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

Rock Cutting: Atmospheric Conditions.
Once the internal friction angle is found, the cohesion can be determined as:
UCS 1
sin UCS
c 2
cos
2
r
(8-8)
So the Mohr-Coulomb relation is:
UCS r 1 UCS r 1
2 r 2 r 2
r
(8-9)
8.2.2. Brittle versus Ductile.
The terms ductile failure and brittle failure are often used in literature for the failure of materials with shear strength
and tensile strength, but what do the words ductile and brittle mean?
In materials science, ductility is a solid material's ability to deform under tensile stress; this is often
characterized by the material's ability to be stretched into a wire. Malleability, a similar property, is a
material's ability to deform under compressive stress; this is often characterized by the material's ability
to form a thin sheet by hammering or rolling. Both of these mechanical properties are aspects of plasticity,
the extent to which a solid material can be plastically deformed without fracture. Ductility and
malleability are not always coextensive – for instance, while gold has high ductility and malleability, lead
has low ductility but high malleability. The word ductility is sometimes used to embrace both types of
plasticity.
A material is brittle if, when subjected to stress, it breaks without significant deformation (strain). Brittle
materials absorb relatively little energy prior to fracture, even those of high strength. Breaking is often
accompanied by a snapping sound. Brittle materials include most ceramics and glasses (which do not
deform plastically) and some polymers, such as PMMA and polystyrene. Many steels become brittle at
low temperatures (see ductile-brittle transition temperature), depending on their composition and
processing. When used in materials science, it is generally applied to materials that fail when there is
little or no evidence of plastic deformation before failure. One proof is to match the broken halves, which
should fit exactly since no plastic deformation has occurred. Generally, the brittle strength of a material
can be increased by pressure. This happens as an example in the brittle-ductile transition zone at an
approximate depth of 10 kilometers in the Earth's crust, at which rock becomes less likely to fracture,
and more likely to deform ductile.” (Source Wikipedia).
Rock has both shear strength and tensile strength and normally behaves brittle. If the tensile strength is high the
failure is based on brittle shear, but if the tensile strength is low the failure is brittle tensile. In both cases chips
break out giving it the name Chip Type. So rock has true brittle behavior. Under hyperbaric conditions however,
the pore under pressures will be significant, helping the tensile strength to keep cracks closed. The result is a much
thicker crushed zone that may even reach the surface. Crushing the rock is called cataclastic behavior. Since the
whole cutting process is dominated by the crushed zone, this is named the Crushed Type. Due to the high pore
under pressures the crushed material sticks together and visually looks like a ductile material. That’s the reason
why people talk about ductile behavior of hyperbaric rock. In reality it is cataclastic behavior, which could also be
named pseudo-ductile behavior.
Now whether the high confining pressure result from a high hyperbaric pressure or from the cutting process itself
is not important, in both cases the pseudo-ductile behavior may occur. Figure 8-2 shows the stress-strain behavior
typical for brittle and ductile behavior. Based on this stress-strain behavior the term ductile is often used for rock,
but as mentioned before this is the result of cataclastic failure.
Gehking (1987) stated that pseudo-ductile behavior will occur when the ratio UCS/BTS15. For 9