I just finished reading a novel in which a major feature was building a dike on the top of Hoover Dam. Actually, I think they built 2 dikes: 1 ten feet tall and another 20 feet tall. Now Lake Mead is pretty huge and the idea of a sandbag dike holding back a lake level of 13 feet higher than Hoover Dam seemed (initially) unlikely. But when I started thinking about it, I realized I didn’t understand the physics of the situation.
Now here is where I show my naivete. How much pressure would the dike need to withstand? The pressure increases as you go deeper in the lake. The dam itself would withstand the worst of the pressure of the depths of the lake. So the dike would only have to withstand the pressure of the “top” of the lake. Is this right?
From here on, let’s assume that the water level just rises and there is no “tidal wave” type effect. Is the pressure on the top ten feet of the lake dependent on the size of the lake? Would the pressure on the dike be greater if there was a mile of water behind it, versus, say only 50 feet of water behind it? Or is the pressure of “10 feet of water” the same no matter how big the body of water is?
Now in the novel, an initial 10 foot dike was built to handle the immediate rising of the lake, with a second 20 foot dike built (can you say concentrically?) just outside the 10 foot dike to handle the ultimate maximum level, which turned out to be 13.5 feet above dam level.
What would be the pressure on this 20 foot dike? Would it be the pressure of only 3 feet of water, or of 13.5 feet of water?
Finally, is it reasonable to believe that a sandbag dike could hold back Lake Mead if it rose 13 feet above dam level? I know they use sandbag dikes when the Mississippi floods and I assume the flowing force of the river would be harder to hold back than a simple water level rise. So it doesn’t seem completely unbelievable.
Note: when I ask about “pressure” above, I’m asking conceptually, not for real numerical values.
It sounds like the 20-foot dike is next to the 10-foot dike, so that water flows over the top of the 10-foot dike, fills up the space between the dikes, then keeps rising until the 10-foot dike is completely submerged (under 3.5 feet of water at the top)? In that case, the 10-foot dike is doing nothing; all 13.5 feet of water pressure is pushing on the second dike (Well, 13.5 feet of pressure is pushing on the very bottom of the second dike. There’s no pressure at all on the dike at 13.51 feet above the dam, and the pressure changes smoothly in between).
As Ambly said, how large the water body is doesn’t matter, it’s only the depth.
My question is whether Hoover Dam is really wide enough to put a 20-foot high sandbag wall next to a 10-foot high one. I don’t know how wide you need to make a 20-foot sandbag wall in order to make it reasonably water-tight, but it’s got to be pretty wide. The vertical strength of the dam might be an issue as well. 20’ high of sandbags, plus the water on top of the dam behind the sandbag wall, will get pretty heavy.
On the flip side, while we’re questioning the book, the huge size of Lake Powell means you need a LOT of water to raise the level at all. Flood control is a major reason for dams: what would flood the river to 20 feet flood will only raise the lake by a couple inches.
In the book, Glen Canyon Dam failed catastrophically releasing Lake Powell. (Also, I assume you mean Lake Mead in your quote above. Lake Mead => Hoover Dam, Lake Powell => Glen Canyon Dam.)
Another critical factor to know is how are they moved from one place to another? I have it on good authority that those transported on two-wheeled vehicles are (generally) stronger than others.
Well, a rise in Lake Powell is unlikely to affect Hoover Dam much at all, given that Lake Powell is created by the Glen Canyon dam a little ways upstream of Hoover but Hoover Dam is thick enough for 2 lanes of traffic to pass over. So that would be what, 30+ feet thick?
The Army Corp of Engineers specification is that the base of a sandbag dike be three times its height. Wikipedia says that the crest width of Hoover dam is 45 ft. Unless the Corp’s requirement is serious overkill, there’s only half of the width necessary to construct the two dikes. You could, however, build a single dike to handle the 13 ft of water.
Well, jharvey’s book claims that Lake Powell was “released ,” so the Glen Canyon Dam is no longer helping hold water back from Lake Mead. Lake Powell is 24,322,000 acre-feet of water and Lake Mead is a bit larger at 28.5 million acre-feet. Whether that combined volume would swamp the Hoover Dam would depend on a lot of things I don’t have a ready answer for. Is the flow rate of the water going from Powell to Mead necessarily greater than the combined discharge rate of all of the Hover Dam’s spillways (including the emergency ones)? What would be the water level before the collapse of the GCD (Lake Mead has been far below its capacity for many years, now)?
Actually, the novel deals with all of these issues in the course of the story and includes some, well, “innovative” ways to lessen the damage to the Colorado river system and surroundings. Additionally, it’s quite a page turner. Even though this is GQ, I guess it won’t hurt to mention the book. It’s Wet Desert by Gary Hansen. Note that I have no relationship with the book or author other than that of a satisfied reader.
(Mods: Go ahead and remove this post if mentioning the book is a no-no.)
There is a good bit of ongoing discussion and research regarding the peak outflow from a dam breach. The most commonly used equations use the height of the water, volume of the reservoir and cross-sectional area of the dam in computing the peak breach outflow.
Computer models now have such equations built-in and can not only simulate the breach, but also route the resulting flood wave through the downstream valley. We can also route the breach hydrograph through a downstream dam and determine if it will be overtopped.
The peak outflow is one thing, but the behavior of the flood hydrograph as it travels downstream is important also. The peak flow will be attenuated somewhat as it travels along; the shape of the valley plays a large part.
Caveat: there is still a great deal of uncertainty in these equations and models.
but Hoover Dam is thick enough for 2 lanes of traffic to pass over. So that would be what, 30+ feet thick?