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A modified hole erosion test (HET-P) to study erosion characteristics of soil Lüthi, Marcel 2011

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 A MODIFIED HOLE EROSION TEST (HET-P) TO STUDY EROSION CHARACTERISTICS OF SOIL     by     MARCEL LUTHI   B.Eng., HSR University of Applied Sciences Rapperswil, 2005     A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF    MASTER OF APPLIED SCIENCE    in    The Faculty of Graduate Studies   (Civil Engineering)    THE UNIVERSITY OF BRITISH COLUMBIA   (Vancouver)     August 2011   © Marcel Luthi, 2011 Abstract     ii Abstract Today’s increasing demand for energy and natural resources requires safe and reliable infrastructure. This includes hydraulic earth structures like dikes, levees, or dams. Such structures are susceptible to piping, a fundamental type of internal soil erosion. Piping is one of the principal causes of failures and accidents affecting embankment dams. The Hole Erosion Test (HET) is based on soil piping, and is used to determine the erodibility and critical shear stress of a soil. A soil specimen with a preformed axial hole is subjected to a constant-head pressure flow, and the rate of enlargement of the soil pipe is determined indirectly from flow rate and hydraulic gradient. This study presents a Modified Hole Erosion Test (HET-P) that introduces a conventional Pitot-static tube to measure total energy head and flow velocity of the exiting jet, which is correlated to a mean velocity within the axial hole. A series of Modified Hole Erosion Tests (HET-P) was performed on non-erodible PVC specimens with axial holes of constant, but different diameter, followed by HET-P tests on two types of soil, namely glacial till material of a dam core and natural clay deposits from Ontario river banks. Results confirmed that sidewall hydraulic head measurements to determine hydraulic gradients in the standard HET overestimate the resulting axial wall shear stress by as much as an order of magnitude. Furthermore, velocity measurements increase the confidence in test results as they allow for a more direct estimate of the axial hole diameter at any time during a test. A Pitot-static tube used in the HET-P for velocity and pressure measurement can easily be incorporated, and yields more transparent and reliable results by eliminating or amending some of the limiting assumptions of the standard test. It is an easy, fast, and economical approach that can be applied to soils in both constructed earth structures including dams and embankments, and to natural river banks to determine their susceptibility to internal and surface erosion.     Table of contents     iii Table of contents Abstract ................................................................................................................................................... ii Table of contents ................................................................................................................................... iii List of tables ......................................................................................................................................... vii List of figures ....................................................................................................................................... viii List of symbols ..................................................................................................................................... xii List of abbreviations ........................................................................................................................... xiv Acknowledgements.............................................................................................................................. xv Dedication ............................................................................................................................................ xvi 1. Introduction ..................................................................................................................................... 1 1.1. Background ................................................................................................................................ 1 1.2. Objective and scope .................................................................................................................. 3 1.3. Outline of the thesis ................................................................................................................... 4 2. Literature review ............................................................................................................................. 5 2.1. Erosion tests category 1: Flow over surface .............................................................................. 6 2.2. Erosion tests category 2: Rotating cylinder ............................................................................... 7 2.3. Erosion tests category 3: Jet impact .......................................................................................... 8 2.4. Erosion tests category 4: Flow through defect .......................................................................... 9 2.5. Hole Erosion Test (HET) .......................................................................................................... 10 2.5.1. UNSW Hole Erosion Test (HET) .................................................................................... 10 2.5.2. HET theory ..................................................................................................................... 13 2.5.3. HET data analysis .......................................................................................................... 15 2.5.4. Modifications to the HET ................................................................................................ 17 2.5.5. Main findings and conclusions ....................................................................................... 20 2.6. Summary and outline of the research program ....................................................................... 23 2.6.1. Outline of the research program .................................................................................... 24 3. Modified Hole Erosion Test (HET-P) ........................................................................................... 25 3.1. Hydraulic review of the HET .................................................................................................... 25 Table of contents     iv 3.1.1. Friction head loss and hydraulic gradient ....................................................................... 25 3.1.2. Minor head losses and entrance length ......................................................................... 27 3.1.3. Flow conditions and axial hole velocity .......................................................................... 28 3.2. HET-P apparatus ..................................................................................................................... 30 3.2.1. Test cell .......................................................................................................................... 31 3.2.2. Pitot-static tube and differential pressure transducer system ........................................ 33 3.2.3. Water flow system .......................................................................................................... 35 3.3. Experimental setup and test procedure ................................................................................... 37 3.3.1. Calibration of measuring instruments ............................................................................. 37 3.3.2. Test preparation ............................................................................................................. 37 3.3.3. Test procedure ............................................................................................................... 38 3.4. Modified analysis ..................................................................................................................... 39 3.4.1. HET-P: based on energy gradient .................................................................................. 39 3.4.2. HET-P (V): based on energy gradient and flow velocity ................................................ 40 4. Non-erodible test specimens ....................................................................................................... 41 4.1. Research program ................................................................................................................... 42 4.2. Results and analysis ................................................................................................................ 43 4.2.1. Head ratio and shear stress ........................................................................................... 43 4.2.2. Flow coefficient and axial hole velocity .......................................................................... 45 4.3. Discussion ................................................................................................................................ 47 4.3.1. Head ratio and shear stress ........................................................................................... 47 4.3.2. Axial hole velocity and hydraulic roughness .................................................................. 48 4.3.3. Upstream total energy head ........................................................................................... 49 4.3.4. Flow conditions and minor losses .................................................................................. 50 4.3.5. Sources of errors ............................................................................................................ 51 4.3.6. Limitations ...................................................................................................................... 52 5. Erodible soil specimens ............................................................................................................... 53 5.1. Research program ................................................................................................................... 54 5.2. Results and analysis ................................................................................................................ 55 Table of contents     v 5.2.1. Soil properties and description ....................................................................................... 55 5.2.2. Head ratio and shear stress ........................................................................................... 57 5.2.3. Axial hole velocity and estimated diameter .................................................................... 60 5.2.4. Erosion rate and critical shear stress ............................................................................. 63 5.2.5. Dam core material .......................................................................................................... 64 5.2.6. Ontario clay samples ...................................................................................................... 65 5.3. Discussion ................................................................................................................................ 68 5.3.1. Head ratio and shear stress ........................................................................................... 68 5.3.2. Axial hole velocity and estimated diameter .................................................................... 69 5.3.3. Erosion rate and critical shear stress ............................................................................. 69 5.3.4. Test soils ........................................................................................................................ 70 5.3.5. Sources of errors ............................................................................................................ 71 5.3.6. Limitations ...................................................................................................................... 72 6. Conclusions and recommendations ........................................................................................... 73 6.1. Summary and conclusions ....................................................................................................... 73 6.2. Recommendations ................................................................................................................... 75 References ............................................................................................................................................ 77 Appendices ........................................................................................................................................... 83 Appendix A: Review of the standard Hole Erosion Test (HET) .......................................................... 84 Appendix B: Engineering drawings ..................................................................................................... 85 Appendix C: Calibration of measuring instruments ............................................................................ 88 Differential pressure transducers .................................................................................................... 88 Custom v-notch weir ....................................................................................................................... 89 Appendix D: HET-P test procedure .................................................................................................... 91 Soil preparation for reconstituted specimens .................................................................................. 91 Specimen preparation for reconstituted specimens........................................................................ 91 Specimen preparation for specimens from undisturbed (intact) soil samples ................................ 92 Test preparation .............................................................................................................................. 92 Test procedure ................................................................................................................................ 93 Table of contents     vi Post-test procedure ......................................................................................................................... 94 Appendix E: Analysis methods ........................................................................................................... 95 Appendix F: Experimental program .................................................................................................... 96 Appendix G: Non-erodible test specimens ....................................................................................... 100 Appendix H: Soil properties .............................................................................................................. 103 Appendix I: Erodible soil specimens ................................................................................................. 105 Dam core material ......................................................................................................................... 105 Ontario clay samples .................................................................................................................... 109     List of tables     vii List of tables Table 1.1: Embankment-dam engineering and safety evaluation ........................................................ 1 Table 2.1: Qualitative relation of representative erosion rate index and progression of internal erosion (Wan and Fell 2002, 2004a, 2004b) ..................................................................... 12 Table 3.1: Specifications SETRA Model 230 Bidirectional Wet-to-Wet Pressure Transducers ......... 34 Table 4.1: Summary of head ratio values, H / h , obtained from the three non-erodible test specimens for turbulent flow with Re > 5000 ..................................................................... 43 Table 4.2: Summary of flow coefficient values, K , obtained from the three non-erodible test specimens for turbulent flow with Re > 5000 ..................................................................... 45 Table 4.3: Summary of estimated axial hole diameters HET-P (V), t , obtained from the three non- erodible test specimens for turbulent flow with Re > 5000 ................................................. 46 Table 5.1: Summary of velocity ratio values obtained from the Ontario clay specimens for turbulent flow with Re > 2000 for HET-P, respectively Re > 5000 for HET-P (V) .............................. 61 Table 5.2: Summary of diameter ratio values obtained from the Ontario clay specimens for turbulent flow with Re > 2000 for HET-P, respectively Re > 5000 for HET-P (V) .............................. 62 Table 5.3: Summary of soil properties for erodible soil specimens .................................................... 66 Table 5.4: Summary of test data and results for erodible soil specimens .......................................... 67 Table A.1: Known challenges and issues of the standard HET with suggested improvements ......... 84 Table E.1: Step by step analysis of test data for different methods .................................................... 95 Table F.1: Test number information .................................................................................................... 96 Table F.2: Test program ..................................................................................................................... 97 Table G.1: Test data and results non-erodible test specimen D1-063 .............................................. 100 Table G.2: Test data and results non-erodible test specimen D1-123 .............................................. 101 Table G.3: Test data and results non-erodible test specimen D1-243 .............................................. 102     List of figures     viii List of figures Figure 1.1: Internal erosion and piping process in earth dams .............................................................. 2 Figure 2.1: Schematic diagram flow over surface .................................................................................. 6 Figure 2.2: Schematic diagram rotating cylinder ................................................................................... 7 Figure 2.3: Schematic diagram jet impact.............................................................................................. 8 Figure 2.4: Schematic diagram flow through defect .............................................................................. 9 Figure 2.5: Schematic diagram Hole Erosion Test HET (adapted from Wan and Fell, 2004) ............. 11 Figure 2.6: Typical results Hole Erosion Test (schematic, no real test data) ...................................... 12 Figure 3.1: Flow pattern upstream and downstream of test specimen, including Energy Grade Line (EGL), and Hydraulic Grade Line (HGL) at wall ................................................................ 27 Figure 3.2: Pitot-static tube with schematic turbulent velocity profile of jet exiting axial hole immediately adjacent to test specimen .............................................................................. 29 Figure 3.3: Schematic diagram of HET-P apparatus ........................................................................... 30 Figure 3.4: Photograph of HET-P apparatus ....................................................................................... 31 Figure 3.5: a) Vertical HET-P test cell, b) Dismantled downstream part of HET-P test cell with bridge element holding 6-mm wire mesh for soil specimen support, piezometer connection, and Pitot-static tube .................................................................................................................. 32 Figure 3.6: Differential pressure transducer system, setup for high range differential pressures ....... 34 Figure 3.7: Schematic hydraulic profile of Modified Hole Erosion Test (HET-P) with Energy Grade Line (EGL) for initial hole diameter o = 6 mm at medium flow rate .................................. 35 Figure 3.8: Downstream constant head tank immediately after failure of soil specimen illustrating performance of flow conditioning plate and v-notch weir at 20-25 l/min ........................... 36 Figure 3.9: Flowcharts describing test analysis of (a) HET, and (b) HET-P (V) (rectangle: measured or deduced, parallelogram: assumed or affected by uncertainty) ..................................... 40 Figure 4.1: Non-erodible PVC specimens with axial holes of 6, 12, and 24 mm diameter .................. 42 Figure 4.2: Head ratio equals shear stress ratio versus flow rate for the three non-erodible test specimens .......................................................................................................................... 44 Figure 4.3: Wall shear stress HET-P using Pitot-static tube data versus wall shear stress HET from sidewall hydraulic heads for the three non-erodible test specimens ................................. 44 Figure 4.4: Flow coefficient, K , versus flow rate for the three non-erodible test specimens .............. 45 Figure 4.5: Mean flow velocity in axial hole using Pitot-static tube data versus mean flow velocity in axial hole using continuity for the three non-erodible test specimens ............................... 46 Figure 4.6: Estimated axial hole diameters HET-P (V), back calculated from Pitot-static tube data versus flow rate for the three non-erodible test specimens ............................................... 47 List of figures     ix Figure 5.1: Head ratio equals shear stress ratio versus estimated mean hole diameter for the Ontario clay specimens .................................................................................................................. 58 Figure 5.2: Wall shear stress HET-P using Pitot-static tube data versus wall shear stress HET from sidewall hydraulic heads for the Ontario clay specimens .................................................. 59 Figure 5.3: Mean flow velocity in axial hole from HET-P and HET-P (V) using Pitot-static tube data versus mean flow velocity in axial hole from HET using continuity for the Ontario clay specimens .......................................................................................................................... 61 Figure 5.4: Estimated axial hole diameter from HET-P and HET-P (V) back calculated from Pitot- static tube data versus estimated axial hole diameter from HET for the Ontario clay specimens .......................................................................................................................... 62 Figure 5.5: Erosion rate versus time for successively increased test heads (S3-993.01) ................... 63 Figure 5.6: Critical shear stress defined on flow rate versus shear stress diagram (S3-993.21) ........ 64 Figure C.1: H-U diagram differential pressure transducer #1 and #2 with fitted linear regression lines to convert output voltage to differential pressure head ..................................................... 88 Figure C.2: H-Q diagram v-notch weir using Kindsvater-Shen relationship (curve fitting) ................... 89 Figure C.3: H-Q diagram v-notch weir using Kindsvater-Shen relationship (head readings) .............. 90 Figure H.1: Gradation curves dam core material (USCS) .................................................................. 103 Figure H.2: Standard compaction test Dam MV4-Altered material (ASTM D698 Method A) ............. 104 Figure H.3: Standard compaction test Dam MV4-Core material (ASTM D698 Method B) ................ 104 Figure I.1: Dam MV4-Altered – S1-003.01 – Measured flow rate & results at point of failure .......... 105 Figure I.2: Dam MV4-Altered – S1-003.01 – Dried specimen .......................................................... 105 Figure I.3: Dam MV4-Altered – S1-003.02 – Measured flow rate & results at point of failure .......... 106 Figure I.4: Dam MV4-Altered – S1-003.02 – Drained test cell US and detail with Pitot tube ........... 106 Figure I.5: Dam MV4-Altered – S1-553.01 – Measured flow rate & results at point of failure .......... 107 Figure I.6: Dam MV4-Altered – S1-553.01 – Drained test cell US and detail with Pitot tube ........... 107 Figure I.7: Dam MV4-Core – S2-553.01 – Measured flow rate & results at point of failure ............. 108 Figure I.8: Dam MV4-Core – S2-553.01 – Drained test cell US and detail with Pitot tube ............... 108 Figure I.9: Ontario Clay – Little Cataraqui – S3-993.01 – Prepared test specimen ......................... 109 Figure I.10: Ontario Clay – Little Cataraqui – S3-993.01 – Measured flow rate ................................. 109 Figure I.11: Ontario Clay – Little Cataraqui – S3-993.01 – Head difference and energy loss ............ 110 Figure I.12: Ontario Clay – Little Cataraqui – S3-993.01 – Head ratio ............................................... 110 Figure I.13: Ontario Clay – Little Cataraqui – S3-993.01 – Axial hole diameter ................................. 111 Figure I.14: Ontario Clay – Little Cataraqui – S3-993.01 – Wall shear stress .................................... 111 Figure I.15: Ontario Clay – Little Cataraqui – S3-993.01 – Erosion rate ............................................ 112 Figure I.16: Ontario Clay – Little Cataraqui – S3-993.01 – Flow rate versus shear stress ................ 112 Figure I.17: Ontario Clay – Little Cataraqui – S3-993.01 – Drained test cell US and plaster cast ..... 113 Figure I.18: Ontario Clay – Little Cataraqui – S3-993.01 – DS side of specimen pre- and post-test . 113 List of figures     x Figure I.19: Ontario Clay – Little Cataraqui – S3-993.02 – Prepared test specimen ......................... 114 Figure I.20: Ontario Clay – Little Cataraqui – S3-993.02 – Measured flow rate ................................. 114 Figure I.21: Ontario Clay – Little Cataraqui – S3-993.02 – Head difference and energy loss ............ 115 Figure I.22: Ontario Clay – Little Cataraqui – S3-993.02 – Head ratio ............................................... 115 Figure I.23: Ontario Clay – Little Cataraqui – S3-993.02 – Axial hole diameter ................................. 116 Figure I.24: Ontario Clay – Little Cataraqui – S3-993.02 – Wall shear stress .................................... 116 Figure I.25: Ontario Clay – Little Cataraqui – S3-993.02 – Erosion rate ............................................ 117 Figure I.26: Ontario Clay – Little Cataraqui – S3-993.02 – Flow rate versus shear stress ................ 117 Figure I.27: Ontario Clay – Little Cataraqui – S3-993.02 – Drained test cell US ................................ 118 Figure I.28: Ontario Clay – Little Cataraqui – S3-993.02 – Test specimen after testing (DS) ............ 118 Figure I.29: Ontario Clay – Bear Brook – S3-993.12 – Prepared test specimen ................................ 119 Figure I.30: Ontario Clay – Bear Brook – S3-993.12 – Measured flow rate ....................................... 119 Figure I.31: Ontario Clay – Bear Brook– S3-993.12 – Head difference and energy loss ................... 120 Figure I.32: Ontario Clay – Bear Brook – S3-993.12 – Head ratio ..................................................... 120 Figure I.33: Ontario Clay – Bear Brook – S3-993.12 – Axial hole diameter ....................................... 121 Figure I.34: Ontario Clay – Bear Brook – S3-993.12 – Wall shear stress .......................................... 121 Figure I.35: Ontario Clay – Bear Brook – S3-993.12 – Erosion rate .................................................. 122 Figure I.36: Ontario Clay – Bear Brook – S3-993.12 – Flow rate versus shear stress ....................... 122 Figure I.37: Ontario Clay – Bear Brook – S3-993.12 – Drained test cell US and plaster cast ........... 123 Figure I.38: Ontario Clay – Bear Brook – S3-993.12 – Extracted test specimen after testing ........... 123 Figure I.39: Ontario Clay – Wilton Creek – S3-993.21 – Prepared test specimen ............................. 124 Figure I.40: Ontario Clay – Wilton Creek – S3-993.21 – Measured flow rate ..................................... 124 Figure I.41: Ontario Clay – Wilton Creek – S3-993.21 – Head difference and energy loss ............... 125 Figure I.42: Ontario Clay – Wilton Creek – S3-993.21 – Head ratio ................................................... 125 Figure I.43: Ontario Clay – Wilton Creek – S3-993.21 – Axial hole diameter ..................................... 126 Figure I.44: Ontario Clay – Wilton Creek – S3-993.21 – Wall shear stress ........................................ 126 Figure I.45: Ontario Clay – Wilton Creek – S3-993.21 – Erosion rate ................................................ 127 Figure I.46: Ontario Clay – Wilton Creek – S3-993.21 – Flow rate versus shear stress .................... 127 Figure I.47: Ontario Clay – Wilton Creek – S3-993.21 – Drained test cell US and plaster cast ......... 128 Figure I.48: Ontario Clay – Wilton Creek – S3-993.21 – Test specimen after testing (DS) ............... 128 Figure I.49: Ontario Clay – Wilton Creek – S3-993.22 – Prepared test specimen ............................. 129 Figure I.50: Ontario Clay – Wilton Creek – S3-993.22 – Measured flow rate ..................................... 129 Figure I.51: Ontario Clay – Wilton Creek – S3-993.22 – Head difference and energy loss ............... 130 Figure I.52: Ontario Clay – Wilton Creek – S3-993.22 – Head ratio ................................................... 130 Figure I.53: Ontario Clay – Wilton Creek – S3-993.22 – Axial hole diameter ..................................... 131 Figure I.54: Ontario Clay – Wilton Creek – S3-993.22 – Wall shear stress ........................................ 131 Figure I.55: Ontario Clay – Wilton Creek – S3-993.22 – Erosion rate ................................................ 132 List of figures     xi Figure I.56: Ontario Clay – Wilton Creek – S3-993.22 – Flow rate versus shear stress .................... 132 Figure I.57: Ontario Clay – Wilton Creek – S3-993.22 – Drained test cell US ................................... 133 Figure I.58: Ontario Clay – Wilton Creek – S3-993.22 – Test specimen after testing (DS) ............... 133     List of symbols     xii List of symbols   = cross-sectional area of axial hole m2 Ce = coefficient of soil erosion s/m Cp = Pitot tube coefficient – Cv = velocity coefficient – D = diameter of flow chamber m fL = friction factor for laminar flow conditions kg/m 2 s fT = friction factor for turbulent flow conditions kg/m 3     = forcing force N    = retaining force N g = acceleration of gravity m/s 2  Gs = specific gravity of soil – hd = measured downstream sidewall hydraulic head m hf = friction head loss m hu = measured upstream sidewall hydraulic head m hv = centerline velocity head m h = hydraulic head difference across test specimen m Hd = measured downstream total energy head m Hu = upstream total energy head m H = energy head loss along test specimen m i = H / L = energy gradient across the specimen in modified HET-P –      = HET erosion rate index – K = CpCv = flow coefficient – L = length of axial hole m LT = transition length turbulent to laminar flow m LL = liquid limit of soil % p = fluid pressure N/m 2  ps = static pressure (Pitot-static tube) N/m 2  pt = total pressure (Pitot-static tube) N/m 2  pv = dynamic pressure (Pitot-static tube) N/m 2  p / g = pressure head m P =  = wetted perimeter ≡ circumference of circular cross section m PL = plastic limit of soil % Q = measured flow rate m 3 /s Re = Reynolds number – List of symbols     xiii s = h / L = hydraulic gradient across the specimen in standard HET – Sr = degree of saturation % t = elapsed time s T = water temperature °C umax = centerline jet velocity m/s V = mean flow velocity in circular hole or pipe m/s Vd = downstream flow velocity (flow chamber) m/s Vt = estimated mean flow velocity in axial hole m/s Vu = upstream flow velocity (flow chamber) m/s wf = final water content (post-test) % wo = initial water content (pre-test) % wopt = optimum water content %     = erosion rate per unit surface area kg/s/m2       = estimated erosion rate per unit surface area of the axial hole in HET kg/s/m 2          = estimated erosion rate per unit surface area of the axial hole in HET-P kg/s/m 2   = Darcy friction factor –  = kinematic viscosity (water at 20°C:  = 1.004E-06 m 2 /s) m 2 /s d = dry density of soil kg/m 3  d,max = standard maximum dry density kg/m 3  m = density of total (moist) soil specimen kg/m 3  w = density of water used as eroding fluid kg/m 3  g = specific weight of eroding fluid N/m 3   = hydraulic shear stress along wetted area N/m 2  c = estimated critical shear stress for initiation of erosion N/m 2       = estimated wall shear stress along axial hole in HET N/m 2         = estimated wall shear stress along axial hole in HET-P N/m 2  o = initial shear stress N/m 2   = hole diameter m f = measured final hole diameter m o = initial diameter of preformed hole m t = estimated mean diameter of axial hole m   List of abbreviations     xiv List of abbreviations DHT = Drill Hole Test EFA = Erosion Function Apparatus EGL = Energy Grade Line HET = Hole Erosion Test (Wan and Fell 2002, 2004a, 2004b) HET-P = Modified Hole Erosion Test based on energy gradient HET-P (V) = Modified Hole Erosion Test based on energy gradient and flow velocity HGL = Hydraulic Grade Line ICOLD = International Commission On Large Dams JET = Jet Erosion Test NEF = No Erosion Filter Test RCT = Rotating Cylinder Test UBC = University of British Columbia, Vancouver, Canada UNSW = University of New South Wales, Sydney, Australia USBR = United States Bureau of Reclamation USCS = Unified Soil Classification System     Acknowledgements     xv Acknowledgements I offer my sincere gratitude to my research supervisors Dr. Robert G. Millar and Dr. R. Jonathan Fannin for their patient guidance throughout this research. I am very grateful for the opportunity, and their continued encouragement and support of this challenging interdisciplinary research project.  I would like to extend my thanks to the faculty and staff of the Department of Civil Engineering and the School of Music for the opportunity to learn and teach at UBC. I would like to express my special thanks to Bill Leung, engineering technician at the Civil Engineering workshop, for his valuable time and help in building and setting up of lab equipment. His creative ideas and cheerful soul were always very much appreciated. I thank my fellow students for their friendship inside and outside the class room and laboratory. I always enjoyed the interesting vivid discussions and exchange of ideas.  I would like to express particular thanks to Dr. Colin D. Rennie of the University of Ottawa who provided the Ontario clay samples tested as part of this study, and to Dr. Kerry A. Mazurek and Daniel Cossette of the University of Saskatchewan for carrying out soil property tests and providing the soil property data for the Ontario clay samples.  I owe particular thanks to my colleagues at my former employer, Basler & Hofmann, Consulting Engineers AG, Switzerland, for their wide support during the course of this program, both financially and by providing me with valuable information to complete my studies. I am very grateful for the generous financial support received from the Pestalozzi-Stiftung, Switzerland, with special thanks to Käthi Schmidt and Barbara Schürmann. I am thankful for the financial assistance and support from Swiss Engineering STV, the University of British Columbia Faculty of Graduate Studies, and Swiss Association for Road and Transportation Experts (VSS).  My final and utmost thanks I owe to my family, especially my fiancée, who never stopped believing in me, and whose invaluable support and love inspired me each day and made sad days joyful.     Dedication     xvi Dedication    To Yvonne, my fiancée for her endless love and faith in me    Chapter 1. Introduction     1 1. Introduction 1.1. Background Hydraulic earth structures, which include dikes, levees, or dams, are used worldwide to restrict standing or flowing water within an assigned area. But the presence of water in such structures may cause severe damage that could lead to a failure of the structure, eventually resulting in the loss of lives and catastrophic damage. The three main mechanisms causing substantial damage are structural causes and slope instability, overtopping, and internal erosion (Table 1.1). The latter appears to be a main cause of dam instabilities. According to statistics by ICOLD (1995) and Foster et al. (2000a, 2000b), about 30-50% of failures and accidents affecting embankment dams are caused by piping as one of the fundamental types of internal soil erosion.   Table 1.1: Embankment-dam engineering and safety evaluation Primary causes of failures of embankments (ICOLD 1995)  Failure statistics for large dams (Foster et al. 2000a, 2000b) Mode of failure %  Mode of failure % Internal erosion (Piping) 31  Internal erosion (Piping) 48 - through embankment 17  - through embankment 31 - through foundation 14  - through foundation 15 - embankment to foundation ---  - embankment to foundation 2 Overtopping 33  Overtopping 46 Structural causes 26  Slope instability 4 Other causes 11  Earthquake 2   The term internal erosion is used herein to describe conditions where seepage flow from the reservoir erodes soil particles from within the structure and transports them downstream. Suffusion and piping are the two fundamental types of internal erosion (e.g. Wan and Fell 2002) and describe the manner in which eroded particles are transported downstream (Figure 1.1).  Suffusion, also referred to as internal instability, describes the selective erosion of fine particles which are removed through the constrictions between the larger particles. This process leaves behind an intact soil skeleton formed by the coarser particle fraction.  Piping involves the formation and development of a continuous tunnel or pipe within an earth structure through erosion of the surrounding soil material driven by a hydraulic gradient. Piping failure Chapter 1. Introduction     2 may occur in one of three modes (e.g. Foster et al. 2000a, 2000b), namely piping through the embankment, piping from the embankment to the foundation, and piping through the foundation (Figure 1.1). Fell et al. (2003) divided the process of internal erosion and piping into four phases; i) initiation of erosion, ii) continuation of erosion, iii) progression to form a pipe, and iv) formation of a breach. Piping may be initiated by means of backward erosion or concentrated leaks (e.g. Sherard et al. 1984; Sherard and Dunnigan 1985; Sherard 1986). Backward erosion usually commences at the downstream side where the hydraulic gradient is high enough to cause a displacement of soil particles, and progressively continues upstream. Concentrated leaks originate within the structure, and are caused by differential settlement (crack through core), hydraulic fracturing (crack jacked open by penetrating water), poor compaction (high permeable zone, e.g. around concrete structures or rock foundations), or digging animals and vegetation. Whether or not initiated erosion progresses and a final breach is formed depends on various factors (e.g. Fell et al. 2003), like hydraulic gradient (implied flow velocity and shear stress), the ability of the soil to sustain an open pipe, upstream conditions to provide crack filling material, downstream conditions to receive or stop eroded soil (filter design criteria, free opening), and the rate of enlargement of the hole (erosion resistance).    Figure 1.1: Internal erosion and piping process in earth dams Seepage through foundation embankment to foundation through embankment Suffusion Piping Chapter 1. Introduction     3 Internal erosion and piping are potentially extremely dangerous. There may be little or no external evidence that piping erosion has developed. Common signs are sand boils that may be hidden under water, or sinkholes at the crest of a dam. Sophisticated surveillance and monitoring pore pressures and seepage can help to warn about potential problems. In most cases however, early stages of internal erosion and piping are very hard to detect (Fell et al. 2003).  Internal soil erosion and piping are complex processes that are very difficult to describe by theoretical analysis, and are influenced by many hardly quantifiable factors. For this reason, various researchers have developed a number of tests to investigate internal erosion characteristics of soil, one of which is the Hole Erosion Test (HET). The HET is an accepted laboratory index test method, developed to study piping erosion in concentrated leaks in earth dams (Wan and Fell 2002, 2004a, 2004b). In the HET, a soil specimen with preformed axial hole is subjected to head-controlled flow, and measured hydraulic gradient and flow rate are used to indirectly determine the rate of enlargement of the idealized soil pipe.  The main advantages of the HET are that it is simple and straightforward to use, and that tests can be performed in an economical manner without the requirement for large amounts of soil. Thus, it has been applied in several research projects, and there is a growing data base for erosion characteristics of many different types of soil that will help to understand the relationship between basic engineering properties and erosion characteristics. However, the development of the HET is still a work in progress. Studies revealed various challenges and issues affiliated to the HET, including systematic differences between the HET and other commonly used erosion test methods (Lim 2006; Bonelli et al. 2006; Farrar et al. 2007; Bonelli and Brivois 2008; Wahl et al. 2008, 2009; Marot et al. 2011).   1.2. Objective and scope To tie in with U.S. Bureau of Reclamation’s goal to “quantify the HET for standardization so engineers now will have a readily available test for piping and internal erosion for risk analysis” (Farrar et al. 2007), the main objective of this study is to improve the test configuration and procedure, and to enhance the science-based framework for the interpretation of the Hole Erosion Test. Emphasis is placed on expanding the focus to fluid mechanics, which influences erosion mechanisms both within the soil specimen and at the upstream and downstream soil-water interface. This will increase the potential of obtaining more accurate results, implying possible applications of the HET beyond index testing.  Chapter 1. Introduction     4 Hydraulic effects and how they influence procedure and analysis of the HET will be investigated by means of a hydraulic review of the standard HET to identify problems and possible improvements that will guide the design and setup of a modified test apparatus. In question are in particular the interpretation of the hydraulic gradient, so far believed to be responsible for erosion, and velocity measurements with the potential to simplify the method of analysis. Laboratory tests not only on erodible soil specimens but also using a novel method by means of non-erodible test specimens to prove the applied changes will conclude this study.   1.3. Outline of the thesis The structure of this report is based on the type of the different investigations as part of this study, and is organized as follows:  Chapter 1: Introduction to the topic of internal soil erosion and piping, and description of the objective and scope of this study.  Chapter 2: A review of research literature dealing with surface erosion as the principal mechanism in piping with focus on the Hole Erosion Test (HET), as well as a concluding summary and outline of the research program.  Chapter 3: Description of the Modified Hole Erosion Test (HET-P), including a hydraulic review of the standard HET, followed by details about the modified design, setup, testing procedure, and two new energy based methods of analysis of HET-P test data.  Chapter 4: Research program, results and analysis, and discussion of findings from HET-P tests on three non-erodible test specimens as a novel approach to test the applicability of the modified apparatus and suggested methods of analysis.  Chapter 5: Research program and main findings from HET-P tests on two types of erodible soil specimens from four different origins, including a discussion of results and description of the soil samples used in this study.  Chapter 6: Conclusions and recommendations for further research based on the two completed series of laboratory tests presented in Chapter 4 and Chapter 5.   Chapter 2. Literature review     5 2. Literature review This chapter presents a review of research literature related to soil erosion characteristics with respect to laboratory tests to quantify critical shear stress and erosion rate for surface erosion. These types of tests can be grouped into the following categories: 1. Flow over surface; 2. Rotating cylinder; 3. Jet impact; 4. Flow through defect.  These four categories, and the related testing procedures, are summarized in the following sections 2.1, 2.2, 2.3, and 2.4, respectively. The main focus of the review, however, is on the Hole Erosion Test (HET), an erosion test of category 4, and its modifications, which is described comprehensively in Section 2.5. A final summary and outline of the research program is given in Section 2.6.  Various other test methods had been developed and used by researchers to simulate other soil erosion mechanisms, but were not meant to determine critical shear stress and erosion rate for surface erosion. These include, but are not limited to, dispersivity tests like the Pinhole Test (Sherard et al. 1976, ASTM D4647-06), the No Erosion Filter Test (NEF) in which dam core and filter materials are tested at the same time (Sherard and Dunnigan 1985, 1989; Foster and Fell 2001; Soroush et al. 2008, 2009), or other various methods of internal erosion tests by means of flow through intact soil samples using permeameter cells. They had been summarized extensively by others, and were not addressed in detail in this study.   Chapter 2. Literature review     6 2.1. Erosion tests category 1: Flow over surface - Gibbs (1962) - Lyle and Smerdon (1965) - Kandiah and Arulanandan (1974) - Arulanandan and Perry (1983) - Shaikh et al. (1988a, 1988b) - Ghebreiyessus et al. (1994) - Briaud et al. (1999, 2001) - Ravens and Gschwend (1999) - Zhang et al. (2003) Figure 2.1: Schematic diagram flow over surface  This category comprises test methods for investigating surface erosion in river channels or unlined canals, where water is flowing parallel to the soil surface at a certain speed and depth. This erosion mechanism is modelled using hydraulic flume tests, where the specimens are placed on the flume bed and subjected to open channel flow. Erosion rate is mostly only visually observed and described, while hydraulic shear stress on the soil surface is deduced from flow velocity and water depth. While this test is relatively simple, it requires large equipment and suffers from a lack of reproducibility because of difficulties in controlling surface and soil properties.  Various criteria were developed to describe and evaluate erosion resistance of soil based on Atterberg limits (Gibbs 1962; Lyle and Smerdon 1965), gradation (Gibbs 1962; Shaikh et al. 1988a), void ratio (Lyle and Smerdon 1965), water content (Kandiah and Arulanandan 1974; Shaikh et al. 1988a), critical shear stress (Arulanandan and Perry 1983), chemistry (Kandiah and Arulanandan 1974; Shaikh et al. 1988b), or bulk density (Ghebreiyessus et al. 1994).  Flume tests have also been used to compare test results with other test methods like the Rotating Cylinder Test (RCT). Kandiah and Arulanandan (1974) showed that the two tests produce similar critical shear stresses, but different erosion rates. Others compared reconstituted and undisturbed soil samples, showing that reconstituted specimens are less erosion resistant than undisturbed samples (Zhang et al. 2003).  Special types of flow over surface type of tests are the Erosion Function Apparatus (EFA) developed by Briaud et al. (1999, 2001) to test undisturbed thin wall tube specimens, or portable flume tests for in-situ measurements (e.g. Ravens and Gschwend 1999). Chapter 2. Literature review     7 2.2. Erosion tests category 2: Rotating cylinder - Moore and Masch (1962) - Masch et al. (1963) - Arulanandan et al. (1973, 1975) - Kandiah and Arulanandan (1974) - Sargunan (1977) - Arulanandan and Perry (1983) - Chapuis (1986a, 1986b) - Chapuis and Gatien (1986) - Lim (2006) Figure 2.2: Schematic diagram rotating cylinder  The several designs of erosion test apparatus for measuring erosion resistance of cohesive soils using a rotating cylindrical fluid chamber are known as Rotating Cylinder Test (RCT). A soil specimen is submerged and suspended inside the rotating cylindrical chamber. The chamber is rotated relative to the soil specimen, which induces a flow around the specimen that applies shear stress to the soil surface. Shear stress is deduced from the measured torque applied to the stationary specimen. The most recent methods also allow for measurement of erosion rates by removing the eroded material from the rotating chamber, and weighing the oven-dried mass. The RCT is difficult to perform, and the apparatus is costly, but it provides accurate measures of erosion parameters (Lim 2006). However, test results are influenced by the way the specimen is prepared as different sample preparation methods may yield a different surface roughness of the specimen (Chapuis 1986a, 1986b).  The RCT was originally developed by Moore and Masch (1962) and Masch et al. (1963), and similar designs have been used by others (see above). Chapuis (1986a, 1986b) and Chapuis and Gatien (1986) developed a more advanced design that allowed testing both reconstituted as well as undisturbed soil specimens, and more accurate measurement of erosion rates. Most recent, Lim (2006) designed and used a more elaborate apparatus, which allowed for accurate shear stress measurement, and easier control of the testing process. Lim (2006) also compared RCT results with HET results, which is described in Section 2.5.5 below.    Chapter 2. Literature review     8 2.3. Erosion tests category 3: Jet impact - Dunn (1959) - Moore and Masch (1962) - Hanson (1991, 1992) - Hanson and Robinson (1993) - Hanson and Simon (2001) - Hanson and Cook (2004) - Hanson and Hunt (2006) - Wahl et al. (2008, 2009) - Marot et al. (2011) Figure 2.3: Schematic diagram jet impact  Jet erosion tests are primarily designed to simulate erosion of spillway channels from a submerged jet. The Jet Erosion Test (JET) – also called Submerged Jet Erosion Test – uses a nozzle positioned above the center of the submerged specimen to produce a jet perpendicular to the soil surface. The jet, driven by a constant water head, applies a shear stress to the soil surface, which in turn experiences scouring. The measured geometry of the produced scour is used to determine both shear stress and erosion rate, which are used for qualitative classification of the erodibility of soils. The JET is relatively easy and straight forward to perform, and can be carried out on a wide range of cohesive soils.  Dunn (1959) first proposed the use of the JET before Moore and Masch (1962) used the JET and RCT in their research on cohesive soils. Hanson and his companion researchers further developed the JET, which has become an ASTM standard (ASTM D5852-00). Hanson et al. (see above) developed advanced and simplified designs to carry out in-situ and laboratory tests using reconstituted or undisturbed tube samples.  Wahl et al. (2008, 2009) used the JET in their research at the United States Bureau of Reclamation (USBR), which is developing tools for risk evaluation of piping and internal erosion (Farrar et al. 2007). They have compared the JET with the Hole Erosion Test (HET), showing that the two tests yield different results for shear stress and soil erodibility classification. Based on this work, Marot et al. (2011) developed a new energy based method to obtain a unique soil erosion classification for HET and JET.   Head ASTM D5852-00 Chapter 2. Literature review     9 2.4. Erosion tests category 4: Flow through defect - Christensen and Das (1973) - Hjeldnesa and Lavania (1980) - Lefebvre et al. (1985, 1986) - Rohan et al. (1986) - Wan and Fell (2002, 2004a, 2004b)     Figure 2.4: Schematic diagram flow through defect  Flow through defect erosion tests were categorized as internal erosion tests, and were set out to simulate conditions along a crack or any other flow path in an earth structure. These types of tests involve an undisturbed or reconstituted soil specimen in which a preformed defect is introduced prior to testing. The prepared specimen is then subjected to head or flow rate controlled pressure flow, while the hydraulic conditions are monitored in order to determine shear stress and erosion rate.  Various methods have been suggested to model the defect and monitor hydraulic conditions. Christensen and Das (1973) used a 3 mm thick soil lining inside a brass tube to investigate the relation between erosion rate and critical shear stress. Another method was developed by Hjeldnesa and Lavania (1980), who formed a crack by applying tension to the soil specimen. But the use of this method was very limited since the dimensions of the crack were not determined.  Lefebvre et al. (1985) and Rohan et al. (1986) presented a more sophisticated device, the Drill Hole Test (DHT). They applied a flow rate controlled pressure flow to a cylindrical clay sample with a predrilled axial hole. The friction head loss along the specimen was measured to determine shear stress, and any eroded material was collected in a downstream sedimentation tank to calculate erosion rate. Using the DHT, Lefebvre et al. (1986) showed that naturally structured clay was highly erosion resistant and considerably less erodible than de-structured and reconstituted specimens.  Wan and Fell (2002, 2004a, 2004b) developed two head controlled devices, the Slot Erosion Test (SET) and Hole Erosion Test (HET). The two tests are based on the same concepts, which are comprehensively explained for the HET in Section 2.5. The SET used a larger 1 m long reconstituted soil specimen with preformed slot along the side rather than in the center of the specimen. Head Chapter 2. Literature review     10 2.5. Hole Erosion Test (HET) The Hole Erosion Test (HET) was developed at the University of New South Wales (UNSW) as an index test to model piping erosion in concentrated leaks in earth dams (Wan and Fell 2002, 2004a, 2004b). It is generally a faster and more economical alternative to the Slot Erosion Test (SET) mentioned above with the goal to study relationships between basic engineering properties and erosion characteristics of different types of soil. It allows testing of a much smaller soil specimen at lower water heads. In a HET, a reconstituted soil specimen with predrilled axial hole is subjected to a constant-head pressure flow. Erosion rate and shear stress are determined using measured flow rate, hydraulic gradient, and final hole diameter. With most emphasis on the rate of erosion rather than critical shear stress, test soils are characterized by a soil group number, which typically ranges from 1 (extremely rapid erosion) to 6 (extremely slow erosion) (Wan and Fell 2002, 2004a, 2004b).  Further work at UNSW (Lim 2006) and the United States Bureau of Reclamation USBR (Farrar et al. 2007; Wahl et al. 2008, 2009) yielded technical improvements to the test apparatus and procedure, and interpretation of test data. French researchers also developed a non-dimensional numerical model for the interpretation of HET data, which simplifies post-test measurements and data analysis (Bonelli et al. 2006; Bonelli and Brivois 2008). Most recently, Marot et al. (2011) developed an energy based model for providing a unique erodibility ranking for different erosion tests.   2.5.1. UNSW Hole Erosion Test (HET) In a standard HET, a soil specimen is reconstituted by compaction inside a standard compaction mold at 95% maximum dry density and optimum water content. These properties are standardized because test results are strongly influenced by the degree of compaction and water content (Wan and Fell 2002, 2004a, 2004b). An axial hole with diameter o = 6 mm is drilled prior to testing. The specimen is subjected to a constant-head pressure flow (Figure 2.5). The hydraulic head difference, h , over the length of the soil specimen, L , describes the hydraulic gradient, s , which is increased stepwise until progressive erosion (enlargement) of the hole is produced. Ideally, the upstream head is initially set to a height where progressive erosion immediately starts. But choosing an appropriate upstream head requires a few trial test runs. Once progressive erosion is produced, the upstream head remains constant until the end of the test. A test is stopped before the eroded hole expands to the side of the mold, or the maximum available flow rate is reached. During a standard HET, the hydraulic gradient across the specimen, s , and flow rate, Q , are measured at select time intervals. After the test, the size and shape of the eroded hole is carefully recorded, and a final hole diameter, f , representative of the entire length of the eroded axial hole is defined. Chapter 2. Literature review     11  Figure 2.5: Schematic diagram Hole Erosion Test HET (adapted from Wan and Fell, 2004)   Measured hydraulic gradient across the soil specimen and flow rate are used to indirectly determine the erosion rate per unit surface area,       , and wall shear stress along the axial hole,      , at any time during the test. A plot of        versus      (Figure 2.6) is then used to graphically determine critical shear stress, c , coefficient of soil erosion, Ce , and erosion rate index,      , presuming:    Equation (2.1a) expresses soil erodibility in terms of erosion rate when the applied shear stress exceeds the critical value. The rate of mass removal per unit surface area to represent the erosion rate is considered most appropriate because porosity and density of the soil material is taken into account. The coefficient of soil erosion is defined as the slope of the linear best-fit line where both        and       increase. Critical shear stress describes the ease of erosion and has the physical meaning of the value of shear stress at which erosion starts. It is defined as the x-intercept of the extrapolated linear best-fit line as illustrated in Figure 2.6. (2.1) Q L Eroding fluid circulation system H yd ra u lic  h ea d  d if fe re n ce ,  h  =  h u  -  h d  (5 0 -1 2 0 0 m m ) Upstream flow chamber filled with 20-mm gravel Downstream flow chamber, empty Compacted soil specimen with 6 mm axial hole Two vertical piezometer tubes, connected to sidewall of flow chambers, providing hydraulic head upstream, hu , and downstream, hd Constant head tank, adjustable in height 50 mm diameter pipe     Chapter 2. Literature review     12  Figure 2.6: Typical results Hole Erosion Test (schematic, no real test data)   The erosion rate index, IHET , defined in equation (2.1b) was introduced instead of Ce , which usually is a small number ranging from 10 -1  to 10 -6 . Typical values of IHET  range from 0 to 6, where a low value indicates a soil that erodes more rapidly than a soil with a higher value. Test soils are classified into six groups based on their representative erosion rate index, which describes the standardized value of IHET  at 95% maximum dry density and optimum water content (Table 2.1).   Table 2.1: Qualitative relation of representative erosion rate index and progression of internal erosion (Wan and Fell 2002, 2004a, 2004b) Group number Erosion rate index, IHET Progression of internal erosion 1 < 2 Extremely rapid 2 2 – 3 Very rapid 3 3 – 4 Moderately rapid 4 4 – 5 Moderately slow 5 5 – 6 Very slow 6 > 6 Extremely slow  0.000 0.001 0.002 0.003 0.004 0.005 0.006 0.007 0.008 100 150 200 250 300 350 400 Es ti m at e d  e ro si o n  r at e  p e r u n it  s u rf ac e  a re a o f th e  h o le , e ̇ HE T [k g/ s/ m 2 ] Estimated wall shear stress, HET [N/m 2] Coefficient of soil erosion, Ce defined as the slope of the linear best-fit line: Ce = 3.96E-5 s/m Erosion rate index, IHET = -log10(Ce) : IHET = 4.4 Critical shear stress, c defined as the x-intercept of the linear best-fit line: c = 190 N/m 2 Early stage: disturbed and loose material is removed. Later stage: both e ̇HET and HET are increasing. 4 22 t wHET tdtd HET gs tdt d    e     Chapter 2. Literature review     13 2.5.2. HET theory The underlying theory to derive shear stress is based on the force equilibrium on the body of eroding fluid along a differential length of an axial circular hole:   where:    = retaining force, N    = forcing force, N  = hydraulic shear stress along wetted area, N/m 2  P =  = wetted perimeter ≡ circumference of circular cross section, m  = hole diameter, m L = length of axial hole, m   = cross-sectional area of axial hole, m2 p = fluid pressure, N/m 2   In a uniform circular cross section with fully developed flow, the differential pressure    along can be expressed by the energy head loss due to wall friction, or friction head loss,     :   where: g = specific weight of eroding fluid, N/m 3   Combining equations (2.2) and (2.3) gives                   The term       in equation (2.4) is called hydraulic radius, and is equal to           for a circular cross section. Equation (2.4) is integrated over the total length of the soil specimen by introducing the following assumptions: 1. Flow through the soil matrix is negligible; 2. Only the soil surface along the preformed hole provides shear resistance; 3. Energy losses due to the eroding fluid entering and exiting the preformed hole are negligible; 4. Uniform circular cross section along the length of the soil specimen; 5. Fully developed flow profile in the preformed hole throughout the length of the soil specimen; 6. Hydraulic head difference across the soil specimen, h , equals total friction head loss, hf . (2.2) (2.3) (2.4) Chapter 2. Literature review     14  For a given diameter, the shear stress is then directly proportional to the friction head loss along the length of the soil specimen, which is represented by the hydraulic gradient across the soil specimen:                   where: HET = estimated wall shear stress along axial hole, N/m 2  w = density of water used as eroding fluid, kg/m 3  g = acceleration of gravity, m/s 2  t = estimated mean diameter of axial hole, m L = length of axial hole, m s = hydraulic gradient across the soil specimen in standard HET hu = measured upstream sidewall hydraulic head, N/m 2  hd = measured downstream sidewall hydraulic head, N/m 2   Further, the erosion rate per unit surface area is given by:                  where:   = erosion rate per unit surface area, kg/s/m2 d = dry density of the soil, kg/m 3        = change in cross-sectional area with time, m2/s        = change in diameter with time, m/s        = change in diameter t  over a short time interval t , m/s  Equation (2.7) makes use of the following two additional approximations: 7. The change in radius             , which yields           and thus          ; 8. The derivative          can be approximated by         ;   (2.5) (2.6) (2.7) Chapter 2. Literature review     15 2.5.3. HET data analysis Both shear stress,      , and erosion rate,       , depend on the diameter of the preformed and eroded axial hole, t , which cannot be measured directly during a HET, and has to be indirectly estimated from the measured flow rate, Q , and hydraulic gradient, s . It is assumed that the change in diameter correlates to the change in assumed friction factors, fL  and fT , which are based on continuity and known common relations between shear stress,  , and velocity, V, for laminar and turbulent flow conditions:            Equations(2.5), (2.8), (2.9), and (2.10) can be combined to:            Since diameter and flow conditions are known for both the beginning and the end of a test, the initial and final friction factors can be determined, and interpolated over time to estimate diameter at any particular time t during a HET:                The flow conditions to determine whether Equation (2.12a) or (2.12b) will be used, are governed by the Reynolds number, Re :      where: Vt = estimated mean flow velocity in axial hole, m/s  = kinematic viscosity, m 2 /s (water at 20°C:  = 1.004E-06 m 2 /s)  (2.8) (2.9) (2.10) (2.11) (2.12) (2.13) Chapter 2. Literature review     16 Flow is laminar below a critical value of Re , defined below. For the use in HET, flow is considered turbulent if the Reynolds number exceeds this critical value.  The above analytical solution to analyze HET data requires the following additional assumptions and approximations: 9. Shear stress is proportional to V 2  in turbulent flow conditions; 10. Pure laminar or turbulent flow throughout the entire test; 11. Friction factor fL or fT is linearly interpolated between its initial (t = 0) and final value (t = tf); 12. Flow conditions are turbulent if Reynolds number Re > 5000; 13. The measured final hole diameter, f , is representative of the entire length of the eroded hole.   The complete analysis of HET data involves the following steps: i) Define initial and final flow conditions using Equations (2.8) and (2.13), and identify a representative flow condition (laminar or turbulent) to be used for this test; ii) Estimate the initial friction factor fL,o  or fT,o  based on the initial diameter of the preformed hole, o = 6 mm, using Equation (2.11); iii) Estimate the final friction factor fL,f  or fT,f  based on the measured final diameter of the eroded hole, f , using Equation (2.11); iv) Interpolate the friction factor fL  or fT  linearly between its initial (t = 0) and final value (t = tf); v) Estimate the diameter of the axial hole, t , at any time during the test using Equation (2.12); vi) Plot a curve of estimated diameter, t , against time, t ; vii) Estimate the slope         , if appropriate approximated by         ; viii) Estimate wall shear stress, HET , using Equation (2.5); ix) Estimate erosion rate ,      , using Equation (2.7); x) Plot        against HET , and fit a linear straight line through the rising part of the curve; xi) Determine coefficient of soil erosion, Ce , and erosion rate index, IHET , using Equation (2.1); xii) Graphically obtain critical shear stress, c , as illustrated in Figure 2.6.    Chapter 2. Literature review     17 2.5.4. Modifications to the HET Lim (2006), University of New South Wales UNSW Lim (2006) noted some problems with the Hole Erosion Test during his PhD work at UNSW. The preformed hole was introduced by drilling. It was observed that this method can lead to smearing and remoulding of the surrounding soil, which lead to a denser surface layer and a higher critical shear stress. Compaction of the soil into the test mold introduced inhomogeneity that could lead to vertical layering with different densities. Both of these problems eventually lead to delayed erosion that affected test results. Another problem was the effects of slaking, where soil particles detached from the specimen due to the presence of water (hydrostatic conditions), rather than the applied shear stress. This lead to a reduced hole length and difficulties defining a representative final hole diameter. To avoid these problems, Lim (2006) proposed modifications to: 1. the estimation of friction factors fL  and fT ; 2. the specimen preparation; 3. the interpretation if a test was affected by slaking.  It was found that the friction factors fL  and fT do not vary linearly with time, and a better correlation was found between the friction factor and diameter. It was assumed that the friction factors are linearly proportional to the diameter of the eroded hole. However, this implied practical difficulties because the diameter is not known until the analysis is complete. An iterative predictor approach was thus adopted, introducing new assumptions and complexity to the analysis. It is further proposed herein that a better correlation between friction factors and diameter can be assumed since diameter is used to calculate friction factors (Equation (2.11)).  With respect to specimen preparation, it was recommended to increase the number of compaction layers to produce a more homogeneous test specimen. To reduce the effect of remoulding during drilling of the preformed hole, it was further recommended to use a slowly penetrating and sharp auger drill. Emphasis was also placed on measuring the final hole diameter as precisely as possible, since this measurement is crucial for the estimation of shear stress.  The effect of slaking and the resulting reduced hole length was investigated in terms of estimated wall shear stress. It was found that small reductions of the hole length up to about 20 mm can be ignored. Ignoring slaking up to about 40 mm resulted in minor errors of less than 10% for the estimated wall shear stress, and negligible errors for the HET erosion rate index. Lim (2006) proposed a method to correct for slaking if the amount was more than 40 mm. However, it is questionable how representative a HET would be if almost half of the soil specimen is lost by failing mechanisms under hydrostatic conditions. Chapter 2. Literature review     18 Farrar et al. (2007), Wahl et al. (2008, 2009), the United States Bureau of Reclamation USBR The Hole Erosion Test was further studied at the United States Bureau of Reclamation USBR (Farrar et al. 2007; Wahl et al. 2008, 2009). During the research program at USBR, the apparatus and data collection procedures proposed by Wan and Fell (2002, 2004a, 2004b) were considerably improved: - Flow rate was measured by a custom 10° v-notch weir at the downstream end of the setup; - Automated head measurements upstream and downstream of the soil specimen, as well as at the v-notch weir using pressure transducers and computerized data acquisition system with recording intervals of 5 s throughout a test; - High-head HET setup to produce test heads of up to 5400 mm; - Successively doubled test head during a HET until progressive erosion was observed, starting at a low test head of usually 50 mm.  The USBR further defined 5 major issues affecting the HET interpretation: 1. Identification of erosion regimes; 2. Curve fitting procedures; 3. Laminar versus turbulent flow; 4. Variation of friction factors; 5. Determination of final hole diameter and length.  Progressive erosion was indicated by an accelerating flow rate at a constant test head. The USBR emphasized that only data collected during the period of progressive erosion should be considered in the data analysis to determine erosion parameters. Data collected prior to progressive erosion described the removal of disturbed and loose material, and were not useful for defining erosion characteristics of the intact soil.  The development of the hole diameter, t , during progressive erosion was assumed to follow a polynomial function, whose time derivative defines the erosion rate,       , as shown in Equation (2.7). The degree of the fitted polynomial curves varied between different types of soils. To find the coefficient of soil erosion, Ce , from the             plot, another linear curve fitting was necessary. This need for data smoothening and adjustment adds complexity to the analysis procedure.  The USBR reported difficulties in justifying the use of the “virtual” friction factors fL and fT introduced by Wan and Fell (2002, 2004a, 2004b) in regards of flow conditions. They also questioned the high critical Reynolds number of Re,crit = 5000 used at the UNSW. They declared flow conditions as turbulent if Reynolds number Re > 2000, as it is widely recognized in traditional fluid mechanics.  Chapter 2. Literature review     19 Friction factors were assumed to vary linearly with time. This could cause erroneous results, especially if a test was started at a low head. In such cases, erosion was computed in the early stage of a test, even though there was no observable sign of erosion. Also irregularities in computed hole diameter suggested that the friction factors were incorrectly modeled. An independent investigation of this problem revealed a better relationship between the friction factor and estimated hole diameter, similar to the findings of Lim (2006). But the iterative solution method used by the USBR to determine friction factors and hole diameter showed problems obtaining convergence. Thus, this method was simplified by assuming that friction factors vary in proportion to             for laminar flow and              for turbulent flow. These terms are substitutes for the hole diameter, t .  Also the USBR experienced difficulties in measuring the final hole diameter due to irregularities of the eroded hole. These were observed especially at the entrance and exit of the soil specimen. These points are prone to slaking and scouring due to eddies at the soil interface. To reduce these problems, they introduced end plates with an orifice opening of 15 mm for stronger soils or 25 mm for weaker soils. Unfortunately this method was less effective than expected. They also investigated several methods to measure the final hole diameter, including measurements from plaster castings of the eroded hole. To account for the changing length of the eroded hole in some tests, they assumed that the length of the eroded hole varies linearly with time.   Bonelli et al. (2006), Bonelli and Brivois (2008), Cemagref, France French researchers around Stéphane Bonelli developed a universal erosion model for permanent flow over erodible soil. They adapted their model for piping erosion to be applicable to the Hole Erosion Test by spatial integration of the system over a cylindrical volume representing the axial hole. It provides an alternative method for analysing HET data, which allows the determination of the estimated erosion characteristics without the need of measuring and interpolating the hole diameter. This non-dimensional numerical model correlates a dimensionless hole radius with critical shear stress, hydraulic gradient, and a dimensionless test time. It has only two unknown parameters that can be solved with a simple non-linear numerical solver. The model is promising, but the list of assumptions and limitations restricts its applicability to tests with (not conclusive): - constant pressure drop (constant test head and hydraulic gradient); - turbulent flow conditions (large Reynolds numbers); - no variation of the friction factor; - constant length and uniform diameter of the eroded axial hole; - test heads exceeding critical shear stress, c ; - data only collected during progressive erosion period. Chapter 2. Literature review     20 Marot et al. (2011), Université de Nantes and the United States Bureau of Reclamation USBR The Université de Nantes in collaboration with the USBR developed a new method to analyze HET and Jet Erosion Test (JET) data based on fluid energy dissipation and measurement of eroded mass to provide a unique erodibility classification of test soils. In HET, energy dissipated by erosion (friction head loss) is correlated with measured hydraulic gradient and flow rate. An energy balance equation for the fluid was applied between the upstream and downstream point where the hydraulic heads are measured at the sidewall of the flow chamber (Figure 2.5). It takes into account minor head losses due to fluid entering (flow contraction) and exiting (flow expansion) the axial hole, and assumes same average velocities in both measuring sections. It was thus assumed that the hydraulic head difference across the soil specimen, h , equals total energy head loss, which is the sum of friction and minor energy head losses. Based on a series of HET on a non-erodible poly-acrylic model of the specimen with predrilled 6-mm hole, an empirical constant was determined to isolate unknown friction head losses responsible for erosion. It was found that, for this particular hole diameter, only about 25% of the measured hydraulic head difference across the soil specimen, h , is due to wall friction.   2.5.5. Main findings and conclusions Wan and Fell (2002, 2004a, 2004b), University of New South Wales UNSW Wan and Fell (2002, 2004a, 2004b) did extensive tests on 13 different soil samples covering a range of soil properties and origins. Most soils were from borrow areas used for dam construction in Australia, but also included one each from the USA and New Zealand. The utility of the HET was demonstrated by a total of 225 HET’s carried out in this research program. It was found to be fast, simple, and easy to reproduce under identical test conditions.  They found that fine-grained and some plastic soils are more erosion resistant than coarse- grained non-plastic soils and soils with low plasticity. Most of the soils showed higher erosion resistance if they were compacted to the wet side of optimum water content and a higher dry density. Results further suggested that the mineralogy, especially iron oxides content, plays an important role regarding erosion resistance of a soil.  They suggested using an initial shear stress, o , rather than critical shear stress, c , in order to describe initiation of erosion. Results of critical shear stress were mostly scattered, possibly due to extrapolation of data, observed non-linearity in the coefficient of soil erosion, and other simplifications and assumptions in the process of data analysis. The initial shear stress, o , refers to the shear stress corresponding to the minimum water head at which erosion is first initiated. It is obtained experimentally by multiple HET trial runs on identical test specimens. Chapter 2. Literature review     21 Wan and Fell (2002, 2004a) further proposed predictive equations to estimate the HET erosion rate index, IHET , based on multiple linear regression models obtained from statistical analysis of HET data. They are not presented herein because it was recommended to use them with great caution as they are based on a limited number of soils, and may not imply any strong relationship between the erosion rate and the predictor variables.  In summary, the HET was considered a simple and rapid index test, but one that does not intend to provide accurate quantitative measurements since all derived erosion parameters are indirectly estimated from a few measured hydraulic parameters.   Lim (2006), University of New South Wales UNSW Lim (2006) conducted a total of 139 HET’s at the UNSW on 9 natural clay soils and 5 engineered artificial soil mixtures. The main findings were similar to those by Wan and Fell (2002, 2004a, 2004b). A distinction was made between dispersive and non-dispersive erosion. Dispersive erosion, indicated by dirty or cloudy outflow, was characterized by immediate erosion and fast enlargement of the hole, implying considerable erosion at small shear stress. These soils were rarely affected by effects of slaking, and erosion occurred evenly over the surface of the axial hole. Non-dispersive soils, on the other hand, experienced severe slaking and reduction of the hole length, and the shape of the eroded hole was usually irregular. Lim (2006) also claimed that the HET provides limited information about the erosion behaviour of clay soils due to the reported deficiencies. A comparison with Rotating Cylinder Test (RCT) results further revealed that the erosion rate indices from HET were significantly higher than those from the RCT for non-dispersive soils, indicating slower erosion and higher shear stresses.   Farrar et al. (2007), Wahl et al. (2008, 2009), the United States Bureau of Reclamation USBR The USBR tested a total of 10 soil samples. Test specimens were either reconstituted or undisturbed. They claimed the HET to be difficult and less reproducible, especially for weak and very strong soils, while it was good for intermediate soils. Collapsing and scouring were the main problems in weak soils, while clogging of the axial hole and insufficient test head limited the success rate in testing strong soils. These problems often lead to subjective interpretations and combinations of analysis methods. They introduced a subjectivity index to quantify the level of uncertainty in test results. It ranges from 0 to 3, with low values indicating high confidence in test results. They further compared HET with Jet Erosion Test (JET) results. The JET indicated lower erosion resistance for all test soils, including critical shear stresses that were as much as an order of magnitude smaller than those from HET. With reference to Lim (2006), it was noted that differences between HET and JET are of a similar order of magnitude as between HET and RCT. Chapter 2. Literature review     22 Bonelli et al. (2006), Bonelli and Brivois (2008), Cemagref, France The numerical model developed by Bonelli et al. (2006) was tested on 17 (18 in Bonelli and Brivois, 2008) HET data sets from 9 different soil samples collected by Wan and Fell at the University of New South Wales. Despite the many simplifying assumptions, they showed good agreement between the analytical solution proposed by Wan and Fell (2002, 2004a, 2004b) and the new numerical solution. This method was also successfully applied by the USBR (Farrar et al. 2007; Wahl et al. 2008, 2009) and Marot et al. (2011), solely or in combination with the analytical solution. Recognizing that the model is based on even more restrictive assumptions than the analytical solution, and that it only considers processes within the cylindrical volume of the eroded hole, it deals with similar issues as the analytical solution.   Marot et al. (2011), Université de Nantes and the United States Bureau of Reclamation USBR The motivation for the new energy-based method developed by Marot et al. (2011) to obtain a unique soil erosion classification for HET and JET was based on observed differences between the two tests. Consistent with previously reported data by the USBR (Farrar et al. 2007; Wahl et al. 2008), results from 17 paired HET and JET tests on seven different soil samples with a large range of erodibility showed that erosion rate indices from HET were consistently larger than those from JET, and that critical shear stresses from JET were on average about 50 times smaller than those from HET. Thus, the two tests yielded different soil classifications. Based on the new method, Marot et al. (2011) introduced an erosion resistance index,    , used for soil erodibility classification similar to the classification system proposed by Wan and Fell (Table 2.1). Test soils are classified into six categories of soil erodibility, ranging from highly erodible for      , to highly resistant for      .They showed that the new energy based method applied to the 17 paired tests yields the same soil classification for both the HET and JET. However, it is important to note that this method only provides an erosion resistance index for soil erodibility classification, and no absolute values of erosion rate and, more importantly, critical shear stress.    Chapter 2. Literature review     23 2.6. Summary and outline of the research program After the development of various field and laboratory tests to investigate different mechanisms of soil erosion, the Hole Erosion Test (HET) was developed as a simple and economical laboratory test to simulate soil erosion in a crack or pipe within an earth dam. Understanding the mechanisms involved in the HET is a work-in-progress. After the development and first improvements of the HET at the UNSW, the USBR automated and further improved the test, and also applied it in several cases. Bonelli et al. added a mathematical background to the more pragmatic approach, while Marot et al. introduced an energy-based method for providing a unique soil erosion ranking to be comparable with JET. Extensive testing had been done using the HET with various attempts to improve specimen preparation, testing and analysis procedures. Table A.1 in Appendix A provides a compiled list of challenges and issues affecting the HET and offers suggestions how they might be addressed.  Most of this work focused on the behaviour of the axial hole, with the boundaries set at the soil- water interface upstream and downstream of the test specimen. However, the HET involves more considerations. The specimen is placed inside a hydraulic pipe system that interacts in more ways than just applying a shear stress to the soil specimen. There is a need to combine soil and fluid mechanics, and investigate the interacting mechanisms involved. Furthermore, very limited testing has been done under controlled and steady flow conditions on non-erodible materials as a reference to support findings from HET. The main question to be asked is:  Are measurements and what they represent in the standard HET influenced by any hydraulic effects not captured in the current methods, and how could they be further improved?  The only measurements recorded during a HET are the hydraulic gradient, s , and flow rate, Q . Since flow rate is usually measured at the downstream end of the system, it is most likely unaffected by any local hydraulic effects. The hydraulic gradient, on the other hand, involves hydraulic head measurements (Figure 2.5) that are affected by local turbulences, such as eddy formations due to a change in flow area downstream of the soil specimen. The resulting wall shear stress, HET , will be directly affected, if the hydraulic heads, and thus the hydraulic gradient, were in fact erroneous (Equation (2.5)).  This question is supported by various researchers as described above (Lim 2006; Farrar et al. 2007; Wahl et al. 2008; Marot et al. 2011), who compared HET data with other surface erosion tests like the Jet Erosion Test (JET) and Rotating Cylinder Test (RCT). All reported results agree that standard HET generally produces higher erosion indices, and overestimates critical shear stress by up to an order of magnitude or more. Given that all these tests were designed for similar purposes, Chapter 2. Literature review     24 reasons for this behaviour were generally assumed to be in conceptual differences between the compared tests, like the manner of hydraulic attack, geometric factors, and methods to measure or estimate erosion parameters.   2.6.1. Outline of the research program The main objectives of this research program were to investigate hydraulic effects and how they influence data collection and analysis of the Hole Erosion Test, and to use these findings to improve the testing procedure and analytical solution. This research consisted of the following four main parts:  1. Hydraulic review of the standard HET to identify problems and possible improvements; 2. Design and setup of a modified test apparatus incorporating suggested improvements; 3. Laboratory calibration and applicability tests using non-erodible PVC specimens; 4. Modified Hole Erosion Tests on reconstituted and undisturbed erodible soil samples.  A critical hydraulic review was conducted on the whole system with focus on the test cell including test specimen and adjacent flow cambers (Figure 2.5). Hydraulic effects upstream and downstream of the soil specimen were analysed to identify possible influences on measurements and interactions with the soil specimen. The review was restricted to the ideal case of a test specimen with a straight axial hole of uniform circular cross section.  Based on findings from the hydraulic review, improvements to the test apparatus were implied in a modified design with additional measurements, accompanied by an improved and simpler method to analyse HET data (analytical solution). The modified design was used in subsequent laboratory experiments to test the proposed modifications.  The first set of laboratory experiments was conducted on non-erodible PVC specimens with axial holes of different diameter. They were used to simulate various stages in a HET under controlled and steady flow conditions. This assured a robust framework to test the modified test apparatus and analysis procedure. Details of these tests are given in Chapter 4 below.  To demonstrate its applicability to soils testing, reconstituted and undisturbed soil samples from different Canadian sites were tested in a final set of laboratory experiments using the modified test apparatus. The improved method of analysis was used in conjunction with the originally proposed analytical solution to identify advantages and weaknesses of the Modified Hole Erosion Test (HET-P). Chapter 5 presents the details and findings from this set of tests. Chapter 3. Modified Hole Erosion Test (HET-P)     25 3. Modified Hole Erosion Test (HET-P) This chapter presents details about the Modified Hole Erosion Test (HET-P) that was developed and used in this study. A hydraulic review of the standard HET is presented in Section 3.1, describing shortcomings and suggested improvements of the standard test method. Section 3.2 describes the design of the modified HET-P apparatus based on findings of the hydraulic review. The experimental setup and test procedure of the HET-P is outlined in Section 3.3, including calibration of instruments and test preparation. Two modified energy gradient-based analysis methods for HET-P test data are introduced in Section 3.4.   3.1. Hydraulic review of the HET 3.1.1. Friction head loss and hydraulic gradient Head loss due to wall friction is defined as the difference in total energy head across a uniform test section (Bernoulli’s theorem, Equation (3.1)). The HET assumes that the friction head loss along the axial hole, hf , is represented by the hydraulic gradient across the specimen, s , determined by the difference between the hydraulic heads measured at the sidewall of the flow chamber just upstream and downstream of the test specimen (Equation (2.5) and (2.6)). This approach is commonly used in testing porous media, such as in the Gradient Ratio Test (ASTM D5101-01 2006), where velocity heads, V 2  / 2g , are small and can be ignored because the energy grade line (EGL) and hydraulic grade line (HGL) remain parallel. As assumed by Marot et al. (2011) for the HET, this approach can also be used in applications with similar velocities in both measuring sections, where the velocity heads upstream and downstream are of equal value (Vu 2  / 2g ≈ Vd 2  / 2g), and the EGL and HGL have similar slopes. In both cases, the difference between the sidewall hydraulic heads upstream and downstream does provide a good measure of total energy head losses along the test section.  However, in the HET this approach is questionable for a number of reasons. Firstly, it is well known from pipe-flow hydraulics (e.g. see Orifice Meter, Finnemore and Franzini 2002, p. 522) that an abrupt expansion, such as on the downstream side of the specimen in a HET, leads to flow recirculation and a reduction in the hydraulic head, hd , measured at the sidewall (Figure 3.1). Thus, the sidewall hydraulic head may not be representative of the entire pipe section at that point. Secondly, the velocity head downstream would not likely be equal to the upstream approach flow because of the high-velocity jet exiting the axial hole. The velocity head downstream can be significant and would cause a considerable additional reduction in the sidewall hydraulic head, hd . Thirdly, expansion losses downstream of the test specimen are expected to be significant. These expansion Chapter 3. Modified Hole Erosion Test (HET-P)     26 losses represent a total energy head loss, but not a friction head loss, and would not contribute to erosion along the axial hole. The consequence for the standard HET is that the hydraulic head difference across the soil specimen, h = (hu – hd) , is not necessarily representative of the friction head loss along the axial hole of the test specimen, hf , and shear stress derived from this assumption would likely be overestimated.  Applying Bernoulli’s theorem to the HET yields:                               where:      = pressure head, m z = elevation head, m       = velocity head, m H = energy head loss along the test specimen, m h =          = hydraulic head, m H = total energy head, m u = subscript denoting upstream d = subscript denoting downstream   To capture the friction head loss along the axial hole and exclude downstream expansion anomalies, the upstream and downstream total energy head need to be measured close to the specimen. The upstream total energy head, Hu , can be determined by adding the upstream velocity head, Vu 2  / 2g , to the measured upstream sidewall hydraulic head, hu (Equation (3.1)). The downstream total energy head, Hd , can be measured using a Pitot tube positioned at the point with the highest local energy head in the center of the specimen where the jet emerges from the axial hole. The tip of the probe must be pointing directly into the flow (Figure 3.1).   (3.1) Chapter 3. Modified Hole Erosion Test (HET-P)     27  Figure 3.1: Flow pattern upstream and downstream of test specimen, including Energy Grade Line (EGL), and Hydraulic Grade Line (HGL) at wall   3.1.2. Minor head losses and entrance length In turbulent flow, minor head losses develop in addition to friction head losses at the entrance and exit of the axial hole due to eddy turbulences induced by a sudden change in cross section. Minor entrance losses due to flow contraction can be assumed as negligible because head losses in accelerating flow like this are usually small, and continue over a considerable length downstream exceeding the length of the axial hole (L ≈ 117 mm). They are primarily the result of turbulences created as the stream enlarges between the vena contracta (minimum flow area) and the end of the entrance length upon the flow is fully developed. There is no single equation to estimate the entrance length because it depends on various factors like entrance conditions or wall roughness, but it can be assumed that flow is fully developed within 20 to 40 pipe diameters (e.g. see Viscous Sublayer in Turbulent Flow, Finnemore and Franzini 2002, p. 271). Minor exit losses due to flow expansion are avoided if the total energy head is measured at the point where the jet emerges from the axial hole.      Fl o w  p ro fi le  Specimen   HGL (at wall)       EGL Upstream     Standard HET:     Modified HET-P: H ET :            Downstream            H ET -P :          Chapter 3. Modified Hole Erosion Test (HET-P)     28 3.1.3. Flow conditions and axial hole velocity Conditions of either laminar or turbulent flow can be expected in the piping and flow chambers upstream and downstream of the test specimen. While flow conditions in the piping are turbulent, it may still be laminar in the flow chambers. The change in cross section from piping to the upstream flow chamber will cause a transition from turbulent to laminar flow within the flow chamber at low to medium flow rates (approx. 4-11 l/min). To assure fully-developed and uniform flow at the upstream specimen interface, the flow chamber needs to be adequately long. A rule-of-thumb suggests a transition length of LT ≈ (6-10)D , where D = diameter of flow chamber. Wan and Fell (2002) suggested using flow chambers of the same size as the standard compaction mold the specimen is prepared in (4x4 in), which is too short. In order to avoid positive feedback of downstream expansion anomalies described above, the downstream flow chamber must be of adequate length as well, preferably the same length as upstream.  With respect to measuring the downstream total head, Hd , of the exiting jet with a Pitot tube (Figure 3.1), it would be practical to use a combined Pitot-static tube with the advantage of getting a measure of the centerline jet velocity, umax , which can be correlated to the mean flow velocity in the axial hole, Vt  (Figure 3.2). This would simplify the analysis of HET data significantly, as described in Section 3.4.2 below. The theoretical ratio of the mean pipe flow velocity to the centerline velocity in a uniform circular pipe depends on the velocity profile, and can be described by the pipe factor for the corresponding flow regime (e.g. see Laminar Flow in Circular Pipes, Finnemore and Franzini 2002, p. 264; Velocity Profile in Turbulent Flow, Finnemore and Franzini 2002, p. 276):             where:  = Darcy friction factor  In laminar flow, the velocity profile is a parabola, and independent of pipe roughness. However, due to the small hole diameter compared to relatively high flow rates, it is more likely that turbulent flow conditions are observed in HET (Wan and Fell 2002, 2004b; Wahl et al. 2008). The shape of the velocity profile in turbulent flow depends on Reynolds number, diameter, and pipe roughness, as indicated by the Darcy friction factor,  , in Equation (3.2b). It is steeper near the center for a rough pipe than for a smooth pipe. The numerical constant 1.326 in Equation (3.2b) is a theoretically derived value that may be replaced by an empirical value of 1.44. Equation (3.2b) yields values for the pipe factor of about 0.74 to 0.88 for rough pipes with typical values of  = 0.01-0.07. (3.2) Chapter 3. Modified Hole Erosion Test (HET-P)     29    Figure 3.2: Pitot-static tube with schematic turbulent velocity profile of jet exiting axial hole immediately adjacent to test specimen   Total pressure, Static pressure, Pitot-static tube; KIMO TPL-03-200 0.2 0.4 0.6 0.8 1.0 Vt umax  Dynamic pressure, Pipe Factor:  laminar:  turbulent:       Sensing tip Turbulent velocity profile Total pressure probe Holes for static pressure Chapter 3. Modified Hole Erosion Test (HET-P)     30 3.2. HET-P apparatus The HET-P apparatus incorporates a conventional Pitot-static tube in order to obtain additional measurements of the total energy head, Hd , and velocity head, hv , close to the outlet of the axial hole, so as to exclude downstream expansion anomalies, and to obtain a measure of the centerline jet velocity, umax , for a more direct estimate of the mean flow velocity and diameter of the axial hole.  The general setup and design of the apparatus was based on the standard Hole Erosion Test assembly by Wan and Fell (2002, 2004a, 2004b), and the more recent modifications by the U.S. Bureau of Reclamation (Farrar et al. 2007; Wahl et al. 2008, 2009). A schematic diagram and photograph of the HET-P apparatus is shown in Figure 3.3 and Figure 3.4, respectively. The apparatus consisted of three major components; 1. Test cell, including flow chambers, test specimen with axial hole, and hydraulic head measurements upstream and downstream of the specimen; 2. Pitot-static tube and differential pressure transducer system; 3. Water flow system, including upstream (US) constant head tank to control test head, and downstream (DS) constant head tank with flow rate and temperature measurements.   Figure 3.3: Schematic diagram of HET-P apparatus hd hv Test cell: flow chambers and test specimen hu Hd DS US  Datum: +/- 0.0 Sidewall hydraulic head US, hu , and DS, hd Inflow Pitot-static tube Gate valve DS Total energy head Centerline velocity head Constant head tank, adjustable in height Outflow Constant head and sedimentation tank, 10° v-notch weir for flow rate, Q Q Outflow T Water temperature Chapter 3. Modified Hole Erosion Test (HET-P)     31  Figure 3.4: Photograph of HET-P apparatus   3.2.1. Test cell The test cell is the core of the new HET-P apparatus, and includes the test specimen with axial hole, and extended flow chambers with hydraulic head measurements upstream and downstream of the specimen (Figure 3.5a). A detailed engineering drawing of the test cell is presented in Appendix B. All hydraulic heads were measured relative to the common datum, located at mid-height of the test specimen (Figure 3.3). This assured that elevation heads were included in the measurements, and that measurements were not affected by the orientation of the apparatus (Equation (3.1)).  The mold containing the soil specimen was made of HDPE pipe, and had an inner diameter and length of 100 mm. Intermediate flanges were used to fix the mold and hold it in place during assembling of the test cell. Replaceable bridge elements were used between the mold and intermediate flanges to easy accommodate different outside diameters of the mold and non-erodible Inflow High back pressure tank Outflow Upstream constant head tank Test cell Flexible 50-mm tubing Outflow (Figure 3.8) Gate valve DS (Figure 3.8) Piezometer board Low back pressure tank Differential pressure transducer system 10° v-notch weir Downstream constant head and sedimentation tank  Scale: 0   0.2   0.4   0.6   0.8   1 m (center) Chapter 3. Modified Hole Erosion Test (HET-P)     32 PVC specimens. The downstream bridge element had a slightly smaller inner diameter to hold a 6-mm wire mesh with 30-mm center opening to support the soil specimen (Figure 3.5b). The center opening assured that no gravel size material accumulated on top of the mesh.  The upstream and downstream flow chambers consisted of a smooth 100-mm acrylic pipe with a length of 500 mm and attached flanges to securely tighten the cell. Gradual expansion and contraction fittings were used for a smooth transition to the smaller diameter piping, connecting the test cell with the constant head tanks. This setting assured minimal head loss, fully developed and uniform flow at the upstream specimen interface, and reduced downstream turbulences as suggested in the hydraulic review in Section 3.1. The clear acrylic pipe also allowed visual access inside the flow chambers.  Similar to previous studies, hydraulic heads hu and hd were measured 50 mm upstream and downstream of the specimen using pressure tapping on the wall of the flow chambers (Figure 3.1), connected to traditional vertical piezometer tubes for manual readout. The piezometer board was equipped with a rough 100-mm overall measuring scale for fast readings, and a measuring tape at each tube for accurate readings of hydraulic heads.    Figure 3.5: a) Vertical HET-P test cell, b) Dismantled downstream part of HET-P test cell with bridge element holding 6-mm wire mesh for soil specimen support, piezometer connection, and Pitot-static tube (b) (a) Piezometer connection Chapter 3. Modified Hole Erosion Test (HET-P)     33 3.2.2. Pitot-static tube and differential pressure transducer system A conventional Pitot-static tube was installed in the HET-P test cell, positioned in the center at the downstream side of the test specimen with the tip of the probe pointing directly into the flow. This provided the total and static pressure of the exiting jet immediately (tip of probe 5 mm) downstream of the specimen. The velocity head, hv , which is the difference of total and static pressure heads, was measured directly using a differential pressure transducer connected to the Pitot-static tube. Using the same transducer, the total energy head, Hd , was measured relative to the common datum.  The installed probe was a KIMO Pitot-static tube type L (KIMO TPL-03-200) as shown in Figure 3.2. It is a curved NPL model 1  made of stainless steel 4/4 with an outside diameter of 3 mm and ellipsoidal head. The Pitot tube coefficient, Cp , (see Section 3.4.2 below) provided by the manufacturer is 1.0015, but it was recommended to carry out a calibration of the Pitot-static tube to determine its exact coefficient. The accuracy of the probe is given as 1% for a ± 10° alignment to the fluid flow, as Pitot-static tubes are most sensitive to flow angularity (yaw and pitch angle error). The Pitot-static tube was permanently installed, and only periodically removed for inspection and cleaning.  The differential pressure transducer system to obtain pressure head readings from the Pitot-static tube included two SETRA Systems Model 230 bidirectional wet-to-wet pressure transducers, valve trees, short vinyl tubing, and two elevated back pressure tanks. The SETRA Systems Model 230 are high output, low differential pressure transducers with a fast-response capacitance sensor that provides a highly accurate, linear analog output proportional to pressure. Two transducers with different pressure ranges were installed for the use in low head respectively high head tests (Table 3.1). The transducer in use was connected to a conventional voltmeter for manual voltage readout corresponding to the pressure head difference between the high and low side of the transducer. The total pressure port of the Pitot-static tube was permanently connected to the high side of the transducer. The velocity head, hv , was measured by connecting the static pressure port of the Pitot- static tube to the low side of the transducer. The total energy head, Hd , was measured relative to the common datum by switching the low side of the transducer to a piezometer tube with constant water level set at ± 0.0 (Figure 3.6). Two back pressure tanks, one just above the test cell, the other somewhat higher than the maximum level of the upstream constant head tank (Figure 3.4), were used for system saturation and applying a back pressure to avoid particles entering the Pitot-static tube during setup. The high back pressure, connected to the tip of the probe, further allowed back flushing during a test in case the Pitot-static tube got clogged by eroding particles. De-aerated water was used to saturate and back flush the transducer system to avoid accumulation of dissolved air in the water inside the system with time, which would negatively affect head readings.  1  Developed between 1952 and 1954 by the U.K. National Physical Laboratory (NPL) Chapter 3. Modified Hole Erosion Test (HET-P)     34   Table 3.1: Specifications SETRA Model 230 Bidirectional Wet-to-Wet Pressure Transducers Specification Transducer #1: low range Transducer #2: high range Differential pressure range ± 1.0 psi ± 703 mm H2O ± 2.5 psi ± 1758 mm H2O Proof pressure high side 40 psi 28.1 m H2O 100 psi 70.3 m H2O Proof pressure low side 2.5 psi 1758 mm H2O 6.25 psi 4394 mm H2O Accuracy RSS* 1  (at const. temp.) ± 0.0025 psi ± 1.8 mm H2O ± 0.00625 psi ± 4.4 mm H2O Resolution * 2  0.0002 psi 0.1 mm H2O 0.0005 psi 0.4 mm H2O Response time 30-50 ms 30-50 ms Excitation 24 VDC 13-30 VDC Output 4-20 mA 0-10 VDC  * 1   Residual sum of squares (RSS) of non-linearity, non-repeatability and hysteresis: ± 0.25% full scale (FS). * 2   Infinite, limited only by output noise level (0.02% FS).    Figure 3.6: Differential pressure transducer system, setup for high range differential pressures  Transducer #1, low range, NOT connected Transducer #2, high range High back pressure for system saturation and back flushing Total pressure (high) from Pitot-static tube Low back pressure for system saturation Piezometer tube with constant water level set at system’s datum (±0.0) Static pressure (low) from Pitot-static tube Chapter 3. Modified Hole Erosion Test (HET-P)     35 3.2.3. Water flow system The water flow system was hydraulically optimized to confine the major energy head losses within the test cell. This mainly involved reducing pipe length, pipe roughness and number of pipe fittings. A schematic hydraulic profile with the major system components and corresponding relative energy head losses is presented in Figure 3.7. The total energy head loss across the whole system represents the difference between the upstream and downstream control water level, and is therefore referred to as test head, which is not necessarily equal to the hydraulic head difference across the specimen, h .   Figure 3.7: Schematic hydraulic profile of Modified Hole Erosion Test (HET-P) with Energy Grade Line (EGL) for initial hole diameter o = 6 mm at medium flow rate   In a manner similar to previous studies, flow was controlled by adjusting the height of the upstream constant head tank. It was adjustable to a maximum height of 2400 mm above the center of the specimen. Tap water was fed directly into the upstream tank, capable of providing a flow rate of up to 40 l/min. The gate valve at the downstream side of the test cell was used to prevent water flow during setup, and remained fully open throughout a test. C o n st an t H ea d  T an k Fl o w  E xp an si o n Fl o w  C h am b er  U S Sp ec im en Fl o w  C h am b er  D S Fl o w  C o n tr ac ti o n 9 0 ° El b o w G at e V al ve C o n st an t H ea d  T an k -2 30 En e rg y H e ad Chainage [not to scale] Te st  H ea d  = To ta l E n er gy  H ea d  L o ss Test CellUpstream Downstream EGL 50-mm flexible tubing Chapter 3. Modified Hole Erosion Test (HET-P)     36 The downstream constant head tank was fixed in height, and the water level was controlled by a custom thin-plate 10° v-notch weir for measuring flow rate. The minimum water level was set 100 mm above the center of the specimen to ensure the specimen was submerged at all times. The tank was divided into three compartments; 1) inflow, 2) weir, and 3) outflow (Figure 3.8). To account for changes in viscosity, water temperature was measured in the inflow compartment intended for sedimentation of soil particles and dissipation of vertical kinetic energy. A perforated vertical flow conditioning plate between the inflow and weir compartment assured horizontal flow and reduced turbulences in the weir compartment, yielding a still water level behind the v-notch weir for more accurate water level readings to determine flow rate. A piezometer connected to the tank and a fixed ruler next to the v-notch weir provided two redundant water level readings in the weir compartment. Concrete blocks were placed behind the weir to reduce the change of volume necessary to adjust the water level for varying flow rates, while maintaining a large flow area between the inflow and weir compartment. The outflow compartment mainly collected the effluent, discharging it to the sewer system. An overflow pipe was inserted to the outlet as needed to create a water pocket for further particle settlement.    Figure 3.8: Downstream constant head tank immediately after failure of soil specimen illustrating performance of flow conditioning plate and v-notch weir at 20-25 l/min  Scale: 0   0.2   0.4   0.6   0.8   1 m (center) Still water level behind v-notch weir Vertical flow conditioning plate Energy dissipation in inflow compartment Gate valve DS Outflow Horizontal flow in weir compartment 1 2 3 Chapter 3. Modified Hole Erosion Test (HET-P)     37 3.3. Experimental setup and test procedure 3.3.1. Calibration of measuring instruments The differential pressure transducers connected to the Pitot-static tube were calibrated before installation to obtain the relation between differential pressure head and output voltage from the transducers. Different water pressure heads were applied to the high side of the transducers, while a constant reference water pressure head was maintained at the low side of the transducers. Applied differential pressure heads ranged from ± 0 mm to 1000 mm for the low range transducer #1 and ± 0 mm to 2400 mm for the high range transducer #2 with a resolution of 10-20 mm at low heads respectively 50-100 mm at high heads. The transducers were subjected to both pressure paths low- high and high-low to detect possible hysteresis. The plot of differential pressure head versus output voltage showed a linear output proportional to pressure (Figure C.1 in Appendix C) for both pressure paths with only very little hysteresis. Linear regression trend lines were fitted to the data, yielding equations to convert output voltage to differential pressure head.  Calibration was also necessary in order to obtain the relation between flow rate through the custom v-notch weir and water level reading in the downstream constant head tank. The flow rate was calculated for various constant water levels by measuring the time to collect a control volume of water overflowing the weir. The water levels in the downstream constant head tank were set to water heads relative to the crest of the weir ranging from ± 0.0 mm to 120 mm with an average resolution of about 5 mm. The Kindsvater-Shen relationship 2  (ASTM D5242-92 (2007)) was adapted to fit a curve through measured data of water head relative to the crest versus discharge (Figure C.2 in Appendix C). Zero readings at the piezometer connected to the tank and at the fixed ruler next to the v-notch weir were used to convert water level readings to water heads relative to the crest.   3.3.2. Test preparation Test preparation included preparing the test specimen, transferring the specimen to the HET-P apparatus, installing measuring instruments, assembling the test cell, and saturating the water flow system. Details of this procedure are given in Appendix D, and are summarized below.  Test specimens used in this study were either non-erodible PVC specimens or erodible soil specimens. Each PVC specimen had a preformed axial hole and did not need any further preparation. Reconstituted soil specimens were sieved to remove any particles larger than about one-tenth of the  2  V-notch weir equation suggested by various organizations for standardization like ASTM or ISO. Chapter 3. Modified Hole Erosion Test (HET-P)     38 mold diameter, and compacted in three layers inside the test mold at 95% maximum dry density and optimum water content (or any other desired degree of compaction) using the custom compaction device shown in Appendix B. The soil was compacted around a vertical 6-mm rod in the center of the mold, which was removed prior to testing to open up the preformed hole. This method was preferred over drilling to avoid problems like smearing and remoulding that could lead to a dense surface layer of the axial hole. Undisturbed soil samples were carefully trimmed and centered in the mold. The remaining gap between soil and mold was sealed with modelling clay and topped with epoxy glue in a manner that no sealant would penetrate into the soil matrix where it affects the strength of the soil. The preformed hole was introduced by drilling using a drill press and wood auger bit.  Preparing the apparatus started by choosing the appropriate differential pressure transducer according to expected pressure heads, connecting it to the Pitot-static tube, and saturating the transducer system and piezometer tubes with de-aerated water. Starting at the downstream constant head tank, the whole system was then carefully saturated by constantly raising the water level. The control valve downstream was closed after the water level reached the crest of the weir, and saturation continued from the upstream side. The test specimen was carefully placed on top of the downstream flow chamber in a manner to prevent any air pockets to be trapped underneath the specimen. Finally, the test cell was securely tightened and connected to the upstream constant head tank after placing the upstream flow chamber and connecting the piezometer tubes.   3.3.3. Test procedure The HET-P test procedure was consistent with methods described by Wan and Fell (2002, 2004a, 2004b), and Wahl et al. (2008, 2009), and described in detail in Appendix D. Starting with an upstream hydraulic head (tank elevation) of 150 mm above datum, the specimen was subjected to a constant- head pressure flow. Elapsed time, hydraulic head upstream and downstream of the specimen, total and velocity head from the Pitot-static tube, height of water level above v-notch weir (flow rate) and water temperature were taken at select time intervals. The upstream tank was raised to increase the test head if the flow rate became steady. Upstream hydraulic head increments were generally 20 mm or 100 mm for PVC specimens and about 30-50% of the previous head for soil specimens. The upstream hydraulic head was maintained for several minutes once progressive erosion initiated in soil specimens, indicated by an increasing flow rate. Ideally, the test was stopped before the axial hole expanded to the sidewall of the mold. After the test, the system was drained, and the mold containing the soil specimen carefully removed for visual inspection of the eroded hole. A representative portion of the remaining soil specimen was oven-dried to determine water content after a plaster cast of the eroded hole was made to determine the final hole diameter and effective length. Chapter 3. Modified Hole Erosion Test (HET-P)     39 3.4. Modified analysis 3.4.1. HET-P: based on energy gradient According to the findings in Section 3.1.1 as illustrated in Figure 3.1, an energy gradient based method was introduced, herein after referred to as HET-P. It uses the difference of upstream total energy head, Hu , and downstream total energy head, Hd , measured with the Pitot-static tube. Equation (2.5) and (2.6) were modified by redefining the friction head loss along the axial hole, hf , and replacing the hydraulic gradient, s , by the energy gradient, i . This assumed that minor head losses due to the fluid entering the axial hole in turbulent flow conditions are negligible:                     The upstream total energy head, Hu , was determined according to Equation (3.1), using the velocity in the upstream flow chamber, Vu , based on continuity (Equation (2.8)). Equation (2.11) and (2.12) were modified accordingly by replacing s  by i :                          The HET-P analysis procedure is based on the original analytical method introduced by Wan and Fell (2002, 2004a, 2004b). Modifications regarding interpolation of friction factors (Lim 2006; Wahl et al. 2008, 2009) were not applied in this study. Using measured flow rate, Q , energy gradient, i , and final hole diameter, f , the analysis of test data remains the same as outlined in Section 2.5.3, except for the following adjustments: - Flow conditions are considered turbulent if Reynolds number Re > 2000 (Wahl et al. 2008); - Length of axial hole is assumed to vary linearly with time where applicable (Wahl et al. 2008); - Equation (2.5), (2.11) and (2.12) are replaced by Equation (3.3), (3.5) and (3.6), respectively.  Table E.1 in Appendix E presents a step by step analysis of test data for the different methods. (3.3) (3.4) (3.5) (3.6) Chapter 3. Modified Hole Erosion Test (HET-P)     40 3.4.2. HET-P (V): based on energy gradient and flow velocity The combined Pitot-static tube also provided an independent measure of the mean axial hole velocity, Vt , which in turn was used to estimate the diameter of the axial hole, t . This method combined with the energy gradient based method introduced above is herein after referred to as HET-P (V). The velocity head of the jet exiting the axial hole, hv , was used to estimate Vt :   where: Vt = estimated mean flow velocity in axial hole, m/s Cp = Pitot tube coefficient (1.0015 for the installed Pitot-static tube) Cv = velocity coefficient hv = velocity head, m  The Pitot tube coefficient, Cp , is a coefficient of instrument, and accounts for both local directional velocity fluctuations due to turbulences, and reading errors due to the shape of the sensing tip. The velocity coefficient, Cv , was introduced to convert measured center line velocity to the mean flow velocity in the axial hole. It is comparable with the theoretical pipe factor described above.  Using measured Q  together with Vt  from the Pitot-static tube (Equation (3.7)), the diameter of the axial hole, t , can be simply estimated from continuity (Equation (2.8)) assuming a cylindrical axial hole, while there is no need to determine the final hole diameter. This simplified analysis of test data significantly by eliminating steps i) to iv) outlined in Section 2.5.3 (Figure 3.9). The remaining steps are the same as for the HET-P method, except that Equation (3.6) is replaced by Equation (3.7) and (2.8).    Figure 3.9: Flowcharts describing test analysis of (a) HET, and (b) HET-P (V) (rectangle: measured or deduced, parallelogram: assumed or affected by uncertainty) (3.7) (b) Q s o f fT,o fT,f fT  t t(fT) dt / dt e ̇HET HET Ce IHET c H ET  EN D  Q i Vt t HET-P dt / dt e ̇HET-P Ce IHET c H ET -P  ( V ) EN D    (a) Chapter 4. Non-erodible test specimens     41 4. Non-erodible test specimens This chapter presents experimental studies conducted on non-erodible test specimens. This series of experiments was performed in order to test the applicability of the modified apparatus and suggested methods of analysis. The approach of using non-erodible test specimens eliminates the uncertainty in shape and size of the eroded axial hole, and assures a robust framework to test suggested procedures under controlled conditions.  Section 4.1 presents an overview of the research program and specified test procedure. Details about the experimental program can be found in Appendix F, including test number information and a detailed table of tests performed in this and the subsequent series of experiments. Results and analysis of test data are described in Section 4.2, showing the differences between standard HET and modified HET-P tests, and presenting advantages of the modified methods over the standard HET. Detailed tables with test data and results for all non-erodible specimens are presented in Appendix G. Findings, sources of errors and limitations of the modified methods are discussed in Section 4.3.    Chapter 4. Non-erodible test specimens     42 4.1. Research program Non-erodible PVC specimens with an axial hole of constant diameter were used in this series of tests. Three different specimens were tested, with axial holes of 6, 12 and 24 mm, drilled into 100 mm long solid PVC cylinders (Figure 4.1). These diameters covered the range expected for erodible soil specimens in a typical HET. Each PVC specimen was placed directly into the test cell as described above, replacing the mold otherwise containing the soil specimen.    Figure 4.1: Non-erodible PVC specimens with axial holes of 6, 12, and 24 mm diameter   A series of three independent tests was performed on each PVC specimen using the modified apparatus described in Section 3.2 with the high range differential pressure transducer #2 (Table 3.1). Applied test heads as defined in Figure 3.7 ranged from 5 mm to 2240 mm with a minimum upstream sidewall hydraulic head of hu ≥ 150 mm. With the 24-mm specimen, test heads could not exceed 160 mm at maximum flow rate, providing limited data of low accuracy using the high range differential pressure transducer #2. Thus, an additional test was performed on the 24-mm specimen using the low range differential pressure transducer #1 to increase accuracy at these low test heads. Measurements were taken as described above for each test head when the water level in the downstream tank reached steady state. This could take several minutes at low flow rates.   Scale:  0      2      4      6      8     10 cm 0        1        2        3        4        5 in Chapter 4. Non-erodible test specimens     43 4.2. Results and analysis Test data were analysed according to the following three methods as introduced above: 1. HET Original method proposed by Wan and Fell (2002, 2004a, 2004b); 2. HET-P New method based on energy gradient; 3. HET-P (V) New method based on energy gradient and flow velocity.  Observed flow rates ranged from about 1 l/min to 8 l/min for the 6-mm specimen and about 2 l/min to 36 l/min for the 12 and 24-mm specimen. Only turbulent flow (Re > 2000) was observed for the applied test heads. Results were generally less scattered for Reynolds numbers Re > 5000. Thus, a further distinction was made regarding flow regime in the results presented below. More specifically, a distinction was made between a critical zone with 2000 < Re < 5000, where flow could be either laminar or turbulent, and complete turbulent flow with Reynolds numbers Re > 5000.   4.2.1. Head ratio and shear stress The differences between the HET and HET-P tests can be described by the head ratio, defined here as H / h . The value of head ratio was found to be approximately constant for each of the test specimens, but varies with hole diameter (Figure 4.2). It tended to decrease with increasing diameter for the range of tested diameters. The values obtained for the three non-erodible test specimens are summarized in Table 4.1.   Table 4.1: Summary of head ratio values, H / h , obtained from the three non-erodible test specimens for turbulent flow with Re > 5000 Hole diameter, o Head ratio, H / h [mm] Mean Standard deviation Number of observations 6 0.27 0.01 22 12 0.10 0.01 23 24 0.03 0.02 23   The head ratio also reflects the relative values of shear stress obtained from the HET-P and HET tests, and equals the shear stress ratio, HET-P / HET , for a given diameter. Figure 4.2 and Figure 4.3 show that the shear stress values from HET-P tests, HET-P , were up to one, almost two orders of magnitude smaller than those from HET tests, HET , for all three specimens. Chapter 4. Non-erodible test specimens     44  Figure 4.2: Head ratio equals shear stress ratio versus flow rate for the three non-erodible test specimens    Figure 4.3: Wall shear stress HET-P using Pitot-static tube data versus wall shear stress HET from sidewall hydraulic heads for the three non-erodible test specimens  0.27 0.10 0.03 0 0.1 0.2 0.3 0.4 0 0.1 0.2 0.3 0.4 0 5 10 15 20 25 30 35 40 Sh e ar  S tr e ss  R at io ,  H ET -P / H ET [ - ] H e ad  R at io ,  H / h [ - ] Flow Rate, Q [l/min] 6 mm (Re>5000) 12 mm (Re>5000) 24 mm (Re>5000) 6 mm (Re=2000-5000) 12 mm (Re=2000-5000) 24 mm (Re=2000-5000) 6 mm Mean (Re>5000) 12 mm Mean (Re>5000) 24 mm Mean (Re>5000) 0.1 1 10 100 1000 0.1 1 10 100 1000 W al l S h e ar  S tr e ss  H ET -P ,  H ET -P [N /m 2 ] Wall Shear Stress HET, HET [N/m 2] 6 mm (Re>5000) 6 mm (Re=2000-5000) 12 mm (Re>5000) 12 mm (Re=2000-5000) 24 mm (Re>5000) 24 mm (Re=2000-5000) 1:1 Line Chapter 4. Non-erodible test specimens     45 4.2.2. Flow coefficient and axial hole velocity For the Pitot-static tube to be of use in HET-P (V) tests, it is essential that the product CpCv  in Equation (3.7) is constant throughout a test. For simplicity, this product was called flow coefficient, K , and was determined using Equation (3.7) and flow velocities obtained from continuity (Equation (2.8)) using measured flow rate and known axial hole diameter of the non-erodible test specimens. Measurements from the three non-erodible specimens across a range of discharges indicated an essentially constant value for the flow coefficient, K , of about 0.825 as summarized in Table 4.2. However, a slight but noticeable increase in K was observed with increasing flow rate (Figure 4.4).   Table 4.2: Summary of flow coefficient values, K , obtained from the three non-erodible test specimens for turbulent flow with Re > 5000 Hole diameter, o Flow coefficient, K = CpCv [mm] Mean Standard deviation Number of observations 6 0.816 0.008 22 12 0.830 0.013 23 24 0.827 0.015 23 All 0.825 0.014 68    Figure 4.4: Flow coefficient, K , versus flow rate for the three non-erodible test specimens  0.0 0.2 0.4 0.6 0.8 1.0 0 5 10 15 20 25 30 35 40 Fl o w  C o e ff ic ie n t,  K  [  - ] Flow Rate, Q [l/min] 6 mm (Re>5000) 12 mm (Re>5000) 24 mm (Re>5000) 6 mm (Re=2000-5000) 12 mm (Re=2000-5000) 24 mm (Re=2000-5000) Linear best fit K = 0.825 v continuity vvvpt gh V KghKghCCV 2 22  Chapter 4. Non-erodible test specimens     46 Using a constant value K = 0.825, good agreement was achieved for mean flow velocity in the axial hole from Equation (3.7), and calculated from continuity (Equation (2.8)) based on the known axial hole diameters of the non-erodible test specimens (Figure 4.5).    Figure 4.5: Mean flow velocity in axial hole using Pitot-static tube data versus mean flow velocity in axial hole using continuity for the three non-erodible test specimens   Accordingly, estimated axial hole diameters HET-P (V), back calculated from continuity and mean flow velocities in the axial hole using Pitot-static tube data, corresponded well with the known axial hole diameter of the non-erodible test specimens, which is summarized in Table 4.3 and illustrated in Figure 4.6.   Table 4.3: Summary of estimated axial hole diameters HET-P (V), t , obtained from the three non-erodible test specimens for turbulent flow with Re > 5000 Hole diameter, o Estimated axial hole diameter HET-P (V), t [mm] Mean Standard deviation Number of observations 6 5.97 0.03 22 12 12.04 0.10 23 24 24.02 0.17 23 0.0 1.0 2.0 3.0 4.0 5.0 6.0 0.0 1.0 2.0 3.0 4.0 5.0 6.0 V e lo ci ty  f ro m  P it o t- st at ic  t u b e  [ m /s ] Velocity from Continuity [m/s] 6 mm (Re>5000) 6 mm (Re=2000-5000) 12 mm (Re>5000) 12 mm (Re=2000-5000) 24 mm (Re>5000) 24 mm (Re=2000-5000) 1:1 Line Chapter 4. Non-erodible test specimens     47   Figure 4.6: Estimated axial hole diameters HET-P (V), back calculated from Pitot-static tube data versus flow rate for the three non-erodible test specimens   4.3. Discussion 4.3.1. Head ratio and shear stress The head ratio H / h  was used to describe differences between the HET and HET-P tests. Results showed that for a given diameter, the head ratio equals the shear stress ratio HET-P / HET . This is because the hydraulic shear stress on the boundary of the preformed hole is directly proportional to the friction head loss, hf  (Equation (2.4)  (2.5) and (3.3)). A ratio of 1.0 would indicate complete agreement between the two methods. But the head ratio was found to be consistently less than unity, indicating that shear stress values obtained from the standard HET were overestimated. This finding is a consequence of the energy gradient, i , rather than the hydraulic gradient, s , being used to calculate shear stress.  The average head ratio for the 6-mm specimen (0.27, Table 4.1) was similar to the result reported by Marot et al. (2011), who found that, based on calculated energy losses, roughly 25% of the measured hydraulic gradient, s , is transformed into friction and erosion. This is equivalent to a head ratio of H / h = 0.25. Unlike Marot et al. (2011), results of the current study showed that this value is 6 12 24 0 5 10 15 20 25 30 0 5 10 15 20 25 30 35 40 H o le  D ia m e te r H ET -P  ( V ),   t [m m ] Flow Rate, Q [l/min] 6 mm (Re>5000) 12 mm (Re>5000) 24 mm (Re>5000) 6 mm (Re=2000-5000) 12 mm (Re=2000-5000) 24 mm (Re=2000-5000) 6 mm Diameter 12 mm Diameter 24 mm Diameter Chapter 4. Non-erodible test specimens     48 not constant, but varies with hole diameter (Figure 4.2). While for the axial hole diameters tested herein the head ratio decreased with increasing diameter, the value is expected to ultimately increase with hole diameter and converge to unity in the extreme case where the diameter of the axial hole approaches the diameter of the flow chamber (100 mm).  The findings that HET-P  was less than HET  may explain the observation of Lim (2006) that the erosion rate index from HET was significantly higher than that from the RCT for non-dispersive soils, implying slower erosion and higher shear stresses, and the companion observation by the USBR (Farrar et al. 2007; Wahl et al. 2008) and Marot et al. (2011) that the JET also yields critical shear stress values that are significantly less than those obtained from the standard HET.   4.3.2. Axial hole velocity and hydraulic roughness In Hole Erosion Tests, flow and geometric conditions of the axial hole change with time. The approximately constant value for the flow coefficient K = 0.825, found independent of flow rate and hole diameter, and a good agreement between velocities from Pitot-static tube data and continuity, confirmed the applicability of a Pitot-static tube for velocity measurements downstream of the test specimen.  The velocity coefficient, Cv , introduced in Equation (3.7), represents the ratio of the mean pipe flow velocity to the centerline velocity (which is measured using the Pitot-static tube), given by the pipe factor defined in Equation (3.2). Using K = CpCv = 0.825 and the value of the Pitot tube coefficient provided by the manufacturer, Cp = 1.0015 ≈ 1.0, a constant velocity coefficient could be determined as Cv = 0.825, which is within the range expected for turbulent pipe flow (Figure 3.2).  The pipe factor in turbulent flow, and thus Cv  depends on Reynolds number, diameter, and pipe roughness (Equation (3.2)). For a given diameter and roughness, Cv  is expected to increase with Reynolds number and thus flow rate until complete turbulent flow is developed, where the Darcy friction factor is constant and independent of Re . Complete turbulence was not achieved using the PVC specimens due to the low pipe roughness. This explains the slight increase in K  and thus Cv observed for the three non-erodible test specimens (Figure 4.4).  Ideally, the theoretical value of Cv  in HET-P (V) tests should be either constant, or at least experience only a minimum rate of change. Referring to the Moody diagram, this would be the case for higher Reynolds numbers in rougher pipes of smaller diameter. In typical Hole Erosion Tests on erodible soil specimens, Reynolds number, axial hole diameter and pipe roughness all increase with Chapter 4. Non-erodible test specimens     49 time. Thus, and given the very small observed change in Cv  for the PVC specimens, the change in Cv is expected to be insignificantly small, and assuming a constant value is a reasonable approximation in testing erodible soil specimens.  For certain applications, Pitot-static tubes can also be aligned in the direction of the flow, rather than having the tip of the probe pointing directly into the flow. However, these applications are rather limited, and tests on the non-erodible PVC specimens using a Pitot-static tube at the upstream side of the specimen did not reveal any consistent results to be of use in HET-P tests.  As introduced with the HET-P (V) method, the velocity obtained using the Pitot-static tube (Equation (3.7)) can be used to determine the mean diameter of the axial hole from continuity during testing of erodible soil specimens. This is a crucial aspect of the analysis, because the erosion rates are determined from the increase in the hole diameter (Equation (2.7)). Because it is not possible to directly measure the diameter during testing, it has been necessary to back-calculate the diameter using an assumed hydraulic roughness (Wan and Fell 2002, 2004a, 2004b), which has been reported as problematic (Lim 2006; Wahl et al. 2008, 2009). The Pitot-static tube can therefore provide a more direct estimate of axial hole velocity and diameter, and potentially simplify the analysis of HET data.   4.3.3. Upstream total energy head The HET-P method includes the velocity head in the upstream flow chamber, Vu 2  / 2g , to calculate the upstream total energy head, Hu  (Equation (3.4)) needed to determine shear stress based on the energy gradient, i . Using continuity (Equation (2.8)), a maximum upstream velocity head of Vu 2  / 2g ≈ 0.4 mm was deduced from measured flow rate in the later stage of testing. This value appears insignificantly small compared to the resolution of measured hydraulic heads, and one could argue that the upstream sidewall hydraulic head, hu , could be approximated as total energy head. However, neglecting the upstream velocity head introduces a significant error at low heads and high flow rates as observed with the 24-mm specimen. Absolute values of Vu 2  / 2g  could take up as much as 15-20% of the energy head loss along the test specimen in HET-P tests if the upstream velocity head was neglected. Thus, it is recommended to include Vu 2  / 2g  in all calculations of Hu .  Wan and Fell (2002, 2004a, 2004b) suggested filling the upstream flow chamber with 20-mm gravel to diffuse the fluid and assure an even pressure/flow distribution upstream of the test specimen. This would cause an unknown reduction in effective cross sectional area and an increase in velocity. Assuming equally distributed flow paths, this would result in a decrease in the sidewall hydraulic head, hu , and thus introduce an error in the upstream total energy head, Hu . It is therefore necessary not to Chapter 4. Non-erodible test specimens     50 fill the upstream flow chamber with any material. This goes along with findings of Wahl et al. (2008), who found that there was no need to place gravel into the upstream flow chamber for testing erosion- resistant soils.   4.3.4. Flow conditions and minor losses In HET-P tests, flow conditions were considered turbulent if Reynolds number Re > 2000. This is a widely recognized lower critical value (e.g. see Critical Reynolds Number, Finnemore and Franzini 2002, p. 256), and was also suggested by Wahl et al. (2008) to be used in HET. However, there is no guarantee that flow is turbulent right above this value. Going from low to high Reynolds numbers, the laminar-flow zone is followed by a critical zone, in which laminar flow could be maintained up to an upper critical Reynolds number of about 4000 or higher. The analysis of test data revealed difficulties in getting meaningful results for data sets within this critical zone, even up to Reynolds numbers of about 5000. This finding is consistent with the original suggestion of Wan and Fell (2002, 2004a, 2004b), who used Re = 5000 as critical value above which flow was considered turbulent. Even though Reynolds numbers most likely exceed 5000 in testing erodible soil specimens, it is suggested to distinguish between complete turbulent flow and a critical zone with 2000 < Re < 5000 in the analysis and interpretation of HET data.  The minor losses due to the eroding fluid entering the axial hole in turbulent flow conditions were estimated by calculating the major friction head losses along the axial hole using the Darcy-Weisbach equation and an explicit approximation of the Colebrook-White equation for pipe roughness (Haaland 1983), and subtracting this from the measured total head loss across the specimen. This indicated that the minor entrance losses were insignificant, and can be ignored. One reason for this is that the entrance length over which the minor entrance losses develop exceeded the length of the specimen by as much as a factor of 10. This indicated that the test specimen was too short for the flow to become fully developed, which is a problem already stated by Bonelli and Brivois (2008), because the interpretation of test data assumes uniform flow conditions.  Furthermore, minor entrance losses very much depend on the conditions at the entrance of the axial hole. The upstream end of the axial hole in erodible soil specimens usually develops a rounded or funnel shaped form during a test. This implies a gradual contraction with almost no vena contracta, and therefore no minor entrance losses. The minor exit losses are avoided by measuring the downstream total energy head using the Pitot-static tube close to the point where the jet exits the axial hole.  Chapter 4. Non-erodible test specimens     51  4.3.5. Sources of errors The main sources of errors in HET-P and HET-P (V) tests were associated with: - Location of measurements; - Flow irregularities; - Measuring instruments.  There were uncertainties and implied errors regarding the location of measurements and their assigned meaning in the analysis and interpretation of test data. Including the upstream velocity head, Vu 2  / 2g , in the calculation of the upstream total energy head, Hu , is only correct if the difference between the EGL and HGL equals Vu 2  / 2g . But the relative magnitude of the HGL at the location of measurement hu  was unsure, because the sidewall hydraulic head increases, and its value converges to that of the total energy head at the corner of the wall and specimen, due to centrifugal action caused by curved stream lines (Figure 3.1). It was in fact unknown at which point upstream of the specimen that the HGL started to rise. Depending on flow conditions, it has to be assumed that measurements of hu  are slightly affected by this local hydraulic phenomenon, resulting in overestimated values of Hu .  The Pitot-static tube was located in a zone with a relatively high local energy gradient and increasing HGL, depending on axial hole diameter and flow rate (Figure 3.1). This implied two sources of error. Firstly, the tip of the Pitot tube was placed 5 mm downstream of the specimen, but the measurement was assigned to the downstream end of the specimen. This means that measurements of Hd  would have been slightly underestimated, and resulting head ratios overestimated. Secondly, the holes for static pressure were located even further downstream (30 mm from specimen) at a point with an increased static pressure due to the expanding jet and decreased flow velocity. Combing the two sources would imply a slightly underestimated measured velocity head, hv , and estimated mean flow velocity in the axial hole, Vt .  Flow irregularities in the system caused slight fluctuations in all readings, except in the downstream tank and water temperature, which both had a relatively slow response time. Common practice was to record mean values observed over a certain period of time appropriate to current flow conditions. This method also introduced possible human errors.  Errors introduced by measuring instruments included piezometer level readings, accuracy of the differential pressure transducers, and form and alignment of the Pitot-static tube. Piezometer levels were recorded with a resolution of ±0.5 mm H2O over the whole range of pressure heads. The Chapter 4. Non-erodible test specimens     52 introduced error depends on the relative difference between compared piezometer levels and varies with test head and flow rate. The downstream total energy head, Hd , was occasionally affected by a rising water level in the reference piezometer tube caused by a volume change due to the flexibility of the measuring system. It was not always deemed necessary or possible to reset the water level to the system’s datum before each reading. The two differential pressure transducers used in this study had different accuracies depending on the differential pressure range. Transducers were not switched during a test. Thus, readings in tests covering a wide range of differential pressure heads were less accurate, introducing reading errors especially at low differential pressure heads.  Possible errors introduced by the Pitot-static tube could have different origins. Firstly, and most importantly, the probe could have been slightly out of angle causing the flow not being parallel to the sensing tip. Secondly, the installed probe was not affected by Mach number errors, since velocities in HET were below critical values, and there were no compressive effects on the fluid. Thirdly, the Pitot- static tube was not affected by viscosity effects because Reynolds numbers exceeded a minimum value of about 30-70. Fourthly, even though the probe was placed outside the hole adjacent to the specimen, and a sufficient distance away from solid boundaries, static pressure could have been affected by locally accelerated flow due to the presence of the test specimen or confined jet, forming a Venturi-type passage around the sensing tip. Lastly, errors introduced by an increased response time due to the small diameter were reduced to a minimum by using short tubing and observing voltage outputs over an appropriate period of time before recording the data.   4.3.6. Limitations The present study was limited to turbulent flow with Reynolds numbers larger than 2000. Generally, interpreted results are further limited to flow conditions of complete turbulence with Reynolds numbers exceeding 5000.  The experimental studies were limited to non-erodible PVC specimens with uniform axial holes and a limited number of three different axial hole diameters of up to 24 mm. Results may vary for larger diameters and non-uniform axial holes.  The repeatability of the test methods was demonstrated by consistent results from a series of three, respectively four tests on each PVC specimen. However, all test results were linked to the same limitations regarding accuracy of measuring instruments and other sources of errors implied by the test apparatus used in this study.  Chapter 5. Erodible soil specimens     53 5. Erodible soil specimens After the successful testing of non-erodible PVC specimens, the Modified Hole Erosion Test (HET-P) was used to test erodible soil specimens of different type and erosion resistance. The objective of this test series was to confirm findings from previous tests on PVC specimens, and to demonstrate the applicability of the implemented modifications to real soil testing.  Presented in this chapter is a summary of the research program (Section 5.1), which is supplemented by Appendix F that includes test number information and a detailed list of tests performed in this and the preceding series of experiments. The main findings from tests on erodible soil specimens are presented in Section 5.2. It ranges from the description of soil samples used in this study to observed differences between the HET and HET-P methods regarding head ratio, shear stress, estimated axial hole diameter, and critical shear stress. These differences are further discussed and compared to previous studies in Section 5.3 that also includes errors and limitations associated with this study.   Chapter 5. Erodible soil specimens     54 5.1. Research program The laboratory experiments conducted in this test series included basic material property tests and Modified Hole Erosion Tests (HET-P) on five different soil samples. Two types of soil were tested in this study, reconstituted glacial till material from a dam core and undisturbed clay samples of natural river bank deposits from various Ontario rivers.  The soil samples were classified using the Unified Soil Classification System (USCS) according to ASTM Standard D2487-11. Grain size distribution tests were conducted using mechanical sieve and hydrometer analysis following ASTM Standards D421-85 (2007), D422-63 (2007) and D6913-04 (2009). The Atterberg Limits of test soils, namely liquid limit, LL , and plastic limit, PL , were determined as described in ASTM Standard D4318-10. Standard compaction tests were performed according to ASTM Standard D698-07 to determine optimum water content, wopt , and standard maximum dry density, d,max , for reconstituted samples. If possible, standard compaction test Method B was used with material passing the 3/8 in (9.5 mm) sieve to be consistent with the maximum particle size used in HET-P tests. Water content of the soil samples respectively prepared specimens was taken before (wo) and, if possible, after testing (wf) following ASTM Standard D2216-05. Prior to testing, the moist density, m , and dry density, d , of the prepared soil specimen were determined by the direct measurement method (Method B) as described in ASTM Standard D7263-09.  Using the modified apparatus, HET-P tests were conducted on soil specimens prepared from each soil sample according to the procedure described in Section 3.3. A total of four soil specimens from the reconstituted dam core material, and five soil specimens from undisturbed Ontario clay samples were tested. Expected progressions of internal erosion, according to Wan and Fell (Table 2.1), ranged from rapid for the glacial till material to slow for the clay samples.   Chapter 5. Erodible soil specimens     55 5.2. Results and analysis As with the non-erodible test specimens, HET-P test data were analysed according to the following three methods as introduced in Chapter 2 and 3 above: 1. HET Original method proposed by Wan and Fell (2002, 2004a, 2004b); 2. HET-P New method based on energy gradient; 3. HET-P (V) New method based on energy gradient and flow velocity.  Observed flow rates ranged from about 1 l/min to 40 l/min. At failure, flow rate could occasionally exceed the system’s maximum of 40 l/min, but would not maintain a constant upstream water head. Laminar flow (Re < 2000) was rare, and only observed in the very beginning of a test. A critical Reynolds number of Re = 2000 was applied to all tests, with precaution to interpretation regarding data points falling within the critical zone where 2000 < Re < 5000.  Presented below is first a description of the soils used in this study with obtained soil properties, followed by the results from HET-P testing. Tests on the glacial till material from the dam core were very difficult to perform, and did not yield enough data for a complete analysis. Thus, the general outcome is presented using solely results from tests on Ontario clay samples, while tests on the dam core material are described separately.  A summary of soil properties for all tested samples described below, and a summary of test data and results for all the erodible soil specimens tested in this study is provided at the end of this section in Table 5.3 and Table 5.4, respectively. Appendix H and Appendix I provide additional soil property information and detailed test data and results for each specimen in form of figures and photos.   5.2.1. Soil properties and description Dam core material The first type of soil tested in this study was material obtained from the core of a dam. The dam is located on the Columbia River in British Columbia, Canada. The dam was designed with a wide core, constructed of clayey glacial till material from local borrow areas within today’s reservoir. The material was placed in layers of 25 cm thickness or less, and compacted in eight passes by a 57-ton pneumatic-tired roller. Water content was within 2% below and 1% above optimum.  The soil sample used in this study, labelled as MV4-Core, was excavated from the existing dam core at a depth of approximately 7 m (23 ft) from the road elevation on August 25, 2003. Protected by Chapter 5. Erodible soil specimens     56 a plastic cover to prevent moisture loss, the soil was delivered to the UBC geotechnical laboratory in a steel storage drum, in which it was stored ever since. The soil had a medium brown color, and was classified as SC-SM; silty, clayey sand with gravel. The grain size distribution and Atterberg Limits of the MV4-Core material were obtained by Abelardo A. Julio at UBC in 2009. The reproduced gradation curve is presented in Appendix H, Figure H.1. Compaction data were obtained by the standard compaction test Method B (maximum particle size 9.5 mm) and dry preparation of the sample (Figure H.3). The water content of the whole sample was taken from various locations within the steel drum prior to any other testing, and ranged from 5.2% to 8.2%. Densities and water content listed in Table 5.3 are for the one test specimen prepared for HET-P testing.  Due to a limited amount of soil available for HET-P testing, three specimens were prepared and tested beforehand using a dummy soil consisting of dam core material previously tested as part of ongoing research at UBC. This altered sub-sample, denoted by MV4-Altered, had a maximum particle size passing the 3 in (75 mm) sieve and a significantly reduced fines content of about 7%. Atterberg Limits were not determined for this sample. The standard compaction test Method A (maximum particle size 4.75 mm) was used to obtain compaction data (Figure H.2). Table 5.3 also gives estimates of maximum dry density and optimum water content corrected for a maximum particle size of 9.5 mm. The presence of oversize fraction in the test specimen would results in a higher maximum dry density and lower optimum water content.  A rapid progression of internal erosion was expected for specimens prepared from the dam core material (MV4-Core and MV4-Altered). According to Wan and Fell (2002, 2004a, 2004b), most soils show higher erosion resistance if they were compacted to the wet side of optimum water content. Thus, the test specimens were prepared with tendency to the wet side with water contents not exceeding 1% above optimum. One specimen was prepared at 3% above optimum to test the erosion behaviour for varying water contents.   Ontario clay samples The rest of the tested soil samples were taken from natural river bank deposits of various Ontario rivers. The samples were provided by Dr. Colin D. Rennie of the University of Ottawa. Samples were collected by driving a 100-mm diameter stainless steel tube into the soil. Two samples each from five different sites were collected, sealed with cling wrap, and shipped to the UBC geotechnical laboratory. Later inspection showed that some cling wrap seals were broken during the transport, and the soil samples probably lost some moisture content. Upon inspection, all samples were re-sealed with cling wrap and stored in a moist room until they were tested. The delivered samples provided just enough material to carry out the HET-P tests. Thus, soil property tests were performed on different samples at Chapter 5. Erodible soil specimens     57 the University of Saskatchewan Department of Civil & Geological Engineering. They are described in Cossette and Mazurek (2011), and are summarized in Table 5.3, which shows mean values from tests on two samples of each origin.  Five of the provided samples, two each from Jock River and Raisin River, and one from Bear Brook, were not suitable for HET-P testing. Sample Bear Brook 1/2 fell apart upon extrusion form the steel tube, leaving intact portions too small for testing. Samples from Jock River and Raisin River were all penetrated by heavy vegetation and organic matter, and in some instances contained insufficient material for testing.  The tested samples from Little Cataraqui were classified as CL; lean clay with sand. They contained some organic matter like little pieces of wood, and light to no vegetation. The soil had a grey-brown colour with red-brown speckled areas, and showed some layering in form of horizontal cracks, probably caused by the sampling method and possible loss of moisture content.  Sample Bear Brook 2/2, classified as CL-ML; sandy silty clay, had a red speckled dark brown color with a sandy texture, and a medium vegetation and organic matter content. Exposing the plaster cast after testing revealed a single 3-mm root crossing the specimen diagonally through the center at about a third from the bottom. The root was separated by drilling the preformed hole, but hold in place during the test by the remaining surrounding soil.  The two soil samples from Wilton Creek had a slightly green tinted grey-brown color with red tinted/speckled patches. This soil was classified as CL; sandy lean clay. The samples had medium to heavy vegetation and organic matter present. Soil erosion during the HET-P test on sample Wilton Creek 2/2 revealed a large 5-mm root with complex root hairs at the bottom of the specimen.   5.2.2. Head ratio and shear stress The head ratio, H / h , which was used to describe the differences between HET and HET-P tests, varied during each test because of the changing axial hole diameter (Figure 5.1). The value of head ratio first decreased with increasing axial hole diameter as seen with the non-erodible test specimens. After a certain diameter, the reverse behaviour was observed, and values of head ratio increased with increasing diameter. The rate of initial decrease and the point of change were different between soil samples and test specimens. Initial values of head ratio ranged from 0.3 to 0.9 and decreased to a minimum of about 0.1 to 0.7. Test S3-993.21, Wilton Creek, showed a different behaviour with no initial decrease in head ratio. Chapter 5. Erodible soil specimens     58    Figure 5.1: Head ratio equals shear stress ratio versus estimated mean hole diameter for the Ontario clay specimens   The shear stress ratio, HET-P / HET , which is interchangeable with the head ratio, was smaller than unity in all cases. This is also reflected in Figure 5.2, where shear stresses from all three methods, HET , HET-P , and HET-P (V) , were directly compared. Shear stress values from HET-P and HET-P (V) tests were up to one order of magnitude smaller than those from HET tests, especially at lower values, where results were more scattered due to the accuracy of the measuring devices. At higher values, data points gathered around the linear relationship HET-P = 0.5 HET , with a trend towards the 1:1 line with increasing shear stress resulting from an increase in axial hole diameter as the test progresses. Generally, HET-P and HET-P (V) tests yield similar results with only very little deviation compared to HET tests.   0.0 0.2 0.4 0.6 0.8 1.0 1.2 0.0 0.2 0.4 0.6 0.8 1.0 1.2 6 10 14 18 22 26 30 Sh e ar  S tr e ss  R at io ,  H ET -P / H ET [ - ] H e ad  R at io ,  H / h [ - ] Estimated Mean Diameter, t [mm] S3-01/02: Little Cataraqui S3-11/12: Bear Brook S3-21/22: Wilton Creek ? ? Chapter 5. Erodible soil specimens     59  Figure 5.2: Wall shear stress HET-P using Pitot-static tube data versus wall shear stress HET from sidewall hydraulic heads for the Ontario clay specimens   0.1 1 10 100 1000 0.1 1 10 100 1000 0.1 1 10 100 1000 W al l S h e ar  S tr e ss  H ET -P  ( V ),   H ET -P  ( V ) [N /m 2 ] W al l S h e ar  S tr e ss  H ET -P ,  H ET -P [N /m 2 ] Wall Shear Stress HET, HET [N/m 2] S3-01/02: Little Cataraqui - HET-P S3-01/02: Little Cataraqui - HET-P (V) S3-11/12: Bear Brook - HET-P S3-11/12: Bear Brook - HET-P (V) S3-21/22: Wilton Creek - HET-P S3-21/22: Wilton Creek - HET-P (V) 1:1 Line Linear: y=0.5x Chapter 5. Erodible soil specimens     60 5.2.3. Axial hole velocity and estimated diameter Mean flow velocities in the axial hole were obtained from Pitot-static tube data (Equation (3.7)), and used in the HET-P (V) method to estimate axial hole diameters. Velocity data from the Pitot-static tube were analysed using a constant value for the flow coefficient of K = 0.825, as found by testing non-erodible specimens (Section 4.2.2).  Using continuity (Equation (2.8)), values of mean velocity and diameter of the axial hole were determined for all three methods, and compared among each other. Differences between methods were described by the velocity ratio respectively diameter ratio, defined here as the ratio of values from the corresponding modified method to values obtained according to the standard HET. Values of both ratios were close to 1.0 for most of the successful tests, indicating relatively good agreement between methods. However, with a deviation of up to 51%, the HET-P (V) method does not agree well with the other two methods for flow conditions with Reynolds numbers smaller than about 5000. A statistical summary of the two ratios is presented in Table 5.1 (velocity) and Table 5.2 (diameter).  A direct graphical comparison between mean flow velocities (Figure 5.3) respectively diameters (Figure 5.4) obtained using the HET-P methods and standard HET supported these findings. Excluding data with Re < 5000 for the HET-P (V) method, most data points did fall within a deviation of about 20% (velocity) and 10% (diameter) from the 1:1 line of agreement, respectively.   Chapter 5. Erodible soil specimens     61  Table 5.1: Summary of velocity ratio values obtained from the Ontario clay specimens for turbulent flow with Re > 2000 for HET-P, respectively Re > 5000 for HET-P (V) Soil Sample Velocity Ratio HET-P and HET-P (V), Vt,HET-P / Vt,HET and Vt,HET-P (V) / Vt,HET Mean Standard deviation Number of observations Test # HET-P HET-P (V) * 1  HET-P HET-P (V) * 1  HET-P HET-P (V) * 1  S3-993.01  * 2  0.76 n/a 0.09 n/a 29 23 (6) S3-993.02 0.90 0.93 (0.62) 0.17 0.09 (0.04) 20 16 (4) S3-993.12 1.06 0.95 (0.76) 0.06 0.07 (0.09) 21 17 (4) S3-993.21  * 3  0.79 1.43 (1.18) 0.10 0.11 (0.10) 73 61 (12) S3-993.22 1.04 0.84 (0.49) 0.04 0.12 (0.13) 18 13 (5)  * 1  HET-P (V): values in parentheses represent data points where 2000 < Re < 5000 * 2  S3-993.01: Pitot-static tube measured flow through intact axial hole at the bottom of the specimen (Figure I.18). * 3  S3-993.21: 2 flow paths, Pitot-static tube measured mainly flow through primary axial flow path (Figure I.47).    Figure 5.3: Mean flow velocity in axial hole from HET-P and HET-P (V) using Pitot-static tube data versus mean flow velocity in axial hole from HET using continuity for the Ontario clay specimens   0.125 0.25 0.5 1 2 4 0.125 0.25 0.5 1 2 4 0.125 0.25 0.5 1 2 4 V e lo ci ty  P it o t- st at ic  t u b e  H ET -P  ( V ),  V t [m /s ] V e lo ci ty  f ro m  C o n ti n u it y H ET -P , Q  / A H ET -P [m /s ] Velocity from Continuity HET, Q /AHET [m/s] S3-01/02: Little Cataraqui - HET-P S3-11/12: Bear Brook - HET-P S3-21/22: Wilton Creek - HET-P S3-01/02: Little Cataraqui - HET-P (V) S3-11/12: Bear Brook - HET-P (V) S3-21/22: Wilton Creek - HET-P (V) 1:1 Line 1:1 ±20% HET-P (V): Re > 5000 Chapter 5. Erodible soil specimens     62  Table 5.2: Summary of diameter ratio values obtained from the Ontario clay specimens for turbulent flow with Re > 2000 for HET-P, respectively Re > 5000 for HET-P (V) Soil Sample Diameter Ratio HET-P and HET-P (V), t,HET-P / t,HET and t,HET-P (V) / t,HET Mean Standard deviation Number of observations Test # HET-P HET-P (V) * 1  HET-P HET-P (V) * 1  HET-P HET-P (V) * 1  S3-993.01  * 2  1.15 n/a 0.07 n/a 29 23 (6) S3-993.02 1.06 1.04 (1.27) 0.09 0.05 (0.04) 20 16 (4) S3-993.12 0.97 1.03 (1.15) 0.03 0.04 (0.07) 21 17 (4) S3-993.21  * 3  1.14 0.84 (0.92) 0.08 0.04 (0.04) 73 61 (12) S3-993.22 0.98 1.10 (1.46) 0.02 0.09 (0.18) 18 13 (5)  * 1  HET-P (V): values in parentheses represent data points where 2000 < Re < 5000 * 2  S3-993.01: Pitot-static tube measured flow through intact axial hole at the bottom of the specimen (Figure I.18). * 3  S3-993.21: 2 flow paths, Pitot-static tube measured mainly flow through primary axial flow path (Figure I.47).    Figure 5.4: Estimated axial hole diameter from HET-P and HET-P (V) back calculated from Pitot-static tube data versus estimated axial hole diameter from HET for the Ontario clay specimens   6 12 24 6 12 24 6 12 24 Es ti m at e d  D ia m e te r H ET -P  ( V ),   t, H ET -P  ( V ) [m m ] Es ti m at e d  D ia m e te r H ET -P ,  t, H ET -P [m m ] Estimated Diameter HET, t,HET [mm] S3-01/02: Little Cataraqui - HET-P S3-11/12: Bear Brook - HET-P S3-21/22: Wilton Creek - HET-P S3-01/02: Little Cataraqui - HET-P (V) S3-11/12: Bear Brook - HET-P (V) S3-21/22: Wilton Creek - HET-P (V) 1:1 Line 1:1 ±10% HET-P (V): Re > 5000 Chapter 5. Erodible soil specimens     63 5.2.4. Erosion rate and critical shear stress Starting at a low upstream hydraulic head (tank elevation), and using successively increased head increments during HET-P tests, revealed a distinct behaviour of observed erosion rate (Figure 5.5). Before reaching critical conditions, each increase of the test head resulted in a peak in erosion rate with following decrease at constant test head. Absolute peak values generally decreased with increasing test heads, resulting in a flattening curve of erosion rate until a critical point at which failure occurred in the form of progressive erosion.    Figure 5.5: Erosion rate versus time for successively increased test heads (S3-993.01)   Plots of erosion rate,   , versus shear stress,  , rarely presented themselves in the form described by Wan and Fell (Figure 2.6), and it was not possible at all to fit a reasonable linear best-fit line in order to determine the coefficient of soil erosion, Ce , erosion rate index, IHET , and critical shear stress, c . Thus, critical shear stress was not defined as the x-intercept of the extrapolated linear best-fit line on a      plot, but rather at the point where the erosion rate progressively increased. It was found that this point was distinct on a plot of flow rate, Q , versus shear stress,  , as illustrated in Figure 5.6. The initially steep curve did flatten as the test progressed, and an increase of the slope was observed at the critical point where failure started. Thus, critical shear stress was defined at the point with the minimum slope on a Q –   plot. 0 0.002 0.004 0.006 0.008 0.01 0.012 0.014 0.016 0.018 00:00:00 00:30:00 01:00:00 01:30:00 02:00:00 02:30:00 Es ti m at e d  e ro si o n  r at e  p e r u n it  s u rf ac e  a re a o f th e  a xi al  h o le , ε ̇[ kg /s /m 2 ] Time, t [hh:mm:ss] HET HET-P Critical point: c start of failure Peak and decreasing erosion rate with each test head. Chapter 5. Erodible soil specimens     64    Figure 5.6: Critical shear stress defined on flow rate versus shear stress diagram (S3-993.21)   5.2.5. Dam core material All four specimens prepared from the dam core material experienced immediate erosion, together with very turbid outflow. The soil started to collapse right upon wetting during placement of the specimen. Mostly fine material and occasional small aggregates of particles separated from the specimen and dispersed into the downstream flow chamber during setup. This was visually observed by a major non-transparent discolouration inside the downstream flow chamber and later of the effluent during testing.  In the case of test S1-553.01 (MV4-Altered), this pre-test failure caused the preformed axial hole to collapse and become completely blocked after placing the specimen. No flow was observed up to a test head of about 2300 mm, at which the specimen suddenly collapsed and completely eroded within less than a minute. Shear stress and erosion rate analysis was not possible for this test.  The other three tests all showed similar behaviour. Very rapid erosion started right after the first test head increment from about 50 mm to 160 mm (doubling of upstream hydraulic head from 150 mm to 300 mm). The specimens completely eroded within 1 to 3 minutes, except in test S1-003.01, where 0 2 4 6 8 10 12 14 16 18 20 0 100 200 300 400 500 600 700 800 900 1000 M e as u re d  F lo w  R at e , Q [l /m in ] Estimated wall shear stress,  [N/m2] HET HET-P HET-P (V) Critical point: c,HET-P start of failure Critical shear stress defined at point with minimum slope. Critical point: c,HET start of failure c Chapter 5. Erodible soil specimens     65 the supporting wire mesh clogged and retained a significant portion of the specimen. It was not possible to obtain plots of erosion rate,   , versus shear stress,  , to determine erosion parameters (Figure 2.6). Thus, critical shear stress was defined at the point where sudden progressive erosion started, and the progression of internal erosion was estimated based on observations rather than from deduced coefficient of soil erosion, Ce , and erosion rate index, IHET . HET analyses revealed very low critical shear stresses of less than about 30-40 N/m 2  (Table 5.4). HET-P and HET-P (V) analyses were not possible in most cases because the Pitot-static tube was either blocked or internally clogged. The progression of internal erosion for this soil was estimated as very rapid.   5.2.6. Ontario clay samples All specimens prepared from Ontario clay samples showed non-dispersive erosion behaviour (relatively clear outflow) with an estimated progression of internal erosion of “very slow” to “moderately slow” (according to Wan and Fell, cf. Table 2.1). Test S3-993.12, Bear Brook, was the only completely successful test. Problems with all other tests on the Ontario clay samples partially affected test results. During test S3-993.01, Little Cataraqui, a portion of the bottom part of the specimen remained intact, including the preformed axial hole. This resulted in invalid velocity data from the Pitot-static tube.  Results of both test S3-993.02, Little Cataraqui, and S3-993.22, Wilton Creek, showed only a small increase in diameter over time before the specimen suddenly collapsed. Further, diameters are in relatively good agreement between all three methods of analysis (Table 5.2). Along with continuous erosion observed in the lab and post-test examination of the eroded specimens, this suggested that a cavity developed along the wall of the mold by backward erosion, which collapsed upon further increase of the test head.  Test S3-993.21, Wilton Creek, showed a similar behaviour, but with the difference that axial hole diameters determined from Pitot-static tube data were constantly low, also reflected in a low diameter ratio for the HET-P (V) method (Table 5.2). This was consistent with test S3-993.01, and suggested that backward erosion created a second flow path through the specimen, slowly enlarging from the bottom until failure occurred (sudden enlargement on top).   Chapter 5. Erodible soil specimens     66 Table 5.3: Summary of soil properties for erodible soil specimens Soil sample United Soil Classification System Grain size distribution (USCS) Atterberg limits Standard compaction test Prepared soil specimen Gravel > 4.75 mm Sand > 0.075 mm Silt > 0.002 mm Clay < 0.002 mm Liquid Limit, LL Plastic Limit, PL Standard maximum dry density, d,max Optimum water content, wopt Moist density, m Dry density, d Initial water content, wo Test # USCS [%] [%] [%] [%] [%] [%] [kg/m 3 ] [%] [kg/m 3 ] [kg/m 3 ] [%] Dam MV4-Altered S1-003.01 SP-SC 41 52 7 – – 2121 * 1   (2170-2200) 7.8 * 1   (7.4-7.1) 2331 2106 10.7 S1-003.02 2373 2187 8.5 S1-553.01 2268 2094 8.3 Dam MV4-Core S2-553.01 SC-SM 35.3 36.5 20.5 7.7 22 15 2141 8.2 2186 2023 8.1 Ontario Clay – Little Cataraqui S3-993.01 CL 0 17 67 16 46 27 – – 1895 1445 31.1 S3-993.02 1817 1401 29.7 Ontario Clay – Bear Brook S3-993.12 CL-ML 0 33 57 10 25 20 – – 1880 1651 13.9 Ontario Clay – Wilton Creek S3-993.21 CL 0 33 58 9 26 18 – – 1899 1558 21.9 S3-993.22 1766 1507 17.2  * 1   Compaction data based on Method A; dmax = 4.75 mm, yielding lower dry density and higher water content than Method B. Values in parentheses are corrected for dmax = 9.5 mm.  Chapter 5. Erodible soil specimens     67 Table 5.4: Summary of test data and results for erodible soil specimens Soil sample Specimen Axial hole Post-test measurements Critical shear stress Failure mechanism reconstituted undisturbed drilled fixed center rod f Lf wf c,HET c,HET-P Test # [mm] [mm] [%] [N/m 2 ] [N/m 2 ] Dam MV4-Altered S1-003.01 X  X  45 10 – ≤ 40 ≤ 32 very rapid progression of internal erosion S1-003.02 X  X  – – – ≤ 27 – very rapid progression of internal erosion S1-553.01 X   X – – – – – very rapid progression of internal erosion Dam MV4-Core S2-553.01 X   X – – – ≤ 28 – very rapid progression of internal erosion Ontario Clay – Little Cataraqui S3-993.01  X X  28.3 93 30.0 742 297 moderately slow progression of internal erosion S3-993.02  X X  9 75 38.9 92 26 structural failure (backward erosion) Ontario Clay – Bear Brook S3-993.12  X X  16.3 73 20.4 141 80 very slow progression of internal erosion Ontario Clay – Wilton Creek S3-993.21  X X  11.6 58 28.9 785 556 structural failure (backward erosion + 2 nd  flow path) S3-993.22  X X  9.8 79 32.8 89-149 * 1  58-86 * 1  structural failure (backward erosion)  * 1   Lower value = last measurement at lower test head of 300 mm, higher value = estimated values at higher test head of about 500 mm at which failure occurred.   Chapter 5. Erodible soil specimens     68 5.3. Discussion 5.3.1. Head ratio and shear stress The results from testing erodible soil specimens agree with the findings from tests on the non- erodible PVC specimens, as it was shown that the head ratio, and hence shear stress ratio, was also consistently less than 1.0 (Figure 5.1). This confirmed that shear stress values obtained from the standard HET are generally overestimated due to the use of the hydraulic gradient, s , which is affected by various downstream flow expansion anomalies (Chapter 3).  As observed with the non-erodible test specimens and unlike assumed by Marot et al. (2011), values of head ratio were not constant throughout a test, and generally decreased with increasing diameter of the axial hole. Based on theoretical considerations regarding uniform axial holes, it was surmised earlier that the values of head ratio would converge to unity in the extreme case where the diameter of the axial hole approaches the diameter of the flow chamber. Results confirmed that head ratio increases with diameter after a certain point of change (Figure 5.1), but suggested that it would converge to unity even earlier in a test. The reason for this behaviour is most likely in the fact that soil specimens developed a funnel shaped entrance and exit to the axial hole (also Wan and Fell 2002, 2004a, 2004b; Lim 2006; Wahl et al. 2008), which reduces hydraulic turbulences downstream and eventually yields a head ratio of 1.0.  Values of head ratio were generally higher compared to those from non-erodible PVC specimens. This was due to a significantly higher hydraulic pipe roughness in the soil specimens. This increased the portion of the hydraulic gradient, s , responsible for friction losses, and yielded better agreement between HET and HET-P tests.  Some specimens experienced a sudden structural failure involving extensive “uncontrolled” erosion of the whole specimen, rather than “controlled” progressive erosion around the axial hole. In these cases, the point of change in Figure 5.1 is misleadingly shifted to the left because of a lack of intermediate measuring points, and the estimated maximum diameter does not necessarily reflect the final diameter of the eroded hole.  Even though less significant than with PVC specimens, it was found that HET-P  was less than HET , which further confirms that observed differences between the HET and RCT (Lim 2006), and the HET and JET (Farrar et al. 2007; Wahl et al. 2008; Marot et al. 2011) may be due to an incorrect interpretation of the hydraulic gradient assigned to friction head losses in the standard HET.  Chapter 5. Erodible soil specimens     69  5.3.2. Axial hole velocity and estimated diameter The relatively good agreement found for deduced velocities and diameters between all three methods of analysis, HET, HET-P and HET-P (V) (Table 5.1 and Table 5.2), confirmed the applicability of velocity measurements using a Pitot-static tube at the downstream end of the specimen. However, it also showed that the standard HET method yields reasonably accurate estimates of axial hole diameters, which suggests that velocity measurements are not as crucial for the interpretation of HET data as the downstream total energy head. However, the Pitot-static tube does provide a more direct estimate of axial hole velocity and diameter, and potentially simplifies the analysis of HET data. Considering both methods in parallel would increase confidence in the interpretation of HET results.   5.3.3. Erosion rate and critical shear stress Wan and Fell (2002, 2004a, 2004b) described the early stage in a HET, in which decreasing erosion rate was observed with increasing shear stress, as the period where disturbed and loose material is being removed (Figure 2.6). However, erosion rate behaved differently using successively increased test heads during HET-P tests (Figure 5.5). The initial period of increasing and decreasing erosion rate at lower test heads may reflect a process of successive armouring, where smaller and looser particles are removed from the area directly adjacent to the axial hole, while the course soil matrix remains intact. This creates a rougher and more erosion-resistant surface with time. Once shear stress exceeds an upper critical value, which is high enough to destroy and remove the developed armouring, the whole specimen starts to erode because the less erosion-resistant intact soil underneath is now exposed to an excessive force.  This raises the question whether or not a model scaling factor should be applied to HET-P results. Scalping the gradation curve of test soils to a maximum grain size of 9.5 mm or less, as it is required for test specimens of that size, does not necessarily reflect field conditions. Thus, obtained critical shear stresses may not be directly applicable to actual building materials, and need to be adjusted to the corresponding coarser fraction. However, no adjustment is necessary if the HET-P was used as a simple index test to characterize test soils in terms of relative progression of internal erosion as initially suggested by Wan and Fell (2002, 2004a, 2004b).  Determining the critical shear stress based on a plot of erosion rate versus shear stress according to the standard HET method is associated with various problems and uncertainties, including scattered results for repeated tests, non-linearity in the coefficient of soil erosion, data smoothening, extrapolation of data, and complex curve fitting procedures (Section 2.5). Wan and Fell (2002, 2004a, Chapter 5. Erodible soil specimens     70 2004b) already suggested to use an initial shear stress, o , corresponding to the minimum upstream hydraulic head at which erosion is first initiated, rather than critical shear stress, c , in order to describe initiation of erosion. The newly introduced definition of critical shear stress being at the point with the minimum slope on a Q –   plot follows up on this suggestion, with the only difference that the corresponding minimum hydraulic head was not found by multiple HET trial runs on identical test specimens. It also depicts the reasoning on the process of surface armouring. The critical shear stress would represent the erosion resistance of an exposed coarser fraction of the soil matrix. This method further involved considerably less uncertainties because a highly-biased variable was replaced by the measured flow rate, and shear stress could be obtained more directly using the HET-P (V) method.   5.3.4. Test soils Some of the Ontario clay specimens experienced unexpected erosion behaviour like backward erosion and the development of a second flow path, while the preformed axial hole remained more or less intact. Several reasons could be responsible for that. Firstly, drilling may have introduced a disturbed and denser surface layer around the axial hole that was more erosion-resistant than the surrounding soil. Secondly, possible lost of moisture content and disturbance of the sample caused by the sampling method may have introduced weak points in form of cracks or fractures. Thirdly, the gap between soil and mold due to a slightly smaller diameter of the soil samples may not have been properly sealed, creating a point of weakness to initiate erosion.  It is known that soil specimens developed a funnel shaped entrance and exit to the axial hole in the course of a HET. This was also observed for the Ontario clay specimens. The amount of remoulding on the upstream side was usually smaller that at the downstream side. Other researchers assigned this phenomenon to a process called slaking, where soil particles detached from the specimen due to the presence of water (hydrostatic conditions), rather than the applied shear stress. Recalling the hydraulic review of the HET (Section 3.1), it is most likely that these geometries are the results of corresponding flow patterns (Figure 3.1), forcing the soil into hydraulically optimal shapes. Higher turbulences and flow recirculation at the downstream side may explain the larger amount of remoulding at the bottom of the specimen, and increases the risk of backward erosion.  The erosion behaviour of the two types of soil tested in the current study is comparable with observations for clay soils by Lim (2006), who distinguished between dispersive and non-dispersive soils. Soil specimens prepared from the dam core material showed immediate and very rapid erosion with turbid outflow, which is consistent with the erosion behaviour of dispersive clay soils observed by Lim (2006). The Ontario clay specimens, on the other hand, had a relatively clear outflow, and showed Chapter 5. Erodible soil specimens     71 a slower rate of erosion, together with a considerable reduction of the hole length and irregular shape of the eroded axial hole. This erosion behaviour is characteristic for non-dispersive unsaturated clay soils (Lim 2006).  According to Soroush et al (2008), a formed crack may collapse and self-heal upon wetting, and would rarely sustain in soils with 15% or less fines passing the #200 sieve based on an adjusted gradation curve with a maximum particle size of 4.75 mm (#4 sieve). This may explain the problems experienced with the dam core material. Dam MV4-Altered had an adjusted fines content of about 12%, which is less than the reported threshold of 15%, and a collapsing of the hole as it occurred in test S1-553.01 could be expected. The response of pressure gauges right after the start of test S2- 553.01 on Dam MV4-Core material indicated that the preformed axial hole did stay open upon wetting, which can be expected with an adjusted fines content of about 44%. However, this does not guarantee that a soil is erosion resistant. In fact, Wan and Fell (2002, 2004a, 2004b) characterized the progression of internal erosion of soils with fines content up to 42% as extremely to moderately rapid.   5.3.5. Sources of errors The main sources of errors have already been described in Chapter 4 on the non-erodible test specimens. Additional sources related to tests on erodible soil specimens include non-uniformity of the eroded axial hole, remoulding of the downstream side of the specimen, and a delay in flow rate measurement.  The preformed axial hole could develop a wide range of non-cylindrical shapes, which made it challenging to assign a representative final diameter to the eroded hole. This problem was also reported and discussed extensively by others (Section 2.5), and is not further addressed herein.  A funnel shaped downstream end of the eroded hole as it developed during HET-P tests causes the distance from the end of the effective hole length (begin of downstream funnel) to the Pitot-static tube to increase. This may cause an error in downstream head and velocity readings. This would cause a lower total energy head and thus an increase in the energy gradient across the test specimen, i , and thus estimated shear stress. The velocity, determined from the Pitot-static tube reading, would decrease and a higher estimated diameter would be the result.  At very low flow rates, it took several minutes for the downstream tank to adjust the water level to the corresponding height above the v-notch weir. This caused a delay in flow rate measurements, which was reflected in a temporary decrease of estimated axial hole diameter. This delay decreased Chapter 5. Erodible soil specimens     72 rapidly with increasing flow rates, and was minimized by reducing the tank volume using concrete blocks placed behind the v-notch weir. This error cannot be completely eliminated and needs to be accounted for in the interpretation of HET-P results. However, it could be significantly reduced by using an in-line flow meter an appropriate distance downstream of the test specimen, where the measurements would not be influenced by flow disturbances caused by the test specimen.   5.3.6. Limitations All test results were limited to the accuracy of measuring instruments and other sources of errors implied by the test apparatus used in this study and described above.  As for the non-erodible test specimens, this test series on erodible soil specimens was limited to turbulent flow with Reynolds numbers larger than 2000. Using a constant value for the flow coefficient, K , did limit the applicability of velocity measurements to flow conditions with Reynolds numbers exceeding 5000. It was possible to use Pitot-static tube data below this threshold, but it required caution and additional judgement in the interpretation of results as additional errors were introduced.  Absolute values of critical shear stress were limited to conditions created and observed in the lab. This especially involves scalping of the gradation curve by limiting the maximum particle size for testing. Test results should be corrected for oversize fraction if absolute values should be used in field applications.  Tests on highly erodible and dispersive soils (dam core) were difficult to perform, because the erosion process started right upon wetting during placing of the specimen, and progressed very rapid after the test was started. This made it nearly impossible to collect enough high quality data for a representative and accurate analysis, which reduced the confidence in interpreted results.  Furthermore, clogging of the Pitot-static tube by eroding particles was a common problem in testing highly erodible and dispersive soils (dam core). The incorporated back flush mechanism before each reading could clear any particles from the Pitot-static tube without disturbing the downstream side of the soil specimen. However, back-flushing was not always completely successful, and the partially or totally clogged Pitot-static tube produced erroneous HET-P data.   Chapter 6. Conclusions and recommendations     73 6. Conclusions and recommendations 6.1. Summary and conclusions The standard Hole Erosion Test (HET) was modified by incorporating a conventional Pitot-static tube at the downstream side of the test specimen that allows for an improved energy based analysis of test data. The modified test is referred to as the HET-P. The HET-P provides an additional measure of the total energy head, Hd , and centerline velocity head, hv , at the point where the fluid jet exits the axial hole. Two modified methods of analysis (2, 3) were introduced and compared to the method originally proposed by Wan and Fell (1):  1. HET Original method proposed by Wan and Fell (2002, 2004a, 2004b); 2. HET-P New method based on energy gradient using Hd ; 3. HET-P (V) New method based on energy gradient and flow velocity using Hd and hv .  Two series of tests, one on non-erodible PVC specimens (10 tests), and one on erodible soil specimens (9 tests), yield the following conclusions:  - The differences between the modified HET-P and the standard HET are described by the head ratio, H / h , which is usually smaller than unity. Further, unlike suggested by Marot et al. (2011), values of H / h  are not constant throughout a test, but vary with axial hole diameter and hydraulic pipe roughness. Values are closer to unity for higher hydraulic pipe roughness. With increasing diameter, values of H / h  initially decrease to a minimum, after which they start converging unity as the axial hole enlarges and approaches the diameter of the flow chamber. The development of a funnel shaped exit to the axial hole in soil specimens reduces downstream hydraulic turbulences, causing an earlier and faster rate of increase.  - The head ratio, H / h , also reflects the relative values of energy gradient and hydraulic gradient across the test specimen, i / s , as well as shear stress obtained from the HET-P and HET tests, HET-P / HET . The deduced shear stress from HET-P is significantly smaller than that obtained from the HET. This is mainly a result of the total energy head measured with the Pitot-static tube at the exit of the axial hole exceeding the hydraulic head measured at the sidewall of the device just downstream of the test specimen, in a region affected by high turbulence, flow separation and eddies. The downstream sidewall hydraulic head yields a hydraulic gradient that is not representative of the friction head loss along the axial hole of the test specimen. This may explain differences observed between the HET and RCT (Lim 2006), Chapter 6. Conclusions and recommendations     74 and between HET and JET (Farrar et al. 2007; Wahl et al. 2008; Marot et al. 2011). It further confirms the findings by Marot et al. (2011) that only a portion of the measured hydraulic gradient, s , is transformed into friction and erosion in the standard HET.  - In addition, the Pitot-static tube also provides a direct measure of the centerline jet velocity escaping the axial hole, which can be used to determine the mean velocity in the axial hole, Vt . This yields a simplified and more direct estimate of the axial hole diameter, t , and corresponding erosion parameters without any assumptions regarding the hydraulic roughness of the axial hole, which are required by the standard HET (Wan and Fell 2002, 2004a, 2004b; Wahl et al. 2008, 2009). However, velocity measurements are affected by flow conditions, and it has to be distinguished between laminar and turbulent flow.  - This study assumed turbulent flow conditions if Reynolds numbers exceed 2000 (Wahl et al. 2008). However, experience showed that results were less variable and could be interpreted with higher confidence in flow conditions with Reynolds numbers exceeding 5000. The range where 2000 < Re < 5000 is called the critical zone, in which flow could be either laminar or turbulent. In this highly complex hydraulic system, it should be distinguished between complete turbulent flow (Re > 5000) and this critical zone in the analysis and interpretation of HET-P data.  - Hole Erosion tests, standard and modified, are difficult to perform on highly erodible and dispersive soils like the dam core material used in this study. This is consistent with results reported by others (Wan and Fell 2002, 2004a, 2004b; Lim 2006; Farrar et al. 2007; Wahl et al. 2008, 2009). Further difficulties arise if the desired uniform erosion of the axial hole is superseded or accompanied by other unintended erosion mechanisms like backward erosion or the development of a second flow path. These may interfere with analysis assumptions or create additional need for subjective judgement in the process of data analysis and interpretation.  - With more confidence in the interpretation of the critical shear stress, c , using velocity measurements and the Q- diagram, the HET-P could be used beyond index testing. With c from HET-P tests representing a critical shear stress corresponding to the maximum particle size used in testing, laboratory results could be scaled to values to be used in the field for design purposes or safety evaluations of existing structures.  Chapter 6. Conclusions and recommendations     75 - The tests performed in this study showed a significant potential for the introduction of a conventional Pitot-static tube in HET for pressure and velocity measurements downstream of the test specimen. Incorporating a Pitot-static tube into a HET apparatus requires modest technical effort, and is relatively easy to implement. Operation of the instrument is simple, and it can easily be integrated in an automated data acquisition system. Overall, the Pitot-static tube is a simple low cost method that yields more transparent and reliable results, making the Modified Hole Erosion Test (HET-P) a technically and economically feasible method to study erosion characteristics of soil with applications in both constructed earth structures including dams and embankments, and natural river banks.   6.2. Recommendations The following recommendations for further research are made from experiences in this study on the Modified Hole Erosion Test (HET-P):  - To further investigate the hydraulic component of the Hole Erosion Test and its implications on erosion behaviour and data analysis, it is recommended to carry out tests on non-erodible test specimens with non-uniform axial holes. That is testing axial hole geometries as they may develop in soil specimens during the course of a test, especially the often observed funnel shaped deformation of the entrance and exit to the axial hole (e.g. Figure I.17 or Figure I.37) that implies changes to hydraulic conditions and flow patterns at the points of measurement.  - Besides hydraulic conditions and flow patterns, the hydraulic pipe roughness inside the axial hole plays a major role regarding erosion resistance. In stable conditions where            , roughness describes the resistance to flow, and governs the relationship between the energy head loss along the test specimen, H , and flow rate, Q . PVC specimens and specimens from different soil samples experience different hydraulic pipe roughness, which implies different H-Q relationships. Further, roughness tends to increase during a Hole Erosion Test as fines are eroded or washed out more easily than the coarser particles. Testing non-erodible specimens with different hydraulic pipe roughness would help to obtain a better understanding of the implications of changing hydraulic pipe roughness inside the axial hole.  - The HET-P apparatus has been tested on limited soil samples. In order to obtain a comprehensive data base for this test, and to improve the confidence in the testing procedure, more tests should be performed on a number of different soil samples. Chapter 6. Conclusions and recommendations     76  - This study showed that the differences between the standard HET and the modified HET-P could explain the differences observed between the standard HET and other soil erosion test methods (Lim 2006; Farrar et al. 2007; Wahl et al. 2008; Marot et al. 2011). To prove this statement, paired testing of HET-P and RCT, HET-P and JET, and other possible test methods would be necessary.    References     77 References ASTM Standard D421-85, 1985 (2007), Standard Practice for Dry Preparation of Soil Samples for Particle-Size Analysis and Determination of Soil Constants, ASTM International, West Conshohocken, PA, 2007, www.astm.org. ASTM Standard D422-63, 1963 (2007), Standard Test Method for Particle-Size Analysis of Soils, ASTM International, West Conshohocken, PA, 2007, www.astm.org. 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Experiments on the Scour Resistance of Cohesive Sediments. Journal of Geophysical Research, 67(4), 1437-1449. Ravens, T. M., & Gschwend, P. M. (1999). Flume measurement of sediment erodibility in Boston Harbor. Journal of Hydraulic Engineering, ASCE, 125(10), 998-1005. Rohan, K., Lefebvre, G., Douville, S., & Milette, J. (1986). NEW TECHNIQUE TO EVALUATE EROSIVITY OF COHESIVE MATERIAL. Geotechnical Testing Journal, 9(2), 87-92. Sargunan, A. (1977). Concept of Critical Shear Stress in Relation to Characterization of Dispersive Clays, In Dispersive Clays, Related Piping, and Erosion in Geotechnical Projects. ASTM Special Technical Publication 623, Sherard, J.L. and Decker R.S. Eds., 390-397. Schmertmann, J. H. (2004). Time for development of internal erosion and piping in embankment dams" by robin fell, chi fai wan, john cyganiewicz, and mark foster. Journal of Geotechnical and Geoenvironmental Engineering, 130(9), 980-980. References     81 Shaikh, A., Ruff, J.F., & Abt, SR. (1988a). Erosion rate of compacted NA-montmorillonite soils. Journal of Geotechnical Engineering, ASCE, 114(3), 296-305. Shaikh, A., Ruff, J.F., Charlie, W.A., & Abt, S.R. (1988b). Erosion rate of dispersive and nondispersive clays. Journal of Geotechnical Engineering, ASCE, 114(5), 589-600. Sherard, J. L., & Dunnigan, L. P. (1989). Critical filters for impervious soils. Journal of Geotechnical Engineering, 115(7), 927-947. Sherard, J. L. (1986). HYDRAULIC FRACTURING IN EMBANKMENT DAMS. Journal of Geotechnical Engineering, 112(10), 905-927. Sherard, J. L., & Dunnigan, L. P. (1985). FILTERS AND LEAKAGE CONTROL IN EMBANKMENT DAMS. Seepage and Leakage from Dams and Impoundments. Proceedings of a Symposium in Conjunction with the 1985 ASCE National Convention. 1-30. Sherard, J. L., Dunnigan, L. P., & Decker, R. S. (1976). IDENTIFICATION AND NATURE OF DISPERSIVE SOILS. American Society of Civil Engineers, Journal of the Geotechnical Engineering Division, 102(4), 287-301. Sherard, J. L., Dunnigan, L. P., Decker, R. S., & Steele, E. F. (1976). PINHOLE TEST FOR IDENTIFYING DISPERSIVE SOILS. American Society of Civil Engineers, Journal of the Geotechnical Engineering Division, 102(1), 69-85. Sherard, J. L., Dunnigan, L. P., & Talbot, J. R. (1984a). BASIC PROPERTIES OF SAND AND GRAVEL FILTERS. Journal of Geotechnical Engineering, 110(6), 684-700. Sherard, J. L., Dunnigan, L. P., & Talbot, J. R. (1984b). FILTERS FOR SILTS AND CLAYS. Journal of Geotechnical Engineering, 110(6), 701-718. Soroush, A., Aminzadeh, A., & Shourijeh, P. T. (2008). Identifying low-fines soils not suited to NEF testing. Proceedings of the Institution of Civil Engineers: Geotechnical Engineering, 161(4), 181- 188. Soroush, A., & Shourijeh, P. T. (2009). A review of the no erosion filter test. Geotechnical Testing Journal, 32(3), 209-218. Wahl, T. L., Regazzoni, P., & Erdogan, Z. (2008). Determining erosion indices of cohesive soils with the hole erosion test and jet erosion test (Hydraulic Laboratory (HL) No. DSO-08-05). Denver, Colorado: U.S. Department of the Interior, Bureau of Reclamation, Technical Service Center. Wahl, T. L., Regazzoni, P., & Erdogan, Z. (2009). Practical improvements for the hole erosion test. 33rd IAHR Congress: Water Engineering for a Sustainable Environment, Vancouver. 6383-6390. Wan, C. F., & Fell, R. (2002). Investigation of internal erosion and piping of soils in embankment dams by the slot erosion test and the hole erosion test (UNICIV Report No. R-412). Sidney, Australia: The University of New South Wales. Wan, C. F., & Fell, R. (2004a). Investigation of rate of erosion of soils in embankment dams. Journal of Geotechnical and Geoenvironmental Engineering, 130(4), 373-380. References     82 Wan, C. F., & Fell, R. (2004b). Laboratory tests on the rate of piping erosion of soils in embankment dams. Geotechnical Testing Journal, 27(3), 295-303. Zhang, G. H., Liu, B. Y., Liu, G. B., He, X. W., & Nearing, M. A. (2003). Detachment of undisturbed soils by shallow flow. Soil Science Society of America Journal, 67(3), 713-719.     Appendices     83 Appendices     Appendices     84 Appendix A: Review of the standard Hole Erosion Test (HET) Table A.1: Known challenges and issues of the standard HET with suggested improvements Stage Reported challenge or issue Suggested improvement Specimen preparation Introduced inhomogeneity by specimen reconstitution Increase number of compaction layers from 3 to 6 or more  Dense surface layer due to smearing and remoulding during drilling Use sharp auger drill at low speed, slowly advanced, and repeatedly cleaned  Different initial roughness of the preformed hole introduced by drilling Clean out drilled hole in a uniform manner, e.g. with wire brush  Testing  Temporary or partial blockage of the preformed hole (soil dependent) Restrict particle size, interrupt test to free preformed hole if possible  Effects of slaking (detachment of particles due to the presence of water) End plates with orifice openings of a size appropriate to the erosion resistance of the test soil, e.g. 15 mm for stronger and 25 mm for weaker soils  Scouring at entrance and exit due to eddies at the soil interface  Change of geometry of preformed hole due to swelling (soil dependent) Control curing time of prepared specimen, time of introducing hole, and test time  Non-uniform cross section along the length of the soil specimen   The length of the preformed hole can change Interpolate hole length over time in data analysis  Specimen too short for establishing fully developed flow   Flow conditions are mostly turbulent, but can change throughout a test   Difficult to assign a representative final hole diameter to the eroded hole  Advanced measuring technique, e.g. from plaster casting of the eroded hole Numerical model by Bonelli et al.  Different critical hydraulic gradients between soil samples and/or specimens of the same sample Good quality soil samples, standardized procedures and experienced technicians  Absent or significantly low normal stress  Analysis & Interpretation 13+ assumptions and approximation in analytical solution Best engineering practice unless otherwise noted  The length of the eroded hole is assumed to vary linearly with time   Curve fitting procedures and extrapolation of data Numerical model by Bonelli et al.   Only data collected during the period of progressive erosion are considered useful to determine erosion parameters   Virtual, not physically existing friction factors fL and fT Numerical model by Bonelli et al.   Non-linearity in friction factors fL  and fT with time Friction factors assumed to be linear proportional to eroded hole diameter  Increase of estimated diameter, t , even at times with no erosion  Non-linearity in the coefficient of soil erosion, Ce  (time dependent)   Graphical extrapolation to find critical shear stress, c  (imprecise results) Use of initial shear stress, o , to describe initiation of erosion  Appendices     85 Appendix B: Engineering drawings    Appendices     86     Appendices     87     Appendices     88 Appendix C: Calibration of measuring instruments Differential pressure transducers   Figure C.1: H-U diagram differential pressure transducer #1 and #2 with fitted linear regression lines to convert output voltage to differential pressure head   y = 671.650x + 31.539 R² = 1.000 y = 669.061x + 32.834 R² = 1.000 y = 353.221x - 1'829.847 R² = 1.000 y = 352.678x - 1'824.900 R² = 1.000 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 0 500 1000 1500 2000 2500 0 2 4 6 8 10 12 14 D if fe re n ti al  P re ss u re ,  p [p si ] D if fe re n ti al  P re ss u re  H e ad ,  h [m m  H 2 O ] Voltage, U [V] Differential Pressure Transducer #1: low-high Differential Pressure Transducer #1: high-low Differential Pressure Transducer #2: low-high Differential Pressure Transducer #2: high-low Appendices     89 Custom v-notch weir   Figure C.2: H-Q diagram v-notch weir using Kindsvater-Shen relationship (curve fitting) 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 0 10 20 30 40 50 60 70 80 90 100 110 120 130 0 10 20 30 40 50 60 70 80 90 100 110 120 130 0 5 10 15 20 25 30 35 40 W at e r h e ad  r e la ti ve  t o  c re st , h [m m ] W at e r h e ad  r e la ti ve  t o  c re st , h [m m ] Flow Rate, Q [l/min] Best Fit C3-001.01: Blue C3-002.01: Blue C3-001.01: Red C3-002.01: Red C3-001.01: MM 7 C3-002.01: MM 7 Kindsvater-Shen Relationship Fitted Curve: Q = discharge over weir [m3/s] C = effective discharge coefficient [ - ] C = 0.6700 h = head on the weir [m] k = head correction factor [m] k = 0.0000 m q = angle of v-notch [degrees] q = 9.5° (measured)   2 5 2 tan36.2 khCQ        q Flow Rate: 0-40 l/min Flow Rate: 0-4 l/min Appendices     90    Figure C.3: H-Q diagram v-notch weir using Kindsvater-Shen relationship (head readings) 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 105 115 125 135 145 155 165 175 185 195 205 215 225 235 18 28 38 48 58 68 78 88 98 108 118 128 138 148 0 5 10 15 20 25 30 35 40 H e ad  R e ad in g P ie zo m e te r 7  [ m m ] H e ad  R e ad in g Ta n k - B lu e  S ca le  [ m m ] Flow Rate, Q [l/min] Kindsvater-Shen Relationship Fitted Curve: Q = discharge over weir [m3/s] C = effective discharge coefficient [ - ] C = 0.6700 h = head on the weir [m] k = head correction factor [m] k = 0.0000 m q = angle of v-notch [degrees] q = 9.5° (measured)   2 5 2 tan36.2 khCQ        q Flow Rate: 0-40 l/min Flow Rate: 0-4 l/min Appendices     91 Appendix D: HET-P test procedure Soil preparation for reconstituted specimens 1. Take a sub-sample of the soil selected for testing, large enough to obtain about 3 kg of material passing the 9.5 mm (3/8 in) sieve. 2. Depending on the type of soil, oven-dry the sub-sample or proceed with step 3. 3. Sieve the sub-sample through a 9.5 mm (3/8 in) sieve. 4. If the sub-sample was NOT oven-dried, take the water content of the material passing the 9.5 mm sieve according to ASTM Standard D2216-05. 5. If the water content is too high, air-dry the sub-sample and repeat step 4 and 5 as necessary. 6. Calculate the desired compaction parameters: a. Mass of soil (air- or oven-dry, or water content as received); b. Mass of water to be added; c. Mass of wet soil per compaction layer; d. Height of each compaction layer. 7. Place the soil in a tray over a balance and add the calculated amount of water. 8. Thoroughly mix the soil and water, and place the prepared soil in an air-tight container or plastic bag to cure (preferably in a moist room). Curing time depends on the type of soil. Overnight (16 h) is appropriate in most cases (e.g. ASTM Standard D698-07e1).   Specimen preparation for reconstituted specimens 1. Clean the test mold, base, collar and 6-mm center brass rod. 2. Assemble the base, test mold and center brass rod. 3. Take the mass of the assembled mold (base + test mold + center rod). 4. Attach the collar on top of the test mold. 5. Evenly distribute and compact the first layer of soil to the calculated height using the custom compaction device (Appendix B). 6. Repeat step 5 for layer 2 and 3. 7. Remove the collar, and carefully trim the compacted specimen using a straight edge to form a plane surface even with the top of the test mold. 8. Take the mass of the compacted specimen including base, test mold and center brass rod. 9. Take the water content of the trimmed material according to ASTM Standard D2216-05. 10. Seal the prepared specimen in plastic bags and/or cling wrap to prevent moisture loss, and cure overnight before testing.  Appendices     92  Specimen preparation for specimens from undisturbed (intact) soil samples 1. Clean the test mold, base and collar. 2. Assemble the base and test mold. 3. Take the mass of the assembled mold (base + test mold). 4. Trim the soil sample to a length 10-20 mm longer than the test mold and if necessary to a diameter as close to the diameter of the test mold as possible. 5. Take the mass of the trimmed sample including base, test mold and collar. 6. Place the collar onto the base and underneath the test mold in order to elevate the test mold. 7. Place the trimmed sample centrically inside the test mold, and fix it such that it equally overtops on either side of the test mold. To do so, place wooden or plastic elements with a diameter equal to that of the test mold inside the collar to fill the space between base and soil. 8. Record the size of the gap between the soil and the wall of the test mold. 9. Close the gap between soil and test mold with modeling clay 5-10 mm below the top of the test mold, and fill the remaining gap with epoxy sealant. 10. Seal the assembled mold and trimmed sample in plastic bags and/or cling wrap to prevent moisture loss, and let the epoxy sealant harden. 11. Carefully turn the trimmed sample and test mold upside down and repeat step 9 and 10. 12. Take the mass of the trimmed sample including filler, base, test mold and collar. 13. Calculate the mass of the filler (modelling clay and epoxy sealant). 14. Carefully trim the soil using a straight edge to form a plane surface even with the top and the bottom of the test mold. 15. Take the mass of the prepared specimen including base and test mold. 16. Take the water content of the trimmed material according to ASTM Standard D2216-05. 17. Drill an axial 6 mm (1/4 in) hole centrically through the specimen using a drill press and wood auger bit.   Test preparation 1. Prepare the bridge elements and rubber o-rings, and assemble the downstream flow chamber, intermediate flange and bridge element with supporting wire mesh. 2. Decide on an appropriate differential pressure transducer according to test heads expected for the prepared soil specimen, and connect it to the Pitot-static tube. 3. Saturate the transducer system and piezometer tubes with de-aerated water. Make sure that there is no air left in the system before proceeding to the next step. Appendices     93 4. Check the alignment of the Pitot-static tube, and slightly open the valves connecting the back pressure tanks to the Pitot-static tube to allow a low back flow in order to prevent any particles from entering the Pitot-static tube during setup. 5. Fill the downstream constant head tank with water, slightly overtopping the v-notch weir. 6. Carefully open the downstream gate valve until the water level reaches the top of the downstream bridge element. 7. Connect the downstream piezometer tube as soon as the connection is fully submerged. 8. Carefully remove the center rod from the soil specimen if necessary, and place the mold containing the prepared soil specimen on top of the bridge element and wire mesh, making sure no air is trapped underneath the soil specimen. 9. Place the upstream intermediate flange, and fix the mold to hold it in place centrically above the Pitot-static tube. 10. Assemble the upstream flow chamber, and securely tighten the test cell. 11. Proceed saturating the system by slowly filling the upstream flow camber with water. 12. Connect the upstream piezometer tube as soon as the connection is fully submerged. 13. Raise the upstream constant head tank to its maximum height, and connect it to the upstream flow chamber. 14. Proceed saturating the system by slowly filling the upstream constant head tank with water, and making sure that there are no air pockets trapped inside the flexible tubing. 15. Position the upstream constant head tank at the desired starting head level, and adjust the inflow to an appropriate rate. Tests usually start at a tank level of 150 mm. 16. Connect the voltmeter, turn it on, and close all back pressure valves.   Test procedure 1. Open the gate valve DS, and start the timer. 2. Take the following readings in intervals of 1-2 minutes: a. Elapsed time, t ; b. Sidewall hydraulic head upstream, hu , and downstream, hd ; c. Total energy head downstream, Hd  (voltage output); d. Centerline velocity head, hv  (voltage output); e. Tank level downstream for flow rate, Q ; f. Water temperature, T . 3. The intervals may be reduced if erosion is rapid, or increased if there is no noticeable erosion. 4. Raise the upstream constant head tank to increase the test head soon after the flow rate stabilizes at a given head, and repeat steps 2 through 4. The upstream tank level is usually Appendices     94 doubled, unless there are reasons to believe that critical conditions may occur at an intermediate level. 5. Maintain the upstream tank level until the end of the test if the flow rate increases. 6. Stop the test by closing the gate vale DS if one of the following applies: a. Maximum test head is maintained for at least one hour with no noticeable erosion; b. At least several minutes of accelerating flow is observed; c. Flow rate exceeds inflow; d. The eroded axial hole expanded to the wall of the test mold.   Post-test procedure 1. Disconnect all electronic devices. 2. Drain the apparatus in reverse order according to steps 5 through 14 of the test preparation. 3. Take pictures of the upstream and downstream side of the eroded soil specimen inside the test mold with appropriate labels. 4. Roughly sketch the shape of the eroded hole and estimate the final hole diameter. 5. Assemble the base and the test mold with the eroded soil specimen, and fill the eroded hole with Plaster of Paris if reasonable. Otherwise proceed with step 7, 9 and 10. 6. Seal the assembled mold containing soil and Plaster of Paris in plastic bags and/or cling wrap to prevent moisture loss, and let the plaster cast harden. 7. Carefully extract the plaster cast, and take the water content of the remaining soil specimen according to ASTM Standard D2216-05. 8. Determine the exact shape, volume, final axial hole diameter, f , and effective hole length, L , from the plaster cast. Take at least five measurements in each direction along the length respectively circumference of the plaster cast. 9. Remove all the remaining soil from the test apparatus and test mold. Make sure to use sedimentation tanks in combination with sediment traps to prevent soil particles entering the sewer system. 10. Clean and reassemble everything as necessary to prepare the equipment for the next test.    Appendices     95 Appendix E: Analysis methods Table E.1: Step by step analysis of test data for different methods Step HET (Wan and Fell 2002, 2004) HET-P based on energy gradient, i HET-P (V) based on i and velocity, Vt i) Define initial and final flow conditions using Equation (2.8) and (2.13), and identify a representative flow condition to be used for this test: - laminar; Re < 5000 - turbulent; Re > 5000 Define initial and final flow conditions using Equation (2.8) and (2.13), and identify a representative flow condition to be used for this test: - laminar; Re < 2000 - turbulent; Re > 2000  ii) Estimate the initial friction factor fL,o  or fT,o  based on the initial diameter of the preformed hole, o = 6 mm, using Equation (2.11) Estimate the initial friction factor fL,o  or fT,o  based on the initial diameter of the preformed hole, o = 6 mm, using Equation (3.5)  iii) Estimate the final friction factor fL,f  or fT,f  based on the measured final diameter of the eroded hole, f , using Equation (2.11) Estimate the final friction factor fL,f  or fT,f  based on the measured final diameter of the eroded hole, f , using Equation (3.5)  iv) Interpolate the friction factor fL or fT  linearly between its initial (t = 0) and final value (t = tf) Interpolate the friction factor fL or fT  linearly between its initial (t = 0) and final value (t = tf)  v) Estimate the diameter of the axial hole, t , at any time during the test using Equation (2.12) Estimate the diameter of the axial hole, t , at any time during the test using Equation (3.6) Estimate the diameter of the axial hole, t , at any time during the test using Equation (3.7) and (2.8) vi) Plot a curve of estimated diameter, t , against time, t Plot a curve of estimated diameter, t , against time, t Plot a curve of estimated diameter, t , against time, t vii) Estimate the slope         , if appropriate approximated by  Estimate the slope         , if appropriate approximated by  Estimate the slope         , if appropriate approximated by  viii) Estimate wall shear stress,      , using Equation (2.5) Estimate wall shear stress,        , using Equation (3.3), assuming the length of the axial hole varies linearly with time where applicable Estimate wall shear stress,        , using Equation (3.3), assuming the length of the axial hole varies linearly with time where applicable ix) Estimate erosion rate,       , using Equation (2.7) Estimate erosion rate,         , using Equation (2.7) Estimate erosion rate,         , using Equation (2.7) x) Plot,       , against      , and fit a linear straight line through the rising part of the curve Plot,         , against        , and fit a linear straight line through the rising part of the curve Plot,         , against        , and fit a linear straight line through the rising part of the curve xi) Determine coefficient of soil erosion, Ce , and erosion rate index, IHET , using Equation (2.1) Determine coefficient of soil erosion, Ce , and erosion rate index, IHET , using Equation (2.1) Determine coefficient of soil erosion, Ce , and erosion rate index, IHET , using Equation (2.1) xii) * 1  Graphically obtain critical shear stress, c , as illustrated in Figure 2.6 Graphically obtain critical shear stress, c , as illustrated in Figure 2.6 Graphically obtain critical shear stress, c , as illustrated in Figure 2.6  * 1  Alternatively, critical shear stress, c , may be obtained graphically using the Q- plot as illustrated in Figure 5.6.  Appendices     96 Appendix F: Experimental program Table F.1: Test number information a) Test number Type Name abc Type No. 0-9 Series No. 0-9 Test No. 0-9 b) Universal nomenclature Setup No. 0 n/a (P) No data recorded (T, C, D, S) 1 DS Pitot Tube, "large" manometer tubes, 10° V-Notch. 2 DS Pitot Tube, p transducers at Pitot Tube, concrete blocks in inflow tank DS to reduce volume. 3 as #2, concrete blocks in inflow tank DS modified, total head DS using MM 4 as datum (±0.00) R Reproduced using data by others z1 z2 c) Specific nomenclature Type Type No. Series Numbers T Test runs 1 Preliminary n/a 2 Stage 1 3 Stage 2 n/a C Calibration 1 Tank US n/a 2 Manometers 3 Tank DS n/a 4 Equipment D PVC specimens 1 Uniform defect 0 2-digit # Hole diameter 1:  6 mm 1 2-digit # Hole diameter 2: 12 mm 2 2-digit # Hole diameter 3: 24 mm 6 2-digit # Hole diameter 1:  6 mm 2 2-digit # Hole diameter 2: 12 mm 4 2-digit # Hole diameter 3: 24 mm P Soil properties 1 Soil 1 Dummy 11 Gradation Sieving 2 Soil 2 Dam 12 Hydrometer 3 Soil 3 O-Clay 13 Combined Methods 21 Compaction Standard 22 Modified 31 32 S Soil specimens 1 Soil 1 Dummy 0 Special conditions (water content) 2 Soil 2 Dam 5 Optimum water content 3 Soil 3 O-Clay 9 Water content as received 0 Special conditions (dry density) 5 95% standard max. dry density 9 Dry density as received y3 Ax - y1y2y3 . z1z2 A x y z y2 Continuous two-digit test number y1 y2 y1 y2 y1 y2 y 1 y 2 y 1 y 2 y 1 y 2 y1   Appendices     97 Table F.2: Test program Test number Date Audio Data sheet Analysis Notes  Test runs T1-001.01 02.12.2009 X   V-notch weir preliminary design (10°)  T1-000.01 03.12.2009 X X  V-notch weir improved preliminary design (10°)   T2-000.01 12.01.2010 X X  Setup 1, empty soil mold Leakages T2-000.02 15.01.2010 X X  Setup 1, empty soil mold Leakages T2-000.03 22.01.2010 X X  Setup 1, empty soil mold Test okay T2-001.01 26.01.2010 X   Setup 1, D1-06 Pitot slow  T3-002.01 22.02.2010 X   Setup 2, D1-06, Differential p. transducers Test okay  Calibration C1-001.01 22.01.2010 X   Maximum overflow capacity   C2-001.01 26.01.2010 X   Zero readings piezometer board setup 1  C2-002.01 22.02.2010 X   Zero readings piezometer board setup 2  C2-002.02 26.02.2010 X  V1.1 Calibration 1 Differential Pressure Transducers  C2-002.03 02.03.2010 X  V1.1 Calibration 2 Differential Pressure Transducers  C2-003.01 27.04.2010 X  V1.1 Calibration 3 Differential Pressure Transducers  C2-Summary X X X V3.1 Summary Differential Pressure Transducers  C2-003.02 03.05.2010 X X  Height instruments and connections setup 3   C3-001.01 22.01.2010 X  V2.1 Calibration 1 v-notch weir  C3-002.01 19.02.2010 X  V2.1 Calibration 2 v-notch weir  C3-Summary X X X V1.2 Summary v-notch weir  C3-003.01 10.05.2010 X  V1.3 Head-Volume Relationship Inflow Tank DS setup 3   C4-003.01 22.07.2010 X   Dimensions Compaction Mold (white) and Center Brass Rod  Appendices     98 Test number Date Audio Data sheet Analysis Notes  Non-erodible test specimens D1-061.01 27/28.01.10 X  V1.3 2-day full range (US head) test setup 1 Pitot slow, air D1-062.01 12.03.2010 X  V2.4 Full range (US head) test setup 2: two DT DT1 error  D1-063.01 09.04.2010   V6.3 Uniform defect: diameter = 6 mm No flow restrictions Max flow rate approx. 7.8 l/min Test okay D1-063.02 27.04.2010   Test okay D1-063.03 27.04.2010   Test okay  D1-123.01 03.05.2010   V6.3 Uniform defect: diameter = 12 mm No flow restrictions Max flow rate approx. 36 l/min Test okay D1-123.02 03.05.2010   Test okay D1-123.03 03.05.2010   Test okay  D1-243.01 04.05.2010   V6.3 Uniform defect: diameter = 24 mm No flow restrictions Max flow rate approx. 39 l/min Low accuracy D1-243.02 04.05.2010   Low accuracy D1-243.03 04.05.2010   Low accuracy D1-243.04 17.06.2011   V6.3 Low range p transducer for better accuracy Test okay  D1-Summary X X X V6.3 Comparison of all three dummy specimens (6,12,24 mm)   Soil properties P1-110.01 07.07.2010 X  V3.3 Gradation - Sieving - ASTM D 6913-04 (2009)  P1-210.01 08.07.2010 X  V3.3 Standard Compaction Test - ASTM D 698-07e1 - Method A  P1-210.02 21.07.2010 X  V3.3 Compaction Test - adapted from ASTM D 698-07e1 - Method B  P2-13R.01 19.07.2010 X  V3.1 Gradation - Sieving and Hydrometer Analysis Reproduced P2-13R.02 29.07.2010 X  V1.2 Gradation - Sieving and Hydrometer Analysis Reproduced P2-210.01 16.07.2010 X  V4.2 Standard Compaction Test - ASTM D 698-07e1 - Method B   P3 09.06.2011 X X X Soil property data received from D. Cossette, Civil & Geological Engineering, University of Saskatchewan Appendices     99 Test number Date Audio Data sheet Analysis Notes  Erodible soil specimens S1-003.01 11.05.2010   V6.3 Supporting wire mesh clogged Failed S1-003.02 12.05.2010   V6.3 Specimen collapsed, Pitot DS clogged Failed (blowout)  S1-553.01 22.07.2010   X Specimen collapsed, Pitot DS clogged Failed (blowout)   S2-553.01 23.07.2010   X Specimen collapsed, Pitot DS clogged Failed (blowout)   S3-Little Cataraqui  S3-993.01a 27.08.2010   X Part 1: hole blocked Test aborted S3-993.01b 27.08.2010   V6.3 Part 2: bottom part intact => V unusable, Plaster cast made Partial test S3-993.02 08.11.2010   V6.3 Spec. suddenly collapsed at H = 0.5 m, t = 1:00 h Structural failure  S3-Bear Brook  S3-993.11 07.10.2010 X X X Sample disturbed and cannot be tested Failed S3-993.12 12.10.2010   V6.3 Duration too short, Plaster cast made Test okay  S3-Wilton Creek  S3-993.21 12.11.2010   V6.3 Spec. suddenly collapsed at H = 2.0 m, Plaster cast made Structural failure S3-993.22 15.10.2010   V6.3 Spec. suddenly collapsed at H = 0.6 m Structural failure  S3-Raisin River X X X Not tested: lots of organic matter   S3-Jock River X X X Cannot be tested: specimen too small, lots of organic matter   S3-Summary X X X V6.3 Comparison of qualitative results for all soils type S3    Appendices     100 Appendix G: Non-erodible test specimens Table G.1: Test data and results non-erodible test specimen D1-063 o Head Q hu hd hv Hd Re CpCv Vt t s i H/h HET HET-P HET-P (V) [mm] [mm] [l/min] [mm] [mm] [mm] [mm] [ - ] [ - ] [m/s] [mm] [ - ] [ - ] [ - ] [N/m 2 ] [N/m 2 ] [N/m 2 ] 6 20 0.8 151 131 14 145 2.62E+03 0.878 0.43 6.2 0.20 0.06 0.29 3.0 0.9 0.9 6 23 0.8 154 131 14 145 2.36E+03 0.922 0.43 6.3 0.23 0.09 0.41 3.4 1.4 1.5 6 67 1.2 202 135 42 180 3.39E+03 0.804 0.75 5.9 0.68 0.22 0.33 9.9 3.3 3.2 6 156 2.1 299 142 109 251 5.62E+03 0.829 1.21 6.0 1.58 0.48 0.31 23.2 7.1 7.1 6 255 2.6 400 146 184 325 8.32E+03 0.808 1.57 5.9 2.57 0.76 0.30 37.7 11.2 11.0 6 345 3.1 494 148 251 397 8.97E+03 0.827 1.83 6.0 3.49 0.98 0.28 51.3 14.4 14.4 6 451 3.6 602 151 344 491 9.76E+03 0.812 2.14 6.0 4.56 1.12 0.25 66.9 16.5 16.4 6 550 3.9 703 152 410 553 1.15E+04 0.806 2.34 5.9 5.57 1.52 0.27 81.7 22.3 22.0 6 640 4.2 795 154 470 618 1.19E+04 0.824 2.50 6.0 6.47 1.79 0.28 95.1 26.3 26.2 6 739 4.6 895 156 565 713 1.26E+04 0.820 2.75 6.0 7.47 1.83 0.25 109.7 26.9 26.9 6 842 4.8 999 156 622 770 1.35E+04 0.811 2.88 5.9 8.52 2.31 0.27 125.1 34.0 33.7 6 949 5.2 1107 157 692 851 1.41E+04 0.825 3.04 6.0 9.60 2.58 0.27 140.9 38.0 38.0 6 1048 5.4 1207 158 784 943 1.47E+04 0.808 3.24 5.9 10.60 2.67 0.25 155.7 39.2 38.8 6 1137 5.7 1298 159 848 996 1.54E+04 0.818 3.36 6.0 11.51 3.05 0.27 169.0 44.8 44.6 6 1234 5.7 1395 159 897 1060 1.56E+04 0.804 3.46 5.9 12.48 3.39 0.27 183.3 49.8 49.1 6 1343 6.0 1505 160 978 1144 1.63E+04 0.805 3.61 5.9 13.59 3.64 0.27 199.6 53.5 52.8 6 1436 6.3 1599 161 1070 1215 1.72E+04 0.813 3.78 6.0 14.53 3.88 0.27 213.3 57.0 56.6 6 1533 6.5 1697 161 1134 1275 1.78E+04 0.816 3.89 6.0 15.52 4.26 0.27 227.8 62.6 62.2 6 1635 6.7 1800 161 1190 1356 1.83E+04 0.818 3.99 6.0 16.56 4.48 0.27 243.1 65.8 65.5 6 1738 7.0 1904 162 1293 1445 1.86E+04 0.822 4.15 6.0 17.59 4.64 0.26 258.3 68.1 68.0 6 1843 7.1 2009 162 1353 1505 1.95E+04 0.816 4.25 6.0 18.66 5.10 0.27 273.9 74.8 74.4 6 1925 7.3 2092 162 1420 1568 2.00E+04 0.818 4.35 6.0 19.49 5.29 0.27 286.3 77.7 77.3 6 2035 7.5 2202 163 1515 1664 2.00E+04 0.816 4.50 6.0 20.60 5.44 0.26 302.4 79.9 79.4 6 2132 7.8 2300 163 1568 1731 2.12E+04 0.827 4.58 6.0 21.59 5.75 0.27 317.0 84.5 84.5 6 2242 7.8 2410 163 1649 1798 2.13E+04 0.810 4.69 5.9 22.70 6.18 0.27 333.3 90.8 90.0 Appendices     101  Table G.2: Test data and results non-erodible test specimen D1-123 o Head Q hu hd hv Hd Re CpCv Vt t s i H/h HET HET-P HET-P (V) [mm] [mm] [l/min] [mm] [mm] [mm] [mm] [ - ] [ - ] [m/s] [mm] [ - ] [ - ] [ - ] [N/m 2 ] [N/m 2 ] [N/m 2 ] 12 8 1.9 149 142 7 148 2.55E+03 0.770 0.30 11.6 0.08 0.01 0.11 2.2 0.2 0.2 12 14 2.6 160 147 12 159 3.47E+03 0.790 0.40 11.7 0.13 0.01 0.09 3.9 0.4 0.4 12 46 4.9 204 158 40 198 6.71E+03 0.814 0.74 11.9 0.46 0.06 0.13 13.6 1.7 1.7 12 134 8.4 304 170 122 293 1.15E+04 0.802 1.27 11.8 1.35 0.11 0.08 39.7 3.3 3.2 12 219 11.0 397 177 198 371 1.50E+04 0.824 1.62 12.0 2.22 0.26 0.12 65.1 7.7 7.7 12 313 13.1 496 182 286 463 1.73E+04 0.814 1.95 11.9 3.17 0.34 0.11 93.1 9.9 9.9 12 408 14.8 595 185 381 551 1.97E+04 0.799 2.26 11.8 4.14 0.45 0.11 121.6 13.1 12.9 12 505 16.7 696 189 466 653 2.22E+04 0.815 2.49 11.9 5.13 0.43 0.08 150.5 12.7 12.6 12 606 18.5 800 191 558 749 2.45E+04 0.824 2.73 12.0 6.15 0.52 0.08 180.7 15.3 15.2 12 699 20.2 896 193 646 833 2.68E+04 0.838 2.94 12.1 7.10 0.63 0.09 208.5 18.6 18.7 12 806 21.5 1006 195 738 936 2.85E+04 0.833 3.14 12.1 8.19 0.71 0.09 240.6 20.8 20.9 12 905 22.8 1107 196 830 1014 3.02E+04 0.833 3.33 12.1 9.20 0.94 0.10 270.2 27.7 27.9 12 995 23.9 1199 198 901 1102 3.16E+04 0.836 3.47 12.1 10.11 0.98 0.10 296.9 28.8 29.0 12 1091 25.1 1297 198 996 1190 3.32E+04 0.836 3.65 12.1 11.10 1.08 0.10 326.0 31.7 31.9 12 1192 26.0 1399 200 1095 1278 3.45E+04 0.828 3.82 12.0 12.11 1.22 0.10 355.7 35.8 35.9 12 1299 27.3 1508 200 1194 1370 3.51E+04 0.830 3.99 12.0 13.21 1.39 0.11 388.0 40.9 41.0 12 1387 28.3 1598 203 1275 1448 3.74E+04 0.832 4.13 12.1 14.09 1.52 0.11 413.8 44.5 44.7 12 1482 29.5 1694 202 1346 1554 3.80E+04 0.847 4.24 12.2 15.07 1.42 0.09 442.6 41.6 42.1 12 1590 30.4 1804 202 1473 1642 3.91E+04 0.833 4.43 12.1 16.18 1.64 0.10 475.2 48.0 48.3 12 1690 31.3 1905 206 1540 1724 4.14E+04 0.839 4.53 12.1 17.16 1.84 0.11 504.0 53.9 54.3 12 1783 32.1 1999 205 1635 1780 4.13E+04 0.835 4.67 12.1 18.12 2.21 0.12 532.2 65.0 65.4 12 1876 33.2 2094 206 1709 1900 4.27E+04 0.845 4.78 12.1 19.07 1.96 0.10 560.0 57.6 58.3 12 1983 34.1 2202 208 1815 2003 4.52E+04 0.843 4.92 12.1 20.14 2.02 0.10 591.5 59.2 59.9 12 2086 35.0 2306 208 1900 2084 4.50E+04 0.844 5.04 12.1 21.19 2.25 0.11 622.3 66.0 66.7 12 2193 35.9 2414 208 2003 2197 4.62E+04 0.845 5.17 12.1 22.28 2.20 0.10 654.4 64.5 65.3  Appendices     102 Table G.3: Test data and results non-erodible test specimen D1-243 o Head Q hu hd hv Hd Re CpCv Vt t s i H/h HET HET-P HET-P (V) [mm] [mm] [l/min] [mm] [mm] [mm] [mm] [ - ] [ - ] [m/s] [mm] [ - ] [ - ] [ - ] [N/m 2 ] [N/m 2 ] [N/m 2 ] 24 0 3.7 153 153 2 154 2.62E+03 0.704 0.16 22.2 0.00 -0.01 n/a 0.0 -0.8 -0.8 24 0 3.7 153 153 2 154 2.62E+03 0.704 0.16 22.2 0.00 -0.01 n/a 0.0 -0.4 -0.4 24 5 7.1 172 167 5 171 5.01E+03 0.816 0.27 23.9 0.05 0.00 0.07 2.7 0.2 0.2 24 5 7.1 172 168 5 171 4.87E+03 0.816 0.27 23.9 0.05 0.01 0.18 2.7 0.5 0.5 24 12 10.6 190 179 12 190 7.26E+03 0.808 0.40 23.7 0.11 0.00 0.00 6.7 0.0 0.0 24 12 10.6 190 179 12 190 7.26E+03 0.808 0.40 23.7 0.11 0.00 0.00 6.7 0.0 0.0 24 23 14.6 210 189 22 209 9.92E+03 0.815 0.54 23.8 0.22 0.01 0.06 12.8 0.7 0.7 24 24 14.3 210 188 22 209 9.77E+03 0.808 0.54 23.8 0.22 0.01 0.03 12.9 0.3 0.3 24 24 14.6 211 189 22 209 9.92E+03 0.815 0.54 23.8 0.22 0.02 0.07 13.1 0.9 0.9 24 24 14.6 211 189 22 209 9.92E+03 0.821 0.54 23.9 0.22 0.02 0.07 13.1 0.9 0.9 24 36 17.9 230 197 33 229 1.19E+04 0.827 0.66 24.0 0.33 0.01 0.02 19.6 0.5 0.5 24 37 17.9 231 197 33 230 1.19E+04 0.827 0.66 24.0 0.34 0.01 0.04 20.2 0.9 0.9 24 52 21.2 252 205 45 250 1.41E+04 0.830 0.78 24.1 0.47 0.02 0.04 27.7 1.1 1.1 24 52 21.2 252 205 46 250 1.41E+04 0.827 0.78 24.0 0.47 0.02 0.04 27.7 1.1 1.1 24 65 23.7 270 211 58 269 1.57E+04 0.816 0.88 23.9 0.60 0.01 0.02 35.0 0.6 0.6 24 65 23.7 270 211 58 269 1.57E+04 0.816 0.88 23.9 0.60 0.01 0.02 35.0 0.6 0.6 24 80 26.7 289 216 72 286 1.77E+04 0.828 0.98 24.0 0.74 0.03 0.04 43.3 1.8 1.9 24 81 26.7 290 216 71 286 1.77E+04 0.832 0.97 24.1 0.75 0.04 0.06 43.9 2.4 2.5 24 96 29.3 309 222 86 307 1.94E+04 0.832 1.07 24.1 0.88 0.02 0.03 51.9 1.4 1.4 24 96 29.3 309 222 86 307 1.94E+04 0.832 1.07 24.1 0.88 0.03 0.03 51.9 1.6 1.6 24 111 31.5 327 226 99 326 2.08E+04 0.832 1.15 24.1 1.02 0.02 0.02 59.9 0.9 0.9 24 112 31.5 328 226 99 326 2.08E+04 0.833 1.15 24.1 1.03 0.02 0.02 60.5 1.1 1.1 24 129 34.2 349 231 116 347 2.27E+04 0.835 1.25 24.2 1.19 0.02 0.02 70.0 1.2 1.3 24 129 34.2 349 231 116 347 2.27E+04 0.834 1.25 24.1 1.19 0.02 0.02 70.0 1.2 1.3 24 133 35.1 354 232 120 352 2.32E+04 0.842 1.27 24.2 1.23 0.02 0.02 72.4 1.2 1.2 24 133 35.1 354 232 121 353 2.32E+04 0.839 1.27 24.2 1.23 0.02 0.01 72.4 1.0 1.0 24 134 35.8 356 233 121 353 2.37E+04 0.855 1.27 24.4 1.24 0.03 0.03 73.0 1.8 1.9 Appendices     103 Appendix H: Soil properties  Figure H.1: Gradation curves dam core material (USCS)  3''2''1½''1''¾''⅜''410204060100200 0 10 20 30 40 50 60 70 80 90 100 0.0001 0.001 0.01 0.1 1 10 100 P e rc e n t Fi n e r Th an Grain Size [mm] Dam MV4-Core Dam MV4-Altered COBBLE SIZE GRAVEL SIZE FINE COARSE SAND SIZE COARSEMEDIUMFINE FINES Sieve No. Appendices     104   Figure H.2: Standard compaction test Dam MV4-Altered material (ASTM D698 Method A)    Figure H.3: Standard compaction test Dam MV4-Core material (ASTM D698 Method B)  7.8%; 20.80 4.0%; 19.76 11.3%; 19.76 18.0 18.5 19.0 19.5 20.0 20.5 21.0 21.5 0% 2% 4% 6% 8% 10% 12% 14% 16% 18% 20% 22% D ry  u n it  w e ig h t [k N /m 3 ] Water Content [%] Compaction Data Compaction Curve Optimum 95% Max. Std. Dry Unit Weight Water Content Limits Sr = 1.0 (Zero Air Voids Curve) Gs wreceived Std-wopt Std-gd,max Std-d,max Std-Sr,opt = 2.72 (assumed) =  0.2 % =  7.8 % =  20.80 kN/m3 =  2121 kg/m3 =  76 % 8.2%; 21.00 2.7%; 19.95 11.0%; 19.95 18.0 18.5 19.0 19.5 20.0 20.5 21.0 21.5 0% 2% 4% 6% 8% 10% 12% 14% 16% 18% 20% 22% D ry  u n it  w e ig h t [k N /m 3 ] Water Content [%] Compaction Data Compaction Curve Optimum 95% Max. Std. Dry Unit Weight Water Content Limits Sr = 1.0 (Zero Air Voids Curve) Gs wreceived Std-wopt Std-gd,max Std-d,max Std-Sr,opt = 2.72 (assumed) =  5.2-8.2 % =  8.2 % =  21.00 kN/m3 =  2141 kg/m3 =  83.2 % Appendices     105 Appendix I: Erodible soil specimens Dam core material  Figure I.1: Dam MV4-Altered – S1-003.01 – Measured flow rate & results at point of failure    Figure I.2: Dam MV4-Altered – S1-003.01 – Dried specimen 0 5 10 15 20 25 30 35 40 00:00:00 00:15:00 00:30:00 00:45:00 M e as u re d  F lo w  R at e , Q [l /m in ] Time, t [hh:mm:ss] Sudden very rapid progressive erosion: h H t L c,HET c,HET-P = 160 = 130 = 10 = 99 ≤ 40 ≤ 32 mm mm mm mm N/m2 N/m2 Upstream (US) Downstream (DS) Appendices     106   Figure I.3: Dam MV4-Altered – S1-003.02 – Measured flow rate & results at point of failure    Figure I.4: Dam MV4-Altered – S1-003.02 – Drained test cell US and detail with Pitot tube  0 5 10 15 20 25 30 35 40 00:00:00 00:05:00 00:10:00 00:15:00 00:20:00 00:25:00 00:30:00 M e as u re d  F lo w  R at e , Q [l /m in ] Time, t [hh:mm:ss] Sudden very rapid progressive erosion: h H t L c,HET c,HET-P = 148 = null = 7-8 = 99 ≤ 27 ≤ null mm mm mm mm N/m2 N/m2 Appendices     107   Figure I.5: Dam MV4-Altered – S1-553.01 – Measured flow rate & results at point of failure    Figure I.6: Dam MV4-Altered – S1-553.01 – Drained test cell US and detail with Pitot tube  0 5 10 15 20 25 30 35 40 00:00:00 00:05:00 00:10:00 00:15:00 00:20:00 00:25:00 00:30:00 M e as u re d  F lo w  R at e , Q [l /m in ] Time, t [hh:mm:ss] Sudden very rapid progressive erosion: h H t L c,HET c,HET-P = 2300 = null = 0.0 = 99 ≤ null ≤ null mm mm mm mm N/m2 N/m2 max test head hole collapsed h not representative Appendices     108   Figure I.7: Dam MV4-Core – S2-553.01 – Measured flow rate & results at point of failure    Figure I.8: Dam MV4-Core – S2-553.01 – Drained test cell US and detail with Pitot tube  0 5 10 15 20 25 30 35 40 00:00:00 00:05:00 00:10:00 00:15:00 00:20:00 00:25:00 00:30:00 M e as u re d  F lo w  R at e , Q [l /m in ] Time, t [hh:mm:ss] Sudden very rapid progressive erosion: h H t L c,HET c,HET-P = 187 = null = 6 = 99 ≤ 28 ≤ null mm mm mm mm N/m2 N/m2 Appendices     109 Ontario clay samples  Figure I.9: Ontario Clay – Little Cataraqui – S3-993.01 – Prepared test specimen    Figure I.10: Ontario Clay – Little Cataraqui – S3-993.01 – Measured flow rate  0 5 10 15 20 25 30 35 40 45 50 00:00:00 00:30:00 01:00:00 01:30:00 02:00:00 02:30:00 M e as u re d  F lo w  R at e , Q [l /m in ] Time, t [hh:mm:ss] Critical point: start of failure Appendices     110   Figure I.11: Ontario Clay – Little Cataraqui – S3-993.01 – Head difference and energy loss    Figure I.12: Ontario Clay – Little Cataraqui – S3-993.01 – Head ratio  0 200 400 600 800 1000 1200 1400 1600 1800 2000 0 200 400 600 800 1000 1200 1400 1600 1800 2000 00:00:00 00:30:00 01:00:00 01:30:00 02:00:00 02:30:00 En e rg y h e ad  lo ss  a lo n g te st  s p e ci m e n  (H ET -P ),   H  [ m m ] H yd ra u lic  h e ad  d if fe re n ce  a cr o ss  t e st  s p e ci m e n  (H ET ),   h [m m ] Time, t [hh:mm:ss] HET HET raw HET-P HET-P raw HET-P (V) HET-P (V) raw Critical point: start of failure 0.0 0.2 0.4 0.6 0.8 1.0 1.2 00:00:00 00:30:00 01:00:00 01:30:00 02:00:00 02:30:00 H e ad  R at io ,  H / h [ - ] Time, t [hh:mm:ss] Head Ratio (Re>2000) Head Ratio raw Critical point: start of failure Appendices     111   Figure I.13: Ontario Clay – Little Cataraqui – S3-993.01 – Axial hole diameter    Figure I.14: Ontario Clay – Little Cataraqui – S3-993.01 – Wall shear stress  0 10 20 30 40 50 60 70 00:00:00 00:30:00 01:00:00 01:30:00 02:00:00 02:30:00 Es ti m at e d  m e an  d ia m e te r o f ax ia l h o le ,  t [m m ] Time, t [hh:mm:ss] HET HET raw HET-P HET-P raw HET-P (V) HET-P (V) raw HET-P (V): The Pitot-static tube measured a velocity according to an almost constant diameter, because the bottom of the specimen remained partially intact, including the preformed axial hole. Critical point: start of failure 0 200 400 600 800 1000 1200 1400 1600 00:00:00 00:30:00 01:00:00 01:30:00 02:00:00 02:30:00 Es ti m at e d  w al l s h e ar  s tr e ss ,  [N /m 2 ] Time, t [hh:mm:ss] HET HET raw HET-P HET-P raw HET-P (V) HET-P (V) raw Critical point: start of failure Appendices     112   Figure I.15: Ontario Clay – Little Cataraqui – S3-993.01 – Erosion rate    Figure I.16: Ontario Clay – Little Cataraqui – S3-993.01 – Flow rate versus shear stress  0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04 00:00:00 00:30:00 01:00:00 01:30:00 02:00:00 02:30:00 Es ti m at e d  e ro si o n  r at e  p e r u n it  s u rf ac e  a re a o f th e  a xi al  h o le , ε ̇[ kg /s /m 2 ] Time, t [hh:mm:ss] HET HET raw HET-P HET-P raw HET-P (V) HET-P (V) raw Critical point: start of failure Peak and decreasing erosion rate with each test head. 0 5 10 15 20 25 30 35 40 45 50 0 200 400 600 800 1000 1200 1400 1600 M e as u re d  F lo w  R at e , Q [l /m in ] Estimated wall shear stress,  [N/m2] HET HET raw HET-P HET-P raw HET-P (V) HET-P (V) raw Critical point: start of failure Critical point: start of failure Critical shear stress defined at point with minimum slope. Appendices     113   Figure I.17: Ontario Clay – Little Cataraqui – S3-993.01 – Drained test cell US and plaster cast    Figure I.18: Ontario Clay – Little Cataraqui – S3-993.01 – DS side of specimen pre- and post-test  Post-test: a portion of the bottom part of the specimen remained intact. Appendices     114   Figure I.19: Ontario Clay – Little Cataraqui – S3-993.02 – Prepared test specimen    Figure I.20: Ontario Clay – Little Cataraqui – S3-993.02 – Measured flow rate  0 5 10 15 20 25 30 35 40 45 50 00:00:00 00:15:00 00:30:00 00:45:00 01:00:00 01:15:00 M e as u re d  F lo w  R at e , Q [l /m in ] Time, t [hh:mm:ss] Critical point: start of failure Specimen suddenly collapsed! Appendices     115   Figure I.21: Ontario Clay – Little Cataraqui – S3-993.02 – Head difference and energy loss    Figure I.22: Ontario Clay – Little Cataraqui – S3-993.02 – Head ratio  0 50 100 150 200 250 300 350 0 50 100 150 200 250 300 350 00:00:00 00:15:00 00:30:00 00:45:00 01:00:00 01:15:00 En e rg y h e ad  lo ss  a lo n g te st  s p e ci m e n  (H ET -P ),   H  [ m m ] H yd ra u lic  h e ad  d if fe re n ce  a cr o ss  t e st  s p e ci m e n  (H ET ),   h [m m ] Time, t [hh:mm:ss] HET HET raw HET-P HET-P raw HET-P (V) HET-P (V) raw Specimen suddenly collapsed! Critical point: start of failure Critical point: start of failure 0 0.2 0.4 0.6 0.8 1 1.2 00:00:00 00:15:00 00:30:00 00:45:00 01:00:00 01:15:00 H e ad  R at io ,  H / h [ - ] Time, t [hh:mm:ss] Head Ratio (Re>2000) Head Ratio raw Specimen suddenly collapsed! Critical point: start of failure Appendices     116   Figure I.23: Ontario Clay – Little Cataraqui – S3-993.02 – Axial hole diameter    Figure I.24: Ontario Clay – Little Cataraqui – S3-993.02 – Wall shear stress  0 5 10 15 20 25 30 35 40 00:00:00 00:15:00 00:30:00 00:45:00 01:00:00 01:15:00 Es ti m at e d  m e an  d ia m e te r o f ax ia l h o le ,  t [m m ] Time, t [hh:mm:ss] HET HET raw HET-P HET-P raw HET-P (V) HET-P (V) raw Specimen suddenly collapsed! Critical point: start of failure 0 10 20 30 40 50 60 70 80 90 100 00:00:00 00:15:00 00:30:00 00:45:00 01:00:00 01:15:00 Es ti m at e d  w al l s h e ar  s tr e ss ,  [N /m 2 ] Time, t [hh:mm:ss] HET HET raw HET-P HET-P raw HET-P (V) HET-P (V) raw Specimen suddenly collapsed! Critical point: start of failure Critical point: start of failure Appendices     117   Figure I.25: Ontario Clay – Little Cataraqui – S3-993.02 – Erosion rate    Figure I.26: Ontario Clay – Little Cataraqui – S3-993.02 – Flow rate versus shear stress  0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 00:00:00 00:15:00 00:30:00 00:45:00 01:00:00 01:15:00 Es ti m at e d  e ro si o n  r at e  p e r u n it  s u rf ac e  a re a o f th e  a xi al  h o le , ε ̇[ kg /s /m 2 ] Time, t [hh:mm:ss] HET HET raw HET-P HET-P raw HET-P (V) HET-P (V) raw Specimen suddenly collapsed! Critical point: start of failure Peak and decreasing erosion rate with each test head. 0 5 10 15 20 25 30 35 40 45 50 0 10 20 30 40 50 60 70 80 90 100 M e as u re d  F lo w  R at e , Q [l /m in ] Estimated wall shear stress,  [N/m2] HET HET raw HET-P HET-P raw HET-P (V) HET-P (V) raw Specimen suddenly collapsed! Critical point: start of failure Critical point: start of failure Critical shear stress defined at point with minimum slope. Appendices     118   Figure I.27: Ontario Clay – Little Cataraqui – S3-993.02 – Drained test cell US    Figure I.28: Ontario Clay – Little Cataraqui – S3-993.02 – Test specimen after testing (DS)  Appendices     119   Figure I.29: Ontario Clay – Bear Brook – S3-993.12 – Prepared test specimen    Figure I.30: Ontario Clay – Bear Brook – S3-993.12 – Measured flow rate  0 2 4 6 8 10 12 14 16 18 20 00:00:00 00:15:00 00:30:00 00:45:00 01:00:00 01:15:00 01:30:00 M e as u re d  F lo w  R at e , Q [l /m in ] Time, t [hh:mm:ss] Critical point: start of failure Appendices     120   Figure I.31: Ontario Clay – Bear Brook– S3-993.12 – Head difference and energy loss    Figure I.32: Ontario Clay – Bear Brook – S3-993.12 – Head ratio  0 50 100 150 200 250 300 350 400 450 0 50 100 150 200 250 300 350 400 450 00:00:00 00:15:00 00:30:00 00:45:00 01:00:00 01:15:00 01:30:00 En e rg y h e ad  lo ss  a lo n g te st  s p e ci m e n  (H ET -P ),   H [m m ] H yd ra u lic  h e ad  d if fe re n ce  a cr o ss  t e st  s p e ci m e n  (H ET ),   h [m m ] Time, t [hh:mm:ss] HET HET raw HET-P HET-P raw HET-P (V) HET-P (V) raw Critical point: start of failure Critical point: start of failure 0 0.2 0.4 0.6 0.8 1 1.2 00:00:00 00:15:00 00:30:00 00:45:00 01:00:00 01:15:00 01:30:00 H e ad  R at io ,  H / h [ - ] Time, t [hh:mm:ss] Head Ratio (Re>2000) Head Ratio raw Critical point: start of failure Appendices     121   Figure I.33: Ontario Clay – Bear Brook – S3-993.12 – Axial hole diameter    Figure I.34: Ontario Clay – Bear Brook – S3-993.12 – Wall shear stress  0 2 4 6 8 10 12 14 16 18 20 00:00:00 00:15:00 00:30:00 00:45:00 01:00:00 01:15:00 01:30:00 Es ti m at e d  m e an  d ia m e te r o f ax ia l h o le ,  t [m m ] Time, t [hh:mm:ss] HET HET raw HET-P HET-P raw HET-P (V) HET-P (V) raw Critical point: start of failure 0 50 100 150 200 250 00:00:00 00:15:00 00:30:00 00:45:00 01:00:00 01:15:00 01:30:00 Es ti m at e d  w al l s h e ar  s tr e ss ,  [N /m 2 ] Time, t [hh:mm:ss] HET HET raw HET-P HET-P raw HET-P (V) HET-P (V) raw Critical point: start of failure Critical point: start of failure Appendices     122   Figure I.35: Ontario Clay – Bear Brook – S3-993.12 – Erosion rate    Figure I.36: Ontario Clay – Bear Brook – S3-993.12 – Flow rate versus shear stress  0 0.002 0.004 0.006 0.008 0.01 0.012 0.014 0.016 0.018 00:00:00 00:15:00 00:30:00 00:45:00 01:00:00 01:15:00 01:30:00 Es ti m at e d  e ro si o n  r at e  p e r u n it  s u rf ac e  a re a o f th e  a xi al  h o le , ε̇  [ kg /s /m 2 ] Time, t [hh:mm:ss] HET HET raw HET-P HET-P raw HET-P (V) HET-P (V) raw Critical point: start of failure Peak and decreasing erosion rate with each test head. 0 2 4 6 8 10 12 14 16 18 20 0 50 100 150 200 250 M e as u re d  F lo w  R at e , Q [l /m in ] Estimated wall shear stress,  [N/m2] HET HET raw HET-P HET-P raw HET-P (V) HET-P (V) raw Critical point: start of failure Critical point: start of failure Critical shear stress defined at point with minimum slope. Appendices     123   Figure I.37: Ontario Clay – Bear Brook – S3-993.12 – Drained test cell US and plaster cast    Figure I.38: Ontario Clay – Bear Brook – S3-993.12 – Extracted test specimen after testing  Appendices     124   Figure I.39: Ontario Clay – Wilton Creek – S3-993.21 – Prepared test specimen    Figure I.40: Ontario Clay – Wilton Creek – S3-993.21 – Measured flow rate  0 2 4 6 8 10 12 14 16 18 00:00:00 00:30:00 01:00:00 01:30:00 02:00:00 02:30:00 03:00:00 M e as u re d  F lo w  R at e , Q [l /m in ] Time, t [hh:mm:ss] Specimen suddenly collapsed! Critical point: start of failure Appendices     125   Figure I.41: Ontario Clay – Wilton Creek – S3-993.21 – Head difference and energy loss    Figure I.42: Ontario Clay – Wilton Creek – S3-993.21 – Head ratio  0 200 400 600 800 1000 1200 1400 1600 1800 2000 0 200 400 600 800 1000 1200 1400 1600 1800 2000 00:00:00 00:30:00 01:00:00 01:30:00 02:00:00 02:30:00 03:00:00 En e rg y h e ad  lo ss  a lo n g te st  s p e ci m e n  (H ET -P ),   H [m m ] H yd ra u lic  h e ad  d if fe re n ce  a cr o ss  t e st  s p e ci m e n  (H ET ),   h [m m ] Time, t [hh:mm:ss] HET HET raw HET-P HET-P raw HET-P (V) HET-P (V) raw Specimen suddenly collapsed! Critical point: start of failure 0 0.2 0.4 0.6 0.8 1 1.2 00:00:00 00:30:00 01:00:00 01:30:00 02:00:00 02:30:00 03:00:00 H e ad  R at io ,  H / h [ - ] Time, t [hh:mm:ss] Head Ratio (Re>2000) Head Ratio raw Specimen suddenly collapsed! Critical point: start of failure Appendices     126   Figure I.43: Ontario Clay – Wilton Creek – S3-993.21 – Axial hole diameter    Figure I.44: Ontario Clay – Wilton Creek – S3-993.21 – Wall shear stress  0 2 4 6 8 10 12 14 16 18 20 00:00:00 00:30:00 01:00:00 01:30:00 02:00:00 02:30:00 03:00:00 Es ti m at e d  m e an  d ia m e te r o f ax ia l h o le ,  t [m m ] Time, t [hh:mm:ss] HET HET raw HET-P HET-P raw HET-P (V) HET-P (V) raw Specimen suddenly collapsed! Critical point: start of failure 0 100 200 300 400 500 600 700 800 900 1000 00:00:00 00:30:00 01:00:00 01:30:00 02:00:00 02:30:00 03:00:00 Es ti m at e d  w al l s h e ar  s tr e ss ,  [N /m 2 ] Time, t [hh:mm:ss] HET HET raw HET-P HET-P raw HET-P (V) HET-P (V) raw Specimen suddenly collapsed! Critical point: start of failure Appendices     127   Figure I.45: Ontario Clay – Wilton Creek – S3-993.21 – Erosion rate    Figure I.46: Ontario Clay – Wilton Creek – S3-993.21 – Flow rate versus shear stress  0 0.005 0.01 0.015 0.02 00:00:00 00:30:00 01:00:00 01:30:00 02:00:00 02:30:00 03:00:00 Es ti m at e d  e ro si o n  r at e  p e r u n it  s u rf ac e  a re a o f th e  a xi al  h o le , ε ̇[ kg /s /m 2 ] Time, t [hh:mm:ss] HET HET raw HET-P HET-P raw HET-P (V) HET-P (V) raw Specimen suddenly collapsed! Critical point: start of failure Peak and decreasing erosion rate with each test head. 0 2 4 6 8 10 12 14 16 18 20 0 100 200 300 400 500 600 700 800 900 1000 M e as u re d  F lo w  R at e , Q [l /m in ] Estimated wall shear stress,  [N/m2] HET HET raw HET-P HET-P raw HET-P (V) HET-P (V) raw Specimen suddenly collapsed!Critical point: start of failure Critical point: start of failure Critical shear stress defined at point with minimum slope. Appendices     128   Figure I.47: Ontario Clay – Wilton Creek – S3-993.21 – Drained test cell US and plaster cast    Figure I.48: Ontario Clay – Wilton Creek – S3-993.21 – Test specimen after testing (DS)  Appendices     129   Figure I.49: Ontario Clay – Wilton Creek – S3-993.22 – Prepared test specimen    Figure I.50: Ontario Clay – Wilton Creek – S3-993.22 – Measured flow rate  0 5 10 15 20 25 30 00:00:00 00:15:00 00:30:00 00:45:00 01:00:00 M e as u re d  F lo w  R at e , Q [l /m in ] Time, t [hh:mm:ss] Increase test head: Specimen suddenly collapsed! Critical point: start of failure Appendices     130   Figure I.51: Ontario Clay – Wilton Creek – S3-993.22 – Head difference and energy loss    Figure I.52: Ontario Clay – Wilton Creek – S3-993.22 – Head ratio  0 50 100 150 200 250 300 350 0 50 100 150 200 250 300 350 00:00:00 00:15:00 00:30:00 00:45:00 01:00:00 En e rg y h e ad  lo ss  a lo n g te st  s p e ci m e n  (H ET -P ),   H [m m ] H yd ra u lic  h e ad  d if fe re n ce  a cr o ss  t e st  s p e ci m e n  (H ET ),   h [m m ] Time, t [hh:mm:ss] HET HET raw HET-P HET-P raw HET-P (V) HET-P (V) raw Increase test head: Specimen suddenly collapsed! Critical point: start of failure 0 0.2 0.4 0.6 0.8 1 1.2 00:00:00 00:15:00 00:30:00 00:45:00 01:00:00 H e ad  R at io ,  H / h [ - ] Time, t [hh:mm:ss] Head Ratio (Re>2000) Head Ratio raw Re < 5000 Increase test head: Specimen suddenly collapsed! Critical point: start of failure Appendices     131   Figure I.53: Ontario Clay – Wilton Creek – S3-993.22 – Axial hole diameter    Figure I.54: Ontario Clay – Wilton Creek – S3-993.22 – Wall shear stress  0 5 10 15 20 25 30 35 00:00:00 00:15:00 00:30:00 00:45:00 01:00:00 Es ti m at e d  m e an  d ia m e te r o f ax ia l h o le ,  t [m m ] Time, t [hh:mm:ss] HET HET raw HET-P HET-P raw HET-P (V) HET-P (V) raw Re < 5000 Increase test head: Specimen suddenly collapsed! Critical point: start of failure 0 10 20 30 40 50 60 70 80 90 100 00:00:00 00:15:00 00:30:00 00:45:00 01:00:00 Es ti m at e d  w al l s h e ar  s tr e ss ,  [N /m 2 ] Time, t [hh:mm:ss] HET HET raw HET-P HET-P raw HET-P (V) HET-P (V) raw Increase test head: Specimen suddenly collapsed! Critical point: start of failure Appendices     132   Figure I.55: Ontario Clay – Wilton Creek – S3-993.22 – Erosion rate    Figure I.56: Ontario Clay – Wilton Creek – S3-993.22 – Flow rate versus shear stress  0 0.01 0.02 0.03 0.04 0.05 0.06 00:00:00 00:15:00 00:30:00 00:45:00 01:00:00 Es ti m at e d  e ro si o n  r at e  p e r u n it  s u rf ac e  a re a o f th e  a xi al  h o le , ε ̇[ kg /s /m 2 ] Time, t [hh:mm:ss] HET HET raw HET-P HET-P raw HET-P (V) HET-P (V) raw Increase test head: Specimen suddenly collapsed! Critical point: start of failure Peak and decreasing erosion rate with each test head. 0 5 10 15 20 25 30 0 10 20 30 40 50 60 70 80 90 100 M e as u re d  F lo w  R at e , Q [l /m in ] Estimated wall shear stress,  [N/m2] HET HET raw HET-P HET-P raw HET-P (V) HET-P (V) raw Increase test head: Specimen suddenly collapsed! Critical point: start of failure Critical point: start of failure Critical shear stress defined at point with minimum slope. Appendices     133   Figure I.57: Ontario Clay – Wilton Creek – S3-993.22 – Drained test cell US    Figure I.58: Ontario Clay – Wilton Creek – S3-993.22 – Test specimen after testing (DS) 

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