Slope stability in geotechnical engineering — the factor of safety against sliding along a potential slip surface is defined as which ratio?

Introduction / Context:
Slope stability analyses in civil engineering compare available resistance to the tendency for sliding along a potential failure surface. The comparison is made through a factor of safety, which can be expressed either in terms of overall shear strength mobilized versus shear stress demanded, or, in special cases, as the ratio of available material parameters (such as cohesion) to those required for equilibrium.

Given Data / Assumptions:

• Slope is analyzed for limit equilibrium along a candidate slip surface.
• Soil obeys a Mohr–Coulomb type strength envelope with parameters c and phi.
• Stresses and pore pressures are evaluated consistently for the slip surface.

Concept / Approach:

By definition, factor of safety (FS) = resisting capacity / driving demand. In general terms, FS = shear strength / shear stress along the surface. For special idealized cases (e.g., purely cohesive soil with phi = 0), the same concept reduces to FS = actual cohesion / cohesion required for limiting equilibrium. Both descriptions are consistent because they are merely different parameterizations of the same ratio of available to required resistance.

Step-by-Step Solution:

Verification / Alternative check:

Alternative limit-equilibrium methods (Swedish circle, Bishop simplified, Morgenstern–Price) all reduce to a ratio of available to required shear components; numerical values of FS should agree within method assumptions.

Why Other Options Are Wrong:

Option (a) alone is not universally applicable; it is a special case. Option (b) alone is correct but the question recognizes both equivalent forms; hence (d) is most complete. Option (c) and the unrelated ratio in (e) do not represent the standard definition of FS.

Common Pitfalls:

Mixing total and effective stresses; ignoring pore pressure variations; treating c and phi as fully mobilized without checking stability conditions.

Final Answer:

both (a) and (b)