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PAGE 1 1 DESIGN OF A TWO SCREEN PROBE TO MEASURE IN SITU HORIZONTAL AND VERTICAL HYDRAULIC CONDUCTIVITIES UNDER SATURATED AND UNSATURATED CONDITIONS By BASSEL NEMER A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY UNIVERSITY OF FLORIDA 2008 PAGE 2 2 2008 Bassel Nemer PAGE 3 3 To those who fed my curiosity for knowledge, encouraged my continued education, and made this research possible PAGE 4 4 ACKNOWLEDGMENTS I would like to thank all the people who contributed to this project and to my becoming an engineer and scientist. But mostly, I would like to thank God for guiding me through the difficult times in my life. First, I would like to thank my advisor Dr. Kirk Hatfield and my Co Chair Dr. Dave Bloomquist for grantin g me the opportunity to work on this project and for their continued support and guidance throughout my gra duate career. They will always be remembered for their encouragement, concern and g enerosity I would also like to thank Dr. Harald Klammler for his patience and willingness to explain difficult concepts and his step by step involvement is very much appre ciated. Many thanks go to Dr. Louis Motz; his advice and teachings during the early phases of this project were invaluable to me. Dr. Jean Claude Bonzongo, my masters faculty advisor has my gratitude for accepting to serve on my project committee and for his important guidance through my four years at the University of Florida especially in the Environmental and Engineering Sciences. Special thanks go to the staff at the Civil Engineering Laboratory especially to Chuck Broward, and Curtis Stepherd for their help, support, and technical guidance, without which this project would have never come to fruition. My father, Wahib Nemer, taught me to question the ways of life and to uncover the facts of any question. To him I attribute my love for finding out the way things work and for reading and learning. Without his approval and encouragement, I would not have begun, much less finished, my graduate work. I would also like to dedicate this rese arch to family whom I have lost. Additionally, I must thank all m y family and my fiance, Silvia. I appreciate their love, help, and support during these tough years especially while writing this dissertation. I would like to extend my thanks to Nancy Been, Doretha Ray, and all of the Civil Engineering staff for their help over the years I would also like to thank Dr Mark Newman, for his encouragements and moral support. Finally I would like to thank all the faculty and staff at the PAGE 5 5 University of Florida especially in Civil and Coastal Engineering department for mak ing my experience at UF exciting and unforgettable PAGE 6 6 TABLE OF CONTENTS page ACKNOWLEDGMENTS .................................................................................................................... 4 LIST O F TABLES ................................................................................................................................ 9 LIST OF FIGURES ............................................................................................................................ 10 LIST OF ABBREVIATIONS ............................................................................................................ 14 ABSTRACT ........................................................................................................................................ 17 CHAPTER 1 INTRODUCTION ....................................................................................................................... 19 1.1 Overview of Hydraulic Conductivity ................................................................................. 19 1.2 Goals and Objectives ........................................................................................................... 21 2 LITERATURE REVIEW ........................................................................................................... 23 2.1 Hydraulic Conductivity and Intrinsic Permeability ........................................................ 23 2.2 Range of Hydraulic Conductivity for Different Types of Soils ......................................... 24 2.3 Factors Affecting Permeability ............................................................................................ 24 2.3.1 Size of the Soil Particles ............................................................................................ 25 2.3.2 Structure of the Soil and Anisotropy ......................................................................... 25 2.3.3 Viscosity of Water ...................................................................................................... 26 2.3.4 Ex istence of Discontinuities and Degree of Saturation ........................................... 26 2.4 Methods for Determining Hydraulic Conductivity in Saturated Media ............................ 26 2.4.1 Laboratory Methods ................................................................................................... 27 2.4.1.1 Constant head test ............................................................................................ 27 2.4.1.2 Falling head test ............................................................................................... 28 2.4.1.3 Flexible wall permeameter .............................................................................. 29 2.4.2 Insitu Methods for Determining the Coefficient of Permeability .......................... 30 2.4.2.1 Pump test .......................................................................................................... 31 2.4.2.2 Slug t est ............................................................................................................ 32 2.4.2.3 Packer test ........................................................................................................ 34 2.4.2.4 Dipole probe ..................................................................................................... 35 2.4.2.5 Direct push method .......................................................................................... 37 2.4.3 Indirect and Empirical Methods ................................................................................ 38 2.5 Methods for Determining Hydraulic Conductivity in Unsaturated Media ........................ 39 2.5.1 Infiltrometers .............................................................................................................. 39 2.5.1. 1 Open and closed single rings .......................................................................... 40 2.5.1.2 Open and closed double rings ......................................................................... 40 2.5.2 Borehole Infiltration Tests ......................................................................................... 40 2.5.2.1 Constant head well permeameter (CHWP) .................................................... 41 PAGE 7 7 2.5.2.2 Subsurface Confined Cavity Test (SCCT) ..................................................... 42 2.6 Factors Affecting Hydraulic Conductivity Determined from Slug Tests ......................... 43 2.6.1 The Shape Factor or F Factor .................................................................................... 44 2.6.2 Anisotropy Increase as a Result of Applied Compressive Strength........................ 44 2.6.3 Radius of Influence of Flow Field............................................................................. 45 2.7 Vertical and Horizontal In situ Permeameter (VAHIP) .................................................... 47 2.7.1 Development of VAHIP ............................................................................................ 47 2.7.2 Description of VAHIP 2006 ...................................................................................... 48 2.7.3 Limitations of VAHIP 2006 ...................................................................................... 49 3 THEORETICAL METHODOLOGY ........................................................................................ 50 3.1 A xisymmetric Flow Field Method ...................................................................................... 50 3.1.1 Confined Aquifer (Impermeable Top and Bottom Boundaries with Artesian Lateral Boundary) ...................................................................................................... 52 3.1.2 Artesian Top and Bottom Boundaries with Impermeable Lateral Boundary ......... 57 3.1.3 Unconfined Aquifer (Artesian Top and Impermeable Bottom Boundaries with Impermeable Lateral Boundary) ............................................................................... 61 3.1.4 Shape Factor or F factor ............................................................................................ 62 3.1.5 Anisotropy .................................................................................................................. 64 3.1.5.1 Injection and Recirculation Tests ................................................................... 64 3.1.5.2 Injection Test and Head Observation ............................................................. 66 3.2 Volume of Influence (VOI) of Flow Field .......................................................................... 70 3.2.1 Objectives of VOI ...................................................................................................... 70 3.2.2 Determination of VOI Using P otential and Stream Functions ................................ 71 3.2.3 Determination of VOI Using Derivatives of Potential and Stream Functions ....... 74 3.3 Influence of Screen Slots on F factor and Head Change along the Probe Screen ............ 80 3.3.1 Confined Aquifer ........................................................................................................ 81 3.3.2 Arte sian Top and Bottom Boundaries (No Boundaries Effect) ............................... 86 3.3.3 Example Application of VAHIP ............................................................................... 89 3.4 Hydraulic Resistance due to Compaction and Screen Effects ........................................... 91 3.5 Comparison between VAHIP Results and the Axisymmetric Model ............................... 92 3.6 Hydraulic Conductivity Measureme nts under Unsaturated Conditions ............................ 97 4 LABORATORY EXPERIMENTS .......................................................................................... 100 4.1 Objectives ............................................................................................................................ 100 4.2 Design and Construction of the TwoScreen Probe .......................................................... 100 4.3 Barrel Tests .......................................................................................................................... 101 4.4 Experimen tal Design and Laboratory Results .................................................................. 103 4.4.1 Independent Permeability Measurement (Constant Head Test) ............................ 104 4.4.2 Testing under Saturated Conditions ........................................................................ 106 4.4.2.1 Injection and Recirculation Tests Using a TwoScreen Probe ................... 107 4.4.2.2 Injection Test with Head Observation .......................................................... 111 4.4.3 Testing under Unsaturated Conditions .................................................................... 114 4.4.3.1 Injection Test Using a Single Screen Probe with Different Flow Rates .... 114 PAGE 8 8 4.4.3.2 Injection Test through Two Dif ferent Screen Lengths with Equal Flow Rates ................................................................................................................ 116 5 FIELD APPLICATION ............................................................................................................ 119 5.1 Alternative Solutions for VAHIP Problems ...................................................................... 119 5.1.1 Mechanical Problems ............................................................................................... 119 5.1.2 Clogging Problems ................................................................................................... 120 5.1.3 Practicality of Testing Procedure ............................................................................ 124 5.2 Proposed Probes .................................................................................................................. 124 5.2.1 One screen Probe with Piezometer ......................................................................... 125 5.2.2 Proposed TwoScreen Probe .................................................................................... 126 5.2.3 TwoScreen Probe for Unsaturated Case ................................................................ 126 6 CONCLUSIONS AND RECOMMENDATIONS ................................................................. 129 6.1 Conclusions ......................................................................................................................... 129 6.2 Recommendations and Future Research............................................................................ 130 6.2.1 Effect of Compaction on K Estimates ..................................................................... 130 6.2.2 Laboratory Testing ................................................................................................... 132 6.2.3 Variation of K in Relation with the Location of Heterogeneity ............................ 133 6.2.4 Passive Flux Meter (PFM) ....................................................................................... 133 LIST OF REFERENCES ................................................................................................................. 135 BIOGRAPHICAL SKETCH ........................................................................................................... 140 PAGE 9 9 LIST OF TABLES Table page 2 1 Comparison between hydraulic conductivity and intr insic permeability ........................... 23 2 2 Hydraulic conductivity of some soils .................................................................................... 24 2 3 Ranges of intrinsic permeability and hydraul ic conductivities ........................................... 24 3 1 Comparison between the axisymmetric model and V AHIP results .................................... 96 5 1 Constant head test for high permeability sand ................................................................... 105 5 2 Constant head test for intermediate permeability sand ...................................................... 105 5 3 Constant head test for low permeability sand..................................................................... 105 5 4 Different probe geometries .................................................................................................. 108 5 5 Hydraulic conductivity measurements using injection test (Ki) at probe1a ..................... 109 5 6 Hydraulic conductivity results using recirculation test (Kc) at probe1a ........................... 109 5 7 Hydraulic conductivity measurements using injection test (Ki) at probe 1b .................... 110 5 8 Hydraulic conductivity results using injection test (Ki) at probe 2 ................................... 110 5 9 Hydraulic conductivity measurements using injection test (Ki) at probe 3 ...................... 111 5 10 Hydraulic conductivity results using recirculation test (Kc) at probe 3 ............................ 111 5 11 Isotropic conductivity measurements Kiso for different probe geometries ....................... 113 5 12 Analysis results using different probe geometries with different flow rates .................... 115 5 13 Results for unsaturated case using different probe geometry with Q = 8.47 cc/s ............ 117 5 14 Results under unsaturated conditions with Q = 9.02 cc/s .................................................. 117 PAGE 10 10 LIST OF FIGURES Figure page 2 1 Anisotrop ic bed of particles ................................................................................................... 25 2 2 Constant head permeameter ................................................................................................... 28 2 3 Falling head permeameter ...................................................................................................... 29 2 4 Flexib le wall permeameter .................................................................................................... 30 2 5 Pumping test in a confined aquifer ........................................................................................ 31 2 6 Pumping test in an u nconfined aquifer ................................................................................. 32 2 7 Slug test con figuration ........................................................................................................... 33 2 8 Slug test for confined and unconfined aquifers .................................................................... 34 2 9 Packer sy stem in a borehole .................................................................................................. 35 2 10 Dipole flow test ...................................................................................................................... 36 2 11 Direct push method ................................................................................................................ 38 2 12 Infiltrometers: (a b) open and closed single rings (c d) open and closed double ri ngs ..... 39 2 13 Well with a fi nite line source ................................................................................................. 41 2 14 Well and aquifer geomet ry .................................................................................................... 46 2 15 Vertical and horizontal in situ permeameter (VAHIP) A) 2004, B) 2005, C) 2006 .......... 48 3 1 Impermeable top and bottom boundary conditions of two inje ction screens ..................... 51 3 2 Stream and potential functions for impermeable top, bottom and lateral artesian boundaries, in the case of two screen injection test ............................................................. 57 3 3 Potential and stream functions for artesian top, bottom and lateral impermeable boundaries ............................................................................................................................... 61 3 4 Relative F factor for different distances and types of horizontal boun dary conditions ..... 63 3 5 Relative F factor for injection (Fi/a) and recirculation (Fc/a) tests for two screen probe with no boundary effect ......................................................................................................... 64 PAGE 11 11 3 6 Two screen probe for injection (left) and recirculation (right) test to measure vertical and horizontal hydraulic conductivities under saturated conditions ................................... 65 3 7 Determination of anisotropy from the ratio of head at injection screen and head at pressure screen with no boundary effects (d=100, b=Infinity) ........................................... 69 3 8 Relative Fi/s versus the relative scaled probe radius a/s with no boundaries effect (d=100, b=Infinit y) ................................................................................................................. 69 3 9 Potential function for artesian boundaries, in the case of one screen injection test (s/a=10) ................................................................................................................................... 72 3 10 Example of resulting flow field properties for injection/extraction with close by vertically confining layers ..................................................................................................... 73 3 11 Contour lines of the equipotential and stream functions in the case of recirculation test with p/s = 5 ............................................................................................................................. 73 3 12 Streamfunction for axisymmetric fl ow: Cylindrical coordinates ........................................ 75 3 13 Contour lines of the magnitude gradient of potential function ) ( z r using a single injection screen ....................................................................................................................... 75 3 14 Contour lines of the magnitude gradient of stream function ) ( z r using a single injection screen ....................................................................................................................... 76 3 15 Radial (Vr/a [ ]) and vertical extent (Vz/a [ ]) of VOI with respect to the screen length (s/a [ ]) using ) ( z r for a single injection screen ............................................................ 77 3 16 Contour lines of the magnitude gradient of potential function ) ( z r using recirculation test with p/s= 5 ................................................................................................. 78 3 17 Contour lines of the magnitude of ) ( z r with large separation between screens using recirculation test (p=15 and s=3) ........................................................................................... 79 3 18 Radial (Vr/a [ ]) extent of VOI with respect to the relative screen length (s/a [ ]) using ) ( z r for recirculation test ............................................................................................... 79 3 19 Vertical extent (Vz/a [ ]) of VOI with respect to the relative screen length (s/a [ ]) using ) ( z r for recirculation test ...................................................................................... 80 3 20 Physical configuration of one slotted (left) and continuous screens (right) for confined aquifer ..................................................................................................................................... 82 3 21 The ratio of the F factors between slotted and continuous screen (Fslot/Fcont [ ]) or mean head of slotted screen [ ] for ss/a=0 02 ................................................................................. 83 PAGE 12 12 3 22 The F factors ratio (Fslot/Fcont [ ]) or mean head of slotted screen [ ] for ss/a=0.5 ............. 83 3 23 The ratio of the F factors (Fslot/Fcont [ ]) for a confined case with ds/ss = 27 ...................... 84 3 24 The F factors ratio (Fslot/Fcont [ ]) with ds/ss = 11 using confined aquifer ........................... 85 3 25 The ratio of the F factors (Fslot/Fcont [ ]) with ds/ss= 4 using confined case ........................ 85 3 26 Physical configurations of two slotted (left) and continuous screens (right) for infinite flow domain ............................................................................................................................ 87 3 27 The F factor ratio (Fslot/Fcont [ ]) versus s/a [ ] for boundaries far away and ps/ss= 26 ...... 87 3 28 The ratio of the F factors (Fslot/Fcont [ ]) for infinite flow domain and ps/ss= 10 ................ 88 3 29 The F factors ratio (Fslot/Fcont [ ]) versus relative screen length (s/a [ ]) for boundaries far away and ps/ss=3 ............................................................................................................... 88 3 30 The ratio of the F factors (Fslot/Fcont [ ]) versus relative distance to top and bottom boundaries (d/s [ ]) with s/a= 20 (Ns =10 slots) ................................................................... 89 3 31 Example of variable head distribution along slotted screen using method of images for 11 periodical repetitions ......................................................................................................... 90 3 32 Example of constant head along the slotted screen width and variable head distribution along the impermeable part of the screen using VAHIP case ............................................. 90 3 33 Testing at depth = 91.5 cm from ground s urface ................................................................. 93 3 34 Illustration of the VAHIP probe dim ensions ........................................................................ 93 3 35 Boundary conditions for axisymmetric flow domain of si ngle injection screen ................ 95 3 36 Relative F factor for different injection screen and boundaries are located far away from the inject ion screen (d/s=50, b/a=1000) ASTM and Hvorslev methods are shown for comparison ........................................................................................................................ 97 3 37 Two screen probe with different equivalent spherical radii r1 and r2 for injection test under unsaturated conditions ................................................................................................. 99 4 1 Different probe dimensions (not to scale) .......................................................................... 101 4 2 Two screen probe with s = 7.4 cm and p = 14.4 cm ......................................................... 102 4 3 Three barrels with three different types of test material .................................................... 102 4 4 Perastaltic pump with two flow meters and pressure transducers (left). Power supply with two voltme ters (right) .................................................................................................. 103 PAGE 13 13 4 5 Barrel configuration for laboratory testing under saturated and unsaturated conditions 104 4 6 Physical configuration of the permeameter with a screen length of A) s = 7.4 cm. B) s =3.7 cm. C) s = 2.4 cm. ........................................................................................................ 108 5 1 Modified probe to solve clogging problems and to detect water table elevation, before injection (Left) and after injection (Right) ......................................................................... 121 5 2 Twisted screened probe (left) rotating vane (top view) (right) ......................................... 122 5 3 Three different flow meter ranges for conductivity estimates ........................................... 122 5 4 Two screen prob e covered with two inflatable packers A) before inflation B) after inflation ................................................................................................................................. 123 5 5 Two screen probe shielded with filters ............................................................................... 123 5 6 Modified probe to solve rod tubing installation problem .................................................. 124 5 7 Proposed single injection screen probe with small openings for head observation ......... 125 5 8 Proposed twoscreen probe for injection and recirculation tests ....................................... 126 5 9 Alternative probe design for different packer lengths ....................................................... 127 5 10 Proposed probe for compressed rubbers between the top and bottom screens ................ 128 6 1 Proposed coned three screened drive point probe for injection test to measure field saturated hydraulic conductivities in fully and partiall y penetrated zones ....................... 131 6 2 Experimental configuration for the effect of compaction on K estimates ........................ 132 PAGE 14 14 LIST OF ABBREVIATIONS A Cross sectional area of specimen [L2] a Probe radius [L] Bo,u Fourier coefficient of zero frequency of unit injection head [ L] b Distance from the probe axis (r = 0) to the lateral Boundary [L] d Distance betwe en top and bottom boundaries [L] De Characteristic effective grain size [L] D Distance from bottom of screen to lower confining unit [L] F Shape factor [L] Finj Injection F factor [L] Fcir Circulation F factor [L] g Gravitational constant [LT2] Ht Total Head [L] Kr Horizontal Hydraulic Conductivity [LT1] Kz Vertical Hydraulic Conductivity [LT1] Ki Injection Hydraulic Conductivity [LT1] Kc Recircula tion Hydraulic Conductivity [LT1] Kfs Field saturated hydraulic conductivity [LT1] Kiso Isotropic hydraulic conductivity [LT1] k20 Coefficient of permeability at 20oC [L/T] kT Coefficient of permeabilit y at the test temperature [L/T] k Intrinsic permeability [L2] L Length of sample [L] n Porosity [ ] PAGE 15 15 N Quality of approximation [ ] R Hydraulic resistance [TL2] Re Effective radius of influence [L] r Equivalent spherical radius of injection cavity [L] r0 Saturated bubble radius rc Radius of casing [L] rs Radius of borehole [L] rw Horizontal distance from the well center to the original aquifer [L] S Degree of saturation [% ] s S cr een length located at the center of the flow domain [L] Tr Tortuosity in the horizontal direction [ ] Tz Tortuos ity in the vertical direction [ ] Vz Vertical extent of volume of influence [L] Vr Horizontal extent of volume of influence [L] Vv Volume of void [L3] Vs Volume of dry soil [L3] yt Difference of water level between the inside and outside of the well at time t [L] Potential function [L2T1] Stream function [L3T1] Magnitude gradient of potential function [ L/T ] Magnitude gradient of stream function [ L2/T ] Total head loss [L] Anisotropy ratio [ ] Sor ptive number [L1] PAGE 16 16 Capillary length or sorptive length [L] Moisture content [ % ] Injection head [L] T Viscosity of the fluid at the test temperature [ML1T1] 20 Viscosity of the fluid at 20oC [ML1T1] PAGE 17 17 Abstract of Dissertation Presented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy DESI GN OF A TWO SCREEN PROBE TO MEASURE IN SITU HORIZONTAL AND VERTICAL HYDRAULIC CONDUCTIVITIES UNDER SATURATED AND UNSATURATED CONDITIONS By Bassel Nemer December 2008 Chair: Kirk Hatfield Cochair: David Bloomquist Major: Civil Engineering The horizontal and vertical conductivities (K) of soil layers are factors of great importance for many engineering developments, including pond and dam des ign, drainage, soil compaction and remediation of contaminated soils. Previous attempts to measure K, such as pump or slug tests, have encountered man y problems, such as soil disturbance and clogging, which affect the accuracy of the results. Furthermore, only the effective K can be obtained from these tests, rather than separate horizontal and vertical hydraulic conductivities. In 2004, the Florida De partment of Transportation (FDOT) sponsored a research project at the University of Florida to design a device, the Vertical and Horizontal In situ Permeameter (VAHIP), for easy and cost effective measurements of horizontal and vertical conductivity at v arious depths of soil formation. However, problems were encountered during testing, indicating that further studies were needed to improve the design of VAHIP and to prototype another device to measure the anisotropic conductivity under saturated conditio ns and the isotropic conductivity under unsaturated conditions In this project, the axisymmetric potential flow theory was used to model the saturated horizonta l and vertical conductivities and volume of influence (VOI) for various probe designs. PAGE 18 18 The mod el considers soi ls with different conductivities and applications to various types of boundary conditions and several boundary locations with respect to the probe. The hydraulic conductivity predictions were tested in the laboratory with four total probe designs. Under saturated conditions, t wo screen probes were used for in jection and recirculation tests ; additionally an injection test with injection from one screen and head measurement at the other screen was used. Under unsaturated conditions, another method was used to measure the saturated hydraulic conductivity. Also, the equivalent spherical radius for c ylindrical injection cavities was improved by using the principle of equivalent shape factors F. T he results of anisotropic conductivities under saturated conditions and isotropic conductiv ity under unsaturated conditions compared well to independent testing via the constant head test and other existing methods. Using the theoretical and laboratory results, improvements to subsurface testing probes were suggested and possi ble probe designs were described to perform all the tests in a single device. PAGE 19 19 CHAPTER 1 INTRODUCTION 1.1 Overview of Hydraulic Conductivity Hydraulic conductivity of soil layers is an important factor to consider for many industries ; for example for se lecting pond or dam locations and the remediation of contaminated soils as well as in cases of seepage of a fluid that c an affect health and /or the environment (Kirkham, 1955). The measurement of hydraulic conductivity, K has been the focus of much research a nd has undergone many progressive st eps (Weigth and Sonderegger 2001, Cassiani, 1998, Zaslavsky and Kirkham 1965). Different methods of laboratory testing exist; however, insitu tests are considered more accurate and reliable especially in the case of sub surface investigation. However, many limitations exist even when performing in situ tests. A common probl em is the disturbance and compaction of the soil when drilling a borehole. These limitations tend to impede the measurements and cause erroneous results (Taylor and Weatcraft 1990). In the case of saturated anisotropic soils, slug tests and pump tests me asure the effective hydraulic conductivity rather than the hori zo ntal and vertical conductivities (Hvorslev, 1951). T he dipole flow test was proposed to quantify both horizontal and vertical conductivity by pumping a constant flow rate, Q, from one screen of a well to an other, but limitations such as the skin effect were encountered while using this method (Zlotnik and Ledder 1996; Kabala and Xiang 1992). In the vadoze zone, some field techniques fo r measuring insitu hydraulic conductivity were develo ped for near surface measurements (Stephens and Neuman 1982). Another subsurface testing method involves the injection of water into soil and the monitoring of steady state pressure distrib utions around the injection location (Chao and Stephens 1993). Sh ani and Or (1995) developed the Subsurface Confined Cavity Test (SCCT) which is identical in PAGE 20 20 principal to the Constant Head Well Permeameter (CHWP) (Reynolds et al., 1985) but SCCT accounts for the effect of capillarity and gravity. The CHWP method used uncased boreholes whereas SCCT used a packer to confine infiltration to the bottom of the borehole. Most field measurements of hydraulic conductivity require the installation of boreholes, depend on the geometrical properties of the borehole and the injec tion cavities, and are influenced by the loc ation of the flow field boundaries (Hvorslev, 1951). Recent research was undertaken to create probes to overcome the issues mentioned above such as compaction and general disturbance of soils. The Florida Depart ment of Transportation (FDOT) sponsored a research project at the University of Florida to design a device, the Vertical and Horizontal In Situ Permeameter (VAHIP), to measure the hori zontal and vertical conductivities and flow at various depths of a soi l formation (Bloomquist et al., 2007). The probe developed in 2006 consisted of an external stainless steel tip with a vertical flow port. From 2004 to 2006, various deficiencies were noted while using the probe. One of the main problems encountered was du ring the opening of the probe tip and pulling up its inner part; this process did not allow operators to determine whether the tip was efficiently opened or not. Another issue was the time and effort spent in removing and replacing the Plexiglas standpipe at every depth required for testing. In addition, clogging of the screen was an obstacle to the accuracy of the results especially in clayey soils. Therefore, to overcome these deficiencies, a study is required for further modifications of VAHIP. The equations used in the original VAHIP design were based on borehole permeability tests under saturated conditi ons ( Bloomquist et al., 2007). In this study a theoretical method is needed to measure the vertical and horizontal hydraulic conductivities under saturated conditions for any combination of artesian and impermeable top, bottom and lateral boundaries. PAGE 21 21 Furthermore, another method is required to measure the hydraulic conductivity under unsaturated conditions. It is also important to characterize the v olume of influence of the flow domain interrogated for different probe radii and sizes of the injection cavities. Therefore, both laboratory and in situ testing are essential for the assessment and evaluation o f hydraulic conductivity which serve to valid ate the theoretical model 1.2 Goals and Objectives The first goal of this research is to improve the design of the existing VAHIP probe and to prototype another device capable of accurate measurements of b oth vertical and horizontal hydraulic conductivit ies under both saturated and unsaturat ed conditions. Another goal is to determine the volume of influence (VOI) of a flow domain using an axisymmetric potential flow field method under various probe dimensions and boundaries taken far away from the probe a xis The third and final goal is to validate t heory and probe performance through laboratory tests To achieve these goals, the following research objectives will be perused: Theoretical: 1 Determine the axisymmetric potential flow field through analytical potential and stream functions and their derivatives for any combination of artesian or impermeable top, bottom and lateral boundaries 2 Conduct a theoretical evaluation of the volume of influence (VOI) of the flow domain interrogated for any probe dimensi on. 3 Study the influence of the screen slot geometry on F factor and head change in confined and unconfined aquifers. Evaluate the effect of the screen slots and their width on the accuracy of K measurements. 4 Evaluate the hydraulic resistance (R) due to com paction and screen effects. Evaluate its effect on K measurements. 5 Develop another method that can measure K by injecting from one screen and observing the head from the other screen. 6 Compare Vertical and Horizontal In Situ Permea meter (VAHIP) in situ results with the proposed theory. PAGE 22 22 7 Develop a method that can measure the saturated hydraulic conductivity K and capillarity effects under unsaturated conditions and evaluate the equivalent spherical radius by equating F factors instead of surface areas La boratory: 1 Validate the axisymmetric theory by performing two kinds of tests: The injection test to measure horizontal hydraulic conductivity (Kr ~ Kinjection) and the recirculation test (Kz ~ Krecirculation) to measu re vertical hydraulic conductivity unde r saturated conditions. Another validation method involves performing injection test from one screen and use the other screen as a piezometer. 2 Validate the theory by using sub sequently two probes with different screen lengths to measure hydraulic conductivity under unsaturated conditions. Evaluate the independent measurement of sorption length. In situ: 1 Provide solution s for screen clogging when the probe is being introduced into media such as clayey soils. Such clogging would decrease the effective area o f the screen in an unpredictable way creating inaccurate measurements of the conductivity. 2 Provide a practical solution that can help save time and effort when the probe is being driven into the ground. Essentially eliminate the current deficiency of the V AHIP design which uses a P lexiglas standpipe that has to be removed and replaced frequently when testing over multiple depths. 3 Propose different configuration of probes under saturated and unsaturated conditions, and combine their applications into a sing le device. PAGE 23 23 CHAPTER 2 LITERATURE REVIEW 2.1 Hydraulic Conductivity and Intrinsic Permeability The saturated h ydraulic conductivity (Ks [LT1]) which is referred to as hydraulic conductivity (K) defines the movement of water through the soil relative to a difference in head It depends on the degree of saturation, soil pore geometry as well as the fluid viscosity and density. Intrinsic permeability or permeability (k [L2]), is the ability of soil to pass liquid through void spaces. Unlike saturated hydraulic conductivity, intrinsic permeability is a parameter of a porous medium wh ich is independent of the fluid Table 2 1 shows a comparison between hydraulic conductivity and intrinsic permeability which are related through the following equa tion: k K where 2T2 is the dynamic viscosity of water ML1T1 Table 2 1. Comparison between hydraulic conductivity and intrinsic permeability (Skopp, 1994) Hydraulic Conductivity ( K ) Intrinsic Permeability ( k ) Dependent on t emperature and f luid viscosity () Independent of t emperature and unaffected by fluid viscosity () Changes with structure modification Changes with structure variation Dimensions [LT 1 ] depend on flux and gradient; time is a component. Dimensions are unit of area (L 2 ); time is not a component. Based on Darcys law (1856), permeability is defined as the specific discharge under a unit hydraulic gradient. He concluded through experimental observation that the relationship between rate of flow of water, Q, flowing through a cross sectional area, A of soil normal to the direction of flow under hydraulic gradient i is linear and can be expressed by the formula, A i Q k (2 1) PAGE 24 24 wher e Q is the flow rate (L3 / T) i is the hydraulic gradient (L / L) = A is the total cross sectional area of flow (L2) k is the coef ficient of permeability (L / T) 2. 2 Range of Hydraulic Conductivity for Different Type s of Soils In general the hydraulic conductivity can be classified by soil type. Ta bles 2 2 and 23 show different degree s of permeabil ity for respective soil type s and drainage conditions. Table 2 2 Hydraulic conductivity of some s oils ( Casagrande and Fadum 1940) Degree of permeability K (cm/sec) Soil type s Drainage conditions High High Medium Low Very low Very low 10 1 to 10 2 101 101 to 104 105 106 10 7 to 10 9 G ravels S and S and and gravel Very fine sand Silt Clayey soils Good Good Good Poor Poor Impervious Table 2 3 Ranges of intrinsic permeability and hydraulic conductivities ( Fetter 2001) Material Intrinsic Permeability k (cm/s) Hydraulic Conductivity K (cm/s) Well sorted gravel Silty sands, fine sands Silt, sandy silts, clayey sands Clay 1 10 2 102 1 103 101 10 6 10 3 10 3 10 1 105 103 106 104 10 9 10 6 Values of hydraulic conductivity estimated for sands typically range from 101 cm/sec to 103 cm/sec for coarse to fine sands and 10 3 cm/sec to 105 cm/sec for fine sands to sil ty sands (Lamb, 1932). Clay may be defined as soil particles that exhibit plasticity when mixed with wa ter in certain proportions (Daniel and Trautwein 1993). 2.3 Factors Affecting Permeability Since permeability is defined a s the ab ility of soil to pass liquid through void spaces, it depend s not only on the characteristics of the fluids but also on the soil type, composition and other factors (Cedergren, 1989): PAGE 25 25 1 Size and connectivity of the pore spaces, which depend on: (a ) Size of the soil particles, (b ) Structure of the soil and anisotropy. 2 Viscosity. 3 Existence of discontinuities and degree of saturation 2.3.1 Size of the Soil Particles Extensive analyses have demonstrated that the permeability is proportiona l to the square of the diameter of the soil particles by using Hansens empirical formula ek2CD In general, the larger the particle size the h igher permeable is the soil media. 2.3.2 Structure of the Soil and Anisotropy The soil structure affects the permeabilit y due to the particle arrangement and orientation. Many researchers have realized t he effect of particle orientation on the magnitude of the directional permeability (Fowler and Herte l 1940). The permeability in the direction parallel to the planes of stratification can be higher than in the direction perpendicular to the bedding. If the permeability of a porous medium varies with the direction of fluid flow the permeability is anisotropic (i.e., the vert ical and horizontal permeability are different) Due to the flatness, and orientation of the particles, p ermeability anisotropy occurs (Rice et al, 1970). Figure 2 1 shows this patter n in various structures and stratifications of in situ and water deposited soils. Figure 2 1 A nisotropic bed of particles (Rice, 1970) K h K v PAGE 26 26 2.3.3 Viscosity of Water Viscosity is a measure of fluid frict ion which is being deformed by parallel or tangential stress. Because t he viscosity of the fluid decreas es when the te mperature increases, the permeability of water through soils increases as the temperature increases The effect of viscosity is eliminated by specifying 20o C as a standard temperature to evaluate the permeability 20 T T 20k k (2 2) where k20 is the permeability at 20oC kT is the permeability at the experiment temperature T is the viscosity of water at the experiment temperature 20 is the viscosity of water at 20oC. 2.3.4 Existence of Discontinuities and Degree of Saturation The presence of cracks and voids may convert the impermeable soil into a porous material Another factor which can affect hydraulic conductivity, is the degree of saturation which is t he proportion of the pores in a soil filled with water. I n general, a greater degree of saturation leads to higher permeability (Bear 1972 ). 2.4 Methods for Determining Hydraulic Conductivity in Saturated Media Two types of tests laboratory and in situ, have been used to determine the soil permeability. In gen eral, results of laboratory tests are different from the actual permeability in field. In mo st of the cases, the laboratory permeability result s are higher than the in situ results because of the disturbance of soil and other factors. The differences between laboratory and in situ tests are discussed below: 1 The size of the sample taken to the laboratory is much smaller than the field size which can cover a large area. 2 S oil collected for laboratory tests has a different degree of compaction than soil i n the field, thus increasing the measured permeability of sand compared to the field conductivity estimates. PAGE 27 27 3 Because t he actual field boundar y conditions are different from the cylinder walls boundary laboratory tests can give inaccurate results for co nductivity measurements. 4 The situation encountered in the field might have cracking in the soil formation, but laboratory experiments do not realize this problem. 5 The entrapped air in the laboratory sample might give erroneous permeability results. 6 Water used in the laboratory has characteristics different from groundwater flow. The above list illustrates the greater importance of field methods compared to laboratory testing (Charbeneau, 2000). 2.4.1 Laboratory Methods The advantage of laboratory methods is that the sample size and the applied head are well defined and easily controlled. However, results for the disturbed sample in the laboratory are higher than the actual conduct ivity estimates in the field. The experimental process generally uses a cylin drical sample with defined dimensions where a difference in head is applied between the upper and lower part of the sample to measure the hydraulic conductivity of soil. In general, three types of permeability tests are applied in the laboratory to determi ne the hydraulic conductivity of soils under saturated conditions. 2.4.1.1 Constant head t est The constant head test is usually used for high ly permeable sand with a coefficient of permeability greater than 103 cm/s (Terzaghi and Peck 1967). T he vertica l permeability is obtained by applying one dimensional Darcys law (1856). The volume of water passing through the sample over a specified period of time is recorded with a graduated cylinder. This flow rate is directly proportional to the cross sectional area of the sample (A) and the head difference between top and bottom of the test material ( the t esting material (L) (Figure 2 2 ) PAGE 28 28 HA t QL k (2 3) where: k is the coefficient of permeability [L/T] Q is the total quantity of water which flowed through the sample in elapsed time t [L3] t is the elapsed time [T] is the total head loss [L] A is the cross se ctional area of the specimen [L2] L is the length of sample [L] Figure 2 2 Constant head permeameter ( Fetter, 2001) 2.4.1.2 Falling h ead test The falling hea d test is used for low permeability soils with a coefficient of permeability less than 1 cm/s (Terzaghi and Peck 1967). Figure 2 3 shows a configuration of the falling head permeameter with the dimensions. In addition to the setup for the constant head test, the apparatus includes a long standpipe to measure the time it takes the water to drop from the initial to the final height PAGE 29 29 T he permeability of the soil is then determined by applying Darcys law as follows: Figure 2 3 Falling head permeameter (Fetter, 2001) 1 0 eH H log At rL k (2 4) where t is the time elapsed between the initial head H0 [L] and the final head H1 [L]; r [L] is the radius of the standpipe connected to the bottom cylinder. Either the constant head or fallin g head tests can measure the hydraulic conductivity of the test sample by controlling the pressure. 2.4.1.3 Flexible w a ll p ermeameter This method is idea l for low hydraulic conductivities with a coefficient of p ermeability less than 1 x 103 cm/s. The procedures for preparing the test sample s are discussed by Daniel and Trautwein (1993) Chapuis (2003) and others. The main advantage of the flexible wall PAGE 30 30 permeameter is that the applied stress on the sample is controlled. Figure 2 4 shows a schematic of the device. Figure 2 4 Flexible wall permeameter (ASTM 1998) A flexible wall permeameter is preferred to a ri gid wall permeameter to avoid short circuiting of flow on the e dges of the apparatus However, the rigid wall permeameter is less expensive and easier to use. 2.4.2 In situ Methods for Determining the Coefficient of Permeability Compa red to laboratory testing, i n situ testing is considered more consistent and representative of actual field co nditions Furthermore, subsurface methods are able to measure permeability at different depths giving more information about the composition of t he soil PAGE 31 31 S urface methods which are easier to perform represent the conditions at shallow depths only. Different methods exist for the field measurement of permeability under saturated conditions. This section describes t he pump and slug tests which are p erformed to measure the anisotropic conductivities for larger or smaller scale analysis. The packer and dipole flow tests are also dis cussed. 2.4.2.1 Pump test The p umping or aquifer test is a large scale method in which water is extracted from one well at a constant rate while observing the drawdown in the observation wells (Fetter, 2001) The permeability can then be estimated the cases of both confined and unconfined aquifers. Figure 2 4 shows the configuration of the well pumping test. Figure 2 5 Pumping test in a confined aquifer (Fetter, 2001) For the confined aquifer, two observation wells are separated from the pumping well at distances r1 and r2. The well is assumed to be fully penetrated into a homogeneous and isotropic aquifer under st eady state flow conditions. Dupuit assumptions are also used to calculate the PAGE 32 32 perm eability of the soil (Cedergren 1989). T he permeability is determined using the following Theim equation: 1 2 1 2r r ln ) h h ( b2 Q k (2 5) where b [L] is the thickness of the confined aquifer and the other var iables are defined in Figure 2 5 For the unconfined aquifer (Figure 2 6 ), the radial flow is given by a modified Theim equation : 1 2 2 1 2 2r r ln ) h h ( Q k (2 6) The p umping test is applied for larg e scale investigation s, while a slug test is usually used if a smaller volume of aquifer needs to be tes ted (Bear 1972 ). Figure 2 6 Pumping test in an unconfined aquifer (Fetter, 2001) 2.4.2.2 Slug test A slug test, shown in Figure 2 7 uses a single borehole for smaller scale investigation s and it measures the recovery of head in a well after a near instanta neous change in head. Therefore, the response in head is used to estimate the aquifer permeability. This test can be PAGE 33 33 performed easily and cost effectively, where no pumping of possibly contaminated water to the surface is required. However the disadvantages of slug test s include the inaccuracy of permeability measurements due to the dirt left in the borehole (Butler 1997). Many a nalytical methods have been developed including those by Cooper and Jacob (1946), Hvorslev (1951) Dagan (1978), Bouwer and Rice (1976), and others, but each depends upon the applied conditions in the field. Figure 2 7 Slug t est configuration (Cooper et al., 1967) For example, Hvorslevs method (1951) is based on solving the radial flow equations for a fully penetrating well in a confined aquifer. t 0 s 0 2 sH H ln r b ln ) t t ( b 2 r k (2 7) where b is the length of the intake area PAGE 34 34 rs [L]is the radius of the borehole H0 and Ht [L] are the changes in heads from time to to t. In Hvorslevs method, the permeability is calculated by t 0H H ln versus the time difference (tot). The slope is equal to b r ln r kb 2s 2 s (Domenico and Schwartz 1990). Another method for determining the hydraulic conductivity for both confined and unconfined aquifers is based on the Bouwer and Ri ce (1976) slug test (Figure 2 8 ). The hy draulic conductivity is calculated as follows: t 0 w e e c 2y y ln r R ln t L 2 r k (2 8 ) where rc is the radius of casing yt is the difference of water level between the inside and outside of t he well at time t Le is the effective screen length rw is the horizontal distance from the well center to the original aquifer Re is the effective radius of influence Figure 2 8 Slug test for confined and unconfined aquifers (Bouwer and Rice 1976) 2.4.2.3 Packer test In the Packer test (Figure 2 9 ), many sections of a borehole are separated with inflatable packers to measure the in situ permeability. The p ermeability is calculated for different screen lengths from the following formulas: PAGE 35 35 10r L r for r 2 L sinh a Lh 2 Q k (2 9 ) 10r L for r L ln Lh 2 Q k (2 10) wher e L is the distance betwee n the upper and bottom packers r [L] is the radius of the borehole Q [L3/T] is the flow rate h [L] is the applied head. Figure 2 9 P acker system in a borehole (Heath 1983) P roblems associated with the Packer test include leakage aroun d the packers, clogging air bubbles in the system and others (Cedergren, 1989). 2.4.2. 4 Dipole p robe The main application of the dipole flow test (Figure 2 10) is for aquifer remediation where the flow rate and the head difference between the two chambers are essential to estimate the horizontal and vertical conductivity of the aquifer (Zlotnik and Ledder 1996).The design consists of injection and extraction source chambers separated by an impermeable casing, with an immersed pump circulating water between the upper and lower chambers. L r PAGE 36 36 Figure 2 10. D ipole flow test (Zlotnik et al, 1998) Under steady state conditions, the radial hydraulic conductivity Kr [L/T] can be calculated from the head difference following equation: w rer h Q K ) ( 4 ln ) ( 2 (2 11) T he dipole shape f actor ) ( is between 0.5 and 1, where is equal to L/ ], 2L is the distance between the two screens center and 2 is the screen length Undisturbed zone Disturbed zone (skin) PAGE 37 37 Dipole flow pr esents the flow induced by recirculation wells (Zlotnik and Ledder 1994). Recirculation wells have finite geometry surrounded by known boundary conditions. A dipole flow field has an equally distributed line source and line sink wi th known separation. The Dipole flow test (DFT) has proven to have limited sensitivity to the presence of aquifer boundaries in many cases (Zlotnik and Zurbuchen, 1998). Other limitations of the dipole flow test include bore sto rage, the skin effect and additional factors affecting the accuracy of the hydraulic conductivity (Kabala, 1993). DFT is much more sensitive to high conductivity skin cause d by drilling tha n to horizontal flow (Zlotnik and Zurbuchen, 1998). Each of the insitu methods has limitations that affect the accuracy of th e results. The major problem is related to the presence of clayey soils which create more disturbances to the test and gives inac curate measurements for permeability estimates. 2.4.2.5 Direct push method Direct push technology has become a broadly used technique for pushing prob es into the subsurface by using cone penetrometer (CPT) and hydraulic hammer instead of drilling a boreh ole (Thorton et al, 1997) (Figure 2 11). This test is capable to perform many slug tests while driving the probe into different depth s The advantages of this method are that it ha s less soil disturbance while driving the probe into the soil formation as well as its cost efficient Furthermore, it has a well organized procedure where the screen is only uncovered to soil formation during testing which can prevent clogging of screen. However the disadvantage of this method is that the inner rod must be repea tedly removed from and returned to the outer rod before proceeding to a deeper formation (Thorton et al, 1997) Hvorslev (1951) (Equation 2 7 ) and Bouwer and Rice ( 1976) (Equation 2 8 ) are the most commonly used methods to calculate the hydraulic conductiv ity (Butler et al, 2000) PAGE 38 38 Figure 2 11. D irect push method (Butler et al 2000) 2.4.3 Indirect and Empirical Methods Indirect methods use empirical relationships between permeability and physical quantities that are not directly related to the flow. The most common empirical formulas are the Hansen Kozeny Carman and Hagen Poiseuille equations (Charbeneau, 2000) For indirect p ermeability measurements, Hazen (1911) developed a relation between the grain size distribution and the coeffici ent of permeability : k = C D10 2 (2 12) where k is the permeab ility [L/T] and D10 is the effective grain size corresponding to 10% passing with the constant C=1. As shown in equation 2 12, the permeability decreases with the soil grain size In the present study only direct methods are used to determine hydraulic c onductivity PAGE 39 39 2.5 Methods for Determining Hydraulic Conductivity in Uns aturated Media Several methods are available to determine the field saturated hydraulic conductivity K under unsaturated conditions However, most of these methods are limited to shallow measurements, such as the borehol e flow net method (Stephens and Neuman, 1982), or the disc permeameter (White and P erroux 1987). Some shallow methods consist of measuring t he flow rate of water through open or closed rings installed at the desired depth. Other methods for use in the su bsurface aquifer involve tens iometer measurements of matric potentia ls (Shan and Stephens 1993), lea di ng to indirect measurements of K T his study is restricted to direct methods for the measurement of saturated hydraulic conductivity in unsaturated medium. 2.5.1 Infiltrometers Infil trometers are u sed to evaluate the percolation rate of water through soils. These devices are easy to use, and they are cost effective The infiltration rates are estimated by dividing the volume of water percolated into the soil by the area a nd time (Dani el and Trautwein, 1993). These tests are limited to shallow soil under unsaturated conditions. The most common types of infiltrometer are shown in Figure 2 12 and discussed briefly below. Figure 2 12. Infiltr omet ers: (a b ) open and clos ed single rings. (c d ) open and closed double rings (Daniel and Trautwein 19 9 3 ) PAGE 40 40 2.5.1.1 Open and c losed s ingle r ings An open single ring infiltrometer is kept at constant head and the flowrate is recorded to measure the vertical hydraulic conductivity by the Green Ampt mo del (Green, 1911, Chen and Young 2006) As shown i n Figure 2 12 a and b, t he only difference between the open and closed ring is that the latter minimizes the evaporation effects by closing the upper part of the infiltrometer. The closed single ring is ma inly applied for low permeable sand since it requires a longer time for percolation (Daniel and Trautwein, 1993) 2.5.1.2 Open and c losed d ouble r ings In these adaptations a second inner ring is added to the ope n ring. The outer ring acts as an obstacle t o push only vertical flow from the inner ring into the ground. The closed double ring is mainly applied for low permeable sand, since it provides better accuracy (Daniel and Trautwein, 1993) 2.5.2 Borehole Infiltration Tests The borehole infiltration tes ts are based on injecting water at a specific position and record ing the steady state p ressure around the s ource. Analytical solutions are used for steadystate conditions with either a constant head using a single injection test or different heads using multiple injection tests (Shan and Stephens 1993). Stephens and Neuman (1982) discussed the constant head borehole infiltration tests used to determine th e field saturated conductivity K with some simplifying assumptions th at do not account for capillarity. The two main complexities of unsaturated conditions are the effects of gravity and capillarity. The latter effect depends on the degree of partial saturation while gravity effects are constant (Stephens and Neuman, 1982) PAGE 41 41 2.5.2.1 Constant h ead w ell p ermeameter (CHWP) Due to its practicality in the field, the constant head well permeameter (CHWP) also called Guelph permeameter is the most frequently used technique to meas ure the saturated permeability K [L/T] accountin g for both gravity and capillarity (Reynolds et al. 1985). Under steady state conditions, different heads and infiltration rates are recorded to determine the hydraulic conductivity and capillary effects. T he setup is shown in Figure 2 13. Figure 2 13. W ell with a finite line source (R eynolds et al. 1985) The value of K is given by 2 2 mH a2 C 1 H 2 H 2CQ K (2 13) w here 2 2 2 1 2) b H ( H a H ) b H ( H a a ) b H ( sinh H ) b H ( H C (2 14) and the anisotropy ratio that depends on soil properties is 2 2H a 2 C 1 K H 2 CQ HK 2 (2 15) where m is the matric flux potential Well b z r a Line source h H PAGE 42 42 T he other parameters ar e provide d in the notation of Figure 2 13. This method is used in shallow boreholes to infiltrate water at different constant heads. Cassiani (1998 ) applied a semi analytical solution (Greens function approach) to solve the boundary value problem for a constant head permeameter test. However, this solution assumes no g ravity flow and capillarity modeled in a quasi linear approach. Therefore, another method is needed to m easure the permeability for subsurfac e boreholes and to account for gravity. 2.5.2.2 Subsurface C onfined Cavity Test (SCCT) With this consideration, the subsurface confined cavity test (SCCT) developed by Shani and Or (1995), uses a packer to prevent infiltration to the base of a borehole where water is injected at different head pressures and flow rates Q. Under steady and Q follow linear relationship s, and the saturated conductivity K [L/T] and th [L] are determined from the slope (y) and intercept (y) of best linear fit to the observed data. y 1 (2 16) ryy 8 ) r y 2 ( K (2 17) T he equivalent spherical radius r of the injection cavity is determined by equating the active surface areas to give: 2 1 b b)] r L 2 ( r [ 2 1 r where rb is the radius of bore hole L is the height of the cavity from the bottom of borehole to the bottom packer. Friefeld and Oldenburg (2000) developed a new permeamete r, Restricted Interval Guelph P ermeameter with a single packer to apply two different heads and record two different PAGE 43 43 flow rates 1, Q12, Q2) The resulting saturated hydraulic conductivity K [L/T] and 1] are as follows: ) ( r 4 Q Q K2 1 2 1 (2 18) and 1 2 2 1 2 1Q Q Q Q (2 19) w here and the equivalent spherical radius r is calculated the same way as Shani and Or method. The radius of the saturated bulb r0 [L] is obtained as : K 4 Q r0 (2 20) The advantage of this model is that it is simple to apply in the field and does not require extensive use of numerical calcul ation. 2 .6 Factors Affecting Hydraulic Conductivity Determined from Slug Tests Slug tests are low cost rapid methods to m easure hydraulic conductivity in the area surrounding well screen. The hydraulic conductivi ty is derived as a functi on of the geometry of the well screen length, radius of the casing, as well as the art esian or impermeable boundary conditions applied to the top, bottom or lateral distances to the casing (Henebry and Robbins 2005). One of the most sensitive factors is the well skin effect around the screen which, if erroneous can lead to underestimating the hydraulic conductivity. To prevent this, care should be taken during well drilling to minimize the disturbance of the surrounding soil. In cases of m ore permeable well skin the radius of influence can be increased by using a larger head change (Peursem et al 1999) PAGE 44 44 2.6.1 The Shape Factor or F Factor Hvorslev (1951) evaluated the hydraulic conductivity for different types of wells and intakes. F Q [L3/T] to the hydraulic conductivity of the test medium K [L/T] as follows K Q F (2 21) T o use Darcys law to measure the permeability, t he dimensions of the soil being tested are required. Because these dimensions cannot be determined in the field, the shape factor F was established based on the probe dimensions and boundary conditions (Hvorslev, 1951 and Klammler, 2007) 2.6.2 Anisotropy Increase as a Result of Applied Compressive Strength Research commonly uses in situ tests due to the inaccuracy of calculations based upon laboratory measurements. However, the insitu metho d s also have flaws leading to inaccurate permeability values. These occur during the drilling of the borehole which disturbs and compacts the soil. Multiple scenarios are given to evaluate the increase of anisotropy due to the applied compressive forces, r elated to the skin effect, flow path tortuosity and void ratio. Drilling activities and the compaction of soil cause changes in anisotropy and permeability near the well bore; this is known as skin effect (Ba tu, 1997). Figure 2 10 shows an analysis performed by Kabala (1993) and Peurse m et al (1999), which includes the effect of the disturbed zone around the well with a n equivalently distributed source/sink line over the screened well. As the skin compaction zone around the well in creases it distorts the steamlines radial ly inward. A skin with higher conductivity than the ambient anisotropic aquifer tends to create short circuiting d ue to compacted zone, whereby a part of flow moves between the two chamber s without ever entering the undisturbed aq uifer (Peursem et al., 1999) These effects l ead PAGE 45 45 to inaccurate results of anisotropic permeability; therefore, they are eliminated by moving the chamber centers further apart When the chambers extend to the horizo ntal boundaries of the aqui fer the influence of the skin is minimal because of the large separation of chamber cen ter s (Peursem et al, 1999). Another scenario studied by Scholes et al., ( 2007) illustrate s the effect of the compress ion of soil particles on the permeability anisotropy as a function of flow path tortuosity T [L/L] which is related to the anisotropy ratio [ ], by : 2 r zT T (2 22) It is important to study how the ratio of tortuosities may cha nge as the medium is compressed. Scholes et al (2007) and Chapuis (1989) showed that the tortuosity in the horizontal dir ection decreases with increasing tension in the direction of compression. In contrast, the vertical flow paths become more tortuous with increasing vertical tension As a result, the permeability anisotropy ( ) incr eases nonlinearly. The two methods described above the skin effect and flow path tortuosity, fo r determining anisotropy yield higher values for the horizontal per meability than the vertical. However, to date, knowledge of per meability anisotropy resulting from the application of a compressive force to a deformable medium and skin effect is not precise. Therefore, alternative methods are needed to eliminate the compaction ef fect in order to obtain accurate permeabilities 2.6.3 Radius of Influence of Flow Field Many definitions have been given to the radius of influence (Hvorslev 1951, Barker and Black 1983, Sageev 1986 and Chirlin 1989) Bouwer and Rice (1976) identified the r adius of influence as the radial distance over which the initial head drop is dissipated. The radius of influence is needed to estimate the volume of aquifer affected by a slug test. Bouwer and Rice PAGE 46 46 (1976) studied the radius of influence using a two dimensional electrical resistance analog for different well and aquifer geometries and they obtained the following relationships: 1 ia s C a s ln 1 1 a R ln (2 23) Figure 2 14. W ell and aquifer geometry (Binkhorst and Robbins 1994) Referring to Fig ure 2 14, Ri is the radius of influence a is the well screen radius, s is the screen length, bt is the aquifer thickness, ds is the distance from water table to bottom of screen and C is given by: a d b ln B A Cs t where A, B, C are empirical constants which are functions of a s [] and can be obtained from graphs given by Bouwer and Rice (1976). The r adius of influence increases linearly with the screen length s, and is approximately s/3. This distance is also related to the degree of well skin effects and to the influence of b t s Water table Lower confining unit a d s PAGE 47 47 boundar y conditions. Binkhorst and Robbins (1994, 1998) proved that the shap e factor decreases exponentially as the radius of influence increases The reduction in F factor results in an increase in the hydraulic conductivity. T his method for the determination of Ri is restricted to two dimensions and steady sta te conditions. In addition, inaccurate values of the empirical constants A, B and C may result in an erroneous radius of influence (Dagan 1978). 2.7 V ertical and Horizontal Insitu P ermeameter (VAHIP) The main objective of the VAHIP project was develop ment of a device that can quickly and inexpensively measure the horizontal and vertical permeability at various depths. Field tests of V AHIP compare d well with the laboratory results but the pr obe did not work well in low permeable sand such as clay due t o clogging problems (Bloomquist et al., 2007) 2.7. 1 Development of VAHIP Figure 2 15 shows VAHIP in various stages of development from 2004 to 2006. In the first design (stage I, 2004), the probe wa s pushed downward and the vertical flow ports were opened to measure the vertical permeability (Kz). Then the probe was pulled upward to close the vertical flow port s, the horizontal ports were opened to inject water through the PVC pipe and measure the horizontal permeability (stage II). However, sand i n the g ap prevented the probe from switch ing from stage II back to stage I. Another problem area was the PVC pipe which was not sufficiently rigid. In 2005, the gap was eliminated by placing a sand shield cover to prevent sand from entering the void. F urthermore, the PVC pipe was replaced by a stainless steel screen. However th e main problem of this design was clogging of the tiny vertical flow ports at probe tip while driving the probe into the soil especially in clayey material. As a result, inaccura te measurements of verti cal permeability were obtained. In 2006, the vertical flow ports were closed while driving the probe into soil and opened by pulling upward the probe tip prior to Kz PAGE 48 48 measurements; h owever some problems have been encountered while us ing this design (Bloomquist et al., 2007) Figure 2 15. Vertical and horizontal in situ permeameter ( VAHIP ) A) 2004, B) 2005, C) 2006 (Bloomquist et al 2007) 2.7. 2 Description of VAHIP 2006 The 2006 probe design has a stainless steel external core with a vertical flow port and one injection screen. On t he first stage of the test, is water injected throug h the screen to meas ure the horizontal permeability. The second stage consists of injecting water through the vertical port to mea sure the vertical permeability. The bottom part of the probe is closed while driving the probe into the soil and is opened pri or to testing (Bloomquist et al., 2007) The permeability is ca lculated using Hvorslev (1951) E quation 2 21 for radial flow. The F factor can be determined by using multiple Fourier expansions (Kirkham 1959) which consider the presence of the probe in t he soil in addition to the correct boundary conditions. Hvorslev (1951) also provided a table for F factor estimation. With VAHIP 2006, the constant (C) (B) (A) PAGE 49 49 head method is used for high permeable sand and the falling head test is used for low permeable sand 2.7. 3 Limitations of VAHIP 2006 The main problem with the 2006 design is mechanical difficulty when pulling the probe tip upward and opening the vertical flow port. The resulting soil disturbance creates inaccurate Kv measurements. The second problem is clogging of the screen while driving the probe into the soil especially in low permea ble soils. The final problem is the practicali ty of testing procedure s in terms of time and effort. Every ti me the probe is pushe d further into the ground, the Plexiglass standpipe, used to mon itor the flow rate and head must be removed and replaced by rods (Bloomquist et al., 2007) PAGE 50 50 CHAPTER 3 THEORETICAL METHODOL OGY T heoretical methods are pr esented in seven major sections. The first section is related to the theoretical and numerical methods for developing an axisymmetric potential flow field model and deriving pertinent potential and stream functions and their derivat ives. The second section concerns the determination of t he volume of i nfluence (VOI), which can be used to determine the limit of the volume of soil being tested. A methodology for determining the flow field based on (r,z) (r,z) and their derivatives will be used to eval uate the volume of influence (VOI) of a flow domain The third and fourth sections discuss the influence of the screen slot geometry and hydraulic resistance of the screen on permeability measurements in confined and unconfined aquifers. The fifth section is a comparison of the axisymmetric model to validate the theory with known methods. All these sections are applied to a saturated media. Finally, the six th section addresses the measurements of permeability in unsaturated conditions. 3.1 Axisymmetric Flo w Field Method In a general approach, the case of a double screen cylindrica l device with a radius of a [L] is considered for both injection and recirculation tests as shown in Figure 3 1. The screens are allowed to vary independently in position and wid th, creating more flexibility for the testing. An exact solution of the axisymmetric potential flow problem for different boundary types and locations will be considered under saturated conditions The system is axisymmetric around the z axis where all com binations of the following boundary conditions will be considered: L ateral artesian or impermeable boundary (condition I) a t finite and infinite radial distance b [L] from the center of the device. Top and bottom artesian and/or impermeable boundaries (conditions II and III) at finite distance d [L]. PAGE 51 51 Boundary conditions V and VII, positioned between h1 [L], h2 [L], and between h3 [L], h4 [L] respectively, represent the constant screen injection head over the permeabl e portion of the device. C onditions IV, VI and VIII correspond to the no flow conditions along the impermeable portions of the device. Figure 3 1 Impermeable top and bottom boundary conditions of two injection screens (Klammler, 2007) function d z. This problem is solved by assuming the probe tip is conceptually extended to infinity and by using multiple Fourier expansions with Bessel function coefficients. Given the complicated aspect of these equations, a comput er based method, Matlab, is used to solve for the parameters. 2T1] [L3T1] in cylindrical coordinates are (Lamb, 1932, Smith, 1950, Zaslavsky and Kirkham, 1964) 0 z r r 1 r2 2 2 2 (3 1) d h 2 2a h 3 I I I I II I V VI V z r b VIII VII h 1 h 4 PAGE 52 52 a nd 0 z r r 1 r2 2 2 2 (3 2) G eneral solution s of Equations 3 1 and 3 2 are given by Zaslavsky and Kirkham (1964) as L Kz a r J a r Iz mr H mr G mz F mz E nr D nr C nz B nz A z r ) / ln( ) / ln( ) ( Y ) ( J ) cosh( ) sinh( ) ( K ) ( I ) cos( ) sin( ) (0 0 0 0 (3 3 ) 1 1 2 1 2 1 1 2 1 2 1 1 1 2 1 2 1 1 ) ( Y ) ( J ) cosh( ) sinh( ) ( K ) ( I ) cos( ) sin( ) ( H z G r F z r E z D z C r z D z C mr B mr A r mz B mz A z r (3 4 ) where A through L, a, m and n are arbitrary real constants and I0, K0, J0 and Y0 are Bessel functions of order zero (Dwight 1947). 3.1.1 Confined Aquifer (I mp ermeable Top and Bottom Boundaries with Artesian Lateral Bounda ry ) For the case of top and bottom impermeable and lateral artesi an boundary, the conditions of F igure 3 1 can be formulated as: d z b r I 0 for at 0 (3 5 ) b r a d z z II for at 0 (3 6 ) b r a z z III for 0 at 0 (3 7 ) 10 for at 0 h z a r r IV (3 8 ) 2 1 1for at h z h a r V (3 9 ) 3 2for at 0 hz h a r r VI (3 10) 4 3 2for at h z h a r VII (3 11) PAGE 53 53 d z h a r r VIII 4for at 0 (3 1 2 ) By modifying the potential and stream functions used by Kirkham (1959), the constants in Equations 3 3 and 3 4 are chosen such that N n nd z n d r n r B a b r b B z r,... 2 1 0 0) / cos( ) / ( ) / ln( ) / ln( ) ( (3 13) N n nd z n d r n rr B a b z B z r,... 2 1 1 0) / sin( ) / ( ) / ln( ) ( (3 14) w ith ) d / b n ( I ) d / a n ( I ) d / b n ( K ) d / a n ( K ) d / b n ( I ) d / r n ( I ) d / b n ( K ) d / r n ( K ) d / r n ( r0 0 0 0 0 0 0 0 0 (3 15) and ) d / b n ( I ) d / a n ( I ) d / b n ( K ) d / a n ( K ) d / b n ( I ) d / r n ( I ) d / b n ( K ) d / r n ( K ) d / r n ( r0 0 0 0 0 1 0 1 1 (3 16) Equation 3 1 4 is an alternative representation for the same solution of the potential function but in terms of the stream function where respected coefficients of both solutions are related to each other (Kirkham, 1964) Kirkham (1959) simplified r0 and r1 in Equation s 3 15 and 3 16, for lateral artesian boundary located far away from probe axis (b/a >10), to ) d / a n ( K ) d / r n ( K ) d / r n ( r0 0 0 (3 17) a nd PAGE 54 54 ) d /a n ( K ) d / r n ( K ) d / r n ( r0 1 1 (3 18) Equation 3 13 demonstrates that boundary conditions I, II and III are satisfied, since 00 and Bn are calculated based on boundary conditions IV, V, VI, VII and VIII. In general the se boundary conditions along the probe can be applied to reflect more than two screens with d ifferent known head s and radial flux distribution s Condition IV: (3 19) Condition V: 2 1 1 ,... 2 1 0for )/ cos( ) ( h z h d z n B B z aN n n (3 20) Condition VI : 3 2 ,... 2 1 1 0for 0 ) / cos( ) / ( ) / ln( h z h d z n d a n r d n B a b a B rN n n a r (3 21) Condition VII : 4 3 2 ,... 2 1 0for ) / cos( ) ( h z h d z n B B z aN n n (3 22) Condition VIII : d z h d z n d a n r d n B a b a B rN n n a r 4 ,... 2 1 1 0for 0 ) / cos( ) / ( ) / ln( (3 23) where 1 ) / (0 d a n r and using dK0(x)/dx = K1(x). A steady way of solving this system for a finite N is to divide the interval 0 into N+ 1 equidistant subinterval which i n combination with the Equations 3 19 to 3 23 leads to the followi ng N+ 1 condition (Klammler, 2007) 1 ,... 2 1 1 00 for 0 ) / cos( ) / ( ) / ln( h z d z n d a n r d n B a b a B rN n n a r PAGE 55 55 1 1 ,... 2 1 1 1 1 0 00 for 0 ) / sin( ) / ( ) / ln(1h z d z n d a n r B a b a z B dz rN n n z a r (3 24) 2 2 1 1 2 1 ,... 2 1 1 2 1 2 0for ) / sin( )/ sin( ) (2 1h z h h z d h n d z n n d Bh z B dz z aN n n z h (3 25) 3 3 2 ,... 2 1 2 3 1 2 3 0for 0 )/ sin( ) / sin( ) / ( ) / ln(3 2h z h d h n d zn d a n r B a b a h z B dz rN n n z h a r (3 26) 4 4 3 3 4 2 ,... 2 1 3 4 34 0for ) / sin( ) / sin( ) (4 3h z h h z d h n d zn n d B h z B dz z aN n n z h (3 27) d z h d hn d z n d a n r B a b a h z B dz rN n n z h a r 5 4 ,... 2 1 4 51 4 5 0for 0 ) / sin( ) / sin( ) / ( ) / ln(5 4 (3 28) where z1, z2, z3, z4 and z5 represent the N limits of the N+1 intervals shown in Equations 3 24 through 3 28. Solving the linear system of Equations 324 through 3 28 results in B0 and Bn, the coeffici ents required for Equations 3 13 and 3 14. The total flow Q [L3/T] leaving the injection screen is then obtained from: 0 d 0 a r 2 1B a b ln d K 2 dz r aK 2 Q Q Q (3 29) where K [L/T] is the hydraulic conductivity of the test medium. B0 (such as all Bn) depends on the probe screen position and size, and they can be shown to be proportional 1. T hus by taking B0,u = B01 [ ], the s hape factor F [L] for impermeable top and bottom boundaries becomes PAGE 56 56 u 0B a b ln d 2 F (3 30) a nd K can be obtained from an in The injection rates Q1 [L3/T] and Q2 [L3/T] for the bottom and top screen, respectively, divide themselves into: N ,... 2, 1 n 1 2 1 n 1 2 0 h h a r 1) d / h nsin( ) d / h n sin( ) d / a n ( r B ) a / b ln( a hh B aK 2 dz r aK 2 Q2 1 (3 31) and N ,... 2, 1 n 3 4 1 n 3 4 0 h h a r 2) d / h nsin( ) d / h n sin( ) d / a n ( r B ) a / b ln( a hh B aK 2 dz r aK 2 Q4 3 (3 32) If K is not known, three estimates of K can be obtained from Equations 3 29, 331 and 3 32, by measuring the injection rates Q, Q1 and Q2 1 2. Under conditions of homogeneity of an isotropic te st medium, the three estimates of K should be identical. In the case of dis crepancy between the values of K an assumption of heterogeneity or anisotropy of the test medium can be made. 2T13T1] functions in Equations 3 13 and 3 14 are plotted in Figure 3 2 with reference to the radial (R/a) and vertical (Z/a ) distances. It is shown that the constant head is presented along the double screen s between Z/a = 2 0 and Z/a = 3 0 for the bottom screen and Z/a = 7 0 and Z/a = 8 0 for the top screen In the surrounding of the screen, where the gradient of the potential is large over a smaller radial dist ance, the stream function has a bigger slope. On the other hand, where the gradients decrease away from the screen the slope of the stream function is smaller and the stream lines tend to become horizontal. It is noted t hat the gradient of the head decre ases with an increase in radial PAGE 57 57 distance r [L ] with its maximum value is at the scre en location. The stream lines are normal to the potential lines. Figure 3 2 Stream and potential functions for impermeable top, bottom and lateral artesia n boundaries, in the case of two screen injection test Streamline spacing is inversely proportional to the speed of flow for which a small spacing gives high velocity, and a lar ge sp acing gives low velocity (Anderson and Woessner, 2006). A streamline is plotted as a curve tangent to the velocity vector at every poin t in the flow field. In a homogeneous and isotropic medium, streamlines and equipotential lines intersect at right angles (Figure 3 2 ). The stream function is analogous to the equipotential function in that head is constant along an equipotential line while the stream function i s constant along a streamline. 3.1.2 Artesian Top and Bottom Boundaries with Impermeable Latera l Boundary The other situation is when top and bottom imperme able boundaries (conditions 3 6 and 3 7 ) become artesian boundaries ( conditions 3 34 and 335), while the lateral a rtesian boundary (condition 3 5 ) becomes impe rmeable boundary (condition 3 33). T he conditions are as follows: PAGE 58 58 d z 0 for b r at 0 r Ic (3 33) b r a for d z at Jz IIc (3 34) b r a for 0 z at 0 IIIc (3 35) where J[ ] is the vertical hydraulic gradient that may exist between the top and bottom boundaries. Conditions IV to VIII are the same as conditions 3 8 to 3 12 discussed in the case of a confined aquifer. the stream fun ,z) correspond to Equations 3 36 and 337 whic h fulfill boundary conditions Ic, IIc and IIIc, a nd they are obtained as follows: N n nd z n d r n r B Jz z r,... 2 1 0) / sin( ) / ( ) ( (3 36) N n nd z n d r n rr B Jr z r,... 2 1 1 2) / cos( ) / ( 2 ) ( (3 37) where J [ ] is the vertical hydraulic gradient and N n n a rd z n d r n r d n B r,... 2 1 1) / sin( ) / ( (3 38) The impermeable lateral boundary at a finite radial distance from the probe axis is based on a modification of the functions r0 and r1 to give ) / ( ) / ( ) / ( )/ ( ) / ( )/ ( ) / ( ) / ( ) / (1 1 1 1 1 0 1 0 0db n I d a n I d b n K d a n Kd b n I d rn I d b n K d r n K d r n r (3 39) and PAGE 59 59 ) / ( ) / ( ) / ( ) / ( ) /( ) / ( ) / ( ) / ( ) / (1 1 1 1 1 1 1 1 1d b n I d a n I d b n K d a n K d b n Id r n I d b n K d r n K d r n r (3 40) which assure that r1 As for a confined aquifer, Kirkham (1959) simplified r0 and r1 in Equations 3 39 and 3 40, for lateral impermeable boundary located far away from probe axis (b/a >10), to ) d / a n ( K ) d / r n ( K ) d / r n ( r1 0 0 (3 41) and ) d / a n ( K ) d / r n ( K ) d / r n ( r1 1 1 (3 42) With r1 from Equatio n 340, the interval 0 < z scretized into N equidistant subinterva ls. Next, integration over z of boundary conditions IV through VIII yields the following system of equations (Klammler, 2007) : 1 1 ,... 2 1 1 1 00 for 0 1 ) / cos( ) / (1h z d z n d a n r B dz rN n n z a r (3 43) 2 2 1 1 2 1,... 2 1 1 2 2 1 2 2for ) / cos( ) / cos( 2 ) (2 1hz h h z d h n d z n n d B J h z dz z aN n n z h (3 44) 3 3 2 ,... 2 1 2 3 1for 0 )/ cos( ) / cos( ) / (3 2h z h d h n d z n d an r B dz rN n n z h a r (3 45) 4 4 3 3 4 2,... 2 1 3 4 2 3 2 4for ) / cos( ) / cos( 2 ) (4 3hz h h z d h n d z n n d B J h z dz z aN n n z h (3 46) PAGE 60 60 d z h d h n d z n d a n r Bdz rN n n z h ar 5 4 ,... 2 1 4 5 1for 0 ) /cos( ) / cos( ) / (5 4 (3 47) where z1 through z5 represent the total N 1 limits of the N intervals and are defined in a similar way as with Equations 3 24 through 3 28. Thus, the above system in N equations may be solved for the N unknown coefficients Bn of Equations 3 3 6 and 3 3 7 in order to determine the potential distri but ion for a given geomet ry 1 2. Knowing K the total injection rate Q [L3/T] is obtained as N ,... 5 3 1 n 1 n d 0 a r 2 1) d / a n ( r B aK 4 dz r aK 2 Q Q Q (3 48) where the injection rates Q1 [L3/T] and Q2 [L3/T] for the bottom and top screen, respectively, di vide themselves into N ,... 2 1 n 1 2 1 n h h a r 1) d / h n cos( )d / h n cos( ) d / a n ( r B aK 2 dz r aK 2 Q2 1 (3 49) N ,... 2 1 n 3 4 1 n h h a r 2) d / h n cos( )d / h n cos( ) d / a n ( r B aK 2 dz r aK 2 Q4 3 (3 50) As with a confined aquifer, if K i s not known three estimates of K can be obtai ned from Equations 3 48, 3 49 and 3 50, by measuring the injection rates Q, Q1 and Q2 for the applied 1 2. A clear presentation of the axisymmetric flow field can be constructed using computational methods, such as Matlab, that solve for the coefficients of the potential and the stream functio ns. PAGE 61 61 Figure 3 3 P otential and stream functions for artesian top, bottom and lateral impermeable boundaries. As shown in Figure s 3 3 for the case of injecting from two screens, the streamlines bend up and down towards the artesian top and bottom boundaries if the screens are close to the horizontal boundaries. On the other hand, if the distance between the screens and boundaries are large enough, one can assume that there is no such effect of the boundaries and the flow field will approach the properties of spherical flow away from the injection locations 3.1.3 Unconfined Aquifer (Artesian Top and Impermeable Bottom Boundaries with Impermeable Lateral Boundary) In addition to the potential and stream functions for different sets of boundary conditions, more functions were developed to take into account the case of an unconfined aquifer. The system is modeled assuming a shallow unconfined aquifer with artesian top an d impermeable bottom boundaries. The constants in Equations 3 3 and 3 4 are chosen such that, after superposition, the potential and stream functions are as follows, PAGE 62 62 N ,... 3 1 n 0 n)) d 2 /( z n sin( )) d 2 /( r n ( r B ) z r ( (3 51) and N ,... 3 1 n 1 n)) d 2 /( z n cos( )) d 2 /( r n ( rr B ) z r ( (3 52) which can be assume d 0 and r1 are the same as Equations 3 39 and 3 40 for impermeable lateral boundary, which satisfy the governing partial diff erential equation and assure r1 2 d) = 0. Inspection of equation 3 51 demonstrates that boundary conditions Ic, IIc and IIIc are satisfied, while B0 and Bn are calculated based on boundary conditions IV, V, VI, VII and VIII (conditions 3 8 to 3 12). Another situation can also be studied with impermeable top boundary (Equation 3 6 ) and artesian bottom boundary ( Equation 3 35). The lateral boundary can be artesian with r0 and r1 calculated from Equations 3 15 and 3 16 for close by boundary or Equations 3 17 and 3 18 for boundary located far away from the screen Moreover, t he lateral boundary condition can be impermeable with r0 and r1 calculated fro m Equations 3 39 and 3 40 for close by boundary or Equations 3 41 and 342 for boundary located far away from the screen 3.1.4 Shape Factor or F factor One of the main reasons to determin e the flow field is to evaluate the shape factor F [L] fo r differen t boundary conditions Figure 3 4 shows the graphs of the F fact or for any combinati on of artesian or impermeable top, bottom and lateral boundary conditions (Klammler 2007). As shown in Figure 3 4 the ratio of F factor to the probe radius (F/a [ ]) depe nds on the relative distance between horizontal boundarie s and screen length (d/s [ ]). I n addition, F/a PAGE 63 63 depends on the type of top and bottom boundaries for an artesian lateral boundary at a constant radial distance (b/a = 1000) and for different injectio n screen length s to radius ratios s/a [ ]. Figure 3 4. Relative F factor for different distances and types of horizontal boundary conditions (Klammler 2007) For all boundary cases, F/a approaches a constant value as d/s increases ; this means that the F factors for artesian and impermeable conditions are the same when the top, bottom and lateral boundaries are located far away from the probe. For impermeable top and bottom boundaries, F/a decreases significantly with the decrease o f d/s towards 1. d/s =1 is equivalent to flow leaving a fully penetrating well in a confined aquifer. For the combination of artesian and impermeable boundaries, the F factor approaches infinity when d/s de creases. Figure 3 5 represents F as a function of screen geometry for artesian top, bottom and lateral boundary conditions located far away from the two screens. When the relative distance between the two screens (p/s) increases, the relative F factor for injection Fi/a increases because there is less co mpetition of injected flows between the two Artesian top and bottom boundaries Artesian top and impermeable bottom boundaries Impermeable top and bottom boundaries 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 0 10 20 30 40 50 60 log10(d/s) []F/a [] s/a = 20 s/a = 10 s/a = 5 s/a = 0.5 PAGE 64 64 screens, which become more independent. On the other hand, the relative F factor for recirculation Fc/a decreases when p/s increases because it is harder to recirculate the flow between them, and the flow path be come longer. Figure 3 5 Relative F factor for injection (Fi/a) and recirculation (Fc/a) tests for two screen probe with no boundary effect 3.1.5 Anisotropy Two methods are presented to transform anisotropic to isotrop ic media and measure the horizontal (Kr) and vertical (Kz) conductivities: 1 Inject ion and recirculation tests. 2 Injection test and head observation. 3.1.5.1 Injection and Recirculation Tests By assuming ho mogeneous and anisotropic media (i. e. the horizontal conductivity Kr [LT1] is not equa l to the vertical conductivity Kz [LT1]), a proper scaling of one axis of the flow domain exist s to make the three estimates of K coincide in Equations 3 29, 331 and 3 32 for the confined case and in Equations 3 48, 349 and 3 50 for the artesian cas e (Klammler, 2007). PAGE 65 65 Using Kiso as an isotropic equivalent conductivity, scaling of r zK K r r enables the flow domain to be treated as isotropic in cases with horizontal Kr and a vertical conductivity Kz (Hvorslev, 1951). The sc aling factor of the radial axis is the anisotropy ratio ( [ ]) such that: z r isoK K K (3 53) and r zK K (3 54) Different scaling of the vertical and horizontal coordinates are possible to achieve isotropic conditions. In general, flows have to be scaled to maintain the continuity of flows. By scaling the radial coordinate and selecting Kiso as z rK K flows dont have to be scaled (Hvorslev, 1951) Figure 3 6 Two screen probe for injection (left) and recirculation (right) test to measure vertical and horizontal hydraulic conductivities under saturated conditions Screened PVC pipe Circulate at same flow rate Inject at same Head Tube PAGE 66 66 Two different tests (Figure 3 5 ) can be performed t o measure Kr and Kz using recorded injection head and flow rate data. The first test injects water from both screens resulti ng in a horizontal flow field with K approximately equal to Kr. The second test is a recirculation test, where the amount of water injected through one screen is extracted by the other screen, thus creating a vertical flow field with K approximately equal to Kz. A difference in estimates in Kr and Kz can be eliminated by selecting the right scaling of the radial coordinate such that the F factor for injection (Fi [L]) and recirc ulation ( Fc [L]) of the scaled domain result in conductivity estimates Ki and Kc equal to Kiso. Therefore, t he ratio of Fi/Fc of the scaled domain is equal to a measured value (Qic) /(Qci) which corresponds to the identical conductivity measurements of the scaled domain (Ki = Kc ) (Klammler, 2007). This measured value can be used to get the scaled probe radius a which is equal to r zK K a and subsequently the anisotropy ratio r zK K is obtained by dividing a over the probe radius a. By assuming different values of Kz / Kr, the scaled pro be radius a is obtained by tria l and error in which particular value of a makes Ki equal to Kc After knowing the scaled probe radius a, the scaled F factor of injection or recirculation is needed to calculate Ki or Kc, which is equal to the effective isotropic conductivity (Kiso). Con sequently, Kr and Kz can be determined from Equations 3 53 and 354 after calculating Kiso 3.1.5.2 Injection Test and Head Observation The main problem encountered while performing recirculation test s is fine sand entrapped in the hydraulic system which affects water flow Therefore, another method is needed to eliminate the usage of the extraction screen for anisotropic conductivity measurements. The theory requires injecting from one screen and recording the head at the observation screen separat ed by a distance p from the injection screen. PAGE 67 67 The effective iso tropic hydraulic conductivity (Kiso [L/T]) resulting from different values of horizontal and vertical conductivities can be evaluated using a si mple injection test from one screen. However, Kr and Kz cannot be calculated separately without the additional head observation at the pressure screen which is needed to determine the anisotropy ratio. The system of equations used to calculate the F factor for injection screen and the expect ed head 1 at observation screen are: 1 1 N ,... 2 1 n 1 nh z 0 for 0 1 ) d / z n cos( B (3 55) 2 2 1 1 1 2 N ,... 2 1 n 1 2 0 nh z h for 0 h z ) d / h n cos( ) d / z n cos( ) d / a n ( r n d B (3 56) 3 3 2 N ,... 2 1 n 2 3 nh z h for 0 ) d / h n cos( ) d / z n cos( B (3 57) 4 2 3 2 3 4 N ,... 2 1 n 3 4 0 nh z h for h z ) d / h n cos( ) d / z n cos( ) d / a n ( r n d B (3 58) d z h for 0 ) d / h n cos( ) d / z n cos( B3 4 N ,... 2 1 n 4 5 n (3 59) 0 ) d / h n cos( ) d / h n cos( B a 2N ,... 2 1 n 1 2 n (3 60) i N n nQ d h n d h n B a ,... 2 1 3 4) / cos( ) / cos( 2 (3 61) The above system of N+ 1 equations (3 55 to 3 60) may be solved for the N+ 1 unknown coefficient Bn and the observation head 1. The F factor is calculated from the ratio of injection PAGE 68 68 rate Qi [L3/T] (Equation 3 61) over the known injection head 2 [L]. The flow rate a t the pressure screen is kept equal to zero by Equation 3 60 w ith an unknown constant head 1 while the injec tion flow rate Q2 and injection head 2 are nonzero and known. As above F is calculated by t akin g into account the injection screen geometry and th e presence of the pressure screen with zero flow and constant head. This observation screen does not affect the flow field since the F factors have practically the same values for different distances between injection scree n and pressure screen (p/s) (Figure 3 8 ). When the obse rvation screen becomes short (s/a<<1) it can be reduced to small holes, which also wont affect t he flow field. T he theoretical ratio between 1 2) [ ] is determined for different anisotropy ratio s (Figure 3 7 ). The measured ratio between those heads is then matched with the theoretical ratio in Figure 3 7 in order to find the respective anisotropy ratio which is equal to the ratio between the scaled prob e radius (a) and the probe radius (a). The effective isotropic conductivity Kiso is calculated from the scaled F factor (Fi) for a single injection screen (Figure 3 8 ). Consequently Kr and Kz are calculated from Equations 3 53 and 3 54 after knowiniso. Note that Figure 3 7 represents the actual field conditions with the boundaries located far away from the screens. Figure 3 1/ 2) decreases as the relat ive distance between the screen and the small openings (p/s) increases, and the head ratio increases as the relative scaled pro be radius ( s a /' ) increases. For large values of log (a/s) on the x axis or large anisotropy ratio the horizontal conductivity is smaller than the vertical conducti vity. However, this is not likely to happen in practice. Figure 3 7 shows that there is an optimum distance between the injection screen and the head observation location 1 2 has the largest sensitivity to the PAGE 69 69 anisotropy ratio (steepest part of the curves between 1 and 1). If the pressure screen is very far from the injection screen there will be no difference in head observed in the pressure screen. Yet, if the pressure screen is very close to the injection screen th e hea d at the pressure screen should always be very s imilar to the injection head. Figure 3 7 Determination of aniso tropy from the ratio of head at injection screen and head at pressure screen w ith no boundary effects (d=100, b=Infinity) Figure 3 8 Relative Fi/s versus the relative scaled probe radius a/s with no boundaries effect (d=100, b=Infinity) PAGE 70 70 12 and anisotropy ratios (between 0. 0 0 1 and 10), to guarantee maximum s ensitivity. The extremes are when the horizontal conductivity is smaller than the vertical conductivity, and the horizontal conductivity is much larger than the vertical conductivity. 3.2 Volume of Influence (VOI) of F low F ield 3.2.1 Objectives of VOI Th e v olume of influence (VOI) is de fined as the region of soil being tested when injecting or recirculating through the screens. It describes the scale of a conductivity measurement, and additional importance lies in determining the extent of remediation of c ontaminated soil The main objective of this section is to investigat e a general criterion that may be appropriate to define the volume of influence of the flow field interrogated by the probe The been used by Kabala and Xiang, 1992 to determine the VOI for recirculation test. However, the stream function is not applicable to estimate the volume of influence for injection test, since the stream lines do not form a closed volume around the screen On the other hand, can be used for injection test because the potential lines form closed contour lines around the screens. However, the potential function is not appropriate for recirculation test because potential lines do not fo rm closed contour lines around the screens. Therefore, the magnitude of the potential function gradient ) ( z r and the magnitude of the stream function gradient ) ( z r can be used for both injection and recirculation tests. In this analysis, the injection from a single screen is studied with the top, bottom and lateral boundaries taken far away from the screen to evaluate the volume o f influence of the flow PAGE 71 71 field. Thus, a very large aquifer is applied without the interference of boundary conditions. A magnitude gradient of potential function ) ,( z r and stream function ) ,( z r with different injection screen lengths to see which is adequate to describe the volume of influence of the flow field. 3.2.2 Determination of VOI Using Potential and Stream Functions Boundaries are taken far away from the screen(s) to study the volume of influence. This can be t heoretically tested by comparing the F factors for the case of artesian and impermeable boundaries; if F factors for both cases are approximately the same, there is no significant effect of boundary conditions on the flow field and on the VOI evaluation. T hen, the choice of screen configuration (one or two screens) and test type (injection or recirculation) determine s whi ch function is not applicable in defining VOI. For example, stream lines for the injection test and potential lines for the recirculation test do not define closed volumes around the probe and cannot be used. Among the remaining functions (including the derivatives, leading to lines of equal local fluxes or local gradients), potential lines for the injection test from one screen (Figure 3 9 ) and stream lines for the recirculation test (Figure 3 11) from double screens pr ove to be an adequate presentation of the VOI determination. The fi rst approach uses Equations 3 42 and 3 43 to represent the potential and stream functions, with no vertical hydraulic gradient (J = 0 ). As shown in Figure 3 9, t he screen opening is between the values of Z/a = 122.5 and Z/a = 127.5 with s/a =10. The extent of the VOI based on the potential function is defined on the radial (Vr) and vertical (Vz) limits By defi ning the VOI as the volume where 90% of the injection head is lost, Vz and Vr are defined as the vertical and horizontal extent of the equipotential surface that includes 90 % of the head drop. PAGE 72 72 Figure 3 10 gives a clear presentation of the radial flux distribution along the probe as well as the head along the probe. The flux is variable along the probe screen with high values at the extreme of the screen and lower values at the center of the scre en. The constant head along the probe screen and the zero flux along the impermeable part of the probe give a validation to the solution. Figure 3 9 P ot ential function for artesian boundaries, in the case of one screen injection test (s/a=10 ) The abo ve solutions for injection from a single screen can be applied for injection from two or more screens. For the case of recirculating flow between screens, a circulating flow, Q1, is 1 2 between the two well screens an 1 and 2, are recorded. Analytically this means a substitution of Q2 = Q1 in E quation 3 54. As shown in Figure 3 11, the flow is recirculated between the top and bottom screens while the VOI is defined as the volume enclosed by Vr and Vz th at contains 90% of the flow. Because it is PAGE 73 73 difficult to specify the boundaries locations on site, the boundaries are taken far enough to assume no boundary effect. Figure 3 10. Example of resulting flow field properties for inj ection/extraction with close by vertically confining layers. Figure 3 11. Contour lines of the equipotential and stream functions in the case of recirculation test with p/s = 5. PAGE 74 74 3.2.3 Determination of VOI Using Derivatives of Potential and Stream Functions Another approach to determine VOI is by evaluating the magnitudes gradient of potential and stream functions ) ,( z r and ) ,( z r T he respective expressions f obtained analytically as fo llows: N n nd z n d r n r d n B r z r,... 2 1 1) / sin( ) / ( ) ( (3 62) N n nd z n d r n r d n B z z r,... 2 1 0) / cos( ) / ( ) ( (3 63) Magnitude of 2 2) z ) z r ( ( ) r ) z r ( ( ent gradi z) r ( (3 64) z z r r r z r r z r r z z r ) ( ) ( ) ( ) ( (3 65) N n nd z n d r n r d n r B z z r,... 2 1 1) / sin( ) / ( ) ( (3 66) N n nd z n d r n r d n r B r z r,... 2 1 0) / cos( ) / ( ) ( (3 67) Magnitude of 2 2) z ) z r ( ( ) r ) z r ( ( ent gradi z) r ( (3 68) Substitution of Equa tions 3 65 into Equations 3 64 and 3 68 gives Magnitude of ) z r ( r Magnitude of ) z r ( (3 69) Flux = ) ( z r q = ) ( 1 z r r (3 70) As a physical interpretation to Equation 3 69, the flow known from the gradient of the stream function ) ( z r is r times the local flux known from the potential gradient ) ( z r The gradient of the potential function directly gives the loc al Darcy flux (Darcys law at a point). By using the stream function for axisymmetric coordinates, the gradient of the stream function directly gives the flow at that location for a unit radian angle of the flow domain. As shown in Figure 3 12, f low fields are always defined for axi parallel planes with an increasing thickness as the radius increases ( i.e., the flow domain opens up like a wedge away PAGE 75 75 from the pr obe) For a unit radian angle of the flow domain, the circumference of such a wedge of the flow domain is exactly r. The flow over the whole wedge known from the gradient of the stream function is then r times the local flux known from the potential gradient. Figure 3 12. Streamfunction for axisymmetric flow: Cylindrical coordinates ( Kundu et al., 2004) Figure 3 13. Contour lines of the magnitude gradient of potential function ) ( z r using a single injection screen. PAGE 76 76 Figure 3 14. Contour lines of the magnitude gradient of stream function ) ( z r using a single injection screen The der ivatives reflect the singularities of the flow at the screen ends where very large local flow s exist next to the screen, which drop away form the screen extremes. In Figures 3 13 and 3 14, the contours of the magnitudes of the gradi ents of potential and stream functions form closed semi circles around the screen extremes, and then it includes the whole screen length (s /a=10 ). Similar to the potential function, the extent of the VOI is define d by the volume enclosed by iso lines of ) ( z r and ) ( z r as shown on Figures 3 13 and 3 14. The gradient iso lines in this case are defined as a percentage of the gradient at the screen center which represents 100% gradient. Values corresponding to iso lines increase f rom the screen center (100% isoline ) to the screen ends because local fluxes are large st at screen en ds, and then they decrease again. The VOI is assumed to be represented by the vol ume enclosed by the 10% isoline with respect to the value of magnitude gradient of potential function ) ( z r or magnitude gradient of stream function ) z ,r ( at the screen center PAGE 77 77 In this particular case, the injection from a single screen is studied with the top, bottom (d /s = 50) and la teral (b/a=1000) boundaries taken far away from the screen to evaluate the volume of influence of the flow field based on the magnitude of the gradient of the potential function configuration The gradient of stream function is not used on VOI evaluation because it gives the flow in an axi parallel vertical plane with an opening angle in the horizontal plane of one radian. The respective circumference of one radian is r and the division by r gives the actual local flux as from the potential gradient. Another reason for choosing the magnitude gradient of potential function on VOI evaluati on is by inspecting Figures 3 13 and 314 with the second half of the probe where the volume enclosed around the screens give s a more pleasant shape for the magnitude g radient of potential function than the magnitude gradient of stream function. Figure 3 15. Radial (Vr/a [ ]) and vertical extent (Vz/a [ ]) of VOI with respect to the screen length (s/a [ ]) using ) ( z r for a single injection screen Figure 3 15 shows a general interpretation of the VOI for dif ferent injection screen geometri es, based on magnitude gradient of potential function ) ( z r For every specifi cation of the limit of radial (Vr / a [ ]) and vertical (Vz / a [ ]) extent there is a specific dimension of the PAGE 78 78 probe defined by the ratio of scree n length to radius (s/a [ ]). When the normalized screen length increases, the radial extent increases to reach a constant value while the vertical extent keeps increasing and approaching a line of 450 with large values of s/a. Figure 3 16 is generated for the magnitude of potential functi on gradient for the recirculation test. The VOI is defined as the volume that encloses the local fluxes larger than 10% of the local flux at the center of the screen. Figure 3 16. Contour lines of the magnitude gradient of potential function ) ( z r using recirculation test with p/s= 5. If the flow is recirculated between the two screens which are separated further apart, the local fluxes between them are very low Therefore, the VOI would be split up into one VOI around the injection screen and another VOI around the extraction screen (Figure 3 17). In that case, different results are obtained than when using the stream func tion which only define VOI with one big bubble covering both screens. For the recirculation test, Figure s 3 18 and 3 19 are equivalent to Figure 3 14 for different values of p/s (0.5, 1, 2 and 5) using the magnitude gradient of potential function ) ( z r PAGE 79 79 Figure 3 17. Contour lines of the magnitude of ) ( z r with large separation between screens using recirculation test ( p=15 and s=3). Figure 3 18. Radial (Vr/a [ ]) extent of VOI with respect to the relative screen length (s/a [ ]) using ) ( z r for recirculation test. PAGE 80 80 Figure 3 19. Vertical extent (Vz/a [ ]) of VOI with respect to the relative screen length (s/a [ ]) using ) ( z r for recirculation test In general, the best defini tion of VOI is based on the magnitude of the gradient of potential function ) ( z r which gives the local flux, and it can be applied t o injection and recirculation tests If heterogeneity is present beyond the VOI, its effect on K measurement s is negligible. However, the effect on the VOI will be greater if the heterogeneity is close to the screen with higher values of local flux. Local fluxes allow for both mathematical ly and physically pleasant interpretation of a VOI for a given flow field 3.3 Influence of S creen S lots on F factor and H ead C hange a long the P robe S creen The aim of this section is to investigate the change of head and F factor as a function of probe screen length and slot frequency or open area. In previous research, it was assumed that the head is constant over the screen length and is independent of screen slot size or frequency. However the head may be constant only at sc reen openings and it may vary between slots. PAGE 81 81 Therefore, it is important to study the effect of screen slot geome try on K estimates since they are directly proportional to the F factor [L] applied. 3.3. 1 Confined Aquifer The effect of the slots will be evaluat ed using the following model. A screen with one large opening is compared to a slotted screen with smaller openings. Each element of the screen is considered as a confined aquifer with an impermeable top, bottom and artesian lateral boundary. The flow fields for more than one slot can be constructed by the method of images from the flow field of one si ngle slot. Also, the F factor of each image (slot) can be added. So, a comparison is made between the constant head large screen and the variable head slotted screen based on head distribution along the screen and the F factor. Theref ore, it is important t o check whether it is appropriate to assume a slo tted screen as continuous by changing the locations and types of boundary conditions and by varying the parameters s/a, d/s and b/a. The shape factor F [L] for impermeable top bottom and a rtesian lateral bo undary is derived from E quation 3 30. Keeping d and b/a the same for slotted and continuous screen s the ratio of F factors for both cases is obtained by: d s d sF F = d s u d s uB B 0 0 (3 71) For a continuous screen (s=d): d z d n n d B d B dz z aN n nd 0 for ) 0 sin( ) sin( ) (,... 2 1 0 01 which gives: d usB B 0 01 (3 72) and a b ln s 2 Fd s This reduces to the case of a fully penetrating well in a confined aquifer. PAGE 82 82 By substituting Equation 3 72 into 3 71, we get d s d sF F = d s uB 0 which is the Fourier coefficient of zero frequency or the mean head of slotted screen. The equation used to estimate the head distribution along the screen opening is: 2 1 ,... 2 1 0for ) / cos( ) ( h z h d z n B B z aN n n (3 73) Therefore, the mean head of slot ted screen ( d s uB 0 ) or the ratio of Fslotted / Fcontinuous can be evaluated by varying one slot dimension using different slot geometries (ds/ss = 2, 3, 5, 7, 10, 20 and 50) and various distances to the lateral boundary (b/a = 5, 10, 50, 100 and 1000) (Figure 3 20). As stated earlier, the F factor is calculated for one slot, and th en it is evaluated for the entire screen opening by using the metho d of images and by adding all slots together. Figure 3 20. Physical configuration of one slotted (left) and continuous screens (right) for confined aquifer r d s h 1 2a h 2 I II III z b s s r d=s 2a I II III z b PAGE 83 83 Figure 3 21. The ratio of the F f actor s between slotted and continuous screen ( Fslot/Fcont [ ]) or m ean head of slotted screen [ ] for ss/a=0.02 Figure 3 22. The F factors ratio ( Fslot/Fcont [ ]) or mean head of slotted screen [ ] for ss/a=0.5 As shown in Figures 3 21 and 3 22, Fslot / Fcont or the mean head of the slotted screen becomes closer to the constant head of a continuous screen as the radial distance b/a from the PAGE 84 84 probe axis to the artesian lateral boundar y increases from 5 to 1000. However, Fslot / Fcont decrease when the relative dista nce to the horizontal boundary (ds/ss) increases. On the other hand, Fslot / Fcont decrease when the relative screen length (ss/a) increases from 0.02 (Figure 3 21) to 0.5 (Figure 322). Preliminary results indicate that the error in assuming a slotted sc reen as a continuous screen is minimal if the following combination of conditions holds : Low ds/ss; Low ss/a; Large b/a; On the other hand, this assumption can induce a fairly large error in measurements of F when the following combination of conditions exists: Large ds/ss; Large ss/a; Low b/a; Figure 3 23. The ratio of the F factors ( Fslot/Fcont [ ]) for a confined case with ds/ss = 27 PAGE 85 85 Figure 3 24. The F f actors ratio ( Fslot/Fcont [ ]) with ds/ss = 11 using confined aquifer Figure 3 25. The ratio of the F factors ( Fslot/Fcont [ ]) with ds/ss= 4 using confined case Figures 3 23, 3 24 and 3 25 are plotted for different slot width (ds/ss = 27, 11 and 4) corresponding to practical standard sizes and different number of slots (1, 2, 5, 10 and 20) with PAGE 86 86 the artesian lateral boundary is taken far away from the screen (b/a=1000). The error in assuming a slotted screen as a continuous screen for b/a approximately 1000 is minimal when the number of slots is increasing from 1 to 20 slots, and when the slot width is increasing from ds/ss = 27 (Figure 3 23) to ds/ss = 11 (Figure 3 24) and ds/ss = 4 (Figure 3 25). Equation 2 21 shows that for a given Q, the F Consequently, over estimation of the F factor by a certain factor, by failing to consider the slot separation, leads to underestimating K by the same factor. 3.3. 2 Artesian Top and Bottom Boun daries (No Boundaries Effect) The above conclusion based on the method of images is only applicable when the impermeable boundaries are present immediately o n top and bottom of the screen. In more practical case of having the horizontal boundaries away from the screen, the above method cant be applied anymore. When artesian top and bottom boundaries are applied, F no longer approaches zer o as the lateral boun dary is moved fa rther away, and the behavior without boundaries can be studied. However, the method of images cannot be used to simplify the problem. Every screen slot geometry is analyzed individually wi th different relative distances between screen slots ( ps/ ss = 3, 10 and 26), different number of slots (Ns= 2, 5, 10 and 20) and different relative distances to the top and bot tom boundaries (d/s). The screen length s the slot width ss, and the distance between screen slots ps are shown in Figure 3 26. The pr imary objective is to study the effect of screen slot on F factor with no close by boundaries The influence of top, bottom and lateral boundaries on F factor is eliminated by taking the boundaries at a distance of VOI (larger value of Vr or Vz) from the solution for a sing le injection screen (Figure 3 15). PAGE 87 87 Figure 3 26. Physical configurations of two slotted (left) and continuous screens (right) for infinite flow domain For boundaries far away the error in assuming a slotted screen as a continuous screen is minimal when the number of slots is increasing from 2 to 20 slots, and when the slot width is increasing or ps/ss is decre asing from 26 to 3 (Figures 327 to 3 2 9 ). These Figures show that the wider the slots, the smaller will be the e rror in F factor. Smaller slots lead to a higher resistance to flow and lower F factor. Figure 3 27. The F factor ratio ( Fslot/Fcont [ ]) versus s/a [ ] for boundaries far away and ps/ss= 26 r d h2 2a h3 I II III z b h 1 h 4 ss ps r d 2a I II III z b h 1 h2 s s s PAGE 88 88 Figure 3 2 8 The ratio of the F factors ( Fslot/Fcont [ ]) for infinite flow domain and ps/ss= 10 Figure 3 29. The F factors ratio ( Fslot/Fcont [ ]) versus relative screen length ( s/a [ ]) for boundaries far away and ps/ss=3 PAGE 89 89 The F factor for continuous screen and the F factor for slotted screen ar e calculated for different slot frequencies or widths with different relative distances to the top and bottom boundaries (d/s) which is equal to the relative distance from probe axis to the lateral boundary (b/s). The boundaries are taken as far away as the VOI in order to approximate the infinite flow domain. Figure 3 30 shows that the boundaries have very small influence on the flow field compared to when the boundaries are infinitely far away. It is shown that Fslot/Fcont remains approximately constant for boundaries out side the VOI. This was also checked for different values of s/a d/s and number of slots Ns. Figure 3 30. The ratio of the F factors ( Fslot/Fcont [ ]) versus relative distance to top and bottom boundaries ( d/s [ ]) with s/a= 20 (Ns = 10 slots) 3.3.3 Example Application of VAHIP As a VAHIP example application of this analysis, values for the differ ent variables (s, a, and d) are considered and a comparison between the c ontinuous and slotted screen is est ablished. The pertinent input parameters are as f ollows (Figure 3 31): PAGE 90 90 Total screen length s = 4.45 cm Slotted scre en ss/a= 0.041, ps/ss = 4, Number of slots Ns= 11 Figure 3 31. Example of variable head distribution along slotted screen using method of images for 11 periodical repetitions Figure 3 32. Example of constant head along the slotted screen width and variable head distribution along the impermeable part of the screen using VAHIP case d s Injection Screen z r b Slot s s 4s s PAGE 91 91 Figure 3 32 shows how the head is varied along the slotted screen compared to a constant head along continuous screen (Equation 3 73). For the confined case, the decrease in F factor (1 5% ) for slotted screen is minimal compared to the continuous screen However, the impermeable case is not reasonable in practice, since the top and bottom boundaries are close to the screen. For boundaries far away the percentage difference between the slotted and continuous screen is equal to 7.5 % for ps/ss = 4. As a result, it can be conc luded that it is more reasonable to have the larger error with boundaries far away than the smaller error. An inaccuracy of 7.5 % is still within the margins of error that can be considered acceptable for conductivity measurements. T herefore, the head can be considered co nstant in the presence of slots and the F factor of the ideal continuous screen is valid for boundaries far away 3.4 Hydraulic Resistance due to Compaction and Screen Effects A comparison of the effect of compaction conceptualized by a hydraulic resistance R inside a screen, is studied between injection and recirculation tests. In the case of the injection test through both screens the head loss due to hydraulic resistance R is only half in each screen, since only half of the flow is pass ing through each screen. I n the case of t he recirculation test, the flow is subjected to the head loss twice: the first time b y injection through the first screen and the second time by extracting into t he other screen. This double s the effect of R, which means that the recirculation Kc is four times more sensitive to the compaction effect than the injection Ki. In isotropic media, the difference in injection (Ki [L/T]) and recirculation ( Kc [L/T] ) tests ma y be attributed to a resistance to flow at the scree ns due to soil compaction while driving the probe into the soil formation or due to the screen itself. In th eor y, the hydraulic resistance R [T/L2] is responsible for a head loss inside the screens and due to soil compaction The injection head i and recirculation head c may be written as (Klammler, 2007) : PAGE 92 92 2 R Q KF Qi i i i (3 74) R Q 2 KF Qc c c c (3 75) By multiplying Equation 3 74 by 4 and dividing it by Qi as well as dividing Equation 3 75 by Qc, the following equations are obtained: R 2 KF 4 Q 4i i i with i i i iF K 1 Q (3 76) R 2 KF 1 Qc c c with c c c cF K 1 Q (3 77) E stimate s of K and R are obtain ed by subtracting Equations 3 76 and 3 77: c i i c i cK F K F 4 F F 4 K (3 78) and c i c iF 4 F K 1 K 1 as 4 R (3 79) For Ki = Kc, it is seen that K = Ki = Kc and R = 0. 3.5 Comparison b etween VAHIP Results and the Axisymmetric Model The proposed aim of this research section is to compare VAHIP lateral permeability res ults using ASTM and Packer/Lugeon equations with the axisymmetri c potential flow model under the constant head test. Under saturated condition, the horizontal perm eability is measured at depths 91.5 and 1 5 2.4 cm below the ground surface, as shown in Figure 3 33 (Bloomquist et al., 2007). PAGE 93 93 Figure 3 33. Tes ting at depth = 91.5 cm from ground surface (Bloomquist et al., 2007) Figure 3 34. Illustration of the VAHIP probe dimensions (Bloomquist et al., 2007) Using the ASTM equation, the permeability measured in the horizontal plane given a constant head is: H PAGE 94 9 4 H D L D 2 Q K AST M (3 80) where D is the internal diameter of the probe L is the scre en length H is the head For D = 4.13 cm and L = 4.45 cm (Figure 3 34), the ASTM equation gives the shape factor cm 5 9 26 D L D 2 F and K = 2.78 E 03 cm/s As shown in the ASTM equation, the shape factor F depends on the diameter of the probe and the screen length. This method does not give a detailed representation of field condition s related to the types and distances between boundary conditions. On the other hand, the exact axisymmetric potential flow field model is able to solve the problem for different boundary types and locations. According to the Packer/Lugeo n Equation 2 9 the calculated values of F and k are obtained from Equation s 3 81 and 382. cm 2 30 r 2 L sinh a L 2 F (3 81) s / cm 10 48 2 FH Q K3 (3 82) A conceptualized physical configuration of a single screen injection test is illustrated in Figu re 3 35. It consists of a fully penetrating impermeabl e cylindrical device of radius a [L] between artesian top (water table) and impermeable bottom boundaries (c o nditions II and III). Boundary c ondition I defines an artesian lateral boundary at a rad ial distance b [L] from the center of the device. This distance is purposely large (b/a =10 00) to prevent interaction between the lateral boundary and the flow field. PAGE 95 95 At depths of 91.5 cm and 152.4 cm the system is modeled assuming a shallow unconfined aquifer (artesian top and impermeable bottom boundaries) with negligible fluctuations in the water table due to the injection b ased on the potential and stream functions in Equations 3 51 and 3 52. Figure 3 35. Boundary conditions for axisymmetric flow domain of single injection screen (Bloomquist et al. 2007) The solution of a series of equations and conditions can be implemented as shown previously to compute F factors. Therefore, an approximate estimate of horizontal permeability K is obtained from an injection test for the two depths as: (3 83) The vertical permeability cannot be evaluated in this approach because only one screen is used in VAHIP. Kc can be measured by using another screen and recirculating the flow between them. Therefore the medium is assumed isotropic with Ki = Kc. d Injection Screen (Q, ) 2a z b s 2a I III II N ,... 5 3 1 n 1 n) d / a n ( r B a 2 Q K PAGE 96 96 In Table 3 1, a preliminary comparison is made for horizontal permeability estim ates given by ASTM, Packer/Lugeo n and the ax isymmetric potential flow model using the fol lowing input parameters: d is the d is tance between top and bottom boundaries (L) a is the p robe radius (L) s is the s creen length (L) located at the center of the flow domain b is the d istance from the probe axis (r =0) to the lateral b oundary (L) F is the s hape factor (L) H is the head differen ce between the water table and the Marriott tank (L) K is the hydraulic conductivity (L/T) Table 3 1 Comparison between the axisymmetric model and VAHIP results It is important to know the field conditions for which the ASTM and Packer/Lugeon equations can be used to estimate the horizontal permeability. Therefore, the boundary conditions used during VAHIP testing are analyzed as an unconfined aquifer with an artesian top boundary (water table). As shown in Table 3 1, preliminary results of the axisymmetric po tential flow model (2.62*103 cm/s) falls between the estimated re sults from ASTM and Packer Lugeon at depths of 91.5 and 1 5 2.4 cm Results of previous l aborato ry permeability tests performed on a grey fine sand sample are also close to those of the probe t est. Equal values of conductivities at different d epths illustrate a homogeneous soil formation. The present work incorporates a n exact semi analytical solutio n for the related flow field and F factor, thus potentially serving as a validation of previous approximate results. For top, bottom and lateral boundaries located far away from the screen, F factor is obtained from Figure 3 36 as 26.9 cm with s/a = 2 K is equal to 2.78 E 03 cm/s and compares well with Model ASTM Packer/Lugeo n F F F D ept h H Q a d s factor K factor K factor K (cm) (cm) (cc/s) (cm) (cm) (cm) (cm) (cm/s) (cm) (cm/s) (cm) (cm/s) 91.5 76.2 5.7 2.07 250 4.45 28.50 2.62 E 03 26.95 2.78 E 03 30.20 2.48 E 03 152.4 76.2 5.5 2.07 250 4.45 28.47 2.53E 03 26.95 2.68E 03 30.20 2.39E 03 PAGE 97 97 ASTM results Figure 3 36 shows graphs of the relative F factor, as a function of s/a for boundaries located far away from injection screen (d/s = 50 and b/a =1000). Figure 3 36. Relative F factor for different injectio n screen and boundaries are located far away from the injection screen (d/s=50, b/a=1000) ASTM and Hvorslev methods are shown for comparison Hvorslev, 1951 is equivalent to Packer Lugeon approach, since both use the ellipsoidal approximation surface approximation to the screen interval. The axisymmetric potential f low field method is close to ASTM and Packer Lugeon between s/a = 2 and 10. When s/a goes to zero, the axisymmetric model is close to ASTM and far from Hvorslev be cause of ellipsoidal approximation 3.6 Hydraulic Conductivity Measurements under Unsaturated Conditions The flow for unsaturated condition is evaluated using a different method. Philip, 1992 presented an approximate analysis of steady state spherical sa turated unsaturated flow, that included the influence of gravity (Equation 3 84). W arrick, 1993 presented an approximate solution to the same quasi linear point source problem that neglected gravity PAGE 98 98 1 2 r 1 Kr 4 Q (3 84) where r is the equivalent spherical radiu s of the injection cavity, and gravity. Shani and Or (1995) use Equation 3 84 for their subsurface confined cavity test (Equation 2 17), and Friefeld and Oldenburg, 2000 uses the same equation but with no gravi ty effe ct to calculate K (Equation 2 18). The equivalent spherical radius of the injection cavity r [L] is calculated by equating the cylindrical side area with the area of the sphere. Using the f ormula provided by Philip (1992) and by using two different injection screens geometry with two different equivalent spherical radii, r1 and r2, for example F igure 3 37. T he difference in injection heads with equal flow rates Q is repre sented by the following conductivity estimate under steady state conditions : 1 2 1 2r 1 r 1 4 Q K (3 85) where 12 [L] are the injection heads in the cavity Q [ L3/T] is the constant injection flow rate through both screens r1 and r2 [L] are the equivalent spherical ra dii of the injection cavity K [L/T] is the field saturated hydraulic conductivity The advantage of this method is that K is o btained independent of gravity and capillarity (1/ T 1] is obt ained by replacing Equation 385 int o the head difference in Equation 3 84 (assuming gravity effect is neglected ) (Warrick, 1993) : 1 1 2 2 2 1) ( r r r r (3 86) where 2/ and the gravity effect is negligible for 2Q/K < 4 The radius of the saturated bulb r0 is obtained from Equation 2 20. PAGE 99 99 Although the actual injection geometry is a cylinder, water is assumed to be released from an equivalent sphere, the surface area of which is the same as the surface area of the cylinder ( s r rcyl sph 2 42 ). In order to obtain an appropriate approxim ation of the spherical flow, individual screen lengths are chosen to be approximately equal to respective diameters. Another method ba sed on the present approach uses the principle of equivalent shape factors F and equating F factors instead of surface are as. The F factors have already been evaluated for different s creen configurations (Figure 3 4 ), and they are calculated for different spherical injection cavi ties For the spherical injection cavities, the injection head is rK 4 / Q (assuming no gravity and capillarity effects). Therefore, the F factor for a sphere is r4 which can be equated to the F factors for the screen that were calculated previously in Matlab to evaluate the equivalent spherical radius r. Kno wing the probe radius and the screen length (log10 (a/s)), F is obtained from Figure 3 4 to give the spherical equivalent radius 4 / F r Figure 3 37. Two screen probe with different equivalent spherical radii r1 and r2 for injection test under unsaturated conditions. 2a r 2 r 1 PAGE 100 100 CHAPTER 4 LABORATORY EXPERIMENTS 4.1 Objectives The objectives of the laboratory tests for the two screen probe are to: 1 Validate the axisymmetric potential flow t heory by performing various injection and recirculation tests 2 Design and construct different probe geometries for measurement of horizontal a nd vertical conductivities. 3 Assemble three barrels with dif ferent sand types (coarse, intermediate and very fine ) intended to cover a variety of permeability estimates under both saturated and unsaturated conditions 4 Compare the probe results to independent permeability measurements of the material s, using a constant head test. 4.2 Design and Construction of the Two Screen P robe A screened P VC pipe (diameter = 3.5 cm) was designed containing three cylindrical impermeab le regions as shown in Figure 4 1. The uppermost part prevent s water infiltration into th e top chamber. The middle part serves as an impermeable boundary between the top and bottom screens to prevent water infiltration into the bottom chamber. The third im permeable section prevent s water infiltration from below the bottom screen in to the sand. Two 6.5 mm diameter tubes provide water separately to t he top and bottom chambers (Figure 4 1 ). The two screen probe which is 97.5 cm long with a n inner diameter o f 3.5 cm is made of screene d PVC pipe with a pointed PVC tip. The lengths of the PVC separators between the top and bottom screens are 7.2, 14.4 and 24.4 cm respectively. This design is used to show the effects of separator length on the F factor the f low field and the measured permeability of the soil. For all probes, the individual screens must be hydraulically independent. For individual pumping, there can be no connection between screens inside the pipe and the separation tubing to each screen. Th e configurations of different probe geometries are presented in Figure 4 1 for the screen lengths, s = 7.4, 3.7 and 2.4 cm, and the impermeable separations between the two screens PAGE 101 101 p = 14.4, 7.2 and 24.4 cm. Figure 4 2 is a photograph of a completed two scr een probe with s = 7.4 cm and p = 14.4 cm. Figure 4 1. Different probe dimensions (not to scale) 4.3 Barrel T ests Three barrels, approximately 92 cm high and 60 cm in diameter and graduated in 5 gallon increments, are wet packed with 6 cm of highly permeable gravel in the bottom and 70 cm of test material above (Figure 4 3 ). The respective test m aterial for each barrel are very fine, intermediate and coarse sand in order to cover a permeability range of approximately 106 to 102 m/s. Small mesh screen is used to avoid intrusion of the test material into the gravel. For the injection test two flow meters and pressure transducers are used to monitor the flow independently at the two screens while pumping at the same head. For the recirculation test, the flow i s recirculated between the two screens at the same flow rate 4 cm 10 cm 50 cm 24.4 cm 30 cm Probe 3 4 cm 10 cm 50 cm 7.2 cm 15 cm Probe 2 4 cm 10 cm 50 cm 14.4 cm 30 cm Probe 1 PAGE 102 102 Figure 4 2. Two screen probe with s = 7.4 cm and p = 14.4 cm Figure 4 3 Three barrels with three different types of test material PAGE 103 103 Figure 4 4 Perastaltic pump with two flow me ters and pressure transducers (left). P ower supply with two voltmeters (right). Two flow meters (Omega, FL 1800 series) with a range of 15 to 541 mL/min, and two p ressure transducers (Omega, PX 180B series) wit h a range of 0 to 6 psi provide a maximum head of 13.8 ft (4.2 m ) for the tests. Two tube s are installed into the top and bottom screen chambers and the pressure is measured from transducers located at the same elevation from the ground surface using a powe r supply and two voltmeters, sho wn in Figure 4 4 4.4 Experimental Design and Laboratory Results The homogeneous and isotropic sand is wet packed into the barrel where a two screen probe is pushed to the center of the test material to estimate the hydraulic conductivity in both satur ated and unsaturated zones. Before installing the probe inside the barrel, a constant head test was also performed to evaluate the independen t measurements of permeability. Figure 4 5 shows the general setup of the laboratory sand barrel experiments for the validation of the theory. The two flow meters and pressure transducers allow for independent flow monitoring at the two screens while pumping at the same head and recirculating flow between the screens. Measurements of the laboratory hydraulic conductivity under saturated and unsaturated condit ions are compared to each other PAGE 104 104 Figure 4 5 Barrel configuration for laboratory testing under saturated and unsaturated conditions. 4. 4 .1 Independent Permeability M easurement (Constant Head Test) Under saturated conditions, a constant head conductivit y test is performed by applying a constant head difference between the top and bottom of the test material. A tube is connected to the bottom of the barrel (gravel) to create a head difference ( of 10 cm above the sand column A Mariott tank (10 gallons ) can also be used to provide a constant pressure to deliver a constant flow rate. Gravel Pack (k >> k fs ) Constant Water Level Sand (k fs ) Water Column Interface Constant Head Res. B arrel Valve Two screens Two Flow meters Probe Pump/Vacuum Two Pressure Transducers Connected to Voltmeters bucket PAGE 105 105 Using a one dimensional flow model, Henry Darcy (1856) determined that the flow rate Q through sand is directly proportional to the cross sectional area (A = 2596.72 cm2) a nd the difference in head ( (Equation 2 3). Table 5 1. Constant head test for high perm eability sand Avg. Avg. Time Q Temp K 29c K 20c K 20c K 29c (s) (cm) (cm 3 ) ( o C) (cm/s) (cm/s) (cm/s) (cm/s) Trial 1 30 82.5 2673.38 29 0.029 2.38E 02 2.7E 02 2 60 82.5 6343.62 29 0.035 2.82E 02 3.3E 02 3 120 82.5 12777.85 29 0.035 2.84E 02 4 180 82.5 19121.47 29 0.035 2.83E 02 Table 5 2. Constant head test for intermediate permeability sand Avg. Avg. Time Q Temp K 29c K 20c K 20c K 29c (s) (cm) (cm 3 ) ( o C) (cm/s) (cm/s) (cm/s) (cm/s) Trial 1 30 83 906.3 29 9.81E 03 8.01E 03 7.9E 03 9.7E 03 2 60 83 1812.48 29 9.81E 03 8.01E 03 3 120 83 3534 29 9.56E 03 7.81E 03 4 180 83 5256 29 9.48E 03 7.74E 03 Table 5 3. Constan t head test for low permeab ili ty sand Avg. Avg. Time Q Temp K 29c K 20c K 20c K 29c (s) (cm) (cm 3 ) ( o C) (cm/s) (cm/s) (cm/s) (cm/s) Trial 1 30 83 550 29 5.95E 03 4.86E 03 4.6E 03 5.7E 03 2 60 83 1050 29 5.68E 03 4.64E 03 3 120 83 2050 29 5.55E 03 4.53E 03 4 180 83 3100 29 5.59E 03 4.57E 03 The coefficient of permeability is inversely proportional to the viscosity of the permeating fluid. The viscosity of water is a function of temperature. It is common practice to standardize the coefficient of permeability at 20C by means of Equation 2 2 knowing the PAGE 106 106 viscosity of water at temperatures 20020C = 1.00E 03 Ns/m2) and 29029C = 8.18E 04 Ns/m2). Four constant head tests were performed for highly permeable sand to measure the average conductivity at 29C as Kavg = 3.3E 02 cm/s (Table 5 1) The coefficient of permeability is also calculated for the temperature correction as K20c = 2.7E 02 cm/s. These values are used for comparison to the injection and recirculation test result s using the highly permeable sand. The same constant head test is p erformed for fine sand (Kavg = 9.7E 03 cm/s) and for low permeable sand (Kavg = 5.7E 03 cm/s) (Tables 5 2 and 5 3). In general, isotropic condu ctivity is expected to exist in the barrels. H owever, for an independent estimate of the horizontal perme ability, the sand in a cubic container can be packed in the same way as in the barrels. Flow can be applied between the lateral sides to estimate th e horizontal conductivity with the top and bottom boundaries function ing as confined units. In this study, the measu rements of vertical and horizontal permeability are assumed equal and they are compared to the two screen permeability estimates. 4. 4.2 Testing under Saturated Conditions Two methods are presented to measure the horizontal (Kh) and vertical (Kv) conductivities separately. The first meth od requires two different steps: 1) inject ing water from both screens resulting in horizontal permeability measurements and 2) recirculat ion between the two screens, where the same amount of water injected through one screen is extracted by the other screen, thereby generating a verti cal permeability measurement. The second method is necessary t o avoid the problems faced in the field and laboratory tests, such as sand entrapped in the system when extracting the flow from the bottom scre en. This method requires injecting water from one screen to measure the isotropic conductivity, while at the same time the head observation from the bottom screen is used to calculate the anisotropy ratio. PAGE 107 107 4.4.2.1 Injection a nd Recircul ation Tests Using a Two Screen Probe By installing the probe vertically at the center of a barrel, the pump injects water at the same head through both s creens (Figure 3 6 left) while the respective flow rates for each screen are recorded individually. Dr ainage is created at the top of the barrel to withdraw excess water due to injection. The pressure transducers are connected under water to prevent air from entering the system and affecting the head measurements. During the rec irculation test, one screen was disconnected from the pump outlet and connecte d to the pump inlet (Figure 3 6 right). By pumping at a given head, recirculating flow was established between the screens, and the respective flow rate was measured. If the screens are rather close to the top and bottom boundaries, then some flow leaving the injection screen will actually end up in the nearby boundary with the remainder going to the extraction screen. On the other hand, the extraction screen will draw some flow from its nearby boundary. I n an ext reme case, recirculation occurs through the boundaries by having them connected by a tube. In this experiment, the probe screens are installed in the middle of the test material and the flow is recirculated between them. The same connection between the top and bottom artesian boundaries used for the inj ection test was applied to compensate for the flow between the scr eens and boundaries. No water was added or withdrawn from the system. The injection and recirculation F factors, which relate the rati o of injection head to injection rate to the hydraulic conductivity of the test mediu m, were calculated for the probe s geometries using the axisymmetrical flow model discussed earlier. Figure 4 6 represent s the physical configurations of the permeameters in the barrels. They all consist of an impermeable cylindrical device with a 1.75 cm radius between the two horizontal artesian top (water table) and bottom boundaries (gravel pack) and a separation of d = 70 cm. Also, an impermeable boundary is locate d at the edges of the barrels with a separation b = PAGE 108 108 30 cm f rom the probe axis. These devic es have constant head injection screens between h1 and h2 and between h3 and h4. Figure 4 6. Physical configuration of the permeameter with a screen length of A) s = 7.4 cm. B) s =3.7 cm C) s = 2.4 cm. Table 5 4. Different probe geometries Probe 1a and ba Probe 2 Probe 3 (p/s =1.95) (p/s =1.95) (p/s =10.17) s (cm) 7.4 3.7 2.4 p (cm) 14.4 7.2 24.4 h1 (cm) 20.4 27.7 20.4 h2 (cm) 27.8 31.4 22.8 h3 (cm) 42.2 38.6 47.2 h4 (cm) 49.6 42.3 49.6 Finj (cm) 57.1 38.5 36.1 Fcir (cm) 18.1 13.5 9.9 a Probe 1a and 1b are identical except for slot size (P robe 1a, 0.50mm; Probe 1b, 0. 25 mm). The specific case found in the laboratory is that of a saturated medium with a finite impermeable lateral boundary (barrel wall) and finite artesian top (water column) and bo ttom (gravel pack) boundaries (Figure 4 5). By using the theoretical flow model, the horizontal and vertical permeability were estimated from the recorded pumping heads and flow rates for the artesi an case The results are also compared to independent per meability measurements (Table 5 1). r r d h 2 2a h3 I II III z b h1 h 4 s p Probe 1 d h2 2a h3 I II III z b h1 h 4 Screen Probe 2 d h 2 2a h3 I II III z b h 1 h 4 Screen Probe 3 r PAGE 109 109 The injection test was also performed in a barrel filled with water to account for the losses through the probe screens and tubing system. These heads were then subtracted from the heads measured in the barrel packed wit h sand to calculate Ki. Note that the heads are measured with respect to the ground surface datum. For the recirculation test (Table 5 6), the head is the difference in the pressure transducers readings between the top and bottom screens since the elevati on of the pressure transducers with respect to the screens and the elevation of w ater table cancel each other. The data and conductivity results for injection and recirculation tests with Probe 1a are presented in Tables 5 5 and 56. Table 5 5. Hydraulic c onductivity measurements using injection test (Ki) at probe1a Q Head in Head in Difference 2screens V 2 /2g water barrel sand barrel in head K i (cc/s) (cm) (cm) (cm) (cm) (cm/s) 9.13 0.004 12.39 17.50 5.11 0.031 13.17 0.009 21.88 28.05 6.17 0.037 16.93 0.015 35.55 42.82 7.28 0.041 A verage 13.08 0.009 25.94 29.46 6.18 0.037 Table 5 6. Hydraulic conductivity results using recirculation test (K c ) at probe1 a Q Head in Head in Difference 1screen water barrel sand barrel in head K c (cc/s) (cm) (cm) (cm) (cm/s) 4.57 31.10 38.20 7.10 0.035 6.58 45.99 54.88 8.89 0.041 8.47 69.43 80.21 10.78 0.043 Average 6.54 48.84 57.76 8.92 0.041 As shown in Tables 5 5 and 5 6, the conductivities estimated for injection (0.036 cm/s) and recirculation tests (0.040 cm/s) are close to the independent measurements of K (0.033 cm/s) by the constant head test, and the velocity head (V2/2g) is minimal Tables 5 7 and 58 present the injecti on test results for Probe 1b (0.25 mm slots) and Probe 2. PAGE 110 110 Table 5 7. Hydraulic conductivity measurements using injection test (K i ) at probe 1 b Q Head in Head in Difference 2screens V 2 /2g water barrel sand barrel in head K i (cc/s) (cm) (cm) (cm) (cm) (cm/s) 9.13 0.004 22.83 26.99 4.17 0.038 13.17 0.009 37.60 42.82 5.22 0.044 16.93 0.015 56.65 62.88 6.22 0.048 A verage 13.08 0.009 39.03 44.23 5.20 0.043 Table 5 8. Hydraulic conductivity results using injection test (Ki) at probe 2 Q Head in Head in Difference 2screens V 2 /2g water barrel s and barrel in head K i (cc/s) (cm) (cm) (cm) (cm) (cm/s) 9.13 0.004 26.05 32.27 6.22 0.038 13.17 0.009 42.94 51.27 8.33 0.041 16.93 0.015 63.04 72.37 9.33 0.047 Average 13.08 0.009 44.01 51.97 7.96 0.042 T he horizonta l hydraulic conductivities for P robe 1 a with larger slots (0.036 cm/s), Probe 1b with smaller slots (0.043 cm/s) and P robe2 (0.042 cm/s) are close to the independent measurements of K (0.033 cm/s). However, the recirculation tests (data not shown) for Probes 1b and 2 yielded unsatisfactory results with high permeability values due to sand entrapped in the system. Tables 5 9 and 510 present the data from injection and recirculation test, respectively, for Probe 3. As shown in Tables 5 9 and 5 10, the difference in hea d between sand in barrel and water in barrel measurements increases with increasing flow rate, with the horizontal (0.045 cm/s) and vertical conductivities (0.039 cm/s) comparing well with the independent measurements of K (0.033 cm/s). However, the permeability values for the four probes are close to the constant head measurements These injection and recirculation tests apply only for coarse sand. However, as mentioned previously, the intermediate and lo w permeable sand testing did not perform as expected, due to fi ne sand entrapped in the hydraulic system clogging water flow. PAGE 111 111 Table 5 9. Hydraul ic conductivity measurements using injection test (Ki) at p robe 3 Q Head in Head in Difference 2screens V 2 /2g water barrel sand barrel in Head K i (cc/s) (cm) (cm) (cm) (cm) (cm/s) 9.13 0.004 21.83 28.05 6.22 0.041 13.17 0.009 34.71 42.82 8.11 0.045 16.93 0.015 52.32 61.82 9.50 0.049 Average 13.08 0.009 36.29 44.23 7.94 0.045 Table 5 10. Hydraulic conductivity results using recirculation test (K c ) at probe 3 Q Water in Barrel Sand in Barrel Difference in 1screen Applied Head Applied Head head K c (cc/s) (cm) (cm) (cm) (cm/s) 4.57 42.10 54.88 12.77 0.036 6.58 66.99 84.43 17.44 0.038 8.47 104.43 124.53 20.10 0.042 Average 6.54 71.17 87.95 16.77 0.039 In order to calculate the hydraulic resistance of the screens, R is related to the injection and recirculation conductivities and Ffactors by Equation 3 79. This case is when no water barrel correction has been made. After calculating the hydraulic resistance (R = 61.73 s/cm2) for P robe 3, the saturated conductivity results in a negative value (Equation 3 78 ) due to the large head losses in the tubing and screens. Further research need to be done by incorporating larger tube diameter s to minimize head losses. 4.4 .2.2 Injection Test with Head Observation As stated in section 3.1.5.2 this test requires injecting into one screen using the pump (or constant head reservoir, e.g., Marriot tank) and recording the head from the second screen located at a distance p from the injection screen. First the pump injects through the top and bottom screen s to saturate the tubes and expel air out of the system. Then, water is supplied only through the top screen by closing the valve of the bottom screen flow meter. An injection test is PAGE 112 112 then performed to measure the flow rate and head at the top screen, whi le the head at the bottom screen is recorded separately using the pressure transducer readings. The effective (isotopic) conductivity, defined in section 3.1.5.1 is estimated from the head, flow rate and F factor in the injection screen and the anisotropy ratio is estimated from the head observation at the bottom screen which is used as piezometer Figure 4 7. Determination of anisotropy from the ratio of applied head at top screen and the head o bservation of the bottom screen for laboratory case Figures 4 7 and 4 8 are specific cases using the boundary conditions of the ba rrel and the probe dimensions for different p/s. The distance between the top and bottom artesian boundary d is equal to 70 cm, and the distance between the probe axis and impermeable lateral boundary conditions b is equal to 30 cm. The terms b and a denote the barrel and probe radii respectively scaled for a certain anisotropy ratio. The head ratio between bot tom and top sc reen in Figure 4 7 and the scaled F factor in Figure 4 8 are different than in Figures 3 7 and 38 because the nearby impermeable la teral boundary is considered in the laboratory experiments. PAGE 113 113 Figure 4 8 Fi over scaled probe radius a for laboratory case Table 5 11. Isotropic conductivity measurements K iso for different probe geometries Head at Bottom screen Corrected Head at Top Screen F i K p/s V 2 /2 g Q 1 2 1 2 Factor isotropic K r K z ( ) (cm) (cc/s) (cm) (cm) ( ) ( ) (cm/s) (cm/s) (cm/s) (cm/s) 1 .95 b 3.7 27 3.44 21.11 0.16 0.9 74.0 0.02 0.022 0.018 10.17 c 4.0 27.1 2.11 33.77 0.06 0.9 19.0 0.04 0.044 0.036 b p=14. 4 cm and s=7.4 cm c p=24.4 cm and s=2.4 cm In Table 5 11, for a 2 is corrected for the head loss by computing the difference in heads between sand in barrel and water in barrel thus 1 is the head change at the bottom screen due to injection f rom the top screen. T 1 2 is then used in Figure 4 7 ing a/ a, which happens to be approximately equal to 1; thus the results identify the absence of anisotropy as to be expected for the sand barrels. T he value of log10 (a/s) is then used in Figure 4 8 to PAGE 114 114 determine Fi, which in turn is used to calculate the isotropic effective hydraulic conductivity Kiso. Subsequently, the horizontal (Kr) and vertical (Kz) conductivities are determined from Equations 3 53 and 3iso. Given the isotropi c conditions of the sand in the barrel, the vertical and horizontal conductivities are approximately equal to the isotropic conductivity Kiso ~ Kr ~ Kz. The closest conductivity value to the independent measure ments of K (0.033 cm/s) was 0.02 cm/s for p/s = 1.95 and 0.04 cm/s for p/s = 10.17. Table 5 11 shows that when p/s increases from 1.95 to 10.17, the change in head decreases from 0.16 to 0.06. This occurs because the injected flow from the top screen has less influence on the bottom head screen which is located further away from the injection screen. The results discussed above are for coarse sand. Future testing should be performed for both intermediate and low permeable sand. However, for the high permeable sand, the two probe geometries gave consi stent results for K and for the independent measurements. 4. 4.3 Testing under Unsaturated Conditions After calculating the saturated permeability, test barrels are drained through the bottom gravel pack to achieve unsaturated or partially saturated test condition s whe re different degrees of saturation can be a chieved by varying the duration of the draini ng periods. The method, which is presented in section 3.6, is validated in the laboratory against the Friefeld and Oldenburg (2000) method discusse d in section 2.5.2.2. Furthermore, t he estimates of the saturated hydraulic permeability are compared against the independent measurements of K. 4.4.3.1 Injection Test Using a Single Screen Probe with Different Flow R ates The solution by Freifeld and Olde nburg (2000) is based on injecting through a single cavity with two different heads and flow rates (Equations 2 18 to 2 20) The results for different probe geometries are presented in Table 5 12. PAGE 115 115 Table 5 12 Analysis result s using different probe geometries with different flow rates Difference gravity Degree of in Head effect Sat uration s r Q K 2 Q/K r 0 S (cm) (cm) (cc/s) (cm) (cm/s) (cm 1 ) (cm) ( ) (cm) (%) 2.4 1.5 9.02 4.22 0.045 0.155 12.88 4.82 2.48 10.6 8.47 3.57 3.7 2.07 9.02 0.93 0.041 0.135 14.81 3.69 2.33 8.47 0.42 T he head listed in Table 5 12 accounts for losses in the screen and the tubes by subtracting the head measured in the barrel with sand from the head in an empty barrel. This head is the pressure transducer reading with respect to atmospheric pressure. The saturated hydraulic conductivity evaluated in Table 5 12 compares well with the independent measurements of K = 0.033 cm/s. The gravity effect for probe 3 is slightly above the limit 2Q/K = 4.82 > 4), but the results are still satisfactory. In this case, the test is performed after the water is continually drained for three days through the bottom gravel pack in order to decrease the degree of saturation of the test medium. After the three days of draining the sand is assumed to reach field capacity which is the maximum amount of water that t he unsaturated soil can hold by capillary force, before the water is drained by gravity and / or evaporated from the ground surface (Israelson and West, 1922, Veihmeyer and Hendrickson, 1931). K nowing the porosity of the test medium, the actual degree of saturation achieved is determined from the volume of water drained from the barrel. The porosity of the test medium (n) is calculated from the known volume of dry sand (Vs) and the total volume (V ) by V n Vs) 1 ( With Vs = 166, 248 cm3 and V = 197, 920 cm3, the porosity n is equal to 0.16. This appears to be a rather small value for the narrow grain size distribution of the sa nd. The pore volume of the sand barrel is calculated from the porosity by Vv = n*V = 31, 672 cm3. The degree of saturation (S = Vw/Vv) is calculated from the ratio of the amount of PAGE 116 116 water drained through the bottom gravel (Vw) and the volume of voids (Vv), accounting for water above and below the sand column The values in T able 5 12 correspond to a degree of saturation of 10.6 % with a volume of 3.36x103 cm3 of water drained through the bottom of the barrel. The moisture content (V / Vw = 1.7 %) is also calculated by the amount of water contained in the test materia l. This sand is considered moist with the degree of saturation between 1 and 25 % (Terzaghi and Peck, 1967). 4.4.3.2 Inje ction T est through T w o Different Screen Lengths with Equal F low Rates Another way of measuring the saturated hydraulic conductivity k under unsaturated conditions is to use two d ifferent probes with two screened intervals in addition to two different screen lengths instead of radii and inject an equal flow rate through both screens, while observing the steady state heads at the screens. This test is performed with the same flow rates for different probe screen lengths, which are approximately equal to the respective diameters in order to best appr oximate a sphere. T herefore, this method can be applied without constructing a conical probe with different radii. The same probes are used with different equivalent spherical radii of the injection cavity r1 and r2, by using the principl e of equivalent shape factors, F, discussed in section 3.6. The dimensions of the two probes with different equivalent spherical radii r1 and r2 are given in Table 5 13 and 514 for equal flow rates of 8.47 cm3/s and 9.02 cm3/s. The saturated hydraulic conductivity (K) and 85 and 3 86. As described in section 3.6, t he gravity effect can be neglected because 2Q/K is less than 4. PAGE 117 117 In Tables 5 13 and 5 14, t he saturated hydraulic conductivity K (0.039 cm/s) and capillary length (15.75 cm) compares well with the solution of Freifeld and Oldenburg (2000) (K = 0.041 cm/s capillary length = 14.81 cm). K also compares well with the independent measurements in the constant head test (0.033 cm/s). The saturated bulb radius r0 (Equation 2 20) is greater than the equival ent spherical radius. Note that the degree of saturation is kept the same as above. However, an elevated initial degree of saturation decreases th e effect of capillarity and thereby suggests a n important project for future studies. Different degrees of saturation should be performed in order to observe the variation of the L1) and the similarity with the conductivity measurements. Two screens with different radii (Figure 4 9 ), with screen lengths equal to respective radii, can be used instead of the two screens with equal radii and different lengths, such that the spherical flo w approximation would be modeled more accurately. Table 5 13. Resul ts for unsaturated case using different probe geometry with Q = 8.47 cc/s Diff. Grav ity Degree of in effect Saturation s r Q Head K 2 Q/K r0 S (cm) (cm) (cc/s) (cm) (cm/s) (cm 1 ) (cm) ( ) (cm) (%) 2.4 1.5 8.47 3.57 0.039 0.127 15.75 3.67 2.18 10.6 3.7 2.07 8.47 0.42 Table 5 14. Re sults under unsaturated conditions with Q = 9.02 cc/s Diff. Grav ity Degree of in effect Saturation s r Q Head K 2 Q/K r0 S (cm) (cm) (cc/s) (cm) (cm/s) (cm 1 ) (cm) ( ) (cm) (%) 2.4 1.5 9.02 4.22 0.04 0.129 15.45 3.75 2.31 10.6 3.7 2.07 9.02 0.93 PAGE 118 118 Figure 4 9. Coned probe for injection test under unsaturated conditions (Klammler, 2007) r2 r1 Q Q r2 r1 Q Q PAGE 119 119 CHAPTER 5 FIELD APPLICATION An ideal probe for field tests can be i nstalled vertically into the ground without drilling a borehole and measurements at variable depth can be easily obtained. Probe s with diameters in the lower centimeter range (e.g., 2 5 cm) are considered reasonable for minimizing soil disturbance and they will have sufficient mechanical resistance if constructed from stainless steel Generally, for all testing, the probe should be driven into the ground with a hydraulically operated CPT rig, to minimize the stresses on the probe during driving (Bloomquist et al., 2007). 5.1 Alternative S olutions for VAHI P P roblems The Florida Department of Transportation (FDOT) sponsored research at the University of Florida to design a device Vertical and Horizontal In Situ Permeability VAHIP t o measure horizontal and vertical conductivity and flow at various depths of a soil formation (Bloomquist et al., 2007) Various component alterations of the VAHIP 2006 probe are suggested and are listed below: 5.1.1 Mechanical P roblems A problem occurred with the existing VAHIP 2006 probe design when pulling up the inner part of the probe to open the vertical port to measure the vertical permeability. There fore, an alternative method is suggested to eliminate the moving parts in the probe and allow for a s maller probe diameter (approximately 2 cm). Another well screen and horizontal flow port should be added and separated from the lower screen by an impermeable layer to prevent inflow inside the probe In this case, the flow will circulate between the injec tion / extraction screens at a constant rate in order to measure the vertical permeability (Kz ~ Krecirculation). PAGE 120 120 5.1.2 Clogging P roblems For future investigations, four proposed solutions to screen clogging problems are discussed: A second variation of t he VAHIP 2006 probe will have the filters covered by a thin metal tube, which is a continuati on of the outer core shoulder, to protect t he screens from soil infiltration while driving the probe into the soil (Bloomquist et al., 2007) The installation will be stopped slightly above the desired level and the screen will be pushed further into the soil by rotating the external cover through the threaded edge of the probe. This rotation will affect only the external cover but not the body of the probe (Figure 5 1 ) and should minimize any clogging in the screens. Additional changes will include a device introduced to the tip in order to locate the water elevation using a flow sensor. A cylindrical opening will be introduced through the tip slightly sloped in order to detect water inflow of underground water, allowing the detection of saturated soils. Different probe configurations are proposed below to solve clogging screen pr oblems for future design. The steel sheet covering the screened part of the probe closes the slot openings to prevent soil infiltration into the screen chambers while driving the probe into the soil. Before testing at the desired level the steel shaft in the middle of the probe is twisted gradually upward to open the steel sheets to the required opening depending on the permeability of the test material (Figure 5 2). If the soil is highly permeable, a small opening is enough to release water from the scree n. For low permeability, a larger opening is needed to deliver water to the soil formation. As shown in Figure 5 3, water passes first through the high range flow meter. If the float material rises, water will continue to the intermediate range flow meter. If water is stabilized in the low flow meter range, then low permeable sand is present and a larger opening is required to inject flow. PAGE 121 121 Another proposal for resolving the clogging problem involves installing two inflatable packers to the top an d bottom screens (Figure 5 4) while the probe is being driven into the. Then, before testing at the desired level the packers are deflated to inj ect water through both screens. The fourth proposal (Figure 5 5) involves installing filters around the screens to prevent any entrapped fine material from entering the injection and/or extraction screen and clogging the hydraulic circuit for the recirculation test Figure 5 1 Modified p robe to solve clogging problems and to detect water table elevation, b efore injection (Left) a nd after injection (Right) After injection Opened cover Threaded outer core Before injection Cylindrical opening Screen Pressure sensor or Piezometer Thin metal cylindrical Cover PAGE 122 122 Figure 5 2 Twisted screened probe (left) rotating vane (top view) (right) Figure 5 3. T hree different flow meter ranges for conductivity estimates High Medium Low Flow Vane Rotating steel bar Screen Vane Twisted steel sheets Threaded rotating steel bar Impermeable rubber Twisted steel s heets PAGE 123 123 Figure 5 4. Two s creen probe covered with two inflatable packers A) before inflation B) after inflation Figure 5 5. Two screen probe shielded with filters Filter Tube Screen Inflatable packers Screen Nitrogen and v acuum PAGE 124 124 5.1.3 Practicality of Testing P rocedure In order to solve the complication created by the Plexiglas standpipe, it should be replaced by flexible tubes installed inside the steel rods. The top of the probe and each rod will be threaded to facilitate the addition of rods to drive the probe into the soil (Figure 5 6 ). Figu re 5 6. Modified p robe to solve rod tubing installation problem 5 .2 Proposed P robe s Different designs of proposed probes are discussed in detail in the following sections for saturated and unsaturated conditions. For saturated conditions, two proposed probes are presented to measure the anisotropic conductivities. The first is one screen probe with injection from one screen and head observation in the holes. The second is twoscreen probe with injection from one screen and extraction from the other screen. For unsaturated conditions, twoscreen probe with different screen lengths is used to measure the isotropic conductivity. PAGE 125 125 5.2.1 One screen Probe with P iezometer The proposed probe is shown in Figure 5 7. In this test, there is no need to perform the recirculation test, thus eliminating the problem of fine sand intrusion. Using the isotropic equivalent permeability and anisotropy ratio method, the proposed probe w ill be applicable in the laboratory as well as in the field. This test is applied in a more practical and easier way in the field using one additional head observation in an injection test. A Marriott tank is used for the injection from one screen and a ma nometer tube is used in the small openings to record the head estimates. Thus, the flow injection rate from the top screen and the head difference between screens are recorded separately. Then the elevation of the water table can be used to estimate the he ads in the screen and small holes. For laboratory testing, the bottom screen is used as a piezometer for pressure observation instead of the small holes in the probe. For field applications, three or four small holes can be drilled around the probe at a ce rtain distance from the injection screen. Figure 5 7. Proposed single injection screen probe with small open ings for head observation Injection screen Holes PAGE 126 126 5.2.2 Proposed TwoScreen P robe Figure 5 8 shows a prototype of the proposed twoscreen probe, which is composed of three parts. The top and bottom screens are separated by an imp ermeable middle part including two pressure tran sducers in each screen All these parts are connected via a threaded system, which can be easily assembled for different probe geometries in which the screens and tubes are separated for individual pumping. Figure 5 8. Proposed twoscreen probe for injection and recirculation tests 5.2.3 TwoScreen Probe for Unsaturated C ase Two different probe configurations are proposed for unsaturated conditions by using two different screen lengths. Instead of designing different types of probes corresponding to different conditions, a single probe can be designed to measure the permeability for both saturated and unsaturated conditions. Screen Tubes Pressure t ransducers PAGE 127 127 The rotating rod in the center of the probe in Figure 5 9 is turned around the threaded system to compress the soft rubber to the edge of the screen perimeter and thus prevent water percolation from top screen into the bottom one. Water is supplied through the rod to the screens. This will allow the distance between the two screens and their lengths to be varied. Figure 5 10 shows another design for an unsaturated soil case. More flexibility is achieved by adding more than two screens in the probes. Using the same concept as in the previous design, the length of the screens is manipulated by allowing vertica l movement of the middle rubber. A cylindrical rubber will be squeezed inside the pipe to create two separate chambers with no flow bet ween the top and bottom screens Finally, under unsaturated c onditions, a twoscreen probe with two different spherical equivalent radii or screen lengths can be designed instead of a conical probe, in order to apply the theoretical method of injecting through both screens at equal flow rates and different heads. Figure 5 9. Alternative probe design for different packer lengths Water Soft rubber Rotating rod Water Screen Compressed threaded s ystem PAGE 128 128 Figure 5 10. Proposed probe for compressed rubbers between the top and bottom screens Soft rubber Threaded Rotating rod Screen PAGE 129 129 CHAPTER 6 CONCLUSIONS AND RECO MMENDATIONS 6.1 Conclusions The theoretical methods applied in this study were capable of measuring horizontal and vertical conductivities using injection and recirculation tests at different depths under saturated conditions. Moreover, another method was able to determine the field isotropic hydraulic conductivity, the sorption lengt h and the equivalent spherical radius above the water table The advantage of the modeling system used is that it recognizes the physical presence of the probe in the soil and provides a clear representation of the flow field, as well as the correct type and location of the boundary conditions. It is also flexible in that the input factors such as the probe diameter, screen length, and distance between boundaries can be changed easily and their effect s on the shape factor can be analyzed. A general criterion of volume of influence of the flow field was also determined using various probe dimensions This information can play an important role in evaluating the extent of the volume of soil being tested, as well as the remediation zone of contaminated soil. The influence of the screen slots geometry on K measurements was also studied in the cases of the confined aquifer and artesian top and bottom boundaries. The laboratory testing results obtained from t he two screen probes generally compares well with the independent measurements of K using the constant head test for high ly permeable sand. However, the recirculation test did not function well with low permeability sand where sand was entrapped in the sys tem while pulling water from the bottom screen. Thus, another method was developed to replace the extraction screen with screen head observation or small holes while keeping the other opening as an injection screen. The results obtained in the laboratory were satisfactory for highly permeable sand for both saturated and unsaturated media. PAGE 130 130 However, more testing should be performed in the laboratory to validate the theory for different types of soils and different probe designs. This study presents a single device that can measure horizontal and v ertical conductivity under saturated conditions and isotropic conductivity under unsaturated conditions The most practical proposed probe that can be used in the field is the one with the two screen probe with diff erent screen lengths This probe can be constructed with the concept of twisted steel shee ts around the screen to solve the clogging problems encountered while driving t he probe into the soil 6 .2 Recommendations and Future R esearch The main objective of t his research was to provide the theoretical basis to enhance the VAHIP (Vertical and Horizontal In situ Permeameter) and to prototype another device that can measure the horizontal and vertical conductivity under saturated and unsaturated conditions. The d evice was tested in the laborator y using different probe geometries in different types of soils. It is recommended that the effect s of compaction on K be analyzed using a threescreen probe with various radii to account for the densification of the surroun ding soil around the periphery of the prob e while driving in low permeability soil. 6.2.1 Effect of Compaction on K Est imates Two methods are suggested for minimizing the effect of compaction on the measurements. The first method uses a threescreen probe having multiple radii, as shown in Figure 6 1 Considering the various radii values, permeability can be measured by inducing flow through each screen The measured permeability is then plotted versus the probe radius to measure the trend of variation. It will be assumed that the smaller the radius, the higher the value of the permeability since the compaction effect will be redu ced. This trend will allow extrapolation of an accurate value of the permeability corres ponding to a zero radius with no PAGE 131 131 compaction effect. However this method has some limitations in the case of clayey soils where compaction is more likely and where the method of extrapolation could lead to erroneous results. Figure 6 1 Proposed c oned thr ee screened drive point probe for injection test to measure field saturated hydraulic conductivities in fully and partially penetrated zones. The second method uses a two screen probe with different assemblies inside the barrel: the first is packing the sand around the p robe and the second by pushin g the probe inside the barrel. T hen the results of both tests are compared. The proposed procedure to study the effect of compaction on K measurements is as follows (Figure 6 2) : 1 Fix the probe vertically i n the middle of the barrel, and start backfilling around it with five wet layers in 15 cm increments. Next, calculate the weight and the volume for each layer to obtain the density. Finally, run the injection and recirculation tests to calculate Kh1 and Kv1. Note that the screen opening will be located in the middle of one of these layers. 2 Pack the sand under the water in the same way as step 1 with the same densities. Then push the probe vertically into the middle of the barrel. Lastly, run the injection a nd recirculation tests to calculate Kh2 and Kv2. 3 The difference between Kv1, Kv2 and Kh1, Kh2, will provide an indication of how much compaction occurred when the probe was pushed into the sand. Therefore, it can be observed how the anisotropy ratio increa ses with the compaction effect. PAGE 132 132 Figure 6 2 Experimental configuration for the effect of compaction on K estimates 6.2.2 Laboratory T esting If an anisotropic permeability is created in the barrel, an independent estimate of the horizontal permeability is needed in the laboratory to compare to. In this case, the sand in a cubed cont ainer can be packed in the same way as in the barrels. Flow is applied between the lateral sides to estimate the horizontal conductivity with the top and bottom boundaries function ing as confined units. In general, an isotropic perme ability exists in the barrels. H owever, anisotropy can be created in the barrel by usi ng a platelet grain shape to create a different horizontal and vertical permeability. In previous methods, the probe was installed vertically inside the barrel while the horizontal permeability was measured by the injection test, and the vertical permeabil ity was measured by the recirculation test. However, another method can be performed in the laboratory in which the probe is installed horizontally. In this case, the horizontal permeability is measured Weight (W 5 ), Volume (V 5 ), Density ( 5 ) W 2 V 2 2 W 1 V 1 1 Gravel W 3 V 3 3 W 4 V 4 4 15 cm 15 cm 15 cm 15cm 15 cm PAGE 133 133 by the recirculation test, and the vertical permeabil ity is measured by the injection tes t, taking into account the boundary conditions. 6.2.3 Variation of K in Relation with the Location of Heterogeneity In the laboratory, the soil is considered homogeneous within the volume of influence, which is the regi on where the effective conductivity is measured, regardless if it is homogeneous or not. The effect of heterogeneity of the soil should be tested and recreated in the laboratory procedures. If heterogeneity is present beyond the volume of influence, its effect on K measurements is negligible. However, the volume of influence effect will be greater if the heterogeneity is close to the screen with h igher values of head gradient. This problem needs to be reproduced in the laboratory testing procedure in ord er to better represent the actual soil conditions. To create an artificial heterogeneous condition in the proximi ty of the screen, the probe should be installed next to the barrel wall and moved further to the center of the barrel until there is no boundar y condition effects (barrel walls) on the F factor or K measurements. The effect of the position of the probe in comparison to the barrel wall should be tested in the laboratory to analyze the variability of K with the location of the heterogeneity. This c an be theoretically tested by calculating the F factor for the impermeable and artesian bou ndaries. If there is no change in F factor values, there should be no boundary c ondition effects on the F measurements. This can be used to locate possible heterogeneities in the field. More importantly, it will allow one to observe how the boundaries affect permeability measurements 6.2.4 Passive Flux M eter (PFM) An other function can be included in the proposed probe. A passive flux meter can be integrated inside the probe to measure water and contaminant mass fluxes. In the field, PFMs PAGE 134 134 discharge tracers and absorb contaminants, and the concentrations are subsequently determined in the laboratory (F igure 2 10) (Klammler, 2007) . PAGE 135 135 LIST OF REFERENCES Anderson, M., Woessner, W., 2006. Applied Gr oundwater modeling, Department of Geology and Geophysics, University of Wisconsi n, Elsevier, San Diego, California. ASTM Standards, 1998. Standard te st method for instantaneous change in head (slug) test for determining hydraulic properties of aquifers, Conshohocken, PA, D 404496. Barker, J., Black, J., 1983. Slug tests in fissure d aquifers, Water Resources Research, 19 (6), 15581564. Batu, V., 1997. A comprehensive guide to hydrogeol ogic data analysis, Aquifer Hydraulics, John Wiley & Sons Inc., New York, NY, 646. Bear, J., 1972. Dynamics of Fluids in Porous Media, American Elsevier Publishing Company, Inc., New York, NY, 764. Binkhorst, G., Robbings, G., 1994. A review and assessment of factors affecting hydraulic conductivity values determined form slug te sts, Department of Geology and Geophysics, University of Connecticut, Storrs, CT. Binkhorst, G., Robbins, G., 1998. Conducting and in terpreting slug tests in monitoring wells with partially submerged screens, Ground Water, 36 (2), 225. Bloomquist, D., Viala A., Gartner M., 2007. Development of a field permeability apparatus, the Vertical and Horizontal Insitu Permeameter (VAHIP) Report, University of Florida, Gainesville, Florida, 104108. Bouwer, H., 1989. The Bouwer and Ri ce slug test, Ground Water 27 (3), 304. Bouwer, H., Rice, R., 1976. A slug test for dete rmining hydraulic conductivity of unconfined aquifers with completely or partially penetrating wells, Water Resources Research, 12 (3), 423. Butler, J., 1998. The design, performance, and an alysis of slug tests, Lewis Publishers, New York, NY, 252. Butler, J., Lanier, A., Healy, J., Selwood, S ., 2000. Directpush hydraulic profiling in an unconsolidated alluvial aquifer, Kansas Geol ogical Survey, University of Kansas, Wesley McCall and Elizabeth Garnett Geoprobe Syst ems, Inc, KGS open file report 200062 Casagrande, A., Fadum, R., 1940. Notes on soil testing for engineering purposes, Harvard University, Graduate School E ngineering Publication, No. 8. Cassiani, G. 1998. A new method fo r the interpretation of the c onstanthead well permeameter, Hydrology, 210 (14), 1120. PAGE 136 136 Cedergren, H., 1989. Seepage, drainage, and flow nets, Wiley Interscience, New York, NY, Third edition. Chao, S., Stephens D., 1993. A borehole field method to determine unsaturated hydraulic conductivity, Water resources research, 29 (8), 27632769. Chapuis, R., 2003. Permeability tests in rigid wall permeameters: Determining the degree of saturation, its evolution and its influence on test results, Ecole Polytechnique, Montreal, Quebec, Canada. Chapuis, R., Gill, D., 1989. Hydraulic a nisotropy of homogeneous soils and rocks: influence of the densification process, Bulletin Associate Engineering Geology, 39, 75 86. Charbeneau, R., 2000. Groundwater Hydraulics and Pollutant Transport PrenticeHi ll Inc. Englewood Cliffs, N.J 593. Ch en, L., Young, M., 2006. GreenAmpt infiltration model for sloping surfaces, American Geophysical Union, Washington, Water resources research, 42 (7), W07420, doi:10.1029/2005WR004468. Chirlin, G., 1989. A critique of the Hvorslev method for slug test ana lysis: the fully penetrating well, Ground Water Monitor ing and Remediation, 9, 57 65. Cooper, H., Jacob C., 1946. A generalized graphical method for evaluating formation constants and summarizing well field history, American Geophysics Union Transition, 2 7, 526534. Cooper, J., Bredehoeft, I., Papadopulos, S., 1967. Response of a finite diameter well to an instantaneous charge of water, Water Resources, 3 (1), 263 269. Dagan, D. 1978. A note on packer, slug and recovery tests in unconfined aquifers, Wat er Resources Research, 14 (5), 929934. Daniel, D., Trautwein, S., 1993. Hydraulic conductivity and waste contaminant transpo rt in soil, ASTM STP 1142, Philadelphia, 30 71. Darcy, H., 1856. The Public Fountains of the City of Dijon, Paris, France, Translat ed by Brown G and Cateni B. Groundwater, 43 (3), 457460. Domenico, P Schwartz F., 1990. Physical and Chemical Hydrogeology, John Wiley & Sons, Inc., New York NY, 824 Dwight, H. 1947. Tables of integrals and other mathematical data, MacMillan Company New York NY PAGE 137 137 Fetter, C., 2001. Applied Hydrogeology, Prentice Hall Inc., 4th ed., Upper Saddle River, New Jersey, 598. Fowler, J., Hertel, K., 1940. Flow of a gas through porous media, Journal Applied Physics 11, 496 502. Friefeld, B ., Oldenburg, C., 2000. Restricted interval Guelph permeameter: Theory and application, Water Resources Research, 36 (6), 1373 1380. Green, H., Ampt, A., 1911. The flow of air and water through soils, Studies on soil physics I, Journal of Agriculture, 4 1 24 Hazen, A., 1911. D iscussion of Dams on sand foundations American Society of Civil Engineers, 73, 199 203. Heath, R. 1983. Basic GroundWater Hydrology, U.S. Geological Survey Water Supply Paper 2220, 84. Henebry, B., Robbins, G., 2005. Reducing the influence of skin effects on hydraulic conductivity determinations in multilevel samplers installed with Direct Push methods, Department of Geology and Geophysics, University of Connecticut, Groundwater, 38 (6), 882 886. Hvorslev, M.1951. Time lag and soil permeability i n groundwater observations, U.S. Army Corps of Engineers, Waterway Experimentation Station, Vicksburg, Mississippi, Bulletin 36. Israelson, W., West, L., 1922. Water holding capacity of irrigated soils, Logan, Utah State, Agricultural Experiment Station, Bulletin No. 183, 1 24. Kabala, Z. 1993. The dipole flow test: A new single borehole test for aquifer characterization, Water Resources Research, 29 (1), 99 107. Kabala, Z., Xiang J., 1992. Skin effect and its elimination for single borehole aquifer tests, Computational Methods in Water Resources IX, Vol. 1, Elsevier, New York, NY, 467 474. Kirkham, D. 1955. Measurement of hydraulic conductivity of soil in place, Journal of Geophysical Research, 64 (9), 8097. Kirkham, D. 1959. Exact theory of flow into a partially penetrating well, Geophysical Research, 64 (9), 13171327. Klammler, H., 2007. Development of Field Permeability Apparatus, GRIP Conference Vienna, Austria PAGE 138 138 Kundu, P., Cohen, I., Hu, H., 2004. Fluid Mechanics, Elsevier Academic Press, New York, NY, 191. Lamb, H. 1932. Hydrodynamics, Cambridge Universtiy Press 6th edition, New York, NY, 134. Peursem, D., Zlotnik V., Ledder, G., 1999. Groundwater fl ow near vertical recirculatory wells: effect of skin on flow geometry and travel times with implications for aquifer remediation, Hydrology, 222, 109 122. Philip, J., 1992. What happens near a quasi linear point source? Water Resource Research 28(1), 475 2. Reynolds, W., Elrick, D., Clothier, B., 1985. The constant head well permeameter: effect of unsaturated flow, Soil Science, 139, 172180. Rice, P., Fontugne, D., Latini, R., Barduhn, A., 1970. Anisotropic permeability in porous media, Industrial Engineering Chemistry, 62 (6), 23 31. Sageev, A., 1986. Slug test analysis, Water Resources, 22 (8), 1323 1333. Scholes, O., Clayton, S., Hoadley, A., Tiu, C. 2007. Permeability anisotropy due to consolidation of compressible porous media, Transport Porous Media, 68 (3), 365387. Shan, C., Stephens, D., 1993. A borehole field method to determine unsaturated hydraulic conductivity, Water Resources Research, 29 (8), 27632769. Shani, U., Or, D., 1995. In situ method for estimating subsurface unsaturated hydr aulic conductivity, Water Resources Research, 31 (8), 18631870. Skopp, J., 1994. Class notes: Physical concepts of soils, University of Nebraska, Lincoln, Nebraska. Smith, R., 1950. Static and dynamic electricity, Cambridge University Press second editi on New York, NY, 169 Sneddon, I., 1966, Mixed boundary valu e problems in potential theory North Holland Publishing Company, Amsterdam, Holland Stephens, D., Neuman, S., 1982. Vadose zone permeability tests: steady state results, Journal of the Hydraul ics Division, Proceedings of the American Society of Civil Engineers, 108 (HY5), 640659. Taylor, K., Wheatcraft S., 1990. Evaluation of methods for determining the vertical distribution of hydraulic conductivity, Groundwater, 28 (1), 88 98. PAGE 139 139 Terzaghi K., Peck R., 1967. Soil mechanics in Engineering practice, 2nd edition, John Wiley and Sons Inc, New York, NY, 729. Thorton, D., Ita, S., and Larsen, K., 1997. Broader use of innovative gro und water access technologies, I n Proceedings Volume 2, Hazardous Waste World Superfund XVIII Conference Proceedings Washington, DC, 639646. Veihmeyer, J., Hendrickson, H., 1931. The moisture equivalent as a measure of the field capacity of soils, Soil Science 32, 181 193. Warrick, W., 1993, Comme nt on What happens near a quasi linear point source? by J.R. Philip, Water Resources Research, 29 (9), 32993300 Weight, W., Sonderegger, J., 2001. Manual of applied field hydrogeology, McGraw Hill New York, NY White, I., Perroux, K., 1987. Use of s orptivity to determine field soil hydraulic properties, Soil Science Society of America 51 (5), 1093 1101. Zaslavsky, D., Kirkham, D., 1964. The streamline function for axially symmetric groundwater movement, Soil Science Society of America Proceedings, 28, 156160 Zlotnik, V., Ledder G., 1994. Effect of boundary conditions on dipole flow, Computational Met hods in Water Resources X, 2, Kluwer Academic, Norwell, MA 907914. Zlotnik, V. Ledder, G., 1996. Theory of dipole flow in uniform anisotropic aq uifers, water resources research, 32 (4), 1119, 1128. Zlotnik, V., Zurbuchen B., 1998. Dipole probe: Design and field application of a single borehole device for measurements of small scale variations of hydraulic conductivity, Ground Water, 36 (6) 8848 92. Zlotnik, V., Zurbuchen, B., Butler, J., Healey, J., 1998. The Dipole Flow Test for site characterization: some practical considerations, Kansas Geological Survey open file report 9820, Lawrence, Kansas, 23. PAGE 140 140 BIOGRAPHICAL SKETCH Bassel Wahib Nemer was born in Selmieh, Kuwait in 1979. In 1987, he moved to Lebanon where he attended SaintCoeur BeitC habab College, a French accredited school. Directly afterwards, Bassel joined the Civil E ngineering Department at the Lebanese American University (LAU) in October 1997 and earned his Bachelor of Engineering (B.E.) in June 2002. After graduation, Bassel worked as a project/site engineer fo r two years in a construction company (Alfred and Jack Matta) responsible for the Notre Dame University project. In August 2004, Bassel was accepted into the Building Construction Department at the University of Florida, Gainesville, FL. However, he became in terested in environmental studies when he took some classes related to this field. Afterward, he quickly joined the M.E. program in the Environmental Engineering Sciences Department under the supervision of Professor JeanClaude Bonzongo. He graduated in 2005, and he published a paper with his advisor on Hydrologic controls on water chemistry and mercury biotrans formation in a closed river system: The Carson River, Nevada. As he was introduced to the subfields of environmen tal engineering, Bassel found special interest in the fiel d of water resources. In the la st stages of the M.E. program, Bassel was accepted into the Ph.D. program in th e Civil and Coastal Engineering Department at the University of Florida, under the tutelage of Professor Kirk Hatfield. Bassel completed his doctorate in three years; he defended his dissertation on November 26, 2008, and graduated officially with a Ph.D. in civil engineer ing, water resources an d hydrology, December 2008. Bassel is currently preparing to move to Qata r, where he will be working in a construction company with his family. 