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7.9: Nomenclature

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    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

    7.9: Nomenclature is shared under a not declared license and was authored, remixed, and/or curated by LibreTexts.

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