Bearing Capacity Factor Dependent on Unit Weight for Local Shear Failure Calculator

Bearing Capacity Factor Formula:

\[ N_γ = \frac{q_{fc} - \left(\left(\frac{2}{3} \times C_s \times N_c\right) + (\sigma_s \times N_q)\right)}{0.5 \times \gamma \times B} \]

Ultimate Bearing Capacity (q_fc):

kPa

Cohesion of Soil (C_s):

kPa

Bearing Capacity Factor (N_c):

Effective Surcharge (σ_s):

kPa

Bearing Capacity Factor (N_q):

Unit Weight of Soil (γ):

kN/m³

Width of Footing (B):

Bearing Capacity Factor (N_γ):

1. What is Bearing Capacity Factor Dependent on Unit Weight?

Definition: This calculator determines the bearing capacity factor (N_γ) which accounts for the contribution of soil's unit weight to the ultimate bearing capacity in local shear failure conditions.

Purpose: It's essential for geotechnical engineers designing shallow foundations to ensure soil can support structural loads without shear failure.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ N_γ = \frac{q_{fc} - \left(\left(\frac{2}{3} \times C_s \times N_c\right) + (\sigma_s \times N_q)\right)}{0.5 \times \gamma \times B} \]

Where:

\( N_γ \) — Bearing capacity factor dependent on unit weight
\( q_{fc} \) — Ultimate bearing capacity in soil (kPa)
\( C_s \) — Cohesion of soil (kPa)
\( N_c \) — Bearing capacity factor dependent on cohesion (±5%)
\( \sigma_s \) — Effective surcharge (kPa)
\( N_q \) — Bearing capacity factor dependent on surcharge (±5%)
\( \gamma \) — Unit weight of soil (kN/m³)
\( B \) — Width of footing (m)

3. Importance of Bearing Capacity Factor

Details: Accurate calculation of N_γ is crucial for determining the safe bearing capacity of soil, preventing foundation failures, and optimizing foundation design.

4. Using the Calculator

Tips: Enter all required parameters. Default values are provided for N_c (9) and N_q (2.01) with ±5% tolerance. All values must be positive.

5. Frequently Asked Questions (FAQ)

Q1: What is local shear failure?
A: Local shear failure occurs when the soil fails only beneath the foundation with some soil resistance remaining at the sides.

Q2: Why are N_c and N_q given with ±5%?
A: These factors vary slightly based on soil conditions, so a 5% tolerance accounts for typical variations.

Q3: When would cohesion (C_s) be zero?
A: For cohesionless soils like sand, cohesion is typically zero.

Q4: How is effective surcharge determined?
A: It's the vertical stress from soil or other loads at the foundation base level.

Q5: What's a typical range for N_γ?
A: Values typically range from 0.1 to 2.0, depending on soil type and conditions.