2.1: Introduction

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Cutting processes of soil distinguish from the classical soil mechanics in civil engineering in the fact that:

Classical soil mechanics assume:

Small to very small strain rates.
Small to very small strains.
A very long time span, years to hundreds of years.
Structures are designed to last forever.

Cutting processes assume:

High to very high strain rates.
High to very high strains and deformations in general.
A very short time span, following from very high cutting velocities.
The soil is supposed to be excavated, the coherence has to be broken.

For the determination of cutting forces, power and specific energy the criterion for failure has to be known. In this book the failure criterion of Mohr-Coulomb will be applied in the mathematical models for the cutting of sand, clay and rock. The Mohr–Coulomb theory is named in honor of Charles-Augustin de Coulomb and Christian Otto Mohr. Coulomb's contribution was a 1773 essay entitled "Essai sur une application des règles des maximis et minimis à quelques problèmes de statique relatifs à l'architecture". Mohr developed a generalized form of the theory around the end of the 19th century. To understand and work with the Mohr-Coulomb failure criterion it is also necessary to understand the so called Mohr circle. The Mohr circle is a two dimensional graphical representation of the state of stress at a point. The abscissa, σ, and ordinate, τ, of each point on the circle are the normal stress and shear stress components, respectively, acting on a particular cut plane under an angle α with the horizontal. In other words, the circumference of the circle is the locus of points that represent the state of stress on individual planes at all their orientations. In this book a plane strain situation is considered, meaning a two- dimensional cutting process. The width of the blades considered w is always much bigger than the layer thickness h_i considered. In geomechanics (soil mechanics and rock mechanics) compressive stresses are considered positive and tensile stresses are considered to be negative, while in other engineering mechanics the tensile stresses are considered to be positive and the compressive stresses are considered to be negative. Here the geomechanics approach will be applied. There are two special stresses to be mentioned, the so called principal stresses. Principal stresses occur at the planes where the shear stress is zero. In the plane strain situation there are two principal stresses, which are always under an angle of 90^o with each other.

In order to understand the cutting processes in sand, clay and rock, it is required to have knowledge of basic soil and rock mechanics. The next chapters 2.2-2.7 cover this knowledge and have been composed almost entirely from information from the public domain, especially internet. Most information comes from Wikipedia and Answers.com.