Unit Weight of Soil for Rectangular Footing given Shape Factor Calculator

Unit Weight of Soil Formula:

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

Ultimate Bearing Capacity (q_fc):

kPa

Cohesion (C):

kPa

Bearing Capacity Factor (N_c):

Width of Footing (B):

Length of Footing (L):

Effective Surcharge (σ_s):

kPa

Bearing Capacity Factor (N_q):

Bearing Capacity Factor (N_γ):

Unit Weight of Soil (γ):

1. What is Unit Weight of Soil for Rectangular Footing?

Definition: This calculator determines the unit weight of soil required to support a rectangular footing with given bearing capacity factors and shape factors.

Purpose: It helps geotechnical engineers and construction professionals design stable foundations by calculating the necessary soil properties.

2. How Does the Calculator Work?

The calculator uses the formula:

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

Where:

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

Explanation: The formula accounts for the shape of the footing through the B/L ratio terms.

3. Importance of Unit Weight Calculation

Details: Accurate soil unit weight calculation ensures proper foundation design, preventing settlement or failure of structures.

4. Using the Calculator

Tips: Enter all required parameters. Bearing capacity factors typically have ±5% uncertainty. Width and length must be > 0.

5. Frequently Asked Questions (FAQ)

Q1: Why are bearing capacity factors given with ±5%?
A: These factors are empirically determined and typically have about 5% variability in practical applications.

Q2: How do I determine the bearing capacity factors?
A: They depend on soil friction angle. Use standard geotechnical tables or our Bearing Capacity Factor Calculator.

Q3: What if my footing is square?
A: For square footings (B = L), the shape factors simplify to 1.3 and 0.8 respectively.

Q4: How does footing shape affect the result?
A: Rectangular footings typically have higher bearing capacity than square ones of the same area.

Q5: What are typical values for unit weight of soil?
A: Most soils range from 16-22 kN/m³, but organic soils can be lower and dense gravels higher.