AN ANALYTICAL METHOD OF PORE PRESSURE CALCULATIONS WHEN CUTTING WATER SATURATED SAND.

Dr.ir. S.A. Miedema1

Z. Yi2

ABSTRACT In the cutting of water-saturated sand, the phenomena of dilatation causes the development of pore vacuum pressures. These vacuum pressures result in an increase of the grain stresses, resulting in very high cutting forces. Until now the calculation of the pore vacuum pressure has been a matter of Finite Element Calculations. The Finite Element Calculations have resulted in dimensionless coefficient tables. To use these tables (as published by Miedema), one had to use interpolation or extrapolation methods. This is all very time consuming and it makes the use difficult and hard to understand. By using an electrical analogon for the pore vacuum pressures, almost the same results can be obtained by using the theory of parallel resistors. Only a few lines of programming code are required. The FEM calculations have been carried out again to get a correct reference. It appeared that the results of the FEM calculations have not changed much. The difference between the calculations carried out by Miedema [23] in the 80's and the calculations carried out by Yi [30] in 2000 is less then 1%. The results of the analytical method differ more, within 10% for the relevant cases, depending on the blade geometry, but this is still very good for a first estimate of the pore vacuum pressures. The paper will first show the state of the art Finite Element results and then the electrical analogon. The results will be compared. Keywords: Dredging, soil mechanics, cutting theories

INTRODUCTION

One of the strong non-linear effects in the equilibrium equations of motion for the determination of the cutter-suction and dredging-wheel dredger motions, is the interaction between the excavating element and the soil. A good description of the cutting process is essential for a reliable simulation of the ship motions, in order to be able to predict the usability and the design of sea-going dredging vessels.

Although calculation models for the determination of the cutting forces for dry sand were available for a long time (Hettiaratchi & Reece [3, 4, 5, 6, 7, 26], Hatamura & Chiiwa [2] etc.) it is only since the seventies and the eighties that the cutting process in saturated sand is extensively researched at the Delft Hydraulics in Delft (WL, CSB), at the Delft University of Technology and at the Mineral Technological Instituut (MTI, IHC). First the process is described, for a good understanding of the terminology used in the literature discussion.

1 Associate Professor, Delft University of Technology, Mechanical Engineering, Dredging Technology, Mekelweg 2, 2628 CD Delft, The Netherlands, Tel: +31-15-2788359, Fax: +31-15-2781397, s.a.miedema@wbmt.tudelft.nl. 2 MSc student, Delft University of Technology, Mechanical Engineering, Dredging Technology, Mekelweg 2, 2628 CD Delft, The Netherlands, Tel: +31-15-2786780, y.zhao@student.tudelft.nl. College of Mechanics & Electronics, Hohai University, Changzhou 213022, Jiangsu Province, China.

Figure 1: The cutting process modeled as a continuous process.

Miedema, S.A. & Zhao Yi, "An Analytical Method of Pore Pressure Calculations when Cutting Water Saturated Sand". Texas A&M 33nd Annual Dredging Seminar, June 2001, Houston, USA 2001.

Copyright: Dr.ir. S.A. Miedema

From literature it is known that, during the cutting process, the sand increases in volume (see figure 1). This increase in volume is accredited to dilatancy. This is the change of the pore volume as a result of shear in the sand package. This increase of the pore volume has to be filled with water. The flowing water experiences a certain resistance, which causes vacuum pressure in the pore water in the sand package. As a result the grain stresses increase and therefore the needed cutting forces. The speed of the increase of the pore volume in the dilatancy zone, the volume strain rate, is proportional to the cutting velocity. If the volume strain rate is high, there is a chance that the pore pressure reaches the saturated water vapor pressure and cavitation occurs. A further increasing volume strain rate will not be able to cause a further decrease of the pore pressure. This also implies that, with a further increasing cutting velocity, the cutting forces cannot increase as a result of the dilatancy properties of the sand. The cutting forces can, however, still increase with an increasing cutting velocity as a result of the inertia forces and the flow resistance.

The cutting process can be subdivided in 5 areas in relation with the cutting forces:

1. Very low cutting velocities, a quasi static cutting process. The cutting forces are determined by the gravitation, cohesion and adhesion.

2. The volume strain rate is high in relation to the permeability of the sand. The volume strain rate is however so small that inertia forces can be neglected. The cutting forces are dominated by the dilatancy properties of the sand.

3. A transition region, with local cavitation. With an increasing volume strain rate, the cavitation area will increase so that the cutting forces increase slightly as a result of dilatancy.

4. Cavitation occurs almost everywhere around and on the blade. The cutting forces do not increase anymore as a result of the dilatancy properties of the sand.

5. Very high cutting velocities. The inertia forces part in the total cutting forces can no longer be neglected but form a substantial part.

CUTTING THEORY, LITERATURE SURVEY

In the seventies extensive research is carried out on the forces that occur while cutting sand under water. A conclusive cutting theory has however not been published in this period. However qualitative relations have been derived by several researchers, with which the dependability of the cutting forces with the soil properties and the blade geometry are described (Joanknecht [9], van Os [24, 25]).

Afterwards it turned out that, in non-published reports for the confidential research program CSB, as indicated in the reference list of [12], Van Os had already developed the basic theory for the cutting of saturated packed sand. Ahead of the real publication, [12] is provided by the Delft Hydraulics Laboratory in August 1986. A process that has a lot of similarities with the cutting of sand as far as water pressure development is concerned, is the, with uniform velocity, forward moving breach. Meijer and van Os [13] 1976 and Meijer [14, 15] 1981/1985 have transformed the storage equation for the, with the breach, forward moving coordinate system.

Figure 2: An example of the pore pressure distribution around the blade.

Miedema, S.A. & Zhao Yi, "An Analytical Method of Pore Pressure Calculations when Cutting Water Saturated Sand". Texas A&M 33nd Annual Dredging Seminar, June 2001, Houston, USA 2001.

Copyright: Dr.ir. S.A. Miedema

t

e

k

g

x

e

k

vg

y

p

x

p wcw2

2

2

2

∂∂

⋅⋅ρ

∂∂

⋅⋅⋅ρ

=∂∂

+∂∂

(1)

In case of a stationary process, the second term on the right hand side is zero, resulting:

x

e

k

vg

y

p

x

p cw2

2

2

2

∂∂

⋅⋅⋅ρ

=∂∂

+∂∂

(2)

Van Os [24, 25] 1977 describes the basic principles of the cutting process, with special attention for the determination of the water vacuum pressures and the cavitation. Van Os uses the non-transformed storage equation for the determination of the water vacuum pressures.

t

ek

g

y

p

x

p w2

2

2

2

∂∂

⋅⋅ρ

=∂∂

+∂∂

(3)

Figure 3: The volume balance over the shear zone.

The average volume strain rate has to be substituted in the term ∂e/∂t on the right hand side. The average volume strain rate is the product of the average volume strain of the sand package and the cutting velocity and arises from the volume balance over the shear zone. Van Os gives a qualitative relation between the water vacuum pressures and the average volume strain rate:

kehv

::p ic ⋅⋅ (4)

Miedema, S.A. & Zhao Yi, "An Analytical Method of Pore Pressure Calculations when Cutting Water Saturated Sand". Texas A&M 33nd Annual Dredging Seminar, June 2001, Houston, USA 2001.

Copyright: Dr.ir. S.A. Miedema

The problem of the solution of the storage equation for the cutting of sand under water is a mixed boundary-value problem, for which the water vacuum pressures along the boundaries are known (hydrostatic). Joanknecht [8, 9] 1973 assumes that the cutting forces are determined by the vacuum pressure in the sand package. A distinction is made between the parts of the cutting force caused by the inertia forces, the vacuum pressure behind the blade and the soil mechanical properties of the sand. The influence of the geometrical parameters gives the following qualitative relation:

bhv::F 2icci ⋅⋅

(5)

The cutting force is proportional to the cutting velocity, the blade width and the square of the initial layer-thickness. A relation with the pore percentage and the permeability is also mentioned. A relation between the cutting force and these soil mechanical properties is however not given. It is observed that the cutting forces increase with an increasing blade angle. In the eighties research has led to more quantitative relations. In 1984 Van Leussen and Nieuwenhuis [11] discuss the soil mechanical aspects of the cutting process. The forces models of Miedema [20, 23] and Steeghs [28, 29] are published 1985/86, while the CSB (Combinatie Speurwerk Baggertechniek) model (van Leussen en van Os [12]), however developed in the early seventies at the Delft Hydraulics Laboratory (van Os [24, 25]), has been published in 1987. Brakel [1] 1982 derives a relation for the determination of the water vacuum pressures based upon, over each other rolling, round grains in the shear zone. The force part resulting from this is added to the model of Hettiaratchi and Reece [6]. Miedema [19] 1983 has combined the qualitative relations of Joanknecht [8, 9] and Van Os [24, 25] to the following relation:

m

2icw

cik

ebhvg::F ⋅⋅⋅⋅⋅ρ

(6)

With this basic equation calculation models are developed for a cutterhead and for the periodical moving cutterhead in the breach. The proportionality constants are determined empirically.

Figure 4: The flow of the pore water towards the shear zone.

Van Leussen and Nieuwenhuis [11] 1984 discuss the soil mechanical aspects of the cutting process. Important in the cutting process is the way shear takes place and the shape or angle of the shear plane, respectively shear zone. In literature no unambiguous image could be found. Cutting tests along a windowpane gave an image in which the shape of the shear plane was more in accordance with the so-called "stress characteristics" than with the so-called "zero-extension lines". Therefore, for the calculation of the cutting forces, the "stress characteristics method" is used

Miedema, S.A. & Zhao Yi, "An Analytical Method of Pore Pressure Calculations when Cutting Water Saturated Sand". Texas A&M 33nd Annual Dredging Seminar, June 2001, Houston, USA 2001.

Copyright: Dr.ir. S.A. Miedema

(Mohr-Coulomb failure criterion). For the calculation of the water vacuum pressures, however, the "zero-extension lines" are used, which are lines with a zero linear strain. A closer description has not been given for both calculations. Although the cutting process is considered as being two-dimensional, Van Leussen and Nieuwenhuis found, that the angle of internal friction, measured at low deformation rates in a triaxial apparatus, proved to be sufficient for dredging processes. Although the cutting process can be considered as a two-dimensional process and therefore it should be expected that the angle of internal friction has to be determined with a "plane deformation test". A sufficient explanation has not been found. Little is known about the value of the angle of friction between sand and steel. Van Leussen and Nieuwenhuis don't give an unambiguous method to determine this soil mechanical parameter. It is, however, remarked that at low cutting velocities (0.05 mm/s), the soil/steel angle of friction can have a statistical value which is 1.5 to 2 times larger than the dynamic soil/steel angle of friction. The influence of the initial density on the resulting angle of friction is not clearly present, because loose packed sand moves over the blade. The angles of friction measured on the blades are much larger than the angles of friction measured with an adhesion cell, while also a dependency with the blade angle is observed. With regard to the permeability of the sand, Van Leussen and Nieuwenhuis found that no large deviations of Darcy's law occur with the water flow through the pores. The found deviations are in general smaller than the accuracy with which the permeability can be determined in situ. The size of the area where ∂e/∂t from equation (5) is zero can be clarified by the figures published by Van Leussen and Nieuwenhuis. The basis is formed by a cutting process where the density of the sand is increased in a shear band with a certain width. The undisturbed sand has the initial density while the sand after passage of the shear band possesses a critical density. This critical density appeared to be in good accordance with the wet critical density of the used types of sand. This implies that outside the shear band the following equation is valid:

0y

p

x

p2

2

2

2

=∂∂

+∂∂

(7)

Values for the various densities are given for three types of sand. Differentiation of the residual density as a function of the blade angle is not given. A verification of the water pressure calculations is given for a 60° blade with a blade-height/layer-thickness ratio of 1.

Figure 5: The course mesh as applied in the pore vacuum pressure calculations.

Miedema, S.A. & Zhao Yi, "An Analytical Method of Pore Pressure Calculations when Cutting Water Saturated Sand". Texas A&M 33nd Annual Dredging Seminar, June 2001, Houston, USA 2001.

Copyright: Dr.ir. S.A. Miedema

Miedema [18, 19] 1984 gives a formulation for the determination of the water vacuum pressures. The deformation rate is determined by taking the volume balance over the shear zone, as Van Os [24, 25] did. The deformation rate is modeled as a boundary condition in the shear zone , while the shear zone is modeled as a straight line instead of a shear band as with Van Os [24, 25] and Van Leussen and Nieuwenhuis [11]. The influence of the water depth on the cutting forces is clarified, as is shown in figure 3. Steeghs [28] 1985 developed a theory for the determination of the volume strain rate, based upon a cyclic deformation of the sand in a shear band. This implies that not an average value is taken for the volume strain rate but a cyclic, with time varying, value, based upon the dilatancy angle theory. Miedema [20, 21] 1985 derives equations for the determination of the water under-pressures and the cutting forces, based upon [16, 18, 19]. The water vacuum pressures are determined with a finite element method. Explained are the influence of the permeability of the disturbed and undisturbed sand and the determination of the shear angle. The derived theory is verified with model tests. On basis of this research nmax is chosen for the residual pore percentage instead of the wet critical density.

Figure 6: The fine mesh as applied in the pore vacuum pressure calculations.

Steeghs [28, 29] 1985/1986 derives equations for the determination of the water vacuum pressures according an analytical approximation method. With this approximation method the water vacuum pressures are determined with a modification of equation (4) derived by Van Os [24, 25] and the storage equation (7). Explained is how cutting forces can be determined with the force equilibrium on the cut layer. Also included are the gravity force, the inertia forces and the vacuum pressure behind the blade. For the last influence factor no formulation is given. Discussed is the determination of the shear angle. Some examples of the cutting forces are given as a function of the cutting velocity, the water depth and the sub-pressure behind the blade. A verification of this theory is not given. Miedema [22] 1986 develops a calculation model for the determination of the cutting forces on a dredging-wheel based upon [20, 21]. Also nomograms are published with which the cutting forces and the shear angle can be determined in a simple way. Explained is the determination of the weighted average permeability from the permeability of the disturbed and undisturbed sand. Based upon the calculations it is concluded that the average permeability forms a good estimation. Miedema [23] 1986 extends the theory with adhesion, cohesion, inertia forces, gravity, and vacuum pressure behind the blade. The method for the calculation of the coefficients for the determination of a weighed average permeability are discussed. It is concluded that the additions to the theory lead to a better correlation with the tests results. Van Os and Van Leussen [12] 1986 summarize the publications of Van Os [24, 25] and of Van Leussen and Nieuwenhuis [11] and give a formulation of the theory developed in the early seventies at the Delft Hydraulics

Miedema, S.A. & Zhao Yi, "An Analytical Method of Pore Pressure Calculations when Cutting Water Saturated Sand". Texas A&M 33nd Annual Dredging Seminar, June 2001, Houston, USA 2001.

Copyright: Dr.ir. S.A. Miedema

Laboratory. Discussed are the water pressures calculation, cavitation, the weighed average permeability, the angle of internal friction, the soil/steel angle of friction, the permeability, the volume strain and the cutting forces. Verification is given of a water pressures calculation and the cutting forces. The water vacuum pressures are determined with equation (4) derived by Van Os [24, 25]. The water pore pressure calculation is performed with the finite difference method, in which the height of the shear band is equal to the mesh width of the grid. The size of this mesh width is considered to be arbitrary. From an example, however, it can be seen that the shear band has a width of 13% of the layer-thickness. Discussed is the determination of a weighed average permeability. The forces are determined with Coulomb's method.

DETERMINATION OF THE PORE UNDER-PRESSURE AROUND THE BLADE

The cutting process can be modeled as a two-dimensional process, in which a straight blade cuts a small layer of sand (figure 1). The sand is deformed in the shear zone, also called deformation zone or dilatancy zone. During this deformation the volume of the sand changes as a result of the shear stresses in the shear zone. In soil mechanics this phenomenon is called dilatancy. In densely packed sand the pore volume is increased as a result of the shear stresses in the deformation zone. This increase in the pore volume is thought to be concentrated in the deformation zone, with the deformation zone modeled as a straight line (line sink). Water has to flow to the deformation zone to fill up the increase of the pore volume in this zone. As a result of this water flow the grain stresses increase and the water pressures decrease. Therefore there are water vacuum pressures. This implies that the forces necessary for cutting densely packed sand under water will be determined for an important part by the dilatancy properties of the sand. At low cutting velocities these cutting forces are also determined by the gravity, the cohesion and the adhesion for as far as these last two soil mechanical parameters are present in the sand. Is the cutting carried out at high velocities, than the inertia forces will have an important part in the total cutting forces.

Figure 7: The distribution of the pore vacuum pressure in the sand around the blade.

If the cutting process is assumed to be stationary, the water flow through the pores of the sand can be described in a blade motions related coordinate system. The determination of the water vacuum pressures in the sand around the blade is then limited to a mixed boundary conditions problem. The potential theory can be used to solve this problem. For the determination of the water vacuum pressures it is necessary to have a proper formulation of the boundary condition in the shear zone. Miedema [19] 1984 derived the basic equation for this boundary condition. In 1985 [20, 21] and 1986 [23] a more extensive derivation is published. If it is assumed that no deformations take place outside the deformation zone, then:

Miedema, S.A. & Zhao Yi, "An Analytical Method of Pore Pressure Calculations when Cutting Water Saturated Sand". Texas A&M 33nd Annual Dredging Seminar, June 2001, Houston, USA 2001.

Copyright: Dr.ir. S.A. Miedema

0y

p

x

p2

2

2

2

=∂∂

+∂∂

(8)

applies for the sand package around the blade. The boundary condition is in fact a specific flow rate (fig. 3) that can be determined with the following hypothesis. For a sand element in the deformation zone, the increase in the pore volume per unit of blade length, is:

( )β⋅∆⋅∆⋅=∆⋅∆⋅=∆⋅=∆ sinlxehxeAeV i (9)

In which:

max

imax

n1nn

e−−

−−== (10)

For the residual pore percentage is chosen for nmax on the basis of the ability to explain the water vacuum pressures, measured in the laboratory tests.

Figure 8: The distribution of the pore vacuum pressure in the sand around the blade.

The volume flow rate flowing to the sand element, is equal to:

( ) ( )β⋅∆⋅⋅=β⋅∆⋅∂∂

⋅=∂∂

=∆ sinlvesinltx

etV

Q c (11)

With the aid of Darcy's law the next differential equation can be derived for the specific flow rate. perpendicular to the deformation zone:

Miedema, S.A. & Zhao Yi, "An Analytical Method of Pore Pressure Calculations when Cutting Water Saturated Sand". Texas A&M 33nd Annual Dredging Seminar, June 2001, Houston, USA 2001.

Copyright: Dr.ir. S.A. Miedema

( )β⋅⋅=∂∂

⋅⋅ρ+∂∂

⋅⋅ρ=+=∂∂

= sinvenp

g

k

np

g

kqq

lQ

q c

2w

max

1w

i21

(12)

The partial derivative ∂p/∂n is the derivative of the water vacuum pressures perpendicular on the boundary of the area, in which the water vacuum pressures are calculated (in this case the deformation zone). The boundary conditions on the other boundaries of this area are indicated in figure 3. A hydrostatic pressure distribution is assumed on the boundaries between sand and water. This pressure distribution equals zero in the calculation of the water vacuum pressures, if the height difference over the blade is neglected. The boundaries that form the edges in the sand package are assumed to be impermeable. Making equation (12) dimensionless is similar to that of the breach equation of Meijer and Van Os [13]. In the breach problem the length dimensions are normalized by dividing them by the breach height, while in the cutting of sand they are normalized by dividing them by the cut layer thickness. Equation (12) in normalized format:

( )max

icw

21max

i

ksinhevg

'np

'np

kk β⋅⋅⋅⋅⋅ρ

=∂∂

+∂∂

⋅ (13)

With: n' = n/hi

Figure 9: The pore vacuum pressure distribution on the blade and on the shear zone.

This equation is made dimensionless with:

maxicw

'

k/hevg'n

p

np

⋅⋅⋅⋅ρ∂∂

=∂∂

(14)

The accent indicates that a certain variable or partial derivative is dimensionless. The next dimensionless equation is now valid as a boundary condition in the deformation zone:

( )β=∂∂

+∂∂

⋅ sinnp

np

kk '

21

'

max

i

(15)

Miedema, S.A. & Zhao Yi, "An Analytical Method of Pore Pressure Calculations when Cutting Water Saturated Sand". Texas A&M 33nd Annual Dredging Seminar, June 2001, Houston, USA 2001.

Copyright: Dr.ir. S.A. Miedema

The storage equation also has to be made dimensionless, which results in the next equation :

0y

p

x

p '

2

2'

2

2

=∂∂

+∂∂

(16)

Because the right hand side of this equation equals zero, it is similar to equation (8) The water vacuum pressures distribution in the sand package can now be determined using the storage equation and the boundary conditions. Because the calculation of the water vacuum pressures is dimensionless the next transformation has to be performed to determine the real water vacuum pressures. The real water vacuum pressures can be determined by integrating the derivative of the water vacuum pressures in the direction of a flow line, along a flow line, so:

dssp

p '

'

'scalc ⋅∫ ∂

∂=

On a streamline s' (17)

This is illustrated in figure 4. Using equation (14) this can be written as:

dssp

khevg

dssp

p ''

's max

icw

sreal ⋅

∂∂

∫ ⋅⋅⋅⋅⋅ρ

=⋅∫ ∂∂

=

(18)

With: s' = s/hi This gives the following relation between the really emerging water under-pressures and the calculated water under-pressures:

calcmax

icwreal p

khevg

p ⋅⋅⋅⋅⋅ρ

= (19)

In table 1 the calculated water vacuum pressures are listed in relation with the blade angle, the shear angle, the blade-height/layer-thickness ratio and the ratio between the permeability of the disturbed and undisturbed sand. Using equation (19) or equation (14) also the water vacuum pressures, measured in the cutting tests, can be made dimensionless. To be independent of the ratio between the initial permeability ki and the maximum permeability kmax, kmax has to be replaced with the weighed average permeability km before making the measured water vacuum pressures dimensionless.

NUMERICAL WATER PORE PRESSURE CALCULATIONS

The water vacuum pressures in the sand package on and around the blade are numerically determined using the finite element method. A standard program package is used (Segal [27]). With the in this package, available "subroutines" a program is written, with which water vacuum pressures can be calculated and be output graphically and numerically. The solution of such a calculation is however not only dependent on the physical model of the problem, but also on the next points:

1. The size of the area in which the calculation takes place. 2. The size and distribution of the elements 3. The boundary conditions

The choices for these three points have to be evaluated with the problem that has to be solved in mind. These calculations are about the values and distribution of the water under-pressures in the shear zone and on the blade. A variation of the values for point 1 and 2 may therefore not influence this part of the solution. This is achieved by on

Miedema, S.A. & Zhao Yi, "An Analytical Method of Pore Pressure Calculations when Cutting Water Saturated Sand". Texas A&M 33nd Annual Dredging Seminar, June 2001, Houston, USA 2001.

Copyright: Dr.ir. S.A. Miedema

the one hand increasing the area in which the calculations take place in steps and on the other hand by decreasing the element size until the variation in the solution was less than 1% (see figures 5 and 6). The distribution of the elements is chosen such that a finer mesh is present around the blade tip, the shear zone and on the blade, also because of the blade tip problem. A number of boundary conditions follow from the physical model of the cutting process, these are: The boundary condition in the shear zone. This is described by equation (15). The boundary condition along the free sand surface. The hydrostatic pressure, at which the process takes place, can be chosen, when neglecting the dimensions of the blade and the layer in relation to the hydrostatic pressure head. Because these calculations are meant to obtain the difference between the water vacuum pressures and the hydrostatic pressure it is valid to take a zero pressure as the boundary condition. The boundary conditions along the boundaries of the area where the calculation takes place that are located in the sand package are not determined by the physical process. For this boundary condition there is a choice between:

1. A hydrostatic pressure along the boundary. 2. A boundary as an impermeable wall. 3. A combination of a known pressure and a known specific flow rate.

None of these choices complies with the real process. Water from outside the calculation area will flow through the boundary. This also implies, however, that the pressure along this boundary is not hydrostatic. If, however, the boundary is chosen with enough distance from the real cutting process the boundary condition may not have an influence on the solution. The impermeable wall is chosen although this choice is arbitrary. Figure 3 gives an impression of the size of the area and the boundary conditions, while figures 5 and 6 show the element mesh. Figures 2, 7 and 8 show the two-dimensional distribution of the water vacuum pressures, while figure 9 shows the vacuum pressure distribution on the blade and in the shear zone.

THE BLADE TIP PROBLEM

During the physical modeling of the cutting process it has always been assumed that the blade tip is sharp. In other words, that in the numerical calculation, from the blade tip, a hydrostatic pressure can be introduced as the boundary condition along the free sand surface behind the blade. In practice this is never valid, because of the following reasons:

1. The blade tip always has a certain rounding, so that the blade tip can never be considered really sharp. 2. Trough wear of the blade a flat section develops behind the blade tip, which runs against the sand surface

(clearance angle ≤ zero) 3. If there is also dilatancy in the sand underneath the blade tip it is possible that the sand runs against the

flank after the blade has passed. 4. There will be a certain vacuum pressure behind the blade as a result of the blade speed and the cutting

process. A combination of these factors determines the distribution of the water vacuum pressures, especially around the blade tip. The first three factors can be accounted for in the numerical calculation as an extra boundary condition behind the blade tip. Along the free sand surface behind the blade tip an impenetrable line element is put in, in the calculation. The length of this line element is varied with 0.0· hi , 0.1· hi and 0.2· hi. It showed from these calculations that especially the water vacuum pressures on the blade are strongly determined by the choice of this boundary condition as indicated in figure 10. Table 1 shows the dimensionless pore vacuum pressures.

Figure 10: The average pore vacuum pressure on the blade and in the shear zone as a function of the length of the flat wear zone w.

Miedema, S.A. & Zhao Yi, "An Analytical Method of Pore Pressure Calculations when Cutting Water Saturated Sand". Texas A&M 33nd Annual Dredging Seminar, June 2001, Houston, USA 2001.

Copyright: Dr.ir. S.A. Miedema

It is hard to estimate to what degree the influence of the vacuum pressure behind the blade on the water vacuum pressures around the blade tip can be taken into account with these extra boundary condition. Since there is no clear formulation for the vacuum pressure behind the blade available, it will be assumed that the extra boundary condition at the blade tip describes this influence. The laboratory research of Miedema [23] has made this more evident.

Table 1: The dimensionless pore pressures p1m in the shearzone (s) and p2m on the blade surface (b) as a function of the blade angle αα, de shear angle ββ, the ratio between the blade height hb and the layer thickness hi and the ratio between the permeability of the situ sand ki and the permeability of the sand cut kmax, with a wear zone behind the edge of the blade of 0.2· hi.

hb/hi ki/kmax=1 ki/kmax=0.25

ββ =30°° 37.5°° 45°° 30°° 37.5°° 45°°

1 (s) 0.156 0.168 0.177 0.235 0.262 0.286

2 (s) 0.157 0.168 0.177 0.236 0.262 0.286

3 (s) 0.158 0.168 0.177 0.237 0.262 0.286

1 (b) 0.031 0.033 0.035 0.054 0.059 0.063

2 (b) 0.016 0.017 0.018 0.028 0.030 0.032

αα =15°°

3 (b) 0.011 0.011 0.012 0.019 0.020 0.021

ββ =25°° 30°° 35°° 25°° 30°° 35°°

1 (s) 0.178 0.186 0.193 0.274 0.291 0.308

2 (s) 0.179 0.187 0.193 0.276 0.294 0.310

3 (s) 0.179 0.187 0.193 0.277 0.294 0.310

1 (b) 0.073 0.076 0.078 0.126 0.133 0.139

2 (b) 0.049 0.049 0.049 0.084 0.085 0.086

αα =30°°

3 (b) 0.034 0.034 0.033 0.059 0.059 0.059

ββ =20°° 25°° 30°° 20°° 25°° 30°°

1 (s) 0.185 0.193 0.200 0.289 0.306 0.325

2 (s) 0.190 0.198 0.204 0.304 0.322 0.339

3 (s) 0.192 0.200 0.205 0.308 0.325 0.340

1 (b) 0.091 0.097 0.104 0.161 0.174 0.187

2 (b) 0.081 0.082 0.083 0.146 0.148 0.151

αα =45°°

3 (b) 0.067 0.065 0.063 0.120 0.116 0.114

ββ =15°° 20°° 25°° 15°° 20°° 25°°

1 (s) 0.182 0.192 0.200 0.278 0.303 0.324

2 (s) 0.195 0.204 0.211 0.314 0.339 0.359

3 (s) 0.199 0.208 0.214 0.327 0.350 0.368

1 (b) 0.091 0.103 0.112 0.158 0.184 0.205

2 (b) 0.100 0.106 0.109 0.182 0.196 0.204

αα =60°°

3 (b) 0.094 0.095 0.093 0.174 0.176 0.174

Miedema, S.A. & Zhao Yi, "An Analytical Method of Pore Pressure Calculations when Cutting Water Saturated Sand". Texas A&M 33nd Annual Dredging Seminar, June 2001, Houston, USA 2001.

Copyright: Dr.ir. S.A. Miedema

ANALYTICAL WATER PORE PRESSURE CALCULATIONS

As is shown in figure 4, the water can flow from 4 directions to the shear zone where the dilatancy takes place. Two of those directions go through the sand which has not yet been deformed and thus have a permeability of ki , while the other two directions go through the deformed sand and thus have a permeability of kmax. Figure 2 shows that the flow lines in 3 of the 4 directions have a more or less circular shape, while the flow lines above the blade have the character of a straight line. If a point on the shear zone is considered, then the water will flow to that point along the 4 flowlines as mentioned above. Along each flow line, the water will encounter a certain resistance. One can reason that this resistance is proportional to the length of the flow line and reversibly proportional to the permeability of the sand, the flow line passes. Figure 11 shows a point on the shear zone and it shows the 4 flow lines. The length of the flow lines can be determined with the equations 20, 21, 22 and 23. The variable "Lmax" in these equations is the length of the shear zone, which is equal to hi/sin(β), while the variable "L" starts at the free surface with a value zero and ends at the blade tip with a value "Lmax".

Figure 11: The flow lines used in the analytical method.

β−α−π=θ

α+θ⋅−+π

⋅θ⋅−=

2:with

)sin(h)sin()LL(2

)cos()LL(s

1

b111 maxmax

(20)

β+α=θ

θ⋅=

2

22

:with

Ls

(21)

β−π=θ

θ⋅=

3

33

:with

Ls

(22)

Miedema, S.A. & Zhao Yi, "An Analytical Method of Pore Pressure Calculations when Cutting Water Saturated Sand". Texas A&M 33nd Annual Dredging Seminar, June 2001, Houston, USA 2001.

Copyright: Dr.ir. S.A. Miedema

β+π=θ

π⋅⋅+θ⋅−=

4

i44

:with

h1.0)LL(s max

(23)

The total resistance on the flow lines can be determined by dividing the length of a flow line by the permeability of the flow line. The equations 24, 25, 26 and 27 give the resistance of each flow line.

ksR

max

11= (24)

ksR

max

22= (25)

ksR

i

33= (26)

ksR

i

44 = (27)

Since the 4 flow lines can be considered as 4 parallel resistors, the total resulting resistance can be determined according to the rules for parallel resistors. Equation 28 shows this rule.

R1

R1

R1

R1

R1

4321t+++= (28)

The resistance Rt in fact replaces the hi/kmax part of the equations 13, 14, 18 and 19, resulting in equation 29 for the determination of the pore vacuum pressure of the point on the shear zone.

R)sin(evgp tcw ⋅β⋅⋅⋅⋅ρ=∆ (29)

The average pore vacuum pressure on the shear zone can be determined by summation or integration of the pore vacuum pressure of each point on the shear zone. Equation 30 gives the average pore vacuum pressure by summation.

nL

il:withpp i

n

0iim1 n

1⋅=∑∆=

=

(30)

The determination of the average pore vacuum pressure on the blade cannot be carried out by integration or summation, because the calculation only gives the pore vacuum pressure at the tip (edge) of the blade. It is known that the pore vacuum pressure at the top of the blade equals zero, because the sand at that point is in direct contact with the surrounding water. If the pore vacuum pressure distribution on the blade is considered linear, then the average pore vacuum pressure equals 50% of the pore vacuum pressure at the blade edge.

f2p

p nm2 ⋅

∆=

(31)

However figure 9 shows (left graph) that this distribution is not linear. Going from the tip (edge) of the blade to the top of the blade, first the pore vacuum pressure increases until it reaches a maximum and then it decreases (non-linear) until it reaches zero at the top of the blade. In this graph, the top of the blade is left and the tip of the blade is right. The graph on the right side of figure 9 shows the pore vacuum pressure on the shear zone. In this graph, the tip

Miedema, S.A. & Zhao Yi, "An Analytical Method of Pore Pressure Calculations when Cutting Water Saturated Sand". Texas A&M 33nd Annual Dredging Seminar, June 2001, Houston, USA 2001.

Copyright: Dr.ir. S.A. Miedema

of the blade is on the left side, while the right side is the point where the shear zone reaches the free water surface. Thus the pore vacuum pressure equals zero at the free water surface (most right point of the graph). Because the distribution of the pore vacuum pressure is non-linear, a shape factor has to be used. From the FEM calculations of Miedema [23] and Yi [30] it is known, dat de shape of the pore vacuum pressure distribution on the blade depends strongly on the ratio of the length of the shear zone and the length of the blade, and on the length of the flat wear zone (as shown in figure 10). A high ratio should result in a shape factor higher then 2, while a low ratio should result in a factor smaller then 0.5. Equation 32 gives the ratio in a modified form. The value of the power has been determined by trial and error.

)sin()sin()sin(

hh

fb

i

2.12/

βα⋅β+α

⋅

=

α⋅−π

(32)

Appendix A shows the source code of a Visual Basic subrountine, calculating the dimensionless pore vacuum pressures similar to table 1 (from the FEM calculations). The subroutine also calculates the cutting forces according to Miedema [23]. The difference between table 1 and this analytical method is less then 10%.

Table 2: A comparison between the numerical and analytical calculated dimensionless pore vacuum pressures.

Ki/kmax=0.25 p1m (table 1) p2m (table 1) p1m (analytical) p2m (analytical) α=30°, β=30°, hb/hi=2 0.294 0.085 0.333 0.072 α=45°, β=25°, hb/hi=2 0.322 0.148 0.339 0.140 α=60°, β=20°, hb/hi=2 0.339 0.196 0.338 0.196

CONCLUSIONS AND RECOMMENDATIONS

In the past decades many research has been carried out into the different cutting processes. The more fundamental the research, the less the theories can be applied in practice. The analytical method as described in this paper, gives a method to use the basics of the sand cutting theory in a very practical and pragmatic way. One has to consider that usually the accuracy of the output of a complex calculation is determined by the accuracy of the input of the calculation, in this case the soil mechanical parameters. Usually the accuracy of these parameters is not very accurate and in many cases not available at all. The accuracy of less then 10% of the analytical method described in this paper is small with regard to the accuracy of the input. This does not mean however that the accuracy is not important, but this method can be applied for a quick first estimate. By introducing some shape factors to the shape of the streamlines, the accuracy of the analytical model can be improved. Figure 4 shows the more or less circular shape of the streamlines. But more or less is not exactly, so a shape factor would improve the accuracy.

REFERENCES

1

Brakel, J.D., "Mathematisch model voor de krachten op een roterende snijkop van een in zeegang werkende snijkopzuiger". Sco/80/96. T.H. Delft 1981.

2

Hatamura, Y. and Chijiiwa, K., "Analyses of the mechanism of soil cutting". 1st report, Bulletin of the JSME, vol. 18, no. 120, June 1975. 2st report, Bulletin of the JSME, vol. 19, no. 131, May 1976. 3st report, Bulletin of the JSME, vol. 19, no. 139, Nov. 1976. 4st report, Bulletin of the JSME, vol. 20, no. 139, January 1977. 5st report, Bulletin of the JSME, vol. 20, no. 141, March 1977.

3

Hettiaratchi, D.R.P. & Witney, B.D. & Reece, A.R., "The calculation of passive pressure in two dimensional soil failure". Journal Agric. Engng. Res. 11 (2), pp. 89-107, 1966.

4

Hettiaratchi, D.R.P. and Reece, A.R., "Symmetrical three-dimensional Soil Failure". J. Terramech. 1967, 4 (3) pp. 45-67.

5 Hettiaratchi, D.R.P., "The mechanics of soil cultivation". AES, paper No. 3/245/C/28, 1967.

Miedema, S.A. & Zhao Yi, "An Analytical Method of Pore Pressure Calculations when Cutting Water Saturated Sand". Texas A&M 33nd Annual Dredging Seminar, June 2001, Houston, USA 2001.

Copyright: Dr.ir. S.A. Miedema

6

Hettiaratchi, D.R.P. & Reece, A.R., "The calculation of passive soil resistance". Geotechnique 24, No. 3, pp. 289-310, 1974.

7

Hettiaratchi, D.R.P. and Reece, A.R., "Boundary Wedges in Two Dimensional Passive Soil Failure". Geotechnique 25,No 2,pp. 197-220, 1975.

8 Joanknecht, L.F.W., "Mechanisch graafonderzoek onder water". T.H. Delft, Febr. 1973. 9 Joanknecht, L.W.F., "Cutting Forces in Submerged Soils". T.H.Delft, 1974, The Netherlands. 10

Koning, J de & Miedema, S.A. & Zwartbol, A., "Soil/Cutterhead Interaction under Wave Conditions". Proc. WODCON X, Singapore, 1983.

11

Leussen, W. van & Nieuwenhuis J.D., "Soil Mechanics Aspects of Dredging". Geotechnique 34 No.3, pp. 359-381.

12

Leussen, W. van & Os, A.G. van, "Basic Research On Cutting Forces In Saturated Sand". Paper submitted for publication in proceedings ASCE. Delft Hydraulics Laboratory, Delft July 1986 (beschikbaar 28 Augustus 1986).

13

Meijer, K.L. & Os, A.G. van, "Pore pressures near moving underwater slope". Geotech. Engng. Div. ASCE 102, No. GT4, pp. 361-372

14

Meijer, K.L., "Berekening van spanningen en deformaties in verzadigde grond". Rapport R 914, deel 1, Waterloopkundig Laboratorium, 1981.

15

Meijer, K.L., "Computation of stresses and strains in saturated soil". Proefschrift T.H. Delft 1985.

16

Miedema, S.A., "De modellering van de grondreacties op een snijkop en het operationeel maken van het computerprogramma DREDMO. CO/82/125, T.H.Delft 1982.

17

Miedema, S.A., "De interactie tussen snijkop en grond in zeegang". Proc. Baggerdag 19/11/1982, T.H. Delft, 1982.

18

Miedema, S.A., "Mathematische modelvorming t.a.v. een snijkopzuiger in zeegang". T.H. Delft 1984. (Kivi September 1984), The Netherlands.

19

Miedema, S.A., "The cutting of densely compacted sand under water". Terra et Aqua No. 28, October 1984 pp. 4-10.

20

Miedema, S.A., "Mathematical Modelling of the Cutting of Densely Compacted Sand Under Water". Dredging & Port Construction, July 1985, pp. 22-26.

21

Miedema, S.A., "Derivation of the Differential Equation for Sand Pore Pressures". Dredging & Port Construction, September 1985, pp. 35.

22

Miedema, S.A., "The Application of a Cutting Theory on a Dredging Wheel". Proc. WODCON XI, Brighton 1986.

23

Miedema, S.A., "Calculation of the Cutting Forces when Cutting Water Saturated Sand, 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

Os, A.G. van, "Behaviour of Soil when Excavated Underwater". International Course Modern Dredging. June 1977, The Hague, The Netherlands.

25

Os, A.G. van, "Snelle deformatie van korrelvormig materiaal onder water". pt-p 31 (1976) nr.12, pp. 735-741. pt-b 32 (1977) nr. 8, pp. 461-467.

26

Reece, A.R., "The Fundamental Equation Of Earth Moving Machinery". Proc. Symp. Earth Moving Machinery, Inst. of Mech. Eng. London 1965.

27

Segal, G., "Sepra Analysis, Programmers Guide, Standard Problems and Users Manual". Ingenieursbureau Sepra, Leidschendam, The Netherlands 2001.

28

Steeghs, H., "Snijden van zand onder water (I & II)". Ports & Dredging No. 121, June 1985. Ports & Dredging No. 123, November 1985.

29

Steeghs, H., "Snijden van zand onder water; een theoretisch model". Rapport: GR 37-IIB * MTI-Holland, Kinderdijk, 1986.

30 Yi, Z., "The FEM calculation of pore water pressure in sand cutting process by SEPRAN". Report number is: 2001.BT.5455. 1st MSc assignment, Delft University of Technology, Chair of Dredging Technology. Delft, 2000.

Miedema, S.A. & Zhao Yi, "An Analytical Method of Pore Pressure Calculations when Cutting Water Saturated Sand". Texas A&M 33nd Annual Dredging Seminar, June 2001, Houston, USA 2001.

Copyright: Dr.ir. S.A. Miedema

LIST OF SYMBOLS USED A surface m² b width of the blade of blade element m e volume strain % Fci cutting force (general) kN g gravitation acceleration m/s² hi initial layer thickness m k permeability m/s ki initial permeability m/s kmax maximum permeability m/s km effective permeability m/s l length of the shear zone m n normal on an edge m ni initial pore percentage % nmax maximum pore percentage % p pressure (pore pressure) kPa patm atmospheric pressure kPa pcalc calculated dimensionless pressure (pore pressure) - pdamp saturated vapor pressure (12 cm water column) kPa preal real acting pressure (pore pressure) kPa p1m average pore pressure in the shear zone - p2m average pore pressure on the blade - q, q1 ,q2 specific flow rate m/s Q flow rate per unit blade width m²/s s length of a flow line m s measure for the layer thickness m t time s ∆t time interval s vc cutting velocity perpendicular on the blade edge m/s V volume increase per unit of blade width m² x coordinate m y coordinate m z coordinate m z water depth m α blade angle rad β shear angle rad ϕ angle of internal friction rad δ soil/steel angle of friction rad ρw water density ton/m³ APPENDIX A: The Visual Basic Subroutine Sub Pressure(Fh, Fv, P1m, P2m, Factor) Dim N As Integer, I As Integer Dim Lmax As Single, L As Single, StepL As Single Dim P As Single, DPMax As Single, DP As Single, DP0 As Single, P0 As Single Dim Flag As Boolean, Argument As Single Dim S1 As Single, S2 As Single, S3 As Single, S4 As Single Dim R1 As Single, R2 As Single, R3 As Single, R4 As Single, Rt As Single Dim W1 As Single, W2 As Single, K2 As Single Dim CoefNC As Single, CoefC As Single Dim C1 As Single, C2 As Single, D1 As Single, D2 As Single Dim Teta1 As Single, Teta2 As Single, Teta3 As Single, Teta4 As Single Teta1 = Pi / 2 - Alpha - Beta Teta2 = Alpha + Beta

Miedema, S.A. & Zhao Yi, "An Analytical Method of Pore Pressure Calculations when Cutting Water Saturated Sand". Texas A&M 33nd Annual Dredging Seminar, June 2001, Houston, USA 2001.

Copyright: Dr.ir. S.A. Miedema

Teta3 = Pi - Beta Teta4 = Pi + Beta N = 100 Lmax = Hi / Sin(Beta) StepL = Lmax / N P = 0 DPMax = RhoW * G * (Z + 10) Flag = False For I = 0 To N L = I * StepL + 0.0000000001 S1 = (Lmax - L) * Cos(Teta1) * Pi / 2 + (Lmax - L) * Sin(Teta1) + Hb / Sin(Alpha) S2 = L * Teta2 S3 = L * Teta3 S4 = (Lmax - L) * Teta4 + 0.1 * Hi * Pi R1 = S1 / Kmax R2 = S2 / Kmax R3 = S3 / Ki R4 = S4 / Ki Rt = 1 / (1 / R1 + 1 / R2 + 1 / R3 + 1 / R4) DP = RhoW * G * Vc * E * Sin(Beta) * Rt If I = N Then DP0 = DP P0 = P0 + DP If DP > DPMax Then DP = DPMax Flag = True End If P = P + DP Next I P1m = (P - DP / 2) / N P0 = (P0 - DP0 / 2) / N Factor = (Hi / Hb) ^ (Pi / 2 - Alpha * 1.2) * Sin(Alpha + Beta) * Sin(Alpha) / Sin(Beta) / 2 If Flag Then Argument = -2 * Factor * (P0 - P1m) / P1m Factor = Factor * Exp(Argument) + (1 - Exp(Argument)) End If P2m = DP * Factor If P2m > DPMax Then P2m = DPMax W1 = P1m * Hi * B / Sin(Beta) W2 = P2m * Hb * B / Sin(Alpha) K2 = (W1 * Sin(Phi) + W2 * Sin(Alpha + Beta + Phi)) / Sin(Alpha + Beta + Phi + Delta) Fh = K2 * Sin(Alpha + Delta) - W2 * Sin(Alpha) Fv = K2 * Cos(Alpha + Delta) - W2 * Cos(Alpha) P1m = P1m * Kmax / (RhoW * G * Vc * E * Hi) P2m = P2m * Kmax / (RhoW * G * Vc * E * Hi) CoefC = RhoW * G * (Z + 10) * Hi * B D1 = Fh / CoefC D2 = Fv / CoefC CoefNC = (RhoW * G * Vc * E * Hi ^ 2 * B) / ((Ki + Kmax) / 2) C1 = Fh / CoefNC C2 = Fv / CoefNC End Sub

Miedema, S.A. & Zhao Yi, "An Analytical Method of Pore Pressure Calculations when Cutting Water Saturated Sand". Texas A&M 33nd Annual Dredging Seminar, June 2001, Houston, USA 2001.

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.

Miedema, S.A. & Zhao Yi, "An Analytical Method of Pore Pressure Calculations when Cutting Water Saturated Sand". Texas A&M 33nd Annual Dredging Seminar, June 2001, Houston, USA 2001.

Copyright: Dr.ir. S.A. Miedema

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.

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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.

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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.

Miedema, S.A. & Zhao Yi, "An Analytical Method of Pore Pressure Calculations when Cutting Water Saturated Sand". Texas A&M 33nd Annual Dredging Seminar, June 2001, Houston, USA 2001.

Copyright: Dr.ir. S.A. Miedema

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.

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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.

Miedema, S.A. & Zhao Yi, "An Analytical Method of Pore Pressure Calculations when Cutting Water Saturated Sand". Texas A&M 33nd Annual Dredging Seminar, June 2001, Houston, USA 2001.

Copyright: Dr.ir. S.A. Miedema

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

Miedema, S.A. & Zhao Yi, "An Analytical Method of Pore Pressure Calculations when Cutting Water Saturated Sand". Texas A&M 33nd Annual Dredging Seminar, June 2001, Houston, USA 2001.

Copyright: Dr.ir. S.A. Miedema

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.

Miedema, S.A. & Zhao Yi, "An Analytical Method of Pore Pressure Calculations when Cutting Water Saturated Sand". Texas A&M 33nd Annual Dredging Seminar, June 2001, Houston, USA 2001.

Copyright: Dr.ir. S.A. Miedema

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

Miedema, S.A. & Zhao Yi, "An Analytical Method of Pore Pressure Calculations when Cutting Water Saturated Sand". Texas A&M 33nd Annual Dredging Seminar, June 2001, Houston, USA 2001.

Copyright: Dr.ir. S.A. Miedema

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.

Miedema, S.A. & Zhao Yi, "An Analytical Method of Pore Pressure Calculations when Cutting Water Saturated Sand". Texas A&M 33nd Annual Dredging Seminar, June 2001, Houston, USA 2001.

Copyright: Dr.ir. S.A. Miedema

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.

 

Miedema, S.A. & Zhao Yi, "An Analytical Method of Pore Pressure Calculations when Cutting Water Saturated Sand". Texas A&M 33nd Annual Dredging Seminar, June 2001, Houston, USA 2001.

Copyright: Dr.ir. S.A. Miedema