= Rock strength envelope
{title2=$\sigma_y(z)=\min\{\sigma_{\rm friction}(z),\sigma_{\rm creep}(z)\}$}
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 $\dot\epsilon=A\sigma^n\exp[-(Q+PV^*)/(RT)]$ gives $\sigma_{\rm creep}=(\dot\epsilon/A)^{1/n}\exp[(Q+PV^*)/(nRT)]$. 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”.
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