Factor of Safety given Shear Force in Bishop's Analysis Calculator

Factor of Safety Formula:

\[ FS = \frac{(c' \times l) + (P - (u \times l)) \times \tan(\phi')}{S} \]

Effective Cohesion (c'):

Length of Arc (l):

Total Normal Force (P):

Upward Force (u):

Effective Angle of Internal Friction (φ'):

Shear Force (S):

Tolerance:

Factor of Safety (FS):

Acceptable Range (±5%):

1. What is Factor of Safety in Bishop's Analysis?

Definition: The factor of safety is a measure of how much stronger a slope is than it needs to be to resist failure, calculated using Bishop's simplified method of slices.

Purpose: It helps geotechnical engineers assess slope stability and design safe earth structures.

2. How Does the Calculator Work?

The calculator uses Bishop's simplified method formula:

\[ FS = \frac{(c' \times l) + (P - (u \times l)) \times \tan(\phi')}{S} \]

Where:

\( FS \) — Factor of Safety
\( c' \) — Effective cohesion (Pa)
\( l \) — Length of the slice base (m)
\( P \) — Total normal force (N)
\( u \) — Upward water pressure (Pa)
\( \phi' \) — Effective angle of internal friction (°)
\( S \) — Shear force (N)

3. Importance of Factor of Safety Calculation

Details: A factor of safety greater than 1 indicates a stable slope, while values below 1 suggest potential failure. Typical design values range from 1.3 to 1.5.

4. Using the Calculator

Tips: Enter all required parameters including the tolerance percentage (default ±5%). The calculator provides both the FS value and its acceptable range.

5. Frequently Asked Questions (FAQ)

Q1: What is a typical acceptable factor of safety?
A: For permanent slopes, FS ≥ 1.5 is common, while temporary slopes may accept FS ≥ 1.3.

Q2: How does water pressure affect the factor of safety?
A: Higher pore water pressure (u) reduces the effective stress, lowering the FS.

Q3: What's the purpose of the tolerance percentage?
A: It accounts for uncertainties in soil parameters and provides a safety margin.

Q4: How is the effective angle of internal friction determined?
A: Through laboratory tests like direct shear or triaxial tests on soil samples.

Q5: Can this calculator be used for all slope stability problems?
A: Bishop's method is most suitable for circular failure surfaces in homogeneous soils.