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Thermal conductivity of soils from the analysis of boring logs

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Title:
Thermal conductivity of soils from the analysis of boring logs
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English
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Pauly, Nicole
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University of South Florida
Place of Publication:
Tampa, Fla
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Subjects

Subjects / Keywords:
Thermal Conductivity
Diffusivity
Integrity Testing
Drilled Shaft
Standard Penetration Test
Dissertations, Academic -- Civil & Environmental Eng -- Masters -- USF   ( lcsh )
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non-fiction   ( marcgt )

Notes

Abstract:
ABSTRACT: Recent interest in "greener" geothermal heating and cooling systems as well as developments in the quality assurance of cast-in-place concrete foundations has heightened the need for properly assessing thermal properties of soils. Therein, the ability of a soil to diffuse or absorb heat is dependent on the surrounding conditions (e.g. mineralogy, saturation, density, and insitu temperature). Prior to this work, the primary thermal properties (conductivity and heat capacity) had no correlation to commonly used soil exploration methods and therefore formed the focus of this thesis. Algorithms were developed in a spreadsheet platform that correlated input boring log information to thermal properties using known relationships between density, saturation, and thermal properties as well as more commonly used strength parameters from boring logs. Limited lab tests were conducted to become better acquainted with ASTM standards with the goal of proposing equipment for future development. Finally, sample thermal integrity profiles from cast-in-place foundations were used to demonstrate the usefulness of the developed algorithms. These examples highlighted both the strengths and weaknesses of present boring log data quality leaving room for and/or necessitating engineering judgment.
Thesis:
Thesis (MSCE)--University of South Florida, 2010.
Bibliography:
Includes bibliographical references.
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Statement of Responsibility:
by Nicole Pauly.
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Title from PDF of title page.
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Document formatted into pages; contains X pages.

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usfldc handle - e14.4809
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Thermal Conductivity of Soils from the Analysis of Boring Logs by Nicole M. Pauly A thesis submitted in partial fulfillment of the requirements for the degree of Master of Science in Civil Engineering Department of Civi l and Environmenta l Engineering College of Engineering University of South Florida Major Professor: A. Gray Mullins, Ph.D. Rajan Sen, Ph.D. Mike Stokes, Ph.D. Date of Approval: October 21 2010 Keywords: Thermal Conductivity, Diffusivity, Integrity Testing, Drilled Shaft Standard Penetration Test Copyright 2010, Nicole M. Pauly

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i Table of Contents List of Tables ................................ ................................ ................................ ................. iii List of Figures ................................ ................................ ................................ ............... iv List of Symbols and Abbreviations ................................ ................................ .............. viii A bstract ................................ ................................ ................................ ......................... ix Chapter 1 Introduction ................................ ................................ ................................ ... 1 1.1 Organization of Thesis ................................ ................................ ................... 4 Chapter 2 Literature Review ................................ ................................ .......................... 6 2.1 Overview ................................ ................................ ................................ ....... 6 2.2 Thermal Conductivity of Soils (Background) ................................ ................. 8 2.3 Properties and Measurement Correlations ................................ ..................... 19 2.3.1 Boring Log Measurements ................................ ............................. 19 2.3.2 Density ................................ ................................ .......................... 19 2.3.3 Moisture Content ................................ ................................ ........... 20 2.3.4 Temperature ................................ ................................ ................... 20 2.4 Standard Soil Testing Methods ................................ ................................ ..... 21 2.4.1 Standard Penetration Test ................................ .............................. 22 2.4.2 Thermal Conductivity Testing ................................ ........................ 23 2.4.3 Relative Density Test ................................ ................................ ..... 26 2.4.4 Soil Classi fication ................................ ................................ .......... 28

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ii 2.4.5 Thermal Integrity Profiling ................................ ............................ 29 Chapter 3 Algorithm Development ................................ ................................ .............. 31 3.1 Command Buttons ................................ ................................ ........................ 33 3.2 Soil Classification ................................ ................................ ........................ 33 3.3 Moisture Content ................................ ................................ .......................... 34 3.4 Density ................................ ................................ ................................ ......... 37 3.5 Thermal Conductivity ................................ ................................ ................... 38 3.6 Plotting ................................ ................................ ................................ ........ 46 Chapter 4 Testing and Evaluation ................................ ................................ ................ 48 4.1 Equipment ................................ ................................ ................................ .... 4 8 4.2 Laboratory Testing and Evaluation ................................ ............................... 50 4.2.1 Soil Classification ................................ ................................ .......... 50 4.2.2 Density Variation Testing ................................ .............................. 51 4.2.3 Results of Density Variation Tests ................................ ................. 57 4.2.4 Repeatability and Temperature Tests ................................ ............. 65 4.2.5 Repeatability and Temperature Test Results ................................ ... 66 4.3 Evaluation of Theoretical Algorithms ................................ ........................... 69 4.3.1 Heat Capacity ................................ ................................ ................ 74 Chapter 5 Conclusion ................................ ................................ ................................ .. 75 5.1 Thermal Integrity Profiling ................................ ................................ ........... 75 5.2 Future Studies ................................ ................................ .............................. 83 5.3 Summary ................................ ................................ ................................ ...... 83 List of References ................................ ................................ ................................ .......... 84

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iii List of Tables Table 2.1: Thermal Properties of Common Materials ................................ ....................... 6 Table 2.2: USCS Soil Classification Chart ................................ ................................ ..... 29 Table 4.1: Particle Size Distribution for Soil Sample ................................ ..................... 51 Table 4.2: Mold Dimensions ................................ ................................ .......................... 52 Table 4.3: Dry Soil Moisture Content ................................ ................................ ............ 57 Table 4.4 Wet Soil Moisture Content ................................ ................................ ............. 58 Table 4.5: Dry Soil Test Results ................................ ................................ .................... 58 Table 4.6: Wet Soil Test Results ................................ ................................ .................... 59 Table 4.7: Saturat ed Soil Test Results ................................ ................................ ............ 59 Table 4.8: Saturated Test Soil Mass ................................ ................................ ............ 59 Table 4.9: Dry Soil Test Calculations ................................ ................................ ............ 62 Table 4.10: Wet Soil Test Calculations ................................ ................................ .......... 62 Table 4.11: Saturated Soil Test Calculations ................................ ................................ .. 63 Table 4.12: Results for Repeatability Tests ................................ ................................ .... 66 Table 4.13: Results for Temperature Tests ................................ ................................ ..... 68

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iv List of Figures Figure 1.1: Drilled Shaft with Concrete Void ................................ ................................ .... 2 Figure 1.2: Geothermal Ground Loop ................................ ................................ .............. 3 Figure 2.1: Conductivity vs. Density at varied Saturation (Kersten) ................................ 11 Figure 2.2: Conductivity vs. Density at varied Saturation ( Mickley ) ............................... 1 2 2 Figure 2.4: Conductivity vs. Density at varied Saturation (De Vries) .............................. 13 Figure 2.5: Conductivity vs. Density at varied Saturation (VanRooyen) .......................... 13 Figure 2.6: Conductivity vs. Density at varied Saturation (McGaw) ................................ 14 Figure 2.7: Conductivity vs. Density at varied Saturation (Johansen) .............................. 14 Figure 2.8: Conductivity vs. Density at varied Moisture Contents (Kersten) ................... 15 Figure 2.9: Conductivity vs. Density at varied Moisture Contents (Mickley) ................... 15 Figure 2.10: Conductivity vs. Density at varied Moisture Contents (Gemant) ................. 16 Figure 2.11: Conductivity vs. Density at varied Moisture Co ntents (De Vries) ................ 16 Figure 2.12: Conductivity vs. Density at varied Moisture Content(VanRooyen) .............. 17 Figure 2.13: Conductivity vs. Dens ity at varied Moisture Contents (McGaw) ................. 17 Figure 2.14: Conductivity vs. Density at varied Moisture Contents (Johansen) ............... 18 Figure 2.15 : Thermal Conductivity vs. % Saturation (Duarte) ................................ ......... 18 Figure 2.16: Curves for Density vs. Blow Count Correlation ................................ .......... 19 Figure 2.17: Water T able Effects on Moisture Contents of Florida Soils ......................... 20 Figure 2.18: Mean Annual Ground Temperatures in the United States ............................ 21

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v Figure 2.19 : Split Barrel Sampler ................................ ................................ ................... 22 Figure 2.20: ASTM D5334 08 Typical Probe Components ................................ .......... 24 Figure 2.21: ASTM D5334 08 Temperature vs. Time C urve ................................ ........ 25 Figure 2.22: Steady State Portion of Temperature vs. Time Curve ................................ .. 25 Figure 2.23: Relative Density Test Mold Assembly ................................ ...................... 27 Figure 3.1: Spreadsheet Default Settings ................................ ................................ ......... 32 Figure 3.2: Spreadsheet Inputs ................................ ................................ ........................ 32 Figure 3.3: Moisture Content above Water Table for a Clayey Soil ................................ 35 Figure 3.4: Moisture Content above Water Table for a Silty Soil ................................ .... 36 Figure 3.5: Moisture Content above Water Table for a Sandy Soil ................................ .. 36 Figure 3.6: Blow Count vs. Unit Weight of Soil Graph Showing Slopes ......................... 38 Figure 3.7: Thermal Conductivity vs. Density for a Coarse Soil (Kersten) ...................... 39 Figure 3.8: Thermal Conductivity vs. Density for a Fine Soil (Kersten) .......................... 39 Figure 3.9: Thermal Conductivity vs. Density for a Coarse Soil (Mickley) ..................... 40 Figure 3.10: Thermal Conductivity vs. Density for a Fine Soil (Mickley) ....................... 40 Figure 3.11: Thermal Conductivity vs. Density for a Coarse Soil (Gemant) .................... 41 Figure 3.12: Thermal Conductivity vs. Density for a Fine Soil (Gemant) ........................ 41 Figure 3.13: Thermal Conductivity vs. Density for a Coarse Soil (De Vries) ................... 42 Figure 3.14: Thermal Conductivity vs. Density for a Fine Soil ( De Vries) ...................... 42 Figure 3.15: Thermal Conductivity vs. Density for Coarse Soil (Van Rooyen) ................ 43 Figure 3.16: Thermal Conductivity vs. Densi ty for a Fine Soil (Van Rooyen) ................. 43 Figure 3.17: Thermal Conductivity vs. Density for a Coarse Soil (McGaw) .................... 44 Figure 3.18: Thermal Con ductivity vs. Density for a Fine Soil (McGaw) ........................ 44

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vi Figure 3.19: Thermal Conductivity vs. Density for a Coarse Soil (Johansen) .................. 45 Figure 3.20: Thermal Conductivity vs. Density for a Fine Soil (Johansen) ...................... 45 Figure 3.21: Plotting Preferences ................................ ................................ .................... 46 Figure 3.22: Plotting Result s ................................ ................................ ........................... 47 Figure 4.1: Needle Probes: TR 1 (left), KS 1 (middle), SH 1 (right) ............................... 48 Figure 4.2: Placing Sand into Mold and Attaching it to the Vibrating Table .................... 53 Figure 4.3: Performing Thermal Conductivity Test on Non compacted Soil ................... 53 Figure 4.4: Baseplate Placed on Mold ................................ ................................ ............. 54 Figure 4.5: Placing Weight in Sleeve ................................ ................................ .............. 54 Figure 4.6: Apparatus Set Up ................................ ................................ .......................... 54 F igure 4.7: Measuring Depth ................................ ................................ .......................... 54 Figure 4.8: Saturated Test ................................ ................................ ............................... 56 Figure 4.9: Using a level and Water Bottle to Get Rid of Excess Soil .............................. 56 Figure 4.10: Compaction Curve for Dry Soil Test ................................ ........................... 60 Figure 4.11: Compaction Curve for Wet Soil Test ................................ .......................... 60 Figure 4.12: Compaction Curve for Saturated Soil Test ................................ .................. 60 Figure 4.13: Thermal Conductivity vs. Dry Density for Dry Coarse Soil ......................... 64 Figure 4.14: Thermal Conductivity vs. Density for a Wet Coarse Soil ............................. 64 Figure 4.15: Thermal Conductivity vs. Density for a Saturated Coarse Soil .................... 64 Figure 4.16: Change in Temperature over Time ................................ .............................. 67 Figure 4.17: Change in Thermal Conductivity over Time ................................ ................ 67 Figure 4.18: Change in Temperature over Time ................................ .............................. 68 Figure 4.19: Change in Thermal Conductivity over Time ................................ ................ 68

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vii Figure 4.20: Boring L og for Boring BA 36 ................................ ................................ ..... 69 Figure 4.21: Inputting Project Information ................................ ................................ ...... 70 Figure 4.22: Inputting Elevations ................................ ................................ .................... 70 Figure 4.23: Inputting Depth ................................ ................................ ........................... 71 Figure 4.24: Inputting Blow Count ................................ ................................ ................. 71 Figure 4.25: Inputting Soil Type ................................ ................................ ..................... 71 Figure 4.26 Inputted Boring Log ................................ ................................ .................. 72 Figure 4.27: Results from Clicking the Calculate Button ................................ ................. 73 Figure 4.28: Clicking Update after Selecting Desired Plotting Methods .......................... 73 Figure 4.29: Plot of Selected Methods and Plot of Boring Log ................................ ........ 73 Figure 5.1: TIP Analysis Shaft 14 1 ................................ ................................ ............. 76 Figure 5.2: TIP Analysis Shaft 14 2 ................................ ................................ ............. 77 Figure 5.3: TIP Analys is Shaft 14 3 ................................ ................................ ............. 78 Figure 5.4: Thermal Conductivity and Heat Capacity for Shaft 14 1 ............................... 79 Figure 5.5: Diffusivity and Temperature Profil e for Shaft 14 1 ................................ ....... 79 Figure 5.6: Thermal Conductivity and Heat Capacity for Shaft 14 2 ............................... 80 Figure 5.7: Diffusivity and Temperature for S haft 14 2 ................................ ................... 80 Figure 5.8: Thermal Conductivity and Heat Capacity for Shaft 14 3 ............................... 81 Figure 5.9: Diffusivity and Temperature Profile for Shaft 14 3 ................................ ....... 82 Figure 5.10: Modified Diffusivity and Temperature Profile for Shaft 14 3 ...................... 82

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viii List of Symbols and Abbreviations dry density (g/cm 3 ) unit weight (lb/ft 3 ) and (N/m 3 ) Q heat flow (W/m) thermal conductivity (W/m K) c specific heat (kJ/g K) C Heat Capacity (J/cm 3 K) k diffusivity (m 2 /s) T temperature (C) t time (s)

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ix A bstract Recent cooling systems as well as developments in the quality assurance of cast in place concrete foundations has heightened the need for properly assessing thermal properties of soils. Therein, t he ability of a soil to diffuse or absorb heat is dependent on the surrounding conditions (e.g. mineralogy, saturation, density, and insitu temperature). Prior to this work, the primary thermal properties (conductivity and heat capacity) had no correlation to commonly used soil exploration methods and therefore formed th e focus of this thesis. A lgorithms were developed in a spreadsheet platform that correlated input boring log information to thermal properties us ing know n relationships between density, saturation, and thermal properties as well as more commonly used stre ngth parameters from boring logs. Limited lab t ests were conducted to become better acquainted with ASTM standards with the goal of proposing equipment for future development. Finally, sample thermal integrity profiles from cast in place foundations were used to demonstrate the usefulness of the d eveloped algorithms. These examples highlighted both the strengths and weaknesses of present boring log data quality leaving room for and/or necessitating engineering judgment.

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1 Chapter 1 Introduction Muc h of civil engineering practice involves the use of empirical relationships that cross reference available physical measurements to design parameters that are often difficult to define This is particularly true i n the specialty of soil mechanics where li terally hundreds of correlations have been developed for the S tandard P enetration T est SPT (Kulhawy 19 90 ) Despite numerous advances in subsurface exploration (e.g. cone penetration test, seismic refraction, ground penetrating radar, etc), the SPT remain s the most commonly used and is the primary choice of most design engineers. With regards to bridge foundations, this simple test provides the necessary information to estimate end bearing, side shear, or lateral stiffness of supporting elements such as dr iven piles, drilled shafts, and auger cast in place piles (ACIP) The Standard Penetration Test as defined by ASTM D 1586 entails driving a standard sized split spoon sampler into the ground with a 140 lb hammer, dropped 30 inches. The recorded measurement s include the number of hammer blows to advance the sampler 1 ft into the soil and the characteristics of the physical sample s of the soil recovered from the split spoon. By augering or wash boring down to various depths of interest, SPT information can be obtained as a function of depth thereby providing both a strength and soil type profile. In recent years, the need has arisen to find additional soil information that cannot be commonly discerned from present SPT correlations. This need comes in the wak e of new developments in the quality assurance of cast in place foundation as well as trends

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2 heating/cooling systems. In these cases, the ability of the soil to diffuse or provide thermal energy can only be assessed by knowing t he thermal properties specifi c heat and thermal conductivity, as well as ambient temperature conditions. A new method of assessing the integrity of cast in place concrete measures the internal temperature of curing concrete that stems from the hydration reactions of the cementitious material (Mullins, 200 9 200 7 2005, 2004; Kranc, 2007) When intact concrete is present, a recognizable temperature signature / profile is present W hen part of the concrete cross section is missing the signature is interrup ted Figure 1.1 shows an example of a drilled shaft that exhibited dramatic loss of concrete cross section and emphasizes the severity of an anomaly formation. Accurate knowledge of how the surrounding soi l s dissipate the curing temperature of concrete is present ly difficult to define given the lack of rational correlations between commonly used soil exploration methods and the thermal properties. Figure 1.1: Drilled Shaft with Concrete Void

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3 The same disconnect exists in the emerging fields of geothermal heating and cooling systems. Many of these systems use shallow, buried heat exchange coils or extract and replace ground water from deep wells to dissipate the heat from condensing refrigerants. Well type, water exchange systems are less susce ptible to soil heat transfer, but systems using buried cooling loops, coils or similar rely on the surround ing soil type, ambient temperature, depth, and thermal properties of the soil to optimize such a s ystem design. Figure 1.2 shows a geothermal ground loop located in t he Tampa, Florida area that used cooling loops made of polyethylene tubing, buried in underground trenches as one method of increasing air conditioning efficiency ( Maynard 2010) Figure 1.2 : Geothermal Grou nd Loop

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4 Although the process used to install the polyethylene coils (as shown) disturbs the natur al state of the soil and the associated thermal properties ( increasing or decreasing density ) the use of standard soil exploration methods w ould provide th e system designer a rationale for specifying a finished state or at least provide boundaries for the possible range of thermal properties that are likely to result. The focus of this study was to provide correlations between the boring lo g data from the SP T test and thermal properties of the soils present in the boring log. To that end an Excel spreadsheet was created to take the blow count s and soil profile from the boring log and use them to calculate the thermal conductivity at any depth based on publis hed, predictive approaches This was supplemented with thermal conductivity testing in the lab oratory to validate the results of th e previously published relationships By calculating the thermal properties of soils a b etter understanding of how the surr ounding soils react through the ground when hot water or liquid concrete is pumped into it Th e thermal conductivity and specific heat values of the soil will show how the ground reacts to the heat that it is receiving, and how much of that heat can be sto red This is especially helpful to the futur e of geotechnical engineering when designing geothermal systems and analyzing the structural integrity of concrete drilled shafts 1. 1 Organization of Thesis This thesis is organized into four ensuing chapters describing the background, testing, results, and finally applications of the thesis findings with conclusions. Chapter 2 outlines the histor ical evolution of the modern day understanding of thermal properties of soil. This includes not only the testing a nd predictive efforts to

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5 define these properties, but also the applications that were instrumental in motivating research to that end. Chapter 3 provides the process for developing the algorithms used to design the spreadsheet. Each component of the spread sheet is broken down into a separate section with a thorough e xplanation included for each These provide the reader a step by step over v iew of the process. Chap ter 4 discusses the testing and evaluation of thermal properties. The testing section discusses the equipment used and procedures followed for the laboratory tests conducted along with the evaluation of these tests. This includes the recorded data, calculations and an analysis of the results showing how the experimental data correlates with publis hed thermal conductivity values Chapter 4 concludes with the evaluation of the theoretical algorithms where a simple boring log is presented to aid as example o f how the spreadsheet functions Chapter 5 concludes the report by summariz ing the results and solidifying the correlation between boring log data and thermal properties. This chapter also provides information on current applications and recommendations for future studies on this topic.

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6 Chapter 2 Literature Review A thorough literatur e review was conducted to initiate and focus the scope of this thesis. The topics of this literature review include an overview of thermal properties and usage, a history of thermal conductivity testing, standard soil testing methods, and existing correlat ions defining the thermal properties of soils 2.1 Overview Thermal conductivity and specific heat are the primary parameters affecting the transfer of heat energy through a given material. This transfer is commonly referred to as conductive heat flow w hen it uses these parameters, but often mechanisms including convection or radiation also contribute to the overall transfer particularly in fluids or gases. For solids or particulates, the conductive mechanism overwhelmingly controls. Thermal properties for common materials have been well documented and some examples are listed in Table 2.1. Table 2.1: Thermal Properties of Common Materials Material Name Thermal Conductivity (W/m K) Specific Heat (J/kg K) Dry Air 0.024 775 Saturated Air 0.1 940 Wood, P ine 0.147 240 Fresh Water 0.6 4184 Salt Water 0.8 3850 PCV Plastic Pipe 1.04 1340 Concrete (w=44%) 1.9 850 Concrete (w=40%) 2 900 Concrete (w=36%) 2.3 1100 Steel 14 470 Aluminum 250 900 Silver 429 233

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7 Some values for soils can be found, but they vary widely in value likely caused by being poorly defined V ariations in temperature, density, and moisture content directly affect thermal properties making it difficult to accurately assess them without this information The correlation s between therma l and mechanical properties of soil particles ha ve been cited as being affected by close contact and density whe reby thermo elastic waves transmit heat. Farouki (1966) translated this concept from Debye (1914) where heat flow through a crystalline material occurs as warm atoms vibrate more than cooler atoms causing waves to travel through the material proportional to bond strength between the atoms. From a computational standpoint, these concepts are applied using the general heat equation below which tak es into account the heat production from an added heat source, Q, and the heat dis sipation in the x, y, and z directions (second term) to calculate the change in temperature T, with respect to time, t. D iffusivity, k, is defined as the w here thermal conductivity is the heat flow passing through a unit area A, given a unit temperature gradient a nd

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8 In the application of geothermal heating/cooling systems the source of heat is the hot water or coolant from the H.V.A.C. heat exchanger and can be considered a relatively constant heat f low for a given season For shaft integrity applications, the heat source only exists during concrete curing, after which the second term of the general heat equati on dominates the resultant temperature of the concrete. 2. 2 Thermal Conductivity of Soils (Background) Thermal testing of standard construction materials such as wood, concrete, plaster, and insulations are relatively straight forward when compared to s oils. Until the late at time, Miles S. Kersten conducted a significant amount of research on this topic at the University of Minnesota Studies were performed on 19 diff erent soil types, consisting of a variety of sands, gravels, sandy loams, clays, minerals, crushed rocks, and organics. To quantify the thermal properties of these soils, numerous influential variables were identified including; mineralogy, density, moistu re content, and moisture state. The primary focus of this research was to study the e ffects of the thermal conductivity of soils in permafrost regions in order to address complications arising from construction in these regions. A strong knowledge base of thermal properties was thought to help correct this problem (Kersten 1949 ) From the extensive soil testing, Kersten developed a ratio between the thermal conductivity of the dry 0 and the saturated soil state 1 denoted as the Kersten n umber, K e

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9 Kersten then developed empirical correlations between this number and the degree of saturation S r For unfrozen soils, the Kersten n umbe r was defined as: For f rozen soils it is simply equal to the degree of saturation Acco rding to O istein Johansen t he previous methods for calculating thermal conductivity were based on empirical correlations that were simply approximate determinations with wide tolerance limits (Johansen 1977) Johansen developed and used empirical correlations to de velop theoretical equations to calculate thermal conductivity. The rein, the geometric mean of the thermal conductivity of air, water, and soil was given as the phase components: air, water, and solids For a saturated soil, the term for air can be ignored and this equation reduces to w here n is the volumetric fraction of water Johansen further develop ed a method for predicting thermal conductivity of soils by combining the conductivi ty at the two moisture extremes (dry and saturated) with the emp irical relationship between the Kersten number and the degree of saturation (Johansen 1975).

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10 Omar Farouki (1982) compiled thermal conductivity research from seven different sources among which were Kersten and Johansen. The remaining five researchers were Mickley, Gemant, De Vries, Van Rooyen, and McGaw. Each researcher had devised a method for calculating thermal conductivity for fine grained and coarse grained soils. The data was provided in the form of eith er constant moisture content curves or constant degree of saturation curves of thermal conductivity vs. dry density graphs. The data are plotted in Figures 2. 1 though 2.1 4 In practice, soil is rarely found in its dry state (degree of saturation = 0); howe ver, data from dry soils was provided from Mickley, De Vries, Van Rooyen, and Johansen. Much of the early research was performed on eith er frozen or freeze/thaw soils. Duarte (2006) published a study on unsaturated, tropical soils in Brazil. A sandy clay and a clayey sand were tested using a 1.5 mm diameter ALMEMO thermal probe which functions by heating up the soil sample until the thermal energy being passed into the soil and the thermal energy dissipated from the soil reach equilibrium. Duarte conclude d that much of the earlier work dealt with soils from frozen regions and was therefore no t applicable to tropical climates. This conclusion stemmed from the study findings which reported four fold lower thermal conductivity values for like soils. Amazingly the findings were never disputed even though the thermal conductivity probe used for the study was severely limited and cou ld not measure thermal conductivity values in excess of 0.420 W/m K. All other sources predicted thermal conductivity values as hig h as 2.0 W/m K. As would be expected, all soils tested reported values less than the equipment limit. Duarte presents the experimental data from the limited ALMEMO probe for the clayey sand (coarse grained) and the sandy clay (fine

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11 grained) in thermal cond uctivity vs. percent saturation curves. Duarte provides this data along with data from Johansen. This data is plotted in Figure 2.15. Although the data from this source cannot be considered reliable, the paper does provide an excellent theoretical thermal conductivity history, along with the current probe method for measuring thermal conductivity. The large apparatus Kersten constructed in 1949 has evolved over the years and has been simplified into a probe with dimensions in millimeters connected to a sma ll data logger instead of a device the size of a room Figure 2. 1 : Conductivity vs. Density at varied Saturation (Kersten)

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12 Figure 2.2: Conductivity vs. Density at varied Saturation (Mickley) Figure 2.3: Conductivity vs. Density at varied Saturation (Gemant)

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13 Figure 2.4: Conductivity vs. Density at varied Saturation (De Vries) Figure 2.5: Conductivity vs. Density at varied Saturation (VanRooyen)

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14 Figure 2.6: Conductivity vs. Density at varied Saturation (McGa w) Figure 2.7: Conductivity vs. Density at varied Saturation (Johansen)

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15 Figure 2. 8 : Conductivity vs. Density at varied Moisture Contents (Kersten) Figure 2. 9 : Conductivity vs. Density at varied Moisture Contents (Mickley)

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16 Figure 2. 10 : Conductivity vs. Density at varied Moisture Contents (Gemant) Figure 2. 11 : Conductivity vs. Density at varied Moisture Contents (De Vries)

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17 Figure 2.1 2 : Conductivity vs. Density at varied Moisture Content(VanRooyen) Figure 2.1 3 : Conductivity vs. Density at varied Moisture Contents (McGaw)

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18 Figure 2.1 4 : Conductivity vs. Density at varied Moisture Contents (Johansen) Figure 2.15: Thermal Conductivity vs. % Saturation (Duarte) 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 0 20 40 60 80 Thermal Conductivity (W/m K) Saturation (%) Coarse Soil Duarte Johansen Probe Limit 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 0 20 40 60 80 Thermal Conductivity (W/m K) Saturation (%) Fine Soil Duarte Johansen Probe Limit

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19 2.3 Properties a nd Measurement Correlations 2.3.1 Boring Log Measurements A boring log is a compilation of the data from a S tandard Penetration Test. Boring logs display blow count and soil type as a function of depth and often include moisture content information for f ine grain or clayey soils The soil extracted from the split spoon sampler at each depth is placed in jars and taken to a laboratory to be clas sified using the USCS stan dards to identify the soil type as well as moisture content. 2.3. 2 Density Density is typically referred to as the amount of mass present in a unit volume but often times in design applications, density is presented in the form of weight per unit volume, or unit weight. A correlation exists between unit weight and SPT blow counts for cl ays, silts, and sands. This correlation is depicted in Figure 2. 16 Figure 2. 16 : Curves for Density vs. Blow Count Correlation (Mullins 2004) Any correlations hereafter involving unit weight are converted to density and presented in units of g/cm 3

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20 2. 3. 3 Moisture Content Moisture content is the ratio of the weight of water to dry soil expressed as a percentage Moisture contents vary between different soil types and the location relative to the water table. Depending on the soil type, capillary actio n will pull moisture from the water table up into the soil above the phreatic surface. The data shown in Figure 2. 17 represents the result of capillary action at elevations above the water table for three common soil types. Figure 2. 17 : Water Table Effects on Moisture Contents of Florida Soils (Trout 2010) 2.3. 4 Temperature For all temperature dissipation scenarios involving soil, the temperature of the soil is an important parameter. Although the soil surface is subject ed to seasonal varia tion, at depths greater than 30 feet below the surface, the soil temperature remains relatively constant. This soil temperature is dictated by the mean annual ground temperature and is

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21 dependent on its geographic location. Figure 2. 18 shows the mean annual ground temperature s for the United States ( Virginia Tech 2010 ). Figure 2. 18 : Mean Annual Ground Temperatures in the United States 2.4 Standard Soil Test ing Methods Standardized methods for soil testing are published in section 4 of the Annual Book o f ASTM Standards by the American Society for Testing and Materials International. ASTM standards are technically competent standards that have been critically examined and used as the basis for commercial, legal or regulatory actions (ASTM 1996). In order for a test to conform to ASTM standards, it must meet all pertinent requirements prescribed for the method. The ASTM standards that are applicable to this thesis are the standards for standard penetration tests, thermal conductivity tests, relative density tests, and classification of soils. A brief overview of each is provided herein

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22 2.4.1 Standard Penetration Test The standard penetration test (briefly discussed in Chapter 1) consists of a split barrel sampler which is driven into the ground to obtain a soil sample. The resistance of the soil to the penetration of the sampler, referred to as a blow count or SPT N, represents the number of hammer blows necessary to advance the sampler 1 ft. The procedure for the SPT test is outlined in ASTM D1586, the Sta ndard Test Method for the Penetration Test and Split barrel Sampling of Soils. This test is conducted to provide a soil sample for laboratory soil classification tests. The SPT N value can be correlated to a variety of different applications (ASTM 1996). Sampling rods with an inside diameter of 1 1/8 inch are used to connect the split barrel sampler to the drive weight assembly, which consists of a hammer and anvil. The requirements for the hammer are that it should weigh 140 lbs, consist of a solid rigid metallic mass, and make steel on steel contact with the anvil when it is dropped. Figure 2. 19 provides the components and dimensions for the split barrel sampler. Figure 2.1 9 : Split Barrel Sampler A = 1.0 to 2.0 in B = 18.0 to 30.0 in C = 1.375 0.005 in D = 1.50 0.05 in E = 0.10 0.02 in F = 2.00 0.05 in G = 16.0 to 23 Open Shoe Tube Ball Head Rollpin Vent A F B C D E G

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23 Once a bor ing has been advanced to desired elevation, the split barrel sampler is attached to the sampling rods and lowered into the hole. The drive weight is then positioned above and the anvil is attached to the sampling rods. The dead weight of the sampler, rods, anvil and drive weight are rested on the bottom of the boring and a seating blow is applied. The hammer is continuously dropped and the blows are counted over three increments of 6 inches. The sampler is to be tested over the entire 18 inches unless the s oil is dense enough such that 50 blows have been applied over any 6 inch test, a total of 100 blows have been applied, or there is no noticeable advance during the application of 10 blows. When compiling the data into a boring log, the first 6 inches is re ferred to as the seating drive and those blows are omitted. The blow counts of the second and third 6 inch penetrations are summed to provide the number of blow counts from that test. If 6 inches has not been reached within 50 blows, the blows per number o f inches penetrated are recorded. 2.4.2 Thermal Conductivity Testing Methods for measuring thermal conductivity include the transient metho d and the steady state method, t he first of which is the most common. The Standard Test Method for Determination of Thermal Conductivity of Soil and Soft Rock by Thermal Needle Probe, ASTM D5334, is the approved transient heat method for thermal conductivity testing of soils. This method is approved for use in both wet and dry soils, but as moisture increases, percent error increases. Moisture can cause errors in the readings from the redistribution of water due to thermal gradients resulting from heating of the probe ( ASTM 2008 ). This

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24 error increases with greater heating times; therefore, either total heat added should be minimized or heating time should be reduced for soils with high moisture contents. The equipment required for the test is a thermal needle probe, a constant current source, a multimeter, and a data collection device that collects both temperature and time readings. A probe with a large length to diameter ratio is required to simulate an infinitely thin heating source. The typical probe design consists of a copper constantan thermocouple and either manganin or nichrome wire for the heating element enca sed in a stainless steel or similar thin walled, closed end tube The heating element connects to a circuit with a constant current source which generates heat in the probe from the wire resistance when energized. The thermocouple wires are connected to th e data collection device which monitors the temperature changes over time. The typical probe design according to ASTM 5334 08 is depicted in Figure 2. 20 Figure 2. 20 : ASTM D5334 08 Typical Probe Components Thermocouple Jack CU CN DC Heat Source Heating Element N ichrome or Manganin Heating Wire Copper Constantan Epoxy Tip Epoxy Filled Thermocouple Junction

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25 When conducting tests, known amounts of current and voltage are applied to the probe and temperature rises are recorded over a period of time. A minimum of 20 to 30 readings should be recorded for each test. O nce the data is collected, temperature is plotted versus time on a semi log time scale and the linear, steady state portion of the curve is selected. The slope of this portion of the temperature vs. time curve is used to calculate the thermal conductivity. Figure 2. 21 shows the temperature vs. time plot, delineating the non steady state regions to exclude. The transient portion and the portion dominated by edge and end effects should not be used when fitting the curve to determine the slope. Figure 2. 22 sho ws the linear portion of the curve from which the slope is determined and used in the thermal conductivity calculation. Figure 2. 21 : ASTM D5334 08 Temperature vs. Time Curve Figure 2. 22 : Steady State Portion of T emperature vs. Time Curve Time (s econds ) 10 1 10 2 10 4 10 3 Temperature (C) Steady State Portion Transient Portion Portion of data dominated by edge and end effects

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26 Thermal conductivity is determined from the slope of the temperature vs. time graph, S, the heat input, Q, and the calibration factor of the probe, C where the heat input is the product of the current, I, and the voltage, V, divided by the length of the probe, L. 2. 4 .3 Relative Density Test The Standard Test Method for Maximum Index density and Unit Weight of Soils Using a Vibratory Table, ASTM D4253, is used to determine the density index for cohesionless, free draining soils. This test is typically done to evaluate the state of compactness of a soil sample. Two procedures, one for dry soils and one for wet soils, are outl ined in this standard. For this test to be applicable, 100 percent of the soil sample must pass a 3 in sieve and at most, 15 percent of it can pass the No. 200 sieve. Regardless of the percent fines, if the soil does not have the characteristics of a cohes ionless, free draining soil, it does not meet ASTM standards for this test. The testing apparatus comprises a vibrating table and mold assembly. The mold assembly consists of the mold, the guide sleeve, the surcharge weight, the surcharge base plate, and the dial gage holder and indicator. Two standard mold options are available; the 0.1 ft 3 and the 0.5 ft 3 mold. Each mold has a specifically sized guide sleeve, weight, and base plate. To assemble the components, the mold is first attached to the table and the surcharge base plate is place on top. The guide sleeve is then attached to mold, and the

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27 surcharge weight is lowered through the guide sleeve onto the base plate. The assembly described in ASTM D4253 is shown in Figure 2. 23 Figure 2. 23 : Relative Density Test Mold Assembly For the dry method, the mold is filled with ove n dried soil and vibrated for 8 to 12 minutes, depending on if a frequency of 50 or 60 Hertz is chosen. Initial measurements include the mass of the empty mold, the mass of the mold with soil filled in the loosest possible state, and the initial dial gage reading. Final measurements included the total elapsed time and the final dial gage reading. From the dial gage readings, the initial and final volumes ca n be calculated. dmin is the mass of the soil dmax is the mass of the soil divided by the final sample volume. The relative density can be calculated at any point b etween these two values using the following equation: Hoisting Handle 0.10 ft 3 Mold Guide Brackets Soil Specimen Surcharge Base plate Lead Filled Surcharge Weight Clamp Assembly

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28 The only variation between the dry and wet methods is that for the wet method, the mold is initially attached to the table and wet soil is gently placed in it over a period of 5 to 6 minutes while the table is vibrating. This is done prior to attaching the guide sleeve, base plate, and weight to the mold. Because the mold is already bolted to the table when the soil is placed in it, the mold and soil must be dried and weighed at the end of test. 2. 4 .4 Soil Classification The Unified Soil Classification System (USCS) is presented in ASTM D248 7, the Standard for the Classification of Soils for Engineering Purposes. This standard classifies soils into groups based on their particle size characteristics, liquid limit, and plasticity index. Soils are classified into four main groups: gravel (G), sand (S), silt (M), and clay (C). Gravel and sand are classified as coarse grained soils, while silt and clay are classified as fine grained. To be considered coarse grained, at least 50 percent of the soil mass must be retained on the No. 200 sieve, whil e 50 percent has to pass the No. 200 sieve to be considered fine grained. Gravels and sands are separated by the No. 4 sieve. If the soil is retained on the No. 4 sieve, it is classified as a gravel whereas if it passes the No. 4 sieve and is retained on the No. 200, it is classified as a sand. Silts and clays require additional tests before they can be classified. These tests are provided in ASTM D4318. To classify a soil sample, a particle size distribution must be obtained. This entails performing a si eve analysis for the entire soil sample using a series of sieves which should include the 3 in, No. 4, and No. 200 sieves, along with several others. The soil sample is weighed and sieved. Each sieve is weighed and the weight retained is recorded. Using th e

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29 weight retained, the weight passin g and the percent passing each sieve is calculated. For fine grained soils, the liquid limit and plastic limit must be determined. Once this information is know, the USCS classification chart can be followed to classify the soil. The USCS classification chart is provided in Table 2.2. Tabl e 2.2: USCS Soil Classification Chart 2.4.5 Thermal Integrity Profiling The Thermal Integrity Profiler uses the temperature generated by curing cement (hydration energy) to assess the quality of cast in place concrete foundations (i.e. drilled shafts or ACIP piles). Whereas other methods of integrity testing are limited to specific regions of the foundation cross section (e.g. inside the reinforcing cage, between tubes, or within a few inches of an access tube), TIP measurements are sensitive to the concrete quality from all portions of the cross section.

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30 In general, the absence of intact / competent concrete is registered by relative cool regions (necks or inclusions); the presence of additional / extra concrete is registered by relative warm regions (over pour bulging into soft soil s trata). Anomalies both inside and outside the reinforcing cage not only disrupt the normal temperature signature for t he nearest access tube, but the e ntire shaft; anomalies (inclusions, necks, bulges, etc.) are also detected by more distal tubes (but with progressively less effect). Analysis of the data ha s multiple levels of intricacy, but in general it depends on the concrete mix design, shape, and g eometry of the concrete tested as well as the diffusion field (e.g. air, soil, water). As a result, the thermal properties of the soil surrounding the concrete structure are important and form one focus of this thesis.

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31 Chapter 3 Algorithm Dev elopment The primary focus of this thesis was to provide design parameters for engineering problems requiring thermal properties of soils. As the most common soil exploration metho do logy involves SPT borings, a concentrated effort was put forth to relate both thermal conductivity and specific heat to this form of soil data. To that end, presently available correlations between SPT (N) and density were employed along with correlations from density to thermal conductivity This chapter provides detailed deve lopment of such algorithms to correlate the link between SPT (N) to thermal properties. An Excel spre adsheet was created using correlations where the data from a SPT boring log could be inputted and these thermal properties could be c alculated The necessa ry input data for the spreadsheet consists of depth, soil type, blow count, ground surface elevation and the elevation of the water table. Ground surface elevation and water table elevation are both single entry inputs, whereas depth, blow count, and soil type are arrays requiring multiple entries for each field. Using these inputs, the soil structure, moisture content, and density can be properly assigned Once these values are known, the thermal conductivity calculations are simply determined from a serie s of polynomial equations. The parameters listed above are the deciding factors on which one of these equations should be used for each entry. Boring logs are provided in terms of either depth or elevation. Both are acceptable, but depth was chosen as the input parameter for this spreadsheet. To provide the elevation

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32 corresponding to each depth, the input depth is subtracted from the ground surface elevation. Figure 3.1 shows a screen shot of the spreadsheet main page. The spaces for the inputs are shaded to distinguish between the outputs. Numbers must be typed into these boxes for ground surface elevation, water table elevation, depth, and blow count, whereas drop down menus are provided for soil type. Figure 3.2 shows a close up of the required spreadshe et inputs. Figure 3.1: Spreadsheet Default Settings Figure 3.2: Spreadsheet Inputs

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33 3.1 Command Buttons Six command buttons control the spreadsheet. The first command button changes the input units back and forth between Engl ish (feet) and Metric (meters). Thermal Conductivity and Density outputs remain in Metric units to be consistent with historical data but elevations and depths can be inputted in either system of measurement. The second command button clears the calculate d data, but all inputs remain. The third command button, Clear All clears all inputted and calculated data, leaving the spreadsheet ready for new data. The fourth command button is the C alculate button. This calculates density and thermal conductivity, an d plots the selected methods. Below this button is the Update button. If methods are selected or deselected, clicking the update button will update the graph. Command button 6 is the Help button which, when clicked, brings up a detailed list of each object and its function. 3. 2 Soil Classification There are multiple ways to classify soils (e.g. USCS, AASHTO) ; t he refore, a drop down menu (Figure 3.2) was created to avoid typographical errors The soil choices provided are clay, silt, sand, limestone silty sand, clayey sand, silty limestone, clayey limestone, sandy silt, sandy clay, and organics From the soil type a soil structure can be determined. If the soil passes the #200 sieve, it is consi dered a fine grained soil. Clay, s ilt and organic soils fall under this category. If any of these s oil t ypes are chosen, computations for fine grained soils are performed S and and limestone are retained on or above the #200 sieve, so they are categorized as coarse grained. If s and or l imestone are selected, the so il will be identified as coarse grained for that entry and processed

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34 accordingly For the soil types consisting of a mix of coarse and fine grained soils, the soil of both fine and coarse grained soils to their respective volumetric fractions. 3. 3 Moisture Content The moisture content of a soil changes with its position relative to the water table. At the water table and below, it can be assumed that the soil is satu rated for most cases Above the water table, soil type and distance above the water table must be taken into account. The University of South Florida performed studies on the changes in moisture content with relation to the water table for many soil Three common Florida soils were chosen from this analysis: one with a high clay content, one with a high silt content, and one with a high sand content. Limestone was not present in this study but because it is typically found below the water table it can be considered saturated for this application. Because sand and limestone a re coarse grained soils, limestone above the water table is assumed to have the wicking characterist ic s of sand Figures 3. 3 through 3. 5 show the changes in moisture content with respec t to elevation above the water table for the chosen clay, silt, and sand. The equations used to calculate thermal conductivity require moisture contents to be separated into 5%, 10%, 20% and saturated to match available thermal conductivity correlations T o do this, the graphs were sectioned off and labeled accordingly. Figure 3. 3 shows the effect that the water table has on the moisture content of a clayey soil. From the water table to approximately 80 cm above it, the so il has over 20% moisture and is id entified as saturated. Clay typically retains at least 12 % moisture, but th e data from the study was only collected to 200 cm above the water table, so a line was

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35 extrapolated following the same slope, to extend up to a moisture content of 1 2 %. This poin t was 78 0 cm above the water table. Between 80cm and 78 0 cm, the soil is labeled as ha ving a moisture content of 20%. Data for 12% moisture is not available; therefore, the 10% moisture content curves are used for clayey soils greater than 780 cm above the water table. Figure 3. 3 : Moisture Content above Water Table for a Clayey Soil Since clay is a very fine soil that can absorb large currents of water there is no surprise that it retains a higher mo isture content than the other soils. Eve n though silt is a fine grained soil, the properties are often similar to sand. The moisture content of silt at each elevation above the water table should fall in between a typical sand and clay. Figure 3. 4 shows the effect that the water table has on the moisture content of a silty soil. At 200 cm, this silty soil has already reached 10% moisture. Because the graph data cuts off at 200 cm like th at of clay the relationship was extrapolated to where it would provide information for 5% moisture. From the w ater table to approximately 50 cm above it, the soil can be considered saturated. Above that point but below 150 cm, the moisture content is classified as 20% moisture. Between 150 cm and 430 cm, the moisture content is 10%, and above that it is considered to be 5%.

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36 Figure 3. 4 : Moisture Content above Water Table for a Silty Soil Figure 3. 5 shows the effect that the water table has on the moisture content of a common sand in Florida, Myakka Fine Sand. Up to 40 cm above the water table, the m oisture content is already reduced to 20%; therefore, anything between this height and the water table is considered saturated. Only 20 cm above that, at 60 cm above the water table, the soil is at 10% moisture. When the elevation reaches 150 cm, an almost vertical slope shows that it has leveled off at a moisture content of 5%. This is a typical moisture content value near the ground surface for Florida soils. Figure 3. 5 : Moisture Content above Water Table for a Sandy Soil

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37 3. 4 Density The re lationships cited in Chapter 2 for thermal conductivity all relate to the density of the soil as well as the saturation and structure. As a result, making use of correlations from SPT data to density w as a necessary first step. This could also be used to e stablish the void ratio and saturation when the soil is not submerged. See Figure 2.16 in Chapter 2 for the linear correlation between number of blows and the unit weight of clay, silt, and sand. A correlation for limestone was detained from a study on c ohesionless soil performed by the University of Florida (University of Florida 2009) Therein the unit weight varie d from 90lb/ft 3 to 130lb/ft 3 for soft to medium/hard limestone. A linear relationship was assumed where 90 lb/ft 3 represents the density at zero blow counts and 130 lb/ft 3 as the density at 60 blow counts Th e line has a slope of 0.667 and a y intercept of 90. The data from Figure 2. 16 was reproduced and plotted in Figure 3. 6 along with the values produced for limestone. Trendlines were fitte d to the data of each soil type in order to obtain the equation of each line. The spreadsheet uses the inputted soil type to select the appropriate equation. It t hen uses that equation to calculate density, where blow count is the independent variable (x v alue) and density is the dependent value ( y value). The densities that result from using the equations in Figure 3.6 are in terms of lb/ft 3 The thermal conductivity calculations require density to be converted to the metric units of g/cm 3 A conversion fa ctor of 0.016g/cm 3 per 1 lb/ft 3 is automatically applied to each resulting density in the spreadsheet.

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38 Figure 3. 6 : Blow Count vs. Unit Weight of Soil Graph S howing S lopes 3 5 Thermal Conductivity The equations for thermal conductivity were fitte d from a series of cu rves developed from the seven methods cited in Chapter 2. These curves present data for thermal conductivity as a function of dry density with varying degrees of saturation or moisture contents for both coarse and fine grained soils. A ccording to the data presented in Section 3.3 the required curves needed to cons truct this spreadsheet were based on 5% moisture, 10% moisture, 20% moisture, and fully saturated. These four curves are provided for both coarse a nd fine grained soils for ea ch method in Figures 3.7 through 3.13. A trendline was fitted to each curve to obtain the equation of the function. All of the trendlines were a perfect fit out to three decimal places (i.e. R 2 =1). For each equation, the x value represents density and t he y value represents thermal conductivity. Knowing these equations and the algorithms that lead to calculating density, thermal conductivity can be calculated at any depth given th e specified blow count and soil type at that depth.

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39 Figure 3. 7 : Thermal Conductivity vs. Density for a Coarse Soil (Kersten) Figure 3. 8 : Thermal Conductivity vs. Density for a Fine Soil (Kersten)

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40 Figure 3. 9 : Thermal Conductivity vs. Density for a Coarse Soil (Mickley) Figure 3. 10 : Thermal Conductivity vs. Density for a Fine Soil (Mickley)

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41 Figure 3. 11 : Thermal Conductivity vs. Density for a Coarse Soil (Gemant) Figure 3. 1 2 : Thermal Conductivity vs. Density for a Fine Soil (Gemant)

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42 Figure 3.1 3 : Thermal Conductivity vs. Density for a Coarse Soil (De Vries) Figure 3.1 4 : Thermal Conductivity vs. Density for a Fine Soil (De Vries)

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43 Figure 3.1 5 : Thermal Conductivity vs. Density for Coarse Soil (Van Rooyen) Figure 3.1 6 : Thermal Conductivity vs. Density for a Fine Soil (Van Rooyen)

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44 Figure 3.1 7 : Thermal Conductivity vs. Density for a Coarse Soil (McGaw) Figure 3.1 8 : Thermal Conductivity vs. Density for a Fine Soil (McGaw)

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45 Figure 3.1 9 : Thermal Conductivity vs. Density for a Coarse Soil (Johansen) Figure 3. 20 : Thermal Conductivity vs. Density for a Fine Soil (Johansen)

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46 3. 6 Plotting Plotting routines were developed to produce two graphs of the interpreted boring log data The first and foremost is the thermal conductivity vs. depth graph. This graph show s the therm al conductivity changes with variations in depth and soil type. The second graph plots blow count vs. depth. This graph is plotted to allow the user to make comparisons between the thermal conductivity changes and the density changes throughout the boring log while also providing a visual confirmation of proper input All seven thermal conductivity methods are set to calculate each time the spreadsheet is run, but only to plot if they are selected. Check boxes were added and programmed so that if the check box is clicked when the graph is updated the data for that method is plotted An additional check box was added to plot the average of the selected methods. This was designated as a thicker black line on the graph to distinguish it from the rest. A scree n shot of the check boxes is provided in Figure 3.21. Figure 3.2 1 : Plotting Preferences Upon clicking the C alculate button, the graph will plot the selected methods. The default setting selects all the methods and the average, but any method can be selected or unselected simply by clicking on the name. The average of the selected methods will

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47 automatically re calculate, but the Update button must be clicked for the graph to update. Figure 3.22 is a screen shot of the graphs resulting from the selection. Figure 3.2 2 : Plotting Results

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48 Chapter 4 Testing and Evaluation For the lab oratory testing portion of this thesis a thermal probe was rented to perform thermal conductivity testing on selected soils. This was primarily t o validate or dispel the previously published data being used to calculate thermal conductivity in the spreadsheet The probe used for testing is described in the Section 4.1 Equipment t he info rmation pertaining to the test procedures results and evalu ation can be located in Sections 4.2 Laboratory Testing and Evaluation and i mplementation of the spreadsheet, including a boring log example is provided in Section 4. 3 Evaluation of Theoretical Algorithms 4.1 Equipment Inc. The system comes with a handheld controller that records the data from one of three probes. Two of the probes (the KS 1 and the TR 1) are single needle sensors used to measure thermal conductivity and resi stivity for different mediums. The third probe, the SH 1, is a dual needle sensor used to measure specific heat and diffusivity. Figure 4.1 shows the three needle probes. Figure 4 .1 : Needle Probes : TR 1 (left), KS 1 (middle), SH 1 (right)

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49 The K S 1 is a 60 mm long needle with a 1.3 mm diameter and its thermal conductivity range is from 0.02 W/m K to 2.0 W/m K with 5% accuracy. The TR 1 is the larger of the two single needle probes. It is a 100 mm long needle with a 2.4 mm diameter. For thermal conductivity, its range is from 0.10 W/m K to 4.00 W/m K with an accuracy of 10%. The SH 1 is the dual needle probe that consists of two 30 mm long needles with 1.3 mm diameters, spaced 6 mm apart. The KS 1 probe applies a smaller amount of heat for a sh orter period of time than the TR 1 probe, making it more suitable for liquids and insulating materials. T he dual needle probe SH 1, is primarily designed to read specific heat and diffusivity so this probe was not used for thermal conductivity testing. Th e TR 1 probe is designed for use in soil, concrete, rock, and other granular materials. Because of this, the TR 1 probe was chosen for all thermal conductivity testing. Testing times for the TR 1 vary between 5 and 10 minutes. Heat is applied for the firs t half of the test and readings are taken every 5 or 10 seconds, depending on the chosen read time. A total of 60 measurements are taken during each test. The longer read time is suggested for dry granular materials, large grains, or solid samples. A minim um of 2.7 mm of the tested material must surround the probe in all directions to avoid errors while testing. The KD 2 system follows the specifications outlined in ASTM D5334 08.

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50 4.2 Laboratory Testing and Evaluation Three sets of tests were perfor med using the KD2 Pro device. The first were density variation tests which were done to determine the changes in the thermal conductivity of soils with incre asing densities. The second were repeatability tests to check the accuracy of the probe when tests are consecutively conducted versus when tests are conducted with a fifteen minute break between each test Third, tests were conducted to determine the change in thermal conductivity as the temperature of the soil change s. All three test series utilize d th e same soil; therefore, one sieve analysis was performed and can be located in Section 4.2.1. The density variation tests are discussed in Section 4.2.2 and analyzed in Section 4.2.3. The repeatability and temperature tests are presented in Section 4.2.4 a nd the results in Section 4.2.5 4.2.1 Soil Classification A soil sample was chosen for experimentation. The soil from the sample was dry to the touch but it was still placed in an oven at 105C for 24 hours to assure that all the moistur e had been remove d. The sample was then cooled and weighed. The mass of the sample was 1750.10 grams. In order to classify the soil using the USCS specifications, the percentage of particles passing each sieve needed to be calculated. Table 4.1 provides the results of the sieve analysis. The equations used to calculate the values in the table for the mass retained, mass passing, and percent of particles passing each sieve are:

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51 Table 4.1: Particle Size Distribution for Soil Sample Sieve # Sieve size (mm) Mass of Sieve (g) Mass of Sieve + Soil (g) Mass Retained (g) Mass Passing (g) % passing #4 4.76 669.25 669.25 0.00 1750.10 100.00 #10 2.00 487.63 495.90 8.27 1741.83 99.53 #40 0.42 338.10 1348.15 1010.05 731.78 41.81 #6 0 0.25 358.56 743.60 385.04 346.74 19.81 #100 0.15 347.30 643.10 295.80 50.94 2.91 #200 0.07 329.28 380.22 50.94 0.00 0.00 The entire sample passe d the #4 sieve and was retained on the #200 sieve. According to the USCS classification chart (Table 2.2), this soil was classified as a sand. 4. 2. 2 Density Variation Testing Density tests were performed using the KD2 Pro device and a vertically vibrating table in order to obtain thermal conductivity values that correspond to different densities. The proced ure followed the Standard Test Method for Maximum Index Density and Unit Weight of Soils Using a Vibratory Table (ASTM D4253 ). The test set up conformed to the ASTM specifications, but modifications were made to the procedure to include incremental testing that would create a density vs. time curve instead of a linear trend between the minimum and maximum densities. There was an option to use two different size molds, a 0.1 ft 3 or a 0.5 ft 3 mold. As the 0.1 f t 3 (172 in 3 ) mold is sufficient for all sands, cl ays, silts, and small rocks, it was chosen for this experiment. The height and diameter of the mold were measured using a caliper, and the empty mold was weighed. T he cross sectional area and volume were then calculated The dimensions and mass of the mold are provided in Table 4.2, where

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52 and, Table 4.2: Mold Dimensions Mold Dimensions Height of Mold 6.12 I n Diameter of Mold 6.00 I n X sectional Area of Mold 28.27 in 2 Volume of Mold (in3) 172.93 in 3 Volume of Mold (cm3) 2833.75 cm 3 Mass of Mold 3742.80 kg For the dry tests, a scoop was used to gently place soil in the mold while keeping the soil as loosely packed as possible. Once the mold was filled, a leveling tool was used to create an even surface across the top of the mold. The mold with the soil was weighed, and the weight of the mold was subtracted in order to calculate the mass of dry soil. The mold was then attached to the vibrating table (Figure 4.2) A minor amount of settling occurred while in transit, but the change in volume was negligible. To determine the thermal conductivity for the soil at its loosest state in the mold, the probe was inserted near the center of the soil sample and a 10 minute test was performed (Figure 4.3) Upon finishing the test, the probe was removed and the mold was tapped along the sides several times to allow the soil to settle enough to place the surcharge base plate uniformly on top of it ( Figure 4.4) Once the base plate was applied, the guide sleeve was attached to the top of the mold. The surcharge weight was lowered through the sleeve and placed on top of the base plate (Figure 4.5) The complete assembled apparatus is displayed in Figur e 4.6. Using a caliper, the distance from the top of the weight to the top of the sleeve was measured in two places 180 across from each other (Figure 4.7).

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53 Figure 4.2: Placing Sand into Mold and Attaching it to the Vibrating Table Figure 4.3: Performing Thermal Conductivity Test on Non compacted Soil

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54 Figure 4.4: Baseplate Placed on Mold Figure 4.5: Placing Weight in Sleeve Figure 4.6: Apparatus Set Up Figure 4.7: Measuring Depth

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55 The frequency of the vibrating table was set t o 50 hertz and the table was turned on for one secon d Before removing the surcharge weight, two more measurements between the top of the weight and top of the sleeve were taken with the caliper and averaged to provide a second depth measurement. This valu e, subtracted by the initial measurement, gives the displacement of the soil after one second of vibration. After the measurements were taken, the weight and base plate were removed to expose the soil. A 10 minute test was done with the probe to determine the thermal conductivity corresponding to the calculated density. The base plate and weight were placed back on the mold and secured for the next test. Initially, the soil was placed loosely into the mold so it was expected that large changes in density w ould occur during the first few seconds. A total of 12 tests were conducted. To create an accurate density curve, the first four tests were done at one second intervals and the subsequent tests increased up to a test that compacted for four minutes Each time the test was repeated, the vibrating table was turned on and run for the amount of time stated at that point in the testing matrix. Once the table was turned off, depth measurements were taken, and the weight and base plate were removed from the sleev e. At this point, a 10 minute thermal conductivity test was done. Finally, the base plate and weight were carefully placed back into the guide sleeve so that the next test was ready to begin. Tests for wet and saturated soils were conducted as well. A spec ific moisture content was not needed for the wet soil test ; therefore, small amounts of water were simply added to a portion of the soil sample until the soil had a heavily damp feel to it. A small sample was weighed and placed into the oven so that a moi sture content test could

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56 be done. The damp soil was loos ely placed in the mold similar to the procedure for the dry soil The procedure for the saturated tests differs slightly from the previous two in its initial steps. The mold was filled with water prio r to the sand being placed into it The soil was then added slowly, causing the excess water to be displ aced over the sides of the mold (Figure 4.8). This allowed the water to saturate the soil as it settled to the bottom. When the mold was full, the exces s soil was leveled off the top, and a water bottle was used to rinse off any excess t hat had spilled over the sides (Figure 4.9). The mold w as then toweled dry and weighed. From this point on, the same procedure for the dry test was followed. Figure 4.8: Saturated Test Figure 4 .9 : Using a level and Water Bottle to Get Rid of Excess Soil

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57 4.2. 3 Results of Density Variation Tests Moisture content tests were done for the dry and wet soil. For each test, an empty tare was weighed, filled with a sample of the soil, and weighed again. The difference of these two measurements provides the mass of the wet soil. The tare was then placed in an oven at 105C for 24 hours. After this period of time it was removed and weighed. The mass of dry soil in the tare is simply the difference of this measurement and mass of the empty tare To calculate the percentage of moisture for the sample, the difference between the mass of wet soil and the mass of dry soil is divided by the mass of the wet soil The paramete rs and equation for moisture content (% Moisture) are: Calculating dry density of the soil is required to calculate thermal conductivity using the developed algorithms The mass of dry soil in the mold is needed for this density calculation. Knowing both the weight of the wet so il in the mold and the moisture content of that soil, the mass of dry soil in the mold can be calculated. The moisture content results for the dry sand and the wet sand are provided in Table 4.3 and 4.4. Table 4. 3 : Dry Soil Moisture Content Dry Soil Test Moisture Content Results Mass Tare 31.20 kg Mass Tare + Wet Soil 254.90 kg Mass Tare + Dry Soil 254.60 kg Moisture Content (%) 0.12 % Mass of Dry Soil 4459.2 kg

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58 Table 4. 4 Wet Soil Moisture Content Wet Soil Test Moisture Content Results Mass Tare 31.50 kg Mass Tare + Wet Soil 203.60 kg Mass Tare + Dry Soil 183.00 kg Moisture Content (%) 10.12 % Mass of Dry Soil 3907.45 kg Tables were set up prior to testing with predetermined vibration lengths. Loose, dry soil compacts quicker than the wet soil, causing a steeper compaction curve. To account for this, a greater number of one second tests were performed for the dry soil than for the wet and saturated. Each time a test was executed and the soil was compacted, depth measurements were taken and a thermal conductivity test was performed. The data recorded during the dry, wet, and saturated tests is provided in Tables 4. 5 through 4. 7 A moisture content test was not con ducted on the saturated soil; therefore, the soil was oven dried and the mass was determined after the test concluded The results of the dried soil mass calculation are provided in Table 4. 8 Table 4. 5 : Dry Soil Test Results Test Name Time (s) Total Time (s) Depth 1 (in) Depth 2 (in) Thermal Conductivity (W/m K) D1 0 0 2.229 2.237 0.356 D2 1 1 2.543 2.54 0.406 D3 1 2 2.617 2.627 0.424 D4 1 3 2.642 2.665 0.43 D5 1 4 2.665 2.669 0.467 D6 4 8 2.701 2.713 0.458 D7 7 15 2.728 2.746 0.456 D8 15 30 2. 777 2.759 0.456 D9 30 60 2.832 2.814 0.465 D10 60 120 2.868 2.818 0.485 D11 120 240 2.863 2.868 0.507 D12 240 480 2.885 2.963 0.497

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59 Table 4. 6 : Wet Soil Test Results Test Name Time (s) Total Time (s) Depth 1 (in) Depth 2 (in) Thermal Conductivity ( W m K) T1 0 0 2.494 2.490 1.925 T2 1 1 2.975 2.943 2.358 T3 1 2 3.033 3.075 2.534 T4 2 4 3.183 3.206 2.737 T5 2 6 3.282 3.285 2.942 T6 4 10 3.319 3.329 3.013 T7 4 14 3.411 3.406 3.025 T8 8 22 3.478 3.447 3.163 T9 15 37 3.463 3.465 3.155 T10 30 67 3.543 3.503 3.220 T11 60 127 3.528 3.550 3.256 T12 120 247 3.513 3.681 3.424 T13 480 727 3.63 3.601 3.274 Table 4. 7 : Saturated Soil Test Results Test Name Time (s) Total Time (s) Depth 1 (in) Depth 2 (in) Thermal Conductivity (W m K) S1 0 0 2.2 89 2.283 4.009 S2 1 1 2.399 2.400 3.21 S3 1 2 2.452 2.432 3.018 S4 2 4 2.486 2.494 3.106 S5 4 8 2.500 2.492 2.822 S6 8 16 2.587 2.548 3.283 S7 8 24 2.577 2.659 3.844 S8 16 40 2.644 2.616 3.331 S9 30 70 2.669 2.653 3.578 S10 60 130 2.663 2.706 4.21 7 S11 120 250 2.709 2.676 3.855 S12 240 490 2.728 2.706 4.213 S13 480 970 2.753 2.758 3.234 S14 960 1930 2.789 2.779 3.449 Table 4. 8 : Saturated Test Soil Mass Dried Soil Mass Calculation Mass of Pan 231.2 kg Mass of Pan + Dry Soil 4399.8 kg Ma ss of Dry Soil 4168.6 kg

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60 The change in density over time is shown in the compaction curves provided in Figures 4.10 through 4.12. The curves are provided from zero to 100 seconds, where t he majority of compaction occured Figure 4.10: Compactio n Curve for Dry Soil Test Figure 4.11: Compaction Curve for Wet Soil Test Figure 4.12: Compaction Curve for Saturated Soil Test

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61 The two depth measurements from the recorded data were averaged to account for uneven settling. To calculate th e displacement of the soil from compaction, the initial average depth was subtracted from the average depth of the weight for each measurement taken. The average depth and soil displacement equations are: The height of the soil is simply the difference between the height of the mold and the soil displacement. Volume of th e soil can then be calculated by multiplying the soil height by the cross sectional area. The spreadsheet requires volume in SI units so this value was multiplied by the necessary conversion factor to get the result in cm 3 The equations used to calculate the height and volume of the soil in the mold each time compaction occurred are From the results of the moisture content test and the dried soil mass calculation the mass of the dry soil was calculated. For the initial, non compacted test, the volume of the soil was equivalent to the volume of the mold. Otherwise, the volume of t he soil was calculated from the measured soil displacements. Mass of the dry soil and volume of the soil are the two parameters re quired to calculate dry density.

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62 Using the data collected and the equations described in this section, dry den sity was computed for each test. These ca lculations are presented in tabular format for the dry, wet, an d saturated tests in Tables 4.9 through 4.11 Table 4.9 : Dry Soil Test Calculations A verage Depth (in) Displacement (in) Height (in) Volume (in 3 ) Volume (cm 3 ) Dry Density (g/cm 3 ) 2.233 0.000 6.116 172.926 2833.747 1.574 2.542 0.309 5.808 164.20 3 2690.808 1.657 2.622 0.389 5.727 161.927 2653.510 1.680 2.654 0.421 5.696 161.036 2638.915 1.690 2.667 0.434 5.682 160.655 2632.660 1.694 2.707 0.474 5.642 159.524 2614.127 1.706 2.737 0.504 5.612 158.676 2600.227 1.715 2.768 0.535 5.581 157.799 25 85.863 1.724 2.823 0.590 5.526 156.244 2560.380 1.742 2.843 0.610 5.506 155.678 2551.113 1.748 2.866 0.633 5.484 155.042 2540.688 1.755 2.924 0.691 5.425 153.388 2513.583 1.774 Table 4.1 0 : Wet Soil Test Calculations A verage Depth (in) Displacement (in) Height (in) Volume (in 3 ) Volume (cm 3 ) Dry Density (g/cm 3 ) 2.492 0.000 6.116 172.926 2833.747 1.379 2.959 0.467 5.649 159.722 2617.370 1.493 3.054 0.562 5.554 157.036 2573.353 1.518 3.195 0.703 5.414 153.063 2508.255 1.558 3.284 0.792 5.325 150.547 2467.018 1.584 3.324 0.832 5.284 149.402 2448.253 1.596 3.409 0.917 5.200 147.012 2409.102 1.622 3.463 0.971 5.146 145.486 2384.082 1.639 3.464 0.972 5.144 145.443 2383.387 1.639 3.523 1.031 5.085 143.775 2356.050 1.658 3.539 1.047 5.069 143. 323 2348.637 1.664 3.597 1.105 5.011 141.683 2321.763 1.683

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63 Table 4.1 1 : Saturated Soil Test Calculations Average Depth (in) Displacement (in) Height (in) Volume (in 3 ) Volume (cm 3 ) Dry Density (g/cm 3 ) 2.286 0.000 6.116 172.926 2833.747 1.471 2.400 0.167 5.950 168.218 2756.602 1.512 2.442 0.209 5.907 167.016 2736.910 1.523 2.490 0.257 5.859 165.659 2714.670 1.536 2.496 0.263 5.853 165.490 2711.890 1.537 2.568 0.335 5.782 163.468 2678.762 1.556 2.618 0.385 5.731 162.040 2655.363 1.570 2.6 30 0.397 5.719 161.701 2649.803 1.573 2.661 0.428 5.688 160.824 2635.440 1.582 2.685 0.452 5.665 160.160 2624.552 1.588 2.693 0.460 5.657 159.934 2620.845 1.591 2.717 0.484 5.632 159.241 2609.493 1.597 2.756 0.523 5.594 158.152 2591.655 1.608 2.784 0 .551 5.565 157.347 2578.450 1.617 The recorded test data was plotted against and compared with data from the methods provided by Kersten, Mickley, Gemant, De Vries, Van Rooyen, McGaw, and Johansen. The data for dry, coarse soil is provided in Figure 4.1 3. Compar ing the data recorded by the KD2 device to the available data for dry, coarse soils, a consistent thermal conductivity trend can be observed Aside from Mickley, dry soils with densities ranging from 1.6 to 1.9 g/cm 3 have thermal conductivities be tween 0.2 and 0.5 W/m K. The recorded test data f ell within this range. The data from the other two tests are shown in Figures 4.14 and 4.15. When analyzing these graphs, it can be deduced that the saturated condition introduced more variation in results. The soil with 10% moisture still show ed a strong trend when compared to the other methods ; however, the readings from the saturated test are on the higher end. This is most likely due to the longer heating time as noted by the ASTM guidelines All thermal conductivity tests were performed at a length of 10 minutes. If

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64 this time was reduced to 5 minutes, the reduced heating time might have provided a higher level of agreement and perhaps less variability. Figure 4.1 3 : Thermal Conductivity v s. Dry Densi ty for Dry Coarse Soil Figure 4.1 4 : Thermal Conductivity vs. Density for a Wet Coarse Soil Figure 4.1 5 : Thermal Conductivity vs. Density for a Saturated Coarse Soil

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65 4. 2 .4 Repeatability and Temperature Tests The repeatability and temperature test s utilized the same 0.10 ft 3 mold and soil from the same sample as the density tests. The mold was filled to the top with oven dried soil and compacted for 20 minutes using the vibrating table apparatus at a frequency of 50 hertz. This length of time was c hosen to ensure a reasonably compacted soil. All tests were done without removing the probe from the compacted soil after its initial placement. This allows errors due to changing the location of the probe to be excluded from the analysis. The KD2 probe ma nual suggests a 15 minute wait time between tests to obtain maximum accuracy. T ests were done to see how necessary this was. Several tests were set up to observe the changes in accur acy between continuous testing and testing with a 15 minute break in betwe en. The consecutive tests were conducted at both the five and ten minute settings on the probe in order to see if there were variations in the results, whereas the longer tests were done at the 10 minute setting. A refrigerator was used to control the te mperature of the soil matrix. It was initially placed at its warmest setting and allowed to warm up for a period of 36 hours. The mold with the probe still inserted was then placed in the refrigerator with the cord from the probe connected to the data col lection device located outside the refrigerator. At this point, the refrigerator was closed and was not opened until all testing was complete to prevent external temperatures from affecting the readings. The mold was left overnight at this setting to allow the soil to reach a stable temperature Seven tests were done at three different refrigerator settings; low, medium, and high. One set was done each day

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66 for three consecutive days. After the tests were completed each day the refrigerator would be turned to a colder setting and left overnight to cool down. 4. 2 5 Repeatability and Temperature Test Results The results for t he repeatability tests are provided in Table 4.1 2 Temperature and thermal conductivity are plotted against time in Figures 4.1 6 and 4.1 7 From the graph of temperature vs. time, it can be seen that the 10 minute tests are run at a lower temperature both with and without wait time between For the 10 minute test with the 15 minute wait time, the results appear to be linear whereas th ere are variations in the results plotted from the data of the other tests ; therefore, a 15 minute wait time provides more consistent results and does appear to be more reliable Assuming the data for the longer tests with 15 minutes in between each is cor rect, the five minute tests under estimate the thermal conductivity by approximately 12% and the continuous 10 minute tests slightly over estimate the thermal conductivity. Table 4.1 2 : Results for Repeatability Tests Test 1 5 min test s no wait Test 2 5 min test s no wait Test 3 10 min test s no wait Test 4 10 min test s 15 min ute wait Test T (C) K) T (C) K) T (C) K) T (C) K) T1 22.72 0.458 22.64 0.461 21.78 0.527 21.91 0.527 T2 22.97 0.467 22.93 0.473 22.12 0.543 22.20 0.528 T3 23.11 0.469 23.06 0.475 22.30 0.544 22.40 0.527 T4 23.19 0.469 23.15 0.476 22.44 0.543 22.54 0.526 T5 23.26 0.470 23.21 0.476 22.56 0.542 22.66 0.524 T6 23.30 0.469 23.21 0.472 22.66 0.540 22.75 0.524 T7 23.34 0.469 23.29 0.475 22.73 0.538 22.82 0.523 T8 23.36 0.469 23.34 0.476 22.84 0.539 22.89 0.523 T9 23.33 0.466 23.37 0.475 22.92 0 .539 T10 23.40 0.469 23.40 0.476 22.99 0.539 T11 23.40 0.467 T12 23.44 0.469 T13 23.45 0.469

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67 Figure 4. 1 6 : Change in Temperature over Time Figure 4. 1 7 : Change in Thermal Conductivity over T ime The data recorded f rom the temperature test is provided in Table 4.1 3 Temperature vs. time and thermal conductivity vs. time are plo tted in Figures 4.18 and 4.19. Soil t emperature remains reasonably constant over time at the four temperatures, but th ermal conductivity increases slightly at the warmer temperatures and decreases slightly at the colder temperatures.

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68 Table 4.1 3 : Results for Temperature Tests Room Temperature Setting 1 (warmest) Setting 2 Setting 3 (coldest) time (min) T (C) K) T (C) K) T (C) K) T (C) K) 0 21.91 0.527 7.26 1.134 4.87 2.372 3.36 3.280 25 22.20 0.528 7.37 1.180 4.85 2.437 3.38 3.218 50 22.40 0.527 7.26 1.232 4.78 2.427 3.37 3.148 75 22.54 0.526 7.23 1.258 4.85 2.249 3.39 3. 336 100 22.66 0.524 7.34 1.267 4.77 2.362 3.70 3.136 125 22.75 0.524 7.35 1.320 4.79 2.260 3.70 3.130 150 22.82 0.523 7.23 1.363 4.82 2.307 3.55 3.170 Figure 4. 1 8 : Change in Temperature over Time Figure 4. 1 9 : Change in Thermal Conduc tivity over Time

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69 4. 3 Evaluation of Theoretical Algorithms A sample boring log is provided to aid as an example on how the spreadsheet functions. Figure 4.20 shows a boring log for a soil boring performed for the Crosstown / I 4 Connector project in Tampa, FL. Figure 4.20: Boring Log for Boring BA 36 At the top of the spreadsheet are highlighted cells for project name, location, that the projec t information ca n be input (Figure 4.21).

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70 Figure 4.21: Inputting Project Information To input the boring log data into the spreadsheet, the ground surface elevation and the elevation of the water table must be determined. Careful analysis of the boring log shows the g round surface elevation at 11.5 ft and the elevation of the water table at 8.5 ft Figure 4.22 sho ws the elevations as they are input into the spreadsheet. Figure 4.22: Inputting Elevations This boring log is provided in terms of elevation, not depth; therefore, the depth of each input is the difference between the ground surface elevation and current elevation. Only elevations where blow counts we re calculated should be input Figures 4.23 through 4.25 show examples of th e data being input for depth, blow count and soil type. Soil type is selected by clicking on the cell in the soil type column. This will bring up the drop down menu with the different soil type option s

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71 Figure 4.23: Inputting Depth Figure 4.24: Input ting Blow Count Figure 4.25: Inputting S oil Type

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72 the sampler only advanced 5 in. To account for this, the highest poss ible blow count, 60, is input to simulate a harder soil layer ( Figure 4.26). Figure 4.26 Inputted Boring Log Upon completion of the depth, blow count, and soil type inputs for each boring log entry, c licking the C alculate button will calculate elevation, density, the 7 thermal conduc tivity methods, and the average of the selected methods. Figure 4.27 shows the results calculated when this button is clicked. To select which methods to plot and include in the average, the check boxes are clicked to be selected or deselected. Once the de sired methods have been selected, clicking the Update button (Figure 4.28) will update the average and the thermal conductivity vs. depth graph Six methods, including the average are selected and t he resulting plots from the thermal conductivity vs. depth graph and the boring log plot are shown in Figure 4.29.

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73 Figure 4.27: Results from Clicking the Calculate Button Figure 4.28: Clicking Update after Selecting Desired Plotting Methods Figure 4.29: Plot of Selected Methods and Plot of Boring Log

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74 4. 3.1 Heat Capacity As the ultimate thermal property controlling diffusion is diffusivity, an additional module was created to compute the heat capacity from which the diffusivity can be calcu lated for each boring log entry using the following equation fro m chapter 2. Heat capacity C, is a far less intense computation requiring only the fraction of air, water, and soil as well as the mineralogy. This is calculated using th e equation for specific heat, where C S C w and C a are the heat capacities of soil, water, and air, and X S X W and X a are the volumetric fractions of soil, water, and air (Duarte 2006).

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75 Chapter 5 Conclusion Thermal properties of soils vary drastically depending on the mineralogy density, saturation state, and structure. Despite several decades of research on the topic, no rational correlations exist that predict thermal properties using common soil exploration methods. This thesis focused on assembling correlations from existing literature to close the gap between SPT sampling and thermal properties. The direct applications of defining the thermal properties of soils include both geothermal heating/cooling systems and those methods of foundation quality assurance involving therma l integrity profiling. The latter of which is discussed below. 5.1 Thermal Integrity Profiling Thermal integrity profiling is a test method that assesses the intact ness of cast in place concrete with emphasis on an underground structural element (e.g. d rilled shaft or ACIP). The hydration energy of curing concrete is sufficient in magnitude to develop a temperature signature relative to the volume of concrete placed. In cases where the soil is uniform, the developed temperature is also uniform for a perf ectly shaped cylinder. Variations in cross section can cause increases or decreases in the measured temperature proportional to bulges or necks respectively. Figures 5.1 through 5.3 show the temperature variation from TIP testing of shafts constructed with permanent casing in the upper portion along with the SPT blow counts These three shafts provide an interesting case study for this thesis as the cross section is known not to have varied. As a result, the temperature variations recorded are largely t he

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76 effect of thermal properties which can be identified with the developed spreadsheet. Therefore, this comparison is exclusively based on that portion ab ove the bottom of casing (BOC ) Figure 5.1: TIP Analysis Shaft 14 1

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77 Figure 5.2: TIP Analysis Shaft 14 2

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78 Figure 5.3: TIP Analysis Shaft 14 3 Figure s 5.4 and 5.5 show the predicted thermal conductivity, heat capacity, and diffusivity along with the measured TIP results of the first shaft (14 1 ) In the case d region, an increased temperature trend is noted from 3 0 to 60 ft which corresponds to a reduction in the diffusivity. Figures 5.6 and 5.7 show the thermal conductivity, heat capacity, diffusivity, and TIP measurements of the second shaft (14 2) Again, a n increased temperature trend and reduced diffusivity is noted in the cased region, in this case from 40 to 65 ft.

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79 Figure 5.4: Thermal Conductivity and Heat Capacity for Shaft 14 1 Figure 5.5: Diffusivity and Temperature Profile for Shaft 14 1

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80 Figure 5.6: Thermal Conductivity and Heat Capacity for Shaft 14 2 Figure 5.7: Diffusivity and Temperature for Shaft 14 2

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81 C onversely, Figures 5.8 and 5.9 show a nearly ideal temperature profile with the exception of a slight increased zon e from 40 to 45 ft that appears to correspond to a reduced diffusivity at the same depth. The boring log consists entirely of either clayey or silty sands except for in this region, where the soil is labeled as sandy clay. The large increase in heat capaci ty and decreases in thermal conductivity and diffusivity could be due to a misclassificat ion of the soils in this region. As an example, clayey sand was selected for this region instead of sandy cla y and the modified results for diffusivity are plotted nex t to the tem perature profile in Figure 5.10. This shows the sensitivity to soil classification. Figure 5.8: Thermal Conductivity and Heat Capacity for Shaft 14 3

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82 Figure 5.9: Diffusivity and Temperature Profile for Shaft 14 3 Figure 5.10 : Modified Diffusivity and Temperature Profile for Shaft 14 3

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83 Obviously, limitations exist in such an approach in that often times the nearest boring log may not reflect the actual conditions. In those cases, construction logs can be used to explain subtl e variations in soil mineralogy, but can only qualitatively asse s s the effect. 5.2 Future Studies At present, efforts are underway to develop a CPT based thermal conductivity probe. This has the potential to more readily quantify both the soil character istics (i.e. strength, structure, and mineralogy) and the thermal conductivity with vertical depth resolution for more precise measurements (1 data point/cm) than the SPT wherein 1 data point per 1.5 ft is the absolute finest resolution attainable. 5.3 Su mmary This thesis presents a new analysis tool for the purpose of quantifying the thermal properties of soil from commonly used SPT boring log data. It is thought to be the only such attempt to do so and as such will likely incur numerous changes and ref inements in ensuing years. The applicability of the thesis findings are at present somewhat limited but predictive methods in these areas are receiving much needed attention and will benefit from the inroads developed herein.

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84 List of Referen ces ASTM ( 1996 ) Vol. 4.08, D1586, D4253, D4318 ASTM ( 2008 Unsa turated Soils GSP, ASCE, pp. 1707 1718. Earth Temperature and Site Geology. Virginia Tech, Department of Mines Minerals and Energy. Web. http://www.geo4va.vt.edu/A1/A1.htm Farouki, O. ( Report 82 8, US Army Corps of Engineers Cold Regions Research and Engineering Laboratory, pp. 14 23 Farouki, O. ( Thermal Resistivi Washington, DC, pp 25 44 Johansen, O. (1977 ). Cold Regions Research and Engineering Laboratory. Hanover, NH, pp. 1 46 Johansen, pp.407 420 Kersten M.S. ( 1949 e of Technology, Engineering Experiment Station, Vol. LII, No. 21. Design and Optimizati on Symposium, Miami, FL, April 16 18, 2007.

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85 EL 6800, Electric Power Research Institute, Palo Alto, CA. Limestone Properties. Uni versity of Florida. Bridge Software Institute. Web. http://bsi web.ce.ufl.edu/downloads/files/MultiPier_Soil_Table.pdf Mullins, G., Winters, D., and Johnson, K., (2009), "Attenuating Mass Concrete Effects in Drilled Shafts," Final Report, FDOT Project BD544 39, September. Mullins, G and Kranc, S., (2007), "Thermal Integrity Testing of Drilled Shafts," Final Report, FDOT Project BD544 20, May. Mullins, G. and Ashmawy, A., (2005), "Factors Affecting Anomaly Formation in Drilled Shafts," Final Report, FDOT Project BC353 19, March. Mullins, G. and Winters, D. (2004). "Post Grouting Drilled Shaft Tips Phase II Final Report." Final Report submitted Florida Departmen t of Transportation, June. Integrated North Tampa Bay Model Application of the Integrated INTB Model Calibration Report Tampa Bay Water. In press.


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Thermal conductivity of soils from the analysis of boring logs
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ABSTRACT: Recent interest in "greener" geothermal heating and cooling systems as well as developments in the quality assurance of cast-in-place concrete foundations has heightened the need for properly assessing thermal properties of soils. Therein, the ability of a soil to diffuse or absorb heat is dependent on the surrounding conditions (e.g. mineralogy, saturation, density, and insitu temperature). Prior to this work, the primary thermal properties (conductivity and heat capacity) had no correlation to commonly used soil exploration methods and therefore formed the focus of this thesis. Algorithms were developed in a spreadsheet platform that correlated input boring log information to thermal properties using known relationships between density, saturation, and thermal properties as well as more commonly used strength parameters from boring logs. Limited lab tests were conducted to become better acquainted with ASTM standards with the goal of proposing equipment for future development. Finally, sample thermal integrity profiles from cast-in-place foundations were used to demonstrate the usefulness of the developed algorithms. These examples highlighted both the strengths and weaknesses of present boring log data quality leaving room for and/or necessitating engineering judgment.
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Thermal Conductivity
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Integrity Testing
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