The overall lesson to take away from working the examples in Chapters 8 and 9 is the general
approach to the problem.
(1) Threshold channel problem, NEH-654 Chapter 8 Example. This is basically a critical
discharge problem – just like we have been doing up til now. The solution in the handbook
combines momentum, continuity, Manning/Limerinos, and the definition of the critical Shields
Number to solve for critical discharge. The iteration involves reducing the slope until  = c at
the design discharge. The valley slope 0.007 only enters the problem as a constraint. Channel
slope can be less than the valley slope (by meandering), but not greater.
A number of key questions can be raised in doing such an analysis.
1. Grain size. If the intent is that the sediment should not move at the design flow, is the median
size D50 appropriate? How about a smaller size? In general, D50 (of the gravel) provides a
reasonable choice for estimating the critical discharge, but there is scatter in such a relation
(Wilcock 1993) and a risk-based approach might argue for choosing a finer size than D50.
2. Roughness. Limerinos basically accounts for the grain roughness. What other factors might
contribute to roughness in the channel as initially built and as it matures? Also, bank roughness
will be important if the channel is relatively narrow, so an estimate of composite roughness may
be needed.
3. Critical Shields Number. A choice of c = 0.047 is OK for the bulk sediment size
distribution. If it is a surface grain size, a smaller c will be appropriate. Whether using surface
or subsurface grain size, I would use the two-fraction plots for reference Shields Number g in
Wilcock and Kenworthy (attached below).
4. UNCERTAINTY. One can make reasonable choices for grain size, roughness and c, which
will lead to different estimates of the critical discharge. This uncertainty is real – the only
rational approach is to somehow incorporate this uncertainty in the design. For this problem, one
approach would be to program a Monte-Carlo analysis that determined the uncertainty in the
calculated slope at the design discharge. That is, one could recalculate the problem 1000 times
using grain size, roughness and c values drawn from distributions that reflected the uncertainty
in those values. An alternative would be to take the design slope as determined in the exercise
and then calculate the uncertainty in the discharge determined using that slope. This is what
MonteCarloTransport is written to solve. Suppose, for example, that the 90% range of calculated
Qc is about a factor of two. Hence, Qc would be 400 cfs with 90% chance that the actual Qc is
between 283 cfs and 566 cfs. How would you use this in the design? You would take the annual
flood series and calculate the joint probability of flood return interval and Qc, which would give
you the probability of sediment transport. More on this later.
The spreadsheets I developed for the problem are
LimerinosTrap.xls: solves the problem exactly as specified in NEH-654, including calculation
of Manning’s n using the Limerinos relation. Note that the solution in NEH-654 uses =ghS
rather than =gRS, probably reasonable, although using grain stress is probably even more
reasonable.
GrainStressTrap.xls: solves the problem using a grain stress, requiring specification of the total
roughness n. The Manning-Strickler nD is calculated and used to find the grain stress ’, which
is used instead of the total stress. You would use this spreadsheet if you chose an alternative
method for specifying total roughness (which could include the effect of bank roughness).
(2) Alluvial channel problem, NEH-654 Chapter 9 Example 2.
The key to this problem is to first determine a transport rate and grain size for the supply reach at
the design discharge, and to then calculate the design chart for the design discharge and its
associated sediment supply.
I used iSURF to do these calculations. One could use something else.
(1) To get the sediment supply, I first need a value of bed stress (actually, u* = (’/)^(1/2)) and
bed grain size. To get grain stress, I calculated the flow depth in the supply channel using a
composite roughness. See workbook “TrapHydraulics.xls”. That may be a bit of overkill – but
it provides the necessary info.
(2) With u*, I go to worksheet SBTM, which calculates transport rate and transport grain size for
a specified u* and bed grain size. The grain size info provided is incomplete, but I made up a
bed surface grain-size distribution that matches the info available.
(3) With the result from SBTM, I now have a sediment supply to accompany the design
discharge. These are entered into the STAB input worksheet of iSURF, along with the side slope
angle and roughness.
The STAB output is interesting. The calculated slope is remarkably close to the Brownlie
solution given in NEH-654. Note also that the sediment supply rates are large, we are at, or up
on to the supply-sensitive part of the slope curve!
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