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Effective Cohesion of Soil given Shear Force in Bishop's Analysis Formula

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Effective Cohesion is the consistency of soft to hard defined on the basis of the standard CSN 73 1001 for different states of consistency and degree of saturation. Check FAQs

c' = \frac{(S \cdot f s) - ((P - (u \cdot l)) \cdot \tan (\frac{φ' \cdot π}{180}))}{l}

c' - Effective Cohesion?S - Shear Force on Slice in Soil Mechanics?f_s - Factor of Safety?P - Total Normal Force?u - Upward Force?l - Length of Arc?φ' - Effective Angle of Internal Friction?π - Archimedes' constant?

Effective Cohesion of Soil given Shear Force in Bishop's Analysis Example

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Here is how the Effective Cohesion of Soil given Shear Force in Bishop's Analysis equation looks like with Values.

Here is how the Effective Cohesion of Soil given Shear Force in Bishop's Analysis equation looks like with Units.

Here is how the Effective Cohesion of Soil given Shear Force in Bishop's Analysis equation looks like.

3.3029 = \frac{(11.07 \cdot 2.8) - ((150 - (20 \cdot 9.42)) \cdot \tan (\frac{9.99 \cdot 3.1416}{180}))}{9.42}

3.3029Pa = \frac{(11.07N \cdot 2.8) - ((150N - (20Pa \cdot 9.42m)) \cdot \tan (\frac{9.99° \cdot 3.1416}{180}))}{9.42m}

3.3029 = \frac{(11.07 \cdot 2.8) - ((150 - (20 \cdot 9.42)) \cdot \tan (\frac{9.99 \cdot 3.1416}{180}))}{9.42}

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Effective Cohesion of Soil given Shear Force in Bishop's Analysis Solution

Follow our step by step solution on how to calculate Effective Cohesion of Soil given Shear Force in Bishop's Analysis?

FIRST Step Consider the formula

c' = \frac{(S \cdot f s) - ((P - (u \cdot l)) \cdot \tan (\frac{φ' \cdot π}{180}))}{l}

Next Step Substitute values of Variables

∴

c' = \frac{(11.07N \cdot 2.8) - ((150N - (20Pa \cdot 9.42m)) \cdot \tan (\frac{9.99° \cdot π}{180}))}{9.42m}

Next Step Substitute values of Constants

∴

c' = \frac{(11.07N \cdot 2.8) - ((150N - (20Pa \cdot 9.42m)) \cdot \tan (\frac{9.99° \cdot 3.1416}{180}))}{9.42m}

Next Step Convert Units

∴

c' = \frac{(11.07N \cdot 2.8) - ((150N - (20Pa \cdot 9.42m)) \cdot \tan (\frac{0.1744rad \cdot 3.1416}{180}))}{9.42m}

Next Step Prepare to Evaluate

∴

c' = \frac{(11.07 \cdot 2.8) - ((150 - (20 \cdot 9.42)) \cdot \tan (\frac{0.1744 \cdot 3.1416}{180}))}{9.42}

Next Step Evaluate

∴

c' = 3.30285100603297Pa

LAST Step Rounding Answer

∴

c' = 3.3029Pa

Effective Cohesion of Soil given Shear Force in Bishop's Analysis Formula Elements

Variables

Constants

Functions

Effective Cohesion

Effective Cohesion is the consistency of soft to hard defined on the basis of the standard CSN 73 1001 for different states of consistency and degree of saturation.

Symbol: c'

Measurement: PressureUnit: Pa

Note: Value should be greater than 0.

Formulas to find Effective Cohesion

Shear Force on Slice in Soil Mechanics

Shear Force on Slice in Soil Mechanics acting along the base of slice.

Symbol: S

Measurement: ForceUnit: N

Note: Value should be greater than 0.

Formulas to find Shear Force on Slice in Soil Mechanics

Factor of Safety

Factor of Safety expresses how much stronger a system is than it needs to be for an intended load.

Symbol: f_s

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Factor of Safety

Total Normal Force

Total normal force acting at the base of the slice.

Symbol: P

Measurement: ForceUnit: N

Note: Value should be greater than 0.

Formulas to find Total Normal Force

Upward Force

Upward Force due to seepage water.

Symbol: u

Measurement: PressureUnit: Pa

Note: Value should be greater than 0.

Formulas to find Upward Force

Length of Arc

Length of Arc of the slice taken into consideration.

Symbol: l

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Length of Arc

Effective Angle of Internal Friction

Effective Angle of Internal Friction is a measure of the shear strength of soils due to friction.

Symbol: φ'

Measurement: AngleUnit: °

Note: Value should be greater than 0.

Formulas to find Effective Angle of Internal Friction

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 of Soil given Normal Stress on Slice

c' = τ - ((σ normal - u) \cdot \tan (\frac{φ' \cdot π}{180}))

Other formulas in Slope Stability Analysis using Bishops Method category

Go Normal Stress on Slice

σ normal = \frac{P}{l}

Go Length of Arc of Slice

l = \frac{P}{σ normal}

How to Evaluate Effective Cohesion of Soil given Shear Force in Bishop's Analysis?

Effective Cohesion of Soil given Shear Force in Bishop's Analysis evaluator uses Effective Cohesion = ((Shear Force on Slice in Soil Mechanics*Factor of Safety)-((Total Normal Force-(Upward Force*Length of Arc))*tan((Effective Angle of Internal Friction*pi)/180)))/Length of Arc to evaluate the Effective Cohesion, The Effective Cohesion of Soil given Shear Force in Bishop's Analysis is defined as the value of effective cohesion when we have prior information of other parameters used. Effective Cohesion is denoted by c' symbol.

How to evaluate Effective Cohesion of Soil given Shear Force in Bishop's Analysis using this online evaluator? To use this online evaluator for Effective Cohesion of Soil given Shear Force in Bishop's Analysis, enter Shear Force on Slice in Soil Mechanics (S), Factor of Safety (f_s), Total Normal Force (P), Upward Force (u), Length of Arc (l) & Effective Angle of Internal Friction (φ') and hit the calculate button.

FAQs on Effective Cohesion of Soil given Shear Force in Bishop's Analysis

What is the formula to find Effective Cohesion of Soil given Shear Force in Bishop's Analysis?

The formula of Effective Cohesion of Soil given Shear Force in Bishop's Analysis is expressed as Effective Cohesion = ((Shear Force on Slice in Soil Mechanics*Factor of Safety)-((Total Normal Force-(Upward Force*Length of Arc))*tan((Effective Angle of Internal Friction*pi)/180)))/Length of Arc. Here is an example- 1.519412 = ((11.07*2.8)-((150-(20*9.42))*tan((0.174358392274201*pi)/180)))/9.42.

How to calculate Effective Cohesion of Soil given Shear Force in Bishop's Analysis?

With Shear Force on Slice in Soil Mechanics (S), Factor of Safety (f_s), Total Normal Force (P), Upward Force (u), Length of Arc (l) & Effective Angle of Internal Friction (φ') we can find Effective Cohesion of Soil given Shear Force in Bishop's Analysis using the formula - Effective Cohesion = ((Shear Force on Slice in Soil Mechanics*Factor of Safety)-((Total Normal Force-(Upward Force*Length of Arc))*tan((Effective Angle of Internal Friction*pi)/180)))/Length of Arc. This formula also uses Archimedes' constant and Tangent function(s).

What are the other ways to Calculate Effective Cohesion?

Here are the different ways to Calculate Effective Cohesion-

Effective Cohesion=Shear Strength of Soil in Pascal-((Normal Stress in Pascal-Upward Force)*tan((Effective Angle of Internal Friction*pi)/180))

Can the Effective Cohesion of Soil given Shear Force in Bishop's Analysis be negative?

No, the Effective Cohesion of Soil given Shear Force in Bishop's Analysis, measured in Pressure cannot be negative.

Which unit is used to measure Effective Cohesion of Soil given Shear Force in Bishop's Analysis?

Effective Cohesion of Soil given Shear Force in Bishop's Analysis 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 of Soil given Shear Force in Bishop's Analysis can be measured.

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Effective Cohesion of Soil given Shear Force in Bishop's Analysis Formula

​GoEffective Cohesion of Soil given Normal Stress on Slice Formula

Effective Cohesion of Soil given Shear Force in Bishop's Analysis Example

Effective Cohesion of Soil given Shear Force in Bishop's Analysis Solution

Effective Cohesion of Soil given Shear Force in Bishop's Analysis Formula Elements

Other Formulas to find Effective Cohesion

Other formulas in Slope Stability Analysis using Bishops Method category

How to Evaluate Effective Cohesion of Soil given Shear Force in Bishop's Analysis?

FAQs on Effective Cohesion of Soil given Shear Force in Bishop's Analysis

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GoEffective Cohesion of Soil given Normal Stress on Slice Formula