Bearing Capacity Factor Dependent on Surcharge for Local Shear Failure Calculator

Formula:

\[ N_q = \frac{q_f - \left(\frac{2}{3} \times C_s \times N_c + 0.5 \times \gamma \times B \times N_\gamma\right)}{\sigma_s} \]

Ultimate Bearing Capacity (qf):

kPa

Cohesion of Soil (Cs):

kPa

Bearing Capacity Factor (Nc):

Unit Weight of Soil (γ):

kN/m³

Width of Footing (B):

Bearing Capacity Factor (Nγ):

Effective Surcharge (σs):

kPa

Bearing Capacity Factor (Nq):

1. What is Bearing Capacity Factor Dependent on Surcharge?

Definition: This factor (Nq) quantifies the contribution of surcharge to the ultimate bearing capacity of shallow foundations under local shear failure conditions.

Purpose: It's essential for geotechnical engineers to calculate the safe bearing capacity of foundations in cohesive-frictional soils.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ N_q = \frac{q_f - \left(\frac{2}{3} \times C_s \times N_c + 0.5 \times \gamma \times B \times N_\gamma\right)}{\sigma_s} \]

Where:

\( N_q \) — Bearing capacity factor dependent on surcharge
\( q_f \) — Ultimate bearing capacity (kPa)
\( C_s \) — Cohesion of soil (kPa)
\( N_c \) — Bearing capacity factor dependent on cohesion
\( \gamma \) — Unit weight of soil (kN/m³)
\( B \) — Width of footing (m)
\( N_\gamma \) — Bearing capacity factor dependent on unit weight
\( \sigma_s \) — Effective surcharge (kPa)

3. Importance of Nq Calculation

Details: Accurate Nq values are crucial for designing safe foundations that account for both soil strength and surface loads.

4. Using the Calculator

Tips: Enter all required parameters. Default values are provided for Nc (9) and Nγ (1.6) with ±5% accuracy. All other values must be > 0.

5. Frequently Asked Questions (FAQ)

Q1: What is local shear failure?
A: It's a soil failure mode where significant deformation occurs before reaching maximum shear strength, common in loose soils.

Q2: Why the 2/3 factor for cohesion?
A: This reduction accounts for the lower shear resistance in local shear failure compared to general shear failure.

Q3: How accurate are the ±5% values?
A: These represent typical variations in bearing capacity factors based on soil conditions and empirical correlations.

Q4: When would Nγ be zero?
A: For purely cohesive soils (φ=0), Nγ is typically zero as unit weight doesn't contribute to bearing capacity.

Q5: What's a typical Nq value range?
A: Nq typically ranges from 1 to 100+ depending on soil friction angle and failure mode.