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Motivation
fluid injections often show pure shear fractures
hydraulic fractures are often non parallel to 1
some authors explain by combined shear-tensile fracture
this presentation shows why tensile fractures are so rare
Tensile earthquakes in focal mechanisms
tensile events – opening
=> normal stress must have been negative, σneff<0
=> tensile events occupy limited area in Mohr diagrams
(Vavryčuk, 2002)
σneff<0
σn
eff= σn− p < 0
p > σn
Mohr circle, 2D
=> n and acting at any plane lie on the Mohr circle
τ
σσ1σ3
2
60°45°
30°
2 221 3
1
4n s
Material strength
Coulomb (1773) – linear strength f = c + n
shear failure strength cohesion friction
Mohr (1880) – strength envelope is non-linear !
τ
σ2
tensile (Hydraulic) fracture
c
shear fracture
Empirical strength
envelopes granites
limestones
(Parry, 1995)
tensile strength << compression strength 5..10 MPa 50..300 MPa
Intact rock failure (high σ1
- σ3)Big radius = σ1 - σ3
=> Mohr circle touches the strength envelope at σ>0
ISO = 0 DC = 100% high 45° < < ~50°
σ - p
c
p2
σ3
σ1
σ3 σ1
τ
σ-p
c
p
τ
Intact rock failure (small σ1 - σ3)
Small radius = σ1 - σ3
=> Mohr circle touches the strength envelope at σ<0
ISO 0 DC > 0 small ~50° < 90°
σ3
σ1
not well constrained, weak dependance of σn on the angle
pure tension= HF
Depth dependance of σ1-σ3
KTB, Soultz: SH ~ 2 Sh
SH – Sh = 2/3 Sv
tensile fractures possible at < 1-2 km depths
(Brudy et al., 1997)
depth SH-Sh
100m 1.8 MPa
1 km 18 MPa
10 km 180 MPa
How to achieve < 0
high pore pressure – fluid injections stimulations in gas fields, < 3 km
geothermal reservoir stimulations, < 5 km
earthquake swarms, < 10 km
very small depths (small lithostatic pressure) land/rock slides – extensional regime
=> monitoring of ISO component helpful
Conclusions
strength envelope is non-linear !!
tensile earthquakes occur only if deviatoric stress σ1-σ3 is small enough preexisting fractures strike close to σ1
any tensile fracture shows some shear component
tensile frac occurrence decreases with depth
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