Bearing Capacity Factor Dependent on Weight given Passive Earth Pressure Coefficient Calculator

Formula:

\[ N_{\gamma} = \frac{\tan(\phi)}{2} \times \left( \frac{K_P}{\cos^2(\phi)} - 1 \right) \]

Bearing Capacity Factor (N_γ):

1. What is Bearing Capacity Factor Dependent on Weight?

Definition: This is a dimensionless factor used in geotechnical engineering to calculate the ultimate bearing capacity of soil, considering the unit weight of the soil.

Purpose: It helps engineers determine the safe load that can be applied to a foundation without causing shear failure in the soil.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ N_{\gamma} = \frac{\tan(\phi)}{2} \times \left( \frac{K_P}{\cos^2(\phi)} - 1 \right) \]

Where:

\( N_{\gamma} \) — Bearing capacity factor dependent on unit weight
\( \phi \) — Angle of shearing resistance (degrees)
\( K_P \) — Coefficient of passive earth pressure (±5%)

Explanation: The formula relates the bearing capacity factor to the soil's shear strength (φ) and the passive earth pressure coefficient (K_P).

3. Importance of Bearing Capacity Factor

Details: Accurate calculation of N_γ is crucial for designing safe foundations, retaining walls, and other geotechnical structures.

4. Using the Calculator

Tips:

Enter the angle of shearing resistance in degrees
Enter the coefficient of passive pressure (typically between 1.0 and 10.0)
The coefficient has ±5% tolerance as indicated

5. Frequently Asked Questions (FAQ)

Q1: What is a typical range for φ in soils?
A: For common soils, φ ranges from 25° (loose sand) to 45° (dense gravel).

Q2: How is K_P determined?
A: K_P is calculated as (1 + sinφ)/(1 - sinφ) for cohesionless soils.

Q3: Why the ±5% tolerance on K_P?
A: Soil properties can vary, so a 5% tolerance accounts for measurement uncertainties.

Q4: What if my φ is 0°?
A: The formula would give N_γ = 0, which is correct for purely cohesive soils (φ=0).

Q5: How does N_γ affect foundation design?
A: Higher N_γ values indicate greater bearing capacity from soil weight contribution.