Page 74 - Geothermal Energy Systems Exploration, Development, and Utilization

50 2 Exploration Methods
reactivation and leakage potential of any fault population within the stress field
under initial and changing pore pressure conditions. For the EGS project at
Groß Sch¨ onebeck in the Northeast German Basin, this approach was successfully
applied to describe the stress state along faults under initial and modified formation
pressure, and finally to assess the fault reactivation potential and to understand
recorded microseismic events during massive water stimulation (Moeck, Kwiatek,
and Zimmermann, in press).
The slip tendency is the ratio of resolved shear stress to resolved normal stress
on a surface (Morris, Ferrill, and Henderson, 1996). It is based on Amonton’s law
that governs fault reactivation:
∗
τ = µ s σ neff (2.2)
where τ is the shear stress, σ neff the effective normal stress (σ n –P p ), and µ s the
sliding friction coefficient (Byerlee, 1978). According to this law, stability or failure
is determined by the ratio of shear stress to normal stress acting on the plane
of weakness and defined as slip tendency T s (Lisle and Srivastava, 2004; Morris,
Ferrill, and Henderson, 1996). Slip is likely to occur on a surface if resolved shear
stress, τ, equals or exceeds the frictional sliding coefficient and slip tendency is
given as

τ s = T/σ neff ≥ µ s (2.3)
The shear and effective normal stress acting on a given plane depend on the
orientation of the planes within the stress field that is defined by principal effective
stresses σ 1eff = (σ 1 − P p ) > σ 2eff = (σ 2 − P p ) > σ 3eff = (σ 3 − P p )(Jaeger, Cook, and
Zimmerman, 2007):
∗ 2
2
∗ 2
σ neff = σ 1eff l + σ 2eff m + σ 3eff n (2.4)
∗
2 2 2 2 2 2 2 2 2 1/2

T = (σ 1 − σ 2 ) l m + (σ 2 − σ 3 ) m n + (σ 3 − σ 1 ) l n (2.5)
where l, m,and n are the direction cosines of the plane’s normal with respect
to the principal stress axes, σ 1 , σ 2 ,and σ 3 respectively. Equations (2.4 and 2.5)
define effective normal stress and shear stress for compressional stress regimes,
that is, σ 1eff is horizontal. Extensional and strike-slip regimes can be derived by
changing the order of the direction cosines in these equations (Ramsay and Lisle,
2000).
Dilation of faults and fractures is largely controlled by the resolved normal stress
which is basically a function of lithostatic and tectonic stresses and fluid pressure.
On the basis of Equation (2.4), the magnitude of normal stress can be computed
for surfaces of all orientation within a known or suspected stress field. This normal
stress can be normalized by comparison with the differential stress resulting in the
dilation tendency τ d for a surface defined by
(σ 1 − σ n )
τ d = (2.6)
(σ 1 − σ 3 )
Slip and dilation tendency stereoplots are obtained by solving Equations (2.3
and 2.4) for all planes in 3D space, substituting in Equation (2.2) for shear