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Effective Cohesion given Factor of Safety of Earth Dam Formula

GoEffective Cohesion given Factor of Safety in Absence of Flow Net Formula

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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. Check FAQs

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

c' - Effective Cohesion?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?L^' - Length of Slip Arc?π - Archimedes' constant?

Effective Cohesion given Factor of Safety of Earth Dam Example

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Here is how the Effective Cohesion given Factor of Safety of Earth Dam equation looks like with Values.

Here is how the Effective Cohesion given Factor of Safety of Earth Dam equation looks like with Units.

Here is how the Effective Cohesion given Factor of Safety of Earth Dam equation looks like.

4.6448 = \frac{(2.8 \cdot 4.98) - ((5.01 - 2) \cdot \tan (\frac{9.99 \cdot 3.1416}{180}))}{3.0001}

4.6448Pa = \frac{(2.8 \cdot 4.98N) - ((5.01N - 2N) \cdot \tan (\frac{9.99° \cdot 3.1416}{180}))}{3.0001m}

4.6448 = \frac{(2.8 \cdot 4.98) - ((5.01 - 2) \cdot \tan (\frac{9.99 \cdot 3.1416}{180}))}{3.0001}

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Effective Cohesion given Factor of Safety of Earth Dam Solution

Follow our step by step solution on how to calculate Effective Cohesion given Factor of Safety of Earth Dam?

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

c' = \frac{(2.8 \cdot 4.98N) - ((5.01N - 2N) \cdot \tan (\frac{9.99° \cdot π}{180}))}{3.0001m}

Next Step Substitute values of Constants

∴

c' = \frac{(2.8 \cdot 4.98N) - ((5.01N - 2N) \cdot \tan (\frac{9.99° \cdot 3.1416}{180}))}{3.0001m}

Next Step Convert Units

∴

c' = \frac{(2.8 \cdot 4.98N) - ((5.01N - 2N) \cdot \tan (\frac{0.1744rad \cdot 3.1416}{180}))}{3.0001m}

Next Step Prepare to Evaluate

∴

c' = \frac{(2.8 \cdot 4.98) - ((5.01 - 2) \cdot \tan (\frac{0.1744 \cdot 3.1416}{180}))}{3.0001}

Next Step Evaluate

∴

c' = 4.64479189239473Pa

LAST Step Rounding Answer

∴

c' = 4.6448Pa

Effective Cohesion given Factor of Safety of Earth Dam Formula Elements

Variables

Constants

Functions

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

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

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

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 Effective Cohesion

Go Effective Cohesion given Factor of Safety in Absence of Flow Net

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

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 Effective Cohesion given Factor of Safety of Earth Dam?

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

How to evaluate Effective Cohesion given Factor of Safety of Earth Dam using this online evaluator? To use this online evaluator for Effective Cohesion 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') & Length of Slip Arc (L^') and hit the calculate button.

FAQs on Effective Cohesion given Factor of Safety of Earth Dam

What is the formula to find Effective Cohesion given Factor of Safety of Earth Dam?

The formula of Effective Cohesion given Factor of Safety of Earth Dam is expressed as Effective Cohesion = ((Factor of Safety*Sum of all Tangential Component)-((Sum of all Normal Component-Total Pore Pressure)*tan((Effective Angle of Internal Friction*pi)/180)))/Length of Slip Arc. Here is an example- 7.49185 = ((2.8*4.98)-((5.01-2)*tan((0.174358392274201*pi)/180)))/3.0001.

How to calculate Effective Cohesion 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') & Length of Slip Arc (L^') we can find Effective Cohesion given Factor of Safety of Earth Dam using the formula - Effective Cohesion = ((Factor of Safety*Sum of all Tangential Component)-((Sum of all Normal Component-Total Pore Pressure)*tan((Effective Angle of Internal Friction*pi)/180)))/Length of Slip Arc. This formula also uses Archimedes' constant and Tangent (tan) function(s).

What are the other ways to Calculate Effective Cohesion?

Here are the different ways to Calculate Effective Cohesion-

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

Can the Effective Cohesion given Factor of Safety of Earth Dam be negative?

No, the Effective Cohesion given Factor of Safety of Earth Dam, measured in Pressure cannot be negative.

Which unit is used to measure Effective Cohesion given Factor of Safety of Earth Dam?

Effective Cohesion given Factor of Safety of Earth Dam is usually measured using the Pascal[Pa] for Pressure. Kilopascal[Pa], Bar[Pa], Pound Per Square Inch[Pa] are the few other units in which Effective Cohesion given Factor of Safety of Earth Dam can be measured.

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Effective Cohesion given Factor of Safety of Earth Dam Formula

​GoEffective Cohesion given Factor of Safety in Absence of Flow Net Formula

Effective Cohesion given Factor of Safety of Earth Dam Example

Effective Cohesion given Factor of Safety of Earth Dam Solution

Effective Cohesion given Factor of Safety of Earth Dam Formula Elements

Other Formulas to find Effective Cohesion

Other formulas in Stability of Slopes In Earthen Dams category

How to Evaluate Effective Cohesion given Factor of Safety of Earth Dam?

FAQs on Effective Cohesion given Factor of Safety of Earth Dam

Variable Name

GoEffective Cohesion given Factor of Safety in Absence of Flow Net Formula