Stress Measurements - Rock Mechanics Based on an Anisotropic Jointed Rock Model - page 551

K 0 is the gravity-induced stress ratio which for elastic isotropic stress-strain behavior is
equal to (Section 9.2.1)

(9.3)

The algebraic form of Equation (16.24) corresponds to the one that was predicted for
the stress coeffi cient by an elastic spherical shell model of the Earth's crust assuming the
Earth's mantle to be an incompressible liquid (McCutchen 1982, Sheorey 1994). As can
be derived from the asymptotic behavior of (16.24), K with increasing h approaches a
constant value which corresponds to K 0 .
A preliminary data evaluation of the Q-WSM database yielded the following upper
bounds of K for crystalline and sedimentary rocks (Zang et al. 2012):

where z is the height of overburden in km. The lower bound for both rock groups was
found to be

corresponding to an in-situ stress state due to gravity only ( Δσ H = 0), with ν = 0.25 (Fig.

16.36).

Figure 16.36 In-situ stress coeffi cient K = σ H / σ V versus depth (Zang et al. 2012)