Shear Strength given Normal Stress on Slice Calculator

Shear Strength Formula:

\[ \tau = c' + (\sigma_{normal} - u) \times \tan(\phi') \]

Effective Cohesion (c'):

Normal Stress (σ):

Upward Force (u):

Friction Angle (φ'):

Uncertainty Factor:

Shear Strength (τ):

Uncertainty Range (±5%):

1. What is Shear Strength given Normal Stress on Slice?

Definition: This calculator determines the shear strength of soil considering effective cohesion, normal stress, pore water pressure, and internal friction angle.

Purpose: It's essential for geotechnical engineering analysis of slope stability and foundation design.

2. How Does the Calculator Work?

The calculator uses the Mohr-Coulomb failure criterion:

\[ \tau = c' + (\sigma_{normal} - u) \times \tan(\phi') \]

Where:

\( \tau \) — Shear strength (Pa)
\( c' \) — Effective cohesion (Pa)
\( \sigma_{normal} \) — Normal stress on failure plane (Pa)
\( u \) — Pore water pressure (Pa)
\( \phi' \) — Effective angle of internal friction (degrees)

Explanation: The shear strength consists of cohesive strength plus frictional strength which depends on effective normal stress.

3. Importance of Shear Strength Calculation

Details: Accurate shear strength estimation is crucial for assessing slope stability, bearing capacity, and earth pressure calculations.

4. Using the Calculator

Tips: Enter all parameters in consistent units (Pa for stresses). The uncertainty factor (default ±5%) accounts for measurement variability.

5. Frequently Asked Questions (FAQ)

Q1: What is effective cohesion?
A: The portion of shear strength independent of normal stress, representing true cohesion and cementation between particles.

Q2: How do I determine pore water pressure?
A: It can be measured with piezometers or estimated from groundwater flow analysis.

Q3: What's a typical friction angle for soils?
A: Ranges from 25°-30° for loose sand to 40°-45° for dense sand, and 15°-30° for clays.

Q4: Why include an uncertainty factor?
A: Soil properties are naturally variable; ±5-10% accounts for this variability in calculations.

Q5: Can this be used for rock mechanics?
A: The same principle applies but with different parameter ranges and additional considerations for discontinuities.