depth is referred to as a lithostatic state of stress. For
a variable density, ␳, and variable gravitational
acceleration, g, with respect to depth, the stress
components in a body of rock at depth, z ϭϪD,
may follow the relationship:
(6.101)
Jaeger and Cook refer to this as Heim’s rule after
the Swiss geologist Albert Heim (Jaeger and Cook,
1979, p. 371). For the investigation of many structural problems, it is not necessary to consider the
continuous variations in these quantities. Rather,
an average or representative unit weight can be
␴ xy ϭ ␴ yx ϭ ␴ yz ϭ ␴ zy ϭ ␴ zx ϭ ␴ xz ϭ 0
␴ xx ϭ ␴ yy ϭ ␴ zz ϭ Ύ
ϪD
0
␳g dz
230
FORCE, TRACTION, AND STRESS
Fig 6.27 Directions of greatest compressive horizontal
stress from various measurement techniques near the San
Andreas Fault system in California. Reprinted with
permission from Zoback et al. (1987), copyright 1987.
124
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Mojave Desert
Eastern
Transverse
Ranges
CAJON PASS
CALAVERAS
CARRIZO PLAIN
SANTA BARBARA
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Hydraulic
fracturing
Focal
mechanism
Borehole
elongation
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SAN LUIS OBISPO
Geological
NEWPORT-INGLEWOOD
SAN BERNADINO
SAN FRANCISCO