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

GoAngle of Internal Friction given Effective Normal Stress 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 ((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}))

Φ_i - Angle of Internal Friction of Soil?F_s - Factor of Safety in Soil Mechanics?C_s - Cohesion of Soil?γ - Unit Weight of Soil?H - Height from Toe of Wedge to Top of Wedge?θ_i - Angle of Inclination in Soil Mechanics?θ_slope - Slope Angle in Soil Mechanics?π - Archimedes' constant?

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

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Here is how the Angle of Internal Friction given Angle of Inclination and Slope Angle equation looks like with Values.

Here is how the Angle of Internal Friction given Angle of Inclination and Slope Angle equation looks like with Units.

Here is how the Angle of Internal Friction given Angle of Inclination and Slope Angle equation looks like.

88.8814 = a \tan ((2.8 - (\frac{5}{(\frac{1}{2}) \cdot 18 \cdot 10 \cdot (\frac{\sin (\frac{(36.85 - 36.89) \cdot 3.1416}{180})}{\sin (\frac{36.85 \cdot 3.1416}{180})}) \cdot \sin (\frac{36.89 \cdot 3.1416}{180})})) \cdot \tan (\frac{36.89 \cdot 3.1416}{180}))

88.8814° = a \tan ((2.8 - (\frac{5kPa}{(\frac{1}{2}) \cdot 18kN/m³ \cdot 10m \cdot (\frac{\sin (\frac{(36.85° - 36.89°) \cdot 3.1416}{180})}{\sin (\frac{36.85° \cdot 3.1416}{180})}) \cdot \sin (\frac{36.89° \cdot 3.1416}{180})})) \cdot \tan (\frac{36.89° \cdot 3.1416}{180}))

88.8814 = a \tan ((2.8 - (\frac{5}{(\frac{1}{2}) \cdot 18 \cdot 10 \cdot (\frac{\sin (\frac{(36.85 - 36.89) \cdot 3.1416}{180})}{\sin (\frac{36.85 \cdot 3.1416}{180})}) \cdot \sin (\frac{36.89 \cdot 3.1416}{180})})) \cdot \tan (\frac{36.89 \cdot 3.1416}{180}))

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

Follow our step by step solution on how to calculate Angle of Internal Friction given Angle of Inclination and Slope Angle?

FIRST Step Consider the formula

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}))

Next Step Substitute values of Variables

∴

Φ i = a \tan ((2.8 - (\frac{5kPa}{(\frac{1}{2}) \cdot 18kN/m³ \cdot 10m \cdot (\frac{\sin (\frac{(36.85° - 36.89°) \cdot π}{180})}{\sin (\frac{36.85° \cdot π}{180})}) \cdot \sin (\frac{36.89° \cdot π}{180})})) \cdot \tan (\frac{36.89° \cdot π}{180}))

Next Step Substitute values of Constants

∴

Φ i = a \tan ((2.8 - (\frac{5kPa}{(\frac{1}{2}) \cdot 18kN/m³ \cdot 10m \cdot (\frac{\sin (\frac{(36.85° - 36.89°) \cdot 3.1416}{180})}{\sin (\frac{36.85° \cdot 3.1416}{180})}) \cdot \sin (\frac{36.89° \cdot 3.1416}{180})})) \cdot \tan (\frac{36.89° \cdot 3.1416}{180}))

Next Step Convert Units

∴

Φ i = a \tan ((2.8 - (\frac{5000Pa}{(\frac{1}{2}) \cdot 18000N/m³ \cdot 10m \cdot (\frac{\sin (\frac{(0.6432rad - 0.6439rad) \cdot 3.1416}{180})}{\sin (\frac{0.6432rad \cdot 3.1416}{180})}) \cdot \sin (\frac{0.6439rad \cdot 3.1416}{180})})) \cdot \tan (\frac{0.6439rad \cdot 3.1416}{180}))

Next Step Prepare to Evaluate

∴

Φ i = a \tan ((2.8 - (\frac{5000}{(\frac{1}{2}) \cdot 18000 \cdot 10 \cdot (\frac{\sin (\frac{(0.6432 - 0.6439) \cdot 3.1416}{180})}{\sin (\frac{0.6432 \cdot 3.1416}{180})}) \cdot \sin (\frac{0.6439 \cdot 3.1416}{180})})) \cdot \tan (\frac{0.6439 \cdot 3.1416}{180}))

Next Step Evaluate

∴

Φ i = 1.55127296474477rad

Next Step Convert to Output's Unit

∴

Φ i = 88.8813937526386°

LAST Step Rounding Answer

∴

Φ i = 88.8814°

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

Variables

Constants

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.

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