Design of Open Channels

1. Design of Open Channels Riprap

2. Riprap • Riprap- large stones, cobbles or boulders used to stabilize areas subject to erosion. • Protect soil from erosive forces • Improve Stability • In channels where vegetation is not suitable, riprap is often used for stabilization. • Used on both channel sides and bottoms.

3. Riprap • Rocks used for riprap should be resistant to weathering processes. • Rough angular rocks are preferred. • Want to place rock in such a way that segregation by size is avoided. • Surfaces on which riprap is places should be well compacted and stable.

4. Riprap • Design: find a rock size large enough that the force attempting to overturn individual rocks is less than the gravitational force holding the rocks in place. • Riprap is graded so design procedure must include a definition of an appropriate gradation of sizes.

5. Riprap • Proper gradation will leave an armored channel that is stable when smaller particles have eroded. • Must also select an appropriate underlying filter so that water flowing beneath the riprap will not erode the base material. • Minimum layer thickness should be 1.5 times stone diameter, but no less than 6 in.

6. Riprap • Channel sections with riprap should be carefully monitored to ensure stability. • Any damage should be repaired immediately to prevent much more extensive damage.

7. Riprap Design Procedures • Three procedures presented: • The Federal Highway Administration (FHA) procedure. • The Soil Conservation Service (SCS) procedure. • The Colorado State University (CSU) procedure.

8. FHA Procedure • Uses a maximum stable depth of flow given by dmax = mSn, where n = -1.0 and • D50 is the riprap diameter in feet such that 50% of the stones have a diameter smaller than D50. Thus:

9. FHA Procedure • The velocity of flow is given by the Manning-Stickler equation where:

10. FHA Procedure • Channel Design: • Assume a D50 • Compute dmax and v • Determine the appropriate channel dimensions. • Calculations made easier by assuming R = dmax. • Check capacity.

11. SCS Procedure • Based on a chart that can be approximated by: • Simons and Senturk (1977, 1992) recommend that D75 be about 1.5D50 so that:

12. SCS Procedure The SCS also presented a chart based on the Isbash curves which can be approximated by This relationship assumed that D100=2D50

13. SCS Procedure • This equation does not take into account S. • If the expression is substituted into the relationship is:

14. CSU Procedure • Incorporates a safety factor (SF). • If SF=1 then the forces that are holding the riprap in place are just balanced by those tending to move the particles. • An SF 1.5 is preferred to add stability for particles that have diameters < D50. • Both the FHA and SCS procedures result in SF < 1.0 using the CSU criteria. • This indicates potential failure problems.

15. Q FL M4 Fd M3 Channel Bed WsinQ Discrete Particle M2 PR W WcosQ M1 CSU Procedure Based on considering the forces on a particle on a channel bed sloping at an angle, Q, with the moment arms about the point of rotation, PR.

16. CSU Procedure The SF for a given flow situation is the ratio of the resisting moments to the overturning moments. The key to a stable design is to make the SF>1.

17. CSU Procedure • Must manipulate the SF equation so that it has parameters that are readily measurable or can be determined from tables and graphs. • One measurable quantity is the angle of repose, f, of a given riprap, given in Figure 4.17. • For very angular riprap with diameters ≥ 1.5 in. f≈42º.

18. CSU Procedure • When there is no flow FL=Fd=0. • If the angle of the channel bottom, Q, is increased until the particles just begin to move, the particles are at their angle of repose, f, and SF=1, hence

19. Substituting into our original SF equation: or Where hb is a stability factor given by: CSU Procedure

20. or CSU Procedure • The nature of hb can be determined by looking at a plane horizontal bed where q=0 and all weight is acting in the verticle direction.

21. and CSU Procedure • For SFplane=1, the bed is at a point of incipient motion, and the tractive force t is equal to the critical tractive force tc. • Under conditions other than incipient motion on a plane bed we can assume that:

22. For fully turbulent flow: If t = gdS then we can use these equations to design channels if the flow velocity is given by CSU Procedure Where SG is the specific gravity of the particles and D is the representative particle diameter, typically the average diameter (D50). Note: These equations are for channel bottoms only. Banks are considered next.

23. Channel Bank Stability

24. Channel Bank Stability • Forces are different than on channel bed because drag forces are not aligned with the downslope gravitational forces. • The SF for a channel bank is given by:

25. Channel Bank Stability Where tmax is the maximum shear on the channel bank To derive these equations it was assumed that FL/Fd = ½.

26. Selecting Proper Gradation • It is important that the riprap have a gradation such that the voids between larger particles are filled with smaller particles. • This reduces flow beneath the riprap and the formation of open pockets. • Figure 4.19 shows the proposed size distribution of riprap (Simons and Senturk, 1977, 1992).

27. Selecting an Underlying Filter • Filter blanket-underlying layer of gravel or other granular material. • A properly designed filter blanket is needed beneath the riprap when the particle size of the riprap is much larger than the base material. • Criteria for sizing filters were developed for drain pipes to prevent piping of soil into the drain.

28. (1) also (2) also (3) also Filter Criteria

29. Underlying Filter Criteria • Filter thickness should be approximately ½ the thickness of the riprap, but in no case less than 6” to 9”. • Plastic filter cloth is being used in some cases rather than granular filter material.

30. Flow in Channel Bends • Because of bend curvature, the peak velocity tends to be outside of the center line. • The result is steeper velocity gradients and higher shear values on the outside banks than occur in straight channels. • The extra shear must be considered when sizing riprap, vegetation and temporary channel linings.

31. Flow in Channel Bends • Common Procedures: • For riprap lined channels, increase the riprap size in the channel bend. • For vegetated channels, line sharp bends with riprap. • Standard practice to protect the outside bank of the entire bend.

32. Method to Determine Shear in Channel Bends • Determine the velocity in a straight channel. • Determine the radius of curvature of the outside bank, Rd. • Calculate v2/Rd. • Determine the correction factor, k3 from Figure 4.21. • Calculate the corrected bank shear from • Use this shear in the stability parameters h and h’ and determine the required riprap size using the procedures discussed for channel banks. Note: These procedures have limited verification.

33. Channel Linings Final Comments • The flow range over which differing channel linings offer protection depends on channel shape and slope. • Fig. 4.22 is is a reasonable guide to the type of channel lining required for varying flow rates and slopes. • Ranges will change based on side slopes and erodibility of underlying material.