Angle of Internal Friction given Resisting Moment Calculator

✖Resisting Moment is a moment produced by internal tensile and compressive forces.ⓘ Resisting Moment [M_R]			+10% -10%
✖Radius of Slip Circle is the distance between center and one point on slip circle.ⓘ Radius of Slip Circle [r]			+10% -10%
✖Unit Cohesion is the force that holds together molecules or like particles within a soil.ⓘ Unit Cohesion [c_u]			+10% -10%
✖Length of Slip Arc is the length of the arc formed by slip circle.ⓘ Length of Slip Arc [L^']			+10% -10%
✖Sum of all Normal Component means total normal force on slip circle.ⓘ Sum of all Normal Component [ΣN]			+10% -10%

✖Angle of Internal Friction of Soil is a shear strength parameter of soils.ⓘ Angle of Internal Friction given Resisting Moment [Φ_i]

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Formula

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Angle of Internal Friction given Resisting Moment

Formula

`"Φ"_{"i"} = atan((("M"_{"R"}/"r")-("c"_{"u"}*"L"^{"'"}))/"ΣN")`

Example

`"89.9914°"=atan((("20kN*m"/"0.6m")-("10Pa"*"3.0001m"))/"5N")`

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Angle of Internal Friction given Resisting Moment Solution

STEP 0: Pre-Calculation Summary

Formula Used

Angle of Internal Friction of Soil = atan(((Resisting Moment/Radius of Slip Circle)-(Unit Cohesion*Length of Slip Arc))/Sum of all Normal Component)
Φ_i = atan(((M_R/r)-(c_u*L^'))/ΣN)
This formula uses 2 Functions, 6 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

Angle of Internal Friction of Soil - (Measured in Radian) - Angle of Internal Friction of Soil is a shear strength parameter of soils.
Resisting Moment - (Measured in Newton Meter) - Resisting Moment is a moment produced by internal tensile and compressive forces.
Radius of Slip Circle - (Measured in Meter) - Radius of Slip Circle is the distance between center and one point on slip circle.
Unit Cohesion - (Measured in Pascal) - Unit Cohesion is the force that holds together molecules or like particles within a soil.
Length of Slip Arc - (Measured in Meter) - Length of Slip Arc is the length of the arc formed by slip circle.
Sum of all Normal Component - (Measured in Newton) - Sum of all Normal Component means total normal force on slip circle.

STEP 1: Convert Input(s) to Base Unit

Resisting Moment: 20 Kilonewton Meter --> 20000 Newton Meter (Check conversion here)
Radius of Slip Circle: 0.6 Meter --> 0.6 Meter No Conversion Required
Unit Cohesion: 10 Pascal --> 10 Pascal No Conversion Required
Length of Slip Arc: 3.0001 Meter --> 3.0001 Meter No Conversion Required
Sum of all Normal Component: 5 Newton --> 5 Newton No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

Φ_i = atan(((M_R/r)-(c_u*L^'))/ΣN) --> atan(((20000/0.6)-(10*3.0001))/5)

Evaluating ... ...

Φ_i = 1.57064619166991

STEP 3: Convert Result to Output's Unit

1.57064619166991 Radian -->89.9913978909984 Degree (Check conversion here)

FINAL ANSWER

89.9913978909984 ≈ 89.9914 Degree <-- Angle of Internal Friction of Soil

(Calculation completed in 00.020 seconds)

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Home » Engineering » Civil » Geotechnical Engineering » Stability of Slopes In Earthen Dams » The Swedish Slip Circle Method » Angle of Internal Friction given Resisting Moment

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Created by Suraj Kumar

Birsa Institute of Technology (BIT), Sindri

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Meerut Institute of Engineering and Technology (MIET), Meerut

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< 25 The Swedish Slip Circle Method Calculators

Sum of Normal Component given Factor of Safety

Go Sum of All Normal Component in Soil Mechanics = ((Factor of Safety*Sum of All Tangential Component in Soil Mechanics)-(Unit Cohesion*Length of Slip Arc))/tan((Angle of Internal Friction of Soil*pi)/180)

Length of Slip Circle given Sum of Tangential Component

Go Length of Slip Arc = ((Factor of Safety*Sum of all Tangential Component)-(Sum of all Normal Component*tan((Angle of Internal Friction*pi)/180)))/Unit Cohesion

Sum of Tangential Component given Factor of Safety

Go Sum of all Tangential Component = ((Unit Cohesion*Length of Slip Arc)+(Sum of all Normal Component*tan((Angle of Internal Friction*pi)/180)))/Factor of Safety

Total Length of Slip Circle given Resisting Moment

Go Length of Slip Arc = ((Resisting Moment/Radius of Slip Circle)-(Sum of all Normal Component*tan((Angle of Internal Friction))))/Unit Cohesion

Sum of Normal Component given Resisting Moment

Go Sum of all Normal Component = ((Resisting Moment/Radius of Slip Circle)-(Unit Cohesion*Length of Slip Arc))/tan((Angle of Internal Friction))

Resisting Moment given Radius of Slip Circle

Go Resisting Moment = Radius of Slip Circle*((Unit Cohesion*Length of Slip Arc)+(Sum of all Normal Component*tan((Angle of Internal Friction))))

Normal Component given Resisting Force from Coulomb's Equation

Go Normal Component of Force in Soil Mechanics = (Resisting force in Soil Mechanics-(Unit Cohesion*Curve Length))/tan((Angle of Internal Friction of Soil))

Resisting Force from Coulomb's Equation

Go Resisting Force = ((Unit Cohesion*Curve Length)+(Normal Component of Force*tan((Angle of Internal Friction))))

Curve Length of Each Slice given Resisting Force from Coulomb's Equation

Go Curve Length = (Resisting Force-(Normal Component of Force*tan((Angle of Internal Friction))))/Unit Cohesion

Radial Distance from Centre of Rotation given Factor of Safety

Go Radial Distance = Factor of Safety/((Unit Cohesion*Length of Slip Arc)/(Weight of Body in Newtons*Distance))

Distance between Line of Action of Weight and Line Passing through Center

Go Distance = (Unit Cohesion*Length of Slip Arc*Radial Distance)/(Weight of Body in Newtons*Factor of Safety)

Distance between Line of Action and Line Passing through Center given Mobilised Cohesion

Go Distance = Mobilised Shear Resistance of Soil/((Weight of Body in Newtons*Radial Distance)/Length of Slip Arc)

Radial Distance from Centre of Rotation given Mobilised Shear resistance of Soil

Go Radial Distance = Mobilised Shear Resistance of Soil/((Weight of Body in Newtons*Distance)/Length of Slip Arc)

Mobilised Shear resistance of Soil given Weight of Soil on Wedge

Go Mobilised Shear Resistance of Soil = (Weight of Body in Newtons*Distance*Radial Distance)/Length of Slip Arc

Radial Distance from Center of Rotation given Length of Slip Arc

Go Radial Distance = (360*Length of Slip Arc)/(2*pi*Arc Angle*(180/pi))

Arc Angle given Length of Slip Arc

Go Arc Angle = (360*Length of Slip Arc)/(2*pi*Radial Distance)*(pi/180)

Radial Distance from Centre of Rotation given Moment of Resistance

Go Radial Distance = Resisting Moment/(Unit Cohesion*Length of Slip Arc)

Moment of Resistance given Unit Cohesion

Go Resisting Moment = (Unit Cohesion*Length of Slip Arc*Radial Distance)

Sum of Tangential Component given Driving Moment

Go Sum of all Tangential Component = Driving Moment/Radius of Slip Circle

Driving Moment given Radius of Slip Circle

Go Driving Moment = Radius of Slip Circle*Sum of all Tangential Component

Mobilised Shear resistance of Soil given Factor of Safety

Go Mobilised Shear Resistance of Soil = Unit Cohesion/Factor of Safety

Distance between Line of Action and Line Passing through Center given Driving Moment

Go Distance = Driving Moment/Weight of Body in Newtons

Driving Moment given Weight of Soil on Wedge

Go Driving Moment = Weight of Body in Newtons*Distance

Moment of Resistance given Factor of Safety

Go Resisting Moment = Factor of Safety*Driving Moment

Driving Moment given Factor of Safety

Go Driving Moment = Resisting Moment/Factor of Safety

Angle of Internal Friction given Resisting Moment Formula

Angle of Internal Friction of Soil = atan(((Resisting Moment/Radius of Slip Circle)-(Unit Cohesion*Length of Slip Arc))/Sum of all Normal Component)
Φ_i = atan(((M_R/r)-(c_u*L^'))/ΣN)

What is Angle of Internal Friction?

The angle of internal friction is a physical property of earth materials or the slope of a linear representation of the shear strength of earth materials.

How to Calculate Angle of Internal Friction given Resisting Moment?

Angle of Internal Friction given Resisting Moment calculator uses Angle of Internal Friction of Soil = atan(((Resisting Moment/Radius of Slip Circle)-(Unit Cohesion*Length of Slip Arc))/Sum of all Normal Component) to calculate the Angle of Internal Friction of Soil, The Angle of Internal Friction given Resisting Moment is defined as the angle at which a material's resisting moment equals the applied moment, stabilizing movement. Angle of Internal Friction of Soil is denoted by Φ_i symbol.

How to calculate Angle of Internal Friction given Resisting Moment using this online calculator? To use this online calculator for Angle of Internal Friction given Resisting Moment, enter Resisting Moment (M_R), Radius of Slip Circle (r), Unit Cohesion (c_u), Length of Slip Arc (L^') & Sum of all Normal Component (ΣN) and hit the calculate button. Here is how the Angle of Internal Friction given Resisting Moment calculation can be explained with given input values -> 5154.973 = atan(((20000/0.6)-(10*3.0001))/5).

FAQ

What is Angle of Internal Friction given Resisting Moment?

The Angle of Internal Friction given Resisting Moment is defined as the angle at which a material's resisting moment equals the applied moment, stabilizing movement and is represented as Φ_i = atan(((M_R/r)-(c_u*L^'))/ΣN) or Angle of Internal Friction of Soil = atan(((Resisting Moment/Radius of Slip Circle)-(Unit Cohesion*Length of Slip Arc))/Sum of all Normal Component). Resisting Moment is a moment produced by internal tensile and compressive forces, Radius of Slip Circle is the distance between center and one point on slip circle, Unit Cohesion is the force that holds together molecules or like particles within a soil, Length of Slip Arc is the length of the arc formed by slip circle & Sum of all Normal Component means total normal force on slip circle.

How to calculate Angle of Internal Friction given Resisting Moment?

The Angle of Internal Friction given Resisting Moment is defined as the angle at which a material's resisting moment equals the applied moment, stabilizing movement is calculated using Angle of Internal Friction of Soil = atan(((Resisting Moment/Radius of Slip Circle)-(Unit Cohesion*Length of Slip Arc))/Sum of all Normal Component). To calculate Angle of Internal Friction given Resisting Moment, you need Resisting Moment (M_R), Radius of Slip Circle (r), Unit Cohesion (c_u), Length of Slip Arc (L^') & Sum of all Normal Component (ΣN). With our tool, you need to enter the respective value for Resisting Moment, Radius of Slip Circle, Unit Cohesion, Length of Slip Arc & Sum of all Normal Component and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

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