Saturated Unit Weight given Factor of Safety with respect to Shear Strength Calculator

Saturated Unit Weight Formula:

\[ \gamma_{sat} = \left(\frac{\gamma'}{\tan(\phi_{IF})}\right) \times \left(\frac{\tan(\phi)}{FS}\right) \]

Submerged Unit Weight (γ'):

kN/m³

Weighted Friction Angle (φ_IF):

Angle of Internal Friction (φ):

Factor of Safety (FS):

Saturated Unit Weight (γ_sat): kN/m³

1. What is Saturated Unit Weight given Factor of Safety?

Definition: This calculator determines the saturated unit weight of soil considering the factor of safety with respect to shear strength.

Purpose: It helps geotechnical engineers assess soil stability under saturated conditions with safety considerations.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ \gamma_{sat} = \left(\frac{\gamma'}{\tan(\phi_{IF})}\right) \times \left(\frac{\tan(\phi)}{FS}\right) \]

Where:

\( \gamma_{sat} \) — Saturated unit weight (kN/m³)
\( \gamma' \) — Submerged unit weight (kN/m³)
\( \phi_{IF} \) — Weighted friction angle for internal friction (°)
\( \phi \) — Angle of internal friction (°)
\( FS \) — Factor of safety (dimensionless)

Explanation: The formula relates the submerged unit weight to the saturated unit weight through the friction angles and safety factor.

3. Importance of Saturated Unit Weight Calculation

Details: Accurate calculation is crucial for slope stability analysis, foundation design, and earth retaining structures in saturated conditions.

4. Using the Calculator

Tips: Enter submerged unit weight, both friction angles in degrees, and factor of safety (typically 1.5-3.0). All values must be > 0.

5. Frequently Asked Questions (FAQ)

Q1: What is the typical range for factor of safety?
A: For slope stability, FS typically ranges from 1.3 to 1.5 for temporary works and 1.5 to 2.0 for permanent structures.

Q2: How do I determine the weighted friction angle?
A: It's determined through laboratory tests or empirical correlations based on soil type and conditions.

Q3: What's the difference between φ and φ_IF?
A: φ is the basic internal friction angle, while φ_IF is a weighted value considering specific conditions.

Q4: Why does the calculator convert angles to radians?
A: The trigonometric functions in the formula require angles in radians for accurate computation.

Q5: How does saturation affect unit weight?
A: Saturated unit weight is higher than submerged weight as it includes both soil solids and pore water.