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

Formula:

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

Ultimate Bearing Capacity (q_fc):

kPa

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):

Length of Footing (L):

Cohesion in Soil (C):

kPa

Bearing Capacity Factor (N_c):

1. What is Bearing Capacity Factor Dependent on Cohesion?

Definition: This is a dimensionless factor that relates the bearing capacity of soil to its cohesion component for rectangular footings, considering shape factors.

Purpose: It helps geotechnical engineers determine the bearing capacity of rectangular foundations considering the soil's cohesive strength and footing geometry.

2. How Does the Calculator Work?

The calculator uses the formula:

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

Where:

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

3. Importance of This Calculation

Details: Proper calculation ensures safe foundation design by accounting for soil cohesion and rectangular footing shape effects on bearing capacity.

4. Using the Calculator

Tips: Enter all required parameters. Note that bearing capacity factors (N_q and N_γ) have ±5% tolerance. All values must be positive.

5. Frequently Asked Questions (FAQ)

Q1: Why are N_q and N_γ given with ±5% tolerance?
A: These factors are empirically derived and typically have about 5% variation in practice.

Q2: What's a typical range for N_c?
A: For cohesive soils, N_c typically ranges between 5 and 37 depending on soil conditions.

Q3: How does footing shape affect the result?
A: The (B/L) terms account for rectangular footing effects - the factor increases as the footing becomes more square.

Q4: What if my footing is square?
A: For square footings (B = L), the shape factors simplify to 0.8 and 1.3 respectively.

Q5: How accurate is this calculation?
A: This provides a theoretical value - actual field conditions may vary due to soil heterogeneity and other factors.