Factor of Safety given by Bishop Solution

STEP 0: Pre-Calculation Summary
Formula Used
Factor of Safety = Stability Coefficient m in Soil Mechanics-(Stability Coefficient n*Pore Pressure Ratio)
fs = m-(n*ru)
This formula uses 4 Variables
Variables Used
Factor of Safety - Factor of Safety expresses how much stronger a system is than it needs to be for an intended load.
Stability Coefficient m in Soil Mechanics - Stability Coefficient m in Soil Mechanics is a coefficient given by Bishop.
Stability Coefficient n - Stability Coefficient n is a coefficient given by Bishop.
Pore Pressure Ratio - Pore pressure ratio is a crude way of describing pore-water conditions in a slope stability analysis.
STEP 1: Convert Input(s) to Base Unit
Stability Coefficient m in Soil Mechanics: 2.98 --> No Conversion Required
Stability Coefficient n: 0.3 --> No Conversion Required
Pore Pressure Ratio: 0.9 --> No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
fs = m-(n*ru) --> 2.98-(0.3*0.9)
Evaluating ... ...
fs = 2.71
STEP 3: Convert Result to Output's Unit
2.71 --> No Conversion Required
FINAL ANSWER
2.71 <-- Factor of Safety
(Calculation completed in 00.004 seconds)

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Birsa Institute of Technology (BIT), Sindri
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25 Slope Stability Analysis using Bishops Method Calculators

Weight of Slice given Total Normal Force Acting on Slice
Go Weight of Slice = (Total Normal Force in Soil Mechanics*cos((Angle of Base*pi)/180))+(Shear Force on Slice in Soil Mechanics*sin((Angle of Base*pi)/180))-Vertical Shear Force+Vertical Shear Force at other Section
Resultant Vertical Shear Force on Section N+1
Go Vertical Shear Force at other Section = Weight of Slice+Vertical Shear Force-(Total Normal Force in Soil Mechanics*cos((Angle of Base*pi)/180))+(Shear Force on Slice in Soil Mechanics*sin((Angle of Base*pi)/180))
Resultant Vertical Shear Force on Section N
Go Vertical Shear Force = (Total Normal Force in Soil Mechanics*cos((Angle of Base*pi)/180))+(Shear Force on Slice in Soil Mechanics*sin((Angle of Base*pi)/180))-Weight of Slice+Vertical Shear Force at other Section
Effective Cohesion of Soil given Shear Force in Bishop's Analysis
Go Effective Cohesion = ((Shear Force on Slice in Soil Mechanics*Factor of Safety)-((Total Normal Force-(Upward Force*Length of Arc))*tan((Effective Angle of Internal Friction*pi)/180)))/Length of Arc
Factor of Safety given Shear Force in Bishop's Analysis
Go Factor of Safety = ((Effective Cohesion*Length of Arc) +(Total Normal Force-(Upward Force*Length of Arc))*tan((Effective Angle of Internal Friction*pi)/180))/Shear Force on Slice in Soil Mechanics
Effective Angle of Internal Friction given Shear Force in Bishop's Analysis
Go Effective Angle of Internal Friction = atan(((Shear Force on Slice in Soil Mechanics*Factor of Safety)-(Effective Cohesion*Length of Arc))/(Total Normal Force-(Upward Force*Length of Arc)))
Effective Cohesion of Soil given Normal Stress on Slice
Go Effective Cohesion = Shear Strength of Soil in Pascal-((Normal Stress in Pascal-Upward Force)*tan((Effective Angle of Internal Friction*pi)/180))
Normal Stress on Slice given Shear Strength
Go Normal Stress in Pascal = ((Shear Strength of Soil in Pascal-Cohesion in Soil)/tan((Effective Angle of Internal Friction*pi)/180))+Upward Force
Effective Angle of Internal Friction given Shear Strength
Go Effective Angle of Internal Friction = atan((Shear Strength-Effective Cohesion)/(Normal Stress in Mega Pascal-Upward Force))
Radius of Arc when Total Shear Force on Slice is Available
Go Radius of Soil Section = (Total Weight of Slice in Soil Mechanics*Horizontal Distance)/Total Shear Force in Soil Mechanics
Total Weight of Slice given Total Shear Force on Slice
Go Total Weight of Slice in Soil Mechanics = (Total Shear Force in Soil Mechanics*Radius of Soil Section)/Horizontal Distance
Horizontal Distance of Slice from Centre of Rotation
Go Horizontal Distance = (Total Shear Force in Soil Mechanics*Radius of Soil Section)/Total Weight of Slice in Soil Mechanics
Factor of Safety given by Bishop
Go Factor of Safety = Stability Coefficient m in Soil Mechanics-(Stability Coefficient n*Pore Pressure Ratio)
Pore Pressure Ratio given Horizontal Width
Go Pore Pressure Ratio = (Upward Force*Width of Soil Section)/Total Weight of Slice in Soil Mechanics
Unit weight of Soil given Pore Pressure Ratio
Go Unit Weight of Soil = (Upward Force in Seepage Analysis/(Pore Pressure Ratio*Height of Slice))
Height of Slice given Pore Pressure Ratio
Go Height of Slice = (Upward Force in Seepage Analysis/(Pore Pressure Ratio*Unit Weight of Soil))
Pore Pressure Ratio given Unit Weight
Go Pore Pressure Ratio = (Upward Force in Seepage Analysis/(Unit Weight of Soil*Height of Slice))
Length of Arc of Slice given Effective Stress
Go Length of Arc = Total Normal Force/(Effective Normal Stress+Total Pore Pressure)
Pore Pressure given Effective Stress on Slice
Go Total Pore Pressure = (Total Normal Force/Length of Arc)-Effective Normal Stress
Effective Stress on Slice
Go Effective Normal Stress = (Total Normal Force/Length of Arc)-Total Pore Pressure
Length of Arc of Slice given Shear Force in Bishop's Analysis
Go Length of Arc = Shear Force on Slice in Soil Mechanics/Shear Stress of Soil in Pascal
Change in Pore Pressure given Overall Pore Pressure Coefficient
Go Change in Pore Pressure = Change in Normal Stress*Pore Pressure Coefficient Overall
Change in Normal Stress given Overall Pore Pressure Coefficient
Go Change in Normal Stress = Change in Pore Pressure/Pore Pressure Coefficient Overall
Normal Stress on Slice
Go Normal Stress in Pascal = Total Normal Force/Length of Arc
Length of Arc of Slice
Go Length of Arc = Total Normal Force/Normal Stress in Pascal

Factor of Safety given by Bishop Formula

Factor of Safety = Stability Coefficient m in Soil Mechanics-(Stability Coefficient n*Pore Pressure Ratio)
fs = m-(n*ru)

What is Factor of Safety?

The ratio of a structure's absolute strength (structural capability) to actual applied load; this is a measure of the reliability of a particular design.

How to Calculate Factor of Safety given by Bishop?

Factor of Safety given by Bishop calculator uses Factor of Safety = Stability Coefficient m in Soil Mechanics-(Stability Coefficient n*Pore Pressure Ratio) to calculate the Factor of Safety, The Factor of Safety given by Bishop is defined as the value of factor influencing the stability of force that uses the method of slices to discretize the soil mass and determine the FS (Factor of Safety). Factor of Safety is denoted by fs symbol.

How to calculate Factor of Safety given by Bishop using this online calculator? To use this online calculator for Factor of Safety given by Bishop, enter Stability Coefficient m in Soil Mechanics (m), Stability Coefficient n (n) & Pore Pressure Ratio (ru) and hit the calculate button. Here is how the Factor of Safety given by Bishop calculation can be explained with given input values -> 0.03 = 2.98-(0.3*0.9).

FAQ

What is Factor of Safety given by Bishop?
The Factor of Safety given by Bishop is defined as the value of factor influencing the stability of force that uses the method of slices to discretize the soil mass and determine the FS (Factor of Safety) and is represented as fs = m-(n*ru) or Factor of Safety = Stability Coefficient m in Soil Mechanics-(Stability Coefficient n*Pore Pressure Ratio). Stability Coefficient m in Soil Mechanics is a coefficient given by Bishop, Stability Coefficient n is a coefficient given by Bishop & Pore pressure ratio is a crude way of describing pore-water conditions in a slope stability analysis.
How to calculate Factor of Safety given by Bishop?
The Factor of Safety given by Bishop is defined as the value of factor influencing the stability of force that uses the method of slices to discretize the soil mass and determine the FS (Factor of Safety) is calculated using Factor of Safety = Stability Coefficient m in Soil Mechanics-(Stability Coefficient n*Pore Pressure Ratio). To calculate Factor of Safety given by Bishop, you need Stability Coefficient m in Soil Mechanics (m), Stability Coefficient n (n) & Pore Pressure Ratio (ru). With our tool, you need to enter the respective value for Stability Coefficient m in Soil Mechanics, Stability Coefficient n & Pore Pressure Ratio and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.
How many ways are there to calculate Factor of Safety?
In this formula, Factor of Safety uses Stability Coefficient m in Soil Mechanics, Stability Coefficient n & Pore Pressure Ratio. We can use 1 other way(s) to calculate the same, which is/are as follows -
  • Factor of Safety = ((Effective Cohesion*Length of Arc) +(Total Normal Force-(Upward Force*Length of Arc))*tan((Effective Angle of Internal Friction*pi)/180))/Shear Force on Slice in Soil Mechanics
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