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Bishop Simplified Circular Arc Slope Stability Safety Factor Calculator

Easily calculate and compute bishop simplified circular arc slope stability safety factor calculator with accurate equations, live formulas, and expert guidance.

Calculated Result
1.29 FS ratio

Bishop Factor of Safety

Bishop Factor of Safety

1.29 FS ratio

Factor Of Safety Bishop Fs

1.29

Pore Pressure Force Ub Kn

24

Effective Base Normal Force Kn

96

Slope Stability Class

MARGINAL: Sensitive to increased pore pressure

1.29 — FS ratio

Calculation Breakdown

  1. Applied FormulaIteratively calculates circular rotational slip failure Factor of Safety for engineered earth dams and highway cut slopes using Alan W. Bishop’s classic 1955 method of slices.\text{FS} = \frac{\sum \frac{c' b + (W - u b)\tan\phi'}{m_\alpha}}{\sum W \sin\alpha}, \quad m_\alpha = \cos\alpha \left( 1 + \frac{\tan\alpha \tan\phi'}{\text{FS}} \right)

Bishop Slope Stability FS Metric Output

Interactive visualization based on your current inputs

Calculated Value
0.00.30.61.01.3Bishop Factor of Safety

What Is the Bishop Simplified Circular Arc Slope Stability Safety Factor Calculator?

This tool computes bishop simplified circular arc slope stability safety factor calculator with high precision arithmetic.

How Does the Bishop Simplified Circular Arc Slope Stability Safety Factor Calculator Work?

Iteratively calculates circular rotational slip failure Factor of Safety for engineered earth dams and highway cut slopes using Alan W. Bishop’s classic 1955 method of slices.

Bishop Simplified Circular Arc Slope Stability Safety Factor Calculator Formula & Variables

The core mathematical equation utilized by this calculator is expressed as:

FS=∑c′b+(W−ub)tan⁡ϕ′mα∑Wsin⁡α,mα=cos⁡α(1+tan⁡αtan⁡ϕ′FS)\text{FS} = \frac{\sum \frac{c' b + (W - u b)\tan\phi'}{m_\alpha}}{\sum W \sin\alpha}, \quad m_\alpha = \cos\alpha \left( 1 + \frac{\tan\alpha \tan\phi'}{\text{FS}} \right)

Iteratively calculates circular rotational slip failure Factor of Safety for engineered earth dams and highway cut slopes using Alan W. Bishop’s classic 1955 method of slices.

How to Use the Bishop Simplified Circular Arc Slope Stability Safety Factor Calculator

  1. Enter your parameters into the designated input fields to calculate the result immediately.

Step-by-Step Example Calculation

Bishop Simplified Circular Arc Slope Stability Safety Factor Calculator Example

Input Values:

soilCohesionCPrimeKpa:15
soilFrictionAngleDegrees:26
representativeSliceWeightKn:120
representativeSliceWidthMeters:2
sliceBaseInclinationDegrees:28
porePressureRatioRu:0.2
Worked Steps: Sample evaluation based on standard reference conditions.

Understanding Your Result

The calculated primary figure indicates the optimal or required FS ratio.

Factors That Affect the Result

  • Measurement tolerances, operational variance, and real-world conditions.

When Should You Use This Calculator?

  • Everyday budgeting, technical homework, professional estimation, and household projects.

Assumptions & Limitations

  • Assumes standard atmospheric or environmental parameters unless specified.

Frequently Asked Questions

Calculation Accuracy & Reference Note

Double-precision IEEE 754 arithmetic with validated empirical constants.

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