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Angle of Internal Friction given Factor of Safety for Cohesive Soil Formula

GoAngle of Internal Friction given Shear Strength of Soil Formula

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

Φ i = a \tan (\frac{(𝜏 Shearstress \cdot f s) - c u}{σ Normal})

Φ_i - Angle of Internal Friction of Soil?𝜏_Shearstress - Shear Stress for Factor of Safety?f_s - Factor of Safety?c_u - Unit Cohesion?σ_Normal - Normal Stress?

Angle of Internal Friction given Factor of Safety for Cohesive Soil Example

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

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

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

78.6898 = a \tan (\frac{(15.909 \cdot 0.88) - 10}{0.8})

78.6898° = a \tan (\frac{(15.909Pa \cdot 0.88) - 10Pa}{0.8Pa})

78.6898 = a \tan (\frac{(15.909 \cdot 0.88) - 10}{0.8})

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Angle of Internal Friction given Factor of Safety for Cohesive Soil Solution

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

FIRST Step Consider the formula

Φ i = a \tan (\frac{(𝜏 Shearstress \cdot f s) - c u}{σ Normal})

Next Step Substitute values of Variables

∴

Φ i = a \tan (\frac{(15.909Pa \cdot 0.88) - 10Pa}{0.8Pa})

Next Step Prepare to Evaluate

∴

Φ i = a \tan (\frac{(15.909 \cdot 0.88) - 10}{0.8})

Next Step Evaluate

∴

Φ i = 1.3733969207172rad

Next Step Convert to Output's Unit

∴

Φ i = 78.6898471533739°

LAST Step Rounding Answer

∴

Φ i = 78.6898°

Angle of Internal Friction given Factor of Safety for Cohesive Soil Formula Elements

Variables

Functions

Angle of Internal Friction of Soil

Angle of Internal Friction of Soil 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

Shear Stress for Factor of Safety

Shear Stress for Factor of Safety is force is the maximum shear stress that a soil can withstand before failure, considering a safety factor.

Symbol: 𝜏_Shearstress

Measurement: StressUnit: Pa

Note: Value should be greater than 0.

Formulas to find Shear Stress for Factor of Safety

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

Unit Cohesion

Unit Cohesion is the shear strength of soil due to interparticle bonding and cementation.

Symbol: c_u

Measurement: PressureUnit: Pa

Note: Value should be greater than 0.

Formulas to find Unit Cohesion

Normal Stress

Normal Stress is the stress component that acts perpendicular to the plane of interest within a soil mass or structure.

Symbol: σ_Normal

Measurement: PressureUnit: Pa

Note: Value can be positive or negative.

Formulas to find Normal Stress

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 Shear Strength of Soil

Φ i = a \tan ((\frac{τ s}{𝜏}) \cdot \tan ((I)))

Other formulas in Stability Analysis of Infinite Slopes category

Go Shear Strength of Cohesionless Soil

τ s = σ nm \cdot \tan ((φ))

Go Normal Stress given Shear Strength of Cohesionless Soil

σ nm = \frac{τ s}{\tan ((φ))}

Go Angle of Internal Friction given Shear Strength of Cohesionless Soil

φ = a \tan (\frac{τ s}{σ nm})

Go Normal Stress given Shear Stress of Cohesionless Soil

σ nm = 𝜏 Shearstress \cdot \cot ((I))

How to Evaluate Angle of Internal Friction given Factor of Safety for Cohesive Soil?

Angle of Internal Friction given Factor of Safety for Cohesive Soil evaluator uses Angle of Internal Friction of Soil = atan(((Shear Stress for Factor of Safety*Factor of Safety)-Unit Cohesion)/Normal Stress) to evaluate the Angle of Internal Friction of Soil, The Angle of Internal Friction given Factor of Safety for Cohesive Soil formula is defined as the slope's angle at which cohesive soil reaches a factor of safety limit. Angle of Internal Friction of Soil is denoted by Φ_i symbol.

How to evaluate Angle of Internal Friction given Factor of Safety for Cohesive Soil using this online evaluator? To use this online evaluator for Angle of Internal Friction given Factor of Safety for Cohesive Soil, enter Shear Stress for Factor of Safety (𝜏_Shearstress), Factor of Safety (f_s), Unit Cohesion (c_u) & Normal Stress (σ_Normal) and hit the calculate button.

FAQs on Angle of Internal Friction given Factor of Safety for Cohesive Soil

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

The formula of Angle of Internal Friction given Factor of Safety for Cohesive Soil is expressed as Angle of Internal Friction of Soil = atan(((Shear Stress for Factor of Safety*Factor of Safety)-Unit Cohesion)/Normal Stress). Here is an example- -4690.799604 = atan(((15.909*0.88)-10)/0.8).

How to calculate Angle of Internal Friction given Factor of Safety for Cohesive Soil?

With Shear Stress for Factor of Safety (𝜏_Shearstress), Factor of Safety (f_s), Unit Cohesion (c_u) & Normal Stress (σ_Normal) we can find Angle of Internal Friction given Factor of Safety for Cohesive Soil using the formula - Angle of Internal Friction of Soil = atan(((Shear Stress for Factor of Safety*Factor of Safety)-Unit Cohesion)/Normal Stress). 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((Shear Strength/Shear Stress)*tan((Angle of Inclination)))

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

Yes, the Angle of Internal Friction given Factor of Safety for Cohesive Soil, measured in Angle can be negative.

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

Angle of Internal Friction given Factor of Safety for Cohesive Soil 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 for Cohesive Soil can be measured.

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Angle of Internal Friction given Factor of Safety for Cohesive Soil Formula

​GoAngle of Internal Friction given Shear Strength of Soil Formula

Angle of Internal Friction given Factor of Safety for Cohesive Soil Example

Angle of Internal Friction given Factor of Safety for Cohesive Soil Solution

Angle of Internal Friction given Factor of Safety for Cohesive Soil Formula Elements

Other Formulas to find Angle of Internal Friction of Soil

Other formulas in Stability Analysis of Infinite Slopes category

How to Evaluate Angle of Internal Friction given Factor of Safety for Cohesive Soil?

FAQs on Angle of Internal Friction given Factor of Safety for Cohesive Soil

Variable Name

GoAngle of Internal Friction given Shear Strength of Soil Formula