Darcy's law in Dams
"Dams are often under-appreciated for their watery efforts."
Dams are one of humanity’s favourite ways to create a reliable water source and irrevocably alter the landscape at the same time.
With a mighty concrete wall in the way, not one drop can get past without our say so.
Or can it?
As impermeable as your dam wall might be, the reservoir will only stay full if the precious hydroxylic acid does not seep away into the rock and soil on which the reservoir lies.
When a dam is built on porous ground, water will flow under, through the soil, due to the pressure difference between the high pressure (ρgh) at point A and lower (atmospheric) pressure at B,
according to Darcy’s Law.
where A is area, K is permeability, ρ is density, g is acceleration due to gravity, μ is the dynamic viscosity, P denotes pressure, h height, x distance, and d denotes change.
Flow is assumed laminar and slow. [1]
If it gets a little carried away with the ole seepage the underlying soil may undergo liquefaction and the dam will collapse! This is known as piping failure because the water carves out pipes under the dam. Not ideal for anyone innocently running their alpaca farm downstream.
So how to stop this happening? We want to reduce the volumetric flowrate of water so looking at Darcy’s Law, which variables do you think should be changed? Once you have built the model dam below have a go at adjusting these variables to find out how seepage is affected.
HINT: The hydraulic gradient is affected by both the pressure difference and the flowpath length [2].
[1] K. K. Vincent, M.N. Muthama & S.N. Muoki (2014). "Darcy’s Law Equation with Application to Underground Seepage in Earth Dams in Calculation of the Amount of Seepage". American Journal of Applied Mathematics and Statistics, vol. 2, issue 3, pp. 143-149 [Online]. Available:
http://pubs.sciepub.com/ajams/2/3/8/index.html
[2] C. Wineberg. (2018). "How Quicksand Causes Dam Failures". Practical Engineering [Online]. Available: https://practical.engineering/blog/2018/7/16/how-quicksand-causes-dam-failures-1#. [Accessed: 10- Mar- 2019].
Went to Hoover Dam last week, but the water just broke the dust bag :(