KIRK - Falling Head Permeability Test (100%)

Kirk Woo Chong – 809003758 CVNG 2009 – Soil Mechanics II

TABLE OF CONTENTS

Objective..........................................................................................................................3

Introduction......................................................................................................................3

Equipment........................................................................................................................3

Procedure.........................................................................................................................4

Results.............................................................................................................................6

Calculations......................................................................................................................7

Discussion........................................................................................................................9

Errors and Precautions..................................................................................................10

Conclusion.....................................................................................................................11

References.....................................................................................................................11

APPENDIX.....................................................................................................................12

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OBJECTIVE

The aim of the experiment was to determine the coefficient of permeability of red

sand by use of the falling-head method.

INTRODUCTION

Permeability is a soil property which indicates the ease with which water will flow

through the soil (Lambe, 1951), and is dependant upon a number of properties of the

soil which include the grain size, void ratio, shape and arrangement of pores, degree of

saturation and properties of the pore fluid.

Data on the value of the permeability of a given soil has many practical

engineering applications, since this property would come into play in matters such as

drainage, soil behavior under load, groundwater supply and seepage under structures.

In general, permeability has a significant role in the effective strength of a soil and thus

its knowledge is of great importance.

The method being used to determine permeability (also known as coefficient of

permeability) in this experiment is the falling-head test (see FIGURE 1 for required

apparatus) which is used in the case of fine-grained soils.

EQUIPMEN T

o Permeability device

o Cylindrical mould

o Upper and lower porous stones

o Porosity ring

o Spring

o Burette

o Retort stand

o Meter rule

o Beaker

o Measuring cylinder (100ml)

o Stopwatch

o Thermometer

o Electronic balance

o Spatula

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o Tamping hammer

o Metal basin

o Moisture can

o Vernier caliper

o Drying oven

o Mechanical grease

PROCEDURE

1) An electronic balance was used to determine the masses of the cylindrical

mould, porosity ring, upper and lower porous stones, tamping hammer, metal

basin and moisture can which were all recorded.

2) A sample of the red sand to be used was also weighed and placed in the drying

oven so that the moisture content could thereafter be found.

3) The vernier caliper was used to determine the internal diameter of the cylindrical

mould.

4) The bottom ring of the permeability device was greased before the cylindrical

mould was put in place so that water would not leak from the mould. The bottom

porous stone was then inserted.

5) Three layers of the red sand were then placed into the cylindrical mould; each

layer was stamped by the tamping hammer 25 times at a height of 2 inches

above the sand layer.

6) A spatula was then used to even out any red sand which may have stuck to the

sides of the mould.

7) The height of the column of sand was then measured using a vernier caliper.

8) The weight of the cylindrical mould and column of packed sand was then

obtained.

9) The components were then refitted into the bottom portion of the permeability

device.

10)The upper porous stone was then placed over the compacted sand, followed by

the spring and then the greased upper portion of the permeability device, which

was fastened in place by the 3 fastening screws.

11)The valve controlling the water was then opened in order to saturate the sample

and remove any clogs and loose sand from the apparatus, until the water began

to run clear.

12)It was ensured that the apparatus was set up as shown in FIGURE 2.

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13)The initial height of the water in the burette, h1, was measured using the meter

rule, noted and the valve was opened in order to allow the flow of water for 30

seconds through the permeability device and into a beaker, at which point the

valve was closed.

14)The final height of water in the burette, h2, was also noted.

15)The amount of water that flowed into the permeability device, Qin, was read off

and recorded from the burette.

16)The amount of water that flowed out, Qout, was collected from the beaker and

measured in a measuring cylinder.

17)The temperature of the water collected was measured and recorded using a

thermometer.

18)Steps 13 to 17 were then repeated until 3 viable sets of readings were obtained.

19)After step 18 was completed, the saturated soil sample was removed from the

device, placed in the metal basin and reweighed, and placed in the drying oven.

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RESULTS

Test no h1 / cm h2 / cm t /s Qin / cm3 Qout / cm3 T / °C

1 90 54.7 30 61.3 61.0 27

2 90 54.7 30 61.2 61.0 27

3 90 54.3 30 61.8 61.5 27

Average 90 54.6 30 61.4 61.2 27

TABLE 1 SHOWING THE RAW DATA OBTAINED FROM THE FALLING HEAD TEST

Component Mass / g Component Mass / g

Cylindrical mould 159.90 Moisture can 31.19

Porosity ring 6.66 Moisture can & sample 85.00

Upper porous stone 38.62 Moisture can and oven dried sample 83.62

Lower porous stone 40.12 Mould & compacted sand 487.25

Tamping hammer 1271.32 Metal basin & saturated sample 504.27

Metal basin 127.40 Metal basin & oven dried sample 441.80

TABLE 2 SHOWING THE MASSES OF THE VARIOUS COMPONENTS USED FOR THE EXPERIMENT

Measurement 1 2 3 Average / mm

Internal diameter of mould 63.45 63.62 63.70 63.59

Height of sand column 65.00 66.00 67.00 66.00

TABLE 3 SHOWING THE VARIOUS LENGTH MEASUREMENTS USED FOR THE EXPERIMENT

Coefficient of permeability at 27°C 5.95 x 10-3 cm/s

Coefficient of permeability at 20°C 5.06 x 10-3 cm/s

Void ratio of soil sample 0.71

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Moisture content of soil sample 2.56 %

TABLE 4 SHOWING THE CALCULATED PROPERTIES OF THE SOIL SAMPLE

CALCULATIONS

Average hydraulic head across sample at end of test,

h2 = 54.7+54.7+54.3

3 = 54.6 cm

Average volume of water entering permeability device,

Qin = 61.361.2+61.8

3 = 61.4 cm3

Average volume of water leaving permeability device,

Qout = 61.061.0+61.5

3 = 61.2 cm3

Average length of the sample,

L = 65+66+67

3 = 66 mm = 6.6cm

Average diameter of the sample,

d = 63.45+63.62+63.70

3 = 63.59 mm = 6.36 cm

Cross sectional area of the burette,

a = Qout

h1−h2 =

61.290−54.6 = 1.72 cm2

Cross sectional area of soil sample,

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A = π x d2

4 = π x 6.362

4 = 31.77 cm2

Volume of soil sample,

V = A x L = 31.77 x 6.6 = 209.68 cm3

Coefficient of permeability at conducted temperature (27°C),

k = aLAtln

h1h2

= 2.303 aLAtlog

h1h2

= 2.3031.72x 6.631.77 x30

l og9054.6

= 5.95 x 10-3 cms-1

Coefficient of permeability at 20°C,

k20°C = k27°C η27 °Cη20° C

= 5.95 x 10-3 x 0.85021

= 5.06 x 10-3 cms-1

Potential energy generated by tamping hammer,

Ep = mgh = 1.27 x 9.81 x 5.08 x 10-2 = 6.33 x 10-1J

Impact velocity of tamping hammer,

v = √2gh = √2x 9.81 x5.08 x10−2 = 9.98 x 10-1 ms-1

Kinetic energy generated by tamping hammer,

Ek = mv2

2 = 1.27 x (9.98 x 10−1 )2

2 = 6.32 x 10-1J

Dry density of specimen,

ρd = M2−M 1

V = 487.25−159.9

209.68 = 1.56 gcm3

Void ratio of specimen,

e = Gs ρw

ρd - 1 =

2.66 x11.56

- 1 = 0.71

Moisture content of sample,

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w(%) = originalweight of soil−dry weight of soil

originalweight of soil x 100 =

53.81−52.4353.81

x 100 =

2.56%

DISCUSSION

The soil sample used for the experiment (see FIGURE 3) was red sand from the

National Quarries Trinidad Limited, located in the Arouca area. A basic inspection of

the sample reveled that the soil consisted of more or less same sized small grained

particles consistent with that of fine sand. It was also loose and easily crumbled to the

touch. Based on this assessment, a falling-head test (a derivation for this method could

be found in the APPENDIX) was considered suitable for the fine grained material.

The experiment objective was to determine the coefficient of permeability for this

sample and the method employed was the falling-head permeability test. This

technique involved obtaining the volume of water which flowed into and out of the

sample soil in a given time, and in conjunction with other data which could be measured

or calculated from the experiment, the coefficient of permeability was found. The

principle behind this method is based on the concept that a fluid (in this case water)

would flow through different types of soils at different rates. This is privy to the fact that

soil parameters such as the particle size, void ratio and arrangement of pores all

contribute to the pattern and ease of flow through a soil.

With respect to the actual raw experimental data obtained (see in APPENDIX), it

could be seen that there was actually a difference in the volume of water which flowed

into and out of the permeability device. This difference could be mainly attributed to

some of the water filling up the pore spaces within the soil sample. Since the sample

was saturated before the trials were run, none of the water was really taken to “wet” the

particles of the sample.

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When the relevant calculations were conducted, it was found that the coefficient

of permeability for the sample at the conducted temperature of 27°C was 5.95 x 10-3

cms-1, and the coefficient of permeability for the sample at 20°C was 5.06 x 10-3 cms-1,

which corresponds to a soil with good drainage characteristics of medium to high

permeability classification of the general soil type clean sands (see FIGURE 4 for

classification table).

It was convenient to calculate the permeability value for 20°C since it is at this

temperature that the coefficient of permeability is taken as 100%. This variation occurs

because of the permeability being dependent on temperature as a result of the viscosity

of the permeating fluid being affected. Hence a correction factor (see FIGURE 5) was

applied in order to work things to an acceptable standard.

The falling head method obtains the coefficient of permeability to a reasonable

level of accuracy; however there are a number of limitations which prevent the result

from being ideally representative of the actual soil conditions. These include the lack of

in situ pressures, no horizontal flow gradient and variations in soil strata. The method

can thus be improved by implementing a triaxial cell and flexible wall membrane.

ERRORS AND PRECAUTIONS

o Multiple readings were taken for all measurements of length and mass, and the

average value was used to obtain a higher degree of accuracy.

o The bottom ring and upper component of the permeability device were greased

to prevent/ minimize leaking of the water which would have introduced an error

when inspecting Qin and Qout.

o A standard was used when preparing the soil sample (3 layers, 25 blows, a

height of 2 inches above sample) in order so that the results may be reproduced.

o The sample was allowed to become saturated so that each so that each trial

would take place under similar conditions.

o Water was allowed to flow through the sample before the trials were conducted

to allow any clogs and excess loose sand to be removed.

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o There would have been an inaccuracy in the result for Qout as some of the water

could have been left in the beaker in the transfer.

o The graduations in the measuring cylinder and only allowed for an accuracy of

±0.5cm3.

o The experiment was carried out in a controlled temperature environment (via air

conditioning unit) in order to help keep the ‘T’ values for the Qout constant.

o When the cylindrical mould and sample are weighed, some of the grease used

would have been on the mould and thus there may be a small error in using this

value for calculation purposes, however this may not have made any significant

difference but is stated for the sake of completeness.

CONCLUSION

Within the limits of experimental error, it was found that:

1) The coefficient of permeability for the sample at the conducted temperature of

27°C was 5.95 x 10-3 cms-1.

2) The coefficient of permeability for the sample at 20°C was 5.06 x 10-3 cms-1.

3) The soil sample may have been classified as a soil with good drainage

characteristics of medium to high permeability of the general soil type clean

sands.

REFERENCES

Craig, R. F. (2004). Soil Mechanics (7th edition). Taylor and Francis, April 2004.

Lambe, William T. Soil Testing for Engineers. John Wiley and Sons Inc, 1967.

Mitchell, James K.. (1993). Fundamentals of Soil Behavior. Second edition. John

Wiley and Sons, New York.

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Bowles, Joseph E. Engineering Properties of Soils. 4th. Boston: Irwin McGraw–

Hill, 1992.

Budhu, Muni. Soil Mechanics and Foundations. John Wiley and Sons Inc, 2000.

APPENDIX

F IGURE 1 SHOWING THE

REQUIRED

APPARATUS FOR THE

EXPERIMENT

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FIGURE 2 SHOWING THE SETUP FOR

THE EXPERIMENT

FIGURE 3 SHOWING THE SOIL SAMPLE USED FOR THE EXPERIMENT

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FIGURE 4 SHOWING THE BREAKDOWN OF CLASSIFICATIONS BASED ON THE COEFFICIENT OF

PERMEABILITY

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FIGURE 5 SHOWING THE VISCOUSITY CORRECTION TABLE USED IN THE EXPERIMENT

FALLING-HEAD TEST DERIVATION

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Let the drop in head over a period of time define the velocity by: v = - δhδt

And inflow of water to soil is: (qv)in = av = - a δhδt

Inspect Darcy’s law to obtain outflow by: (qv)out = Aki = Ak hL

Observing the continuity condition gives: - a δhδt

= Ak hL

Separation of the variables and integrating between limits: AkaL

∫t1

t2

δt = -∫h1

h2δhh

Solving for k in the vertical direction would then give:

k = aLA ¿¿ ln (

h1h2

)

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KIRK - Falling Head Permeability Test (100%)