I
n the preceding chapter we learned that the
mechanical behavior of rock under certain conditions can be approximated with a linear
elastic material, a mathematical construct formulated using Hooke’s Law to relate stress and
infinitesimal strain. The elastic material is useful
for describing both ancient and modern deformation in the Earth at a variety of length and time
scales. However, the limestone described by King
as “illimitably cleft from north to south” provides
an evocative example of fracturing which is inelastic, non-recoverable deformation. Even if the fracture surfaces were pushed back together they
would not heal. Similarly, the limestone bed pictured in the frontispiece for this chapter from
Lilstock Beach on the southern margin of the
Bristol Channel, England, is broken by numerous
fractures, providing visual evidence of inelastic
behavior (Rawnsley et al., 1998; Engelder and
Peacock, 2001). In this chapter we contemplate the
singular phenomenon that bewildered King and
describe the modern concepts, laboratory data,
and fracture mechanics required to address his
question.
A few fracture tips are visible on the bedding
surface of the Lilstock exposure (Chapter 9, frontispiece). We infer that the stress state reached the
rock strength near the tips of the fractures as they
propagated through the limestone, so the local
stress–strain behavior was non-linear and irrecoverable there. Presumably the tips now visible represent those points where the local stress
dropped below the rock strength and propagation
ceased. We also infer, based on experiments and
theory to be described in this chapter, that the
stress state remained within the elastic range in
much of the rock between the fractures. This
limited extent of inelastic deformation is characteristic of materials that have deformed in a brittle
state. We seek to understand the consequences of
brittle behavior for the state of stress and strain,
the nature of the physical mechanisms that
operate during such deformation, and the
reasons why inelastic deformation may be localized into thin tabular zones.
9.1 Brittle deformation in the
laboratory and in the field
Laboratory experiments on rock samples loaded
beyond their elastic limit under a variety of conditions help us to understand what happens with
the onset of inelastic deformation in the Earth
(Griggs and Handin, 1960b; Paterson, 1978; Carter
et al., 1981; Wong, 1982a,b; Reches, 1983; Reches
and Dieterich, 1983; Duba et al., 1990). Griggs and
Handin (1960a) provide a useful summary in their
illustration (Fig. 9.1) based upon decades of experience testing rock in the laboratory under conditions of triaxial compression and extension. In
these experiments cylindrical specimens are
subject to a uniform compressive radial stress
called the confining pressure and an axial compressive stress. The experiments are referred to as
extension tests (Fig. 9.1a) if the axial stress is the
least compressive stress (designated 1 according
to the sign conventions adopted here) or compression tests (Fig. 9.1b) if the axial stress is the greatest
compressive stress (designated 3 ).
Rock specimens in extension tests (Fig. 9.1a) typically fail by the formation of an extension fracture,
oriented perpendicular to the least compressive
stress, at axial strains less than about 1%. The relative motion of the surfaces of extension fractures is
dominantly opening. In compression tests at low
confining pressures (Fig. 9.1b), splitting fractures
form parallel to the greatest compressive stress at
strains from about 1 to 5% (Fig. 9.2a). Splitting fractures also open although wedge-shaped fractures
with dominantly shearing motion may develop
near the ends of specimens. At modest confining
pressures (Fig. 9.1c), shear fractures form at an acute
angle to the greatest compressive stress at strains
from about 2 to 8% (Fig. 9.2b). At greater confining
pressures (Fig. 9.1d), the deformation is distributed
across a shear zone at strains from about 5 to 10%
(Fig. 9.2c). At high confining pressure (Fig. 9.1e),
shearing is pervasive throughout the specimen,
which deforms in what is called the ductile state and
maintains its integrity to strains greater than 10%.
Distributed flow is a characteristic feature of
ductile deformation, a topic that we take up in a
later chapter. Brittle deformation, in contrast, is
localized into discrete fractures or tabular zones.
334
BRITTLE BEHAVIOR
n the preceding chapter we learned that the
mechanical behavior of rock under certain conditions can be approximated with a linear
elastic material, a mathematical construct formulated using Hooke’s Law to relate stress and
infinitesimal strain. The elastic material is useful
for describing both ancient and modern deformation in the Earth at a variety of length and time
scales. However, the limestone described by King
as “illimitably cleft from north to south” provides
an evocative example of fracturing which is inelastic, non-recoverable deformation. Even if the fracture surfaces were pushed back together they
would not heal. Similarly, the limestone bed pictured in the frontispiece for this chapter from
Lilstock Beach on the southern margin of the
Bristol Channel, England, is broken by numerous
fractures, providing visual evidence of inelastic
behavior (Rawnsley et al., 1998; Engelder and
Peacock, 2001). In this chapter we contemplate the
singular phenomenon that bewildered King and
describe the modern concepts, laboratory data,
and fracture mechanics required to address his
question.
A few fracture tips are visible on the bedding
surface of the Lilstock exposure (Chapter 9, frontispiece). We infer that the stress state reached the
rock strength near the tips of the fractures as they
propagated through the limestone, so the local
stress–strain behavior was non-linear and irrecoverable there. Presumably the tips now visible represent those points where the local stress
dropped below the rock strength and propagation
ceased. We also infer, based on experiments and
theory to be described in this chapter, that the
stress state remained within the elastic range in
much of the rock between the fractures. This
limited extent of inelastic deformation is characteristic of materials that have deformed in a brittle
state. We seek to understand the consequences of
brittle behavior for the state of stress and strain,
the nature of the physical mechanisms that
operate during such deformation, and the
reasons why inelastic deformation may be localized into thin tabular zones.
9.1 Brittle deformation in the
laboratory and in the field
Laboratory experiments on rock samples loaded
beyond their elastic limit under a variety of conditions help us to understand what happens with
the onset of inelastic deformation in the Earth
(Griggs and Handin, 1960b; Paterson, 1978; Carter
et al., 1981; Wong, 1982a,b; Reches, 1983; Reches
and Dieterich, 1983; Duba et al., 1990). Griggs and
Handin (1960a) provide a useful summary in their
illustration (Fig. 9.1) based upon decades of experience testing rock in the laboratory under conditions of triaxial compression and extension. In
these experiments cylindrical specimens are
subject to a uniform compressive radial stress
called the confining pressure and an axial compressive stress. The experiments are referred to as
extension tests (Fig. 9.1a) if the axial stress is the
least compressive stress (designated 1 according
to the sign conventions adopted here) or compression tests (Fig. 9.1b) if the axial stress is the greatest
compressive stress (designated 3 ).
Rock specimens in extension tests (Fig. 9.1a) typically fail by the formation of an extension fracture,
oriented perpendicular to the least compressive
stress, at axial strains less than about 1%. The relative motion of the surfaces of extension fractures is
dominantly opening. In compression tests at low
confining pressures (Fig. 9.1b), splitting fractures
form parallel to the greatest compressive stress at
strains from about 1 to 5% (Fig. 9.2a). Splitting fractures also open although wedge-shaped fractures
with dominantly shearing motion may develop
near the ends of specimens. At modest confining
pressures (Fig. 9.1c), shear fractures form at an acute
angle to the greatest compressive stress at strains
from about 2 to 8% (Fig. 9.2b). At greater confining
pressures (Fig. 9.1d), the deformation is distributed
across a shear zone at strains from about 5 to 10%
(Fig. 9.2c). At high confining pressure (Fig. 9.1e),
shearing is pervasive throughout the specimen,
which deforms in what is called the ductile state and
maintains its integrity to strains greater than 10%.
Distributed flow is a characteristic feature of
ductile deformation, a topic that we take up in a
later chapter. Brittle deformation, in contrast, is
localized into discrete fractures or tabular zones.
334
BRITTLE BEHAVIOR