Page 47 - Global Tectonics

34 CHAPTER 2

fractures and faults. Where these factors are relatively the strength and rheology of the lithosphere mainly

high rocks tend to deform by ductile flow. Measures of comes from observations of isostasy and lithospheric

strain are used to quantify the deformation. flexure (Section 2.11.4). On time scales of millions of

Stress (σ) is defined as the force exerted per unit area years, Earth rheology generally is studied using a con-
of a surface, and is measured in Pascals (Pa). Any stress tinuum mechanics approach, which describes the mac-
acting upon a surface can be expressed in terms of a roscopic relationships between stress and strain, and
normal stress perpendicular to the surface and two their time derivatives. Alternatively, the long-term rhe-
components of shear stress in the plane of the surface. ology of the Earth may be studied using a microphysi-
The state of stress within a medium is conveniently cal approach, where the results of laboratory experiments
specified by the magnitudes and directions of three prin- and observations of microstructures are used to con-

cipal stresses that act on three planes in the medium strain the behavior of rocks. Both of these latter
along which the shear stress is zero. The principal approaches have generated very useful results (e.g. Sec-
stresses are mutually orthogonal and are termed σ 1 , σ 2 , tions 7.6.6, 8.6.2, 10.2.5).
and σ 3 , referring to the maximum, intermediate and
minimum principal stresses, respectively. In the geosci-
ences, compressive stresses are expressed as positive and
tensile stresses negative. The magnitude of the differ- 2.10.2 Brittle deformation
ence between the maximum and minimum principal
stresses is called the differential stress. Deviatoric stress Brittle fracture is believed to be caused by progressive
represents the departure of a stress field from symme- failure along a network of micro- and meso-scale cracks.

try. The value of the differential stress and the charac- The cracks weaken rock by producing local high con-

teristics of deviatoric stress both influence the extent centrations of tensile stress near their tips. The crack
and type of distortion experienced by a body. orientations relative to the applied stress determine the

Strain (ε) is defined as any change in the size or shape location and magnitude of local stress maxima. Fractur-
of a material. Strains are usually expressed as ratios that ing occurs where the local stress maxima exceed the
describe changes in the configuration of a solid, such as strength of the rock.

the change in the length of a line divided by its original This theory, known as the Griffith theory of fracture,

length. Elastic materials follow Hooke’s law where works well under conditions of applied tensile stress or
strain is proportional to stress and the strain is reversible where one of the principal stresses is compressional.
until a critical stress, known as the elastic limit, is reached. When the magnitude of the tensile stress exceeds the
This behavior typically occurs at low stress levels and tensile strength of the material, cracks orthogonal to

high strain rates. Beyond the elastic limit, which is a this stress fail first and an extension fracture occurs.
function of temperature and pressure, rocks deform by Below a depth of a few hundred meters, where all prin-
either brittle fracturing or by ductile fl ow. The yield cipal stresses are usually compressional, the behavior of
stress (or yield strength) is the value of the differential cracks is more complex. Cracks close under compres-
stress above the elastic limit at which deformation sion and are probably completely closed at depths of
becomes permanent. Plastic materials display continu- >5 km due to increasing overburden pressure. This
ous, irreversible deformation without fracturing. implies that the compressive strength of a material is
The length of time over which stress is applied also much greater than the tensile strength. For example, the
is important in the deformation of Earth materials compressive strength of granite at atmospheric pressure
(Park, 1983). Rock rheology in the short term (seconds is 140 MPa, and its tensile strength only about 4 MPa.
or days) is different from that of the same material Where all cracks are closed, fracturing depends
stressed over durations of months or years. This differ- upon the inherent strength of the material and the mag-
ence arises because rocks exhibit higher strength at high nitude of the differential stress (Section 2.10.1). Experi-
strain rates than at low strain rates. For example, when ments show that shear fractures, or faults, preferentially
a block of pitch is struck with a hammer, that is, sub- form at angles of <45° on either side of the maximum
jected to rapid “instantaneous” strain, it shatters. principal compressive stress when a critical shear stress
However, when left for a period of months, pitch on the planes is exceeded. This critical shear stress (σ s *)
deforms slowly by flowing. This slow long-term fl ow of depends upon the normal stress (σ n ) on planes of poten-

materials under constant stress is known as creep. On tial failure and the coeffi cient of internal friction (μ) on
time scales of thousands of years, information about those planes, which resists relative motion across them.