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17.10: Appendix J- The Coefficient d2

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    35277
  • \( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \) \( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}} \)\(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\) \(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\)\(\newcommand{\AA}{\unicode[.8,0]{x212B}}\)

    Table J-1: d2 for hb/hi=1.

    hb/hi=1

    φ

    32o

    37o

    42o

    47o

    52o

    α δ          

    15o

    15o

    0.409

    0.608

    0.816

    1.037

    1.274

    18o

    0.312

    0.528

    0.754

    0.995

    1.255

    21o

    0.205

    0.436

    0.680

    0.939

    1.220

    24o

    0.087

    0.333

    0.592

    0.870

    1.172

    27o

    -0.040

    0.219

    0.493

    0.788

    1.110

    30o

    -0.175

    0.095

    0.382

    0.692

    1.034

    30o

    15o

    0.474

    0.642

    0.828

    1.035

    1.269

    18o

    0.412

    0.588

    0.782

    1.000

    1.249

    21o

    0.341

    0.523

    0.725

    0.954

    1.216

    24o

    0.261

    0.447

    0.657

    0.895

    1.169

    27o

    0.171

    0.361

    0.576

    0.822

    1.108

    30o

    0.071

    0.264

    0.483

    0.735

    1.031

    45o

    15 o

    0.398

    0.553

    0.733

    0.945

    1.196

    18o

    0.325

    0.481

    0.664

    0.879

    1.138

    21o

    0.241

    0.396

    0.579

    0.797

    1.061

    24o

    0.145

    0.298

    0.478

    0.696

    0.962

    27o

    0.037

    0.183

    0.358

    0.572

    0.836

    30o

    -0.086

    0.051

    0.217

    0.421

    0.678

    60o

    15o

    0.195

    0.317

    0.465

    0.650

    0.885

    18o

    0.083

    0.193

    0.329

    0.500

    0.721

    21o

    -0.047

    0.047

    0.164

    0.313

    0.510

    24o

    -0.198

    -0.126

    -0.036

    0.081

    0.238

    27o

    -0.372

    -0.331

    -0.278

    -0.208

    -0.113

    30o

    -0.575

    -0.574

    -0.573

    -0.572

    -0.570

    The dimensionless force d2, perpendicular to the cutting velocity, as a function of the blade angle α, the angle of internal friction φ, the soil/interface friction angle δ, for hb/hi=1.

    Table J-2: d2 for hb/hi=2.

    hb/hi=2

    φ

    32o

    37o

    42o

    47o

    52o

    α δ          

    15o

    15o

    -0.024

    0.262

    0.552

    0.853

    1.170

    18o

    -0.253

    0.064

    0.387

    0.722

    1.076

    21o

    -0.496

    -0.151

    0.202

    0.569

    0.959

    24o

    -0.752

    -0.381

    -0.001

    0.396

    0.820

    27o

    -1.018

    -0.626

    -0.221

    0.204

    0.660

    30o

    -1.294

    -0.884

    -0.458

    -0.007

    0.479

    30o

    15o

    0.266

    0.471

    0.693

    0.938

    1.211

    18o

    0.136

    0.354

    0.592

    0.854

    1.149

    21o

    -0.008

    0.222

    0.473

    0.752

    1.067

    24o

    -0.165

    0.074

    0.337

    0.631

    0.965

    27o

    -0.336

    -0.089

    0.183

    0.490

    0.841

    30o

    -0.520

    -0.268

    0.011

    0.327

    0.693

    45o

    15o

    0.216

    0.393

    0.595

    0.830

    1.107

    18o

    0.087

    0.267

    0.475

    0.718

    1.007

    21o

    -0.059

    0.123

    0.334

    0.582

    0.880

    24o

    -0.221

    -0.040

    0.170

    0.420

    0.723

    27o

    -0.401

    -0.226

    -0.020

    0.227

    0.529

    30 o

    -0.600

    -0.435

    -0.240

    -0.002

    0.293

    60o

    15o

    -0.009

    0.124

    0.285

    0.484

    0.735

    18o

    -0.182

    -0.060

    0.089

    0.275

    0.513

    21o

    -0.379

    -0.274

    -0.145

    0.019

    0.233

    24o

    -0.603

    -0.523

    -0.422

    -0.293

    -0.122

    27o

    -0.859

    -0.812

    -0.753

    -0.676

    -0.571

    30o

    -1.151

    -1.151

    -1.150

    -1.148

    -1.146

    The dimensionless force d2, perpendicular to the cutting velocity, as a function of the blade angle α, the angle of internal friction φ, the soil/interface friction angle δ, for hb/hi=2.

    Table J-3: d2 for hb/hi=3.

    hb/hi=3

    φ

    32o

    37o

    42o

    47o

    52o

    α δ          

    15o

    15o

    -0.552

    -0.177

    0.198

    0.581

    0.979

    18o

    -0.921

    -0.501

    -0.080

    0.350

    0.800

    21o

    -1.306

    -0.846

    -0.384

    0.092

    0.590

    24o

    -1.703

    -1.208

    -0.708

    -0.191

    0.353

    27o

    -2.111

    -1.586

    -1.053

    -0.498

    0.090

    30o

    -2.528

    -1.979

    -1.417

    -0.828

    -0.201

    30o

    15o

    0.020

    0.263

    0.522

    0.805

    1.118

    18o

    -0.182

    0.079

    0.360

    0.667

    1.009

    21o

    -0.402

    -0.124

    0.176

    0.505

    0.873

    24o

    -0.638

    -0.346

    -0.030

    0.319

    0.711

    27o

    -0.890

    -0.588

    -0.259

    0.107

    0.521

    30o

    -1.158

    -0.850

    -0.511

    -0.132

    0.301

    45o

    15o

    0.017

    0.215

    0.440

    0.698

    1.001

    18o

    -0.171

    0.034

    0.267

    0.537

    0.856

    21o

    -0.379

    -0.171

    0.068

    0.346

    0.677

    24o

    -0.608

    -0.400

    -0.160

    0.122

    0.460

    27o

    -0.858

    -0.656

    -0.420

    -0.141

    0.199

    30o

    -1.133

    -0.941

    -0.717

    -0.447

    -0.114

    60o

    15o

    -0.221

    -0.076

    0.097

    0.310

    0.578

    18o

    -0.455

    -0.321

    -0.159

    0.042

    0.298

    21o

    -0.718

    -0.602

    -0.460

    -0.282

    -0.052

    24o

    -1.014

    -0.925

    -0.814

    -0.673

    -0.488

    27o

    -1.349

    -1.297

    -1.231

    -1.147

    -1.034

    30o

    -1.728

    -1.727

    -1.726

    -1.724

    -1.722

    The dimensionless force d2, perpendicular to the cutting velocity, as a function of the blade angle α, the angle of internal friction φ, the soil/interface friction angle δ, for hb/hi=3.


    17.10: Appendix J- The Coefficient d2 is shared under a not declared license and was authored, remixed, and/or curated by LibreTexts.

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