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Permeability Measurement of Granular Materials and Development of an

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Conference Paper · February 2017

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 Proceedings of International Conference on Planning, Architecture and Civil Engineering, 9 - 11 February 2017,
Rajshahi University of Engineering & Technology, Rajshahi, Bangladesh

Permeability Measurement of Granular Materials and Development of

an Equation

M. M. RAHMAN1, M. A. ALIM2, M. SHAHJALAL3

1
Department of Civil Engineering, PUST, Bangladesh (motiur.ce@gmail.com)
2
Department of Civil Engineering, RUET, Bangladesh (maalim@ruet.ac.bd)
3
Department of Civil Engineering, RUET, Bangladesh (shahjalal.ce@gmail.com)

Abstract

The study of the hydraulic conductivity (K) for flow of water through permeable soil media is important in soil
mechanics. It has been recognized that K is statistically related to the grain-size distribution. A series of
permeability test were conducted on five types granular soil (denoted by S-1, S-2, S-3, S-4 and S-5) taken from
different location of Bangladesh. It has been recognized that K is statistically related to the grain-size
distribution. In all, 40 specimens (total 200) of each type of soils were analyzed for grain size distribution, void
ratio and hydraulic conductivity according to ASTM code. The experimental values of hydraulic conductivity
were then compared to the values calculated using 5 different empirical equations which are commonly used to
estimate hydraulic conductivity from grain size analysis. In this study we develop a modified equation that
considerably improve the hydraulic conductivity estimates from grain size data. It was found that expected
hydraulic conductivity equation reduce the error of estimated values.

Keywords: Permeability, Grain-Size, Void Ratio, Hydraulic Conductivity.

1 Introduction

Permeability is defined as the property of porous material which permits the passage or seepage of water or other fluids
through its interconnecting voids. Permeability is considered one of the most important parameters in soil mechanics.
Permeability is measured by the coefficient of permeability or hydraulic conductivity (K). Basically, it is defined by the
quantity of water passing through a soil medium in a certain period, and is determined by in-situ and laboratory tests. In
common practice, the permeability coefficient is usually obtained by constant head permeability test, and is utilized in
filtration-drainage, settlement, and stability calculations. These problems are extremely important for environmental aspects
such as waste water management, slope stability control, erosion, and structural failure related with the ground settlement
issues. In this respect, empirical equations are utilized to predict these parameters; however, these equations have certain
limitations and uncertainties.

Freeze and Chery, 1979 has been recognized that hydraulic conductivity is related to the grain size distribution of granular
porous media. Uma et al., 1985 sampled six soils at seven different locations in the Alabama lower coastal plain and used
regression analysis to determine that percentage of clay sized particles was the best predictor of Ks. Rawls and Brakensiek,
1989 used field data across the U.S. to develop a regression equation that relates porosity and percentage of sand and clay
sized, particles in the sample to Ks. Jabro, 1992 estimated Ks from grain size and bulk density data. Ahuja et al., 1989
estimated Ks using the generalized form of the Kozeny-Carmen equation. Aiyamani and Sen, 1993 proposed the relation
between saturated hydraulic conductivity and soil particles diameters for 32 sandy soil samples.

The objective of this study is to determine the hydraulic conductivity (K) of studied granular materials, compare among the
commonly used empirical formulae and finally develop an empirical equation for granular materials from grain size analysis.

2 Results and Discussions

2.1 Grain-size Analysis

In this study five types sandy soils are used in this study which was collected from different location of
Bangladesh which is denoted by S-1 (Sample S-1 has been collected from Tista river, Rangpur of Bangladesh
which is locally called domer sand from grain size analysis it is found as medium sand), S-2 (Sample S-2 has
been collected from Panchagarh, Bangladesh which is locally called panchagarh sand from grain size analysis it

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 M. M. Rahman, M. A. Alim & M. Shahjalal
ICPACE 2017

is found as medium medium sand), S-3 (Sample S-3 has been collected from Sylhet, Bangladesh which is locally
called sylhet sand from grain size analysis it is found as coarse sand), S-4 (Sample S-4 has been collected from
Rajsahi, Bangladesh which is locally called local sand from grain size analysis it is found as find sand) and S-5
(Sample S-5 has been collected from Pabna, Bangladesh which is locally called padma sand from grain size
analysis it is found as find sand). The grain size distributions curve of soils are shown in Figure 1. By the
analysis of this the values of D5 (grain size corresponding to 5% finer), D10 (grain size corresponding to 10%
finer), D20 (grain size corresponding to 20 % finer), D50 (grain size corresponding to 50% finer), D60 (grain size
corresponding to 60% finer), Io (intercept of the line formed by D10 and D50 with the grain size axis), Cu
(uniformity coefficient) and FM (fineness modulus) are calculate to evaluate the studied established empirical
formulae and proposed empirical formula which are shown in Table 1.

Figure 1. Grain size distribution curve for selected five types of soil samples.

Table 1. Grain-size properties of samples.

D5 D10 D20 D50 D60 Io

Sample ID Cu FM
(mm) (mm) (mm) (mm) (mm) (mm)
S-1 0.25 0.21 0.31 0.70 0.75 3.57 0.16 2.58
S-2 0.31 0.22 0.32 0.50 0.65 2.71 0.l7 2.40
S-3 0.20 0.24 0.40 1.05 1.20 5.45 0.19 3.06
S-4 0.08 0.10 0.18 0.27 0.31 3.10 0.08 1.40
S-5 0.09 0.15 0.20 0.35 0.40 2.67 0.12 1.63

2.2 Basic Properties

Some basic properties are evaluated such as specific gravity, unit weight, OMC, maximum dry density for each
sample which is shown in Table 2. OMC and maximum dry density are calculate from the compaction curve
shown in Figure 2.

Figure 2. Compaction Curve

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 M. M. Rahman, M. A. Alim & M. Shahjalal
ICPACE 2017

Table 2. Basic properties of samples.

Specific Gravity OMC MDD

Sample ID
Gs (%) (kN/m3)
S-1 2.71 12.35 16.38
S-2 2.73 13.11 16.44
S-3 2.74 12.73 16.58
S-4 2.67 14.50 15.79
S-5 2.69 14.87 15.97

2.3 Controlling of Void Ration, e

In this study 4 different void ratio (0.70, 0.75, 0.80 and 0.85) are consider. The mold (size: dia. = 10 cm and
height = 14 cm) are filled with specified void ratio by the calculated soil mass which is shown in Table 3.

Table 3. Mass of sample for various soil sample

V
Void
Volume Vs  Mass of the Sample,
M s  Vs G w
Ratio,
of Mold,
Volume of Sample, 1 e
V (gm)
e (cm3)
(cm3)
S-1 S-2 S-3 S-4 S-5 S-1 S-2 S-3 S-4 S-5
0.70 1099.56 646.8 646.8 646.8 646.8 646.8 17195.2 17322.1 17385.6 16941.4 17068.3
0.75 1099.56 628.3 628.3 628.3 628.3 628.3 16704.0 16827.2 16888.9 16457.4 16580.7
0.80 1099.56 610.9 610.9 610.9 610.9 610.9 16240.0 16359.8 16419.7 16000.2 16120.1
0.85 1099.56 594.4 594.4 594.4 594.4 594.4 15801.0 15917.6 15976.0 15567.8 15684.4

2.4 Permeability Test Program and Procedure

A series of 200 constant head permeability tests were carried out on 5 soil samples referred to as sample S-1, S-2,
S-3, S-3 and S-5. 40 tests were performed for 4 different void ratio (0.70, 0.75, 0.80 and 0.85) on each sample.
10 test were done for each void ratio and average value of this 10 permeability test is considered. To carry out
these tests, a permeameter was placed on a table in the laboratory. After removing the air in the flexible rubber
tubing connecting the tube, the outlet tube of the constant head tank was connected to the inlet nozzle of the
permeameter. The hydraulic head was measured by a meter scale from the bottom outlet of the permeameter to
the water surface in the overhead tank. Stop watch was started and at the same time a beaker was put under the
outlet of the permeameter. The test was run for some convenient time interval. The quantity of water collected in
the beaker was measured during that time. The test was repeated twice more under the same head and for the
same time interval. The temperature of the room was measured by the thermometer.

2.5 Proposed Empirical Equation

The main reason of this study to develop an empirical formulae for hydraulic conductivity (K) based on grain
size distribution. For this reason 200 permeability test were carried out in laboratory and compere these test
result with various parameters from grain-size distribution analysis. Here to develop an empirical formula for
hydraulic conductivity we consider hydraulic conductivity is the function of void ratio, D10, D60, Cu, and fineness
modulus. Mathematically,

K  f (e, D10 , D60 , Fm ,C u ) (1)

By this study, proposed empirical formula

500
K  5  10 5  e  Exp ( Fm )  log (2)
Cu

Where K= hydraulic conductivity (m/sec.), e = void ratio, Fm = fineness modulus and Cu = uniformity coefficient
(Cu= D60/D10, D10 and D60 represent grain size in mm corresponding to 10% and 60% finer
respectively.

2.6 Comparison with Test Result

After conducting laboratory test our result is compared with another five empirical formulae and our proposed
equation. In this study to compare our result we consider empirical formulae which was developed by Hazen,

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 M. M. Rahman, M. A. Alim & M. Shahjalal
ICPACE 2017

Kozeny-Carman, Terzaghi, Vukovic and Soro, Breyer. Table 4 shows the details about these five established
formulae.

Table 4. Empirical equations manifested for permeability prediction of soils

Researcher Equation Limitations, Advantages/Disadvantages

2 Effective diameter changes between 0.1 and 30
Hazen (1892) K  CH d 10 mm (Hazen, 1892; Carrier III, 2003).
Kozeny- g n3 d10<3 mm, for granular soils, the inertia term is not
Carman K  8.3  10 3 [ ]d102 taken into account (Carrier III, 2003).
(1956)  (1  n) 2

2 The selected average value of 0.0084 is actually a

Terzaghi g  n  0.13  2
(1964)
K   Ct   3  d10 classification coefficient typically ranging between
  1 n  0.0061 and 0.00107
g 500 2
Breyer (1998) K   6  10  4 log d10 Cu= 1~20, d10= 0.06~0.6 mm.
 U
Alyamani and The method is more accurate for well-graded
Sen (1993)
K  1300  [ I o  0.025(d 50  d10 )]2 sample (Odong, 2008).

Table 5 shows the variation of the value of hydraulic conductivity estimated from grain-size analysis with respect
to laboratory test results. From this table we show that the estimated value using proposed equation is near with
laboratory test results compared to other established formulae.

Table 5. Comparison of the hydraulic conductivity from test result using various empirical formulae.

Average (10) Estimated Value of Hydraulic Conductivity, K (m/s)

Sample Void value of K
Proposed Kozeny- Alyamani
ID Ratio, e (Laboratory Hazen Terzaghi Breyer
Equation Carman and Sen
Test)
0.70 3.79E-04 3.74E-04 4.85E-04 5.32E-04 4.11E-04 5.57E-04 4.46E-04
0.75 4.07E-04 4.01E-04 4.85E-04 6.36E-04 4.70E-04 5.57E-04 4.46E-04
S-1
0.80 4.35E-04 4.28E-04 4.85E-04 7.51E-04 5.32E-04 5.57E-04 4.46E-04
0.85 4.76E-04 4.55E-04 4.85E-04 8.76E-04 5.94E-04 5.57E-04 4.46E-04
0.70 3.85E-04 3.73E-04 5.18E-04 6.95E-04 5.37E-04 7.68E-04 4.69E-04
0.75 4.30E-04 4.00E-04 5.18E-04 8.31E-04 6.14E-04 7.68E-04 4.69E-04
S-2
0.80 4.55E-04 4.27E-04 5.18E-04 9.80E-04 6.94E-04 7.68E-04 4.69E-04
0.85 4.90E-04 4.53E-04 5.18E-04 1.14E-03 7.76E-04 7.68E-04 4.69E-04
0.70 3.93E-04 3.95E-04 4.36E-04 5.84E-04 4.51E-04 5.59E-04 6.68E-04
0.75 4.08E-04 4.23E-04 4.36E-04 6.98E-04 5.16E-04 5.59E-04 6.68E-04
S-3
0.80 4.49E-04 4.51E-04 4.36E-04 8.24E-04 5.84E-04 5.59E-04 6.68E-04
0.85 4.75E-04 4.80E-04 4.36E-04 9.61E-04 6.52E-04 5.59E-04 6.68E-04
0.70 2.29E-04 2.61E-04 1.58E-04 1.74E-04 1.34E-04 1.94E-04 1.06E-04
0.75 2.49E-04 2.80E-04 1.58E-04 2.08E-04 1.54E-04 1.94E-04 1.06E-04
S-4
0.80 2.72E-04 2.99E-04 1.58E-04 2.45E-04 1.74E-04 1.94E-04 1.06E-04
0.85 2.98E-04 3.17E-04 1.58E-04 2.86E-04 1.94E-04 1.94E-04 1.06E-04
0.70 2.56E-04 2.85E-04 2.48E-04 2.72E-04 2.10E-04 3.01E-04 2.35E-04
0.75 2.66E-04 3.06E-04 2.48E-04 3.25E-04 2.40E-04 3.01E-04 2.35E-04
S-5
0.80 2.78E-04 3.26E-04 2.48E-04 3.83E-04 2.71E-04 3.01E-04 2.35E-04
0.85 3.10E-04 3.46E-04 2.48E-04 4.47E-04 3.03E-04 3.01E-04 2.35E-04

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 M. M. Rahman, M. A. Alim & M. Shahjalal
ICPACE 2017

Figure 3. Variation of Hydraulic Conductivity (K) of Each Sample for Various Empirical Formula.

By the graphical representation (Figure 3) we show that the variation of value of K for proposed equation is less
in compared to other empirical formulae for all samples.

3 Conclusion

Estimating the hydraulic conductivity of soils in terms of grading characteristics can relatively lead to
underestimation or overestimation unless the appropriate method is used. For the studied samples, and
consequently may be for a wide range of soil type, the best overall estimation of permeability is reached based on
Alyamani & Sen for S-1 & S-2, Hazen for S-3, Kozeny-Carman for S-4 and Breyer for S-5. Alyamani and Sen
formula is very sensitive to shape of the grading curve and as such should be used with care. The new suggested
formulae give the better estimation in compared to other formulae. This study is done only for sandy type soil so
this new proposed empirical formula is applicable only for sand.

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