Unit Weight of Soil given Factor of Safety and Safe Bearing Capacity Calculator

Unit Weight of Soil Formula:

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

Safe Bearing Capacity (q_sa):

Factor of Safety (fs):

Cohesion of Soil (C_s):

Bearing Capacity Factor (N_c):

Bearing Capacity Factor (N_q):

Depth of Footing (D):

Width of Footing (B):

Bearing Capacity Factor (N_γ):

Unit Weight of Soil (γ):

1. What is Unit Weight of Soil Calculator?

Definition: This calculator determines the unit weight of soil based on safe bearing capacity, factor of safety, soil cohesion, and various bearing capacity factors.

Purpose: It helps geotechnical engineers and construction professionals in foundation design and soil analysis.

2. How Does the Calculator Work?

The calculator uses the formula:

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

Where:

\( \gamma \) — Unit weight of soil (N/m³)
\( q_{sa} \) — Safe bearing capacity (Pa)
\( fs \) — Factor of safety (±5%)
\( C_s \) — Cohesion of soil (Pa)
\( N_c \) — Bearing capacity factor dependent on cohesion (±5%)
\( N_q \) — Bearing capacity factor dependent on surcharge (±5%)
\( D \) — Depth of footing (m)
\( B \) — Width of footing (m)
\( N_\gamma \) — Bearing capacity factor dependent on unit weight (±5%)

3. Importance of Unit Weight Calculation

Details: Accurate unit weight calculation is crucial for foundation design, slope stability analysis, and earthwork calculations.

4. Using the Calculator

Tips: Enter all required parameters. Default values are provided for common scenarios. Fields marked with ±5% indicate typical variability ranges.

5. Frequently Asked Questions (FAQ)

Q1: What is a typical factor of safety for foundations?
A: Common values range from 2.5 to 3.5, with 2.8 being a typical default.

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

Q3: What if my soil has no cohesion?
A: For cohesionless soils, simply enter 0 for cohesion (C_s).

Q4: Why is there a ±5% range for some factors?
A: These factors often have inherent variability in real-world conditions.

Q5: How does footing depth affect the calculation?
A: Deeper footings generally increase the denominator, resulting in lower required unit weight for the same bearing capacity.