Shear Stress of Soil given Angle of Internal Friction Calculator

Shear Stress Formula:

\[ \tau_i = \frac{\tau_s}{\frac{\tan(\phi)}{\tan(I)}} \]

Shear Strength (τ_s):

MPa

Angle of Internal Friction (φ):

Angle of Inclination (I):

Tolerance:

Shear Stress (τ_i):

1. What is Shear Stress of Soil given Angle of Internal Friction?

Definition: This calculator determines the shear stress acting on soil based on its shear strength, internal friction angle, and inclination angle.

Purpose: It helps geotechnical engineers analyze soil stability and predict potential failure planes.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ \tau_i = \frac{\tau_s}{\frac{\tan(\phi)}{\tan(I)}} \]

Where:

\( \tau_i \) — Shear stress (MPa)
\( \tau_s \) — Shear strength (MPa)
\( \phi \) — Angle of internal friction (degrees)
\( I \) — Angle of inclination (degrees)

Explanation: The shear stress is calculated by dividing the shear strength by the ratio of tangent functions for the friction and inclination angles.

3. Importance of Shear Stress Calculation

Details: Proper shear stress estimation is crucial for designing stable slopes, retaining walls, and foundations.

4. Using the Calculator

Tips: Enter the shear strength in MPa, angles in degrees, and tolerance percentage (default ±5%). All values must be > 0.

5. Frequently Asked Questions (FAQ)

Q1: What is angle of internal friction?
A: It's a measure of soil's shear strength, representing the friction between soil particles under stress.

Q2: Why include a tolerance factor?
A: Soil properties vary naturally, so the tolerance accounts for this variability in calculations.

Q3: Typical values for internal friction angle?
A: Clay: 15-30°, Sand: 30-45°, Gravel: 35-50° depending on density and composition.

Q4: How does inclination angle affect results?
A: Higher inclination angles generally reduce the calculated shear stress.

Q5: When would this calculation be used?
A: For slope stability analysis, foundation design, and earth retaining structure calculations.