Effective Cohesion of Soil given Shear Force in Bishop's Analysis Solution

STEP 0: Pre-Calculation Summary
Formula Used
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
c' = ((S*fs)-((P-(u*l))*tan((φ'*pi)/180)))/l
This formula uses 1 Constants, 1 Functions, 7 Variables
Constants Used
pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288
Functions Used
tan - The tangent of an angle is a trigonometric ratio of the length of the side opposite an angle to the length of the side adjacent to an angle in a right triangle., tan(Angle)
Variables Used
Effective Cohesion - (Measured in Pascal) - Effective Cohesion is the consistency of soft to hard defined on the basis of the standard CSN 73 1001 for different states of consistency and degree of saturation.
Shear Force on Slice in Soil Mechanics - (Measured in Newton) - Shear Force on Slice in Soil Mechanics acting along the base of slice.
Factor of Safety - Factor of Safety expresses how much stronger a system is than it needs to be for an intended load.
Total Normal Force - (Measured in Newton) - Total normal force acting at the base of the slice.
Upward Force - (Measured in Pascal) - Upward Force due to seepage water.
Length of Arc - (Measured in Meter) - Length of Arc of the slice taken into consideration.
Effective Angle of Internal Friction - (Measured in Radian) - Effective Angle of Internal Friction is a measure of the shear strength of soils due to friction.
STEP 1: Convert Input(s) to Base Unit
Shear Force on Slice in Soil Mechanics: 11.07 Newton --> 11.07 Newton No Conversion Required
Factor of Safety: 2.8 --> No Conversion Required
Total Normal Force: 150 Newton --> 150 Newton No Conversion Required
Upward Force: 20 Pascal --> 20 Pascal No Conversion Required
Length of Arc: 9.42 Meter --> 9.42 Meter No Conversion Required
Effective Angle of Internal Friction: 9.99 Degree --> 0.174358392274201 Radian (Check conversion here)
STEP 2: Evaluate Formula
Substituting Input Values in Formula
c' = ((S*fs)-((P-(u*l))*tan((φ'*pi)/180)))/l --> ((11.07*2.8)-((150-(20*9.42))*tan((0.174358392274201*pi)/180)))/9.42
Evaluating ... ...
c' = 3.30285100603297
STEP 3: Convert Result to Output's Unit
3.30285100603297 Pascal --> No Conversion Required
FINAL ANSWER
3.30285100603297 3.302851 Pascal <-- Effective Cohesion
(Calculation completed in 00.004 seconds)

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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

Effective Cohesion of Soil given Shear Force in Bishop's Analysis Formula

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
c' = ((S*fs)-((P-(u*l))*tan((φ'*pi)/180)))/l

What is Cohesion?

Cohesion is the stress (act) of sticking together. Yet, in engineering mechanics, particularly in soil mechanics, cohesion refers to shear strength under zero normal stress, or the intercept of a material's failure envelope with shear stress axis in the shear stress-normal stress space.

How to Calculate Effective Cohesion of Soil given Shear Force in Bishop's Analysis?

Effective Cohesion of Soil given Shear Force in Bishop's Analysis calculator uses 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 to calculate the Effective Cohesion, The Effective Cohesion of Soil given Shear Force in Bishop's Analysis is defined as the value of effective cohesion when we have prior information of other parameters used. Effective Cohesion is denoted by c' symbol.

How to calculate Effective Cohesion of Soil given Shear Force in Bishop's Analysis using this online calculator? To use this online calculator for Effective Cohesion of Soil given Shear Force in Bishop's Analysis, enter Shear Force on Slice in Soil Mechanics (S), Factor of Safety (fs), Total Normal Force (P), Upward Force (u), Length of Arc (l) & Effective Angle of Internal Friction (φ') and hit the calculate button. Here is how the Effective Cohesion of Soil given Shear Force in Bishop's Analysis calculation can be explained with given input values -> 1.519412 = ((11.07*2.8)-((150-(20*9.42))*tan((0.174358392274201*pi)/180)))/9.42.

FAQ

What is Effective Cohesion of Soil given Shear Force in Bishop's Analysis?
The Effective Cohesion of Soil given Shear Force in Bishop's Analysis is defined as the value of effective cohesion when we have prior information of other parameters used and is represented as c' = ((S*fs)-((P-(u*l))*tan((φ'*pi)/180)))/l or 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. Shear Force on Slice in Soil Mechanics acting along the base of slice, Factor of Safety expresses how much stronger a system is than it needs to be for an intended load, Total normal force acting at the base of the slice, Upward Force due to seepage water, Length of Arc of the slice taken into consideration & Effective Angle of Internal Friction is a measure of the shear strength of soils due to friction.
How to calculate Effective Cohesion of Soil given Shear Force in Bishop's Analysis?
The Effective Cohesion of Soil given Shear Force in Bishop's Analysis is defined as the value of effective cohesion when we have prior information of other parameters used is calculated using 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. To calculate Effective Cohesion of Soil given Shear Force in Bishop's Analysis, you need Shear Force on Slice in Soil Mechanics (S), Factor of Safety (fs), Total Normal Force (P), Upward Force (u), Length of Arc (l) & Effective Angle of Internal Friction (φ'). With our tool, you need to enter the respective value for Shear Force on Slice in Soil Mechanics, Factor of Safety, Total Normal Force, Upward Force, Length of Arc & Effective Angle of Internal Friction 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 Effective Cohesion?
In this formula, Effective Cohesion uses Shear Force on Slice in Soil Mechanics, Factor of Safety, Total Normal Force, Upward Force, Length of Arc & Effective Angle of Internal Friction. We can use 1 other way(s) to calculate the same, which is/are as follows -
  • Effective Cohesion = Shear Strength of Soil in Pascal-((Normal Stress in Pascal-Upward Force)*tan((Effective Angle of Internal Friction*pi)/180))
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