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