3 - Permeability Flashcards
What does the permeability of a soil affect?
How quickly water can flow through it and how quickly excess pore pressures can dissipate
What are the 3 intermixed phases of soil?
Solid - mineral particles
Gas - air, H20
Liquid - water, oil…
Soil is a porous medium, what does that mean?
That is has 3 intermixed phases, solid, liquid and gas.
In order to be permeable, what must a porous material containt?
Continuous voids, so that there is a path through the material using voids spaces which are connected.
What is the voids ratio?
Volume of voids / Volume of solid
What is the porosity?
Volume of voids / total volume
What is the water content of a soil?
Mass of water / Mass of solids
What is the degree of saturation?
Volume of water / Volume of voids
What is the volume flow rate, q through a column of water?
q = velocity X area
At the microscopic level, when water is travelling through a soil, what does does water follow?
A tortous path thorugh the pores
In geotechnical problems, what can water be considered to do?
Flow in a straight line under an effective velocity.
What is the seepage velocity?
The ratio of the volume flow rate to the area of voids, Av.
What is the pressure head of water?
The height water would rise to in a standpipe
What is the elevation head?
The distance from a datum to the point at which the pressure head is being measured
What is the total head?
The sum of the elevation head + the pressure head
Why is the concept of total head important?
It is the difference in total head that dictates whether water will flow and controls seepage velcoity.
What is flow of pore water in soLids driven by?
higher total head towards lower total head
What is the hydraulic gradient?
The rate of change of total head along the direction of flow. Change in h / change in s, where s is the straight line distance between the 2 points at which the total head is measured
In a saturated porous media, what did Darcy find the flow veolcity to equal?
The hydraulic gradient, i X the coefficient of permeability, k.
What is the coefficient of permeability, k?
A measure of the conductance that soil provides to the flow of water through its pores
Name 5 factors that the coeffienct of permeability depends on:
- Void or pore size
- Soil structure
- Particle shape
- Degree of satutration
- Viscosity of water
What type of soil is the coefficient of permeability at its lowest?
Very fine soils, such as clays.
What type of soil is the coefficient of permeability at its highest?
Clean gravels
How does the coefficient of permeability of a soil relate to the properties pf the fluid flowing through it?
K = (Yw x K) / n
In a permeability equation, what is K?
The absolute permeability which depends on characteristics of the soil skeleton
In a permeability equation, what does n represent?
n is the viscosity of the water.
In natural, sedimentary solids, what do the layers all typically have?
Different permeability.
To determine the average coefficient of permeability of such deposits, how do we calculate the permeabilty?
Samples are taken and tested
Will the horizontal permeability of a soil be typically greater than the vertical permeability?
Yes.
In stratified soil, in order to maintain continuity of flow, what is the flow rate throughout the layers?
Constant
In stratified soil, what is the total head loss a sum of?
The head loss of all layers
Through derivation, what does the vertical permeability, kv equal?
The sum of Hi divided by (sum of Hi / sum of kvi)
In stratified soil, what is the hydraulic gradient along each layer?
Equal
In stratified soil, what is the total flow acorss all horizontal layers, qh equal to?
The sum of flow across each layer
Using the flow rate equation, we know qH = HkHiH, what does this tell us?
That qH = iH(sum of kHiHi)
What does the average coefficient of permeability in the horizontal direction, kH equal?
(sum of kHi*Hi) / sum of Hi
Name 3 laboratory tests to measure the coefficient of permeability:
-The constant head test
-Falling head test
Oedometer test
What does the constant head test involve?
A cylindrical sample of soil (cross section A, length L) to a constant head and therefore a constant hydraulic gradient. The flow rate is measured through the sample and hence the permeability can be determined.
When is the constant head test used
For coarse grained soils.
What equation for permeability do we obtain from the constant head test?
k = (qL) / A change in h
Change in h is from the water on the right of machine.
When is the falling head test used?
For more fined grained soils which have a lower permeability.
What does the falling head test involve?
A falling head is applied to the top of a cylindrical sample of soil, the rate of change in head is measured and therefore it is not important to measure the actual flow rate.
As the hydraulic gradient and flow rate vary with time the analysis is more complex than the complex head test.
In the falling head test, what does the quantity of flow, dQ equal?
-a(dh/dt) = Ak*(h/L)
In the falling head test, what does k equal?
2.303(a/A)L*(log(h1/h2))/(t2-t1)
How can the coeffiecient of permeability be estimated from an oedometer test?
Indirectly
What does an oedometer test involve?
Determining the compression characteristics of a soil, as we compress the soil the water contained within it gets squeezed out as a function of permeability and magnitude of excess pore pressures
What is the equatiov used to calculate permeability from an oedometer test?
k = cmy
When calculating permeability from the oedometer test, what are cv and mv ?
cv is the coeffient of consolidation, mv is the coefficient of volume change
Name the main way of calculating permeability in a field experminet?
The well - pumping test.
What happens in a well-pumping test?
A number of observation boreholes are installed to measure the hydraulic heads at different distances from the well that is being pumped.
The steady state head h1 and h2 in observation and boreholes at radii r1 and r2 are monitored at flow rate q being pumped from the well
What is the 4 step process of the derivation of the falling head test ?
What is the 3 step process of deriving the permeability from a confined aquifer?
What is the 3 step process of deriving the permeability from a confined aquifer?
How do you derive the permeability from an unconfined aquifer?
What actually is a confined aquifer?
A confined aquifer is an underground layer of water-bearing rock or sediment that is trapped between two impermeable layers (such as clay or rock). These impermeable layers, called aquitards or confining layers, prevent water from flowing freely into or out of the aquifer.
What actually is an unconfined aquifer?
An unconfined aquifer is an underground water storage zone that is directly connected to the surface, without an impermeable layer above it. The water table in an unconfined aquifer is free to rise and fall depending on precipitation, evaporation, and extraction.
What is the main difference between a confined an unconfined aquifer?
Confined aquifers are surrounded by impermeable layers and have pressurized water, while unconfined aquifers are open to the surface and have water that fluctuates with the water table.
Hazen(1930) proposed a relationship between k and D10 (the size which 10 percent of particles are samller than), what was this?
k = c*D10^2
where c varies between 1.0 and 1.5
Casagrande proposed a simple relation for the coefficient of permeability for fine to medium clean sand, what was this?
k = 1.4e^2k0.85
Where k0.85 is the coefficient of permeability at a voids ratio of 0.85
Samarasinghe(1982) suggested that the coefficient of permeability of NC clays can be given by what equation?
k = C*(e^n / 1+e)
Where e is the void ratio.
C and n are constants to be determined experimentally from a plot of k(1+e) against e.
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