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Piping failure | Quick sand condition | Seepage discharge

Piping 


Piping is a condition when backward erosion of soil is caused by the percolating water and the piping begins when the hydraulic gradient 'i' exit the critical gradient 'ic'

The percolation of water into soil is known as seepage. While flowing through soil Seepage pressure is exerted on soil particles in the direction of flow. 

Is case of upward seepage flow the seepage pressure will act upward at the rate same as hydraulic pressure of available head. This hydraulic head difference can be seen in downstream side of dam, the difference in head produces seepage pressure at downstream exit point. 
Piping failure

To understand piping failure let us understand quick sand (boiling) condition.


Quick sand condition

Seepage pressure and quick sand condition

let us take a example as shown in figure above: 
To generate upward flow provide 'h' available head of water, and 'L' be length of soil specimen. 
γsat = saturated density of soil
γw = density of water 

Balancing pressure at bottom of soil sample,

γsat x L = γw x (L + h)

γsat x L = γw x L + γw x h

h / L = (γsat - γw) / γw

h / L = γ' / γw = i

( We know that, (γsat - γw) = γ' = submerged density of soil, & i = hydraulic gradient = h/L) 

So, at condition of upward flow and hydraulic gradient reaching (γ' / γw = ic ) meaning effective stress will be zero at this stage and after which further increase in seepage pressure will lead to piping failure of soil. 

At that critical condition hydraulic gradient is known as critical gradient 
" ic = γ' / γw ".

Also, γ' = ((G - 1) γw / (1 + e))

ic = (G + 1) / (1+ e)

The critical condition when effective pressure becomes zero is known as quick sand condition or boiling of sand etc. At quick sand condition shear strength becomes zero. Note: quick sand is a hydraulic condition and not a type of soil. It mainly occurs in fine sand. Generally clay offers some part of shear strength due to cohesion also, thus quick sand condition does not occur in clay.

The downstream portion of dam is also under same condition and quick sand condition occur in there forming pipe channels below dam known as piping failure of dam.


Seepage discharge and seepage velocity


Seepage discharge is the rate of flow discharging through area in unit time measured in m³/s . Can be determined using flownet diagram.

q = V / t
Where q = seepage discharge
V = volume of water 
t = time

Now, let 'v' be discharge velocity
Then 

v = q / A
A = area of flow

But here we have a issue, the flow is not happening through whole area instead it's happening through voids of soil particles. So the correct velocity is known and seepage velocity.

Seepage velocity is the actual velocity through soil at which seepage is occurring.

vs = seepage velocity

vs = q/ Av 
Av = area of voids 

Area of voids vs cross sectional area


Since we directly cannot measure Area of voids, we have Av = η x A, where η = porosity of soil.

So we have 

vs = q / Av = q / (η x A) = v / η

Since Av < A area of voids is always less than Cross sectional area; vs > v seepage velocity will always be more than discharge velocity.






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