Rock strength envelope (${\sigma }_y(z)=\min \{{\sigma }_{\mathrm{friction}}(z),{\sigma }_{\mathrm{creep}}(z)\}$)

A depth-dependent estimate of the differential stress a rock column can sustain at a specified strain rate, composition, thermal structure and fluid state. In a simple competing-mechanism model, failure occurs by whichever of frictional sliding and ductile material creep requires the lower stress, giving the displayed lower envelope.

Effective confining pressure generally increases frictional strength with depth. In contrast, a power-law creep model $\dot{ϵ}=A{\sigma }^n\exp [-(Q+P{V}^{\ast })/(RT)]$ gives ${\sigma }_{\mathrm{creep}}=(\dot{ϵ}/A{)}^{1/n}\exp [(Q+P{V}^{\ast })/(nRT)]$. At fixed strain rate, the rise of temperature along a geothermal gradient generally lowers the required creep stress. Their crossing is a brittle-ductile transition, while composition changes at the Moho can produce additional peaks. A rock strength envelope is not uniquely determined by depth or by the labels “continental” and “oceanic”.