Ultimate Bearing Capacity given Bearing Capacity Factor Calculator

Ultimate Bearing Capacity Formula:

\[ q_f = (C_s \times N_c) + (\gamma \times D \times N_q) + (0.5 \times \gamma \times B \times N_\gamma) \]

Cohesion of Soil (C_s):

Bearing Capacity Factor (N_c):

Unit Weight of Soil (γ):

N/m³

Depth of Footing (D):

Bearing Capacity Factor (N_q):

Width of Footing (B):

Bearing Capacity Factor (N_γ):

Ultimate Bearing Capacity (q_f): Pa

1. What is Ultimate Bearing Capacity?

Definition: The Ultimate Bearing Capacity is the minimum gross pressure intensity at the base of the foundation at which the soil fails in shear.

Purpose: It helps civil engineers determine the maximum load that a foundation can support before shear failure occurs in the soil.

2. How Does the Calculator Work?

The calculator uses Terzaghi's bearing capacity formula:

\[ q_f = (C_s \times N_c) + (\gamma \times D \times N_q) + (0.5 \times \gamma \times B \times N_\gamma) \]

Where:

\( q_f \) — Ultimate bearing capacity (Pa)
\( C_s \) — Cohesion of soil (Pa)
\( N_c \) — Bearing capacity factor for cohesion (dimensionless)
\( \gamma \) — Unit weight of soil (N/m³)
\( D \) — Depth of footing (m)
\( N_q \) — Bearing capacity factor for surcharge (dimensionless)
\( B \) — Width of footing (m)
\( N_\gamma \) — Bearing capacity factor for unit weight (dimensionless)

Explanation: The formula accounts for three components of bearing capacity: cohesion, surcharge, and soil weight.

3. Importance of Ultimate Bearing Capacity

Details: Proper calculation ensures foundation stability, prevents excessive settlement, and maintains structural integrity.

4. Using the Calculator

Tips: Enter all required parameters. The bearing capacity factors (N_c, N_q, N_γ) typically have ±5% variation.

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, N_γ=1.6, but these vary with soil type and friction angle.

Q2: Why the ±5% variation in factors?
A: Bearing capacity factors depend on soil properties that often have natural variability.

Q3: How does footing depth affect capacity?
A: Deeper footings generally have higher capacity due to increased surcharge pressure.

Q4: What units should I use?
A: Use consistent SI units: Pascals for cohesion and bearing capacity, meters for dimensions.

Q5: Does this account for safety factors?
A: No, this calculates ultimate capacity. Apply appropriate safety factors for design.