predicting the permeability of sandy soils from grain size distributions

8/19/2019 PREDICTING THE PERMEABILITY OF SANDY SOILS FROM GRAIN SIZE DISTRIBUTIONS

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Thesis written by

Emine Mercan Onur

B.S., Middle East Technical University, 2009

M.S., Kent State University, 2014

Approved by

___________________________________, Advisor

___________________________________, Chair, Department of Geology

___________________________________, Dean, College of Arts and Sciences


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TABLE OF CONTENTS

LIST OF FIGURES ........................................................................................................... vi

LIST OF TABLES ........................................................................................................... xiii

ACKNOWLEDGEMENT ............................................................................................... xiv

ABSTRACT ........................................................................................................................ 1

CHAPTER 1: INTRODUCTION ....................................................................................... 3

1.1 Background ............................................................................................................. 3

1.2 Factors affecting Permeability ................................................................................ 4

1.2.1 Effect of Grain Size and Grain Size Distribution ...................................................... 5

1.2.2 Effect of Density and Void Ratio ............................................................................... 7

1.2.3 Effect of Soil Texture and Structure .......................................................................... 7

1.3 Previous Investigations ........................................................................................... 7

1.4 Objectives of the Study ......................................................................................... 11

CHAPTER 2: RESEARCH METHODS .......................................................................... 13

2.1 Sample Collection and Preparation ....................................................................... 13

2.2 Laboratory Investigations ..................................................................................... 13

2.2.1 Grain Size Distribution Test .................................................................................... 13

2.2.2 Compaction Test ...................................................................................................... 15

2.3 Data Analysis ........................................................................................................ 18

2.3.1 Statistical Analysis ................................................................................................... 18

2.3.2 Modeling of Data ..................................................................................................... 20

CHAPTER 3: DATA PRESENTATION ......................................................................... 22

3.1 Grain Size Distribution ......................................................................................... 22


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3.1.1 Grain Size Distribution by Sieve Analysis .............................................................. 22

3.1.2 Grain Size Distribution by the Camsizer Video Grain Size Analyzer ..................... 24

3.1.3 Comparison of Sieve Analysis and the Camsizer Video Grain Size Analyzer ........ 26

3.2 Compaction Test Data ........................................................................................... 32

3.3 Permeability Data.................................................................................................. 32

CHAPTER 4: EFFECT OF GRAIN SIZE DISTRIBUTION AND DENSITY ON

PERMEABILITY ............................................................................................................. 41

4.1 Statistical Analysis ................................................................................................ 41

4.1.1 Statistical Evaluation of Data ................................................................................... 41

4.1.2 Bivariate Analysis .................................................................................................... 44

4.1.3 Multiple Regression Analysis .................................................................................. 51

4.2 New Permeability Index ....................................................................................... 57

4.3 3-D Prediction Model ........................................................................................... 64

CHAPTER 5: DISCUSSION ............................................................................................ 68

CHAPTER 6: CONCLUSIONS AND RECOMENDATIONS ..................................... 76 6

6.1 Conclusions ........................................................................................................... 76

6.2 Recomendations .................................................................................................. 77 7

REFERENCES ............................................................................................................... 78 8

APPENDIX A: GRAIN SIZE DISTRIBUTION PLOTS ................................................ 81

APPENDIX B: COMPACTION AND PERMEABILITY DATA ................................ 92 2

APPENDIX C: HISTOGRAMS OF NON-TRANSFORMED DATA .......................... 94 4

APPENDIX D: HISTOGRAMS AND P-P PLOTS OF TRANSFORMED DATA ........ 99


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APPENDIX E: BIVARIATE ANALYSIS PLOTS OF NON-TRANSFORMED DATA

....................................................................................................................................... 108 8

APPENDIX F: CALCULATION OF NEW PERMEABILITY INDEX ..................... 116 6

APPENDIX G: GRAIN SIZE DISTRIBUTION, DENSITY, PERMEABILITY, AND

NEW PERMEABILITY INDEX DATA FOR THE THREE SOILS (#7 AND 8) USED

FOR VALIDATION PURPOSE .................................................................................... 119


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LIST OF FIGURES

Figure 1.1: Typical grain size distribution curve with commonly used grain size indices ..6

Figure 1.2: Particle shape characterization: (a) chart for visual estimation of roundness

and sphericity (from Krumbein and Sloss, 1963). (b) Examples of particle

shape characterization (from Powers, 1953) ......................................................8

Figure 1.3: Diagram showing horizontal flow through grains (From Das, 2008) ...............8

Figure 2.1: Six sandy soils used in the study .....................................................................14

Figure 2.2: (a) Camsizer video grain size analyzer for grain size distribution analysis; (b)

close up view of grains before falling ..............................................................16

Figure 2.3: Standard compaction test apparatus ................................................................17

Figure 2.4: Constant head permeability test set up ............................................................17

Figure 3.1: Grain size distribution of six soil samples by sieve analysis ..........................23

Figure 3.2: Grain size distribution curves by Camsizer video grain size analyzer. Soil 3,

results of Brooks study, was not available to test by camsizer ........................25

Figure 3.3: Comparison of D 10 values by sieve analysis and Camsizer video grain size

analyzer ............................................................................................................27


analyzer ............................................................................................................27


analyzer ............................................................................................................28

Figure 3.6: Comparison of C u values by sieve analysis and Camsizer methods ...............28


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Figure 3.7: Comparison of C c values by sieve analysis and Camsizer video grain size

analyzer ...........................................................................................................29

Figure 3.8: Comparison of %C values by sieve analysis and Camsizer video grain size

analyzer ...........................................................................................................29

Figure 3.9: Comparison of %M values by sieve analysis and Camsizer video grain size

analyzer ...........................................................................................................30

Figure 3.10: Comparison of %F values by sieve analysis and Camsizer video grain size

analyzer ...........................................................................................................30

Figure 3.11: Comparison of Hazen permeability (k Hazen ) values by using D 10 values both

fromsieve analysis and the Camsizer video grain size analyzer ......................31

Figure 3.12: Permeability (top) and compaction (bottom) curves for soil 1 .....................34






Figure 4.1: Matrix of bivariate scatterplots of non-transformed data. Numbers on left of

the matrix represent the row numbers and numbers at the bottom of the

matrix are the column numbers. Pearson’s correlation coefficient (r) values

are shown in red on the top of the individual plots ........................................45

Figure 4.2: Matrix of bivariate scatter plots of transformed data with Pearson’s

correlation coefficients (r) value shown on the top of each plot ....................46


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Figure 4.3: (a) Permeability vs. percentage of medium sand size (%M) at different

densities. Red square represents loose state permeability; (b) at maximum dry

density (MDD) ...............................................................................................48

Figure 4.4: (a) Permeability vs. D 10 at different densities. Red square represents loose

state permeability; (b) at maximum dry density (MDD) ................................49

Figure 4.5: Transformed data of permeability vs. percentage of medium sand size(%M).50

Figure 4.6: Transformed data of permeability vs. D 10 .......................................................51

Figure 4.7: Frequency distribution of standardized residual values ..................................55

Figure 4.8: Scatter plot of standardized residual and predicted values..............................55

Figure 4.9: Measured versus predicted values of permeability .........................................56

Figure 4.10: Grain size distribution of soil 5 for calculation of new permeability index ..58

Figure 4.11: Relationship between permeability index and permeability with a prediction

equation; Ln (Permeability) =1.19 – 0.22 (Permeability Index) + 0.006

(Permeability Index) 2 ....................................................................................60

Figure 4.12: Measured versus predicted values of permeability for all density based on

Equation 8. Soil 7 and 8 used for validation are represented by the red points.

........................................................................................................................62

Figure 4.13: Measured versus predicted values of permeability for average density. Soil 7

and 8 used for validation are represented by the red point.. ...........................63

Figure 4.14: 3-D plot of permeability index, density, and permeability. The color scale

represents permeability values in 10 -3 cm/sec units .......................................64


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Figure A-9: Comparison of grain size distributions of soil 5 by sieve analysis and

Camsizer video grain size analyzer ................................................................90


Camsizer video grain size analyzer ................................................................91

Figure C-1: Frequency distribution of permeability and density .......................................95

Figure C-2: Frequency distribution of D 10 and C u, ...........................................................96

Figure C-3: Frequency distribution of Cc and %C ............................................................97

Figure C-4: Frequency distribution of %M and %F ..........................................................98

Figure D-1: Frequency histograms (left) and p-p plots (right) of transformations of

permeability with r 2, skewness (Sk), D’Agostino -Pearson test score (DP), and

Kolmogorov-Smirnov test score (KS) ..........................................................100


density with r 2, skewness (Sk) , D’Agostino -Pearson test score (DP), and


Figure D-3: Frequency histograms (left) and p-p plots (right) of transformations of D 10

with r 2, skewness (Sk), D’Agostino -Pearson test score (DP), and



coefficient of uniformity (C u) with r 2, skewness (Sk), D’Agostino -Pearson

test score (DP), and Kolmogorov-Smirnov test score (KS) .........................103


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coefficient of curvature (C c) with r 2, skewness (Sk), D’Agostino -Pearson test

score (DP), and Kolmogorov-Smirnov test score (KS) ................................104


percent of coarse sand size (%C) with r 2, skewness (Sk), D’Agostino -Pearson



percent of medium sand size (%M) with r 2, skewness (Sk), D’Agostino -

Pearson test score (DP), and Kolmogorov-Smirnov test score (KS) ...........106


percent of fine sand size (%F) with r 2, skewness (Sk), D’Agostino -Pearson


Figure E-1: (a) Permeability vs. all measured density. Red square represents loose state

permeability; (b) permeability vs. maximum dry density (MDD) ...............109

Figure E-2: (a) Permeability vs. D 10 at all density. Red square represents loose state

permeability; (b) at maximum dry density (MDD) ......................................110

Figure E-3: (a) Permeability vs. coefficient of uniformity (C u) at all density. Red square

represents loose state permeability; (b) at maximum dry density (MDD) ...111

Figure E-4: (a) Permeability vs. coefficient of curvature (C c)at all density. Red square

represents loose state permeability; (b) at maximum dry density (MDD) ...112


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Figure E-5: (a) Permeability vs. percentage of coarse sand size (%C) at all density. Red

square represents loose state permeability; (b) at maximum dry density

(MDD) ..........................................................................................................113

Figure E-6: (a) Permeability vs. percentage of medium sand size (%M) at all density. Red


(MDD) ..........................................................................................................114

Figure E-7: (a) Permeability vs. percentage of fine sand size (%F) at all density. Red


(MDD) ..........................................................................................................115

Figure G-1: Grain size distribution of soil 7 for calculation of new permeability index. 120

Figure G-2: Permeability (top) and compaction (bottom) curves for soil 7 ....................121

Figure G-3: Grain size distribution of soil 8 for calculation of new permeability index .121

Figure G-4: Permeability (top) and compaction (bottom) curves for soil 8 ....................123


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ACKNOWLEDGEMENT

First and foremost, I would like to express my gratitude to my supervisor Dr.

Abdul Shakoor for his guidance, patience, help and support in every stages of this thesis.

Without the support, encouragement and advices of him this thesis would not be possible.

I would also like to thank to my committee members Dr. Ortiz and Dr. Hacker for their

valuable advices, suggestions and comments.I am grateful to Dr. Kazim Khan for contributions in mathematical modeling. My

sincere thank goes to Dr. Neil Well for his time and helping me to improve my

background in statistical analysis. I would like to thank to Merida for her help on

technical issues.

Funding for this project was generously provided by the Turkish Petroleum

Pipeline Corporation. I am indebted to the company for their financial supports in this

master’s project.

At last but not the least, I would like to express to my gratitude to my parents

Fatos Mercan and Koksal Onur, to my sister Selcan Onur and to my friend Yinal Huvaj.

My parents have been my best friends all my life and thank them for all their advice,

encouragements, and support.


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ABSTRACT

Permeability is one of the most important and frequently used properties of soils.

Grain size distribution and density are known to influence the permeability of sandy soils.

Although the relationships between grain size distribution and permeability has been

quantified in previous studies, the influenced of density has not been quantified. The

objective of this research was to investigate the quantitative relationships between

permeability and grain size distribution indices such as effective particle size (D 10),

coefficient of uniformity (C u), coefficient of curvature (C c), percentage of coarse sand

fraction by weight of sample (%C), percentage of medium sand fraction by weight of

sample (%M), and percentage of fine sand fraction by weight of sample (%F) to

determine whether these relationships could be used for reliable estimates of

permeability. Six samples of sandy soils, ranging from well graded to poorly graded,

were tested in the laboratory to determine their grain size distribution, maximum dry

density (MDD), and optimum water content (OWC). The D 10, Cu, C c, %C, %M, and %F

values for each soil were calculated from the grain size distribution plots. Based on the

compaction curves, five replicate samples of each soil were prepared at varying dry

density values and tested for permeability using the constant head permeability test.

Results show that the lowest permeability for sandy soils is achieved at or slightly

on the dry side of OWC. To investigate the relationship between permeability and grain

size distribution indices, bivariate and step-wise regression analyses were performed.


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The results show that D 10, density, and %M have the strongest correlation (Adjusted R 2 =

0.67) with permeability, explaining 67% of the variability in permeability.

Permeability depends on the sizes and shapes of interconnections between

adjacent pores which, in turn, are influenced by the entire grain size distribution. This

research proposes a new grain size distribution index for predicting permeability,

designated as the “ new pe rmeability index”. In addition to considering the entire grain

size distribution, the new permeability index assigns different weights to different size

fractions in the soil with the finest fraction having the maximum weight and the coarsest

fraction having the least weight. The new permeability index values for the six soils were

correlated with their corresponding permeability values, resulting in a second order

quadratic equation with an R 2 value of 0.76. This relationship can reliably be used to

predict permeability as is indicated by the small amount of residuals between measured

and predicted values of permeability.

A 3-D model was developed to show the combined effect of the new permeability

index and density on permeability.


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variable properties, varying in both horizontal and vertical directions (Jabro, 1992). This

is particularly true for glacial soils which are heterogeneous in nature. In a laboratory,

permeability is usually measured on small samples which do not represent the

heterogeneity of soils in the field (Holtz et al., 2011). No matter how many samples are

tested in the laboratory, one cannot reliably estimate permeability. In addition, reliability

of laboratory test results depends on the quality of undisturbed soil samples collected in

the field (Holtz et al., 2011). Since undisturbed samples cannot be obtained for granular

soils, the accuracy of permeability test results for such soils depends on how well the soil

structure and density of laboratory samples represent the natural state of soil in the field

(DeGroot et al., 2012). To overcome this problem, field pumping tests are generally used

for major engineering projects. However, performing a series of field pumping tests is

both expensive and time consuming (Shepherd, 1989; Jabro, 1992). Also, in situ methods

usually measure horizontal permeability (DeGroot et al., 2012). Because of these

limitations of laboratory and field methods, many researchers (Hazen, 1892; Kozeny,

1927 and Carmen, 1956; Terzagi and Peck, 1964; Kenney et al., 1984; Alyamani and

Sen, 1993) have attempted to develop empirical equations for predicting permeability

from grain size distribution parameters.

1.2 Factors affecting Permeability

Permeability is a complex property that is controlled by physical properties of

both the soil and the permeating fluid (DeGroot et al., 2012). At a constant temperature of

20°C, the common room temperature, the viscosity and unit weight of water remain


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constant. Therefore, physical properties such as grain size distribution, density, void ratio,

and soil texture and structure affect the magnitude of permeability.

1.2.1 Effect of Grain Size and Grain Size Distribution

Grain size distribution of granular soils affects their permeability (Freeze and

Cherry, 1979). There are several ways to characterize grain size distribution of a granular

soil. Commonly used indices include coefficient of uniformity (10

60

D

DC

u ), coefficient of

curvature (6010

230

c DDD

C ), particle sizes, D 10 , D30, and D 60, where D 10, D 30, and D 60 are

particle sizes, in mm, of 10%, 30%, and 60%, by weight of soil, passing the respective

sieve sizes (Figure 1.1). C u is an important shape factor that represents the degree of

sorting of a soil and indicates the slope of the grain size distribution curve (Mitchell and

Soga, 2005). Larger C u values indicate well-graded soils and smaller C u values indicate

uniformly-graded soils (Holtz et al., 2011). Poorly-graded soils have higher porosity and

permeability values than well-graded soils in which smaller grains tend to fill the voids

between larger grains. C c is another important shape factor representing the grain size

distribution that takes into account three points on the grain size distribution curve,

reducing the possibility of considering a gap-graded soil as well-graded.


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Figure 1.1: Typical grain size distribution curve with commonly used grain size indices.


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Figure 1.2: Particle shape characterization: (a) chart for visual estimation of roundness

and sphericity (from Krumbein and Sloss, 1963). (b) Examples of particle shape

characterization (from Powers, 1953).

Figure 1.3: Diagram showing horizontal flow through grains (From Das, 2008).


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210 )D(Ck (1)

Where:

k = coefficient of permeability (cm/sec)

C = constant ranging from 0.4 to 1.2, typically assumed to be 1.0.

D10 = grain size corresponding to 10% by weight passing, also referred to as the

effective size (mm).

The advantage of Hazen’s formula is that D10 from a large number of samples at a

given site can be quickly and easily determined to compute permeability. This helps

evaluate the variability of permeability at a given site in a quick and cost effective

manner. However, a major limitation of Hazen’s formula is that it is more reliably valid

for clean sands with D 10 ranging from 0.1 to 3.0 mm (Holtz et al., 2011). Additionally,

this method is based on only one size fraction, D 10 , which represents the percentage of

fine material in a granular soil.

Another empirical equation for predicting permeability from grain size

distribution, originally proposed by Kozeny (1927) and modified by Carman (1937,

1956), to become the Kozeny-Carman equation is given below. This equation is not

appropriate for soils with effective particle size (D 10) greater than 3 mm or for clayey

soils (Carrier, 2003).


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(2)

Where:

k = permeability (cm/sec)

g = the acceleration due to gravity (cm/sec 2)

v = kinematic viscosity (mm 2/sec)

n = porosity

D10 = grain size corresponding to 10% by weight passing (mm).

Terzaghi and Peck (1964) developed the following empirical equation for

predicting permeability of course grained sands (Cheng and Chen, 2007).

210

2

3/1t D)n1(

13.0nC

vg

k (3)

Where:

k = permeability (cm/sec).

g = the acceleration due to gravity (cm/sec 2).

v = kinematic viscosity (mm 2/sec).

C t = sorting coefficient, ranging between 6.1x10 -3 and 10.7x10 -3.

n = porosity.


Kenney et al. (1984) proposed the following equation for estimating permeability

using only a single point from the grain size distribution curve of the soil.

2102

33 D

)n1(

n10x3.8

vg

k


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25D)005.0(k (4)

Where,

k = permeability (cm/day).


Alyamani and Sen (1993) proposed the following equation which is more

applicable to well-graded soils (Odong, 2007).

210500 )DD(025.0I5046.1k (5)

Where:

k = permeability (m/day)

I0 = the x intercept of the slope of the line formed by D 50 and D 10 of the grain-size

distribution curve (mm)


D10 = grain size corresponding to10% by weight passing (mm).

None of the equations presented above considers the effect of the entire grain size

distribution on the permeability of soils. Since grain size distribution controls the nature

of interconnections between pores, the entire grain size distribution, rather than a single

point on the grain size distribution curve, needs to be considered to reliably estimate the

permeability of granular soils. Furthermore, none of the previously developed equations

considers the effect of soil density on permeability.

1.4 Objectives of the Study

The objectives of this research are as follows:


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1. To investigate the relationships between permeability of sandy soils and their

corresponding values of D 10, Cu, and C c to determine if these grain size

distribution indices can be used to reliably predict permeability while considering

the effect of density.

2. To develop a prediction model relating permeability to grain size distribution and

density.


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CHAPTER 2

RESEARCH METHODS

2.1 Sample Collection and Preparation

Five sandy soils, exhibiting different grain size distribution curves, were collected

for this research from locations around Kent, Ohio. A sixth sandy soil, previously tested

by Brooks (2001), was added to the samples used in this study. Figure 2.1 shows the six

soils used in the study. All soil samples were oven dried at 105°C for 24 hours. The oven-

dried samples were stored in five gallon plastic buckets with covers.

2.2 Laboratory Investigations

Laboratory tests performed on the six soils included grain size distribution,

standartd Proctor, and constant head permeability tests. All tests were conducted

according to American Society for Testing and Materials (ASTM) specifications (ASTM,

1996).

2.2.1 Grain Size Distribution Test

This test was used to determine the percentages of different grain sizes present in

each of the six soils in order to establish the grain size distribution curves and determine

the grain size distribution indices such as effective grain size (D 10), coefficient of

uniformity (C u), and coefficient of curvature (C c). These indices are shown in Figure 1.1


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Figure 2.1: Six sandy soils used in the study.


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of Chapter 1. Sandy soils are classified as well-graded when the C u values are greater

than 6 and the C c falls between 1 and 3. If these criteria are not met, the sandy soils are

classified as poorly-graded. Using these criteria, the six sandy soils were classified

according to Unified Soil Classification System (Holtz et al., 2011).

In addition to sieve analysis, the Camsizer video grain size analyzer was used to

determine grain size distribution to evaluate the importance of a different method for

determining grain size distribution indicies. The results obtained by the two methods

were compared. Sieve analysis is the ASTM procedure for determining grain size

distribution; the Camsizer technique is not a standardized procedure. Camsizer video

grain size analyzer is a digital imaging process that has two cameras: a zoom video that

analyzes smaller grains and a wide angle video that analyzes larger grains (Figure 2.2.).

2.2.2 Compaction Test

The standard Proctor test (ASTM D 698); (ASTM, 1996) was performed on all

soil samples to establish their compaction curves and to determine their maximum dry

density (MDD) and optimum water content (OWC) values. The standard Proctor test

equipment is shown in Figure 2.3.

2.2.3 Constant Head Permeability Test

The constant head permeability test (ASTM D 2434); (ASTM, 1966) was used to

determine the permeability of the six soils (Figure 2.4). Five or six samples of each sandy

soil were compacted at different density values and tested for permeability. The quantity


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(a)

(b)

Figure 2.2: (a) Camsizer video grain size analyzer; (b) close up view of grains before

falling.


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Figure 2.3: Standard compaction test apparatus.

Figure 2.4: Constant head permeability test set up.


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of water passing through the sample in 5 minutes (300 seconds) was collected in a

graduated cylinder to compute permeability in accordance with Darcy’s law (Holz, et

al.,2011). The test was repeated five times for each sample and average permeability

values were computed and reported in cm/sec.

2.3 Data Analysis

Microsoft Excel 2010 was used to generate smooth line plots showing grain size

distribution curves, density versus water content relationships, and density versus

permeability relationships for each soil.

2.3.1 Statistical Analysis

An unpublished computer program, written by Dr. Neil Wells, Department of

Geology, Kent State University, and SPSS program were used for statistical analysis.

Statistical analyses were performed in three steps: univariate, bivariate, and step-

wise regression analyses. In the first step, distribution properties of each variable were

analyzed by univariate analysis. In the second and third steps, bivariate and step-wise

regression analyses were perfomed to investigate the relationships between permeability

as the dependent variable and density and various grain size distribution indices as the

independent variables.

Multiple regressions can be simultaneously or hierarchically performed. In

simultaneous multiple regression analysis, all independent variables are entered into the

equation at one time, whereas, in hierarchical multiple regression, independent variables


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are entered in different steps. The important difference between these two types of

regression analysis is that hierarchical regression is helpful in understanding the effect of

each variable. Variations of hierarchical regression analysis include backward

elimination, forward selection, and stepwise regression analysis (Dielman, 2001). Step-

wise regression, including both backward elimination and forward selection, was used to

evaluate the importance of the independent variables by adding the variable according to

their partial F statistic (Dielman, 2001). Regression started with the variable that had the

largest partial F statistic. When a new variable was entered to the model, partial F statistic

values with other variable were recalculated. The importance of each variable was

evaluated. Based on their importance, variables were re-entered or removed from the

model. The significance level (partial F value) of a variable should be less than 0.05 for it

to enter the model and the significance level of a variable should be more than 0.1 to

remove it from the model to the model and the significance level of a variable should be

more than 0.1 to remove it from the model. When the regression procedure was finalized,

the most important variables contributing to variation in dependent variable stayed in the

model whereas the least important variables were excluded from the model (Dielman,

2001).

Two important assumptions of multiple regression analysis are that the

relationship is linear and is based on a Gaussian (normal) distribution (Kokoska, 2011;

Ghasemi, and Zahediasl, 2012). Therefore, it was important to evaluate the normality of

data both visually and by various statistical tests. Frequency distribution histograms, Q-Q

plots, and P- P plots were used as visual methods whereas the D’Agostino -Pearson (D’A -


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P) test and the Kolmogorov-Smirnov (KS) test were used as statistical means of testing

normality. In D’Agostino -Pearson test, both skewness and kurtosis deviations from

Gaussian are used to calculate the D’A -P score. A deviation of zero is desirable for both

skewness and kurtosis but a score of less than 6 is considered acceptable for 0.05

significance level. If the score exceeds this value at a significance level of 0.05, the

distribution will not be Gaussian (Wells 2013, [unpublished]). In the Kolmogorov –

Smirnov test, the largest vertical difference between the data and a Gaussian curve is

measured on a cumulative curve. A zero value is also the best for Kolmogorov-Smirnov

value. If the deviation in the KS test exceeds 0.238, the data distribution may differ

markedly from Gaussian distribution at a significance level of 0.05 (Wells 2013,

[unpublished]). Since the K-S test is sensitive to extreme values, it should not be the first

choice for testing normality.

Although the importance of the effect of fine grains on permeability is known, the

entire grain size distribution should be taken into account to predict permeability. For this

purpose, the use of a new index , designated as “permeability index”, representing the

entire grain size distribution of a soil, was investigated. Non-linear regression analysis

between permeability and the new index was performed to establish the relationship and

to develop a prediction equation.

2.3.2 Modeling of Data

The relationships between permeability, density, and the new index were

investigated in three dimensions by using the Matlab software program (MathWorks,


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2012). The program generated a combined surface among the three mutually

perpendicular axes representing permeability, density, and the new index.


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Figure 3.1: Grain size distribution of six soil samples by sieve analysis.

Table 3.1: Grain size distribution indices based on results of sieve analysis.

S i e v e

A n a l y s i s

Soil D 10 D30 D60 Cu Cc %C %M %F1 0.19 0.34 0.93 4.89 0.65 18.18 43.81 36.372 0.17 0.22 0.33 1.94 0.86 0.35 31.13 67.653 0.19 0.30 0.80 4.21 0.59 13.64 39.09 40.914 0.34 0.42 0.46 1.35 1.13 0 64.83 35.175 0.14 0.40 1.25 8.93 0.91 21.29 42.08 27.21

6 0.31 0.80 2.35 7.33 0.97 26.48 40.49 13.88


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2011), well-graded sands have C u values greater than 6 and C c values falling between 1

and 3. Based on the grain size distribution curves shown in Figure 3.1 and the C c and C u

data provided in Table 3.1, Soils 1, 2, 3, and 4 can be classified as poorly-graded sands

(SP) and soils 5 and 6 can be classified as close to being well-graded sands (SW), with

their C c values being just below 1 instead of 1.

Table 3.1 shows that soil 4 has the highest D 10 value of 0.34 mm and soil 5 has

the lowest D 10 value of 0.14 mm. Soil 6 has the highest percentage (26.5%) of coarse

sand and soil 2 has the highest percentage (67.7%) fine sand. Percentages of coarse and

fine sand as well as D 10 are expected to influence the permeability of sandy soils.

Additionally, well-graded soils with high C u values are expected to have low

permeability values compared to poorly-graded soils with low C u values.

3.1.2 Grain Size Distribution by the Camsizer Video Grain Size Analyzer

In addition to sieve analysis, Camsizer video grain size analyzer was used to

determine grain size distribution of the six soils and the results were compared with the

sieve analysis method. The purpose was to evaluate the influence of test method on grain

size distribution indices. Figure 3.2 shows grain size distributions of the six soils by the

Camsizer video grain size analyzer method and Table 3.2 provides the values of various

grain size distribution indices.


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Figure 3.2: Grain size distribution curves by the Camsizer video grain size analyzer. Soil

3, results of Brooks study, was not available to test by camsizer.

Table 3.2: Grain size distribution indices based on the Camsizer video grain size

analyzer. Note grain size index data for soil 3, tested by Brooks (2001), are not available.

C a m s i z e r

A n a l y s i s Soil D 10 D30 D60 Cu Cc %C %M %F

1 0.27 0.48 1.17 4.29 0.71 17.50 50.00 23.902 0.20 0.31 0.46 2.29 1.06 0.40 46.60 52.903 - - - - - - - -4 0.58 0.67 0.78 1.35 1.01 0 98.90 1.105 0.31 0.53 1.25 4.03 0.73 19.40 52.20 19.90

6 0.42 0.80 2.67 6.37 0.57 21.80 44.00 10.50


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3.1.3 Comparison of Sieve Analysis and the Camsizer Video Grain Size Analyzer

The grain size distribution curves obtained by the two methods for the five soils

were compared (Appendix A). The plots show that the two methods yield similar results

for the coarse and medium size fractions of the soil samples. Plots of measured values

both from seieve analysis and the Camsizer video grain size analyzer for all grain size

distribution indicies including D 10, D 30, D60, C u, C c, %C, %M, and %F, are shown in

Figures 3.3 to Figures 3.10. Although the Camsizer video grain size analyzer

overestimate D 10, D 30, and D 60 values, differences between sieve analysis and the

Camsizer values decrease from D 10 to D 60. The Camsizer video grain size analyzer

underestimates %C and %F values and overestimate %M values. The highest differances

are seen in D 10 and %F with a high scatter. The two methods provide different

percentages of the finer fractions. For example, D 10 values by the two methods are quite

different. Thus, when H azen’s formula (Hazen, 1892) was used to predict permeability,

the differences in permeability values by the two methods, seen in Figure 3.11, are

significant. The comparison shows that the Camsizer video grain size analyzer plots

generally underestimate the percent passing for a given grain size, as compared to the

sieve analysis. However, this differences can be attributed to the fact that sieve analysis

measures the percentage of particles, by weight, passing a given size where as, Camsizer

video grain size analyzer digitially measures percentage of number of particles of a given

size compare to the total number of particles.


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Figure 3.3: Comparison of D 10 values by sieve analysis and the Camsizer video grain size

analyzer.


analyzer.


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analyzer.

Figure 3.6: Comparison of C u values by sieve analysis and the Camsizer video grain size

analyzer.


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Figure 3.7: Comparison of C c values by sieve analysis and the Camsizer video grain size

analyzer.

Figure 3.8: Comparison of %C values by sieve analysis and the Camsizer video grain size

analyzer.


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Figure 3.11: Comparison of Hazen permeability (k Hazen ) values by using D 10 values both

from sieve analysis and the Camsizer video grain size analyzer.


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3.2 Compaction Test Data

Appendix B provides the compaction test data for the six soils. Figures 3.12 to

3.17 show the compaction curves for all six soils. The compaction curves were used to

determine the maximum dry density (MDD) and optimum water content (OWC) values

for each soil as summarized in Table 3.3. The table shows that soils 5 and 6, being nearly

well-graded (Figure 3.1), have the highest maximum dry density values of 1.92 Mg/m 3

and 1.89 Mg/m 3, respectively, whereas soils 2 and 4, being uniformly-graded (Figure

3.1), have the lowest maximum dry density values of 1.62 Mg/m 3 and 1.64 Mg/m 3,

respectively. As will be demonstrated later, density has a significant influence on the

permeability of sandy soils.

3.3 Permeability Data

Permeability values for the six soils were measured on samples compacted to

different states of density during the compaction test discussed above. Figures 3.12 to

3.17 show the variation of permeability with varying density values. Since a given state

of density is achieved at a specific water content, the plots in Figures 3.12 to 3.17 show

the relationships between compaction water content and permeability for different

samples of the same soil. In these figures, a comparison of the permeability curves on top

with the compaction curves at the bottom shows that permeability of sandy soils

decreases with increasing density, reaching its minimum value at the OWC or slightly on

the dry side of OWC. After reaching its minimum value, the permeability increases as the

density decreases on the wet side of the OWC. It should be noted that soil 4 is a


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uniformly graded soil with nearly round grains. Therefore, the compaction curve for this

soil is relatively flat, showing negligible variations in density with varying water content.

The flat nature of the compaction curve for soil 4 can be attributed to the fact that the

smaller grains required to fill the voids between larger grains are not present in this soil.

Also, the interlocking of grains that reduces pore space, is absent due to the rounded

nature of the grains.

Table 3.3: Optimum water content and maximum dry density of soil samples with

corresponding permeability values.

Soil Optimum WaterContent (%)

Max DryDensity(Mg/m 3)

Permeability at MDD* x 10 -3

(cm/sec)

1 8.40 1.81 1.662 6.00 1.62 0.323 11.40 1.85 0.594 3.80 1.62 3.005 8.50 1.92 0.276 7.30 1.80 1.37

*MDD stands for maximum dry density.

The permeability versus density relationships shown in Figures 3.12 to 3.17

clearly demonstrate the influence of density on permeability. Therefore, any equations

used for predicting permeability from grain size distribution indices alone, such as those

proposed by Hazen (1892), Kozeny (1927), Kozeny and Carmen (1956), Terzagi and

Peck (1964), Kenney et al. (1984), and Alyamani and Sen (1993), ignoring the role of

density, are of limited application.


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Figure 3.12: Permeability (top) and compaction (bottom) curves for soil 1.


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As stated previously, Figures 3.12 to 3.17 show that the minimum permeability

for granular soils is achieved at or slightly on the dry side of the OWC. This finding is

contrary to the permeability behavior of fine-grained soils which exhibit minimum

permeability values at water contents on the wet side of the OWC (Holtz et al., 2011).


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parameters are skewed to the right where mean is smaller than median. Percentage of

medium sand (%M) has the highest skewness value, 1.09. Frequency histograms of

permeability, density, and grain size distribution indices (D 10, C u, C c, %C, %M, %F)

were plotted to examine the data distribution and are provided in Appendix C. Based on

visual evaluation of the frequency histograms, the data show only a small deviation from

normal distribution. Permeability, density, and %F have D’Ag ostino-Pearson ( D’A -P)

scores less than 6 and Kolmogorov-Smirnov (KS) scores less than 0.24 indicating that

their distributions may be Gaussian . D’A -P scores of D 10, Cu, C c, %C, and %M are more

than 6. Therefore, based on D’A -P test, distributions of D 10, C u, C c, %C, and %M are

non-Gaussian. However, K-S scores of D 10, %C, and %M indicates non-Gaussian

distribution whereas distribution of C u and C c are evaluated as Gaussian based on their K-

S scores (Table 4.1).

Table 4.1: Descriptive statistics of all variables.

Permeabilityx10 -3 cm/sec

DensityMg/m 3

D10 mm Cu Cc %C %M %F

Maximum 0.29 1.92 0.34 8.93 1.13 26.48 64.83 67.65Minimum 3.05 1.50 0.14 1.35 0.59 0 31.13 13.88Median 1.32 1.77 0.19 4.21 0.86 13.64 40.49 36.37Mean 1.47 1.73 0.22 4.68 0.85 12.90 43.17 37.86Std. Deviation 0.89 0.11 0.074 2.71 0.18 10.15 10.38 16.91Skewness 0.50 -0.27 0.61 0.26 -0.074 -0.19 1.09 0.53Kurtosis -1.10 -1.16 -1.40 -1.41 -1.25 -1.62 0.19 -0.62D'A-P score 5.26 5.38 13.93 12.6 6,83 27.23 6.42 1.97K-S score 0.10 0.13 0.34 0.20 0.19 0.24 0.31 0.23


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4.1.2 Bivariate Analysis

The effects of each grain size distribution indices and density on the permeability

of the soils tested were analyzed separately using bivariate analysis. The matrix shown in

Figure 4.1 represents all bivariate relations between non-transformed variables. The

independent variables representing the horizontal axes of the plots are shown along the

diagonal of the matrix. The plot in the first row and second column shows the

permeability (k) versus density relationship where permeability is plotted along the

vertical axis and density is plotted along the horizontal axis. The plot of k versus D 10 is

shown in the first row, third column, and so on. The plots below the diagonal are the

same as those above the diagonal, except that the axes are switched. The red numbers on

top of the plots are Pearson’s correlation coefficient (r) values for raw (non-transformed)

data. The first row of the matrix shows the correlations grain size distribution indices and

density have with the property of permeability. As can be seen from the plot between

permeability and density, permeability is inversely correlated with density with an r value

of -0.37. The low correlation coefficient value can be attributed to soil 2 acting as an

outlier even though it shows the same correlation trend as other soils. %M and D 10

exhibit the strongest correlations with permeability with r values of 0.78 and 0.75,

respectively. The correlation plots of permeability and grain size distribution indices in

Figure 4.1 (row 1, columns 3-8) show vertical distributions. These vertical variations

indicate the effect of density. Effects of grain size distribution and density also were

evaluated at maximum dry density and optimum water content. Figure 4.2 shows the

scatter plot matrix for transformed variables; square root of permeability, reflected


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Figure 4. 1: Matrix of bivariate scatterplots of non-transformed data. Numbers on left of

the matrix represent the row numbers and numbers at the bottom of the matrix are the

column numbers. Pearson’s corr elation coefficient (r) values are shown in red on the top

of the individual plots.


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Figure 4.2 : Matrix of bivariate scatter plots of transformed data with Pearson’s

correlation coefficients (r) value shown on the top of each plot.


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(a)

(b)

Figure 4.3: (a) Permeability vs. percentage of medium sand size (%M) at different

densities. Red square represents loose state permeability; (b) at maximum dry density

(MDD).


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(a)

(b)

Figure 4.4: (a) Permeability vs. D 10 at different densities. Red square represents loose

state permeability; (b) at maximum dry density (MDD).


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Figure 4.5: Transformed data of permeability vs. percentage of medium sand size (%M).

Figure 4.6: Transformed data of permeability vs. D 10.


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4.1.3 Multiple Regression Analysis

The percent coarse sand (%C) variable had a considerably high correlation with

density and C u. Therefore, to avoid a colinearity problem, %C was not included in

stepwise regression analysis. Step-wise regression analysis between permeability,

density, D 10, C u, C c, %M, and %F was performed. The square root of permeability was

used as the dependent variable. The independent variables are: reflected inverse of

density, inverse of D 10 , square root of C u, reflected square root of C c, square root of %M,

and square root of %F. Three different models generated during analysis are shown in

Table 4.3. D 10 was evaluated in model 1 and resulted in an R 2 value of 0.54. Addition of

%M and density increased the R 2 value increased by 0.11 and 0.06, in models 2 and 3

respectively. Adjusted R 2 value of 0.67 for model 3 shows that it explains about 67% of

the variance in permeability. Significance levels of D 10, %M, and density were found to

be less than 0.05 whereas C u, C c, and %F had higher significance levels. Therefore, C u,

Cc, and %F did not contribute to the stepwise regression. D 10 explains the most variability

in permeability.


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Table 4.3: Model summary and Anova of stepwise multiple regression analysis

Summaries of Models

Model R RSquareAdjusted R

SquareStd. Error of the

Estimate1 .736 a .54 .52 .262 .807 .65 .62 .233 .840 c .71 .67 .22

a. Predictors: (Constant), D10 (inverse) b. Predictors: (Constant), D10 (inverse), %M (square root)c. Predictors: (Constant), D10 (inverse), %M (square root), Density(reflected inverse)

ANOVA a

Model Sum ofSquares dfMean

Square F Sig.

1Regression 2.37 1 2.37 34.27 .000 b

Residual 2.00 29 0.07Total 4.37 30

2Regression 2.85 2 1.42 26.13 .000 c

Residual 1.53 28 0.05Total 4.37 30

3Regression 3.08 3 1.03 21.49 .000 d

Residual 1.29 27 0.05Total 4.37 30

a. Dependent Variable: Permeability (square root) b. Predictors: (Constant), D10 (inverse)c. Predictors: (Constant), D10 (inverse), %M (square root)d. Predictors: (Constant), D10 (inverse), %M (square root), Density (reflectedinverse)


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As discussed in Chapter 2, assumptions of the step-wise regression model should

be met. Frequency plot of regression standardized residuals was used to evaluate the

normality of disturbance. Figure 4.7 shows that the residuals have a normal frequency

distribution. Moreover, the scatter plot of residuals also shows the model assumptions

were met. It does not show any clear trend (Figure 4.8).

The following regression equation, based on model 3, can be used to predict

permeability from D 10, %M, and density.

ensity)1.28(RInvD%M)0.256(Sqrt)0.085(InvD1.35Sqrt(k) 10 (6)

Where:

Sqrt(k) = Square root of permeability x10-3 (cm/sec).

InvD10 = Inverse of D10.

Sqrt%M = Square root of %M.

RInvDensıty = Reflected inverse of density. Figure 4.9 shows the plot of measured versus predicted values of permeability for

the six soils at varying density values. The residuals (differences between measured and

predicted values) appear to be large, with the maximum residual value being 0.00136

cm/sec which amounts to 74% of the measured value. This large variation in the

predicted value is due to the complex nature of the factors that control permeability.

Additional data from future research can help improve the prediction equation and reduce

the residuals between measured and predicted values.


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Figure 4.9: Measured versus predicted values of permeability.


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4.2 New Permeability Index

As stated in Chapter 1, permeability is a property that is controlled by the entire

grain size distribution of a soil. Therefore, there is a need to find a new index that

represents the effect of the entire grain size distribution on permeability. Furthermore, the

new index needs to take into account the effect of the silt and clay size fraction (material

passing sieve #200) present in the soil as it has the greatest effect on permeability. A new

index considering the relative effect of different size fractions on permeability was

developed in this study and is designated as the “New Permeability Index” . It is defined

as follows:

New Permeability Index n

1 j )075.0 jMS(7

j

100

F (7)

Where:

n = Total number of sieve used in grain size distribution test.

F j = Percentage of the amount of material passing the sieve j.

MS j = Middle size between sieve j and j-1.

In the above equation, F j is for the percentage of the amount of material passing

the sieve j and dominator of the equation represents the relative weights assigned to

different size fraction. For example, six sieves were used to establish the grain size

distribution curve for soil 5. Thus, an n value is 6 and j ranges from 1 to 6. Value of j is 1

for sieve #200; j is 2 for sieve #100 and so on until one reaches 3/8 inch sieve for which j

is 6. Thus, for soil 5, F (1), percent passing through #200 sieve, is 4.67. MS j in the new

permeability i ndex represent the “Midsize”, the middle size of j and j -1 sieves.


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Figure 4.10: Grain size distribution of soil 5 for calculation of new permeability index.

Table 4.5: An example of the calculation of new permeability index for soil 5.

Sieve#

Sievesize

(mm)

Percentpassing(%) F j

j

Middle size(MSJ)

[(M j + M j-1)/2]

MS j-0.075

F j / 100[7*(Mj-0.075)]

Permeabilityindex

0.375 9.51 100 6 7.13 7.06 1.70E-97

16.53

4 4.75 95.25 5 3.38 3.30 6.01E-4510 2 73.96 4 1.21 1.14 8.79E-15

40 0.425 31.88 3 0.29 0.21 0.03100 0.149 10.48 2 0.11 0.04 3.18200 0.075 4.67 1 0.04 -0.03 13.31

0.01 0 Sum 16.53


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For instance, MS (1) is the average size between #200 (0.075 mm) and minimum sieve

sizes (0.01 mm). Figure 4.10 shows the grain size distribution of soil 5 for a new

permeability index calculation. Table 4.5 summarizes the calculation of a new

permeability index for soil 5. A hydrometer test was not performed to measure the exact

minimum size of each soil; therefore, minimum size is considered as 0.01mm because

most sandy soils do not contain particles smaller than 0.01 mm (Holtz et al., 2011). MS (2)

represents the average of the 0.15 and 0.075 (sieves #100 and #200, respectively). Tables

showing details of new permeability index calculations for the 6 samples can be found in

Appendix F.

It is important to consider not only the entire grain size distribution but also the

relative importance of different grain sizes. The proposed new permeability index pays

attention to this relative importance. The higher the percentage of finer grains, the lower

the permeability value because the finer fraction fills the pore space between the coarser

particles. For instance, percentage of fine sand is important for the grains retained on

sieve #40 (medium sand size). Also, the effect of each finer fraction is greater than the

fraction that is just coarser than the finer fraction. That is, the effect of silt and clay is

greater than the effect of fine sand. This effect of relative sizes is incorporated in the new

permeability index equation by the exponent 7 in the dominator. The effect from one

sieve to the next larger sieve decreased by a factor of 100 7 for the soils studied.

Figure 4.11 shows the correlation between the new permeability index and

permeability. The data points along the vertical lines represent different density values at


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Figure 4.11: Relationship between new permeability index and permeability with a

prediction equation; Ln (Permeability) =1.19 – 0.22 (Permeability Index) + 0.006

(Permeability Index) 2.


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which permeability values were measured. Regression between ln of permeability and the

new permeability index, with a quadratic equation, was performed and the correlation

coefficient was calculated. The regression equation, a second order quadratic equation,

has a statistically significant R 2 value of 0.76 (Johnson, 1984);

Ln (Permeability) =1.19 – 0.22 (Permeability Index) + 0.006 (Permeability Index) 2 (8)

Predicted versus measured values of permeability were plotted to evaluate

reliability of the equation. Plots showing predicted versus measured values of

permeability considering all densities and average densities are shown in Figure 4.12 and

4.13, respectively. In these plots the vertical distances of data points from 1:1 line

represent the residuals. Figure 4.13 shows that the predicted values are close to the

measured values, with a maximum residual value of 0.37 below the 1:1 line (Table 4.6).

Although the entire grain size distribution is taken into account, the effect of density on

permeability can be seen in Figure 4.11. The vertical distribution of data illustrates the

density effect. Therefore, this effect needs to be considered to predict the permeability.

For this purpose, data distribution of permeability, density, and new permeability index

were modeled in 3-D as discussed in the following section.


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and 8 used for validation are represented by the red point.

Table 4.6: Residuals of predicted vs. measured permeability values for average density.

SoilPredicted

Permeability x10 -3 (cm/sec)

MeasuredPermeability x10 -

3 (cm/sec)Residuals Deviation(%)

1 1.39 1.76 -0.37 21.022 0.81 0.88 -0.07 7.953 1.06 1.04 0.02 1.924 3.26 3.00 0.26 8.675 0.45 0.70 -0.25 35.716 1.25 1.50 -0.25 16.67

7*8*

0.552.20

0.551.99

0.000.21

0.0010.55

*Soil 7 and 8 are used for validation.


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4.3 3-D Prediction Model

As discussed earlier, density has considerable effect on permeability.

Permeability index, representing grain size distribution, density, representing state of

compaction, and permeability were plotted along three mutually perpendicular axes to

generate a 3-dimensional plot. The relationship between density and permeability is

linear (first order quadratic) and the relationship between permeability index and

permeability is nonlinear (second order quadratic). The following equation was generated

for the regression surface by Matlab software.

Ln (Permeability) = 1.65 - 0.27 (Density) – 0.22 (Permeability index) + 0.006

(Permeability Index) 2 (9)

Regression surface given by the above equation is plotted and shown in Figure

4.14. The color scale in Figure 4.14 represents the permeability values for different color

ranges. Red areas represent the lower permeability whereas blue and pink areas represent

higher permeability values. The relationship between new permeability index and

permeability in Figure 4.11 can also clearly be seen on a curvature of the surface in

Figure 4.14. The higher the new permeability index, the lower is the permeability. The

colors change as one move towards increasing density on the surface. For example,

yellow changes into red with increasing density values indicating a decrease in

permeability.

Figure 4.15 shows a plot of predicted values of permeability, based on equation 9,

versus the measured permeability values considering all density values. Figure 4.16

shows a similar plot considering average density.


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Figure 4.14: 3-D plot of permeability index, density, and permeability. The color scale represents permeability values in 10 -3

cm/sec units.


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Figure 4.15: Measured versus predicted values of permeability for all density based on

Equation 9. Soil 7 and 8 used for validation are represented by the red points.


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and 8 used for validation are represented by the red point.

Table 4.7: Residuals of predicted vs. measured permeability values for average density.

SoilPredicted

Permeability x10 -3 (cm/sec)

MeasuredPermeability x10 -3

(cm/sec)Residuals Deviation(%)

1 1.39 1.76 -0.37 21.022 0.81 0.88 -0.07 7.953 1.06 1.04 0.02 1.924 3.26 3.00 0.26 8.675 0.45 0.70 -0.25 35.71

6 1.25 1.50 -0.25 16.677*8*

0.542.22

0.551.99

-0.010.23

1.8211.56

*Soil 7 and 8 are used for validation.


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CHAPTER 5

DISCUSSION

Permeability is a complex property that depends upon the sizes and shapes of

interconnection between particles in a soil mass. It is the sizes and shapes of

interconnections that control the rate of movement of groundwater. The factors which

influence the nature of interconnections include grain size distribution, particle shape,

and density (degree of compaction). Because of the complex nature of permeability and a

number of factors influencing it, it is not possible to develop a predictive equation that

can explain 100% variability of permeability among different sandy soils.

The effect of density on permeability is clear from Figures 3.12 to Figure 3.17.

These figures show that permeability of sandy soils decreases as density increases, with

the minimum permeability occurring at either maximum dry density or slightly on the

dry side (1-2 %) of the optimum water content. The relationship between density and

permeability of granular soils is different than that of cohesive soils which exhibit their

lowest permeability values on the slightly wet side (1-2 %) of the optimum water content

(Holtz et al.,2011).

The effect of grain size distribution on permeability is intuitively obvious. Coarse-

grained soils have larger pores, as well as larger interconnections between the pores,

whereas fine-grained soils have smaller pores and narrower interconnections between the


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pores. Moreover, smaller grains fill the pore spaces between larger grains in well-graded

soils thereby reducing the void sizes and the associated interconnections. For example,

soil 5 has the lowest permeability because of its well-graded nature as compared to soil 4

which is uniformly-graded. Although the entire grain size distribution controls the

permeability of a sandy soil, the findings of this research demonstrate that the amount of

fines (silt and clay size particles) present has the most significant effect on permeability.

Thus, the weight of different size fractions in influencing permeability cannot be

considered equal. Therefore, in order to develop an equation for predicting permeability,

it is essential to have a grain size distribution index that takes into account the influencing

weights of different size fractions present within the overall grain size distribution of a

soil. The “ new permeability index”, discussed in Chapter 4, section 4.2, is a preliminary

attempt, the first of its kind, at developing such an index.

Figure 4.11 shows the relationship between permeability index and permeability.

Density variations are included in the plot in Figure 4.11, although the relative effect of

density is less than the relative effect of grain size distribution, especially the amount of

fines presents. The regression curve in the figure passes through data points representing

average density values for the soils studied. The prediction equation, a second order

quadratic equation, takes into account the range of density values falling above the curve.

The equation 7 can be expressed as follows:

Ln (Permeability) =1.19 – 0.22 (Permeability Index) + 0.006 (Permeability Index) 2

In spite of the above listed limitations, the prediction equation developed in this

study can be used with a reasonable degree of confidence as indicated by the small values


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of residuals between predicted and measured values (Table 4.6). The equation was further

validated by using two additional soils, not included in the six soils used for developing

the equation. The grain size distribution, permeability index, and permeability of these

soils (soil 7 and soil 8), at varying density values, were determined using the same

procedures as for the other six soils. Appendix G provides the grain size distribution

curves and the new permeability index calcualtions for the two soils. The new

permeability index values were then used to predict permeabilities for the two soils. The

predicted values of permeability for the two soils at varying density values are shown in

Figure 4.12, whereas Figure 4.13 shows the predicted permeability values at average

density values. As can be seen from Figure 4.12, the predicted permeability values for the

two soils used for validation purpose fall on both side of 1:1 line, reflecting the variations

in density values. However, the predicted permeability values computed at average

density values are close to the measured permeability values as seen in Figure 4.13.

The best way to check the combined influence of grain size distribution and

density on permeability of a sandy soil is to develop a 3-D model incorporating all three

parameters. Figure 4.14 shows such a model where density, permeability index, and

permeability are plotted along three mutually perpendicular axes. Color changes in Figure

4.14 represent variations in permeability. The color changes from blue to red as

permeability decreases with increasing permeability index. The effect of changing

density on permeability can also be seen from the gradual alteration of one color into

another color. For example, for a new permeability index of 8, change of light orange into

dark orange or red indicates decreasing permeability with increasing density.


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Equations proposed in this study (Equations 6, 8, and 9) have two main

limitations as listed below;

1. Equations 6, 8, and 9 are based on a small population of six soils. They are

subject to modifications as additional data become available in future research.

2. The proposed equations need to be validated further by testing additional soils.

It is important to check the aplicability of same of the previously established

equations using the data from this study. Figures 5.1 – 5.4 shows the measured versus

predicted values of permeability based on Equations 1, 2, 3, and 4 for the six soils used in

this study. As we can see from figures, Equation 1,2, and 3 overestimate the permeability

and equation 4 underestimates the permeability. The large deviations from 1:1 lines in

these figures may be because of the respective limitations of these equations, because of

different types of soil used, and because of the lack of validations.

A number of previous studies (Hazen, 1892; Kozeny, 1927 and Carmen, 1956;

Terzagi and Peck, 1964; Kenney et al., 1984; Alyamani and Sen, 1993) have attempted to

develop equations for predicting permeability from grain size distribution indices. The

research presented herein is different from those previous studies in the following

respects:

3. It demonstrates that density has a significant influence on permeability which

cannot be ignored in developing a prediction equation.

4. It shows that the influence of density on permeability of sandy soils is different

than that of cohesive soils.


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5. It proposes a new grain size distribution index designated as the “permeability

index” for predicting permeability. This index assigns different weights to

different size fractions within the range of grain size distribution for a given soil

because finer fractions play a greater role in influencing permeability than coarser

fractions.


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Figure 5.1: Measured versus predicted values of permeability based on Equation 1.



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6. It generates a 3-D surface showing the relationship between density, grain size

distribution, and permeability.


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CHAPTER 6

CONCLUSIONS AND RECOMENDATIONS

6.1 Conclusions

The results of this study can be summarized as follows;

1. Based on bivariate and step-wise multivariate analyses, effective particle size

(D10), density, and percentage of medium sand by total weight of sample (%M)

show the best correlation with permeability, explaining 67% of the variability in

permeability.

2. The relationship between density and permeability shows that sandy soils achieve

their minimum permeability values at water contents on the dry side of the

optimum water content, i.e. at a density value of slightly less than the maximum

dry density values. Any predictive model regarding permeability must consider

the effect of density.

3. Permeability index, a parameter accounting for the entire grain size distribution of

sandy soils and emphasizing the importance of finer fractions of the soil, can be

used to predict permeability. The relationship between permeability index and

permeability can be expressed in the form of a second order quadratic equation.


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4. A 3-D model, showing the relationship between the entire grain size distribution,

density, and permeability, can be used to simultaneously evaluate the effect of

both grain size distribution and density on the property of permeability.

6.2 Recomendations

1. This study should be validated using additional sandy soils from different

locations.

2. The concept of permeability index should be verified and refined using additional

soils.


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REFERENCES

Alyamani, M. S. and Sen, Z., 1993, Determination of hydraulic conductivity from grain

size distribution curves: Ground Water, Vol. 31, pp. 551-555.

American Society for Testing and Materials (ASTM), 1996, Annual Book of ASTM

Standards, Soil and Rock (1): V. 4.08, Section 4, 1000p.

Carmen, P.C., 1937, Fluid flow through a granular bed: Transaction of the Institution of

Chemical Engineers, Vol. 15, pp. 150-156.

Carmen, P.C., 1956, Flow of gases through porous media: Academic press, New York.

182 p.

Carrier, W.D., 2003, Goodbye, Hazen; hello, Kozeny-Carman: Journal of Geotechnical

and Geo environmental Engineering.

Cheng, C. and Chen, X., 2007, Evaluation of methods for determination of hydraulic

properties in an aquifer-aquitard system hydrologically connected to river:

Hydrogeology Journal, Vol. 15, pp. 669-678.

Das, B.M., 2008, Advanced soil mechanics: Taylor & Francis, New York, NY, 567 p.

DeGroot, D.J., Ostendorf, D.W., and Judge, A.I., 2012, In situ measurement of hydraulic

conductivity of saturated soils: Geotechnical Engineering Journal of the SEAGS

& AGSSEA, Vol. 43, No. 4, pp. 63-72.

Deilman, T.E., 2001, Applied Regression Analysis for Business and Economics:

Duxbury Thomson Learning, California, 647 p.


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APPENDIX A

GRAIN SIZE DISTRIBUTION PLOTS


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Figure A-1: Grain size distributions of soil 1 replicates.


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Camsizer video grain size analyzer.


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Camsizer video grain size analyzer.

8/19/2019 PREDI

predicting the permeability of sandy soils from grain size distributions

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