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1 CE281Geotechnical Engineering I
Permeability Test
PERMEABILITY TEST OBJECTIVE To determine the coefficient of permeability (k) for a given soil sample using falling head method. INTRODUCTION Permeability (or hydraulic conductivity) refers to the ease with which water can flow through a soil. This property is necessary for estimating the quantity of underground seepage under various hydraulic conditions, for investigating problems involving the pumping of water for underground construction, and for making stability analyses of earth dams and earthretaining structures that are subject to seepage forces. One of the major physical parameters of a soil that controls the rate of seepage through it is hydraulic conductivity, otherwise known as the coefficient of permeability. There are two standard laboratory test methods to determine the hydraulic conductivity of soil: 1. The constant head test method : used for permeable soils (k>104 cm/s) 2. The falling head test method : used for less permeable soils (k<104 cm/s) THEORY Falling head test method The falling head permeability test is a common laboratory testing method used to determine the permeability of fine grained soils with intermediate and low permeability such as silts and clays. This testing method can be applied to an undisturbed sample. Principal of the falling head method is based on Darcy’s law which was proposed by Henry Darcy, a French scientist in 1856. It is a simple equation for the discharge velocity of water through saturated soils.
v = ki where; v = Discharge velocity, which is the quantity of water flowing in unit time through a unit cross sectional area of soil at right angle to the direction of flow, k = Coefficient of permeability i = Hydraulic gradient The rate of flow of the water through the specimen at any time t can be given by, q=k
h dh A=−a l dt
where; q = flow rate a = crosssectional area of the standpipe A = crosssectional area of the soil specimen
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EN 14 5131 38
2 CE281Geotechnical Engineering I
Permeability Test
Figure 1: Diagram of the Fallinghead Method
The equation used to calculate the coefficient of permeability is: h al ln 0 A (t 1−t 0 ) h1
( )
k=
When the equation is arranged in the form of y = mx, ln
h 0 kA = (t 1−t 0 ) h1 al
( )
where; a = crosssectional area of the standpipe A = crosssectional area of the soil specimen l = length of the soil sample t1 – t0 = the time interval h0 = initial water level height from the bottom of the apparatus to the zero mark level of the stand pipe h1 = height measured with time from the bottom of the apparatus to the water level The coefficient of permeability (k) can be determined using the gradient (m) of the graph ln
h0 h1
( )
m=
against (t 1−t 0 ) .
kA al Therefore,
k=
mal A
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3 CE281Geotechnical Engineering I
Permeability Test
The coefficient of permeability is defined as the rate of flow of water under laminar flow conditions through a unit crosssectional area of a porous medium under a unit hydraulic gradient and standard temperature conditions. The unit of k is m/s.
MATERIALS AND APPARATUS 1. 2. 3. 4. 5. 6. 7.
Falling Head Permeability Apparatus Permeameter with its accessories. Standard soil specimen. Stop watch. Measuring jar. Meter scale. Container to collect excess water
Figure 2: Permeameter
Figure 3: Falling Head Permeability Apparatus
PROCEDURE 1. First, it has been checked whether the valve is closed and the tube connecting the permeameter and standpipe is tight, also a container has been place to collect the excess water falling from the valve. 2. Next, water has been filled in from the top of the glass standpipe up to the zero mark. 3. Soil specimen has been kept to get saturate for some time and when the water level dropped, again water has been filled up to the water zero mark level. 4. Then, h0 has been measured from the bottom of the apparatus to the zero mark level using the measuring tape. 5. The valve has been opened and water has been allowed to discharge through it for five minutes time interval. 6. After five minutes, the valve has been closed and h1 (height of the new water level from the bottom of the apparatus) has been recorded.
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4 CE281Geotechnical Engineering I
Permeability Test
7. Similarly record the height of water in the glass standpipe in every 5 minutes time interval for about 50 minutes. h0 8. Using the recorded readings the graph ln h 1
( )
against (t 1−t 0 ) has been plotted.
9. The coefficient of permeability, k has been found by the gradient of the graph.
CALCULATIONS Specimen Calculation 1. The crosssectional area (a) of the standpipe, A=
πd 2 4
0.02 (¿ ¿2) π 4 A=¿
A=3.143 x 10−4 m2
2. The crosssectional area (A) of the soil specimen, A=
πd 2 4
0.1 (¿ ¿2) π 4 A=¿ A=7.857 x 10−3 m2
h1 3. The gradient (m) of the graph ln h 2
( )
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m=
y 2− y 1 x 2−x 1
m=
0.888−0.121 ( 35−5 ) x 60
kA against ( t 2−t 1 ) is, m= a
EN 14 5131 38
5 CE281Geotechnical Engineering I
Permeability Test
−4 −1
m=4.26 x 10 s
4. The coefficient of permeability (k), k=
k=
mal A
( 4.26 x 10−4 ) (3.143 x 10−4 )(127.3 x 10−3 ) 7.857 x 10 −6
−3
−1
k =2.169× 10 ms
RESULTS
t (min)
h0 (cm)
h1 (cm)
h0 h1
ln
h0 h1
( )
0
140.2
140.2
1
0
5
140.2
124.2
1.29
0.121
10
140.2
110.2
1.272
0.241
15
140.2
97.3
1.441
0.365
20
140.2
85.7
1.636
0.492
25
140.2
75.3
1.862
0.622
30
140.2
65.9
2.127
0.755
35
140.2
57.7
2.430
0.888
40
140.2
50.3
2.787
1.025
45
140.2
43.9
3.194
1.161
50
140.2

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6 CE281Geotechnical Engineering I
Permeability Test −6
−1
The calculated coefficient of permeability, k =2.169× 10 ms
DISCUSSION
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7 CE281Geotechnical Engineering I
Chandrasena O.
Permeability Test
EN 14 5131 38
8 CE281Geotechnical Engineering I
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Permeability Test
EN 14 5131 38
9 CE281Geotechnical Engineering I
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Permeability Test
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10 CE281Geotechnical Engineering I
Permeability Test
CONCLUSION
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11 CE281Geotechnical Engineering I
Permeability Test
REFERENCES: Braja M. Das & Khaled Sobhan (2012) Principles of Geotechnical Engineering, 8th edition, United States. Permeability test, [Online], Available: http://www.dot.ca.gov/hq/esc/ctms/pdf/CT_220.pdf [25 July 2015]. Falling head permeability test, [Online], Available: http://www.controlsgroup.com/eng/soiltestingequipment/fallingheadpermeabilityapparatus.php [25 July 2015].
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