Length of Slip Arc given Factor of Safety Calculator

✖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%
✖Unit Cohesion is the force that holds together molecules or like particles within a soil.ⓘ Unit Cohesion [c_u]			+10% -10%
✖Radial Distance is defined as distance between whisker sensor's pivot point to whisker-object contact point.ⓘ Radial Distance [d_radial]			+10% -10%
✖Weight of Body in Newtons is the force with which a body is pulled toward the earth.ⓘ Weight of Body in Newtons [W]			+10% -10%
✖Distance between the line of action and the line passing through the center is the perpendicular distance from a point to a line in a geometric configuration.ⓘ Distance [x']			+10% -10%

✖Length of Slip Arc is the length of the arc formed by slip circle.ⓘ Length of Slip Arc given Factor of Safety [L^']

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Formula

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Length of Slip Arc given Factor of Safety

Formula

`"L"^{"'"} = "f"_{"s"}/(("c"_{"u"}*"d"_{"radial"})/("W"*"x'"))`

Example

`"1.866667m"="2.8"/(("10Pa"*"1.5m")/("8N"*"1.25m"))`

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Length of Slip Arc given Factor of Safety Solution

STEP 0: Pre-Calculation Summary

Formula Used

Length of Slip Arc = Factor of Safety/((Unit Cohesion*Radial Distance)/(Weight of Body in Newtons*Distance))
L^' = f_s/((c_u*d_radial)/(W*x'))
This formula uses 6 Variables

Variables Used

Length of Slip Arc - (Measured in Meter) - Length of Slip Arc is the length of the arc formed by slip circle.
Factor of Safety - Factor of Safety expresses how much stronger a system is than it needs to be for an intended load.
Unit Cohesion - (Measured in Pascal) - Unit Cohesion is the force that holds together molecules or like particles within a soil.
Radial Distance - (Measured in Meter) - Radial Distance is defined as distance between whisker sensor's pivot point to whisker-object contact point.
Weight of Body in Newtons - (Measured in Newton) - Weight of Body in Newtons is the force with which a body is pulled toward the earth.
Distance - (Measured in Meter) - Distance between the line of action and the line passing through the center is the perpendicular distance from a point to a line in a geometric configuration.

STEP 1: Convert Input(s) to Base Unit

Factor of Safety: 2.8 --> No Conversion Required
Unit Cohesion: 10 Pascal --> 10 Pascal No Conversion Required
Radial Distance: 1.5 Meter --> 1.5 Meter No Conversion Required
Weight of Body in Newtons: 8 Newton --> 8 Newton No Conversion Required
Distance: 1.25 Meter --> 1.25 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

L^' = f_s/((c_u*d_radial)/(W*x')) --> 2.8/((10*1.5)/(8*1.25))

Evaluating ... ...

L^' = 1.86666666666667

STEP 3: Convert Result to Output's Unit

1.86666666666667 Meter --> No Conversion Required

FINAL ANSWER

1.86666666666667 ≈ 1.866667 Meter <-- Length of Slip Arc

(Calculation completed in 00.004 seconds)

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Home » Engineering » Civil » Geotechnical Engineering » Stability of Slopes In Earthen Dams » The Swedish Slip Circle Method » Length of Slip Arc given Factor of Safety

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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

Length of Slip Arc given Factor of Safety Formula

Length of Slip Arc = Factor of Safety/((Unit Cohesion*Radial Distance)/(Weight of Body in Newtons*Distance))
L^' = f_s/((c_u*d_radial)/(W*x'))

What is Slip Circle Method?

The Swedish slip circle method assumes a circular failure interface, and analyzes stress and strength parameters using circular geometry and statics. The moment caused by the internal driving forces of a slope is compared to the moment caused by forces resisting slope failure.

How to Calculate Length of Slip Arc given Factor of Safety?

Length of Slip Arc given Factor of Safety calculator uses Length of Slip Arc = Factor of Safety/((Unit Cohesion*Radial Distance)/(Weight of Body in Newtons*Distance)) to calculate the Length of Slip Arc, The Length of Slip Arc given Factor of Safety is defined as value of length of slip arc when we have prior information of other parameters used. Length of Slip Arc is denoted by L^' symbol.

How to calculate Length of Slip Arc given Factor of Safety using this online calculator? To use this online calculator for Length of Slip Arc given Factor of Safety, enter Factor of Safety (f_s), Unit Cohesion (c_u), Radial Distance (d_radial), Weight of Body in Newtons (W) & Distance (x') and hit the calculate button. Here is how the Length of Slip Arc given Factor of Safety calculation can be explained with given input values -> 7.466667 = 2.8/((10*1.5)/(8*1.25)).

FAQ

What is Length of Slip Arc given Factor of Safety?

The Length of Slip Arc given Factor of Safety is defined as value of length of slip arc when we have prior information of other parameters used and is represented as L^' = f_s/((c_u*d_radial)/(W*x')) or Length of Slip Arc = Factor of Safety/((Unit Cohesion*Radial Distance)/(Weight of Body in Newtons*Distance)). Factor of Safety expresses how much stronger a system is than it needs to be for an intended load, Unit Cohesion is the force that holds together molecules or like particles within a soil, Radial Distance is defined as distance between whisker sensor's pivot point to whisker-object contact point, Weight of Body in Newtons is the force with which a body is pulled toward the earth & Distance between the line of action and the line passing through the center is the perpendicular distance from a point to a line in a geometric configuration.

How to calculate Length of Slip Arc given Factor of Safety?

The Length of Slip Arc given Factor of Safety is defined as value of length of slip arc when we have prior information of other parameters used is calculated using Length of Slip Arc = Factor of Safety/((Unit Cohesion*Radial Distance)/(Weight of Body in Newtons*Distance)). To calculate Length of Slip Arc given Factor of Safety, you need Factor of Safety (f_s), Unit Cohesion (c_u), Radial Distance (d_radial), Weight of Body in Newtons (W) & Distance (x'). With our tool, you need to enter the respective value for Factor of Safety, Unit Cohesion, Radial Distance, Weight of Body in Newtons & Distance 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 Length of Slip Arc?

In this formula, Length of Slip Arc uses Factor of Safety, Unit Cohesion, Radial Distance, Weight of Body in Newtons & Distance. We can use 3 other way(s) to calculate the same, which is/are as follows -

Length of Slip Arc = ((Resisting Moment/Radius of Slip Circle)-(Sum of all Normal Component*tan((Angle of Internal Friction))))/Unit Cohesion
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
Length of Slip Arc = (2*pi*Radial Distance*Arc Angle*(180/pi))/360

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