7.9: Nomenclature
- Page ID
- 34822
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)|
a |
Adhesion |
kPa |
|
A |
Adhesive force on the blade |
kN |
|
B |
Frequency (material property) |
1/s |
|
c |
Cohesion |
kPa |
|
cm |
Mobilized shear strength |
kPa |
|
C |
Cohesive force on shear plane |
kN |
|
E |
Energy level |
J/kmol |
|
Ea |
Activation energy level |
J/kmol |
|
El |
Limiting (maximum) energy level |
J/kmol |
|
Esp |
Specific cutting energy |
kPa |
|
f |
Shear force on flow unit |
N |
|
F |
Cutting force |
kN |
|
Fh |
Horizontal cutting force |
kN |
|
Fv |
Vertical cutting force |
kN |
|
G |
Gravitational force |
kN |
|
h |
Planck constant (6.626·10-34 J·s) |
J·s |
|
hb |
Blade height |
m |
|
hb,m |
Mobilized blade height |
m |
|
hi |
Layer thickness |
m |
|
k |
Boltzman constant (1.3807·10-23 J/K) |
J/K |
|
K |
Constant Herschel Bulkley equation |
- |
|
K1 |
Grain force on the shear plane |
kN |
|
K2 |
Grain force on the blade |
kN |
|
i |
Coefficient |
- |
|
I |
Inertial force on the shear plane |
kN |
|
n |
Power of strain rate equation |
- |
|
N |
Avogadro constant (6.02·1026 1/kmol) |
- |
|
N1 |
Normal force on shear plane |
kN |
|
N2 |
Normal force on blade |
kN |
|
p |
Probability |
- |
|
Pc |
Cutting power |
kW |
|
r |
Ratio adhesive force to cohesive force |
- |
|
rm |
Mobilized ratio adhesive force to cohesive force |
- |
|
rT |
Ratio adhesive force to tensile force |
- |
|
R |
Universal gas constant (8314 J/kmol/K) |
J/kmol/K |
|
R1 |
Acting point on shear plane |
m |
|
R2 |
Acting point on blade |
m |
|
S |
Number of bonds per unit area |
1/m2 |
|
S1 |
Shear force due to internal friction on the shear surface |
kN |
|
S2 |
Shear force due to soil/steel friction on the blade |
kN |
|
SPT |
Standard Penetration Test |
Blows/foot |
|
T |
Absolute temperature |
K |
|
T |
Tensile force |
kN |
|
vc |
Cutting velocity |
m/s |
|
w |
Blade width |
m |
|
W1 |
Force resulting from pore under pressure on the shear plane |
kN |
|
W2 |
Force resulting from pore under pressure on the blade |
kN |
|
X |
Function |
- |
|
α |
Blade angle |
rad |
|
β |
Angle of the shear plane with the direction of cutting velocity |
rad |
| \(\ \dot{\varepsilon}_{\mathbf{a}}\) |
Strain rate adhesion |
1/s |
| \(\ \dot{\varepsilon}_{\mathbf{c}}\) |
Strain rate cohesion |
1/s |
| \(\ \dot{\varepsilon}_{0}\) |
Strain rate from triaxial test |
1/s |
| \(\ v\) |
frequency of activation |
1/s |
| λ |
Distance between equilibrium positions |
m |
| λa |
Strain rate factor adhesive force |
- |
|
λc |
Strain rate factor cohesive force |
- |
|
λs |
Strain rate factor average adhesion and cohesion (usually 2) |
- |
|
λ1 |
Acting point factor on shear plane |
- |
|
λ2 |
Acting point factor on blade |
- |
|
λHF |
Horizontal cutting force coefficient Flow Type |
- |
|
λVF |
Vertical cutting force coefficient Flow Type |
- |
|
λHT |
Horizontal cutting force coefficient Tear Type |
- |
|
λVT |
Vertical cutting force coefficient Tear Type |
- |
|
λHC |
Horizontal cutting force coefficient Curling Type |
- |
|
λVC |
Vertical cutting force coefficient Curling Type |
- |
|
dε/dt |
Strain rate |
1/s |
|
dε0/dt |
Frequency (material property) |
1/s |
| \(\ \tau\) |
Shear stress |
kPa |
| \(\ \tau_{\mathrm{a}}\), a |
Adhesive shear strength (strain rate dependent) |
kPa |
| \(\ \tau_{\mathrm{c}}\), c |
Cohesive shear strength (strain rate dependent) |
kPa |
| \(\ \tau_\mathrm{y}\) |
Shear strength (yield stress, material property) |
kPa |
| \(\ \tau_\mathrm{ya}\) |
Adhesive shear strength (material property) |
kPa |
| \(\ \tau_\mathrm{yc}\) |
Cohesive shear strength (material property) |
kPa |
| \(\ \tau_0\) |
Dynamical shearing resistance factor (material property) |
kPa |
|
σe |
Effective stress |
kPa |
|
σn |
Normal stress |
kPa |
|
σN1 |
Normal stress on shear plane |
kPa |
|
σN2 |
Normal stress on blade |
kPa |
|
σt |
Tensile strength |
kPa |
|
φ |
Angle of internal friction |
rad |
|
δ |
Soil/steel friction angle |
rad |