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Unit Weight Of Soil Given Angle Of Shearing Resistance Calculator

Formula Used:

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

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1. What is Unit Weight of Soil?

Unit Weight of Soil mass is the ratio of the total weight of soil to the total volume of soil. It is a fundamental property in geotechnical engineering that affects soil behavior under various loading conditions.

2. How Does the Calculator Work?

The calculator uses the formula:

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

Where:

Explanation: This formula relates the unit weight of soil to the ultimate bearing capacity, footing depth, and the soil's angle of shearing resistance, which represents the soil's internal friction.

3. Importance of Unit Weight Calculation

Details: Accurate calculation of unit weight is crucial for foundation design, slope stability analysis, earth pressure calculations, and overall geotechnical engineering design. It helps determine how soil will behave under different loading conditions.

4. Using the Calculator

Tips: Enter ultimate bearing capacity in Pascals, depth of footing in meters, and angle of shearing resistance in degrees. All values must be valid (qf > 0, D > 0, φ between 0-90°).

5. Frequently Asked Questions (FAQ)

Q1: What is the typical range for unit weight of soil?
A: Unit weight typically ranges from 16-22 kN/m³ for most soils, with sandy soils being heavier and organic soils being lighter.

Q2: How does angle of shearing resistance affect unit weight?
A: Higher angles of shearing resistance generally indicate denser, more compact soils that typically have higher unit weights.

Q3: Why is depth of footing important in this calculation?
A: Depth affects the overburden pressure and confinement of soil, which influences both bearing capacity and the relationship with unit weight.

Q4: Can this formula be used for all soil types?
A: This formula is most applicable for cohesive-frictional soils. Pure clays or pure sands may require different approaches.

Q5: What are common applications of unit weight calculations?
A: Foundation design, retaining wall design, slope stability analysis, settlement calculations, and earthwork quantity estimations.

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