Effective Angle of Internal Friction given Shear Force in Bishop's Analysis Calculator

Formula:

\[ \phi' = \arctan\left(\frac{(S \times fs) - (c' \times l)}{P - (u \times l)}\right) \]

Shear Force on Slice (S):

Factor of Safety (fs):

Effective Cohesion (c'):

Length of Arc (l):

Total Normal Force (P):

Upward Force (u):

Effective Angle of Internal Friction (φ'):

1. What is Effective Angle of Internal Friction?

Definition: The effective angle of internal friction (φ') is a measure of the shear strength of soils due to friction between soil particles under effective stress conditions.

Purpose: It's a critical parameter in slope stability analysis using Bishop's method, helping engineers assess the safety of slopes and embankments.

2. How Does the Calculator Work?

The calculator uses Bishop's analysis formula:

\[ \phi' = \arctan\left(\frac{(S \times fs) - (c' \times l)}{P - (u \times l)}\right) \]

Where:

\( \phi' \) — Effective angle of internal friction (radians or degrees)
\( S \) — Shear force on the slice (N)
\( fs \) — Factor of safety (±5%)
\( c' \) — Effective cohesion (Pa)
\( l \) — Length of the slice base (m)
\( P \) — Total normal force (N)
\( u \) — Upward water pressure force (Pa)

3. Importance in Slope Stability Analysis

Details: Accurate determination of φ' is crucial for:

Assessing slope stability
Designing safe embankments
Preventing landslides
Optimizing construction costs

4. Using the Calculator

Tips:

Enter all required parameters in consistent units
Factor of safety typically ranges from 1.3 to 1.5 (±5%)
For cohesionless soils, set c' = 0
For dry conditions, set u = 0

5. Frequently Asked Questions (FAQ)

Q1: What's a typical φ' value for sandy soils?
A: Usually between 30° to 40° for clean sands, lower for silty sands.

Q2: Why is the factor of safety marked ±5%?
A: This accounts for typical uncertainty in safety factor estimation.

Q3: How does water pressure affect φ'?
A: Higher u reduces the denominator, increasing the calculated φ'.

Q4: What if I get negative φ'?
A: Check your inputs - negative values are physically impossible.

Q5: How accurate is Bishop's method?
A: It's more accurate than ordinary method of slices but still has ±10-15% uncertainty.