The Delft Sand, Clay & Rock Cutting Model, 2019a

Chapter 2: Basic Soil Mechanics.
2.1. Introduction.
Basic Soil Mechanics.
Cutting processes of soil distinguish from the classical soil mechanics in civil engineering in the fact that:
Classical soil mechanics assume:
1. Small to very small strain rates.
2. Small to very small strains.
3. A very long time span, years to hundreds of years.
4. Structures are designed to last forever.
Cutting processes assume:
1. High to very high strain rates.
2. High to very high strains and deformations in general.
3. A very short time span, following from very high cutting velocities.
4. 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 twodimensional
cutting process. The width of the blades considered w is always much bigger than the layer thickness
hi 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 90º 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.
2.2. Soil Mechanics.
2.2.1. Definition.
McGraw-Hill Science & Technology Encyclopedia gives the following description of Soil Mechanics:
The study of the response of masses composed of soil, water, and air to imposed loads. Because both water and
air are able to move through the soil pores, the discipline also involves the prediction of these transport processes.
Soil mechanics provides the analytical tools required for foundation engineering, retaining wall design, highway
and railway sub base design, tunneling, earth dam design, mine excavation design, and so on. Because the
discipline relates to rock as well as soils, it is also known as geotechnical engineering. Soil consists of a multiphase
aggregation of solid particles, water, and air.
This fundamental composition gives rise to unique engineering properties, and the description of the mechanical
behavior of soils requires some of the most sophisticated principles of engineering mechanics. The terms
multiphase and aggregation both imply unique properties. As a multiphase material, soil exhibits mechanical
properties that show the combined attributes of solids, liquids, and gases. Individual soil particles behave as solids,
and show relatively little deformation when subjected to either normal or shearing stresses. Water behaves as a
liquid, exhibiting little deformation under normal stresses, but deforming greatly when subjected to shear. Being
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