ABSTRACT
Seven empirical models for calculating hydraulic conductivities in soils based on grain-size distribution were investigated in this study. The results were compared with hydraulic conductivity of soils computed using the constant head permeability test. Three samples were collected from three trial pits in different locations along the bank of the stream located downstream of National Root Crops Research Institute's earth dam, Umudike, Abia State Nigeria. The samples were subjected to sieve analysis and the constant head permeability tests using standard methods. Hydraulic conductivities in soils computed from the empirical formulae were each compared with hydraulic conductivity calculated using the constant head formula. Results showed that mean hydraulic conductivities for constant head, Hazen, Breyer, Kozeny-Carman, USBR, Kozeny, Terzaghi and Slitcher models were 18.16 m/d, 35.52 m/d, 34.80 m/d, 30.50 m/d, 25.86 m/d, 19.08 m/d, 15.66 m/d and 10.86 m/d respectively. ANOVA results for pairwise comparison indicated that Kozeny formula gave the best performance with a p-value of 0.78 at 0.05 critical value. This was followed by Terzaghi, USBR and Slitcher with p-values of 0.44, 0.11 and 0.059 respectively, while the Kozeny-Carman, Hazen and Breyer performed poorly with p-values of 0.03, 0.008 and 0.007 respectively. Confirmatory test carried out using the Dunnett simultaneous software package for level mean - control mean, produced an adjusted p-value which was highest at 1.000 for Kozeny model. In all the tests, Kozeny, Terzaghi, Slitcher and USBR performed well with p-values 1.000, 0.923, 0.117, and 0.092 above the critical value of 0.05, while the Breyer, Hazen, and Kozeny-Carman performed poorly with p-values 0.000, 0.000 and 0.004 below the same critical value. They result further showed that Slitcher model is the best for estimation of hydraulic conductivity with root mean square error (RMSE) of 6.78, mean absolute error (MAE) of 5.73, relative error (RE) of 26.71 and deviation time (DT) of 1.46, From the results of the adjusted p-value, Kozeny and Terzaghi were the best at 1.0 and 0.923 respectively while Breyer and Hazen were the worst at 0. There exists high level of inconsistencies in the findings from different researchers and therefore further researches are recommended.
TABLE OF CONTENTS
Title page i
Declaration ii
Certification iii
Dedication iv
Acknowledgements v
Table of Contents vi
List of Tables ix
List of Figures x
Abstract xi
CHAPTER 1: INTRODUCTION
1.1 Background of the Study 1
1.2 Statement of Problem 3
1.3 Objectives of Study 4
1.4 Significance of the Study 5
1.5 Scope of Study 5
CHAPTER 2: LITERATURE REVIEW
2.1 Hydraulic Conductivity 6
2.2 Parameters Affecting Hydraulic Conductivity 8
2.2.1 Permeability 10
2.3 Sieve Analysis and Grain-size Distributions (GSDs) 11
2.3.1 Grain size distribution curve 12
2.4 Particle-size Analysis 13
2.4.1 Sieve Analysis in accordance with BS (1377) 14
2.4.2 Sedimentation analysis by hydrometer testing or by pipette method 16
2.4.3 The effective size of a distribution, D10 18
2.4.4 Grading of a distribution 18
2.4.5 The plastic and liquid limits tests (consistency
limits or atterberg tests) 20
2.4.6 Trend and basic background 20
2.4.7 Plasticity index 22
2.4.8 Test methods 23
2.5 Sinkhole plain Indicating deep Plastic Soils over Cavernous Limestone, Developed in Humid Climate (U.S Agricultural Stabilization and Conservation Service) 25
2.5.1 General 25
2.5.2 Soil components 27
2.5.3 Soil moisture 29
2.6 Field Determination of Hydraulic Conductivity 30
2.6.1 Relationship between permeability and soil properties 32
2.6.2 Properties of soil components 33
2.7 Empirical Models of Hydraulic Conductivity Based on the Particle size 42
2.7.1 Kozeny-Carman 43
2.7.2 Terzaghi 44
2.7.3 USBR 44
2.7.4 Breyer 44
2.7.5 Hazen 45
2.7.6 Slitcher 45
2.7.7 Kozeny (1927, 1953) 45
2.8 Summary of Literature Review 45
CHAPTER 3: MATERIALS AND METHODS
3.1 Materials 47
3.1.1 Samples and sampling techniques 47
3.2 Experimental Procedures 48
3.2.1 Particle size analysis 48
3.2.2 K-sat hydraulic conductivity determination test 48
3.2.3 Sieve analysis test - British standard sieving test procedure 49
3.3 Methods of Analysis 50
3.3.1 Analysis of variance 50
3.4 Pairwise Comparison 53
CHAPTER 4: RESULT DISCUSSION AND ANALYSIS
4.1 The Physical Characteristics of the Soil 54
4.2 Hydraulic Conductivity Laboratory Test Results 56
4.3 Empirical Formulae Computation 58
4.3.1 MATLAB results 59
4.4 Pairwise Comparison Result 60
4.5 Analysis of variance ANOVA results 61
4.5.1 Test hypothesis 61
4.5.2 Factor information 62
4.5.3 Analysis of variance tabulated result 62
4.5.4 Model summary 62
4.5.5 Means, standard deviations and confidence interval CI 62
4.5.6 Dunnett multiple comparisons with a control 64
CHAPTER 5: SUMMARY, CONCLUSION AND RECOMMENDATIONS
5.1 Summary 67
5.2 Conclusion 68
5.3 Recommendation 69
REFERENCES
APPENDIX
LIST OF TABLES
2.1: K-value range by soil texture 8
2.2: Plasticity rating 22
3.1: Basic one way ANOVA table 52
4.1: Particle size distribution of samples from sieve analysis 55
4.2: Hydraulic conductivity results from constant head
permeability tests 57
4.3: The gradation parameters from the grain size
analysis of the soil samples 58
4.4: Hydraulic conductivity test results from empirical models 59
4.5: ANOVA results for pairwise comparison 61
4.6: Grouping information using the dunnett method and 95% confidence 64
4.7: Dunnett simultaneous tests for level mean - control mean 65
LIST OF FIGURES
2.1: Sieve analysis 14
2.2: Atterberg boundaries 22
2.3: Diagram of illustrating the atterberg tests for fine soils 23
2.4: The pumping out test 31
2.5: Network of irregular capillary tubes 33
2.6: Typical angularity of bulky grains. PX-D-16266 34
2.7: Test for liquid limit. PX-D-17009 34
2.8: Test for plastic limit. PX-D-16530 34
2.9: Dilatancy test for silt. PX-D-16335 37
2.10: Soil classification chart (laboratory method). (Sheet 1 of 2) 39
3.1: Sieve number and open sizes 49
4.1: Sieve analysis graph for the test soil samples 56
4.2: Hydraulic conductivity for various empirical formulae
using excel and MATLAB. 60
4.3: Interval plot of Lab, K-C, TZ… 63
4.4: Dunnett simultaneous 65
CHAPTER 1
INTRODUCTION
1.1 BACKGROUND OF THE STUDY
Hydraulic conductivity (‘K’) is the simplicity of movement of fluid flow through a granular medium also it is a function of both the medium and the permeating fluid (Strobel, 2005). The most reliable means to obtain hydraulic conductivity is through aquifer pumping tests or laboratory measurement of permeability via constant head permeameter, and variable head permeameter.
Determination of ‘K’ by constant head permeability test, is done using Darcy’s law;
Q=KiA, (1.1)
Substituting for k,i,and A; using the following relationships i= H/L , (1.2)
We have 
(1.3) Where:
K = Constant of proportionality also known as hydraulic conductivity
i= hydraulic gradient
Q = Quantity of water collected in the jar over a specified time
L = length of soil sample in the cylinder
H = Hydraulic head of water
A = cross sectional area of soil
For fine grained/less pervious soil, (‘K’) is determined using the falling – head permeameter tests. The expression is given as
(1.4)
Where A represents the cross – sectional area, L represents the length of the soil sample in the permeameter cylinder, t is the time for water to fall from h_otoh_1.
h_o, h_1 is the head between which the permeability will be determined.
The value of ‘K’ serves to characterize the ease of groundwater flow in underground aquifers. At sites where the aquifers are low in yield, slug tests are conducted. The hydraulic conductivity of natural soil in a place varies from about 50m/day for a silty loam to 0.05m/day for a clay.
Direct estimations of ‘K’ are often backbreaking and expensive. Since it involves personnel for sinking of wells or collecting samples and conducting laboratory experiments, which is why empirical methodologies that indirectly estimate conductivities through the material parameters, such as grain-size, are quite attractive to project managers (Vukovic and Soro, 1992).
In groundwater hydrology, the information on saturated hydraulic conductivity of soil is vital for modeling the water stream in the dirt, both in the saturated and unsaturated zone and transportation of water-dissolvable poisons in the dirt. It is additionally a significant parameter for planning of the waste of a zone and also in the construction of levees and earth dams.
Hydraulic conductivity is the constant of proportionality in Darcy's Law. It is defined as the volume of liquid that will travel through a permeable medium in unit time under a unit hydraulic angle through a unit region estimated at opposite to the stream course (Lambe and Whitman, 1969).
It should not be confused with permeability, which is the easiness with which a liquid can go through a permeable medium and is defined as the volume of liquid released from a unit zone of an aquifer under unit hydraulic gradient in unit time (communicated as m3/m2/d or m/d); it is an inherent property of the permeable medium and is reliant of the properties of the saturating fluid. Permeability considers the properties of the fluid being transmitted (thickness, consistency and temperature); hydraulic conductivity relates explicitly to the development of water. Permeability is important to multiphase flow frameworks which incorporate gas, oil and water stages (Zimmerman and Gudmundur, 1996).
Permeability provides a sign of the straightforwardness with which fluid moves through the subsurface. Hydraulic conductivity provides an indication of the ease with which water moves through the subsurface and is used to calculate rates of groundwater movement.
1.1 STATEMENT OF PROBLEM
The typical form of empirical equations for the determination of hydraulic conductivity comes from dimensional analysis based on the Darcy-Weisbach’s calculation (Kasenow, 2002; Vuković and Soro, 1992). The general challenge with the proposed formulae is imbedded in deciding the characteristic pore diameter and communicating the impact of soil non-consistency and the type of the fitting porosity work which mirrors the soil compaction rate. Some of the empirical formulae developed by different authors vaguely define applicability limits via the simple description of material type without any grain size distribution curves or quantification. This often leads to improper use of these equations. Most of the time the information parameters (in particular the successful grain size) in the experimental formulae should be communicated in units other than those characterized by the SI (for example mm, cm, for example, hydraulic conductivity in cm/day, m/day, and so on).
Numerous strategies for the assurance of hydraulic conductivity under research facility or field conditions have been portrayed in Freeze and Cherry (1979) and Todd and May (2005).
According to Uma et al. (1989), exact estimation of hydraulic conductivity in the field environment is restricted by the absence of exact information on aquifer geometry and hydraulic boundaries. Economic consideration related with field activities and well construction may likewise be a restricting element. On the other hand, techniques for evaluating hydraulic conductivity from observational formulae dependent on grain-size circulation attributes have been created and used to conquer these problems (Odong, 2007). Contrasted with aquifer tests, factual grain-size techniques are more affordable and less reliant on the geometry of permeable media and hydraulic boundaries of the aquifer yet reflects practically all the transmitting properties of the media (Alyamani and Sen, 1993; Award and Al-Bassam, 2001)
.
1.3 AIM AND OBJECTIVES OF STUDY
The aim of the research is to investigate the empirical models for determination of hydraulic conductivity base on grain-size analysis.
The specific objectives through which the aim was achieved are:
i. Determine the grain sizes of each sample through particle size analysis.
ii. Obtain the hydraulic conductivity of each sample using constant head permeability test.
iii. Obtain the values of hydraulic conductivities of each sample using various empirical formulae.
iv. Compare the result from empirical equation with the laboratory result to see if there is correlation and finally determine the most suitable one.
1.4 SIGNIFICANCE OF THE STUDY
The interrelationship between hydraulic conductivity and grain size distribution of a granular porous media is very useful for the prediction of fluid conductivity values where direct permeability data are not available such as the preliminary stages of aquifer exploration. The flow of water in the soil can be modelled both in saturated and unsaturated zone with a deep knowledge of hydraulic conductivity of the soil. It presents a very important parameter for drainage design, dam and levee construction. The hydraulic conductivity property presents important data in the design and analysis of geotechnical works which include; settlement, determination of seepage loss and stability analysis.
1.5 SCOPE OF STUDY
There are many empirical formulae from different researchers, but this study is limited to summarization of the most commonly used which are: Hezen; Kozeny-Carman; Breyer; Slitcher; Terzaghi; USBR and Kozeny. The applicability and reliability of the mentioned formulae were evaluated for unconsolidated fluvial deposits, using the results of laboratory experimental research.
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