Total Length of Slip Circle given Resisting Moment Calculator

✖Resisting Moment is the moment (or torque) that counteracts the applied moment or load that tends to cause rotation or failure in a soil mass or structure.ⓘ 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%
✖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 measure of the shear strength of soil due to friction.ⓘ Angle of Internal Friction of Soil [Φ_i]			+10% -10%
✖Unit Cohesion is the shear strength property of a soil that is solely attributed to cohesive forces between soil particles.ⓘ Unit Cohesion [c_u]			+10% -10%

✖Length of Slip Arc is the length of the arc formed by slip circle.ⓘ Total Length of Slip Circle given Resisting Moment [L^']

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Total Length of Slip Circle given Resisting Moment Solution

STEP 0: Pre-Calculation Summary

Formula Used

Length of Slip Arc = ((Resisting Moment/Radius of Slip Circle)-(Sum of all Normal Component*tan((Angle of Internal Friction of Soil))))/Unit Cohesion
L^' = ((M_R/r)-(ΣN*tan((Φ_i))))/c_u
This formula uses 1 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)

Variables Used

Length of Slip Arc - (Measured in Meter) - Length of Slip Arc is the length of the arc formed by slip circle.
Resisting Moment - (Measured in Kilonewton Meter) - Resisting Moment is the moment (or torque) that counteracts the applied moment or load that tends to cause rotation or failure in a soil mass or structure.
Radius of Slip Circle - (Measured in Meter) - Radius of Slip Circle is the distance between center and one point on slip circle.
Sum of all Normal Component - (Measured in Newton) - Sum of all Normal Component means total normal force on slip circle.
Angle of Internal Friction of Soil - (Measured in Radian) - Angle of Internal Friction of Soil is a measure of the shear strength of soil due to friction.
Unit Cohesion - (Measured in Pascal) - Unit Cohesion is the shear strength property of a soil that is solely attributed to cohesive forces between soil particles.

STEP 1: Convert Input(s) to Base Unit

Resisting Moment: 45.05 Kilonewton Meter --> 45.05 Kilonewton Meter No Conversion Required
Radius of Slip Circle: 0.6 Meter --> 0.6 Meter No Conversion Required
Sum of all Normal Component: 5.01 Newton --> 5.01 Newton No Conversion Required
Angle of Internal Friction of Soil: 82.87 Degree --> 1.44635435112743 Radian (Check conversion here)
Unit Cohesion: 10 Pascal --> 10 Pascal No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

L^' = ((M_R/r)-(ΣN*tan((Φ_i))))/c_u --> ((45.05/0.6)-(5.01*tan((1.44635435112743))))/10

Evaluating ... ...

L^' = 3.50316390388665

STEP 3: Convert Result to Output's Unit

3.50316390388665 Meter --> No Conversion Required

FINAL ANSWER

3.50316390388665 ≈ 3.503164 Meter <-- Length of Slip Arc

(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 » Total Length of Slip Circle given Resisting Moment

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Created by Suraj Kumar

Birsa Institute of Technology (BIT), Sindri

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< The Swedish Slip Circle Method Calculators

Radial Distance from Center of Rotation given Length of Slip Arc

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

Arc Angle given Length of Slip Arc

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

Moment of Resistance given Factor of Safety

LaTeX Go Moment of Resistance with Factor of Safety = Factor of Safety*Driving Moment

Driving Moment given Factor of Safety

LaTeX Go Driving Moment = Resisting Moment/Factor of Safety

Total Length of Slip Circle given Resisting Moment Formula

LaTeX Go

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

What is Slipe Circle Method?

The Swedish Circle method or the method of slices is used for determining the stability of the earth slope of c–ϕ soil.The threshold acceleration and displacement of soil slopes are calculated using the pseudo-dynamic method.

How to Calculate Total Length of Slip Circle given Resisting Moment?

Total Length of Slip Circle given Resisting Moment calculator uses Length of Slip Arc = ((Resisting Moment/Radius of Slip Circle)-(Sum of all Normal Component*tan((Angle of Internal Friction of Soil))))/Unit Cohesion to calculate the Length of Slip Arc, The Total Length of Slip Circle given Resisting Moment formula is defined as the measure of the value of perimeter of the circular failure surface assumed in slope stability analysis. This circle represents the potential slip surface along which a slope might fail under the influence of external forces (such as gravity, water pressure, or seismic forces). Length of Slip Arc is denoted by L^' symbol.

How to calculate Total Length of Slip Circle given Resisting Moment using this online calculator? To use this online calculator for Total Length of Slip Circle given Resisting Moment, enter Resisting Moment (M_R), Radius of Slip Circle (r), Sum of all Normal Component (ΣN), Angle of Internal Friction of Soil (Φ_i) & Unit Cohesion (c_u) and hit the calculate button. Here is how the Total Length of Slip Circle given Resisting Moment calculation can be explained with given input values -> 3.503164 = ((45050/0.6)-(5.01*tan((1.44635435112743))))/10.

FAQ

What is Total Length of Slip Circle given Resisting Moment?

The Total Length of Slip Circle given Resisting Moment formula is defined as the measure of the value of perimeter of the circular failure surface assumed in slope stability analysis. This circle represents the potential slip surface along which a slope might fail under the influence of external forces (such as gravity, water pressure, or seismic forces) and is represented as L^' = ((M_R/r)-(ΣN*tan((Φ_i))))/c_u or Length of Slip Arc = ((Resisting Moment/Radius of Slip Circle)-(Sum of all Normal Component*tan((Angle of Internal Friction of Soil))))/Unit Cohesion. Resisting Moment is the moment (or torque) that counteracts the applied moment or load that tends to cause rotation or failure in a soil mass or structure, Radius of Slip Circle is the distance between center and one point on slip circle, Sum of all Normal Component means total normal force on slip circle, Angle of Internal Friction of Soil is a measure of the shear strength of soil due to friction & Unit Cohesion is the shear strength property of a soil that is solely attributed to cohesive forces between soil particles.

How to calculate Total Length of Slip Circle given Resisting Moment?

The Total Length of Slip Circle given Resisting Moment formula is defined as the measure of the value of perimeter of the circular failure surface assumed in slope stability analysis. This circle represents the potential slip surface along which a slope might fail under the influence of external forces (such as gravity, water pressure, or seismic forces) is calculated using Length of Slip Arc = ((Resisting Moment/Radius of Slip Circle)-(Sum of all Normal Component*tan((Angle of Internal Friction of Soil))))/Unit Cohesion. To calculate Total Length of Slip Circle given Resisting Moment, you need Resisting Moment (M_R), Radius of Slip Circle (r), Sum of all Normal Component (ΣN), Angle of Internal Friction of Soil (Φ_i) & Unit Cohesion (c_u). With our tool, you need to enter the respective value for Resisting Moment, Radius of Slip Circle, Sum of all Normal Component, Angle of Internal Friction of Soil & Unit Cohesion 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 Resisting Moment, Radius of Slip Circle, Sum of all Normal Component, Angle of Internal Friction of Soil & Unit Cohesion. We can use 2 other way(s) to calculate the same, which is/are as follows -

Length of Slip Arc = ((Factor of Safety*Sum of All Tangential Component in Soil Mechanics)-(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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