# Stress field producing tensile earthquakes

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```Motivation
 fluid injections often show pure shear fractures
 hydraulic fractures are often non parallel to s1
 some authors explain by combined sheartensile fracture
 this presentation shows why tensile fractures
are so rare
Tensile earthquakes in focal
mechanisms
tensile events – opening
=&gt; normal stress must have been negative, σneff&lt;0
=&gt; tensile events occupy limited area in Mohr diagrams
σneff&lt;0

σneff= σn− p &lt; 0

p &gt; σn
(Vavryčuk, 2002)
Mohr circle, 2D
σ1
τ
45&deg;
60&deg;

30&deg;
2
σ3
σ1
σ3
1
2
2
s n  s    2  s 1  s 3 
4
=&gt; sn and  acting at any plane lie on the
Mohr circle
σ
Material strength
 Coulomb (1773) – linear strength
f = c + m sn
shear failure strength

cohesion friction
 Mohr (1880) – strength envelope is non-linear !
τ
shear fracture
c
2
tensile (Hydraulic)
fracture
σ
s
Empirical strength
envelopes
 granites
tensile strength &lt;&lt; compression strength
5..10 MPa
50..300 MPa
 limestones
(Parry, 1995)
Intact rock failure (high σ1 - σ3)
τ
Big radius = σ1 - σ3
c
2
σ3
p
σ1

σ1
σ-p
=&gt; Mohr circle touches
the strength envelope
at σ&gt;0
 ISO = 0
σ3
 DC = 100%
 high 
 45&deg; &lt;  &lt; ~50&deg;
Intact rock failure (small σ1 - σ3)
τ
Small radius = σ1 - σ3
c
p
=&gt; Mohr circle touches
the strength
envelope at σ&lt;0
σ1
 ISO  0
σ-p
pure tension
= HF

 DC &gt; 0
σ3
 small 
 ~50&deg; &lt;   90&deg;
 not well constrained, weak dependance of σn on the angle
Depth dependance of σ1-σ3
KTB, Soultz: SH ~ 2 Sh
SH – Sh = 2/3 Sv
depth
SH-Sh
100m
1.8 MPa
1 km
18 MPa
10 km
180 MPa
tensile fractures possible at
&lt; 1-2 km depths
(Brudy et al., 1997)
How to achieve s &lt; 0
 high pore pressure – fluid injections
 stimulations in gas fields, &lt; 3 km
 geothermal reservoir stimulations, &lt; 5 km
 earthquake swarms, &lt; 10 km
 very small depths (small lithostatic pressure)
 land/rock slides – extensional regime
=&gt; 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
```