1. GEOTECHNICAL PROPERTIES (CE1203)
PERMEABILITY
Ms Ikmalzatul

2. Introduction
The permeability of a soil has a considerable effect on the cost and difficulty of many Civil Engineering construction operations e.g. the excavation of soil below the water table, or the rate at which a soft clay stratum consolidates under the influence of the mass of a superimposed load.

3. Definition
Permeability is the passage of water (or oil or gas) through a soil. As soil consists of discrete particles with interconnected pore spaces water can flow within the soil. Such water will flow from areas of high pore pressure to areas of low pore pressure.

4. Hydraulic head across a soil
When considering water flow pressure is usually expressed as a head measured in metres of water. There are, according to Bernoulli’s equation, three components to the head - elevation head (z), pressure head due to pore water pressures ( u/γw ) and velocity head ( v2/2g ). Velocity head is usually ignored in groundwater flow problems as the term in “v” is quite small. The total head causing flow through the soil mass is therefore the sum of the elevation head and the pressure head.

5. Hydraulic gradient ( i )
The hydraulic gradient ( i ) is defined as the hydraulic head ( H ) across the soil divided by the length of flow path through the soil ( L ).

6. Critical hydraulic gradient ( ic )
This is the hydraulic gradient at which the soil becomes unstable - the effective stress becomes zero. Consider a soil in which the flow of water is upward, this will create an upward seepage pressure. If the upward flow of water is large enough the seepage pressure will negate the effective stress and the soil will become unstable. In this situation the soil is said to be in a “quick” condition or

7. Critical hydraulic gradient ( ic )
Cohesionless soils, in particular fine to medium sands, typically exhibit the “quick” condition at hydraulic gradients of around 1.0. Coarse sands and gravels (soils of high permeability) require large flow rates to achieve this “quick” condition and these are seldom found in practice. Cohesive soils do not exhibit “quick” conditions as even at zero normal stress they posses some shear strength.
Example:- A soil has a porosity of 0.4 and saturated unit weight of 19.7 kNm-3. Calculate its critical hydraulic gradient. Gs = 2.7.
Unit weight = density x gravity or

8. Flow of water
The flow of water in a soil is governed by Darcy’s Law, which states that under saturated conditions flow velocity is proportional to the hydraulic gradient.
v  i or
v = k i
where v = velocity of flow
i = hydraulic gradient
k = coefficient of permeability
 the quantity of water flowing ( Q ) is given by
where Q = quantity of water flowing in time t
t = time
A = area through which flow is taking place
or working in unit time, q = k A i

9. Coefficient of permeability
This is defined as the flow velocity produced by a hydraulic gradient of unity. From the flow equations above
and is expressed in ms-1
The value of k ranges from almost zero in the case of clay (impermeable) upto 10 ms-1 for very coarse gravels.
The actual k value for a soil is dependent on a number of factors including the
porosity of the soil,
particle size distribution,
shape of the particles,
degree of saturation and
temperature/viscosity of the water.

10. Typical values of k

11. Laboratory determination of k
The two main laboratory tests used in the determination of k are :-
the constant head permeametre -used for gravels and sands with k values > 10-5 ms-1
the falling head permeametre - used for fine sands, silts and clays with k values between 10-4 to 10-7 ms-1.
A third laboratory test the Hydraulic Cell test, as developed by Rowe and Barden, can be used for soils of very low permeability.

12. Constant Head Test
Apply a vacuum to the sample by opening valve C with valves A and B closed.
Close valve C and open valves A and B and allow water to flow through the sample from the reservoir until steady state flow is achieved (the levels in the two manometers remain constant).
Flow of water through the sample is controlled by adjusting valve A. Once the steady state flow has been achieved the quantity of water flowing ( Q ) in a given time ( t ) is recorded together with the readings on the two manometers.
The difference in the two manometer readings giving the head difference ( H ) over the sample length ( L).

13. Constant Head Test Now but 
Having found a value for k the test is repeated several times at different flow rates/heads and the average value for k calculated.

14. Example 1
A constant head permeameter test has been run on a sand sample 250 mm in length and 2000 mm2 in area. If the head loss was 500mm and the discharge 260 ml in 130 secs determine the coefficient of permeability and comment on the drainage characteristics.
= 0.5 x 10-3 ms-1
Drainage Characteristics: Good drainage

15. Example 2
During a constant head permeameter test a flow of 173 ml was measured in 5 minutes. The sample was 0.1 m in diameter and the head difference of m was measured between tapping points 0.2 m apart. Determine the coefficient of permeability and comment on the drainage characteristics of the soil.
[Answer: 0.24 x 10-3 ms-1]

16. Falling Head Test
This test is used with fine grained soils were the rate of flow of water is too small to be accurately measured using the constant head apparatus/test.
The test is normally carried out on a 100mm dia. undisturbed sample. With the top and bottom filters in place the sample is stood in the water reservoir.
The top of the sample/filter is connected to a glass standpipe of known diameter and the de-aired water contained in the standpipe allowed to seep through the sample. The height of the water (h1 , h2 , etc.) is recorded at several time intervals (t1 , t2 , etc.) during the test.

17. Falling Head Test
The procedure is then repeated using standpipes of different diameters and the average value of k computed. or

18. Example 1
In a falling head permeater test, the water level in the standpipe was originally 1.584m above the overflow, and dropped 1.0m in 15.2 minutes. The sample was 0.1m long and 0.1m in dia, and the area of the standpipe was 67 mm2. Calculate the coefficient of permeability and comment on the drainage characteristics of the soil.

19. Example 2 (from Whitlow)
During a test using a falling head permeameter the following data was recorded. Determine the average value of k.
Diameter of sample = 100mm
Length of sample = 150mm
Recorded data:
Standpipe diameter d
(mm)
Level in Standpipe
Time interval (t2 – t1)
(s)
Initial h1 (mm)
Final h2 (mm)
5.00
1200
800 82
400
149
9.00
900
177
700
169
368
12.50
485
908

20. The End