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Length of Slip Arc Formula

GoTotal Length of Slip Circle given Resisting Moment Formula

GoLength of Slip Circle given Sum of Tangential Component Formula

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Length of Slip Arc is the length of the arc formed by slip circle. Check FAQs

L' = \frac{2 \cdot π \cdot d radial \cdot δ \cdot (\frac{180}{π})}{360}

L^' - Length of Slip Arc?d_radial - Radial Distance?δ - Arc Angle?π - Archimedes' constant?

Length of Slip Arc Example

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Here is how the Length of Slip Arc equation looks like with Values.

Here is how the Length of Slip Arc equation looks like with Units.

Here is how the Length of Slip Arc equation looks like.

3.0002 = \frac{2 \cdot 3.1416 \cdot 1.5 \cdot 2.0001 \cdot (\frac{180}{3.1416})}{360}

3.0002m = \frac{2 \cdot 3.1416 \cdot 1.5m \cdot 2.0001rad \cdot (\frac{180}{3.1416})}{360}

3.0002 = \frac{2 \cdot 3.1416 \cdot 1.5 \cdot 2.0001 \cdot (\frac{180}{3.1416})}{360}

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Length of Slip Arc Solution

Follow our step by step solution on how to calculate Length of Slip Arc?

FIRST Step Consider the formula

L' = \frac{2 \cdot π \cdot d radial \cdot δ \cdot (\frac{180}{π})}{360}

Next Step Substitute values of Variables

∴

L' = \frac{2 \cdot π \cdot 1.5m \cdot 2.0001rad \cdot (\frac{180}{π})}{360}

Next Step Substitute values of Constants

∴

L' = \frac{2 \cdot 3.1416 \cdot 1.5m \cdot 2.0001rad \cdot (\frac{180}{3.1416})}{360}

Next Step Prepare to Evaluate

∴

L' = \frac{2 \cdot 3.1416 \cdot 1.5 \cdot 2.0001 \cdot (\frac{180}{3.1416})}{360}

Next Step Evaluate

∴

L' = 3.00015m

LAST Step Rounding Answer

∴

L' = 3.0002m

Length of Slip Arc Formula Elements

Variables

Constants

Length of Slip Arc

Length of Slip Arc is the length of the arc formed by slip circle.

Symbol: L^'

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Length of Slip Arc

Radial Distance

Radial Distance is defined as distance between whisker sensor's pivot point to whisker-object contact point.

Symbol: d_radial

Measurement: LengthUnit: m

Note: Value can be positive or negative.

Formulas to find Radial Distance

Arc Angle

Arc Angle is the angle formed at the arc of slip circle.

Symbol: δ

Measurement: AngleUnit: rad

Note: Value should be greater than 0.

Formulas to find Arc Angle

Archimedes' constant

Archimedes' constant is a mathematical constant that represents the ratio of the circumference of a circle to its diameter.

Symbol: π

Value: 3.14159265358979323846264338327950288

Other Formulas to find Length of Slip Arc

Go Total Length of Slip Circle given Resisting Moment

L' = \frac{(\frac{M R}{r}) - (ΣN \cdot \tan ((Φ i)))}{c u}

Go Length of Slip Circle given Sum of Tangential Component

L' = \frac{(f s \cdot F t) - (ΣN \cdot \tan (\frac{φ \cdot π}{180}))}{c u}

Other formulas in The Swedish Slip Circle Method category

Go Radial Distance from Center of Rotation given Length of Slip Arc

d radial = \frac{360 \cdot L'}{2 \cdot π \cdot δ \cdot (\frac{180}{π})}

Go Arc Angle given Length of Slip Arc

δ = \frac{360 \cdot L'}{2 \cdot π \cdot d radial} \cdot (\frac{π}{180})

Go Moment of Resistance given Factor of Safety

M r' = f s \cdot M D

Go Driving Moment given Factor of Safety

M D = \frac{M R}{f s}

How to Evaluate Length of Slip Arc?

Length of Slip Arc evaluator uses Length of Slip Arc = (2*pi*Radial Distance*Arc Angle*(180/pi))/360 to evaluate the Length of Slip Arc, The Length of Slip Arc formula is defined as the length along which potential slip or failure could occur within a soil mass. This concept is particularly relevant in slope stability analysis and retaining wall design. Length of Slip Arc is denoted by L^' symbol.

How to evaluate Length of Slip Arc using this online evaluator? To use this online evaluator for Length of Slip Arc, enter Radial Distance (d_radial) & Arc Angle (δ) and hit the calculate button.

FAQs on Length of Slip Arc

What is the formula to find Length of Slip Arc?

The formula of Length of Slip Arc is expressed as Length of Slip Arc = (2*pi*Radial Distance*Arc Angle*(180/pi))/360. Here is an example- 3.00015 = (2*pi*1.5*2.0001*(180/pi))/360.

How to calculate Length of Slip Arc?

With Radial Distance (d_radial) & Arc Angle (δ) we can find Length of Slip Arc using the formula - Length of Slip Arc = (2*pi*Radial Distance*Arc Angle*(180/pi))/360. This formula also uses Archimedes' constant .

What are the other ways to Calculate Length of Slip Arc?

Here are the different ways to Calculate Length of Slip Arc-

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

Can the Length of Slip Arc be negative?

No, the Length of Slip Arc, measured in Length cannot be negative.

Which unit is used to measure Length of Slip Arc?

Length of Slip Arc is usually measured using the Meter[m] for Length. Millimeter[m], Kilometer[m], Decimeter[m] are the few other units in which Length of Slip Arc can be measured.

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