Factor of Safety for Cohesive Soil given Saturated Unit Weight Calculator

Factor of Safety Formula:

\[ F_s = \frac{c' + (\gamma' \times z \times \tan(\phi) \times \cos^2(i))}{\gamma_{sat} \times z \times \cos(i) \times \sin(i)} \]

Effective Cohesion (c'):

Submerged Unit Weight (γ'):

N/m³

Depth of Prism (z):

Angle of Internal Friction (φ):

Inclination Angle (i):

Saturated Unit Weight (γ_sat):

N/m³

Safety Factor (±5%):

Factor of Safety (F_s):

Definition: The factor of safety (F_s) is a measure of how much stronger a soil slope is than it needs to be to resist failure.

Purpose: It helps geotechnical engineers assess the stability of slopes in cohesive soils under saturated conditions.

The calculator uses the formula:

\[ F_s = \frac{c' + (\gamma' \times z \times \tan(\phi) \times \cos^2(i))}{\gamma_{sat} \times z \times \cos(i) \times \sin(i)} \]

Where:

Explanation: The numerator represents resisting forces (cohesion and friction), while the denominator represents driving forces.

Details: Proper F_s calculation prevents slope failures, ensures structural stability, and helps design safe earthworks.

Tips: Enter all required parameters. Angles should be in degrees. The safety factor (±5%) can be adjusted for design requirements.

Q1: What is a typical acceptable factor of safety?
A: For slopes, F_s ≥ 1.5 is typically required, but this depends on project requirements.

Q2: How does saturation affect slope stability?
A: Saturation increases unit weight and reduces shear strength, decreasing stability.

Q3: What if I get F_s < 1?
A: This indicates unstable conditions - the slope would likely fail.

Q4: How do I determine effective cohesion?
A: Through laboratory tests like triaxial or direct shear tests.

Q5: Why include ±5% safety factor?
A: This accounts for uncertainties in soil parameters and calculation methods.