Tensile Failure and the Griffith Tail
Learning objectives
- Define tensile strength as the small negative normal stress at which rock pulls apart
- Show that tensile strength is roughly one eighth to one twelfth of the unconfined compressive strength
- Follow the Griffith envelope as it curves from compression into a rounded tensile cutoff
- Connect tensile failure to the drilling-induced fractures that Part 6 reads as a stress compass
The Weak Side of the Diagram
Everything so far lived on the right of the Mohr diagram, in compression. But rock has a left side, and it is treacherously weak. Pull rock apart, put it into tension, and it fails at a stress far smaller than it survives in compression: the tensile strength , a small negative normal stress, typically only one eighth to one twelfth of the UCS. Our canon reservoir carries MPa against a UCS of 65, close to the one-in-eight rule. The asymmetry is physical: compression closes the microcracks that riddle every rock and makes them carry load, while tension pries them open, and a crack tip concentrates stress so fiercely that a modest far-field pull tears the rock along a plane perpendicular to it. Rock is a material that shrugs off being crushed and splits at the faintest stretch.
Push the stress circle left in the figure, toward and across the zero-normal-stress axis. The straight Coulomb line of the last two sections cannot follow it there; instead the failure envelope curves over into the Griffith tail, a parabola rooted in crack mechanics that closes the envelope at . When the circle's left edge reaches that cutoff, the rock fails in tension, splitting on the plane whose normal is the least principal stress. In this theory the uniaxial compressive strength comes out to eight times the tensile strength exactly, a clean statement of the asymmetry, and while real rocks scatter around the factor, the physical message is exact: cracks make rock strong under squeeze and fragile under pull.
Why the Weak Side Matters Downhole
Tensile failure is not a laboratory curiosity; it is a daily event in a wellbore. When drilling mud is heavy enough, the hoop stress at the borehole wall goes tensile at the azimuth of maximum horizontal stress and the rock splits into drilling-induced tensile fractures, thin axial cracks that image logs pick up cleanly. Because they open perpendicular to the least stress, their orientation is a direct compass for the stress field, and their appearance pins the mud weight against the tensile limit, both of which Part 6 turns into stress measurements. Hydraulic fracturing, in Part 7, is tensile failure done on purpose and at scale: pump hard enough to drive the wall into tension and the rock opens a fracture you can prop and produce through. The weak left side of the Mohr diagram, in other words, is where two of the most important operations in the subsurface do their work. The next section restores the compressive side's realism with a curved criterion, and then the end cap completes the failure surface.
References
- Griffith, A. A. (1921). The phenomena of rupture and flow in solids. Philosophical Transactions of the Royal Society A, 221, 163-198.
- Jaeger, J. C., Cook, N. G. W., & Zimmerman, R. W. (2007). Fundamentals of Rock Mechanics (4th ed.). Blackwell.
- Fjaer, E., Holt, R. M., Horsrud, P., Raaen, A. M., & Risnes, R. (2008). Petroleum Related Rock Mechanics (2nd ed.). Elsevier.