Bearing Capacity Factor Dependent on Surcharge for Rectangular Footing given Shape Factor Calculator

Bearing Capacity Factor Formula:

\[ N_q = \frac{q_{fc} - \left( (C \times N_c \times (1 + 0.3 \times \frac{B}{L})) + (0.5 \times \gamma \times B \times N_\gamma \times (1 - 0.2 \times \frac{B}{L})) \right)}{\sigma_s} \]

Ultimate Bearing Capacity (q_fc):

kPa

Cohesion (C):

kPa

Bearing Capacity Factor (N_c):

Width of Footing (B):

Length of Footing (L):

Unit Weight of Soil (γ):

kN/m³

Bearing Capacity Factor (N_γ):

Effective Surcharge (σ_s):

kPa

Bearing Capacity Factor (N_q):

1. What is Bearing Capacity Factor Dependent on Surcharge?

Definition: This calculator determines the bearing capacity factor (N_q) for rectangular footings considering shape factors, which accounts for the effect of surcharge on the soil's bearing capacity.

Purpose: It helps geotechnical engineers and foundation designers evaluate the bearing capacity of rectangular footings under various soil conditions.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ N_q = \frac{q_{fc} - \left( (C \times N_c \times (1 + 0.3 \times \frac{B}{L})) + (0.5 \times \gamma \times B \times N_\gamma \times (1 - 0.2 \times \frac{B}{L})) \right)}{\sigma_s} \]

Where:

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

Explanation: The formula accounts for both cohesion and weight components of bearing capacity, adjusted by shape factors for rectangular footings.

3. Importance of Bearing Capacity Factor Calculation

Details: Proper calculation ensures safe foundation design by considering how surcharge loads affect the soil's ability to support structural loads.

4. Using the Calculator

Tips: Enter all required parameters. Note that bearing capacity factors (N_c and N_γ) have ±5% uncertainty. All values must be > 0.

5. Frequently Asked Questions (FAQ)

Q1: Why is there a ±5% uncertainty for N_c and N_γ?
A: These factors are empirically derived and can vary based on soil conditions and testing methods.

Q2: What's a typical value for N_q?
A: Values typically range from 10 to 40 for most soils, but can be higher for dense or cohesive soils.

Q3: When would I need to calculate N_q specifically for rectangular footings?
A: When designing rectangular foundations where the length-to-width ratio affects bearing capacity.

Q4: How do I determine the effective surcharge (σ_s)?
A: It's the vertical pressure from any additional loads above the foundation level, including overburden soil.

Q5: Does this calculation account for water table effects?
A: No, you would need to adjust the unit weight (γ) if the water table is present.