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Earth and Space Sciences · 术语表

什么是 Coulomb failure criterion？

又称： cohesion · coefficient of internal friction · angle of internal friction

Definition 16.13 University Earth and Space Sciences — Year 1 · 第 16 章 — Stress, Strain and Rheology

A rock obeys the Coulomb failure criterion if a plane through it breaks, or an existing fracture slips, as soon as on that plane

\tau = C + \mu\,\sigma_n' , \qquad \sigma_n' = \sigma_n - P ,

where $C \ge 0$ is the cohesion of the rock, $\mu$ its coefficient of internal friction and $\phi = \arctan\mu$ its angle of internal friction.

Mohr’s circle in effective stresses and a Coulomb envelope. A plane whose normal makes the angle with _1 is the point at the angle 2 from the _1 end (orange). The circle drawn just touches the envelope: the plane at the point of contact breaks, its normal at = 45 + /2 from _1, the radius there perpendicular to the envelope. Drawn to scale for C = 10\, MPa, = 0.6 and _3' = 20\, MPa, which give _1' = 97.7\, MPa. — Mohr’s circle in effective stresses and a Coulomb envelope. A plane whose normal makes the angle $\theta$ with $\sigma_1$ is the point at the angle $2\theta$ from the $\sigma_1$ end (orange). The circle drawn just touches the envelope: the plane at the point of contact breaks, its normal at $\theta = 45{}^{\circ} + \phi/2$ from $\sigma_1$ , the radius there perpendicular to the envelope. Drawn to scale for $C = 10\,\mathrm{MPa}$ , $\mu = 0.6$ and $\sigma_3' = 20\,\mathrm{MPa}$ , which give $\sigma_1' = 97.7\,\mathrm{MPa}$ .

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