Tuesday, December 24, 2013

Lateral Structure Coefficients

Written by Chris Goodell, P.E., D.WRE  |  WEST Consultants
Copyright © RASModel.com.  2013.  All rights reserved.
Lateral structures can be used in HEC-RAS to transfer flow from a river/reach to a storage area, or to another river/reach.  With the coming release of HEC-RAS with 2D capabilities (estimated beta release January/February 2014), you’ll be able to hook a river/reach to a 2-D area using a lateral structure. 
Although its primary function in HEC-RAS is to transfer flow out of one river/reach into another component (river/reach, storage area, 2D area), a lateral structure can physically represent a wide range of geometric features, including a levee, a flow diversion structure, a morning glory spillway, or even a natural ground or bathymetric profile.  Including a lateral structure in your model to represent a levee is important if the levee is ever overtopped or breached during the simulation.  Flow diversion structures can have multiple outlet features, including culverts, gates, and spillways.  These features are all available in the lateral structure editor in HEC-RAS. 
Another common use of lateral structures is to simulate flow transfer from the river to a tributary during a flood event.  This is especially convenient if you don’t want to model the tributary as an individual reach, but still want to account for it’s available storage, for a proper accounting of flood wave attenuation in the main stem river/reach.  As an example, the following figure shows a storage area representing a tributary to the main stem river.  This storage area is connected to the main stem by a lateral structure (highlighted in red). 
image
Because a lateral structure can represent a variety of different flow transferring structures (or non-structures), the hydraulics in and around the lateral structure can be quite different, depending upon the case.  Every lateral structure in HEC-RAS requires a lateral weir coefficient, and different hydraulics mean different lateral weir coefficients.  Any hydraulics textbook will have a multitude of weir coefficients for “inline” conditions, but it’s rare to find something similar for lateral flows, or diversion flows.  But it is generally agreed that lateral structure weir coefficients should be much lower than a similar inline configuration.  For example, an inline, hydraulically efficient broad-crested weir might have a weir coefficient around 3.0 (US units) or 1.7 (SI Units).  Turn that structure sideways (a lateral structure), and it will have a coefficient closer to 2.0 (US Units) or 1.1 (SI Units).  The difference is due to the energy/momentum loss associated with turning flow lines from their downstream orientation to a lateral direction out of the river/reach.    Unfortunately, there has simply not been a lot of research done on quantifying this energy/momentum loss and what that does to lateral weir coefficients.
The research that is available could be useful and might be worth checking out.  Hagar’s equation is one reference and is actually built into the HEC-RAS lateral structure editor, under Lateral Weir Embankment…Weir Computations.  It will compute an equivalent lateral weir coefficient based on an inline value (the Default Weir Coefficient) and some physical and hydraulic properties of the weir and  the adjacent river/reach. 
image
You can read more about Hagar’s equation in the HEC-RAS Hydraulic Reference Manual on page 8-17. 
Useful references for lateral structure weir coefficients (including Hager’s):
  • Hager, W.H. (1987). “Lateral Outflow over Side Weirs.” Journal of Hydraulic Engineering, ASCE, 113(4).
  • Borghei, S.M.; Malili, M.R.; Ghodsian, M. (1999). “Discharge Coefficient for Sharp-Crested Side Weir in Subcritical Flow.” Journal of Hydraulic Engineering, ASCE, October, 1999.
  • Ranga Raju, K.G.; Prasad, B.; Gupta, S.K. (1979). “Side Weir in Rectangular Channel.” Journal of Hydraulic Engineering, ASCE, 105(5).
  • Subramanya, K.; Awasthy, S.C. (1972). “Spatially Varied Flow over Side Weirs.” J. Hydr. Div., ASCE, 98(1).
  • Singh, R.; Manivannan, D.; Satyanarayana T. (1994). “Discharge Coefficient of Rectangular Side Weirs.” Journal of Irrigation and Drainage Engineering, ASCE, 120(4).
However, none of these references discuss lateral weir coefficients for lateral flow transfers over natural ground, or surface flow (i.e. non-elevation overbank terrain).  HEC has a reference table for lateral structure coefficients that I like to use-it’s also included in the new “Combined 1D and 2D Modeling with HEC-RAS” document that was released in August 2013, in anticipation of the new 2D feature in HEC-RAS expected to be released as a beta version in the January/February 2014 time frame.   Note how low the suggested range of coefficients is for “non-elevated overbank terrain.”  Because they are not dimensionless, be aware that weir coefficients in SI Units are different from US units by a factor of the square root of the ratio of the SI gravitational constant to the US gravitational constant,
image

What is being modeled with the Lateral Structure Description Range of Weir Coefficients
Levee/Roadway – 3 ft (1 meter) or higher above natural ground Broad crested weir shape, flow over Levee/road acts like weir flow US Units: 1.5 to 2.2 (2.0 default)
SI Units:  0.83 to 1.2 (1.1 default)
Levee/Roadway – 1 to 3 ft (0.3 to 1.0 meter) elevated above ground Broad crested weir shape, flow over levee/road acts like weir flow, but becomes submerged easily. US Units:  1.0 to 2.0
SI Units:  0.55 to 1.1
Natural high ground barrier – 1 to 3 ft (0.3 to 1.0 meter) high. Does not really act like a weir, but must flow over high ground to get into 2D (or storage) area. US Units: 0.5 to 1.0
SI Units: 0.28 to 0.55
Non-elevated overbank terrain. Lateral Structure not elevated above ground Overland flow escaping the main river. US Units: 0.1 to 0.5
SI Units:  0.06 to 0.28

*Hydrologic Engineering Center, August 2013.  “Combined 1D and 2D Modeling with HEC-RAS”

Although this table is presented within the context of 1-D to 2-D flow transfers, these values will work with river/reach to storage area or river/reach to river/reach flow transfers as well.  As noted in the referenced document (HEC 2013), “In general, Lateral Structure weir coefficients should be lower than typical values used for inline weirs.  Additionally, when a lateral structure (i.e. weir equation) is being used to transfer flow from the river (1D region) to the floodplain (2D Flow Area), and then [sic] the weir coefficients that are used need to be very low, or too much flow will be transferred.”  Also, “The number 1 problem people have been having with interfacing 1D river reaches with 2D areas, is user’s [sic] have been using way to [sic] high of weir coefficients for the situation being modeled.  If the lateral structure is really just an overland flow interface between the 1D river and the 2D floodplain, then weir coefficients in the range of 0.1 to 0.5 must be used to get the right flow transfer and keep the model stable.” 

The HEC 2013 document ("Combined 1D and 2D Modeling with HEC-RAS") with the Table of lateral weir coefficients can be downloaded from my Google Drive site here:  https://drive.google.com/file/d/0B_s8OLJOgOi0Nm5sdHFhSzFUYkk/edit?usp=sharing.  The lateral weir coefficient table is on page 35.

19 comments:

  1. Chris - excellent stuff, thank you.

    I'm unable to find the "Combined 1D and 2D Modeling with HEC-RAS" document - can you point me in the right direction for that?

    Thanks!

    Andrew

    ReplyDelete
    Replies
    1. I posted it on my dropbox site here:

      https://www.dropbox.com/s/y32u1z4ldol761q/Combined%201D%20and%202D%20Modeling%20with%20HEC-RAS.pdf

      Have Fun-
      @RASModel

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  2. Hi,

    Thank you so much for the blog, very helpful. I looked through the "Combined 1D and 2D Modeling with HEC-RAS" and couldn't find the weir coefficient table that you mention above. Can you point me in the right direction?

    Thank you

    ReplyDelete
    Replies
    1. Try this updated version on page 35.
      https://www.dropbox.com/s/y32u1z4ldol761q/Combined%201D%20and%202D%20Modeling%20with%20HEC-RAS.pdf

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  3. My apologies. I had an older version of the document up on my dropbox site. I've replaced it with the new version that has the table. Please download the new version of the document from the link below. The table is on page 35.

    https://www.dropbox.com/s/y32u1z4ldol761q/Combined%201D%20and%202D%20Modeling%20with%20HEC-RAS.pdf

    @RASModel

    ReplyDelete
  4. Hi Chris

    I'm unable too to find the "Combined 1D and 2D Modeling with HEC-RAS" document - everything you have uploaded has been removed. Is it possible to upload it again? or point me a site I can download it from?

    Thanks in advance!

    Zacharoula

    ReplyDelete
    Replies
    1. Please try this link:
      https://drive.google.com/file/d/0B_s8OLJOgOi0Nm5sdHFhSzFUYkk/edit?usp=sharing

      Delete
  5. I have a detention basin that drains to a stream through two RCBs immediately upstream of a culvert crossing along the stream. I am modeling in Unsteady RAS using a lateral structure with culverts. The lateral structure is connecting the stream to the storage area since you cannot do so directly the other way around. This means that the upstream invert is lower than the downstream invert in the model (since the upstream invert is actually the outlet elevation of the culvert). Based on looking at the peaks in the channel and the detention basin, I would expect outlet control conditions (very little head differential between the detention basin elevation and channel at the peak time) for the culvert at the peak time. However, it does not appear to be calculating it that way. I did not model the outflow from the basin as a reach since it comes into the receiving stream near a culvert crossing which creates stability issues. Any ideas?

    Thanks,

    Rich

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    Replies
    1. Rich, it's hard to say without seeing your model. It could be that the stability issues are creating inlet conditions where you'd expect outlet. Perhaps fixing the stability problems might show outlet computations. You can send me your model if you are running out of ideas and I'll see if a quick look might reveal an easy fix.

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  6. I’m modeling a slanted valley where the proposed river reach is at a higher elevation than an adjacent wetland/tributary system. I placed levees on the left bank to prevent filling of the wetland until overflow of the main channel. When the channel overtops the levees I’ve had problems with the model defaulting to critical depth when the computed WSE is close to the elevation of the levee. It not only defaults for return period storms that are close in elevation to the levee, but for all proceeding storm events (5,10,50, and 100 year storms). I’ve tried adding cross sections and running it in a mixed flow regime but nothing helps. I thought that lateral weirs connected to a storage area might help, but I want to show the geometry of both the channel and tributary in a single cross section. Is there a way to show storage areas within a cross section view so that I can have overbank flow enter a storage area but still show the geometry of the wetland/trib system? It’s a steady state model and I’d appreciate any help that you can give.
    Thanks,
    Jeremy

    ReplyDelete
    Replies
    1. Your idea to go to a lateral structure with a storage area is a good one. Unfortunately, as you discovered, RAS cannot plot a cross section and a storage area on the same figure. You could very easily bring both into Excel and display them together that way. Make sure you "Optimize for split flows" over the lateral structure if running in steady flow mode. Also, be aware that in steady flow, RAS assumes infinte available storage. So for any profiles that overtop the lateral structure, the storage area will be filled to what ever elevation balances the weir equation with the split flow and resulting stage in the river. An unsteady simulation will capture the "filling" of the storage area and will properly simulate the attenuation of the flood wave in your river. Best of luck to you.

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    2. Thanks Chris, I decided to go with lateral weirs to connect the two flow areas and it worked out great. I have one follow up question about the optimization over the lateral weirs. To build the model I basically drew the cross sections across both flow areas and then inserted a lateral weir along the left bank of the higher stream. I then specified that the two adjacent cross sections are connected to each other via the lateral weir. When I ran the model all of the flows optimized, but when I checked the WSE of the different profiles for the two adjacent cross sections, they were different. I assumed that optimization worked by the model calculating a WSE for each cross section based on the given geometry and flow data, then comparing the WSE for adjacent cross sections, and finally determining how much water has to flow over the weir for the elevations to match. If the WSE for adjacent cross sections are not matching for a given profile is that indicating an error? Do I need to adjust my weir coefficient? Or is my assumption on how the optimization process works incorrect? The difference in WSE isn’t too large, but I was just expecting it to be the same. Thanks again for all of your help. And I’m sorry if this is a duplicate post, I wasn’t sure if my last post went through or not.

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    3. Your assumption on how the optimization process works is spot on. There is absolutely nothing wrong with adjacent cross sections in your set up having different water surface elevations. In fact, it should be expected.

      Just make sure that your adjacent cross sections do not overlap each other ( wasn't sure by your description if you had done this or not when you said you "drew the cross sections across both flow areas"). The lateral structure should serve as the boundary between the two adjacent cross sections, with neither crossing the lateral structure.

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  7. My cross sections do not overlap I connected them with the lateral weir. Thank you so much for your help. The model is now working great.

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  8. Is it a problem if 2D flow areas overlap the bank stations of cross sections they are connected (via a weir) too?

    ReplyDelete
    Replies
    1. RAS will run under that scenario, but you will be double counting volume, so your answer will be inaccurate.

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  9. Hi all, and thanks Chris for your very useful blog.
    Regarding lateral weir coefficient, I would like to clarify one thing:
    In the "Lateral Weir Embankment" window, is it asked about :
    - the weir coefficient (C), the one from the table you refer to, wich is different for SI and US units and usually lowest than for an inline strcture ;
    - or the discharge coefficient (Cd), wich is dimensionless (somewhere between 0.5 and 0.6) ?
    in fact, C=2/3 x Cd x square(2g)

    There is uncertainty for both computation available : "standard weir Eqn" or "Hager's Eqn"...
    Thanks,

    ReplyDelete
    Replies
    1. Thanks! To clarify, in all of its input boxes, RAS NEVER asks for the discharge coefficient (the dimensionless Cd value). It only asks for the weir coefficient (different for SI versus US units). Even if it might label the input box as "discharge coefficient", it wants the weir coefficient.

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