Shear Stress given Factor of Safety for Cohesive Soil Calculator

Shear Stress Formula:

\[ \text{Shear Stress} = \frac{C + (\sigma_n \times \tan(\phi))}{FS} \]

Unit Cohesion (C):

Normal Stress (σₙ):

Angle of Internal Friction (φ):

Factor of Safety (FS):

Shear Stress (τ):

1. What is Shear Stress for Factor of Safety?

Definition: This is the maximum shear stress that a cohesive soil can withstand before failure, considering a safety factor.

Purpose: It helps geotechnical engineers determine the safe shear stress capacity of soil in slope stability analysis and foundation design.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ \tau = \frac{C + (\sigma_n \times \tan(\phi))}{FS} \]

Where:

\( \tau \) — Shear stress (Pa)
\( C \) — Unit cohesion (Pa)
\( \sigma_n \) — Normal stress (Pa)
\( \phi \) — Angle of internal friction (degrees)
\( FS \) — Factor of Safety (dimensionless)

Explanation: The formula combines the cohesive strength and frictional strength of soil, divided by a safety factor.

3. Importance of Shear Stress Calculation

Details: Proper calculation ensures safe slope designs, stable foundations, and prevents soil failures in construction projects.

4. Using the Calculator

Tips: Enter cohesion in Pa, normal stress in Pa, friction angle in degrees (0-45°), and safety factor (typically 1.5-3.0). All values must be positive.

5. Frequently Asked Questions (FAQ)

Q1: What is typical cohesion value for clay?
A: Soft clay: 10-25 kPa, Medium clay: 25-50 kPa, Stiff clay: 50-100 kPa.

Q2: Why is angle of friction limited to 45°?
A: Most soils have φ < 45°; higher values are unusual and may indicate input error.

Q3: How to choose safety factor?
A: Depends on project importance: 1.5 for temporary works, 2.0-3.0 for permanent structures.

Q4: What if I get negative shear stress?
A: Check your inputs - all values should be positive and FS > 0.

Q5: Does this work for all soil types?
A: Best for cohesive soils (clays). For granular soils, cohesion (C) would be zero.