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concrete weir design, like a retaining wall, but only water

concrete weir design, like a retaining wall, but only water

concrete weir design, like a retaining wall, but only water

(OP)
I am designing a concrete weir to be placed in a ditch for a project I'm working on.  The basic layout is that of a cantilever retaining wall, except the soil height is the same on both sides of it.  It is designed to hold water back up to the height of the top of the wall.  Do the lateral earth pressures cancel each other out since the soil level is the same height on both sides?  Then would I just have the lateral force of the water to deal with for overturning and sliding stability? Please let me know as soon as possible because I'm not very experienced in these designs.  Thanks.

RE: concrete weir design, like a retaining wall, but only water

From your description, it sounds reasonable to assume that the soil on both sides of the weir will be saturated. With that being the case, the lateral earth pressures do cancel each other.

www.SlideRuleEra.net idea

www.VacuumTubeEra.net r2d2

RE: concrete weir design, like a retaining wall, but only water

(OP)
Yes, the soil on both sides of the weir will be saturated.  I just didn't know if one side was passive and the other side used active earth pressure or what was safe to assume.  So the only overturning force I will have will be the force of the water?

RE: concrete weir design, like a retaining wall, but only water

And any overturning from the dead load of the retaining wall due to the stem wall weight and the relationship of the toe and heel lengths.  If the toe is short and the heel is long, it will add to the overturning of the water.  The opposite subtracts.  If the toe and heel are equal, there is no difference.  

Mike McCann
MMC Engineering

RE: concrete weir design, like a retaining wall, but only water

You will also have to consider erosion on the downstream side.  Depending on the downstream conditions and flow velocity (supercritical vs. subcritical. distance to next and ultimate grade control, penalty for failure, etc.) you may want to treat it as a submerged retaining wall with nothing on the downstream side.

RE: concrete weir design, like a retaining wall, but only water

saturated soil both upstream and downstream may provide little resistance against lateral movement.  also consider that buoyancy will reduce the effective weight of the footing.  Seepage under the footing needs to be considered also For this reason, flood walls / weir walls generally have very large and deep footings to provide stability and prevent seepage.

RE: concrete weir design, like a retaining wall, but only water

Ice loading is generally the governing case.

HTH

RE: concrete weir design, like a retaining wall, but only water

Good Answers on this forum!

RE: concrete weir design, like a retaining wall, but only water

If the water level is up to the top of the weir on one side, what is the minimum water level or water table on the other side?

RE: concrete weir design, like a retaining wall, but only water

(OP)
The design case for water level on the other side would be at the bottom of the ditch, basically the top of the ground level.

I've designed it for the bottom of the foundation to be 5' below the surface, (for frost depth).  This is basically quite a small structure compared with what you are all probably imagining.  The top of the wall will be approximately 9 feet out of the ground, with a 5 ft deep foundation.  The weir will also be about 30 ft in length from one ditch bank to the other.  

Will bouyancy be an issue because the structure is not actually displacing any water?

RE: concrete weir design, like a retaining wall, but only water

I'm just posting a question on this topic for some further discussion:  Will this weir always convey flow?  If this is a ditch and there is some measured flow (as governed by the weir) only during storms, the question pertaining to the "water table" level seems irrelavent - at the time of flow the surface water would be perched and likely not connected to the phreatic surface.  Now if the flow lasted for a matter of days or weeks, there may be some infiltration to "mound" the phreatic surface and there may become some bouyant affects, but this may or may not be the case.  This is the problem with transient flow problems.

I agree that the absence of unbalanced earth pressures means that the overturning forces are water pressure (both static and dynamic) and (good point) ice.  This problem requires a free body diagram showing all external forces and then sum the forces and moments to see just how much of the passive earth pressure is mobilized. The way the questions have responded so far, the sense is that you would look at this as a plane strain problem.  Heck if the weir is only a few feet square, you may also want to look a the forces along the sidewalls too - don't have these details.

Regarding seepage forces, cutoff walls, etc.  The chance of blowing out the weir is pretty great if you don't account for internal drainage along (around) the edges of all concrete.   There are conditions where gravel can be your friend as it's not prone to piping failure.  Without some design sketches, however I could be way off track. . .

Good luck on your project.

f-d

¡papá gordo ain't no madre flaca!

RE: concrete weir design, like a retaining wall, but only water

(OP)
The weir will have a gate which can be closed in the case of flooding downstream to "back up" the water behind it.  99% of the time, this gate will be open and water will be allowed to flow freely.  The gate will only be closed during a flooding situation.  

I've included a quick sketch of what it will look like.  This drawing is not to scale but I've included the dimensions and elevations.  Do I have the basic FBD correct or are there additional forces that I haven't accounted for?

RE: concrete weir design, like a retaining wall, but only water

I was thinking that, in case the flow over the weir wasn't continuous, if the water table on the downside was below the ground level, that would effect the "balance" of soil pressure.

RE: concrete weir design, like a retaining wall, but only water

bhauth - You have not included the weight of the water on the footing (consider it a surcharge). The weight would be uniformly distributed above your "No. 4".

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RE: concrete weir design, like a retaining wall, but only water

I don't think you can say that your soil pressures "balance".  In your sketch, it looks as though your only lateral pressure is γH, where H is 9 feet.  I think you need to calculate your pressures on each side of the wall independently, and include the water level on the left side of the wall.

RE: concrete weir design, like a retaining wall, but only water

(OP)
meicz - The flow through the gate IS continuous.  So I think it is safe to assume the soil is saturated at all times on both sides.

 

RE: concrete weir design, like a retaining wall, but only water

(OP)
Do any of you have an equation for "Surcharge as an equivalent soil height"?  My unit weight of soil is 120 pcf.  Water is 62.4 pcf.   

RE: concrete weir design, like a retaining wall, but only water

bhouth-

In your sketch, your resultant lateral pressure is γH, where H is 14 feet.  The resultant would be applied at  Elevation 1049.67 feet, which is below the ground level.  You showed γH above the ground level.

RE: concrete weir design, like a retaining wall, but only water

Sure, from your sketch:
Saturated Soil Equivalent Height for 9 Ft. of Water =
62.4 pcf (water) / 120 pcf (saturated soil) x 9 ft.

But the free body diagram would be easier to understand if you keep the weight of the water separate (say a "No. 5" item added to your sketch).

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RE: concrete weir design, like a retaining wall, but only water

(OP)
Yeah, that's what I thought the Equivalent Surcharge would be.  The program that I'm using is just making things more confusing than they really are.  I will just keep things separate and do my stability analysis by hand.  Technology is useful if I can fully understand it.  
 

RE: concrete weir design, like a retaining wall, but only water

If you sum the moments from the bottom of the vertical concrete (i.e., at the bearing layer) you get 20.24 k-ft counterclockwise (the weights of the concrete and the soil prisms atop the concrete null out).  If you consider the bearing surface (assuming that you'll find at least 3 ksf), it's likely that you need no lateral earth pressure for your stability.  3 klf over 2/3rds of the footing provides 16 kips and a moment arm of 1.33 ft, which is 21.3 k-ft.  You can apply more finesse if you want to, but I'm just working on the back of an envelope - ha.

I'd worry about piping at either abutment however. . .

f-d

¡papá gordo ain't no madre flaca!

RE: concrete weir design, like a retaining wall, but only water

I see 2 cases:
1.) if the soil is clay, use the 120 psf and water to elevation 1050.
2.) if the soil is sand, the eefective unit weight of the soil will be about 65psf and the net water pressue will reach a maximum at 1050 and the decrease to 0 at 1045.

Sum moments about the toe. Soil masses 3&4 will have same wt, but different moment arms, so they need to be included in calculations. FS should =1.5 Check sliding & Bearing also

RE: concrete weir design, like a retaining wall, but only water

You can't consider the weight of the water as a surcharge unless the material below is free draining and will never be submerged, and the permeability of the material beside it is very low.  

RE: concrete weir design, like a retaining wall, but only water

Unless the forces require the mobilization of lateral earth pressures, the unit weight of the soil doesn't appear too relavent.  You have the same prism of soil on either side of the vertical wall, so these weights do not contribute to overturning stability unless a portion of the bearing goes into tension.  Again, look at the geometry of the sketch.  If built as designed, there is sufficient bearing to offset the overturning of the water pressure.  Summing the horizontal forces only requires either enough friction or passive pressure to offset the unbalanced hydrostatic force, which shouldn't be much of a problem.

I'll retract part of my earlier statement as the calculation of base shear will require unit weight to get the "N" of the NtanDelta.  Just use bouyant unit weight.

O.K., I'll go to bed now. . .

f-d

¡papá gordo ain't no madre flaca!

RE: concrete weir design, like a retaining wall, but only water

(OP)
Ok, so on my FBD, I'll use the unit weights of the saturated soil on top of my footing, the weight of the concrete, and the weight of the water on top of the upstream side of the footing as my clockwise moments.

I'll use the lateral water pressure as my counterclockwise moment placed at 1/3 of the height of the water.

This being said, without doing the calculations, my factor of safety should be sufficient for overturning.

RE: concrete weir design, like a retaining wall, but only water

The lateral water pressure is a triangle from the top of the wall to the bottom of the footing and acts at 1/3rd of that total height, as meicz said.  If the downstream soil is always saturated from continuous flow, there will be a similar resisting triangle of water pressure against the downstream side from the ground surface to the bottom of the footing.  Work with total heights of water, not differential heights.

There will be water pressure upwards against the bottom of the footing, and if there is seepage it will be greater under the upstream edge that the downstream edge. A conservative (usually) assumption is that the water head at the upstream edge is the full headwater elevation and the head at the downstream edge is the tailwater elevation (in your sketch, the ground surface).  In any case, the uplift creates an additional overturning moment.

Hydrostatic uplift is ignored in most retaining wall design, but never in dam design. This is a dam.
  

RE: concrete weir design, like a retaining wall, but only water

My two cents (for whatever it is worth):  Construct a flow net to help determine seepage forces, particularly along the bottom of the footing.  In addition, the hydraulic gradient can be estimated to determine the factor of safety against piping failure.

Also, the soil pressures would cancel out.  In fact, I would model active earth pressures on the water side and passive earth pressures on the ditch side.  

 

RE: concrete weir design, like a retaining wall, but only water

The maximum height of the water on the upward side can be higher than the top of the dam. In order for the water to flow over the dam its has to be some depth higher than the top of dam. This depth depends on the actual flood water flow and needs to be calculated.

Look up flood mitigation for more info.

RE: concrete weir design, like a retaining wall, but only water

Weirs to function correctly, (measure amoint of flow by measuring height of fluid passing over), need a SHARP edge for the fluid to pass over.  Perhaps the top of your weir could have a metal plate with a beveled edge to produce a sharp crested weir.  Otherwise you have built a check dam to produce a constant elevation of fluid behind the dam.

RE: concrete weir design, like a retaining wall, but only water

(OP)
None of the last 2 comments have any merit for the scope and context of this structure.  Its not technically a "weir,"  It is basically a dam at a set elevation that will allow water to divert down a ditch if the water surface gets high enough.  This diversion will lead INTO our Impoundment, which will have a dam at an elevation higher than that of the "weir."

RE: concrete weir design, like a retaining wall, but only water

You definitely need to consider the flow net though.

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