What is the equation for calculating the factor of safety of a slope?

The equation for calculating the factor of safety of a slope is fundamentally related to the forces acting on the slope material and their ability to resist failure. The correct answer captures the essential components involved in assessing slope stability.

In this context, the factor of safety is defined as the ratio of the resisting forces (cohesion and frictional forces, which are influenced by normal stress) to the driving forces (shear stress acting on the slope). Cohesion reflects the internal strength of the soil or rock, while the frictional resistance depends on the angle of internal friction and the normal stress acting perpendicular to the plane of potential failure.

By combining these elements, the equation shows how stability can be evaluated: resisting forces are primarily represented by the sum of cohesion and the frictional forces, which is derived from the normal stress multiplied by the tangent of the friction angle. The denominator, shear stress, represents the forces trying to cause the slope to fail.

This formulation illustrates that when the factor of safety is greater than 1, the slope is deemed stable; when it is less than 1, instability and potential failure are a concern. Understanding this relationship is critical for geologists and engineers when evaluating terrain for construction, landslide risk, and other geological assessments