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Author: Dr.ir. S.A. Miedema The Cutting Forces in Saturated Sand of a Seagoing Cutter Suction Dredger Dr.ir. S.A. Miedema Abstract In dredging it is necessary to know about the conditions under which a dredging operation takes place. Important conditions to design a dredger or to determine the workability of a dredger (under offshore conditions) are the forces and the torque that appear on the excavating element. The paper describes the basic theory of the cutting of water-saturated sand and gives tables by which the cutting forces on a straight blade can be determined. With some assumptions the basic theory can be applied on a cutterhead and a dredging wheel. The equations found are simplified so that by means of tables given, the cutting forces and the torque can be determined. With this knowledge research has been carried out into the forces acting on a cutterhead submitted to simulated offshore conditions. It appeared that for these conditions, a model for a disc bottom cutterhead can be derived by combining the simplified cutterhead and dredging wheel theory. A strategy for the calculation of the cutting forces and the torque on a disc bottom cutterhead is given, whilst a result of the research carried out is shown. The theory given in this paper can be used to calculate the cutting forces and the cutting torque acting on a drag head, a cutterhead or a dredging wheel by means of a pocket calculator. Introduction During previous WODCON's there have been a number of papers on the behavior of seagoing cutter suction dredgers. Wichers 1980, 1983, 1989 has described the program DREDSIM, developed by the Maritime Research Institute Netherlands (MARIN). Keuning & Journee 1983, Keuning, Journee & Miedema 1983, de Koning, Miedema & Zwartbol 1983 and Miedema1986, 1987 have described the computer program DREDMO developed by the Delft University of Technology (D.U.T) and the Delft Hydraulics (D.H.), by means of which the behavior of seagoing cutter suction dredgers can be simulated. This paper describes the theoretical models, based on Miedema 1985, 1987, for the calculation of the cutting forces, the torque and the specific cutting energy in water saturated sand and explains how to use these models. Of interest with respect to this paper are the papers of Joanknecht 1976 on the subject of cutterhead modeling and performance, van Drimmelen, van 't Hoen, Willigen & Eygenraam 1983 on the subject of the cutting forces on a dredging wheel, van Leussen & Nieuwenhuis 1984 on the subject of soil mechanics aspects of sand cutting and van Raalte & Zwartbol 1986 on the subject of cutting forces on a disc bottom cutterhead. The Two-Dimensional Cutting Theory From literature it is known that, during the process of cutting sand, the pore volume of the sand increases. This is caused by the phenomenon dilatancy (see Figure 1). With a certain cutting velocity v c there has to be a flow of water to the shear zone, the area where the pore volume increases. This causes a decrease in the pore pressure of the pore water and because the soil stress remains constant the grain stress will increase. Van Os 1977 stated: "If it is the aim of the engineer to know the average cutting forces needed to push the blade through the soil, he can take an average deformation rate ∂e/∂t to insert into the Biot equation. But it should be noted that this is purely practical reasoning and has nothing to do with Theoretical Miedema, S.A., "On the Cutting Forces in Saturated Sand of a Seagoing Cutter Suction Dredge (Adobe Acrobat 4.0 PDF-File 1.5 MB)". Proc. WODCON XII, Orlando, Florida, USA, April 1989. This paper was given the IADC Award for the best technical paper on the subject of dredging in 1989. Copyright: Dr.ir. S.A. Miedema
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Author: Dr.ir. S.A. Miedema
The Cutting Forces in Saturated Sand of a Seagoing Cutter Suction Dredger
Dr.ir. S.A. Miedema
Abstract
In dredging it is necessary to know about the conditions under which a dredging operation takes place. Important conditions to design a dredger or to determine the workability of a dredger (under offshore conditions) are the forces and the torque that appear on the excavating element. The paper describes the basic theory of the cutting of water-saturated sand and gives tables by which the cutting forces on a straight blade can be determined. With some assumptions the basic theory can be applied on a cutterhead and a dredging wheel. The equations found are simplified so that by means of tables given, the cutting forces and the torque can be determined. With this knowledge research has been carried out into the forces acting on a cutterhead submitted to simulated offshore conditions. It appeared that for these conditions, a model for a disc bottom cutterhead can be derived by combining the simplified cutterhead and dredging wheel theory. A strategy for the calculation of the cutting forces and the torque on a disc bottom cutterhead is given, whilst a result of the research carried out is shown. The theory given in this paper can be used to calculate the cutting forces and the cutting torque acting on a drag head, a cutterhead or a dredging wheel by means of a pocket calculator.
Introduction During previous WODCON's there have been a number of papers on the behavior of seagoing cutter suction dredgers. Wichers 1980, 1983, 1989 has described the program DREDSIM, developed by the Maritime Research Institute Netherlands (MARIN). Keuning & Journee 1983, Keuning, Journee & Miedema 1983, de Koning, Miedema & Zwartbol 1983 and Miedema1986, 1987 have described the computer program DREDMO developed by the Delft University of Technology (D.U.T) and the Delft Hydraulics (D.H.), by means of which the behavior of seagoing cutter suction dredgers can be simulated. This paper describes the theoretical models, based on Miedema 1985, 1987, for the calculation of the cutting forces, the torque and the specific cutting energy in water saturated sand and explains how to use these models. Of interest with respect to this paper are the papers of Joanknecht 1976 on the subject of cutterhead modeling and performance, van Drimmelen, van 't Hoen, Willigen & Eygenraam 1983 on the subject of the cutting forces on a dredging wheel, van Leussen & Nieuwenhuis 1984 on the subject of soil mechanics aspects of sand cutting and van Raalte & Zwartbol 1986 on the subject of cutting forces on a disc bottom cutterhead.
The Two-Dimensional Cutting Theory From literature it is known that, during the process of cutting sand, the pore volume of the sand increases. This is caused by the phenomenon dilatancy (see Figure 1). With a certain cutting velocity vc there has to be a flow of water to the shear zone, the area where the pore volume increases. This causes a decrease in the pore pressure of the pore water and because the soil stress remains constant the grain stress will increase. Van Os 1977 stated: "If it is the aim of the engineer to know the average cutting forces needed to push the blade through the soil, he can take an average deformation rate ∂e/∂t to insert into the Biot equation. But it should be noted that this is purely practical reasoning and has nothing to do with Theoretical
Miedema, S.A., "On the Cutting Forces in Saturated Sand of a Seagoing Cutter Suction Dredge (Adobe Acrobat 4.0 PDF-File 1.5 MB)". Proc. WODCON XII, Orlando, Florida, USA, April 1989. This paper was given the IADC Award for the best technical paper on the subject of dredging in 1989.
Copyright: Dr.ir. S.A. Miedema
Author: Dr.ir. S.A. Miedema
Soil Mechanics". Van Os and van Leussen published their cutting theory in 1987. Steeghs 1985 developed a theory with a cyclic deformation in the shear zone. This means that a cyclic changing deformation rate has to be inserted in the Biot equation. Miedema 1985 uses the average deformation rate as stated by van Os 1977 but instead of inserting this in the Biot equation, the average deformation rate is modeled as a boundary condition in the shear zone. Although the cutting process is not solely dependent upon the phenomenon dilatancy, the above mentioned research showed that for cutting velocities in a range from 0.5 to 5 m/sec the cutting process is dominated by the phenomenon dilatancy, so the contributions of gravitational, cohesive, adhesive and inertial forces can be neglected. This leads to the first two basic cutting equations for the two-dimensional cutting process in water-saturated sand (no cavitation):
m2icw1hnc kebhvgcF ⋅⋅⋅⋅⋅ρ⋅= (1)
m2icw2vnc kebhvgcF ⋅⋅⋅⋅⋅ρ⋅= (2)
maximmax
imax k5.0k5.0kandn1
nne ⋅+⋅≈−
−= (2a)
Figure 1: The two-dimensional cutting process
When the cutting velocity increases, the pore pressure will decrease until the absolute pore pressure reaches water vapor pressure, when cavitation starts to occur. With a further increase in the cutting velocity the pore pressure and thus the cutting forces remain at a constant level, which depends upon the water depth (see Figure 1). This gives the following two basic cutting equations (cavitation):
( ) bh10zgdF iw1hca ⋅⋅+⋅⋅ρ⋅= (3)
Miedema, S.A., "On the Cutting Forces in Saturated Sand of a Seagoing Cutter Suction Dredge (Adobe Acrobat 4.0 PDF-File 1.5 MB)". Proc. WODCON XII, Orlando, Florida, USA, April 1989. This paper was given the IADC Award for the best technical paper on the subject of dredging in 1989.
Copyright: Dr.ir. S.A. Miedema
Author: Dr.ir. S.A. Miedema
( ) bh10zgdF iw2vca ⋅⋅+⋅⋅ρ⋅= (4)
The coefficients c1, c2, d1 and d2 are dependent upon the angle of internal friction of the sand φ, the soil interface friction angle δ, the blade angle α and the blade height-shell thickness ratio hb/hi. Values for these coefficients can be found in the tables 1-4 (Miedema 1987). From the above four basic cutting equations, the specific cutting energy can be calculated. The definition for specific cutting energy is: The power (kW) required to cut (loosen) 1 m³ soil, so:
bhF
vbhvFE
i
h
ci
ch
⋅=
⋅⋅⋅
= (5)
For the non-cavitating (equation 1) and the cavitating (equation 3) cutting process this gives:
micw1nc k
ehvgcE ⋅⋅⋅⋅ρ⋅= (6)
( )10zgdE w1ca +⋅⋅ρ⋅= (7)
Figure 2: The definition of axis for cutterhead and dredging wheel
The Cutting Theory Applied to a Cutterhead
When a few assumptions are made, the two-dimensional cutting theory can be made applicable for a cutterhead, with the axis defined according to Figure 2 and the cutting process according to Figure 3. These assumptions are:
• The coefficients c1, c2, d1 and d2 have to be constant for the case calculated, this means that an average thickness of the layer cut has to be chosen.
• The cutterhead is a conical cutterhead with a top angle ξ. • The blades have an angle ι with the axis of the cutterhead.
Miedema, S.A., "On the Cutting Forces in Saturated Sand of a Seagoing Cutter Suction Dredge (Adobe Acrobat 4.0 PDF-File 1.5 MB)". Proc. WODCON XII, Orlando, Florida, USA, April 1989. This paper was given the IADC Award for the best technical paper on the subject of dredging in 1989.
Copyright: Dr.ir. S.A. Miedema
Author: Dr.ir. S.A. Miedema
• The equation for the thickness of the layer cut is simplified to:
pn60vh:withcossinhh
o
smaximaxii ⋅
⋅=ξ⋅Ω⋅= (8)
• The projected width of a blade on the axis of the cutterhead is:
ξ⋅ι⋅= coscosbbpr (9)
• When the swing velocity is neglected, the cutting velocity can be simplified to:
60nR2v:withcosvv o
ciRciRc⋅⋅π
=ι⋅≈ (10)
The derived model is applicable for a segment of the cutterhead with a projected width bpr and a radius R. For a conical or a crown cutterhead the calculation has to be repeated for each segment. For the momentary forces acting on one blade with a width bpr, (see Figure 3) the following equations can be derived for the axial force:
ξ⋅−ξ⋅ι⋅= sinFcossinFF vha (11)
The force in the swing direction:
( ) Ω⋅ξ⋅+ξ⋅ι⋅−±Ω⋅ι⋅= sincosFsinsinFcoscosFF vhhs (12)
The force perpendicular to the swing direction and the axial direction:
( ) Ω⋅ξ⋅+ξ⋅ι⋅−−Ω⋅ι⋅±= sincosFsinsinFcoscosFF vhhv (13)
For the momentary cutter torque on one blade with radius R, the following equation is valid:
RcosFM h ⋅ι⋅= (14)
The average cutting forces can be obtained by integration of the momentary cutting forces on a blade over the angle covered Ω0 and multiplying the result with the number of blades, according to equation 15.
Ω⋅⋅π
= ∫Ω
dF2pF 0
0 cct (15)
vsac
vtstatct
ForForFF:andForForFF:where
=
=
Miedema, S.A., "On the Cutting Forces in Saturated Sand of a Seagoing Cutter Suction Dredge (Adobe Acrobat 4.0 PDF-File 1.5 MB)". Proc. WODCON XII, Orlando, Florida, USA, April 1989. This paper was given the IADC Award for the best technical paper on the subject of dredging in 1989.
Copyright: Dr.ir. S.A. Miedema
Author: Dr.ir. S.A. Miedema
Figure 3: The cutting process of a cutterhead
When cutting a layer with a constant thickness the non-cavitating and the cavitating cutting processes can be distinguished. When cutting with a cutterhead however, the thickness of the layer cut is not constant but varies from a thickness zero to a thickness himax (when Ω = 90°). This means that cavitation may occur in part of the layer cut (see Figure 3). The angle covered where cavitation starts to occur Ω1 can be determined by equalizing the momentary cutter torques on one blade for both the non-cavitating and the cavitating cutting process (this is allowed because the force Fv is small in comparison to Fh), with: Ω1=<Ω0 this gives:
( )⎟⎟⎠
⎞⎜⎜⎝
⎛⋅⋅
=⎟⎟⎠
⎞⎜⎜⎝
⎛⋅ξ⋅⋅ι⋅⋅
⋅+⋅=Ω
nc1
ca3
maxiciR1
m11 cg
cgarcsinecoshcosvc
k10zdarcsin (16)
Miedema, S.A., "On the Cutting Forces in Saturated Sand of a Seagoing Cutter Suction Dredge (Adobe Acrobat 4.0 PDF-File 1.5 MB)". Proc. WODCON XII, Orlando, Florida, USA, April 1989. This paper was given the IADC Award for the best technical paper on the subject of dredging in 1989.
Copyright: Dr.ir. S.A. Miedema
Author: Dr.ir. S.A. Miedema
The coefficients cnc and cca, which have the dimension of force (kN), can be calculated by the following equations:
m
2maxiciRprwnc k
ehvbg2pc ⋅⋅⋅⋅⋅ρ⋅π
= (17)
( ) maxiprwca h10zbg2pc ⋅+⋅⋅ρ⋅π
= (18) The two coefficients cnc and cca can be considered as a measure for the cutting loads on a cutterhead as a function of the independent process variables. For the calculation of the forces on the cutterhead, the coefficients c1, c2, d1, d2 and the effects of the shape of the cutterhead, by means of the angles ξ and ι, can be put in six new coefficients g1 - g6. The equations 19 - 24 give the expressions for g1 - g6, with after the arrows the expressions for ξ = 0° and ι = 0°.
111 ccoscoscg →ξ⋅ι⋅= (19)
22
212 ccosccossinsincg →ξ⋅+ξ⋅ξ⋅ι⋅−= (20)
113 ddg →= (21)
2214 dcoscosdsintandg →
ιξ
⋅+ξ⋅ι⋅−= (22)
0cossinccossincg 22
15 →ξ⋅ξ⋅+ξ⋅ι⋅= (23)
0cossindcostandg 216 →
ιξ
⋅+ξ⋅ι⋅= (24)
Substitution of the equations 11 - 14 for Fc in equation 15 and simplification of the resulting equations by using equations 17, 18 and 19 - 24, gives the following four equations for the average cutting forces and the average cutter torque. In these equations the notation +/- is used, whereby the upper sign is valid for the over cutting process, while the lower sign is valid for the undercutting process.
[ ] [ ]4433ca2211ncst gfgfcgfgfcF ⋅±⋅⋅+⋅±⋅⋅= (25)
[ ] [ ]4334ca2112ncvt gfgfcgfgfcF ⋅−⋅±⋅+⋅−⋅±⋅= (26)
66na55ncat gfcgfcF ⋅⋅−⋅⋅−= (27)
RgfcRgfcM 36ca15nct ⋅⋅⋅+⋅⋅⋅= (28)
Miedema, S.A., "On the Cutting Forces in Saturated Sand of a Seagoing Cutter Suction Dredge (Adobe Acrobat 4.0 PDF-File 1.5 MB)". Proc. WODCON XII, Orlando, Florida, USA, April 1989. This paper was given the IADC Award for the best technical paper on the subject of dredging in 1989.
Copyright: Dr.ir. S.A. Miedema
Author: Dr.ir. S.A. Miedema
Photo 1: A cutterhead used in the laboratory experiments
The coefficients introduced here f1 - f6 are dependent upon the angles covered Ω0 and Ω1 and can be found in the tables 5 and 6 (Miedema 1987). When the breach height Bν is known, the total angle covered Ω0 can be calculated according to:
⎟⎠⎞
⎜⎝⎛ −=Ω
RB1arccos v
0 (29)
The specific cutting energy when cutting water-saturated sand with a cutterhead can be calculated in accordance with the equations 6 and 7 as follows:
RBBvvM
BBvM
AvvFME
avs
ciRt
avs
t
s
sstt
⋅⋅⋅⋅
≈⋅⋅ω⋅
≈⋅
⋅+ω⋅= (30)
Inserting equations 10 and 28, and given values for the swing velocity vs, the breach height Bν, the step size Ba and the radius of the cutterhead R the specific cutting energy E can be calculated.
The Cutting Theory Applied to a Dredging Wheel The two-dimensional cutting theory can also be made applicable to a dredging wheel with a few assumptions, see Figure 4 for the cutting process of a dredging wheel, these assumptions are:
• The buckets of the dredging wheel have radial cutting edges. • The equation for the thickness of the layer cut is simplified to:
Miedema, S.A., "On the Cutting Forces in Saturated Sand of a Seagoing Cutter Suction Dredge (Adobe Acrobat 4.0 PDF-File 1.5 MB)". Proc. WODCON XII, Orlando, Florida, USA, April 1989. This paper was given the IADC Award for the best technical paper on the subject of dredging in 1989.
Copyright: Dr.ir. S.A. Miedema
Author: Dr.ir. S.A. Miedema
( ) pn60v
vv
vpn60vh
o
s2s
2ci
ci
o
si ⋅
⋅≈
+⋅
⋅⋅
= (31)
• The cutting velocity at a radius r of the dredging wheel can be simplified to (when vs
<< vcir ):
Rvandrr60
n2vvvv ciRo
cir2s
2circr ⋅ω≈⋅ω=⋅
⋅π=≈+= (32)
As with the cutterhead (see equations 17 and 18) two coefficients can be defined with the dimension of force (kN), these coefficients are:
RkAevh
2pgd
mciR
2iwnc ⋅
⋅⋅⋅⋅
π⋅⋅ρ= (33)
( )RAh
2p10zgd iwca ⋅⋅π
⋅+⋅⋅ρ= (34)
The average cutting forces and the average cutting torque on the entire dredging wheel can be determined by applying equation 15 to a dredging wheel. Because the integration has proven to be very difficult and the resulting equations cover about 15 pages, these equations are simplified. It is even more difficult to determine equations for a partially cavitating cutting process, so there are separate equations for the noncavitating and for the cavitating cutting processes. The non-cavitating cutting process gives for the entire dredging wheel:
xtnc nc 1 xncF d c f= − ⋅ ⋅ (35)
stncync2ncytnc FfcdF =⋅⋅= (36)
znc1ncztnc fcdF ⋅⋅−= (37)
RmcdM nc1nctnc ⋅⋅⋅= (38)
The cavitating cutting process gives for the entire dredging wheel:
xca1caxtca fddF ⋅⋅−= (39)
stcayca2caytca FfddF =⋅⋅= (40)
Miedema, S.A., "On the Cutting Forces in Saturated Sand of a Seagoing Cutter Suction Dredge (Adobe Acrobat 4.0 PDF-File 1.5 MB)". Proc. WODCON XII, Orlando, Florida, USA, April 1989. This paper was given the IADC Award for the best technical paper on the subject of dredging in 1989.
Copyright: Dr.ir. S.A. Miedema
Author: Dr.ir. S.A. Miedema
zca1caztca fddF ⋅⋅−= (41)
RmddM ca1catca ⋅⋅⋅= (42)
Figure 4: The cutting process of a dredging wheel
The coefficients fxnc, fync, fznc and mnc can be found in table 7 (Miedema 1987), the coefficients fxca, fyca, fzca and mca can be found in table 8 (Miedema 1987). The specific cutting energy when cutting water saturated sand with a dredging wheel can also be calculated with equation 30, with the exception that for a dredging wheel the non-cavitating and the cavitating cutting process have to be calculated separately, this is done by substituting equation 38 for the non-cavitating case, equation 42 for the cavitating case and equation 32 for vciR. The breach height B has to be substituted for Bν and the step S for Ba. The radius where cavitation starts to occur can be calculated with the following equation (notice the similarity to equation 16):
( )⎟⎟⎠
⎞⎜⎜⎝
⎛⋅⋅
=⋅⋅⋅⋅⋅+⋅
=→nc1
ca1
iciR1
m1canc dc
ddRehvckR10zdr (43)
When partial cavitation occurs the equations for the cavitating cutting process give an upper limit for the forces and the torque. Equations 39 - 42 have to be used when Mtnc is greater than Mtca.
Miedema, S.A., "On the Cutting Forces in Saturated Sand of a Seagoing Cutter Suction Dredge (Adobe Acrobat 4.0 PDF-File 1.5 MB)". Proc. WODCON XII, Orlando, Florida, USA, April 1989. This paper was given the IADC Award for the best technical paper on the subject of dredging in 1989.
Copyright: Dr.ir. S.A. Miedema
Author: Dr.ir. S.A. Miedema
The Three-Dimensional Moving Cutterhead With the models derived above for the cutterhead and the dredging wheel the forces on a 3-dimensional moving cutterhead can be calculated. The cutterhead has to be modeled as a disc-bottom cutterhead with radial bottom blades. The Figure 5 and Figure 6 give an impression of the shape of the breach when the cutterhead undergoes a harmonic oscillation in the radial and the axial plane respectively. The forces acting on the blades at the circumference of the cutterhead can be calculated from the cutterhead model, while the forces acting on the bottom blades can be calculated from the dredging wheel model.
Figure 5: A radial oscillation
If the cutterhead undergoes a harmonic oscillation in the radial plane perpendicular to the swing direction with an amplitude aν and a frequency ων , then the displacement and the velocity can be determined by (the displacement ν(t) is positive breach outwards):
tsinat ⋅ω⋅=ν νν (44)
tcosa)t( ⋅ω⋅ω⋅=ν νννν (45)
Miedema, S.A., "On the Cutting Forces in Saturated Sand of a Seagoing Cutter Suction Dredge (Adobe Acrobat 4.0 PDF-File 1.5 MB)". Proc. WODCON XII, Orlando, Florida, USA, April 1989. This paper was given the IADC Award for the best technical paper on the subject of dredging in 1989.
Copyright: Dr.ir. S.A. Miedema
Author: Dr.ir. S.A. Miedema
Figure 6: An axial oscillation
The resulting radial velocity vrad can now be calculated with:
)t(vv)t(v 22srad ν+= (46)
For the angle between the momentary direction of vrad and the s-axis:
⎟⎟⎠
⎞⎜⎜⎝
⎛ ⋅ω⋅ω⋅=⎟⎟
⎠
⎞⎜⎜⎝
⎛=Ω νννν
ss
'0 v
tcosaarctanv
)t(varctan)t( (47)
The total angle covered Ω0"(t) can be determined by superimposing the radial displacement on the breach height Bν, so:
⎟⎠⎞
⎜⎝⎛ ⋅ω⋅+−=Ω ννν
RtsinaB1arccos"
0 (48)
Because the angle covered Ω0 has to be calculated in relation to the momentary direction of the velocity vrad of the cutterhead, the angle covered Ω0" has to be corrected with the angle Ω0'. With a harmonic oscillating displacement of the cutterhead, part of the breach has already been cut. This part has an angle covered Ω0c, where Ω0c is negative. It is also possible that part of the breach cut is not covered by Ω0' - Ω0' as in Figure 5, this part also has an angle covered Ω0c, where Ω0c is positive. Figure 5 shows the angles covered, the direction of the resulting radial velocity vrad and the direction of the forces acting on the circumference of the cutterhead. The total angle covered Ω0 can now be determined by:
c0'0
"00 )t()t()t( Ω+Ω−Ω=Ω (49)
Miedema, S.A., "On the Cutting Forces in Saturated Sand of a Seagoing Cutter Suction Dredge (Adobe Acrobat 4.0 PDF-File 1.5 MB)". Proc. WODCON XII, Orlando, Florida, USA, April 1989. This paper was given the IADC Award for the best technical paper on the subject of dredging in 1989.
Copyright: Dr.ir. S.A. Miedema
Author: Dr.ir. S.A. Miedema
For the cutting forces this means, that if Ω0c is negative first the forces have to be calculated with an angle covered Ω0"(t)-Ω0'(t), from this the force with an angle covered Ω0c(t) has to be subtracted, so:
( ) ( ) ( ))t(F)t()t(f)t(f c0ct'0
"0ct0ct Ω⋅−Ω−Ω⋅=Ω⋅ (50)
The thickness of the layer cut depends upon the radial velocity vrad of the cutterhead. Without an oscillation this velocity equals the swing velocity vs, however with an oscillation this is not the case. The thickness of the layer cut can be found by integrating the radial velocity vν during the time Δt since the previous blade has passed.
pn60to ⋅
=Δ (51)
The effective radial velocity vνc(t) found by this integration can be calculated with:
( ) )2tt(cosa)tt(sintsin
ta)t(v c Δ−⋅ω⋅ω⋅=Δ−ω−⋅ω⋅Δ
= νννννν
ν (52)
So there is a phase shift ε between the real radial velocity vν and the effective radial velocity vνc according to equation 53.
2t νω⋅Δ
=ε (53)
For the resulting radial velocity that has to be inserted in equation 8 instead of vs for the calculation of the thickness of the layer cut, equation 54 is valid.
)t(vv)t(v 2c
2sradc ν+= (54)
The cutting force calculated with equation 25 is in the direction of vrad, the cutting force calculated with equation 26 is perpendicular to vrad according to Figure 5. The resulting forces in the s and ν direction can be calculated according to (with use of equation 50).
'0
't
'0
'stst sinFcosFF Ω⋅−Ω⋅= ν (55)
'0
't
'0
'stt cosFsinFF Ω⋅−Ω⋅= νν (56)
Miedema, S.A., "On the Cutting Forces in Saturated Sand of a Seagoing Cutter Suction Dredge (Adobe Acrobat 4.0 PDF-File 1.5 MB)". Proc. WODCON XII, Orlando, Florida, USA, April 1989. This paper was given the IADC Award for the best technical paper on the subject of dredging in 1989.
Copyright: Dr.ir. S.A. Miedema
Author: Dr.ir. S.A. Miedema
Figure 7: The step S and the effective axial velocity vac
If the cutterhead undergoes a harmonic oscillation in the axial plane with an amplitude aa and a frequency ωa (see Figure 6), then the displacement and the velocity can be determined by (the displacement a(t) is positive breach outwards):
tsina)t(a aa ⋅ω⋅= (57)
tcosa)t(v aaaa ⋅ω⋅ω⋅= (58)
The projected width of the part of the blades at the circumference of the cutterhead in contact with the breach is now:
pr a a ab (t) B a sin t= + ⋅ ω ⋅ (59)
The effective axial velocity for the determination of the thickness of the layer cut can be calculated according to:
( ) )2Tt(cosa)tt(sintsin
ta)t(v aaaaa
aac Δ−⋅ω⋅ω⋅=Δ−ω−⋅ω⋅
Δ= (60)
Equation 60 shows that there is a phase shift between the axial velocity and the effective axial velocity similar to the phase shift occurring with the radial velocities. When an axial harmonic oscillation occurs, the wavelength of this oscillation is:
Miedema, S.A., "On the Cutting Forces in Saturated Sand of a Seagoing Cutter Suction Dredge (Adobe Acrobat 4.0 PDF-File 1.5 MB)". Proc. WODCON XII, Orlando, Florida, USA, April 1989. This paper was given the IADC Award for the best technical paper on the subject of dredging in 1989.
Copyright: Dr.ir. S.A. Miedema
Author: Dr.ir. S.A. Miedema
asa 2T:withvT)( ω
π=⋅=ωλ (61)
For the displacement in the swing direction yields:
tv)t(s s ⋅= (62)
The step S used in the calculation for the forces on the bottom blades is in this case the distance the cutterhead has traveled since the cutterhead had the same axial position a(t) (see Figure 7), so:
⎟⎠⎞
⎜⎝⎛ ω⋅λ⋅−
ω⋅λ−⋅= )(n
4)()t(s2)t(S a
a (63)
∞=ω⋅λ⋅+ω⋅λ⋅
<<ω⋅λ⋅+ω⋅λ ,2,1n)(n
4)(3)t(s)(n
4)(:when a
aa
a
)(n4
)()t(s)(n4
)(:for0)t(S:And aa
aa ω⋅λ⋅+
ω⋅λ<<ω⋅λ⋅+
ω⋅λ−= (64)
This gives for the area of the cross-section cut by the bottom blades:
ν⋅= B)t(S)t(A (65
Miedema, S.A., "On the Cutting Forces in Saturated Sand of a Seagoing Cutter Suction Dredge (Adobe Acrobat 4.0 PDF-File 1.5 MB)". Proc. WODCON XII, Orlando, Florida, USA, April 1989. This paper was given the IADC Award for the best technical paper on the subject of dredging in 1989.
Copyright: Dr.ir. S.A. Miedema
Author: Dr.ir. S.A. Miedema
Photo2: The laboratory where the research was carried out
The strategy for the calculation of the cutting forces with an oscillation is, to divide a period of the oscillation into time steps, then, per time step: First, make an estimate for the coefficients c1, c2, d1 and d2 based on an average expected thickness of the layer cut. For the radial oscillation:
1. Assume that the forces on the bottom blades are zero, because the thickness of the layer cut by the bottom blades is zero.
2. Calculate the effective radial velocity with equation 52 and insert this velocity in equation 8 to calculate himax.
3. Use equation 10 to calculate vciR. 4. Substitute Ba for bpr in equations 17 and 18 and calculate cnc and cca. 5. Get values for the coefficients f1 - f6 from tables 5 and 6 for the cases Ω0 = Ω0" + Ω0'
and Ω0 = Ω0c. 6. Calculate the cutting forces with equations 25 and 26 and the torque with equation 28
for the two cases mentioned in point 5 and subtract these forces according to equation 50.
7. Transpose the forces found according to equations 55 and 56.
Miedema, S.A., "On the Cutting Forces in Saturated Sand of a Seagoing Cutter Suction Dredge (Adobe Acrobat 4.0 PDF-File 1.5 MB)". Proc. WODCON XII, Orlando, Florida, USA, April 1989. This paper was given the IADC Award for the best technical paper on the subject of dredging in 1989.
Copyright: Dr.ir. S.A. Miedema
Author: Dr.ir. S.A. Miedema
Figure 8: Verification of the radial oscillation model
Miedema, S.A., "On the Cutting Forces in Saturated Sand of a Seagoing Cutter Suction Dredge (Adobe Acrobat 4.0 PDF-File 1.5 MB)". Proc. WODCON XII, Orlando, Florida, USA, April 1989. This paper was given the IADC Award for the best technical paper on the subject of dredging in 1989.
Copyright: Dr.ir. S.A. Miedema
Author: Dr.ir. S.A. Miedema
For the axial oscillation:
1. Calculate the forces and the torque (use equations 17, 18, 25, 26 and 28) on the circumference-blades by inserting equation 59 for bpr, equation 8 for himax and equation 10 for vciR.
2. Calculate the effective axial velocity with equation 60 and insert this velocity in equation 31 to calculate hi.
3. Use equation 65 to calculate the area of the cross-section cut A(t). 4. Use equation 10 to calculate vciR. 5. Insert the found values of hi, A(t) and vciR in equations 33 and 34 to calculate dnc and
dca. 6. Get values for fxnc, fync, fznc, mnc, fxca, fyca, fzca and mca from the tables 7 and 8 by
using Ss(t) and Bν. 7. Calculate the cutting forces and the torque with equation's 35 - 38 for the non-
cavitating process and with equations 39 - 42 for the cavitating cutting process. 8. If Mtnc>Mtca takes the values for the cavitating process, otherwise take the values for
the non-cavitating process.
Miedema, S.A., "On the Cutting Forces in Saturated Sand of a Seagoing Cutter Suction Dredge (Adobe Acrobat 4.0 PDF-File 1.5 MB)". Proc. WODCON XII, Orlando, Florida, USA, April 1989. This paper was given the IADC Award for the best technical paper on the subject of dredging in 1989.
Copyright: Dr.ir. S.A. Miedema
Author: Dr.ir. S.A. Miedema
Figure 9: Verification of the axial oscillation model
Miedema, S.A., "On the Cutting Forces in Saturated Sand of a Seagoing Cutter Suction Dredge (Adobe Acrobat 4.0 PDF-File 1.5 MB)". Proc. WODCON XII, Orlando, Florida, USA, April 1989. This paper was given the IADC Award for the best technical paper on the subject of dredging in 1989.
Copyright: Dr.ir. S.A. Miedema
Author: Dr.ir. S.A. Miedema
The above derived models for the calculation of the forces and the torque on an oscillating disc-bottom cutterhead, have been verified with the results of model tests, mentioned by de Koning, Miedema & Zwartbol in 1983. In 1983 the research resulted in an empiric model. The disc-bottom cutterhead used in this research has a radius of 475 mm, 8 blades and a width of the blades at the circumference of 184 mm. Figure 8 shows the measured and the calculated forces and torque for an overcutting process with a radial oscillation, with: Bν =350 mm, Ba =184 mm, T=2 sec, aν =20 mm, vs =0.109 m/s and no =33 rpm. Figure 9 shows the measured and the calculated forces and torque for an overcutting process with an axial oscillation, with: Bν =350 mm, Ba =184 mm, T=2 sec, aa =20 mm, vs =0.110 m/s and no =44 rpm. In these figures the phase shift according to equation 53 can be noticed with the axial and the radial oscillation. In general the shape of the measured and the calculated signals agree closely. The axial force in Figure 9 is theoretically zero, this means that the measured axial force is not caused by the cutting process but it is caused by friction and inertial forces.
Conclusion The verification of the theory was "satisfying", but the calculation method of the 3-dimensional model is time consuming on a computer. The main result of the research is the understanding of the cutting processes and the possibility to calculate the loads on cutterhead and dredging wheel for non-oscillating processes with the tables given. For the 3-dimensional model the occurrence of a phase shift is important in relation to the simulation of the behavior of a seagoing cutter suction dredger.
Bibliography
1. Drimmelen, N.J. van, t'Hoen, J.P.T.A., Willigen, F.A. and Eygenraam J.A.,
"Development and First Production Unit of the IHC Beaver Wheel Dredger". Proc. WODCON X, Singapore 1983.
2. Joanknecht, L.F.W., "A Review of Dredge Cutterhead Modelling and Performance". Proc. WODCON VII, San Francisco, 1976.
3. Journee, J.M.J. and Miedema, S.A. and Keuning, J.A. "DREDMO, A Computer Program for the Calculation of the Behaviour of Seagoing Cutter Suction Dredgers". T.U. Delft & Delft Hydraulics, 1983.
4. Keuning, P.J. & Journee, J., "Calculation Method for the Behaviour of a Cutter Suction Dredger Operating in Irregular Waves". Proc. Wodcon X, Singapore 1983.
5. Koning, J de & Miedema, S.A. & Zwartbol, A., "Soil/Cutterhead Interaction under Wave Conditions". Proc. WODCON X, Sing., 1983.
6. Leussen, W. van & Nieuwenhuis J.D., "Soil Mechanics Aspects of Dredging". Geotechnique 34 No.3, pp. 359-381.
7. Miedema, S.A., "Mathematical Modelling of the Cutting of Densely Compacted Sand Under Water". Dredging & Port Construction, July 1985, pp. 22-26. "Derivation of the Differential Equation for Sand Pore Pressures". Dredging & Port Construction, September 1985, pp. 35. "Underwater soil cutting: a study in continuity", Dredging & Port Construction, June 1986, pp. 47-53.
8. Miedema, S.A., "The Application of a Cutting Theory on a Dredging Wheel". Proc. WODCON XI, Brighton 1986.
9. Miedema, S.A., "The Calculation of the Cutting Forces when Cutting Water Saturated Sand, Basical Theory and Applications for 3-Dimensional Blade Movements with
Miedema, S.A., "On the Cutting Forces in Saturated Sand of a Seagoing Cutter Suction Dredge (Adobe Acrobat 4.0 PDF-File 1.5 MB)". Proc. WODCON XII, Orlando, Florida, USA, April 1989. This paper was given the IADC Award for the best technical paper on the subject of dredging in 1989.
Copyright: Dr.ir. S.A. Miedema
Author: Dr.ir. S.A. Miedema
Periodicaly Varieing Velocities for in Dredging Usual Excavating Elements" (in Dutch). Doctors thesis, Delft, 1987, the Netherlands.
10. Os, A.G. van, "Behaviour of Soil when Excavated Underwater". International Course Modern Dredging. June 1977, The Hague, The Netherlands.
11. Os, A.G. van & Leussen, W. van, "Basic Research on Cutting Forces in Saturated Sand". Journal of Geotechnical Engineering, Vol. 113, No.12, December 1987.
12. Raalte, G.H. van & Zwartbol, A., "The Disc Bottom Cutterhead: A Report on Laboratory and Field Tests". Proc. WODCON XI, Brighton, England, 1986.
13. Steeghs, H., "Snijden van zand onder water (I & II)". Ports & Dredging No. 121, June 1985. Ports & Dredging No. 123, November 1985. Rapport: GR 37-IIB * MTI-Holland, Kinderdijk, 1986.
14. Wichers, J.E.W.,"On the Forces on a Cutter Suction Dredger in Waves". Proc. WODCON IX, Vancouver, B.C., Canada, 1980.
15. Wichers, J.E.W. and Drimmelen, N.J. van, "On the forces on the cutterhead and the spud of a cutter suction dredger, operating in waves". Proc. WODCON X, Singapore 1983.
16. Wichers, J.E.W., "On the reduction of mooring forces of a cutter suction dredger operating in waves". Proc. WODCON XII, Orlando, Florida, USA, 1989.
List of Symbols used
a Axial oscillation. m aa,ν Amplitude of oscillation. m A Area of cross section cut. m³ b Width of blade. m bpr Width of blade projected on axis. m Ba,ν Breachheight. m cca Coefficient cutting process cutterhead (cav.). kN cnc Coefficient cutting process cutterhead (no-cav.). kN c1,c2 Coefficients (no-cavitation). - dca Coefficient cutting process dredging wheel (cav.). kN dnc Coefficient cutting process dredging wheel (no-cav.). kN d1,d2 Coefficients (cavitation). - e Volume strain. % E Specific cutting energy. kN/m² f1..6 Coefficients cutting forces cutterhead. - fx,y,z Coefficients cutting forces dredging wheel. - Fc Cutting force (general). kN Fa Axial cutting force. kN Fh Cutting force in direction of cutting velocity. kN Fs Cutting force in swing direction. kN Fv Cutting force perpendicular to cutting velocity. kN Fx Cutting force longitudinal to ship. kN Fy Cutting force transversal to ship. kN Fz Cutting force vertical. kN
Fν Cutting force perpendicular to swing direction and perpendicular to axis ofexcavating element. kN
g Gravitational constant (9.81). m/s² g1..6 Coefficients cutting forces cutterhead. -
Miedema, S.A., "On the Cutting Forces in Saturated Sand of a Seagoing Cutter Suction Dredge (Adobe Acrobat 4.0 PDF-File 1.5 MB)". Proc. WODCON XII, Orlando, Florida, USA, April 1989. This paper was given the IADC Award for the best technical paper on the subject of dredging in 1989.
Copyright: Dr.ir. S.A. Miedema
Author: Dr.ir. S.A. Miedema
hi Initial thickness of layer cut. m himax Maximum thickness of layer cut. m hb Height of blade. m ki Initial permeability. m/s kmax Maximum permeability. m/s km Average permeability. m/s mnc,ca Coefficients torque dredging wheel. - M Torque. kNm n Number of periods passed. - no Number of revolutions of excavating element. rpm ni Initial porosity. % nmax Maximum porosity. % p Number of blades excavating element. - r Radius. m R External radius of excavating element. m rnc>ca Radius where cavitation starts to occur. m s Travelled distance. m S Step. m t Time. sec va,ν Oscillating velocity. m/s vac,νc Oscillating velocity corrected. m/s vc Cutting velocity. m/s vci,ciR Circumferential velocity. m/s vrad Resulting radial velocity. m/s vradc Resulting radial velocity corrected. m/s vs Haulage velocity. m/s z Water depth. m α Cutting angle blade. rad
φ Angle of internal friction. rad
δ Soil/interface friction angle. rad ε Phase shift. rad λa Wave length. m ι Angle of blades with axis cutterhead. rad ρw Density water. ton/m³ ωa,ν Angular velocity. rad/s ξ Top angle conical cutterhead. rad ν Radial oscillation. m Ω Angle covered by blade of excavating element. rad Ω0 Total angle covered (cutterhead or dredging wheel). rad Ω1 Angle covered where cavitation starts to occur. rad Indices ca Cavitating cutting proces. nc Non-cavitating cutting proces. t Average of one revolution of excavating element.
Miedema, S.A., "On the Cutting Forces in Saturated Sand of a Seagoing Cutter Suction Dredge (Adobe Acrobat 4.0 PDF-File 1.5 MB)". Proc. WODCON XII, Orlando, Florida, USA, April 1989. This paper was given the IADC Award for the best technical paper on the subject of dredging in 1989.
Copyright: Dr.ir. S.A. Miedema
Author: Dr.ir. S.A. Miedema
Tables
Table 1: The coefficient c1, horizontal force, no cavitation
Miedema, S.A., "On the Cutting Forces in Saturated Sand of a Seagoing Cutter Suction Dredge (Adobe Acrobat 4.0 PDF-File 1.5 MB)". Proc. WODCON XII, Orlando, Florida, USA, April 1989. This paper was given the IADC Award for the best technical paper on the subject of dredging in 1989.
Copyright: Dr.ir. S.A. Miedema
Author: Dr.ir. S.A. Miedema
Table 2: The coefficient c2, vertical force, no cavitation
Miedema, S.A., "On the Cutting Forces in Saturated Sand of a Seagoing Cutter Suction Dredge (Adobe Acrobat 4.0 PDF-File 1.5 MB)". Proc. WODCON XII, Orlando, Florida, USA, April 1989. This paper was given the IADC Award for the best technical paper on the subject of dredging in 1989.
Copyright: Dr.ir. S.A. Miedema
Author: Dr.ir. S.A. Miedema
Table 3: The coefficient d1, horizontal force, cavitation
Miedema, S.A., "On the Cutting Forces in Saturated Sand of a Seagoing Cutter Suction Dredge (Adobe Acrobat 4.0 PDF-File 1.5 MB)". Proc. WODCON XII, Orlando, Florida, USA, April 1989. This paper was given the IADC Award for the best technical paper on the subject of dredging in 1989.
Copyright: Dr.ir. S.A. Miedema
Author: Dr.ir. S.A. Miedema
Table 4: The coefficient d2, vertical force, cavitation
Miedema, S.A., "On the Cutting Forces in Saturated Sand of a Seagoing Cutter Suction Dredge (Adobe Acrobat 4.0 PDF-File 1.5 MB)". Proc. WODCON XII, Orlando, Florida, USA, April 1989. This paper was given the IADC Award for the best technical paper on the subject of dredging in 1989.
Copyright: Dr.ir. S.A. Miedema
Author: Dr.ir. S.A. Miedema
Table 5: The coefficients f1, f2 and f5 for the cutterhead equations 25 - 28
Table 6: The coefficients f3, f4 and f6 for the cutterhead equations 25 - 28
Miedema, S.A., "On the Cutting Forces in Saturated Sand of a Seagoing Cutter Suction Dredge (Adobe Acrobat 4.0 PDF-File 1.5 MB)". Proc. WODCON XII, Orlando, Florida, USA, April 1989. This paper was given the IADC Award for the best technical paper on the subject of dredging in 1989.
Copyright: Dr.ir. S.A. Miedema
Author: Dr.ir. S.A. Miedema
Table 7: The coefficients fxnc, fync, fznc and mnc for the dredging wheel equations 35 - 38
Table 8: The coefficients fxca, fyca, fzca and mca for the dredging wheel equations 39 - 42
Miedema, S.A., "On the Cutting Forces in Saturated Sand of a Seagoing Cutter Suction Dredge (Adobe Acrobat 4.0 PDF-File 1.5 MB)". Proc. WODCON XII, Orlando, Florida, USA, April 1989. This paper was given the IADC Award for the best technical paper on the subject of dredging in 1989.
Copyright: Dr.ir. S.A. Miedema
Bibliography Dr.ir. S.A. Miedema 1980-2010
1. Koert, P. & Miedema, S.A., "Report on the field excursion to the USA April 1981" (PDF in Dutch 27.2 MB). Delft University of Technology, 1981, 48 pages.
2. Miedema, S.A., "The flow of dredged slurry in and out hoppers and the settlement process in hoppers" (PDF in Dutch 37 MB). ScO/81/105, Delft University of Technology, 1981, 147 pages.
3. Miedema, S.A., "The soil reaction forces on a crown cutterhead on a swell compensated ladder" (PDF in Dutch 19 MB). LaO/81/97, Delft University of Technology, 1981, 36 pages.
4. Miedema, S.A., "Computer program for the determination of the reaction forces on a cutterhead, resulting from the motions of the cutterhead" (PDF in Dutch 11 MB). Delft Hydraulics, 1981, 82 pages.
5. Miedema, S.A. "The mathematical modeling of the soil reaction forces on a cutterhead and the development of the computer program DREDMO" (PDF in Dutch 25 MB). CO/82/125, Delft University of Technology, 1982, with appendices 600 pages.
6. Miedema, S.A.,"The Interaction between Cutterhead and Soil at Sea" (In Dutch). Proc. Dredging Day November 19th, Delft University of Technology 1982.
7. Miedema, S.A., "A comparison of an underwater centrifugal pump and an ejector pump" (PDF in Dutch 3.2 MB). Delft University of Technology, 1982, 18 pages.
8. Miedema, S.A., "Computer simulation of Dredging Vessels" (In Dutch). De Ingenieur, Dec. 1983. (Kivi/Misset).
9. Koning, J. de, Miedema, S.A., & Zwartbol, A., "Soil/Cutterhead Interaction under Wave Conditions (Adobe Acrobat PDF-File 1 MB)". Proc. WODCON X, Singapore 1983.
10. Miedema, S.A. "Basic design of a swell compensated cutter suction dredge with axial and radial compensation on the cutterhead" (PDF in Dutch 20 MB). CO/82/134, Delft University of Technology, 1983, 64 pages.
11. Miedema, S.A., "Design of a seagoing cutter suction dredge with a swell compensated ladder" (PDF in Dutch 27 MB). IO/83/107, Delft University of Technology, 1983, 51 pages.
12. Miedema, S.A., "Mathematical Modeling of a Seagoing Cutter Suction Dredge" (In Dutch). Published: The Hague, 18-9-1984, KIVI Lectures, Section Under Water Technology.
13. Miedema, S.A., "The Cutting of Densely Compacted Sand under Water (Adobe Acrobat PDF-File 575 kB)". Terra et Aqua No. 28, October 1984 pp. 4-10.
14. Miedema, S.A., "Longitudinal and Transverse Swell Compensation of a Cutter Suction Dredge" (In Dutch). Proc. Dredging Day November 9th 1984, Delft University of Technology 1984.
15. Miedema, S.A., "Compensation of Velocity Variations". Patent application no. 8403418, Hydromeer B.V. Oosterhout, 1984.
16. Miedema, S.A., "Mathematical Modeling of the Cutting of Densely Compacted Sand Under Water". Dredging & Port Construction, July 1985, pp. 22-26.
17. Miedema, S.A., "Derivation of the Differential Equation for Sand Pore Pressures". Dredging & Port Construction, September 1985, pp. 35.
18. Miedema, S.A., "The Application of a Cutting Theory on a Dredging Wheel (Adobe Acrobat 4.0 PDF-File 745 kB)". Proc. WODCON XI, Brighton 1986.
19. Miedema, S.A., "Underwater Soil Cutting: a Study in Continuity". Dredging & Port Construction, June 1986, pp. 47-53.
20. Miedema, S.A., "The cutting of water saturated sand, laboratory research" (In Dutch). Delft University of Technology, 1986, 17 pages.
21. Miedema, S.A., "The forces on a trenching wheel, a feasibility study" (In Dutch). Delft, 1986, 57 pages + software.
22. Miedema, S.A., "The translation and restructuring of the computer program DREDMO from ALGOL to FORTRAN" (In Dutch). Delft Hydraulics, 1986, 150 pages + software.
23. Miedema, S.A., "Calculation of the Cutting Forces when Cutting Water Saturated Sand (Adobe Acrobat 4.0 PDF-File 16 MB)". Basic Theory and Applications for 3-D Blade Movements and Periodically Varying Velocities for, in Dredging Commonly used Excavating Means. Ph.D. Thesis, Delft University of Technology, September 15th 1987.
24. Bakker, A. & Miedema, S.A., "The Specific Energy of the Dredging Process of a Grab Dredge". Delft University of Technology, 1988, 30 pages.
25. Miedema, S.A., "On the Cutting Forces in Saturated Sand of a Seagoing Cutter Suction Dredge (Adobe Acrobat 4.0 PDF-File 1.5 MB)". Proc. WODCON XII, Orlando, Florida, USA, April 1989. This paper was given the IADC Award for the best technical paper on the subject of dredging in 1989.
26. Miedema, S.A., "The development of equipment for the determination of the wear on pick-points" (In Dutch). Delft University of Technology, 1990, 30 pages (90.3.GV.2749, BAGT 462).
27. Miedema, S.A., "Excavating Bulk Materials" (In Dutch). Syllabus PATO course, 1989 & 1991, PATO The Hague, The Netherlands.
28. Miedema, S.A., "On the Cutting Forces in Saturated Sand of a Seagoing Cutter Suction Dredge (Adobe Acrobat 4.0 PDF-File 1.5 MB)". Terra et Aqua No. 41, December 1989, Elseviers Scientific Publishers.
29. Miedema, S.A., "New Developments of Cutting Theories with respect to Dredging, the Cutting of Clay (Adobe Acrobat 4.0 PDF-File 640 kB)". Proc. WODCON XIII, Bombay, India, 1992.
30. Davids, S.W. & Koning, J. de & Miedema, S.A. & Rosenbrand, W.F., "Encapsulation: A New Method for the Disposal of Contaminated Sediment, a Feasibility Study (Adobe Acrobat 4.0 PDF-File 3MB)". Proc. WODCON XIII, Bombay, India, 1992.
31. Miedema, S.A. & Journee, J.M.J. & Schuurmans, S., "On the Motions of a Seagoing Cutter Dredge, a Study in Continuity (Adobe Acrobat 4.0 PDF-File 396 kB)". Proc. WODCON XIII, Bombay, India, 1992.
32. Becker, S. & Miedema, S.A. & Jong, P.S. de & Wittekoek, S., "On the Closing Process of Clamshell Dredges in Water Saturated Sand (Adobe Acrobat 4.0 PDF-File 1 MB)". Proc. WODCON XIII, Bombay, India, 1992. This paper was given the IADC Award for the best technical paper on the subject of dredging in 1992.
33. Becker, S. & Miedema, S.A. & Jong, P.S. de & Wittekoek, S., "The Closing Process of Clamshell Dredges in Water Saturated Sand (Adobe Acrobat 4.0 PDF-File 1 MB)". Terra et Aqua No. 49, September 1992, IADC, The Hague.
34. Miedema, S.A., "Modeling and Simulation of Dredging Processes and Systems". Symposium "Zicht op Baggerprocessen", Delft University of Technology, Delft, The Netherlands, 29 October 1992.
35. Miedema, S.A., "Dredmo User Interface, Operators Manual". Report: 92.3.GV.2995. Delft University of Technology, 1992, 77 pages.
36. Miedema, S.A., "Inleiding Mechatronica, college WBM202" Delft University of Technology, 1992.
37. Miedema, S.A. & Becker, S., "The Use of Modeling and Simulation in the Dredging Industry, in Particular the Closing Process of Clamshell Dredges", CEDA Dredging Days 1993, Amsterdam, Holland, 1993.
38. Miedema, S.A., "On the Snow-Plough Effect when Cutting Water Saturated Sand with Inclined Straight Blades (Adobe Acrobat 4.0 PDF-File 503 kB)". ASCE Proc. Dredging 94, Orlando, Florida, USA, November 1994. Additional Measurement Graphs. (Adobe Acrobat 4.0 PDF-File 209 kB).
39. Riet, E. van, Matousek, V. & Miedema, S.A., "A Reconstruction of and Sensitivity Analysis on the Wilson Model for Hydraulic Particle Transport (Adobe Acrobat 4.0 PDF-File 50 kB)". Proc. 8th Int. Conf. on Transport and Sedimentation of Solid Particles, 24-26 January 1995, Prague, Czech Republic.
40. Vlasblom, W.J. & Miedema, S.A., "A Theory for Determining Sedimentation and Overflow Losses in Hoppers (Adobe Acrobat 4.0 PDF-File 304 kB)". Proc. WODCON IV, November 1995, Amsterdam, The Netherlands 1995.
41. Miedema, S.A., "Production Estimation Based on Cutting Theories for Cutting Water Saturated Sand (Adobe Acrobat 4.0 PDF-File 423 kB)". Proc. WODCON IV, November 1995, Amsterdam, The Netherlands 1995. Additional Specific Energy and Production Graphs. (Adobe Acrobat 4.0 PDF-File 145 kB).
42. Riet, E.J. van, Matousek, V. & Miedema, S.A., "A Theoretical Description and Numerical Sensitivity Analysis on Wilson's Model for Hydraulic Transport in Pipelines (Adobe Acrobat 4.0 PDF-File 50 kB)". Journal of Hydrology & Hydromechanics, Slovak Ac. of Science, Bratislava, June 1996.
43. Miedema, S.A. & Vlasblom, W.J., "Theory for Hopper Sedimentation (Adobe Acrobat 4.0 PDF-File 304 kB)". 29th Annual Texas A&M Dredging Seminar. New Orleans, June 1996.
44. Miedema, S.A., "Modeling and Simulation of the Dynamic Behavior of a Pump/Pipeline System (Adobe Acrobat 4.0 PDF-File 318 kB)". 17th Annual Meeting & Technical Conference of the Western Dredging Association. New Orleans, June 1996.
45. Miedema, S.A., "Education of Mechanical Engineering, an Integral Vision". Faculty O.C.P., Delft University of Technology, 1997 (in Dutch).
46. Miedema, S.A., "Educational Policy and Implementation 1998-2003 (versions 1998, 1999 and 2000) (Adobe Acrobat 4.0 PDF_File 195 kB)". Faculty O.C.P., Delft University of Technology, 1998, 1999 and 2000 (in Dutch).
47. Keulen, H. van & Miedema, S.A. & Werff, K. van der, "Redesigning the curriculum of the first three years of the mechanical engineering curriculum". Proceedings of the International Seminar on Design in Engineering Education, SEFI-Document no.21, page 122, ISBN 2-87352-024-8, Editors: V. John & K. Lassithiotakis, Odense, 22-24 October 1998.
48. Miedema, S.A. & Klein Woud, H.K.W. & van Bemmel, N.J. & Nijveld, D., "Self Assesment Educational Programme Mechanical Engineering (Adobe Acrobat 4.0 PDF-File 400 kB)". Faculty O.C.P., Delft University of Technology, 1999.
49. Van Dijk, J.A. & Miedema, S.A. & Bout, G., "Curriculum Development Mechanical Engineering". MHO 5/CTU/DUT/Civil Engineering. Cantho University Vietnam, CICAT Delft, April 1999.
50. Miedema, S.A., "Considerations in building and using dredge simulators (Adobe Acrobat 4.0 PDF-File 296 kB)". Texas A&M 31st Annual Dredging Seminar. Louisville Kentucky, May 16-18, 1999.
51. Miedema, S.A., "Considerations on limits of dredging processes (Adobe Acrobat 4.0 PDF-File 523 kB)". 19th Annual Meeting & Technical Conference of the Western Dredging Association. Louisville Kentucky, May 16-18, 1999.
52. Miedema, S.A. & Ruijtenbeek, M.G. v.d., "Quality management in reality", "Kwaliteitszorg in de praktijk". AKO conference on quality management in education. Delft University of Technology, November 3rd 1999.
53. Miedema, S.A., "Curriculum Development Mechanical Engineering (Adobe Acrobat 4.0 PDF-File 4 MB)". MHO 5-6/CTU/DUT. Cantho University Vietnam, CICAT Delft, Mission October 1999.
54. Vlasblom, W.J., Miedema, S.A., Ni, F., "Course Development on Topic 5: Dredging Technology, Dredging Equipment and Dredging Processes". Delft University of Technology and CICAT, Delft July 2000.
55. Miedema, S.A., Vlasblom, W.J., Bian, X., "Course Development on Topic 5: Dredging Technology, Power Drives, Instrumentation and Automation". Delft University of Technology and CICAT, Delft July 2000.
56. Randall, R. & Jong, P. de & Miedema, S.A., "Experience with cutter suction dredge simulator training (Adobe Acrobat 4.0 PDF-File 1.1 MB)". Texas A&M 32nd Annual Dredging Seminar. Warwick, Rhode Island, June 25-28, 2000.
57. Miedema, S.A., "The modelling of the swing winches of a cutter dredge in relation with simulators (Adobe Acrobat 4.0 PDF-File 814 kB)". Texas A&M 32nd Annual Dredging Seminar. Warwick, Rhode Island, June 25-28, 2000.
58. Hofstra, C. & Hemmen, A. van & Miedema, S.A. & Hulsteyn, J. van, "Describing the position of backhoe dredges (Adobe Acrobat 4.0 PDF-File 257 kB)". Texas A&M 32nd Annual Dredging Seminar. Warwick, Rhode Island, June 25-28, 2000.
59. Miedema, S.A., "Automation of a Cutter Dredge, Applied to the Dynamic Behaviour of a Pump/Pipeline System (Adobe Acrobat 4.0 PDF-File 254 kB)". Proc. WODCON VI, April 2001, Kuala Lumpur, Malaysia 2001.
60. Heggeler, O.W.J. ten, Vercruysse, P.M., Miedema, S.A., "On the Motions of Suction Pipe Constructions a Dynamic Analysis (Adobe Acrobat 4.0 PDF-File 110 kB)". Proc. WODCON VI, April 2001, Kuala Lumpur, Malaysia 2001.
61. Miedema, S.A. & Zhao Yi, "An Analytical Method of Pore Pressure Calculations when Cutting Water Saturated Sand (Adobe Acrobat PDF-File 2.2 MB)". Texas A&M 33nd Annual Dredging Seminar, June 2001, Houston, USA 2001.
62. Miedema, S.A., "A Numerical Method of Calculating the Dynamic Behaviour of Hydraulic Transport (Adobe Acrobat PDF-File 246 kB)". 21st Annual Meeting & Technical Conference of the Western Dredging Association, June 2001, Houston, USA 2001.
63. Zhao Yi, & Miedema, S.A., "Finite Element Calculations To Determine The Pore Pressures When Cutting Water Saturated Sand At Large Cutting Angles (Adobe Acrobat PDF-File 4.8 MB)". CEDA Dredging Day 2001, November 2001, Amsterdam, The Netherlands.
64. Miedema, S.A., "Mission Report Cantho University". MHO5/6, Phase Two, Mission to Vietnam by Dr.ir. S.A. Miedema DUT/OCP Project Supervisor, 27 September-8 October 2001, Delft University/CICAT.
65. (Zhao Yi), & (Miedema, S.A.), "
" (Finite Element Calculations To Determine The Pore Pressures When Cutting Water
Saturated Sand At Large Cutting Angles (Adobe Acrobat PDF-File 4.8 MB))". To be published in 2002.
66. Miedema, S.A., & Riet, E.J. van, & Matousek, V., "Theoretical Description And Numerical Sensitivity Analysis On Wilson Model For Hydraulic Transport Of Solids In Pipelines (Adobe Acrobat PDF-File 147 kB)". WEDA Journal of Dredging Engineering, March 2002.
67. Miedema, S.A., & Ma, Y., "The Cutting of Water Saturated Sand at Large Cutting Angles (Adobe Acrobat PDF-File 3.6 MB)". Proc. Dredging02, May 5-8, Orlando, Florida, USA.
68. Miedema, S.A., & Lu, Z., "The Dynamic Behavior of a Diesel Engine (Adobe Acrobat PDF-File 363 kB)". Proc. WEDA XXII Technical Conference & 34th Texas A&M Dredging Seminar, June 12-15, Denver, Colorado, USA.
69. Miedema, S.A., & He, Y., "The Existance of Kinematic Wedges at Large Cutting Angles (Adobe Acrobat PDF-File 4 MB)". Proc. WEDA XXII Technical Conference & 34th Texas A&M Dredging Seminar, June 12-15, Denver, Colorado, USA.
70. Ma, Y., Vlasblom, W.J., Miedema, S.A., Matousek, V., "Measurement of Density and Velocity in Hydraulic Transport using Tomography". Dredging Days 2002, Dredging without boundaries, Casablanca, Morocco, V64-V73, 22-24 October 2002.
71. Ma, Y., Miedema, S.A., Vlasblom, W.J., "Theoretical Simulation of the Measurements Process of Electrical Impedance Tomography". Asian Simulation Conference/5th International Conference on System Simulation and Scientific Computing, Shanghai, 3-6 November 2002, p. 261-265, ISBN 7-5062-5571-5/TP.75.
72. Thanh, N.Q., & Miedema, S.A., "Automotive Electricity and Electronics". Delft University of Technology and CICAT, Delft December 2002.
73. Miedema, S.A., Willemse, H.R., "Report on MHO5/6 Mission to Vietnam". Delft University of Technology and CICAT, Delft Januari 2003.
74. Ma, Y., Miedema, S.A., Matousek, V., Vlasblom, W.J., "Tomography as a Measurement Method for Density and Velocity Distributions". 23rd WEDA Technical Conference & 35th TAMU Dredging Seminar, Chicago, USA, june 2003.
75. Miedema, S.A., Lu, Z., Matousek, V., "Numerical Simulation of a Development of a Density Wave in a Long Slurry Pipeline". 23rd WEDA Technical Conference & 35th TAMU Dredging Seminar, Chicago, USA, june 2003.
76. Miedema, S.A., Lu, Z., Matousek, V., "Numerical simulation of the development of density waves in a long pipeline and the dynamic system behavior". Terra et Aqua, No. 93, p. 11-23.
77. Miedema, S.A., Frijters, D., "The Mechanism of Kinematic Wedges at Large Cutting Angles - Velocity and Friction Measurements". 23rd WEDA Technical Conference & 35th TAMU Dredging Seminar, Chicago, USA, june 2003.
78. Tri, Nguyen Van, Miedema, S.A., Heijer, J. den, "Machine Manufacturing Technology". Lecture notes, Delft University of Technology, Cicat and Cantho University Vietnam, August 2003.
79. Miedema, S.A., "MHO5/6 Phase Two Mission Report". Report on a mission to Cantho University Vietnam October 2003. Delft University of Technology and CICAT, November 2003.
80. Zwanenburg, M., Holstein, J.D., Miedema, S.A., Vlasblom, W.J., "The Exploitation of Cockle Shells". CEDA Dredging Days 2003, Amsterdam, The Netherlands, November 2003.
81. Zhi, L., Miedema, S.A., Vlasblom, W.J., Verheul, C.H., "Modeling and Simulation of the Dynamic Behaviour of TSHD's Suction Pipe System by using Adams". CHIDA Dredging Days, Shanghai, China, november 2003.
http://www.dredgingengineering.com/dredging/media/LectureNotes/miedema/2003_dredging_days/cockle.pdf
82. Miedema, S.A., "The Existence of Kinematic Wedges at Large Cutting Angles". CHIDA Dredging Days, Shanghai, China, november 2003.
83. Miedema, S.A., Lu, Z., Matousek, V., "Numerical Simulation of the Development of Density Waves in a Long Pipeline and the Dynamic System Behaviour". Terra et Aqua 93, December 2003.
84. Miedema, S.A. & Frijters, D.D.J., "The wedge mechanism for cutting of water saturated sand at large cutting angles". WODCON XVII, September 2004, Hamburg Germany.
85. Verheul, O. & Vercruijsse, P.M. & Miedema, S.A., "The development of a concept for accurate and efficient dredging at great water depths". WODCON XVII, September 2004, Hamburg Germany.
86. Miedema, S.A., "THE CUTTING MECHANISMS OF WATER SATURATED SAND AT SMALL AND LARGE CUTTING ANGLES". International Conference on Coastal Infrastructure Development - Challenges in the 21st Century. HongKong, november 2004.
87. Ir. M. Zwanenburg , Dr. Ir. S.A. Miedema , Ir J.D. Holstein , Prof.ir. W.J.Vlasblom, "REDUCING THE DAMAGE TO THE SEA FLOOR WHEN DREDGING COCKLE SHELLS". WEDAXXIV & TAMU36, Orlando, Florida, USA, July 2004.
88. Verheul, O. & Vercruijsse, P.M. & Miedema, S.A., "A new concept for accurate and efficient dredging in deep water". Ports & Dredging, IHC, 2005, E163.
89. Miedema, S.A., "Scrapped?". Dredging & Port Construction, September 2005. 90. Miedema, S.A. & Vlasblom, W.J., " Bureaustudie Overvloeiverliezen". In opdracht
van Havenbedrijf Rotterdam, September 2005, Confidential. 91. He, J., Miedema, S.A. & Vlasblom, W.J., "FEM Analyses Of Cutting Of Anisotropic
Densely Compacted and Saturated Sand", WEDAXXV & TAMU37, New Orleans, USA, June 2005.
92. Miedema, S.A., "The Cutting of Water Saturated Sand, the FINAL Solution". WEDAXXV & TAMU37, New Orleans, USA, June 2005.
93. Miedema, S.A. & Massie, W., "Selfassesment MSc Offshore Engineering", Delft University of Technology, October 2005.
94. Miedema, S.A., "THE CUTTING OF WATER SATURATED SAND, THE SOLUTION". CEDA African Section: Dredging Days 2006 - Protection of the coastline, dredging sustainable development, Nov. 1-3, Tangiers, Morocco.
95. Miedema, S.A., "La solution de prélèvement par désagrégation du sable saturé en eau". CEDA African Section: Dredging Days 2006 - Protection of the coastline, dredging sustainable development, Nov. 1-3, Tangiers, Morocco.
96. Miedema, S.A. & Vlasblom, W.J., "THE CLOSING PROCESS OF CLAMSHELL DREDGES IN WATER-SATURATED SAND". CEDA African Section: Dredging Days 2006 - Protection of the coastline, dredging sustainable development, Nov. 1-3, Tangiers, Morocco.
97. Miedema, S.A. & Vlasblom, W.J., "Le processus de fermeture des dragues à benne preneuse en sable saturé". CEDA African Section: Dredging Days 2006 - Protection of the coastline, dredging sustainable development, Nov. 1-3, Tangiers, Morocco.
98. Miedema, S.A. "THE CUTTING OF WATER SATURATED SAND, THE SOLUTION". The 2nd China Dredging Association International Conference & Exhibition, themed 'Dredging and Sustainable Development' and in Guangzhou, China, May 17-18 2006.
99. Ma, Y, Ni, F. & Miedema, S.A., "Calculation of the Blade Cutting Force for small Cutting Angles based on MATLAB". The 2nd China Dredging Association
http://www.dredgingengineering.com/dredging/media/LectureNotes/miedema/2004_wodcon/paperfrijters.pdf
International Conference & Exhibition, themed 'Dredging and Sustainable Development' and in Guangzhou, China, May 17-18 2006.
100. ,"" (download). The 2nd China Dredging
Association International Conference & Exhibition, themed 'Dredging and Sustainable Development' and in Guangzhou, China, May 17-18 2006.
101. Miedema, S.A. , Kerkvliet, J., Strijbis, D., Jonkman, B., Hatert, M. v/d, "THE DIGGING AND HOLDING CAPACITY OF ANCHORS". WEDA XXVI AND TAMU 38, San Diego, California, June 25-28, 2006.
102. Schols, V., Klaver, Th., Pettitt, M., Ubuan, Chr., Miedema, S.A., Hemmes, K. & Vlasblom, W.J., "A FEASIBILITY STUDY ON THE APPLICATION OF FUEL CELLS IN OIL AND GAS SURFACE PRODUCTION FACILITIES". Proceedings of FUELCELL2006, The 4th International Conference on FUEL CELL SCIENCE, ENGINEERING and TECHNOLOGY, June 19-21, 2006, Irvine, CA.
103. Miedema, S.A., "Polytechnisch Zakboek 51ste druk, Hoofdstuk G: Werktuigbouwkunde", pG1-G88, Reed Business Information, ISBN-10: 90.6228.613.5, ISBN-13: 978.90.6228.613.3. Redactie: Fortuin, J.B., van Herwijnen, F., Leijendeckers, P.H.H., de Roeck, G. & Schwippert, G.A.
104. MA Ya-sheng, NI Fu-sheng, S.A. Miedema, "Mechanical Model of Water Saturated Sand Cutting at Blade Large Cutting Angles", Journal of Hohai University Changzhou, ISSN 1009-1130, CN 32-1591, 2006. 绞刀片大角度切削水饱和沙的力学模型, 马亚生[1] 倪福生[1] S.A.Miedema[2], 《河海大学常州分校学报》-2006年20卷3期 -59-61页
105. Miedema, S.A., Lager, G.H.G., Kerkvliet, J., “An Overview of Drag Embedded Anchor Holding Capacity for Dredging and Offshore Applications”. WODCON, Orlando, USA, 2007.
106. Miedema, S.A., Rhee, C. van, “A SENSITIVITY ANALYSIS ON THE EFFECTS OF DIMENSIONS AND GEOMETRY OF TRAILING SUCTION HOPPER DREDGES”. WODCON ORLANDO, USA, 2007.
107. Miedema, S.A., Bookreview: Useless arithmetic, why environmental scientists can't predict the future, by Orrin H. Pilkey & Linda Pilkey-Jarvis. Terra et Aqua 108, September 2007, IADC, The Hague, Netherlands.
108. Miedema, S.A., Bookreview: The rock manual: The use of rock in hydraulic engineering, by CIRIA, CUR, CETMEF. Terra et Aqua 110, March 2008, IADC, The Hague, Netherlands.
109. Miedema, S.A., "An Analytical Method To Determine Scour". WEDA XXVIII & Texas A&M 39. St. Louis, USA, June 8-11, 2008.
110. Miedema, S.A., "A Sensitivity Analysis Of The Production Of Clamshells". WEDA XXVIII & Texas A&M 39. St. Louis, USA, June 8-11, 2008.
111. Miedema, S.A., "An Analytical Approach To The Sedimentation Process In Trailing Suction Hopper Dredgers". Terra et Aqua 112, September 2008, IADC, The Hague, Netherlands.
112. Hofstra, C.F., & Rhee, C. van, & Miedema, S.A. & Talmon, A.M., "On The Particle Trajectories In Dredge Pump Impellers". 14th International Conference Transport & Sedimentation Of Solid Particles. June 23-27 2008, St. Petersburg, Russia.
113. Miedema, S.A., "A Sensitivity Analysis Of The Production Of Clamshells". WEDA Journal of Dredging Engineering, December 2008.
114. Miedema, S.A., "New Developments Of Cutting Theories With Respect To Dredging, The Cutting Of Clay And Rock". WEDA XXIX & Texas A&M 40. Phoenix Arizona, USA, June 14-17 2009.
115. Miedema, S.A., "A Sensitivity Analysis Of The Scaling Of TSHD's". WEDA XXIX & Texas A&M 40. Phoenix Arizona, USA, June 14-17 2009.
116. Liu, Z., Ni, F., Miedema, S.A., “Optimized design method for TSHD’s swell compensator, basing on modelling and simulation”. International Conference on Industrial Mechatronics and Automation, pp. 48-52. Chengdu, China, May 15-16, 2009.
117. Miedema, S.A., "The effect of the bed rise velocity on the sedimentation process in hopper dredges". Journal of Dredging Engineering, Vol. 10, No. 1 , 10-31, 2009.
118. Miedema, S.A., “New developments of cutting theories with respect to offshore applications, the cutting of sand, clay and rock”. ISOPE 2010, Beijing China, June 2010.
119. Miedema, S.A., “The influence of the strain rate on cutting processes”. ISOPE 2010, Beijing China, June 2010.
120. Ramsdell, R.C., Miedema, S.A., “Hydraulic transport of sand/shell mixtures”. WODCON XIX, Beijing China, September 2010.
121. Abdeli, M., Miedema, S.A., Schott, D., Alvarez Grima, M., “The application of discrete element modeling in dredging”. WODCON XIX, Beijing China, September 2010.
122. Hofstra, C.F., Miedema, S.A., Rhee, C. van, “Particle trajectories near impeller blades in centrifugal pumps. WODCON XIX, Beijing China, September 2010.
123. Miedema, S.A., “Constructing the Shields curve, a new theoretical approach and its applications”. WODCON XIX, Beijing China, September 2010.
124. Miedema, S.A., “The effect of the bed rise velocity on the sedimentation process in hopper dredges”. WODCON XIX, Beijing China, September 2010.
