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Length of Slip Circle given Factor of Safety of Earth Dam Formula

GoLength of Slip Circle given Factor of Safety in Absence of Flow Net Formula

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

L' = \frac{(f s \cdot ΣT) - ((ΣN - ΣU) \cdot \tan (\frac{φ' \cdot π}{180}))}{c'}

L^' - Length of Slip Arc?f_s - Factor of Safety?ΣT - Sum of all Tangential Component?ΣN - Sum of all Normal Component?ΣU - Total Pore Pressure?φ' - Effective Angle of Internal Friction?c' - Effective Cohesion?π - Archimedes' constant?

Length of Slip Circle given Factor of Safety of Earth Dam Example

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Here is how the Length of Slip Circle given Factor of Safety of Earth Dam equation looks like with Values.

Here is how the Length of Slip Circle given Factor of Safety of Earth Dam equation looks like with Units.

Here is how the Length of Slip Circle given Factor of Safety of Earth Dam equation looks like.

3.0032 = \frac{(2.8 \cdot 4.98) - ((5.01 - 2) \cdot \tan (\frac{9.99 \cdot 3.1416}{180}))}{4.64}

3.0032m = \frac{(2.8 \cdot 4.98N) - ((5.01N - 2N) \cdot \tan (\frac{9.99° \cdot 3.1416}{180}))}{4.64Pa}

3.0032 = \frac{(2.8 \cdot 4.98) - ((5.01 - 2) \cdot \tan (\frac{9.99 \cdot 3.1416}{180}))}{4.64}

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Length of Slip Circle given Factor of Safety of Earth Dam Solution

Follow our step by step solution on how to calculate Length of Slip Circle given Factor of Safety of Earth Dam?

FIRST Step Consider the formula

L' = \frac{(f s \cdot ΣT) - ((ΣN - ΣU) \cdot \tan (\frac{φ' \cdot π}{180}))}{c'}

Next Step Substitute values of Variables

∴

L' = \frac{(2.8 \cdot 4.98N) - ((5.01N - 2N) \cdot \tan (\frac{9.99° \cdot π}{180}))}{4.64Pa}

Next Step Substitute values of Constants

∴

L' = \frac{(2.8 \cdot 4.98N) - ((5.01N - 2N) \cdot \tan (\frac{9.99° \cdot 3.1416}{180}))}{4.64Pa}

Next Step Convert Units

∴

L' = \frac{(2.8 \cdot 4.98N) - ((5.01N - 2N) \cdot \tan (\frac{0.1744rad \cdot 3.1416}{180}))}{4.64Pa}

Next Step Prepare to Evaluate

∴

L' = \frac{(2.8 \cdot 4.98) - ((5.01 - 2) \cdot \tan (\frac{0.1744 \cdot 3.1416}{180}))}{4.64}

Next Step Evaluate

∴

L' = 3.00319830956324m

LAST Step Rounding Answer

∴

L' = 3.0032m

Length of Slip Circle given Factor of Safety of Earth Dam Formula Elements

Variables

Constants

Functions

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

Factor of Safety

Factor of Safety is a measure of the load-carrying capacity of a structure or material compared to the actual load or stress that is applied to it.

Symbol: f_s

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Factor of Safety

Sum of all Tangential Component

Sum of all Tangential Component means total tangential component.

Symbol: ΣT

Measurement: ForceUnit: N

Note: Value should be greater than 0.

Formulas to find Sum of all Tangential Component

Sum of all Normal Component

Sum of all Normal Component means total normal force on slip circle.

Symbol: ΣN

Measurement: ForceUnit: N

Note: Value should be greater than 0.

Formulas to find Sum of all Normal Component

Total Pore Pressure

Total Pore Pressure is the total pressure of the fluid in the pore space of the rock, when it exceeds the hydrostatic pressure, over pressure situation occurs.

Symbol: ΣU

Measurement: ForceUnit: N

Note: Value should be greater than 0.

Formulas to find Total Pore Pressure

Effective Angle of Internal Friction

Effective Angle of Internal Friction is the shear strength of soil due to the friction between soil particles when subjected to effective stress.

Symbol: φ'

Measurement: AngleUnit: °

Note: Value should be greater than 0.

Formulas to find Effective Angle of Internal Friction

Effective Cohesion

Effective Cohesion is the cohesive strength of soil that is attributed to the soil's inherent properties, such as chemical bonding and other physicochemical forces between soil particles.

Symbol: c'

Measurement: PressureUnit: Pa

Note: Value should be greater than 0.

Formulas to find Effective Cohesion

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

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.

Syntax: tan(Angle)

Other Formulas to find Length of Slip Arc

Go Length of Slip Circle given Factor of Safety in Absence of Flow Net

L' = \frac{(f s \cdot ΣT) - (ΣN \cdot \tan (\frac{φ' \cdot π}{180}))}{c'}

Other formulas in Stability of Slopes In Earthen Dams category

Go Factor of Safety of Earth Dam

f s = \frac{(c' \cdot L') + ((ΣN - ΣU) \cdot \tan (\frac{φ' \cdot π}{180}))}{ΣT}

Go Sum of All Tangential Component given Factor of Safety of Earth Dam

ΣT = \frac{(c' \cdot L') + ((ΣN - ΣU) \cdot \tan (\frac{φ' \cdot π}{180}))}{f s}

How to Evaluate Length of Slip Circle given Factor of Safety of Earth Dam?

Length of Slip Circle given Factor of Safety of Earth Dam evaluator uses Length of Slip Arc = ((Factor of Safety*Sum of all Tangential Component)-((Sum of all Normal Component-Total Pore Pressure)*tan((Effective Angle of Internal Friction*pi)/180)))/Effective Cohesion to evaluate the Length of Slip Arc, The Length of Slip Circle given Factor of Safety of Earth Dam formula is defined as the value of length of slip circle when we have prior information of factor of safety of earth dam. Length of Slip Arc is denoted by L^' symbol.

How to evaluate Length of Slip Circle given Factor of Safety of Earth Dam using this online evaluator? To use this online evaluator for Length of Slip Circle given Factor of Safety of Earth Dam, enter Factor of Safety (f_s), Sum of all Tangential Component (ΣT), Sum of all Normal Component (ΣN), Total Pore Pressure (ΣU), Effective Angle of Internal Friction (φ') & Effective Cohesion (c') and hit the calculate button.

FAQs on Length of Slip Circle given Factor of Safety of Earth Dam

What is the formula to find Length of Slip Circle given Factor of Safety of Earth Dam?

The formula of Length of Slip Circle given Factor of Safety of Earth Dam is expressed as Length of Slip Arc = ((Factor of Safety*Sum of all Tangential Component)-((Sum of all Normal Component-Total Pore Pressure)*tan((Effective Angle of Internal Friction*pi)/180)))/Effective Cohesion. Here is an example- 3.003198 = ((2.8*4.98)-((5.01-2)*tan((0.174358392274201*pi)/180)))/4.64.

How to calculate Length of Slip Circle given Factor of Safety of Earth Dam?

With Factor of Safety (f_s), Sum of all Tangential Component (ΣT), Sum of all Normal Component (ΣN), Total Pore Pressure (ΣU), Effective Angle of Internal Friction (φ') & Effective Cohesion (c') we can find Length of Slip Circle given Factor of Safety of Earth Dam using the formula - Length of Slip Arc = ((Factor of Safety*Sum of all Tangential Component)-((Sum of all Normal Component-Total Pore Pressure)*tan((Effective Angle of Internal Friction*pi)/180)))/Effective Cohesion. This formula also uses Archimedes' constant and Tangent function(s).

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=((Factor of Safety*Sum of all Tangential Component)-(Sum of all Normal Component*tan((Effective Angle of Internal Friction*pi)/180)))/Effective Cohesion

Can the Length of Slip Circle given Factor of Safety of Earth Dam be negative?

No, the Length of Slip Circle given Factor of Safety of Earth Dam, measured in Length cannot be negative.

Which unit is used to measure Length of Slip Circle given Factor of Safety of Earth Dam?

Length of Slip Circle given Factor of Safety of Earth Dam 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 Circle given Factor of Safety of Earth Dam can be measured.

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Length of Slip Circle given Factor of Safety of Earth Dam Formula

​GoLength of Slip Circle given Factor of Safety in Absence of Flow Net Formula

Length of Slip Circle given Factor of Safety of Earth Dam Example

Length of Slip Circle given Factor of Safety of Earth Dam Solution

Length of Slip Circle given Factor of Safety of Earth Dam Formula Elements

Other Formulas to find Length of Slip Arc

Other formulas in Stability of Slopes In Earthen Dams category

How to Evaluate Length of Slip Circle given Factor of Safety of Earth Dam?

FAQs on Length of Slip Circle given Factor of Safety of Earth Dam

Variable Name

GoLength of Slip Circle given Factor of Safety in Absence of Flow Net Formula