Factor of safety

The factor of safety (FS) of a slope is the ratio of the forces (or shear strength) resisting failure to the forces (or shear stress) driving failure along the potential failure surface.

$$FS = \frac{\text{resisting force (shear strength)}}{\text{driving force (shear stress)}}$$

For plane failure of a block of weight $W$ on a plane of dip $\psi_p$, area $A$, cohesion $c$ and friction angle $\phi$ (dry):

$$FS = \frac{cA + W\cos\psi_p\tan\phi}{W\sin\psi_p}$$

• $FS > 1$: stable; $FS = 1$: limiting equilibrium; $FS < 1$: failure.
• Design values are usually $FS \geq 1.3$ to $1.5$ for permanent slopes and about $1.2$ to $1.3$ for temporary slopes. Water and earthquake loads reduce the factor of safety.