6.1: Introduction

Last updated
Save as PDF

Page ID: 29450

\( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \) \( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}} \)\(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\) \(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\)\(\newcommand{\AA}{\unicode[.8,0]{x212B}}\)

Although calculation models for the determination of the cutting forces for dry soil, based on agriculture, were available for a long time (Hettiaratchi & Reece (1965), (1966), (1967A), (1967B), (1974), (1975) and Hatamura & Chijiiwa (1975), (1976A), (1976B), (1977A) and (1977B) ) it is only since the seventies and the eighties that the cutting process in saturated sand is extensively researched at the Delft Hydraulics Laboratory, at the Delft University of Technology and at the Mineraal Technologisch Instituut (MTI, IHC).

First the process is described, for a good understanding of the terminology used in the literature discussion.

From literature it is known that, during the cutting process, the sand increases in volume (see Figure 6-7). This increase in volume is accredited to dilatancy. Dilatancy 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 sub-pressures in the pore water in the sand package. As a result the grain stresses increase and therefore the required cutting forces. The rate 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:

Very low cutting velocities, a quasi-static cutting process. The cutting forces are determined by the gravitation, cohesion and adhesion.
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.
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.
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.
Very high cutting velocities. The inertia forces part in the total cutting forces can no longer be neglected but form a substantial part.

Under normal conditions in dredging, the cutting process in sand will be governed by the effects of dilatation. Gravity, inertia, cohesion and adhesion will not play a role.