Unit Weight of Soil given Factor of Safety for Cohesive Soil Calculator

Unit Weight of Soil Formula:

\[ \gamma = \frac{c}{(fs - (\frac{\tan(\phi)}{\tan(I)})) \times z \times \cos(I) \times \sin(I)} \]

Cohesion of Soil (c):

Factor of Safety (fs):

Angle of Internal Friction (φ):

degrees

Angle of Inclination (I):

degrees

Depth of Prism (z):

Unit Weight of Soil (γ):

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

Definition: This calculator computes the unit weight of soil based on cohesion, factor of safety, internal friction angle, inclination angle, and prism depth.

Purpose: It helps geotechnical engineers determine the appropriate unit weight of soil for slope stability analysis and foundation design.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ \gamma = \frac{c}{(fs - (\frac{\tan(\phi)}{\tan(I)})) \times z \times \cos(I) \times \sin(I)} \]

Where:

\( \gamma \) — Unit weight of soil (N/m³)
\( c \) — Cohesion of soil (Pa)
\( fs \) — Factor of safety
\( \phi \) — Angle of internal friction (degrees)
\( I \) — Angle of inclination (degrees)
\( z \) — Depth of prism (m)

Explanation: The formula accounts for soil cohesion, safety factors, and geometric parameters to determine the unit weight required for stability.

3. Importance of Unit Weight Calculation

Details: Accurate unit weight estimation is crucial for slope stability analysis, retaining wall design, and foundation engineering.

4. Using the Calculator

Tips: Enter all required parameters. The factor of safety typically ranges from 1.5 to 3.0 (±5%). Angles should be in degrees (0-90°).

5. Frequently Asked Questions (FAQ)

Q1: What is a typical factor of safety for slopes?
A: For permanent slopes, fs is typically 1.5-2.0. For temporary slopes, 1.3-1.5 may be acceptable (±5%).

Q2: How do I determine soil cohesion?
A: Cohesion is determined through laboratory tests like unconfined compression tests or triaxial tests.

Q3: What's the range for angle of internal friction?
A: For cohesive soils, φ typically ranges from 0° to 30°. For granular soils, it can be 30°-45°.

Q4: Why is prism depth important?
A: Prism depth represents the failure plane depth and directly affects the calculated unit weight.

Q5: Can this calculator be used for all soil types?
A: It's primarily for cohesive soils. For purely granular soils (c=0), different formulas apply.