, including Manning’s n.
Manning's Equation
 Manning’s equation is also used for evaluating of drag force which is
a component of momentum equation
 The momentum equation is utilized in situations where water
surface profile is rapidly varied
9
Application of Roughness coefficient in hydraulic model
180
.08
.09
.0225
.09
.08
Legend
WS PF 3
Ground
Bank Sta
160
Elevation (ft)
140
120
100
80
60
2000
3000
4000
5000
6000
7000
8000
9000
10000
Station (ft)
 For less variable roughness, three n values (Left overbank, channel
and Right overbank ) are sufficient to describe the channel geometry.
 For more variable, horizontal variation of n value is used
 Defining ineffective flow area by assigning artificially high roughness
coefficients
10
Application of Roughness coefficient in hydraulic model
 Cross sections subdivision for lateral variation of n values
11
Procedure for Conducting Sensitivity Analyses
of Manning’s n
 We selected a few streams from the State of Alabama, with varying
1% annual chance discharge rates.
 We ran the models with the effective n Values for each stream, and
considered the model run as a control for that stream.
 We varied the Manning's Channel n values from + 10% to +50%, and
-10% to -50% from the value used in the effective analysis.
 Then we compared the computed depths from step 3 with the
effective computed depth, and determined maximum and minimum
change in depths along the streams.
12
Stream locations
Sensitivity of Manning's values for Big Creek
Location:
Pike County, AL
Channel n values:
Overbank n values:
Flow Range:
Average Slope:
0.055
0.12
2,000 cfs – 2,371 cfs
0.0025 (0.25 %)
5362.2
4680.6
Bi
3717.1
Main
gCr e
ek
3207.8
2662.2
2113.8
914.1
55.7
Big Creek
395
Legend
WS P100yr - PLUS50
WS P100yr - PLUS40
WS P100yr - PLUS30
WS P100yr - PLUS20
WS P100yr - PLUS10
WS P100yr - PLUS05
390
WS P100yr - Floodplain
WS P100yr - MINUS05
WS P100yr - MINUS10
WS P100yr - MINUS20
WS P100yr - MINUS30
WS P100yr - MINUS40
Ground
380
5362.2
4680.6
3717.1
3207.8
2662.2
2113.8
375
914.1
Elevation (ft)
WS P100yr - MINUS50
385
370
0
1000
2000
3000
Channel Distance (ft)
4000
5000
6000
Big Creek
Legend
WS P100yr - PLUS50
WS P100yr - PLUS40
WS P100yr - PLUS30
WS P100yr - PLUS20
WS P100yr - PLUS10
394
WS P100yr - PLUS05
WS P100yr - Floodplain
WS P100yr - MINUS05
WS P100yr - MINUS10
WS P100yr - MINUS20
Elevation (ft) (ft)
WS P100yr - MINUS30
WS P100yr - MINUS40
393
WS P100yr - MINUS50
Ground
392
391
390
5000
5100
5200
5300
Channel distance (ft) (ft)
5400
5500
Sensitivity of Manning's n values for Big Creek
Sensitivity of Manning's values for Pea River
Location:
Pike County, AL
Channel n values:
Overbank n values:
Flow Range:
Average Slope:
0.05
0.11
23,490 cfs – 46,357 cfs
0.00037 (0.037%)
192708.5
185582.8
178984.6
170597.5
162145.4
156755.4
i ver
P ea R
Main
147160.6
123560
113369.8
100857.8
83236.1
62583.3
55403.9
31141.8
26100
21430.4
14870.6
5554.9
Pea River
360
Legend
WS P100yr - Plan 02
WS P100yr - PLUS05
WS P100yr - PLUS10
WS P100yr - PLUS20
WS P100yr - PLUS30
340
WS P100yr - PLUS40
WS P100yr - PLUS50
WS P100yr - MINUS05
WS P100yr - MINUS10
WS P100yr - MINUS20
WS P100yr - MINUS30
WS P100yr - MINUS40
WS P100yr - MINUS50
Ground
300
280
192708.5
185582.8
178984.6
170597.5
162145.4
153052.4
156755.4
142483.7
147160.6
133693.5
123560
111322.8
100857.8
89681.6
94031.6
83236.1
73202.9
62583.3
55403.9
42212.4
45507.7
36822.2
21430.4
26100
31141.8
14870.6
260
5554.9
9233
Elevation (ft)
320
240
0
50000
100000
150000
200000
250000
Pea River
Legend
WS P100yr - Plan 02
WS P100yr - PLUS05
298
WS P100yr - PLUS10
WS P100yr - PLUS20
WS P100yr - PLUS30
WS P100yr - PLUS40
WS P100yr - PLUS50
WS P100yr - MINUS05
297
WS P100yr - MINUS10
WS P100yr - MINUS20
WS P100yr - MINUS30
Elevation (ft)
WS P100yr - MINUS40
WS P100yr - MINUS50
296
Ground
295
294
293
34000
36000
38000
40000
42000
Sensitivity of Manning's n values for Pea River
Sensitivity of Manning's values for Conecuh Creek
Location:
Escambia, AL
Channel n values:
Overbank n values:
Flow Range:
Average Slope:
0.045
0.12
46,976 cfs
0.00038 (0.038 %)
75333.8
71260.3
66447
C
on
Main
ec
Ri v
uh
er
59050
DS
38437.2
34188.3
25860.9
20665
13176.4
230.7
4303.7
63755.9
Conecuh Creek
290
Legend
WS P100yr - PLUS50
WS P100yr - PLUS40
WS P100yr - PLUS30
WS P100yr - PLUS20
WS P100yr - PLUS10
WS P100yr - Plan 02
280
WS P100yr - MINUS05
WS P100yr - MINUS10
WS P100yr - MINUS20
WS P100yr - MINUS30
WS P100yr - MINUS40
WS P100yr - MINUS50
260
75333.8
71260.3
68865.9
66447
63755.9
59050
52398.7
49161.6
46769.2
38437.2
34188.3
25860.9
20665
17705.4
13176.4
250
4303....
Elevation (ft)
Ground
270
240
0
20000
40000
60000
80000
Conecuh Creek
270
Legend
WS P100yr - PLUS50
WS P100yr - PLUS40
WS P100yr - PLUS30
WS P100yr - PLUS20
WS P100yr - PLUS10
WS P100yr - Plan 02
268
WS P100yr - MINUS05
WS P100yr - MINUS10
WS P100yr - MINUS20
WS P100yr - MINUS30
WS P100yr - MINUS40
WS P100yr - MINUS50
Elevation (ft)
Ground
266
264
262
260
10000
12000
14000
16000
Sensitivity of Manning's n values for Conecuh Creek
Sensitivity of Manning's values for Tallapoosa River
Location:
Channel n values:
Overbank n values:
Flow Range:
Average Slope:
Elmore County and Montgomery County, AL (River
0.04
0.12
199,800 cfs – 204,000 cfs
0.00007 (0.007%)
Sensitivity of Manning's values for Tallapoosa River (Contd)
Tallapoosa River
190
Legend
WS PF 3 - base+50%
WS PF 3 - base+40%
180
WS PF 3 - base+30%
WS PF 3 - base+20%
WS PF 3 - base+15%
WS PF 3 - base+10%
170
WS PF 3 - base+5%
160
WS PF 3 - base-10%
WS PF 3 - base-20%
WS PF 3 - base-30%
150
WS PF 3 - base-40%
WS PF 3 - base-50%
Ground
140
149350
133000
117400
95070
120
80040
130
51746
Elevation (ft)
WS PF 3 - base
WS PF 3 - base-5%
110
0
20000
40000
60000
Main Channel Distance (ft)
80000
100000
120000
Tallapoosa River
Legend
WS PF 3 - base+50%
180
WS PF 3 - base+40%
WS PF 3 - base+30%
WS PF 3 - base+20%
WS PF 3 - base+15%
WS PF 3 - base+10%
WS PF 3 - base+5%
Elevation (ft)
175
WS PF 3 - base
WS PF 3 - base-5%
WS PF 3 - base-10%
WS PF 3 - base-20%
WS PF 3 - base-30%
170
WS PF 3 - base-40%
WS PF 3 - base-50%
Ground
165
160
45000
46000
47000
48000
49000
Tallapoosa River
3.00
2.00
1.00
% change of Manning's n
-40
0.00
-20
0
20
-1.00
-2.00
-3.00
-4.00
-5.00
-6.00
40
60
Max Change
Change in Depth (ft)
-60
Min Change
% change
in n
-50
-40
-30
-20
-10
-5
5
10
20
30
40
50
change in depth
Max
Min
-5.05
-3.49
-3.47
-2.40
-2.34
-1.58
-1.41
-0.96
-0.64
-0.45
-0.31
-0.19
0.31
0.18
0.55
0.33
1.44
0.71
1.69
1.00
1.94
1.24
2.12
1.46
Sensitivity of Manning's values for Alabama River
Location:
Autauga County, Dallas County, Lowndes County and
Montgomery County, AL
Channel n values:
Overbank n values:
Flow Range:
Average Slope:
0.04 – 0.05
0.08 – 0.12
252,000 cfs - 324,000 cfs
0.00012 (0.012%)
Sensitivity of Manning's values for Alabama River (Contd)
Alabama River
180
Legend
WS PF 3 - base+50%
WS PF 3 - base+40%
WS PF 3 - base+30%
160
WS PF 3 - base+20%
WS PF 3 - base+10%
WS PF 3 - base+5%
140
WS PF 3 - base
WS PF 3 - base-10%
WS PF 3 - base-20%
120
WS PF 3 - base-30%
WS PF 3 - base-40%
WS PF 3 - base-50%
Ground
100
80
45
46
49
53
44
41
42
39
38
3...
36
34
33
31
32
30
29
28
27
26
25
24
21
22
14
15
16
17
18
19
1...
1...
11
10
9
60
7
Elevation (ft)
WS PF 3 - base-5%
40
0
100000
200000
300000
400000
Alabama River
Legend
170
WS PF 3 - base+50%
WS PF 3 - base+40%
WS PF 3 - base+30%
WS PF 3 - base+20%
WS PF 3 - base+10%
WS PF 3 - base+5%
160
WS PF 3 - base
Elevation (ft)
WS PF 3 - base-5%
WS PF 3 - base-10%
WS PF 3 - base-20%
WS PF 3 - base-30%
WS PF 3 - base-40%
150
WS PF 3 - base-50%
Ground
140
130
220000
230000
240000
250000
260000
270000
% change in
n Value
-50
-40
-30
-20
-10
-5
5
10
20
30
40
50
change in depth
Max
Min
-11.57
-9.77
-8.19
-6.75
-5.56
-4.53
-3.31
-2.74
-1.49
-1.27
-0.75
-0.63
0.69
0.56
1.55
0.69
2.85
0.69
3.76
1.51
4.54
1.51
4.94
1.51
Sensitivity of Manning's values for Tennessee River
Location:
Madison County, AL (River mile 316.5 to 342.4)
Channel n values:
Overbank n values:
Flow Range:
Average Slope:
0.02 – 0.03
0.02 – 0.15
305,000 cfs - 405,000 cfs
0.00013 (0.013%)
Sensitivity of Manning's values for Tennessee River (Contd)
Tennessee River
600
Legend
WS PF 3 - base+50%
WS PF 3 - base+40%
WS PF 3 - base+30%
580
WS PF 3 - base+20%
WS PF 3 - base+10%
WS PF 3 - base+5%
560
WS PF 3 - base-10%
WS PF 3 - base-20%
WS PF 3 - base-30%
WS PF 3 - base-40%
540
WS PF 3 - base-50%
Ground
520
43
42
41
40
39
38
37
29
35
28
27
26
25
24
23
22
21
20
19
18
17
16
15
14
13
12
11
10
9
8
7
6
5
4
3
500
2
Elevation (ft)
WS PF 3 - bsae
WS PF 3 - base-5%
480
0
100000
200000
300000
400000
Tennessee River
Legend
WS PF 3 - base+50%
WS PF 3 - base+40%
WS PF 3 - base+30%
WS PF 3 - base+20%
580
WS PF 3 - base+10%
WS PF 3 - base+5%
WS PF 3 - bsae
WS PF 3 - base-10%
WS PF 3 - base-20%
560
WS PF 3 - base-30%
WS PF 3 - base-40%
WS PF 3 - base-50%
Ground
540
520
42
Elevation (ft)
WS PF 3 - base-5%
365000
370000
375000
380000
% change in
N Value
-50
-40
-30
-20
-10
-5
5
10
20
30
40
50
change in depth
Max
Min
-10.42
-1.21
-7.83
-1.21
-5.54
-1.21
-3.49
-0.60
-1.66
-0.25
-0.83
-0.12
0.76
0.12
1.52
0.25
2.90
0.51
4.15
0.77
5.30
1.03
6.35
1.30
Sensitivity of Manning's values for Tombigbee River
Location:
Channel n values:
Overbank n values:
Flow Range:
Average Slope:
Washington County, AL
0.035
0.08
367,000 cfs
0.00001
Sensitivity of Manning's values for Tombigbee River (Contd)
Tombigbee River
110
Legend
WS P100yr - base+50%
100
90
WS P100yr - base+5%
WS P100yr - base
WS P100yr - base-10%
80
70
Ground
60
50
26...
24...
21...
19...
40
1...
Elevation (ft)
WS P100yr - base-5%
30
0
20000
40000
60000
80000
100000
120000
140000
160000
Tombigbee River
Legend
106
104
WS P100yr - base+5%
WS P100yr - base
Elevation (ft)
WS P100yr - base-5%
102
100
Ground
98
96
94
92
118000
120000
122000
124000
126000
% change
in N
-50
-40
-30
-20
-10
-5
5
10
20
30
40
50
change in depth
Max
Min
-3.31
-3.01
-2.29
-2.06
-1.46
-1.34
-0.87
-0.79
-0.39
-0.36
-0.19
-0.17
0.16
0.15
0.33
0.30
0.60
0.54
0.84
0.76
1.04
0.94
1.22
1.10
Summary and Conclusions
 The results of sensitivity analyses for Manning’s n for various streams
sizes, with different discharge rates have been presented.
 The roughness coefficient, Manning’s n, is highly sensitive for larger
stream with discharge rates in the range of 200, 000 CFS+.
 The roughness coefficient, Manning’s n, is less sensitive in the streams
with lower discharge rates.
 The roughness coefficient is less sensitive when increasing the n values,
and is more sensitive when decreasing the n values in computing the
water surface elevations.
Summary and Conclusions
Summary and Conclusions (contd.)
 Appropriate selection of Manning's n is very crucial for larger streams,
with flow > 200,000+ cfs, as a small change in n values can affect the
computed water surface elevations and affect the reasonableness/
accuracy of computed water surface elevations.
 The guidelines need to be followed for the proper selection of
Manning’s n.
Guidelines for Selecting Manning’s n
 Selecting Manning’s n value actually means to estimate the resistance to
flow, which is really a matter of intangibles.
 Although Tables in the textbook may provide a single value for channel;
however, the value of n is variable, and depends on a number of factors.
 Proper determination of the roughness coefficient requires the
understanding the factors that affect the values of n.
Guidelines for Selecting Manning’s n
 Factors affecting Manning’s n
(a) Surface Roughness
(b) vegetation
(c) Channel irregularities
(d) Channel Alignment
(e) silting and scouring
(f) obstructions
(g) stage and discharge
Guidelines for Determining Roughness Coefficient
Guidelines for Determining Roughness Coefficient (Contd)
2.
Consulting with several
available tables:
Tabulation of roughness
coefficients by Scobey
(1933), Chow (1959), Yen
(1991)
3. Comparison of photographs
photographs of channels with determined
Manning’s n values
0.036
Chow (1959), Barnes (1967), Hicks and Mason
(1998), and others
0.073
0.043
4.
Field Measurement
With a discharge measurement, known crosssectional area and slope, n may be backcalculated
5.
Calibration
Manning’s n values should be calibrated
whenever observed water surface profile
information (gaged data, or high water marks)
is available.
Sensitivity of Manning's values for Mobile River
Location
Channel n values:
Overbank n values
Flow Range
Average Slope
: Mobile County, AL
0.035
: 0.1
: 443,552 cfs
: 0.00006
Sensitivity of Manning's values for Mobile River (Contd)
Mobile River
20
Legend
WS PF 3 - base+50%
WS PF 3 - base+40%
WS PF 3 - base+30%
10
WS PF 3 - base+20%
WS PF 3 - base+10%
WS PF 3 - base+5%
0
WS PF 3 - base
WS PF 3 - base-10%
WS PF 3 - base-20%
-10
WS PF 3 - base-30%
WS PF 3 - base-40%
WS PF 3 - base-50%
Ground
-20
-30
52.7
52
51.2
50.4
48....
48.4
48.2
48.0
47.6
-40
46.0
Elevation (ft)
WS PF 3 - base-5%
-50
0
10000
20000
30000
40000
Mobile River
Legend
WS PF 3 - base+50
WS PF 3 - base+40
20
WS PF 3 - base+30
WS PF 3 - base+20
WS PF 3 - base+10
WS PF 3 - base+5%
WS PF 3 - base
Elevation (ft)
WS PF 3 - base-5%
WS PF 3 - base-10
15
WS PF 3 - base-20
WS PF 3 - base-30
WS PF 3 - base-40
WS PF 3 - base-50
Ground
10
5
34000
35000
36000
37000
38000
% change
in N
-50
-40
-30
-20
-10
-5
5
10
20
30
40
50
change in depth
Max
Min
-3.35
-3.22
-2.55
-2.44
-1.82
-1.73
-1.16
-1.09
-0.56
-0.53
-0.29
-0.27
0.26
0.24
0.53
0.50
1.04
0.98
1.53
1.45
2.00
1.90
2.45
2.33

Sensitivity of Hydraulic Models to Manning s n in Computing WSEL

Transcription

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