Saturated Unit Weight given Factor of Safety for Cohesive Soil Calculator

Saturated Unit Weight Formula:

\[ \gamma_{sat} = \frac{C_{eff} + (\gamma_S \cdot z \cdot \tan(\phi) \cdot \cos^2(i))}{FS \cdot z \cdot \cos(i) \cdot \sin(i)} \]

Effective Cohesion (C_eff):

kPa

Submerged Unit Weight (γ_S):

kN/m³

Depth of Prism (z):

Angle of Internal Friction (φ):

Inclination Angle (i):

Factor of Safety (FS):

Saturated Unit Weight (γ_sat):

1. What is Saturated Unit Weight in Soil Mechanics?

Definition: Saturated unit weight is the weight per unit volume of soil when all voids are completely filled with water.

Purpose: It's crucial for analyzing slope stability, bearing capacity, and earth pressure calculations in geotechnical engineering.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ \gamma_{sat} = \frac{C_{eff} + (\gamma_S \cdot z \cdot \tan(\phi) \cdot \cos^2(i))}{FS \cdot z \cdot \cos(i) \cdot \sin(i)} \]

Where:

\( \gamma_{sat} \) — Saturated unit weight (kN/m³)
\( C_{eff} \) — Effective cohesion (kPa)
\( \gamma_S \) — Submerged unit weight (kN/m³)
\( z \) — Depth of prism (m)
\( \phi \) — Angle of internal friction (°)
\( i \) — Angle of inclination to horizontal (°)
\( FS \) — Factor of safety

3. Importance of Saturated Unit Weight Calculation

Details: Accurate calculation helps in designing stable slopes, retaining walls, and foundations in cohesive soils.

4. Using the Calculator

Tips: Enter all required parameters. The factor of safety typically ranges from 1.5 to 3.0 (±5% variation is common).

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between submerged and saturated unit weight?
A: Submerged unit weight considers buoyancy, while saturated unit weight includes the weight of water in voids.

Q2: How does inclination angle affect the result?
A: Higher inclination angles generally require higher saturated unit weights for stability.

Q3: What's a typical factor of safety for slopes?
A: Usually 1.3-1.5 for temporary slopes, 1.5-2.0 for permanent slopes (±5% variation acceptable).

Q4: How do I determine effective cohesion?
A: Through laboratory tests like unconfined compression or triaxial tests on soil samples.

Q5: Why does depth of prism matter?
A: Deeper prisms have more overburden pressure affecting the stability calculations.