roadside ditch design

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CEE453 Urban Hydrology and Hydraulics

April 24, 2012 (Tue)

Unit V: Design of Hydraulic StructuresLecture 26

Roadside Ditch DesignPart I

Roadside Ditch Design

• Primary function

to collect runoff from the highway right of way and tributary areas adjacent to the right of way, and to transport this accumulated water to an acceptable outlet point

• Secondary function

to drain the base of the roadway to prevent saturation and loss of support for the pavement

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http://safety.fhwa.dot.gov/local_rural/training/fhwasa09024/


• Non‐traversable drainage ditches can be safety hazard.

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• Standard ditch

‐ Trapezoidal shape with a defined bottom width and sideslopes

‐

‐ 2 1‐ 2

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bz

d

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• Hydrology

‐ Runoff is from primarily from overland flow → Rational method (peak runoff)

‐ Significant flow contribution from one or more defined watercourses → Other methods (regression equation from USGS, SCS method, HEC)

• Hydraulic

‐ Uniform flow assumption: Manning’s equation and Continuity equation

1.49 / /

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• General Steps

1. Determine the standard or typical ditch cross sections.2. Establish a ditch plan, which shows the proposed ditch

flow patterns.3. Determine the gradients to be used on all proposed

ditches.4. Investigate the capacity of the typical ditch with the

proposed gradients and enlarge any ditch found to be inadequate.

5. Determine the limits and degree of protection necessary to prevent erosion in the ditch system.

6. Determine any special measures necessary to prevent adverse effects at and downstream from ditch outlets points.

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FREEWAY AND EXPRESSWAY NOMENCLATURE Figure 34‐1.A

(BDE)


1. Determine the standard or typical ditch cross sections.‐ Side slopes should not exceed the angle of the repose. Generally it

should be 3:1 or flatter without consideration of the stability of the side slopes. 4:1 or flatter for the safety.

‐ Slopes steeper than 2:1 will usually require special erosion control measures. Shoulder widths: 8 to 10 ft outside (more details in the tables in Chapter 44 through 50, BDE)

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Sample Ditch PlanFigure 9‐201(IDOT Drainage Manual)


2. Establish a ditch plan, which shows the proposed ditch flow patterns.

‐ To determine based on topography, drainage divides, flow directions, etc.

‐ Otherwise some arbitrary value from 100 to 200 ft can be used.

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3. Determine the gradients to be used on all proposed ditches.

‐ To minimize ponding and silt accumulation, a grade of 0.3 % should be provided. Between 0.4 and 0.6 % is desirable.

‐ Channel gradients greater than 2% (up to 10%) may require the use of flexible linings.

‐ There’s no upper limit on ditch grade but steeper grade would cause greater expense for erosion control (riprap, wire‐enclosed riprap).

‐ Frequent breaks in the grade usually reduce earthwork and ditch lining cost. The desirable distance between breaks in rugged terrain is 100 ft and several thousands ft for flat land.

Rebecca Schneider

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4. Investigate the capacity of the typical ditch with the proposed gradients and enlarge any ditch found to be inadequate.

1) Compute the design discharge at the downstream end of the section of ditch. (50 year design storm)

2) Select a trial size for the ditch at this location (the standard ditch is normally used initially), and assign a roughness coefficient for the finished surface of the ditch. Use Table 9‐403 (IDOT Drainage Manual) for n values.

3) Determine the maximum allowable depth of flow in the ditch. The discharge should be confined within the ditch and provide 1’ freeboard below the shoulder of the highway.

4) Check the capacity of this ditch. 5) If the initial ditch is too small, select a larger size or increase the

capacity by other means and return to step 2).

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4. Example problem – ditch capacity

Given:An unlined trapezoidal ditch with a 2' bottom width, 2:1 sides and a gradient of 0.5percent (0.005 ft/ft) is proposed to carry a discharge of 95 ft3/sec. The maximumallowable depth of flow has been set at 2.5 ft.

Find:1. The maximum capacity of this ditch.2. The bottom width which should be used to meet the depth of flow limitation.

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22’

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5. Determine the limits and degree of protection necessary to prevent erosion in the ditch system.

• 10 year as design storm frequency is used for ditch lining.(More details in 9‐5 of IDOT Drainage Manual)

http://www.interstatelandscaping.com/Page_4.html

6. Determine any special measures necessary to prevent adverse effects at and downstream from ditch outlets points.

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Reference

• IDOT Drainage Manual, Chapter 9. Roadside Ditches.

• Mays, L.W., Hydraulic Design Handbook, Chapter 13, Hydraulic Design of Drainage for Highways.

• Illinois Bureau of Design and Environmental Manual (BDE), Chapter 34. Cross Section Elements.

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CEE453 Urban Hydrology and Hydraulics

April 24, 2012 (Tue)

Unit V: Design of Hydraulic StructuresLecture 26

Roadside Ditch DesignPart II

4/24/2012

8

http://safety.fhwa.dot.gov/local_rural/training/fhwasa09024/

Roadside Ditch Design – Scour Design

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© 2010 Arthur R. Schmidt All Rights Reserved

Maximum Velocity Method

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Procedure

1. Estimate n

2. Determine Vmax

3. Calculate R from Mannings to give V = Vmax

4. Guess b, calculate y, A

5. Calculate Q = VA

6. If Q ≠ Qdesign back to 4

7. Estimate required freeboard

8. Summarize results with dimensioned sketch

© 2010 Arthur R. Schmidt All Rights Reserved 17

Example—Maximum velocity

b

1

3

Q = 30 CFS, flow containing solids, ordinary firm loam soil, slope So = 0.005

From table, n = 0.020, Vmax = 3.5 ft/sec

Solve for b and y that gives V=Vmax and Q = 30b =11.8, y = 0.63, giving A = 8.57


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Force on bed = ALtan() or, for small , ALSo

Force per unit bed area = o = ALSo / PL = RSo

For wide channel (R ≈ y), o = ySo

Maximum Tractive Force


Tractive force—bottom


ySo

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≈0.76 ySo

Tractive force on sides


Resisting Force

Tractive force = AeL

where Ae is the exposed area and L is the unit tractive force on a level surface.

Resisting force = Ws tan()

where Ws is the submerged weight and is the angle of repose.

AeL = Ws tan()

or

L = (Ws / Ae )tan()

Bottom


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Resisting ForceSides

Tractive Force Ratio:

Ws cos tan Ws sin 2 Ae s 2

s Ws

Ae

cos tan 1tan2 tan2

K ss

L

cos 1tan2 tan2 1

sin2 sin2


Critical shear:

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Procedure

1. Estimate n, angle of repose ()2. Estimate channel sinuosity and correction factor

3. Assume bottom width, b

4. Assume depth y

5. Determine R,

6. Determine =RS7. If > max go to 4

8. Calculate Q from Mannings

9. If Q ≠ Qdesign back to 3

10. Calculate tractive force on sides S11. Calculate maximum permissible tractive force on sides smax

12. If S > Smax go to 3




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Example—Maximum Shear

b

1

3

Q = 30 CFS, flow containing solids, ordinary firm loam soil, slope So = 0.005 (assume angle of repose = 25o)

From table, n = 0.020, max = 0.15 lb/ft2

Solve for b and y that gives = max and Q = 30b =16.01, y = 0.53, giving A = 9.31, V = 3.22b/y = 30 so Level ≈ ySo; sides ≈ 0.76 ySo = 0.11 lb/ft2Permissible side shear = 0.667; max = 0.10 lb/ft

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Side shear > permissible—try new solution


Example—Maximum Shear

b

1

3

Q = 30 CFS, flow containing solids, ordinary firm loam soil, slope So = 0.005 (assume angle of repose = 25o)

From table, n = 0.020, max = 0.15 lb/ft2; max side shear = 0.10 lb/ft2

Solve for b and y b =21.22, y = 0.45, giving A = 10.15 ft2, V = 2.95 ft/secb/y = 47 so Level ≈ ySo = 0.13 lb/ft2; sides ≈ 0.76 ySo = 0.10 lb/ft2Permissible side shear = 0.667; max = 0.10 lb/ft

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This is good solution


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Vegetated Channels

Resistance n is a function of vegetation type, depth, and velocityUse maximum velocity approach


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Procedure

1. Assume n, determine corresponding VR

2. Select permissible velocity corresponding to slope, soil, vegetation

3. Calculate R from 1 & 2

4. Using Manning eqn. and n compute

5. Repeat steps 1‐4 until values for VR from steps 1 & 4 agree

6. Determine A from design flow and permissible velocity,

7. Determine channel proportions for calculated values of A & R

8. Assume depth and compute A & R

9. Calculate V = Q/A

10. Compute VR

11. Use results of 10 to compute n from figure

12. Use n from 11 and R from 8 and Manning’s eqation to compute V

13. Compare velocities from 9 and 12 and repeat steps 8‐12 until approx. equal




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Example—Vegetated

b

1

3


From Maximum velocity

Solve for b and y that gives V=Vmax

and Q = 30b =74, y = 0.12, giving A = 8.57, V = 3.5 ft/sec

From Maximum shear

max = 0.15 lb/ft2;

max side shear = 0.10 lb/ft2

b =272, y = 0.05, giving A = 14.4, V = 2.09 ft/sec = 0.13, side = 0.10


Example—Vegetated

b

1

3


Use Bermuda grass sometimes mowed to 2.5”, sometimes unmowed


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Example—Vegetated

b

1

3



Maximum velocity = 6.0 ft/secGives A = Q/Vmax = 5 ft

2

Start with mowed—Class D retardance; Guess n=0.05

R = 1.01 VR = 6.06, n = 0.033


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Example—Vegetated

b

1

3



Maximum velocity = 6.0 ft/secGives A = Q/Vmax = 5 ft

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Start with mowed—Class D retardance; Guess n=0.05

R = 1.01 VR = 6.06, n = 0.033R = 0.54, VR = 3.25, n = 0.038R = 0.67, VR = 4.02, n = 0.036R = 0.62, VR = 3.70, n = 0.037R = 0.64, VR = 3.86, n = 0.037


Example—Vegetated

b

1

z=3


Use Bermuda grass mowed to 2.5, Vmax = 6.0 ft/sec

A = Q/Vmax = 5 ft2 ; R = 0.64

Solving gives b = 6.46 ft, y = 0.22 ftCheck: this gives Q = 30 ft3/sec, V = 6 ft/sec


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Example—Vegetated

b

1

3


Now solve for Bermuda grass unmowed, retardance class BBecause unmowed, depth will be greater (more resistance)Use bottom width from mowed (b=6.46 ft)Guess depth, solve for A, R, V = Q / A, VR, & n = f(VR)

y = 0.20, A =4.26, V = 7.04, R = 0.55, VR = 3.88, n = 0.068, Q = 12.6 CFSy = 0.30, A =8.61, V = 3.48, R = 1.03, VR = 3.59, n = 0.070, Q = 37.2 CFSy = 0.28, A =7.50, V = 4.00, R = 0.91, VR = 3.66, n = 0.070, Q = 30.0 CFS


Example—Vegetated

b

1

3


When grass is mowed, will flow at y = 0.22 ft, V = 6.0 ft/secWhen unmowed, will flow at y = 0.28 ft, V = 4.0 ft/secAdd 1.0 ft freeboard, so need grass‐lined trapezoidal channel1.3 ft deep, bottom width = 6.5 ft, top width = 14.3 ft


roadside ditch design

Documents

assumeangleofrepose25o

vmax 5ft2startwithmowedclassdretardance

tan

idotdrainagemanual

tmax 0

tan2o

0ftsecgivesa

sometimesunmowedmaximumvelocity6