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Angle of Internal Friction given Factor of Safety Formula

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Angle of Internal Friction is the angle measured between the normal force and resultant force. Check FAQs

φ = a \tan (\frac{f s \cdot γ sat \cdot \tan ((φ IF))}{γ'})

φ - Angle of Internal Friction?f_s - Factor of Safety?γ_sat - Saturated Unit Weight?φ_IF - Weighted Friction Angle for Internal Friction?γ^' - Submerged Unit Weight?

Angle of Internal Friction given Factor of Safety Example

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Here is how the Angle of Internal Friction given Factor of Safety equation looks like with Values.

Here is how the Angle of Internal Friction given Factor of Safety equation looks like with Units.

Here is how the Angle of Internal Friction given Factor of Safety equation looks like.

9.9384 = a \tan (\frac{2.8 \cdot 9.98 \cdot \tan ((11))}{31})

9.9384° = a \tan (\frac{2.8 \cdot 9.98N/m³ \cdot \tan ((11°))}{31N/m³})

9.9384 = a \tan (\frac{2.8 \cdot 9.98 \cdot \tan ((11))}{31})

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Angle of Internal Friction given Factor of Safety Solution

Follow our step by step solution on how to calculate Angle of Internal Friction given Factor of Safety?

FIRST Step Consider the formula

φ = a \tan (\frac{f s \cdot γ sat \cdot \tan ((φ IF))}{γ'})

Next Step Substitute values of Variables

∴

φ = a \tan (\frac{2.8 \cdot 9.98N/m³ \cdot \tan ((11°))}{31N/m³})

Next Step Convert Units

∴

φ = a \tan (\frac{2.8 \cdot 9.98N/m³ \cdot \tan ((0.192rad))}{31N/m³})

Next Step Prepare to Evaluate

∴

φ = a \tan (\frac{2.8 \cdot 9.98 \cdot \tan ((0.192))}{31})

Next Step Evaluate

∴

φ = 0.173457348461734rad

Next Step Convert to Output's Unit

∴

φ = 9.9383739923893°

LAST Step Rounding Answer

∴

φ = 9.9384°

Angle of Internal Friction given Factor of Safety Formula Elements

Variables

Functions

Angle of Internal Friction

Angle of Internal Friction is the angle measured between the normal force and resultant force.

Symbol: φ

Measurement: AngleUnit: °

Note: Value should be greater than 0.

Formulas to find Angle of Internal Friction

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

Saturated Unit Weight

Saturated Unit Weight is the value of the unit weight of the soil when the soil is completely saturated with water that is all the soil pores are completely filled with water.

Symbol: γ_sat

Measurement: Specific WeightUnit: N/m³

Note: Value should be greater than 0.

Formulas to find Saturated Unit Weight

Weighted Friction Angle for Internal Friction

Weighted Friction Angle for Internal Friction is an effective measure combining materials' friction properties and their relative contributions in geotechnical engineering for stability analysis.

Symbol: φ_IF

Measurement: AngleUnit: °

Note: Value should be greater than 0.

Formulas to find Weighted Friction Angle for Internal Friction

Submerged Unit Weight

Submerged Unit Weight is the effective weight of the soil per unit volume when it is submerged in water.

Symbol: γ^'

Measurement: Specific WeightUnit: N/m³

Note: Value should be greater than 0.

Formulas to find Submerged Unit Weight

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 in Taylor's Stability Number and Stability Curves category

Go Weighted Friction Angle given Factor of Safety with respect to Shear Strength

φ w = a \tan ((\frac{γ'}{γ sat}) \cdot (\frac{\tan ((Φ i))}{f s}))

Go Submerged Unit Weight given Factor of Safety with respect to Shear Strength

γ' = \frac{\tan (\frac{φ w \cdot π}{180})}{(\frac{1}{γ sat}) \cdot (\frac{\tan (\frac{Φ i \cdot π}{180})}{f s})}

Go Factor of Safety with respect to Shear Strength

f s = ((\frac{γ'}{γ sat}) \cdot (\frac{\tan ((φ))}{\tan ((φ IF))}))

Go Saturated Unit Weight given Factor of Safety with respect to Shear Strength

γ sat = ((\frac{γ'}{\tan ((φ IF))}) \cdot (\frac{\tan ((φ))}{f s}))

How to Evaluate Angle of Internal Friction given Factor of Safety?

Angle of Internal Friction given Factor of Safety evaluator uses Angle of Internal Friction = atan((Factor of Safety*Saturated Unit Weight*tan((Weighted Friction Angle for Internal Friction)))/Submerged Unit Weight) to evaluate the Angle of Internal Friction, The Angle of Internal Friction given Factor of Safety formula is defined as the value of angle of internal friction with respect to shear strength. Angle of Internal Friction is denoted by φ symbol.

How to evaluate Angle of Internal Friction given Factor of Safety using this online evaluator? To use this online evaluator for Angle of Internal Friction given Factor of Safety, enter Factor of Safety (f_s), Saturated Unit Weight (γ_sat), Weighted Friction Angle for Internal Friction (φ_IF) & Submerged Unit Weight (γ^') and hit the calculate button.

FAQs on Angle of Internal Friction given Factor of Safety

What is the formula to find Angle of Internal Friction given Factor of Safety?

The formula of Angle of Internal Friction given Factor of Safety is expressed as Angle of Internal Friction = atan((Factor of Safety*Saturated Unit Weight*tan((Weighted Friction Angle for Internal Friction)))/Submerged Unit Weight). Here is an example- 569.4269 = atan((2.8*9.98*tan((0.19198621771934)))/31).

How to calculate Angle of Internal Friction given Factor of Safety?

With Factor of Safety (f_s), Saturated Unit Weight (γ_sat), Weighted Friction Angle for Internal Friction (φ_IF) & Submerged Unit Weight (γ^') we can find Angle of Internal Friction given Factor of Safety using the formula - Angle of Internal Friction = atan((Factor of Safety*Saturated Unit Weight*tan((Weighted Friction Angle for Internal Friction)))/Submerged Unit Weight). This formula also uses Tangent (tan), Inverse Tan (atan) function(s).

Can the Angle of Internal Friction given Factor of Safety be negative?

No, the Angle of Internal Friction given Factor of Safety, measured in Angle cannot be negative.

Which unit is used to measure Angle of Internal Friction given Factor of Safety?

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

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Angle of Internal Friction given Factor of Safety Formula

Angle of Internal Friction given Factor of Safety Example

Angle of Internal Friction given Factor of Safety Solution

Angle of Internal Friction given Factor of Safety Formula Elements

Other formulas in Taylor's Stability Number and Stability Curves category

How to Evaluate Angle of Internal Friction given Factor of Safety?

FAQs on Angle of Internal Friction given Factor of Safety

Variable Name