Skempton's B and Undrained Response

Part 3, Part 2: Strain, Elasticity, and the Poroelastic Rock

Learning objectives

Distinguish drained from undrained loading by whether the fluid has time to escape
State Skempton's B: the pore-pressure rise is B times the mean-stress step under undrained loading
Read the transient: an undrained pressure jump that then decays as the rock drains on its own clock
Explain why a saturated, low-permeability rock briefly feels no change in effective stress when loaded fast

Fast Load, Trapped Fluid

Everything so far assumed the pore fluid could come and go freely, the drained case, where pore pressure is set by whatever the far field dictates. Load a saturated rock faster than its fluid can escape, and a different regime rules. The fluid, having nowhere to go, takes up part of the new load itself, and its pressure jumps. Skempton's coefficient meters the jump: under an undrained change in mean stress $\Delta\sigma_m$ m, the pore pressure rises by $\Delta P_p = B\,\Delta\sigma_m$ , with $B$ running from near 1 in soft, fully saturated rock to near 0 when the pores hold compressible gas or the frame is stiff. A little gas is dramatic: even a few percent gas saturation drops B toward zero, because a compressible bubble absorbs the squeeze the water could not.

Step the mean stress in the figure and watch two clocks. Instantly, undrained, the pore pressure jumps by $B\,\Delta\sigma_m$ m and, because total stress and pore pressure rose nearly together, the effective stress barely moves: the rock is loaded but not yet squeezed in the way that matters. Then the pressure bleeds off on the rock's drainage timescale, the fluid finally escapes, and the effective stress climbs to its drained value. The transient dip in effective stress is the whole point, and it is why saturated slopes fail during rapid loading, why undrained triaxial tests read differently from drained ones, and why a fault can be nudged by a stress change that never touched its far-field pressure.

Two Clocks, One Rock

This is the same poroelastic theory as Biot's alpha, asking the complementary question. Alpha said: given a pore pressure, how much does it offset stress? Skempton's B says: given a stress change, how much pore pressure does it create? The drainage time that separates the two regimes scales with permeability and the square of the drainage distance, which is why a lab plug equilibrates in minutes, a reservoir compartment in years, and a thick shale essentially never, staying undrained on any human timescale. That last fact, undrained shale, is exactly what seals overpressure into the compartments Part 4 will predict, and what lets the storm-wave loading of the seafloor register in the pore pressure of the mud below. Fast is undrained, slow is drained, and knowing which clock governs is half of applied poroelasticity.

References

Skempton, A. W. (1954). The pore-pressure coefficients A and B. Geotechnique, 4(4), 143-147.
Wang, H. F. (2000). Theory of Linear Poroelasticity. Princeton University Press.
Fjaer, E., Holt, R. M., Horsrud, P., Raaen, A. M., & Risnes, R. (2008). Petroleum Related Rock Mechanics (2nd ed.). Elsevier.