The Delft Sand, Clay and Rock Cutting Model

572 Pages·2016·35.74 MB·English

by  Miedema S.A.

THE DELFT SAND, CLAY & ROCK CUTTING MODEL
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The Delft Sand, Clay & Rock
Cutting Model
by
Sape A. Miedema
Amsterdam (cid:115) Berlin (cid:115) Tokyo (cid:115) Washington, DC
© 2014 Dr.ir. S.A. Miedema and IOS Press. All rights reserved.
ISBN 978-1-61499-453-4 (print)
ISBN 978-1-61499-454-1 (online)
DOI 10.3233/978-1-61499-454-1-i
1st edition, 2014
Published by IOS under the imprint Delft University Press. Published online with Open Access by
IOS Press and distributed under the terms of the Creative Commons Attribution Non-Commercial
License.
Publisher
IOS Press BV
Nieuwe Hemweg 6B
1013 BG Amsterdam
Netherlands
fax: [phone]
e-mail: [email protected]
Distributor in the USA and Canada
IOS Press, Inc.
4502 Rachael Manor Drive
Fairfax, VA 22032
USA
fax: [phone]
e-mail: [email protected]
LEGAL NOTICE
The publisher is not responsible for the use which might be made of the following information.
PRINTED IN THE NETHERLANDS
v

This book is dedicated to my wife Thuy,
my daughter Esther, my son Erik
and especially my grandson Tijmen
vi

Preface

In dredging, trenching, (deep sea) mining, drilling, tunnel boring and many other
applications, sand, clay or rock has to be excavated. The productions (and thus the
dimensions) of the excavating equipment range from mm3/sec - cm3/sec to m3/sec. In oil
drilling layers with a thickness of a magnitude of 0.2 mm are cut, while in dredging this
can be of a magnitude of 0.1 m with cutter suction dredges and meters for clamshells and
backhoe’s. Some equipment is designed for dry soil, while others operate under water
saturated conditions. Installed cutting powers may range up to 10 MW. For both the
design, the operation and production estimation of the excavating equipment it is
important to be able to predict the cutting forces and powers. After the soil has been
excavated it is usually transported hydraulically as a slurry over a short (TSHD’s) or a
long distance (CSD’s) or mechanically. Estimating the pressure losses and determining
whether or not a bed will occur in the pipeline is of great importance. Fundamental
processes of sedimentation, initiation of motion and erosion of the soil particles
determine the transport process and the flow regimes. In TSHD’s the soil has to settle
during the loading process, where also sedimentation and erosion will be in equilibrium.
In all cases we have to deal with soil and high density soil water mixtures and its
fundamental behavior.

This book gives an overview of cutting theories. It starts with a generic model, which is
valid for all types of soil (sand, clay and rock) after which the specifics of dry sand, water
saturated sand, clay, atmospheric rock and hyperbaric rock are covered. For each soil
type small blade angles and large blade angles, resulting in a wedge in front of the blade,
are discussed. The failure mechanism of sand, dry and water saturated, is the so called
Shear Type. The failure mechanism of clay is the so called Flow Type, but under certain
circumstances also the Curling Type and the Tear Type are possible. Rock will usually
fail in a brittle way. This can be brittle tensile failure, the Tear Type or the Chip Type,
for small blade angles, but it can also be brittle shear failure, which is of the Shear Type
of failure mechanism for larger blade angles. Under hyperbaric conditions rock may also
fail in a more apparent ductile way according to the Flow Type or Crushed Type of
failure mechanism. This is also called cataclastic failure.

For each case considered, the equations/model for the cutting forces, power and specific
energy are given. The models are verified with laboratory research, mainly at the Delft
University of Technology, but also with data from literature.

The model is named The Delft Sand, Clay & Rock Cutting Model. Up to date information
(modifications and additions) and high resolution graphs and drawings can be found on
the website www.dscrcm.com.
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Table of Contents

Preface. ………………………………………………………………………………..vi

Chapter 1: Introduction. ....................................................................................... 1

1.1. Approach. ...................................................................................................... 1

Chapter 2: Basic Soil Mechanics. ......................................................................... 5

2.1. Introduction. .................................................................................................. 5

2.2. The Mohr Circle. ........................................................................................... 6

2.3. Active Soil Failure. ..................................................................................... 11

2.4. Passive Soil Failure. .................................................................................... 15

2.5. Summary. .................................................................................................... 19

2.6. Shear Strength versus Friction. ................................................................... 21

2.7. Nomenclature. ............................................................................................. 24

Chapter 3: The General Cutting Process. .......................................................... 25

3.1. Cutting Mechanisms. ................................................................................... 25

3.2. Definitions. .................................................................................................. 27

3.3. The Flow/ Shear/Crushed Type. .................................................................. 27

3.3.1. The Equilibrium of Forces. ..................................................................... 28

3.3.2. The Individual Forces. ............................................................................ 31

3.4. The Curling Type. ....................................................................................... 32

3.5. The Tear Type and Chip Type..................................................................... 34

3.6. The Snow Plough Effect.............................................................................. 41

3.6.1. The Normal and Friction Forces on the Shear Surface and Blade. ......... 41

3.6.2. The 3D Cutting Theory. .......................................................................... 42

3.6.3. Velocity Conditions. ............................................................................... 43

3.6.4. The Deviation Force................................................................................ 45

3.6.5. The Resulting Cutting Forces. ................................................................ 46

3.7. Example Program in Visual Basic 6. ........................................................... 47

3.8. Finding the Shear Angle. ............................................................................. 48

3.9. Specific Cutting Energy E . ........................................................................ 49
sp

3.10. Nomenclature. ............................................................................................. 50

Chapter 4: Which Cutting Mechanism for Which Kind of Soil?..................... 53

4.1. Cutting Dry Sand. ........................................................................................ 53

4.2. Cutting Water Saturated Sand. .................................................................... 53
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4.3. Cutting Clay. ............................................................................................... 54

4.4. Cutting Rock Atmospheric. ......................................................................... 56

4.5. Cutting Rock Hyperbaric. ............................................................................ 58

4.6. Summary. .................................................................................................... 58

4.7. Nomenclature. ............................................................................................. 59

Chapter 5: Dry Sand Cutting. ............................................................................. 61

5.1. Introduction. ................................................................................................ 61

5.2. Definitions. .................................................................................................. 61

5.3. The Equilibrium of Forces. ......................................................................... 62

5.4. An Alternative Shape of the Layer Cut. ...................................................... 67

5.5. The Influence of Inertial Forces. ................................................................. 69

5.6. Specific Energy. .......................................................................................... 75

5.7. Usage of the Model for Dry Sand. ............................................................... 76

5.8. Experiments in Dry Sand. ........................................................................... 78

5.8.1. Hatamura & Chijiiwa (1977). ................................................................. 78

5.8.2. Wismer & Luth (1972B). ........................................................................ 81

5.9. Nomenclature. ............................................................................................. 83

Chapter 6: Saturated Sand Cutting. ................................................................... 85

6.1. Introduction. ................................................................................................ 85

6.2. Definitions. .................................................................................................. 86

6.3. Cutting Theory Literature. ........................................................................... 86

6.4. The Equilibrium of Forces. ......................................................................... 91

6.5. Determination of the Pore Pressures. .......................................................... 93

6.6. Numerical Water Pore Pressure Calculations. ............................................. 97

6.7. The Blade Tip Problem. ............................................................................ 103

6.8. Analytical/Numerical Water Pore Pressure Calculations. ......................... 104
6.9. Determination of the Shear Angle (cid:2)(cid:3) ......................................................... 114

6.10. The Coefficients a and a . ........................................................................ 117
1 2

6.11. Determination of the Coefficients c , c , d and d . ................................... 119
1 2 1 2

6.12. Specific Cutting Energy. ........................................................................... 120

6.12.1. Specific Energy and Production in Sand. ......................................... 122

6.12.2. The Transition Cavitating/Non-Cavitating. ...................................... 125

6.12.3. Conclusions Specific Energy ............................................................ 126

6.12.4. Wear and Side Effects. ..................................................................... 126
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6.13. Experiments. .............................................................................................. 130

6.13.1. Description of the Test Facility. ....................................................... 130

6.13.2. Test Program. ................................................................................... 139

6.13.3. Water Resistance. ............................................................................. 140

6.13.4. The Influence of the Width of the Blade. ......................................... 140

6.13.5. Side Effects. ...................................................................................... 141

6.13.6. Scale Effects. .................................................................................... 143

6.13.7. Comparison of Measurements versus Theory................................... 144

6.13.8. Location of the Resulting Cutting Force. .......................................... 145
6.13.9. Verification of the Theory in 200 (cid:4)m Sand. ..................................... 146
6.13.10. Verification of the Theory in 105 (cid:4)m Sand. ..................................... 149
6.13.11. Determination of (cid:5) and (cid:6) from Measurements. ................................ 153

6.14. General Conclusions. ................................................................................ 157

6.15. The Snow Plough Effect............................................................................ 157

6.16. Nomenclature. ........................................................................................... 163

Chapter 7: Clay Cutting. ................................................................................... 167

7.1. Definitions. ................................................................................................ 167

7.2. Introduction. .............................................................................................. 167

7.3. The Influence of Strain Rate on the Cutting Process. ................................ 170

7.3.1. Introduction. .......................................................................................... 170

7.3.2. The Rate Process Theory. ..................................................................... 170

7.3.3. Proposed Rate Process Theory. ............................................................. 172

7.3.4. The Proposed Theory versus some other Theories. .............................. 177

7.3.5. Verification of the Theory Developed. ................................................. 178

7.3.6. Resulting Equations. ............................................................................. 182

7.4. The Flow Type. ......................................................................................... 185

7.4.1. The Forces. ............................................................................................ 185

7.4.2. Finding the Shear Angle. ...................................................................... 188

7.4.3. Specific Energy. .................................................................................... 190

7.5. The Tear Type. .......................................................................................... 195

7.5.1. Introduction. .......................................................................................... 195

7.5.2. The Normal Force on the Shear Plane. ................................................. 196

7.5.3. The Mobilized Shear Strength. ............................................................. 197

7.5.4. The Resulting Cutting Forces. .............................................................. 200
x

7.6. The Curling Type. ..................................................................................... 203

7.6.1. Introduction. .......................................................................................... 203

7.6.2. The Normal Force on the Blade. ........................................................... 203

7.6.3. The Equilibrium of Moments. ............................................................... 206

7.7. Resulting Forces. ....................................................................................... 212

7.8. Experiments in Clay. ................................................................................. 215

7.8.1. Experiments of Hatamura & Chijiiwa (1977). ...................................... 215

7.8.2. Wismer & Luth (1972B). ...................................................................... 219

7.9. Nomenclature. ........................................................................................... 221

Chapter 8: Rock Cutting: Atmospheric Conditions. ...................................... 223

8.1. Introduction. .............................................................................................. 223

8.2. Cutting Models. ......................................................................................... 224

8.2.1. The Model of Evans. ............................................................................. 226

8.2.2. The Model of Evans under an Angle ε. ................................................. 229

8.2.3. The Model of Evans used for a Pick point. ........................................... 231

8.2.4. Summary of the Evans Theory. ............................................................. 233

8.2.5. The Nishimatsu Model. ......................................................................... 235

8.3. The Flow Type (Based on the Merchant Model)....................................... 239

8.4. Determining the Angle β. .......................................................................... 242

8.5. The Tear Type and the Chip Type. ............................................................ 246

8.6. Correction on the Tear Type and the Chip Type. ...................................... 254

8.7. Specific Energy. ........................................................................................ 256

8.8. Nomenclature. ........................................................................................... 257

Chapter 9: Rock Cutting: Hyperbaric Conditions. ......................................... 259

9.1. Introduction. .............................................................................................. 259

9.2. The Flow Type and the Crushed Type. ..................................................... 261

9.3. The Tear Type and the Chip Type. ............................................................ 268

9.4. The Curling Type. ..................................................................................... 269

9.5. Experiments of Zijsling (1987). ................................................................ 275

9.6. Specific Energy. ........................................................................................ 281

9.7. Specific Energy Graphs. ............................................................................ 282

9.8. Nomenclature. ........................................................................................... 285

Chapter 10: The Occurrence of a Wedge. .......................................................... 287

10.1. Introduction. .............................................................................................. 287