17.9: Appendix I- The Coefficient d1
- Page ID
- 35265
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)
hb/hi=1 |
φ |
32o |
37o |
42o |
47o |
52o |
α | δ | |||||
15o |
15o |
1.390 |
1.505 |
1.625 |
1.753 |
1.890 |
18o |
1.626 |
1.766 |
1.913 |
2.069 |
2.238 |
|
21o |
1.860 |
2.028 |
2.205 |
2.393 |
2.597 |
|
24o |
2.092 |
2.291 |
2.501 |
2.726 |
2.970 |
|
27o |
2.324 |
2.557 |
2.803 |
3.068 |
3.358 |
|
30o |
2.556 |
2.826 |
3.112 |
3.423 |
3.764 |
|
30o |
15o |
1.206 |
1.374 |
1.559 |
1.766 |
2.000 |
18o |
1.381 |
1.575 |
1.791 |
2.033 |
2.309 |
|
21o |
1.559 |
1.783 |
2.033 |
2.315 |
2.638 |
|
24o |
1.741 |
1.998 |
2.286 |
2.613 |
2.991 |
|
27o |
1.928 |
2.222 |
2.552 |
2.930 |
3.370 |
|
30o |
2.121 |
2.455 |
2.833 |
3.269 |
3.781 |
|
45o |
15o |
1.419 |
1.688 |
2.000 |
2.365 |
2.800 |
18o |
1.598 |
1.905 |
2.262 |
2.685 |
3.192 |
|
21o |
1.784 |
2.133 |
2.543 |
3.032 |
3.625 |
|
24o |
1.980 |
2.376 |
2.846 |
3.411 |
4.105 |
|
27o |
2.186 |
2.636 |
3.174 |
3.829 |
4.642 |
|
30o |
2.404 |
2.916 |
3.533 |
4.292 |
5.249 |
|
60o |
15o |
1.879 |
2.331 |
2.883 |
3.570 |
4.444 |
18o |
2.099 |
2.615 |
3.252 |
4.054 |
5.090 |
|
21o |
2.336 |
2.925 |
3.661 |
4.602 |
5.837 |
|
24o |
2.593 |
3.267 |
4.120 |
5.228 |
6.711 |
|
27o |
2.872 |
3.645 |
4.639 |
5.952 |
7.746 |
|
30o |
3.179 |
4.069 |
5.232 |
6.798 |
8.991 |
The dimensionless force d1, in the direction of 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.
hb/hi=2 |
φ |
32o |
37o |
42o |
47o |
52o |
α | δ | |||||
15o |
15o |
2.295 |
2.460 |
2.627 |
2.801 |
2.984 |
18o |
2.683 |
2.889 |
3.098 |
3.315 |
3.545 |
|
21o |
3.062 |
3.313 |
3.569 |
3.836 |
4.119 |
|
24o |
3.435 |
3.735 |
4.042 |
4.364 |
4.707 |
|
27o |
3.803 |
4.156 |
4.520 |
4.903 |
5.313 |
|
30o |
4.169 |
4.579 |
5.005 |
5.455 |
5.941 |
|
30o |
15o |
1.729 |
1.934 |
2.156 |
2.401 |
2.674 |
18o |
1.997 |
2.239 |
2.503 |
2.794 |
3.122 |
|
21o |
2.267 |
2.550 |
2.860 |
3.205 |
3.593 |
|
24o |
2.539 |
2.868 |
3.230 |
3.634 |
4.093 |
|
27o |
2.815 |
3.195 |
3.614 |
4.085 |
4.625 |
|
30o |
3.097 |
3.532 |
4.015 |
4.563 |
5.195 |
|
45o |
15o |
1.836 |
2.142 |
2.492 |
2.898 |
3.377 |
18o |
2.093 |
2.447 |
2.854 |
3.330 |
3.897 |
|
21o |
2.357 |
2.765 |
3.238 |
3.794 |
4.462 |
|
24o |
2.631 |
3.100 |
3.646 |
4.296 |
5.084 |
|
27o |
2.917 |
3.454 |
4.085 |
4.843 |
5.772 |
|
30o |
3.217 |
3.830 |
4.558 |
5.442 |
6.541 |
|
60o |
15o |
2.269 |
2.764 |
3.364 |
4.104 |
5.038 |
18o |
2.567 |
3.139 |
3.837 |
4.710 |
5.827 |
|
21o |
2.883 |
3.543 |
4.357 |
5.388 |
6.728 |
|
24o |
3.221 |
3.982 |
4.933 |
6.154 |
7.771 |
|
27o |
3.586 |
4.464 |
5.578 |
7.031 |
8.995 |
|
30o |
3.982 |
4.998 |
6.306 |
8.047 |
10.453 |
The dimensionless force d1, in the direction of 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.
hb/hi=3 |
φ |
32o |
37o |
42o |
47o |
52o |
α | δ | |||||
15o |
15o |
3.145 |
3.362 |
3.578 |
3.799 |
4.028 |
18o |
3.672 |
3.945 |
4.218 |
4.497 |
4.789 |
|
21o |
4.185 |
4.519 |
4.855 |
5.200 |
5.562 |
|
24o |
4.687 |
5.087 |
5.492 |
5.910 |
6.351 |
|
27o |
5.180 |
5.652 |
6.132 |
6.631 |
7.159 |
|
30o |
5.667 |
6.216 |
6.778 |
7.366 |
7.993 |
|
30o |
15o |
2.216 |
2.458 |
2.717 |
3.000 |
3.312 |
18o |
2.567 |
2.858 |
3.169 |
3.510 |
3.889 |
|
21o |
2.919 |
3.262 |
3.632 |
4.038 |
4.492 |
|
24o |
3.272 |
3.673 |
4.107 |
4.587 |
5.127 |
|
27o |
3.629 |
4.093 |
4.599 |
5.162 |
5.799 |
|
30o |
3.991 |
4.525 |
5.110 |
5.766 |
6.515 |
|
45o |
15o |
2.222 |
2.566 |
2.954 |
3.402 |
3.925 |
18o |
2.549 |
2.951 |
3.408 |
3.938 |
4.562 |
|
21o |
2.883 |
3.350 |
3.885 |
4.509 |
5.252 |
|
24o |
3.228 |
3.768 |
4.391 |
5.123 |
6.004 |
|
27o |
3.585 |
4.207 |
4.929 |
5.788 |
6.831 |
|
30o |
3.958 |
4.671 |
5.508 |
6.513 |
7.750 |
|
60o |
15o |
2.632 |
3.170 |
3.817 |
4.610 |
5.605 |
18o |
2.999 |
3.627 |
4.387 |
5.329 |
6.526 |
|
21o |
3.387 |
4.116 |
5.008 |
6.128 |
7.572 |
|
24o |
3.799 |
4.645 |
5.692 |
7.025 |
8.774 |
|
27o |
4.240 |
5.222 |
6.453 |
8.044 |
10.175 |
|
30o |
4.717 |
5.856 |
7.307 |
9.217 |
11.833 |
The dimensionless force d1, in the direction of 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.