Byerlee's Law: Friction Without a Rock Name

Part 3, Part 3: Rock Strength and Failure

Learning objectives

Distinguish intact-rock failure from frictional sliding on a surface that already exists
State Byerlee's law: sliding friction near 0.85 below 200 MPa, then 50 plus 0.6 times normal stress above
Explain why mu near 0.6 is the crust's universal number, nearly independent of rock type
Recognize the clay-gouge exception, where smectite-rich faults slide at friction as low as 0.2

Making a Fault Versus Moving One

Coulomb, in the last section, described breaking intact rock, cohesion and all. But most of the crust is already broken: it is threaded with faults, joints, and bedding planes that failed long ago. Moving one of those costs no cohesion, only friction, and the astonishing empirical fact, established by James Byerlee in 1978 across dozens of rock types, is that the friction is very nearly the same for all of them. Sandstone, granite, gabbro, limestone: pile up their sliding data and it collapses onto two lines. Below about 200 MPa normal stress, $\tau = 0.85\,\sigma_n'$ n′; above it, $\tau = 50 + 0.6\,\sigma_n'$ n′ (MPa). Mineralogy, which dominates intact strength, barely matters once a surface exists. Friction is a property of surfaces in contact, not of the rock's name.

Drag the friction line through the data cloud in the figure. A single coefficient near 0.6 fits the whole reservoir-depth range, and this is the number the course adopts as the crust's working friction, the one that sets $q = 3.12$ and everything downstream. It is not an accident of one lab: it is why the stress states measured in deep wells worldwide cluster against a frictional-failure limit, as Part 5 will show, and why a fault optimally oriented in the canon stress field is already within a whisker of slipping. The crust, over geologic time, has faulted wherever it could until friction alone holds it, so friction is what we find.

The Exception That Proves the Rule

Byerlee's universality has one important escape clause, and toggling it in the figure drops the fit dramatically: clay gouge. Faults lined with smectite and other swelling clays slide at coefficients as low as 0.2 to 0.4, far below the Byerlee value, because the platy clay minerals shear as easily as wet mica. This is not a footnote. Weak clay-rich faults are exactly the ones that creep rather than lock, that seal reservoirs on one side and leak on the other, and that host the slow slip patterns seen on many subduction and basin-bounding faults. The course carries the crustal 0.6 as its default and states it every time, but the honest geomechanicist asks what a specific fault is made of before trusting the number, because a smectite fault reactivates at a quarter of the pressure a bare-rock fault needs, a factor of four that Part 9 will not let you forget.

References

Byerlee, J. (1978). Friction of rocks. Pure and Applied Geophysics, 116(4-5), 615-626.
Zoback, M. D. (2007). Reservoir Geomechanics. Cambridge University Press.
Jaeger, J. C., Cook, N. G. W., & Zimmerman, R. W. (2007). Fundamentals of Rock Mechanics (4th ed.). Blackwell.