Factor of Safety given Sum of Tangential Component Calculator

Factor of Safety Formula:

\[ FS = \frac{(c \times L) + (\Sigma N \times \tan(\phi))}{\Sigma T} \]

Unit Cohesion (c):

kPa

Length of Slip Arc (L):

Sum of Normal Components (ΣN):

Angle of Internal Friction (φ):

Sum of Tangential Components (ΣT):

Factor of Safety (FS):

Definition: The Factor of Safety (FS) is a measure of the stability of a slope, calculated as the ratio of resisting forces to driving forces.

Purpose: It helps geotechnical engineers assess the risk of slope failure and design stable earth structures.

The calculator uses the formula:

\[ FS = \frac{(c \times L) + (\Sigma N \times \tan(\phi))}{\Sigma T} \]

Where:

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

Details: A FS > 1 indicates stable conditions, while FS ≤ 1 suggests potential failure. Typical design values range from 1.3 to 1.5.

Tips: Enter all required parameters. The angle of friction and tangential components include ±5% uncertainty ranges.

Q1: What is a safe Factor of Safety value?
A: Typically 1.3-1.5 for slopes, but depends on consequences of failure and regulations.

Q2: Why is there a ±5% range on some inputs?
A: Soil properties naturally vary, and measurements have inherent uncertainty.

Q3: How do I determine the angle of internal friction?
A: Through laboratory tests like direct shear or triaxial tests on soil samples.

Q4: What if I get FS < 1?
A: The slope is unstable and requires remediation (flattening, reinforcement, or drainage).

Q5: Can this calculator be used for all slope types?
A: It's most appropriate for circular failure surfaces in cohesive-frictional soils.