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Angle of Internal Friction given Effective Normal Stress Formula

GoAngle of Internal Friction given Angle of Inclination and Slope Angle Formula

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Angle of Internal Friction of Soil is is a measure of the shear strength of soil due to friction. Check FAQs

Φ i = a \tan (\frac{F s \cdot ζ soil}{σ effn})

Φ_i - Angle of Internal Friction of Soil?F_s - Factor of Safety in Soil Mechanics?ζ_soil - Shear Stress of Soil in Megapascal?σ_effn - Effective Normal Stress of Soil in Megapascal?

Angle of Internal Friction given Effective Normal Stress Example

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Here is how the Angle of Internal Friction given Effective Normal Stress equation looks like with Values.

Here is how the Angle of Internal Friction given Effective Normal Stress equation looks like with Units.

Here is how the Angle of Internal Friction given Effective Normal Stress equation looks like.

76.8786 = a \tan (\frac{2.8 \cdot 250.09}{163.23})

76.8786° = a \tan (\frac{2.8 \cdot 250.09MPa}{163.23MPa})

76.8786 = a \tan (\frac{2.8 \cdot 250.09}{163.23})

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Angle of Internal Friction given Effective Normal Stress Solution

Follow our step by step solution on how to calculate Angle of Internal Friction given Effective Normal Stress?

FIRST Step Consider the formula

Φ i = a \tan (\frac{F s \cdot ζ soil}{σ effn})

Next Step Substitute values of Variables

∴

Φ i = a \tan (\frac{2.8 \cdot 250.09MPa}{163.23MPa})

Next Step Convert Units

∴

Φ i = a \tan (\frac{2.8 \cdot 2.5E+8Pa}{1.6E+8Pa})

Next Step Prepare to Evaluate

∴

Φ i = a \tan (\frac{2.8 \cdot 2.5E+8}{1.6E+8})

Next Step Evaluate

∴

Φ i = 1.34178398550847rad

Next Step Convert to Output's Unit

∴

Φ i = 76.8785593878928°

LAST Step Rounding Answer

∴

Φ i = 76.8786°

Angle of Internal Friction given Effective Normal Stress Formula Elements

Variables

Functions

Angle of Internal Friction of Soil

Angle of Internal Friction of Soil is is a measure of the shear strength of soil due to friction.

Symbol: Φ_i

Measurement: AngleUnit: °

Note: Value should be between -180 to 180.

Formulas to find Angle of Internal Friction of Soil

Factor of Safety in Soil Mechanics

Factor of Safety in Soil Mechanics 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 in Soil Mechanics

Shear Stress of Soil in Megapascal

Shear Stress of Soil in Megapascal is force tending to cause deformation of a material by slippage along a plane or planes parallel to the imposed stress.

Symbol: ζ_soil

Measurement: StressUnit: MPa

Note: Value should be greater than 0.

Formulas to find Shear Stress of Soil in Megapascal

Effective Normal Stress of Soil in Megapascal

Effective Normal Stress of soil in Megapascal is related to total stress and pore pressure.

Symbol: σ_effn

Measurement: PressureUnit: MPa

Note: Value should be greater than 0.

Formulas to find Effective Normal Stress of Soil in Megapascal

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)

atan

Inverse tan is used to calculate the angle by applying the tangent ratio of the angle, which is the opposite side divided by the adjacent side of the right triangle.

Syntax: atan(Number)

Other Formulas to find Angle of Internal Friction of Soil

Go Angle of Internal Friction given Angle of Inclination and Slope Angle

Φ i = a \tan ((F s - (\frac{C s}{(\frac{1}{2}) \cdot γ \cdot H \cdot (\frac{\sin (\frac{(θ i - θ slope) \cdot π}{180})}{\sin (\frac{θ i \cdot π}{180})}) \cdot \sin (\frac{θ slope \cdot π}{180})})) \cdot \tan (\frac{θ slope \cdot π}{180}))

Other formulas in Slope Stability Analysis using Culman's Method category

Go Height of Wedge of Soil given Weight of Wedge

h = \frac{W we}{\frac{L \cdot γ}{2}}

Go Cohesive Force along Slip Plane

F c = c m \cdot L

Go Mobilized Cohesion given Cohesive Force along Slip Plane

c m = \frac{F c}{L}

Go Height of Wedge of Soil given Angle of Inclination and Slope angle

h = \frac{H \cdot \sin (\frac{(θ i - θ) \cdot π}{180})}{\sin (\frac{θ i \cdot π}{180})}

How to Evaluate Angle of Internal Friction given Effective Normal Stress?

Angle of Internal Friction given Effective Normal Stress evaluator uses Angle of Internal Friction of Soil = atan((Factor of Safety in Soil Mechanics*Shear Stress of Soil in Megapascal)/Effective Normal Stress of Soil in Megapascal) to evaluate the Angle of Internal Friction of Soil, The Angle of Internal Friction given Effective Normal Stress is defined as the value of angle of internal friction when we have prior information of other parameters used. Angle of Internal Friction of Soil is denoted by Φ_i symbol.

How to evaluate Angle of Internal Friction given Effective Normal Stress using this online evaluator? To use this online evaluator for Angle of Internal Friction given Effective Normal Stress, enter Factor of Safety in Soil Mechanics (F_s), Shear Stress of Soil in Megapascal (ζ_soil) & Effective Normal Stress of Soil in Megapascal (σ_effn) and hit the calculate button.

FAQs on Angle of Internal Friction given Effective Normal Stress

What is the formula to find Angle of Internal Friction given Effective Normal Stress?

The formula of Angle of Internal Friction given Effective Normal Stress is expressed as Angle of Internal Friction of Soil = atan((Factor of Safety in Soil Mechanics*Shear Stress of Soil in Megapascal)/Effective Normal Stress of Soil in Megapascal). Here is an example- 4404.817 = atan((2.8*250090000)/163230000).

How to calculate Angle of Internal Friction given Effective Normal Stress?

With Factor of Safety in Soil Mechanics (F_s), Shear Stress of Soil in Megapascal (ζ_soil) & Effective Normal Stress of Soil in Megapascal (σ_effn) we can find Angle of Internal Friction given Effective Normal Stress using the formula - Angle of Internal Friction of Soil = atan((Factor of Safety in Soil Mechanics*Shear Stress of Soil in Megapascal)/Effective Normal Stress of Soil in Megapascal). This formula also uses Tangent (tan), Inverse Tan (atan) function(s).

What are the other ways to Calculate Angle of Internal Friction of Soil?

Here are the different ways to Calculate Angle of Internal Friction of Soil-

Angle of Internal Friction of Soil=atan((Factor of Safety in Soil Mechanics-(Cohesion of Soil/((1/2)*Unit Weight of Soil*Height from Toe of Wedge to Top of Wedge*(sin(((Angle of Inclination in Soil Mechanics-Slope Angle in Soil Mechanics)*pi)/180)/sin((Angle of Inclination in Soil Mechanics*pi)/180))*sin((Slope Angle in Soil Mechanics*pi)/180))))*tan((Slope Angle in Soil Mechanics*pi)/180))

Can the Angle of Internal Friction given Effective Normal Stress be negative?

Yes, the Angle of Internal Friction given Effective Normal Stress, measured in Angle can be negative.

Which unit is used to measure Angle of Internal Friction given Effective Normal Stress?

Angle of Internal Friction given Effective Normal Stress is usually measured using the Degree[°] for Angle. Radian[°], Minute[°], Second[°] are the few other units in which Angle of Internal Friction given Effective Normal Stress can be measured.

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Angle of Internal Friction given Effective Normal Stress Formula

​GoAngle of Internal Friction given Angle of Inclination and Slope Angle Formula

Angle of Internal Friction given Effective Normal Stress Example

Angle of Internal Friction given Effective Normal Stress Solution

Angle of Internal Friction given Effective Normal Stress Formula Elements

Other Formulas to find Angle of Internal Friction of Soil

Other formulas in Slope Stability Analysis using Culman's Method category

How to Evaluate Angle of Internal Friction given Effective Normal Stress?

FAQs on Angle of Internal Friction given Effective Normal Stress

Variable Name

GoAngle of Internal Friction given Angle of Inclination and Slope Angle Formula