Compaction and the End Cap

The Other Way Rock Fails

Everything in this part so far has been about shear failure: a rock breaking on a plane and sliding. But there is a second, quieter way for rock to fail, and it does not involve sliding at all. Squeeze a weak, high-porosity rock, chalk, a young unconsolidated sand, diatomite, under high enough mean stress and its pore framework simply collapses. Grains crush at their contacts, the pore space caves in, porosity drops, and the rock compacts permanently. There is no through-going fracture, no slip plane; the rock yields in bulk. This is compactive or pore-collapse failure, and for the reservoirs that suffer it, it is far more consequential than shear.

To see both modes at once, geomechanics uses the p-q diagram: mean effective stress $p'$ across the horizontal, and differential (shear) stress $q = \sigma_1 - \sigma_3$ up the vertical. Shear failure is a rising line on the left, the Coulomb criterion in new axes; the more the rock is sheared, the sooner it fails. But that line cannot rise forever, because at high mean stress the rock collapses in compaction before it can shear. Closing the yield surface on the right is the end cap, an ellipse that caps how much mean stress the frame can carry.

Drive a stress path across the p-q diagram in the figure. Cross the shear line on the left and the rock fails brittly, on a plane, as the last three sections described. Cross the cap on the right and it fails in compaction, and something new happens: the cap grows. Pore collapse hardens the rock, packing the grains tighter so the frame carries more mean stress next time. That hardening, the cap expanding as the rock compacts, is why a chalk can keep compacting steadily under production rather than failing all at once, and it is the constitutive heart of the Ekofisk subsidence of Part 0.

Which Rocks, and Why It Closes the Part

The end cap matters only for weak, porous rocks: strong low-porosity rock shears long before its mean stress reaches any cap, so for granite and tight sandstone the cap sits so far right it never matters and Coulomb alone suffices. But for the chalks, young sands, and high-porosity carbonates that host many reservoirs, the cap is the failure mode that governs, and depleting such a reservoir walks its stress state, effective mean stress rising as pore pressure falls, straight toward the cap. That is the mechanical sentence behind Ekofisk's six meters and Wilmington's nine: not a fault, not a fracture, but a pore framework collapsing under its own increased load. With shear on the left, tension on the far left, and the compaction cap on the right, the failure surface is now complete, and Part 3 closes. Part 4 turns to the pore pressure whose changes drive stress states across all of these limits: predicting it before the bit arrives.

References

• Wong, T.-f., David, C., & Zhu, W. (1997). The transition from brittle faulting to cataclastic flow in porous sandstones. Journal of Geophysical Research, 102(B2), 3009-3025.
• Schofield, A., & Wroth, P. (1968). Critical State Soil Mechanics. McGraw-Hill.
• Fjaer, E., Holt, R. M., Horsrud, P., Raaen, A. M., & Risnes, R. (2008). Petroleum Related Rock Mechanics (2nd ed.). Elsevier.