Saturated Unit Weight given Shear Strength Calculator

Saturated Unit Weight Formula:

\[ \gamma_{saturated} = \frac{y_S \times \zeta_{soil} \times \tan\left(\frac{\Phi_i \times \pi}{180}\right)}{\tau_f \times \tan\left(\frac{i \times \pi}{180}\right)} \]

Submerged Unit Weight (yS):

kN/m³

Shear Stress (ζ_soil):

kPa

Angle of Internal Friction (Φ_i):

Shear Strength (τ_f):

kN/m³

Angle of Inclination (i):

Saturated Unit Weight (γ_saturated): kN/m³

1. What is Saturated Unit Weight given Shear Strength?

Definition: This calculator determines the saturated unit weight of soil based on shear strength parameters and other soil properties.

Purpose: It helps geotechnical engineers and soil scientists analyze soil stability and bearing capacity under saturated conditions.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ \gamma_{saturated} = \frac{y_S \times \zeta_{soil} \times \tan\left(\frac{\Phi_i \times \pi}{180}\right)}{\tau_f \times \tan\left(\frac{i \times \pi}{180}\right)} \]

Where:

\( \gamma_{saturated} \) — Saturated unit weight of soil (kN/m³)
\( y_S \) — Submerged unit weight (kN/m³)
\( \zeta_{soil} \) — Shear stress (kPa)
\( \Phi_i \) — Angle of internal friction (°)
\( \tau_f \) — Shear strength (kN/m³)
\( i \) — Angle of inclination to horizontal (°)

Explanation: The formula relates soil weight under saturated conditions to its shear strength properties and geometry.

3. Importance of Saturated Unit Weight Calculation

Details: Accurate calculation is crucial for foundation design, slope stability analysis, and earthwork construction in wet conditions.

4. Using the Calculator

Tips: Enter all required parameters. Angles should be in degrees with ±5% tolerance. All values must be positive.

5. Frequently Asked Questions (FAQ)

Q1: What's the typical range for saturated unit weight?
A: Most soils range between 18-22 kN/m³ when saturated, depending on particle density and void ratio.

Q2: Why is angle tolerance important?
A: Soil friction angles can vary ±5% due to natural variability in soil composition and testing methods.

Q3: How does saturation affect unit weight?
A: Saturated weight includes water in voids, making it higher than dry weight but lower than submerged weight.

Q4: When would I need this calculation?
A: For designing foundations, retaining walls, or slopes where groundwater is present.

Q5: How accurate is this calculation?
A: It provides a theoretical estimate; actual field conditions may vary due to soil heterogeneity.