reservoir geomecanics

95 Rock failure in compression, tension and shear
a. 500
b.
450
500
450
400
400
s 3 = 90 MPa
350
s 3
= 90 MPa
350
s 1 (MPa)
300
250
200
150
100
50
s 3
= 0 MPa
s 1 = s 2
s 3
= 30 MPa
s 3
= 60 MPa
Mohr Coulomb criterion
C 0 = 60 MPa
m i = 0.6
s 1 (MPa)
300
250
200
150
100
50
s 3 = 0 MPa
s 1 = s 2
s 3 = 30 MPa
s 3
= 60 MPa
Hoek and Brown criterion
C 0 = 60 MPa
m = 16
s = 1
0
0 50 100 150 200 250 300 350 400 450 500
s 2 (MPa)
0
0 50 100 150 200 250 300 350 400 450 500
s 2 (MPa)
c. 500
d.
450
500
450
400
s 3 = 90 MPa
400
350
350
s 3
= 90 MPa
s 1 (MPa)
300
250
200
150
s 1 = s 2
s 3
= 30 MPa
s 3 = 60 MPa
s 1
(MPa)
300
250
200
150
s 1
= s 2
s 3
= 30 MPa
s 3
= 60 MPa
100
50
s 3
= 0 MPa
Modified Lade criterion
C 0 = 60 MPa
m i = 0.6
0
0 50 100 150 200 250 300 350 400 450 500
s 2 (MPa)
100
50
s 3 = 0 MPa
Modified Wiebols and Cook criterion
C 0 = 60 MPa
m i = 0.6
0
0 50 100 150 200 250 300 350 400 450 500
s 2 (MPa)
e.
500
450
400
s 3 = 30 MPa
350
s 1 (MPa)
300
250
200
s 1 = s 2
s 3
= 0 MPa
150
s 3
= 30 MPa
100
Inscribed Drucker–Prager criterion
Circumscribed Drucker–Prager criterion
50 s 3
= 0 MPa
C 0 = 60 MPa
m i = 0.6
0
0 50 100 150 200 250 300 350 400 450 500
s 2 (MPa)
Figure 4.7. To observe how different compressive failure criteria define the importance of the
intermediate principal stress, σ 2 ,onrock strength, for σ 3 = 0, 30, 60 and 90 MPa and C 0 =
60 MPa and µ i = 0.6, we show the curves corresponding to (a) linearized Mohr–Coulomb
criterion; (b) Hoek–Brown criterion (m = 16 and s = 1); (c) modified Lade criteria; (d) modified
Wiebols–Cook criterion; (e) inscribed and circumscribed Drucker–Prager criteria (shown for only
for σ 3 = 0 and 30 MPa for simplicity). After Colmenares and Zoback (2002). Reprinted with
permission of Elsevier.