F au lt s an d f r ac t u r e s at d e p t h - John T. Foster · 2018. 12. 10. · DPT DPT DPT TJO...

Faults and fractures at depthFaults and fractures at depth

© Cambridge University Press (Fig. 5.5, pp. 150)Zoback, Reservoir Geomechanics

http://www.amazon.com/Reservoir-Geomechanics-Paperback-Author-Zoback/dp/B00EFZ88EQ/ref=sr_1_2?ie=UTF8&qid=1422942834&sr=8-2&keywords=zoback+geomechanics

Geographical coordinate systemGeographical coordinate system

=RG

⎡

⎣

⎢⎢

cos α cos β

cos α sin β sin γ − sin α cos γ

cos α sin β cos γ + sin α sin γ

sin α cos β

sin α sin β sin γ + cos α cos γ

sin α sin β cos γ − cos α sin γ

− sin β

cos β sin γ

cos β cos γ

⎤

⎦

⎥⎥

Interactive widgetInteractive widget

Stress in geographical coordinate systemStress in geographical coordinate system

= SSG RT

GRG

Example: Strike-slip faultingExample: Strike-slip faulting

S =

⎡

⎣

⎢⎢

30

0

0

0

25

0

0

0

20

⎤

⎦

⎥⎥

α

β

γ

= 0∘

= 0∘

= 90∘

Azimuth of SHmax

=S1 SHmax

=S2 Sv

=RG

⎡

⎣

⎢⎢

1

0

0

0

0

−1

0

1

0

⎤

⎦

⎥⎥

=SG

⎡

⎣

⎢⎢

30

0

0

0

20

0

0

0

25

⎤

⎦

⎥⎥

Example: Normal faultingExample: Normal faulting

S =

⎡

⎣

⎢⎢

30

0

0

0

25

0

0

0

20

⎤

⎦

⎥⎥

α

β

γ

= 0∘

= −90∘

= 0∘

Azimuth of Shmin

=S1 Sv

=RG

⎡

⎣

⎢⎢

0

0

−1

0

1

0

1

0

0

⎤

⎦

⎥⎥

=SG

⎡

⎣

⎢⎢

20

0

0

0

25

0

0

0

30

⎤

⎦

⎥⎥

Example: Reverse faultingExample: Reverse faulting

S =

⎡

⎣

⎢⎢

30

0

0

0

25

0

0

0

20

⎤

⎦

⎥⎥

α

β

γ

= 90∘

= 0∘

= 0∘

Azimuth of SHmax

=S1 SHmax

=S2 Shmin

=RG

⎡

⎣

⎢⎢

0

−1

0

1

0

0

0

0

1

⎤

⎦

⎥⎥

=SG

⎡

⎣

⎢⎢

25

0

0

0

30

0

0

0

20

⎤

⎦

⎥⎥


S =

⎡

⎣

⎢⎢

60

0

0

0

40

0

0

0

35

⎤

⎦

⎥⎥

α

β

γ

= 135∘

= 0∘

= 90∘

Azimuth of SHmax

=S1 SHmax

=S2 Sv

=RG

⎡

⎣

⎢⎢⎢

−1

2√

0

1

2√

1

2√

0

1

2√

0

1

0

⎤

⎦

⎥⎥⎥

=SG

⎡

⎣

⎢⎢

47.5

−12.5

0

−12.5

47.5

0

0

0

40

⎤

⎦

⎥⎥

Fault orientationFault orientation



Fault traction and stressFault traction and stress

Traction on fault plane

= ⋅t ⃗ SG n̂

Normal stress to plane

= ⋅Sn t ⃗ ⊺

n̂

Shear stress in dip direction

= ⋅τd t ⃗ ⊺

n̂ d

Shear stress in strike direction

= ⋅τs t ⃗ ⊺

n̂ s


SG

=

⎡

⎣

⎢⎢

30

−8.66

0

−8.66

40

0

0

0

30

⎤

⎦

⎥⎥

strike

dip

= 60∘

= 90∘

=n̂

⎡

⎣

⎢⎢

−0.866

0.5

0

⎤

⎦

⎥⎥ =n̂ s

⎡

⎣

⎢⎢

0.5

0.866

0

⎤

⎦

⎥⎥ =n̂ d

⎡

⎣

⎢⎢

0

0

1.0

⎤

⎦

⎥⎥

= 40 = 0 = 8.66Sn τd τs


SG

=

⎡

⎣

⎢⎢

4000

0

0

0

3000

0

0

0

5000

⎤

⎦

⎥⎥

strike

dip

= 45∘

= 60∘

=n̂

⎡

⎣

⎢⎢

−0.612

0.612

−0.5

⎤

⎦

⎥⎥ =n̂ s

⎡

⎣

⎢⎢

0.707

0.707

0

⎤

⎦

⎥⎥ =n̂ d

⎡

⎣

⎢⎢

−0.3535

0.3535

0.866

⎤

⎦

⎥⎥

= 3875 = −650 = −433Sn τd τs


SG

=

⎡

⎣

⎢⎢

5000

0

0

0

4000

0

0

0

3000

⎤

⎦

⎥⎥

strike

dip

= 225∘

= 60∘

=n̂

⎡

⎣

⎢⎢

0.612

−0.612

−0.5

⎤

⎦

⎥⎥ =n̂ s

⎡

⎣

⎢⎢

−0.707

−0.707

0

⎤

⎦

⎥⎥ =n̂ d

⎡

⎣

⎢⎢

0.3535

−0.3535

0.866

⎤

⎦

⎥⎥

= 4125 = −650 = −433Sn τd τs

Example: Revese faultingExample: Revese faulting

SG

=

⎡

⎣

⎢⎢

2100

−520

0

−520

1500

0

0

0

1000

⎤

⎦

⎥⎥

strike

dip

= 120∘

= 70∘

=n̂

⎡

⎣

⎢⎢

−0.814

−0.470

−0.342

⎤

⎦

⎥⎥ =n̂ s

⎡

⎣

⎢⎢

−0.5

0.866

0

⎤

⎦

⎥⎥ =n̂ d

⎡

⎣

⎢⎢

0.2961

−0.1710

0.9396

⎤

⎦

⎥⎥

= 1441 = 161 = 488Sn τd τs

Shear failure (slip on faults)Shear failure (slip on faults)

Coulomb failure function

= μτ

σn

f = τ − μ ≤ 0σn

Frictional strength of faultsFrictional strength of faults



Induced seismicityInduced seismicity

Fluid injection and seismicity at the Rocky Mountain Arsenal

© Cambridge University Press (Fig. 4.22a, pp. 125)Zoback, Reservoir Geomechanics

F au lt s an d f r ac t u r e s at d e p t h - John T. Foster · 2018. 12. 10. · DPT DPT DPT TJO...

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