I should know this dam principle...

[charliealphabravo]

So you have a dam that is say 10 feet high and 1 foot wide that is retaining water over the full height.

Integrating the water pressure over the height of the dam gives a horizontal force component of 3120 pounds acting on the back of the dam.

So far so good.

Now suppose you construct an identical dam 1 foot behind the first dam so that they are oriented back to back and supporting a column of water that is 1 square foot by 10 feet high. Without thinking too much about it I would say that the calculation of pressure and force on the back of the first dam is unchanged. But I am thinking too much about it. And after thinking about it I realized that I couldn't explain intuitively how a column of water weighting 624 pounds would exert 3120 pounds of force on the first dam.

I'm embarrassed to be drawing a blank here but it has been too long since I thought about this. Can someone point out the blind spot in my thought experiment?

Thanks in advance.

 

[molibden]

What about if you have soil between the dams?

Structural timber engineering

 

[civeng80]

It is conter intuitive. But that is the law of nature. Nagging little problems that develop sfter many years of engineering practice.

Doesn't work for soil because soil have shear resistance in the failure plane and the failure plane does not develop because of the narrow column of soil.

 

[Ron]

It does work for soil. Soil will exert lateral pressure on the wall similar to water, just reduced by internal friction in the soil.

 

[civeng80]

Ron
Fair enough. But how much do you reduce the fricton angle by ?

 

[CarlB]

The earth pressure resulting from a narrow space between 2 retaining walls has been discussed a few times, here's one: thread255-349221
I'd say it's not similar to water, but not sure what space is "narrow".

 

[Ron]

civeng80...you don't reduce the angle of internal friction, but the lateral pressure is constrained by it. Lets suppose we have a soil with a unit weight of 100 pcf. Assume we have a 10' wall height. If the soil were "liquid", then the lateral pressure would be 10 x 100 or 1000 psf. The soil; however, is not liquid and internal friction in the soil prevents some of the pressure from extending past the soil boundary. While it can get complicated with geometry and soil types, let's further assume that we have a granular soil with an internal friction angle of 30 degrees. In its simplest form, the lateral pressure relationship is 1/2 tan phi, so now the lateral pressure is 10 x 100 x (1/2 tan 30) or about 290 psf. As I noted, it can get a lot more complex, but you get the idea.

 

[paddingtongreen]

If you apply Ron's formula in a bin, the pressure builds up until the internal friction prevents flow. Of course, material does flow, so Janssen developed some alternatives. However, material sometimes "bridges" within the bin. It ties in with the difference in behavior in narrow gaps, material bridges preventing the full weight reaching the bottom.

Michael.
"Science adjusts its views based on what's observed. Faith is the denial of observation so that belief can be preserved." ~ Tim Minchin

 

[hetgen]

Hi charliealphabravo,

Picture it this way ...

You will need to exert the same amount of force to submerge a plate into a shallow water or a deep ocean; now if you rotate this analog by 90 deg and visualize the water trying to move instead of the plate you will see why it doesn't mater how wide the gape is between the two dams.

If you are asking why the water particles push the wall i don't think we know, but we have a name called gravity and many theories which include, string, multiverse and a uni-corn

 

[SAIL3]

taking MJB's example...say the gap was 1/32"..the numbers say the same press which is definitely counter-intuitive...how many existing retainin walls have a gap of say 1/32" between it and the soil from soil shrinkage/settlement and if not for good drainage @ the bottom would experience this head of water.

 

[TLHS]

It would only matter if you had an actual water column. The water needs to be supported by the water below it. If the water's working through adhesion, surface tension or capiliary action there won't be pressure at the bottom.

You aren't going to get a 1/32" water column behind a retaining wall in real life because that kind of pressure would push the water back through the soil.

Once you get down to the scale of capiliary action, there is certainly a point where the pressure relation to depth won't hold. That scale is a couple of orders of magnitude below a foot, though.

 

[chrislaope]

Original Poster is puzzled about "how a column of water weighting 624 pounds would exert 3120 pounds of force on the first dam".

I think it can be put in this way: pressure is not always in direct proportion to the weight of the media. you can imagine that weightless air in a closed tube can exert huge amount of pressure/force on its surrounding wall. this example can partly explain "why a column of water weighting 624 pounds would exert 3120 pounds of force on the first dam".

 

[LittleInch]

I think one thing getting in the way from the OP is the use of a very small distance between his walls and the same with respect to the soil issue. For instance what if the distance between your walls wasn't 1 foot, but 100 feet? Then you would have 62,400 lbs of water exerting a force of 3,120 lbs on the wall of your dam. All of a sudden it doesn't seem like such a silly answer.

The other issue is the force is based on no movement whatsoever. In reality for a fixed volume, any slight movement of the walls would result in a drop in level and the amount of work done by the water column for a very small column, or total potential energy is very small. Hence although the force is certainly there and correct, the distance it could move anything is very limited unless you kept topping up your column of water.

My motto: Learn something new every day

Also: There's usually a good reason why everyone does it that way

 

[Archie264]

Triangled, thanks for the link.

 

[RFreund]

hetgen - nice comparison.

Littleinch - very good point as well.

I mind will just not except this for some reason, it just wants to know why/how....

EIT

http://www.HowToEngineer.com

 

[charliealphabravo]

It's just that the formula is so maddeningly simple. Just density times depth. On the macro scale the phenomenon is just a property of a fluid's classical inertia basically. There are no coefficients or pressure/volume/temperature/velocity dependancies like you have in the gas law. On the micro scale I am trying to imagine what is happening when you stack molecules of an incompressible fluid. Perhaps it is some type of wedging/prying action or brownian motion pushing on the wall.

On second thought no I still can't imagine it. If the distance between the walls is only 1/4-inch then the volume of water weighs 13 lbs and the force on the back of the first wall is still 3120 lbs. I'm afraid to calculate the weight of the water at 1/8-inch else I will probably lose my feeble grip on reality ;]

Great thoughts all. Thanks.

 

[paddingtongreen]

You seem to be going round and round linking together two things that are not related.

You live in an environment where you feel the same 14.7 lbs/sqin atmospheric pressure from all directions, regardless of whether you are out in the open or in a sealed tank with only a small hole in the top. Do some thought experiments with that.

Michael.
"Science adjusts its views based on what's observed. Faith is the denial of observation so that belief can be preserved." ~ Tim Minchin