Bearing Capacity Factor Dependent on Unit Weight given Dimension of Footing Calculator

Formula Used:

\[ N_γ = \frac{q_{fc} - \left(\left(\frac{2}{3} \times C \times N_c\right) + \left(γ \times D_{footing} \times N_q\right)\right)}{0.5 \times γ \times B} \]

Ultimate Bearing Capacity in Soil (q_fc):

Cohesion in Soil (C):

Bearing Capacity Factor (N_c):

Unit Weight of Soil (γ):

N/m³

Depth of Footing (D_footing):

Bearing Capacity Factor (N_q):

Width of Footing (B):

Bearing Capacity Factor (N_γ):

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

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

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:

\[ N_γ = \frac{q_{fc} - \left(\left(\frac{2}{3} \times C \times N_c\right) + \left(γ \times D_{footing} \times N_q\right)\right)}{0.5 \times γ \times B} \]

Where:

\( N_γ \) — Bearing capacity factor dependent on unit weight
\( q_{fc} \) — Ultimate bearing capacity in soil (Pa)
\( C \) — Cohesion in soil (Pa)
\( N_c \) — Bearing capacity factor dependent on cohesion (±5%)
\( γ \) — Unit weight of soil (N/m³)
\( D_{footing} \) — Depth of footing (m)
\( N_q \) — Bearing capacity factor dependent on surcharge (±5%)
\( B \) — Width of footing (m)

3. Importance of Bearing Capacity Calculation

Details: Proper calculation ensures foundation stability, prevents settlement issues, and guarantees structural safety.

4. Using the Calculator

Tips: Enter all required parameters. The bearing capacity factors (N_c and N_q) typically have ±5% variability.

5. Frequently Asked Questions (FAQ)

Q1: What are typical values for N_c and N_q?
A: N_c ranges from 5.14 to 37.2, N_q from 1 to 48.9, depending on soil friction angle.

Q2: Why is there a ±5% variation on some factors?
A: These factors are empirically derived and can vary slightly based on soil conditions.

Q3: How does unit weight affect bearing capacity?
A: Higher unit weight generally increases bearing capacity for deeper foundations.

Q4: What's the difference between N_c, N_q, and N_γ?
A: They account for cohesion, surcharge, and unit weight contributions respectively.

Q5: When would I need this calculation?
A: When designing shallow foundations in cohesive-frictional soils.