Unit Weight of Soil given Ultimate Bearing Capacity for Rectangular Footing Calculator

Unit Weight of Soil Formula:

\[ \gamma = \frac{q_{fc} - \left( \left( C \times N_c \right) \times \left( 1 + 0.3 \times \left( \frac{B}{L} \right) \right) + \left( \sigma_s \times N_q \right) \right)}{0.4 \times B \times N_\gamma} \]

Ultimate Bearing Capacity (q_fc):

kPa

Cohesion in Soil (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):

Tolerance:

Unit Weight of Soil (γ):

1. What is Unit Weight of Soil given Ultimate Bearing Capacity?

Definition: This calculator determines the unit weight of soil based on the ultimate bearing capacity of a rectangular footing and other soil parameters.

Purpose: It helps geotechnical engineers and construction professionals estimate soil properties for foundation design.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

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

3. Importance of Unit Weight Calculation

Details: Accurate unit weight estimation is crucial for foundation design, slope stability analysis, and earthwork calculations.

4. Using the Calculator

Tips: Enter all required parameters including the tolerance percentage (default ±5%). All bearing capacity factors must be > 0.

5. Frequently Asked Questions (FAQ)

Q1: What are typical values for bearing capacity factors?
A: Common values are N_c ≈ 9, N_q ≈ 2.01, and N_γ ≈ 1.6, but these vary with soil type and friction angle.

Q2: Why include a tolerance percentage?
A: Soil properties can vary, so the tolerance provides a realistic range for the unit weight.

Q3: What if my soil has no cohesion (C=0)?
A: Simply enter 0 for cohesion - the calculation will still work for cohesionless soils.

Q4: How do I determine ultimate bearing capacity?
A: Use field tests (plate load test) or empirical correlations based on soil properties.

Q5: What's a typical unit weight range for soils?
A: Most soils range from 16-22 kN/m³, with organic soils lower and dense gravels higher.