Bearing Capacity Factor Dependent on Cohesion given Dimension of Footing Calculator

Bearing Capacity Factor Formula:

\[ N_c = \frac{q_{fc} - ((\gamma \times D_{footing} \times N_q) + (0.5 \times \gamma \times B \times N_\gamma))}{(2/3) \times C} \]

Ultimate Bearing Capacity (q_fc):

kPa

Unit Weight of Soil (γ):

kN/m³

Depth of Footing (D_footing):

Bearing Capacity Factor (N_q):

Width of Footing (B):

Bearing Capacity Factor (N_γ):

Cohesion in Soil (C):

kPa

Bearing Capacity Factor (N_c):

1. What is Bearing Capacity Factor Dependent on Cohesion?

Definition: This calculator determines the bearing capacity factor (N_c) which depends on soil cohesion, given the dimensions of the footing and other soil parameters.

Purpose: It helps geotechnical engineers and foundation designers evaluate the bearing capacity of cohesive soils for foundation design.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ N_c = \frac{q_{fc} - ((\gamma \times D_{footing} \times N_q) + (0.5 \times \gamma \times B \times N_\gamma))}{(2/3) \times C} \]

Where:

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

3. Importance of Bearing Capacity Factor

Details: The bearing capacity factor is crucial for determining the safe load that can be applied to a foundation without causing shear failure in the soil.

4. Using the Calculator

Tips: Enter all required parameters. The bearing capacity factors N_q and N_γ typically have ±5% uncertainty. All values must be > 0.

5. Frequently Asked Questions (FAQ)

Q1: What is a typical range for N_c?
A: For cohesive soils, N_c typically ranges between 5 and 10, but can be higher for very cohesive soils.

Q2: Why is there a ±5% uncertainty on some factors?
A: The bearing capacity factors N_q and N_γ are empirically derived and can vary based on soil conditions.

Q3: How do I determine the ultimate bearing capacity (q_fc)?
A: q_fc can be determined through plate load tests or estimated using other bearing capacity formulas.

Q4: What units should I use?
A: Use consistent units: kN/m³ for unit weight, meters for dimensions, and kPa for pressure/stress values.

Q5: Does this consider safety factors?
A: No, the calculated N_c is a theoretical value. Apply appropriate safety factors in design.