The Cutting of Sand, Clay and Rock

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Click on an arrow for explanation.


General cutting equations

Relations between shear forces and normal forces:

`S1N1`

`S2N2`

Horizontal equilibrium of forces:

`HEQ`

Vertical equilibrium of forces:

`VEQ`

This gives for the unknown grain forces `K_1` and `K_2`:

`K1general`

`K2general`

This gives for the unknown normal forces `N_1` and `N_2`:

`N1general`

`N2general`

The horizontal and vertical forces on the cutting blade can now be calculated according to:

`Fhgeneral`

`Fvgeneral`


Cutting forces in dry sand

This gives for the unknown grain forces `K_1` and `K_2`:

`K1drysand`

`K2drysand`

This gives for the unknown normal forces `N_1` and `N_2`:

`N1drysand`

`N2drysand`

The horizontal and vertical forces on the cutting blade can now be calculated according to:

`Fhdrysand`

`Fvdrysand`


Cutting forces in water saturated sand

This gives for the unknown grain forces `K_1` and `K_2`:

`K1wetsand`

`K2wetsand`

This gives for the unknown normal forces `N_1` and `N_2`:

`N1wetsand`

`N2wetsand`

The horizontal and vertical forces on the cutting blade can now be calculated according to:

`Fhwetsand`

`Fvwetsand`

With given values for the pore pressure forces `W_1` and `W_2` and distinguishing the non-cavitating and the cavitating cutting process, this results in:

No cavitation

`Fhnc`

`Fvnc`

Cavitation

`Fhc`

`Fvc`


Cutting forces in clay

This gives for the unknown grain forces `K_1` and `K_2`:

`K1clay`

`K2clay`

This gives for the unknown normal forces `N_1` and `N_2`:

`N1clay`

`N2clay`

The horizontal and vertical forces on the cutting blade can now be calculated according to:

`Fhclay`

`Fvclay`

Conditions

Curling type: `ClayCurlingType`

Tear type: `ClayTearType`


Cutting forces in rock

This gives for the unknown grain forces `K_1` and `K_2`:

`K1rock`

`K2rock`

This gives for the unknown normal forces `N_1` and `N_2`:

`N1rock`

`N2rock`

The horizontal and vertical forces on the cutting blade can now be calculated according to:

`Fhrock`

`Fvrock`

Conditions

Tear type atmospheric: `RockTearType1`

Tear type hydrostatic: `RockTearType2`


 

List of symbols used

 
`A` The adhesive force exerted by the blade on the layer cut. kN
`c_1, c_2` Coefficients for the cavitating cutting process -
`C` The cohesive force exerted by the situ sand on the layer cut. kN
`d_1, d_2` Coefficients for the cavitating cutting process -
`e` Dilatation -
`F_h` Horizontal cutting force kN
`F_v` Vertical cutting force kN
`F_hydr` Force resulting from hydrostatic pressure kN
`g` Gravitational constant (approximately 9.81 m/sec2) m/sec2
`G` The gravitational force on the layer cut. kN
`h_i` The thickness of the layer cut m
`h_b` The blade height m
`I` The inertial force exerted by the situ sand on the layer cut. kN
`k_m` Permeability of the sand m/sec
`K_1` The grain force exerted by the situ sand on the layer cut. kN
`K_2` The grain force exerted by the blade on the layer cut. kN
`N_1` The normal force exerted by the situ sand on the layer cut. kN
`N_2` The normal force exerted by the blade on the layer cut. kN
`S_1` The shear force exerted by the situ sand on the layer cut. kN
`S_2` The shear force exerted by the blade on the layer cut. kN
`v_c` Cutting velocity m/sec
`w` Width of the blade m
`W_1` The force resulting from pore pressures exerted by the situ sand on the layer cut. kN
`W_2` The force resulting from pore pressures exerted by the blade on the layer cut. kN
`z` Waterdepth m
`alpha` The angle of the blade with the horizontal
`beta` The angle of the shear plane with the horizontal
`phi` The angle of internal friction (sand-sand, clay-clay, rock-rock)
`delta` The angle of external friction (sand-steel, clay-steel, rock-steel)
`rho_w` Density of water tons/m3
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Copyright © Dr.ir. S.A. Miedema, Delft University of Technology, Faculty of Mechanical Engineering, Marine Technology & Materials Science
Department of Marine & Transport Technology, The Chair of Dredging Engineering