Shear Strength of Soil given Angle of Internal Friction Calculator

Shear Strength Formula:

\[ \tau_{soil} = \tau \times \left(\frac{\tan(\phi_i)}{\tan(I)}\right) \]

Shear Stress (τ):

MPa

Angle of Internal Friction (φ):

Angle of Inclination (I):

Safety Factor (±5%):

Shear Strength (τ_soil):

1. What is Shear Strength of Soil?

Definition: Shear strength of soil is the maximum shear stress that a soil can withstand without undergoing failure or excessive deformation.

Purpose: It's crucial for geotechnical engineering to assess slope stability, foundation design, and earth retaining structures.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ \tau_{soil} = \tau \times \left(\frac{\tan(\phi_i)}{\tan(I)}\right) \]

Where:

\( \tau_{soil} \) — Shear strength of soil (MPa)
\( \tau \) — Applied shear stress (MPa)
\( \phi_i \) — Angle of internal friction (degrees)
\( I \) — Angle of inclination (degrees)

Explanation: The formula relates the soil's shear strength to its internal friction angle and the slope inclination.

3. Importance of Shear Strength Calculation

Details: Accurate shear strength estimation prevents slope failures, ensures structural stability, and optimizes foundation designs.

4. Using the Calculator

Tips: Enter the shear stress, internal friction angle, inclination angle, and safety factor (±5%). All angles must be between 0-90°.

5. Frequently Asked Questions (FAQ)

Q1: What is angle of internal friction?
A: It's a measure of the shear strength of soil due to friction between soil particles.

Q2: What's a typical internal friction angle for soils?
A: It varies: 25-30° for loose sand, 30-35° for dense sand, 15-25° for silt, and 0-10° for clay.

Q3: Why include a safety factor?
A: To account for uncertainties in material properties and loading conditions (±5% is common).

Q4: How does inclination angle affect results?
A: Steeper slopes (higher I) generally reduce the effective shear strength of the soil.

Q5: What units should I use?
A: Enter angles in degrees and stress in MPa. The calculator handles the unit conversions.