Ultimate Bearing Capacity Given Angle of Shearing Resistance Calculator

Ultimate Bearing Capacity Formula:

\[ q_f = (\gamma \times D) \times \left( \frac{1 + \sin\left(\frac{\phi \times \pi}{180}\right)}{1 - \sin\left(\frac{\phi \times \pi}{180}\right)} \right)^2 \]

Unit Weight of Soil (γ):

kN/m³

Depth of Footing (D):

Angle of Shearing Resistance (φ):

degrees

Ultimate Bearing Capacity (q_f):

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1. What is Ultimate Bearing Capacity?

The Ultimate Bearing Capacity in soil mechanics is defined as the minimum gross pressure intensity at the base of the foundation at which the soil fails in shear. It represents the maximum load per unit area that the soil can support without undergoing shear failure.

2. How Does the Calculator Work?

The calculator uses the ultimate bearing capacity formula:

\[ q_f = (\gamma \times D) \times \left( \frac{1 + \sin\left(\frac{\phi \times \pi}{180}\right)}{1 - \sin\left(\frac{\phi \times \pi}{180}\right)} \right)^2 \]

Where:

\( q_f \) — Ultimate bearing capacity (kN/m²)
\( \gamma \) — Unit weight of soil (kN/m³)
\( D \) — Depth of footing (m)
\( \phi \) — Angle of shearing resistance (degrees)
\( \pi \) — Mathematical constant pi (approximately 3.1416)

Explanation: This formula calculates the ultimate bearing capacity based on soil properties and foundation depth, considering the angle of shearing resistance which represents the soil's frictional strength.

3. Importance of Ultimate Bearing Capacity Calculation

Details: Accurate calculation of ultimate bearing capacity is crucial for foundation design, ensuring structural stability and preventing foundation failure. It helps engineers determine the safe load-bearing capacity of soil for various construction projects.

4. Using the Calculator

Tips: Enter unit weight of soil in kN/m³, depth of footing in meters, and angle of shearing resistance in degrees (0-90°). All values must be valid positive numbers within their respective ranges.

5. Frequently Asked Questions (FAQ)

Q1: What factors affect ultimate bearing capacity?
A: Soil type, density, moisture content, foundation depth, and angle of shearing resistance significantly affect the ultimate bearing capacity.

Q2: How does angle of shearing resistance influence bearing capacity?
A: Higher angles of shearing resistance indicate stronger, more cohesive soils that can support greater loads before failure occurs.

Q3: What is the typical range for angle of shearing resistance?
A: For most soils, the angle of shearing resistance ranges from 0° (pure clay) to 45° (dense gravel), with typical values between 25°-40° for sandy soils.

Q4: How does foundation depth affect bearing capacity?
A: Deeper foundations generally have higher bearing capacity due to increased confining pressure and additional soil weight above the foundation level.

Q5: Are there limitations to this formula?
A: This formula provides a theoretical maximum and may need adjustment for specific soil conditions, water table effects, and foundation shape factors in practical applications.