Stress on a Fault

Part 9, Part 9: Faults and Induced Seismicity

Learning objectives

Resolve the stress tensor onto a fault plane into normal and shear tractions
Define the slip tendency, shear over effective normal stress, and read it on the Mohr circle
Show that orientation controls slip: the canon dip-30 fault is poorly oriented (Ts 0.35), an optimal 60 degree dip is critical (Ts 0.58)
Connect the optimally-oriented fault's slip tendency to the field's mobilized friction

Traction on a Plane

Part 8 built the stress model; now put a fault in it. A fault is a plane, and the stress tensor resolves onto that plane into two tractions: the normal stress $\sigma_n$ n pressing it shut, and the shear stress $\tau$ trying to slide it. Whether it slips is a Coulomb question, the same criterion as intact rock but with no cohesion: the fault slides when $\tau$ reaches $\mu$ times the effective normal stress $\sigma_n'$ n′. The ratio $T_s = \tau / \sigma_n'$ , the slip tendency, measures how close a fault sits to slipping, from zero at no shear up to $\mu$ on the verge.

The figure resolves the Ogbon-1 stress onto a fault and plots it on the Mohr circle. Rotate the dip. The canon fault, dipping 30 degrees, sits low on the circle at $T_s = 0.35$ s=0.35, well below the friction line: poorly oriented, hard to slip, needing 11.3 MPa of added pressure to fail. Rotate it toward 60 degrees and the point climbs until it nearly touches the friction line at $T_s = 0.58$ s=0.58, an optimally-oriented fault on the verge, needing under half a MPa. Same stress, same rock, a different plane, and the difference between inert and dangerous.

Orientation Is Everything

This is the lesson the Mohr circle makes visual: fault reactivation is not about the stress alone but the stress and the orientation. A fault cutting the field at the wrong angle can sit inert through the whole life of the field; a fault at the optimal angle, about 60 degrees dip in this normal-faulting regime, is one nudge from slipping. And there is a clean tie-back: the optimally-oriented fault's slip tendency, 0.58, is exactly the mobilized friction of the field from Section 8.6. The mobilized friction is the slip tendency of the most dangerous plane the stress state allows. Every stress state carries a worst-case fault built into it, whether or not that fault happens to exist in the rock.

The Fault That Matters

So which fault matters? The one nearest optimal orientation that actually exists in the field. Mapping faults from seismic, the work of the 3D Seismic Interpretation course, and reading their dips tells you which are dangerous and which are safe. A poorly-oriented fault is a spectator; a well-oriented one is a hazard the moment pressures change. The next section turns this into a map, the slip-tendency stereonet, where every possible orientation is colored by how close it sits to slipping, so a field's whole fault population can be judged at a glance.

References

Morris, A., Ferrill, D. A., & Henderson, D. B. (1996). Slip-tendency analysis and fault reactivation. Geology, 24(3), 275-278.
Jaeger, J. C., Cook, N. G. W., & Zimmerman, R. W. (2007). Fundamentals of Rock Mechanics (4th ed.). Blackwell.
Zoback, M. D. (2007). Reservoir Geomechanics (ch. 5). Cambridge University Press.