Factor of Safety given Bearing Capacity Factor Calculator

Factor of Safety Formula:

\[ fs = \frac{(C_s \times N_c) + (\sigma_s \times (N_q - 1)) + (0.5 \times \gamma \times B \times N_\gamma)}{(q_{sa} - \sigma_s)} \]

Cohesion of Soil:

Bearing Capacity Factor (Cohesion):

Effective Surcharge:

kPa

Bearing Capacity Factor (Surcharge):

Unit Weight of Soil:

N/m³

Width of Footing:

Bearing Capacity Factor (Unit Weight):

Safe Bearing Capacity:

Factor of Safety:

1. What is Factor of Safety in Bearing Capacity?

Definition: The factor of safety is the ratio of the ultimate bearing capacity of soil to the safe bearing capacity. It accounts for uncertainties in soil properties and loading conditions.

Purpose: It ensures structural stability by providing a margin of safety against soil failure under applied loads.

2. How Does the Calculator Work?

The calculator uses Terzaghi's bearing capacity formula:

\[ fs = \frac{(C_s \times N_c) + (\sigma_s \times (N_q - 1)) + (0.5 \times \gamma \times B \times N_\gamma)}{(q_{sa} - \sigma_s)} \]

Where:

\( fs \) — Factor of Safety
\( C_s \) — Cohesion of Soil (Pa)
\( N_c \) — Bearing Capacity Factor (Cohesion)
\( \sigma_s \) — Effective Surcharge (kPa)
\( N_q \) — Bearing Capacity Factor (Surcharge)
\( \gamma \) — Unit Weight of Soil (N/m³)
\( B \) — Width of Footing (m)
\( N_\gamma \) — Bearing Capacity Factor (Unit Weight)
\( q_{sa} \) — Safe Bearing Capacity (Pa)

3. Importance of Factor of Safety Calculation

Details: Proper calculation prevents foundation failures, ensures structural integrity, and accounts for variability in soil properties and load estimations.

4. Using the Calculator

Tips: Enter all required parameters with appropriate units. The bearing capacity factors typically have ±5% variability. All values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: What is a typical factor of safety for foundations?
A: For buildings, typically 2.5-3.0; for temporary structures, 1.5-2.0 may be acceptable.

Q2: How do I determine the bearing capacity factors?
A: They depend on soil friction angle and can be found in geotechnical references or calculated using empirical formulas.

Q3: What if my denominator (qsa-σs) is zero or negative?
A: This indicates invalid input - safe bearing capacity must be greater than effective surcharge.

Q4: How accurate are these calculations?
A: Results are theoretical estimates - actual field conditions may vary. Always consult a geotechnical engineer.

Q5: Can I use this for deep foundations?
A: This formula is primarily for shallow foundations. Deep foundations require different analysis methods.