In 1982 I started research into the interaction of a seagoing cutter dredge with the soil, resulting in the program Dredmo. From 1983 to 1987 my PhD research resulted in a more fundamental model for the cutting of water saturated sand. The model however already contained terms that made it suitable for other types of soil like clay and rock. First ductile failure modes were investigated and later brittle failure modes were added.

The model distinguishes 6 possible failure mechanisms for small blade angles:

1. The Flow Type. This is the basic mechanism, all other mechanisms start from the Flow Type. The Flow Type describes ductile shear failure in clay and rock.
2. The Shear Type. The Shear Type is mathematically equivalent to the Flow Type, but is applied to sand cutting.
3. The Crushed Type. The Crushed Type is mathematically equivalent to the Flow Type, but is applied to atmospheric and hyperbaric rock cutting.
4. The Curling Type. The Curling Type occurs in clay cutting and hyperbaric rock cutting when cutting a very thin layer of material.
5. The Tear Type. The Tear Type describes tensile failure in clay cutting, so brittle tensile failure.
6. The Chip Type. The Chip Type desribes tensile/shear failure in rock cutting, so brittle tensile or shear failure.

For large blade angles the wedge theory has been developed. A static or dynamic wedge will occur in front of the blade, reducing the cutting forces.

The model is now a generic model for cutting of sand, clay and rock and also hyperbaric rock and is published in October 2014 in a book named: The Delft Sand, Clay & Rock Cutting Model. Published by IOS Press. www.iospress.nl. 

The developments of the model and the book will be updated on this website.

For questions, remarks and requests contact Dr.ir. S.A. Miedema, email: s.a.miedema@tudelft.nl

In August 2012 I was approached by a dredging company with the question which head loss model to use for a project with a cutter dredge and a discharge length of 35 km.

What did the company want to know?

1. How many booster stations to use.
2. What should be the locations of the booster stations.

What were the real issues?

1. What should be the total pump pressure to avoid plugging the line.
2. Where to locate the booster stations to avoid cavitation at the entrance of each pump.
3. How does this depend on the particle size distribution.

These questions trigerred a study in to the existing head loss models. With the knowledge that the main Dutch and Belgium dredging contractors use the Durand & Condolios (1952) and Fuhrboter (1961) models in a modified form, while companies in the USA often use the Wilson (1992) model in a modified form and in Canada the Saskatchewan Research Council model (SRC), the study started with a comparison of these models. Other models that were investigated were the Newitt et al. (1955) model, the Doron & Barnea (1987) model, the Matousek (1997) model and others. Also later models like the 4 component Sellgren & Wilson (2012) model and the 2LM and 3LM models of Wilson (1979-2014) and Matousek (1997-2014) are investigated.

Usually the models perform well in the neighbourhood of the parameters used during the experiments, especially the pipe diameter (small) and the particle diameter, but for real life conditions (large pipe diameters) the models deviate and it's not clear which model matches these conditions. Another issue is that most models are derived for transport volumetric concentrations as input and not the spatial volumetric concentrations. The research into the existing models did not give a satisfactory result.

Reason to develop a new model from scratch, the Delft Head Loss & Limit Deposit Velocity Framework. This DHLLDV Framework is based on the spatial volumetric concentration in the pipe and uniform sands or gravels and consists of a framework containing 12 sub-models.

1. The fixed or stationary bed model (FB).
2. The sliding bed model (SB).
3. The heterogeneous transport model (He).
4. The homogeneous transport model (Ho).
5. The sliding flow model (SF).
6. The limit deposit velocity model (LDV).
7. The holdup or slip factor model.
8. The concentration distribution in the pipe.
9. The transition heterogeneous-homogeneous flow.
10. The bed height model.
11. Graded sands & gravels.
12. Inclined pipes.

The Limit Deposit Velocity divides particles into 5 regions. For each region different physics is used.

The 7th model transforms constant spatial volumetric concentration curves into constant transport volumetric concentration curves.

The concentration distribution is based on the LDV, since at the LDV the bottom concentration has to be the bed concentration.

The transition heterogeneous-homogeneous is at operational conditions for medium sands and requires special attention.

The bed height is also based on the LDV (bedheight zero) and on the holdup function.

The curves for graded sands or gravels are constructed by proportional summation of the curves of the different fractions after adjusting the liquid properties for the fines content.

A last addition is the influence of pipe inclination.

If you like to know more about the DHLLDV Framework, go to DHLLDV in the menu. Over time more information will be added to this website and more publications will follow.

The model is published in a book and is available on ResearchGate.

Constant spatial and delivered concentration curves for uniform and graded sands

Pipe diameters ranging from 1 inch to 1.2 m, particles of 0.5 mm 

Now with Excel Workbook, see Publications.

For questions, remarks and requests contact Dr.ir. S.A. Miedema, email: s.a.miedema@tudelft.nl