Transcript GEOTECHNICAL PROPERTIES (CE1203)

GEOTECHNICAL PROPERTIES
(CE1203)
PERMEABILITY
Ms Ikmalzatul
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.
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.
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.
h= z+
u
w
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 ).
H
i=
L
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
 sat   w
ic 
w
or
Gs 1
ic 
1 e
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
ic 
19.7  9.81
 1.01
9.81
or
0 .4
e
 0.667
1  0 .4
2 .7  1
ic 
 1.01
1  0.667
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=ki
where v = velocity of flow
i = hydraulic gradient
k = coefficient of permeability
 the quantity of water flowing ( Q ) is given by
Q
 kAi
t
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=kAi
Coefficient of permeability
This is defined as the flow velocity produced by a hydraulic gradient of unity.
From the flow equations above
k=
Q/t
Ai
or
q
Ai
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
i. porosity of the soil,
ii. particle size distribution,
iii. shape of the particles,
iv. degree of saturation and
v. temperature/viscosity of the water.
Typical values of k
Laboratory determination of k
The two main laboratory tests used in the determination of k are :i. the constant head permeametre -used for gravels and sands with k
values > 10-5 ms-1
ii. 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.
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).
Constant Head Test
Now
but

q=
k
k=
q
Ai
Q
t
and
Q/t
 H
A 
 L
i=
=
H
L
QL
AHt
Having found a value for k the test is
repeated several times at different flow
rates/heads and the average value for k
calculated.
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.
QL
k
AHt
260 106  0.250
k
= 0.5 x 10-3 ms-1
6
3
2000 10  500 10  130
Drainage Characteristics: Good drainage
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 0.061 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]
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.
Falling Head Test
•
The procedure is then repeated using
standpipes of different diameters and
the average value of k computed.
k=
2.3aLlog10  h1 / h2 
A t 2  t1 
or
aLlnh 1 /h 2 
k=
At 2  t 1 
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.
 1584
2.3  67  100 log10 

584 

k
 0.932 106 m s1
7854 912
 1584
67  100 logn 

584

  0.933 106 m s1
k
7854 912
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
5.00
800
400
149
9.00
1200
900
177
9.00
900
700
169
9.00
700
400
368
12.50
1200
800
485
12.50
800
400
908
The End