Saturated Unit Weight given Shear Stress Component Calculator

Saturated Unit Weight Formula:

\[ \gamma_{saturated} = \frac{\zeta_{soil}}{z \times \cos(i) \times \sin(i)} \]

Shear Stress in Soil Mechanics:

Depth of Prism:

Angle of Inclination:

Tolerance:

Saturated Unit Weight (N/m³):

1. What is Saturated Unit Weight given Shear Stress Component?

Definition: This calculator determines the saturated unit weight of soil based on shear stress, depth of prism, and angle of inclination.

Purpose: It helps geotechnical engineers analyze soil stability and design appropriate foundations or retaining structures.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ \gamma_{saturated} = \frac{\zeta_{soil}}{z \times \cos(i) \times \sin(i)} \]

Where:

\( \gamma_{saturated} \) — Saturated unit weight of soil (N/m³)
\( \zeta_{soil} \) — Shear stress in soil mechanics (Pa)
\( z \) — Depth of prism (m)
\( i \) — Angle of inclination to horizontal (radians)

Explanation: The shear stress is divided by the product of depth and trigonometric functions of the inclination angle.

3. Importance of Saturated Unit Weight Calculation

Details: Accurate calculation helps in determining soil bearing capacity, slope stability, and proper foundation design.

4. Using the Calculator

Tips: Enter shear stress in Pascals, depth in meters, angle in degrees (0-90), and tolerance percentage (default 5%). All values must be > 0.

5. Frequently Asked Questions (FAQ)

Q1: What is typical saturated unit weight for common soils?
A: Clay: 18-22 kN/m³, Sand: 19-22 kN/m³, Gravel: 20-23 kN/m³ (multiply by 1000 for N/m³).

Q2: Why include a tolerance percentage?
A: Soil properties vary naturally; tolerance accounts for this variability in real-world conditions.

Q3: How does angle of inclination affect the result?
A: Higher angles increase the denominator, resulting in lower calculated unit weight.

Q4: What if I get unrealistic values?
A: Verify your input values, especially shear stress and depth. Consider soil testing for accurate parameters.

Q5: Can this be used for unsaturated soils?
A: No, this formula specifically calculates saturated unit weight when pore spaces are filled with water.