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

✖Shear Force on Slice in Soil Mechanics acting along the base of slice.ⓘ Shear Force on Slice in Soil Mechanics [S]			+10% -10%
✖Factor of Safety expresses how much stronger a system is than it needs to be for an intended load.ⓘ Factor of Safety [f_s]			+10% -10%
✖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.ⓘ Effective Cohesion [c']			+10% -10%
✖Length of Arc of the slice taken into consideration.ⓘ Length of Arc [l]			+10% -10%
✖Total normal force acting at the base of the slice.ⓘ Total Normal Force [P]			+10% -10%
✖Upward Force due to seepage water.ⓘ Upward Force [u]			+10% -10%

✖Effective Angle of Internal Friction is a measure of the shear strength of soils due to friction.ⓘ Effective Angle of Internal Friction given Shear Force in Bishop's Analysis [φ']

⎘ Copy

👎

Formula

✖

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

Formula

`"φ'" = atan((("S"*"f"_{"s"})-("c'"*"l"))/("P"-("u"*"l")))`

Example

`"9.874119°"=atan((("11.07N"*"2.8")-("4Pa"*"9.42m"))/("150N"-("20Pa"*"9.42m")))`

Calculator

LaTeX

Reset

👍

Download Slope Stability Analysis using Bishops Method Formulas PDF PDF Image

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

STEP 0: Pre-Calculation Summary

Formula Used

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)))
φ' = atan(((S*f_s)-(c'*l))/(P-(u*l)))
This formula uses 2 Functions, 7 Variables

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)
atan - Inverse tan is used to calculate the angle by applying the tangent ratio of the angle, which is the opposite side divided by the adjacent side of the right triangle., atan(Number)

Variables Used

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.
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.
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.
Length of Arc - (Measured in Meter) - Length of Arc of the slice taken into consideration.
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.

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
Effective Cohesion: 4 Pascal --> 4 Pascal No Conversion Required
Length of Arc: 9.42 Meter --> 9.42 Meter No Conversion Required
Total Normal Force: 150 Newton --> 150 Newton No Conversion Required
Upward Force: 20 Pascal --> 20 Pascal No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

φ' = atan(((S*f_s)-(c'*l))/(P-(u*l))) --> atan(((11.07*2.8)-(4*9.42))/(150-(20*9.42)))

Evaluating ... ...

φ' = 0.17233587966936

STEP 3: Convert Result to Output's Unit

0.17233587966936 Radian -->9.87411856373062 Degree (Check conversion here)

FINAL ANSWER

9.87411856373062 ≈ 9.874119 Degree <-- Effective Angle of Internal Friction

(Calculation completed in 00.004 seconds)

You are here -

Home » Engineering » Civil » Geotechnical Engineering » Slope Stability Analysis using Bishops Method » Effective Angle of Internal Friction given Shear Force in Bishop's Analysis

Credits

Created by Suraj Kumar

Birsa Institute of Technology (BIT), Sindri

Suraj Kumar has created this Calculator and 2200+ more calculators!

Verified by Ishita Goyal

Meerut Institute of Engineering and Technology (MIET), Meerut

Ishita Goyal has verified this Calculator and 2600+ more calculators!

< 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 Angle of Internal Friction given Shear Force in Bishop's Analysis Formula

What is Angle of Internal Friction?

A measure of the ability of a unit of rock or soil to withstand a shear stress. It is the angle (φ), measured between the normal force (N) and resultant force (R), that is attained when failure just occurs in response to a shearing stress (S).

How to Calculate Effective Angle of Internal Friction given Shear Force in Bishop's Analysis?

Effective Angle of Internal Friction given Shear Force in Bishop's Analysis calculator uses 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))) to calculate the Effective Angle of Internal Friction, The Effective Angle of Internal Friction given Shear Force in Bishop's Analysis is defined as the value of effective angle of internal friction when we have prior information of other parameters used. Effective Angle of Internal Friction is denoted by φ' symbol.

How to calculate Effective Angle of Internal Friction given Shear Force in Bishop's Analysis using this online calculator? To use this online calculator for Effective Angle of Internal Friction given Shear Force in Bishop's Analysis, enter Shear Force on Slice in Soil Mechanics (S), Factor of Safety (f_s), Effective Cohesion (c'), Length of Arc (l), Total Normal Force (P) & Upward Force (u) and hit the calculate button. Here is how the Effective Angle of Internal Friction given Shear Force in Bishop's Analysis calculation can be explained with given input values -> 1801.86 = atan(((11.07*2.8)-(4*9.42))/(150-(20*9.42))).

FAQ

What is Effective Angle of Internal Friction given Shear Force in Bishop's Analysis?

The Effective Angle of Internal Friction given Shear Force in Bishop's Analysis is defined as the value of effective angle of internal friction when we have prior information of other parameters used and is represented as φ' = atan(((S*f_s)-(c'*l))/(P-(u*l))) or 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))). 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, 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, Length of Arc of the slice taken into consideration, Total normal force acting at the base of the slice & Upward Force due to seepage water.

How to calculate Effective Angle of Internal Friction given Shear Force in Bishop's Analysis?

The Effective Angle of Internal Friction given Shear Force in Bishop's Analysis is defined as the value of effective angle of internal friction when we have prior information of other parameters used is calculated using 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))). To calculate Effective Angle of Internal Friction given Shear Force in Bishop's Analysis, you need Shear Force on Slice in Soil Mechanics (S), Factor of Safety (f_s), Effective Cohesion (c'), Length of Arc (l), Total Normal Force (P) & Upward Force (u). With our tool, you need to enter the respective value for Shear Force on Slice in Soil Mechanics, Factor of Safety, Effective Cohesion, Length of Arc, Total Normal Force & Upward Force 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 Angle of Internal Friction?

In this formula, Effective Angle of Internal Friction uses Shear Force on Slice in Soil Mechanics, Factor of Safety, Effective Cohesion, Length of Arc, Total Normal Force & Upward Force. We can use 1 other way(s) to calculate the same, which is/are as follows -

Effective Angle of Internal Friction = atan((Shear Strength-Effective Cohesion)/(Normal Stress in Mega Pascal-Upward Force))

Home

FREE PDFs

🔍 Search