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Slope Angle given Shear Strength along Slip Plane Formula

GoSlope Angle given Shear Stress along Slip Plane Formula

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Slope Angle in Soil Mechanics is defined as the angle measured between a horizontal plane at a given point on the land surface. Check FAQs

θ slope = a \cos (\frac{ζ soil - (C s \cdot L)}{W wedge \cdot \tan (\frac{φ \cdot π}{180})})

θ_slope - Slope Angle in Soil Mechanics?ζ _soil - Shear Strength?C_s - Cohesion of Soil?L - Length of Slip Plane?W_wedge - Weight of Wedge in Newton?φ - Angle of Internal Friction?π - Archimedes' constant?

Slope Angle given Shear Strength along Slip Plane Example

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Here is how the Slope Angle given Shear Strength along Slip Plane equation looks like with Values.

Here is how the Slope Angle given Shear Strength along Slip Plane equation looks like with Units.

Here is how the Slope Angle given Shear Strength along Slip Plane equation looks like.

90 = a \cos (\frac{0.025 - (5 \cdot 5)}{267 \cdot \tan (\frac{46 \cdot 3.1416}{180})})

90° = a \cos (\frac{0.025MPa - (5kPa \cdot 5m)}{267N \cdot \tan (\frac{46° \cdot 3.1416}{180})})

90 = a \cos (\frac{0.025 - (5 \cdot 5)}{267 \cdot \tan (\frac{46 \cdot 3.1416}{180})})

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Slope Angle given Shear Strength along Slip Plane Solution

Follow our step by step solution on how to calculate Slope Angle given Shear Strength along Slip Plane?

FIRST Step Consider the formula

θ slope = a \cos (\frac{ζ soil - (C s \cdot L)}{W wedge \cdot \tan (\frac{φ \cdot π}{180})})

Next Step Substitute values of Variables

∴

θ slope = a \cos (\frac{0.025MPa - (5kPa \cdot 5m)}{267N \cdot \tan (\frac{46° \cdot π}{180})})

Next Step Substitute values of Constants

∴

θ slope = a \cos (\frac{0.025MPa - (5kPa \cdot 5m)}{267N \cdot \tan (\frac{46° \cdot 3.1416}{180})})

Next Step Convert Units

∴

θ slope = a \cos (\frac{25000Pa - (5000Pa \cdot 5m)}{267N \cdot \tan (\frac{0.8029rad \cdot 3.1416}{180})})

Next Step Prepare to Evaluate

∴

θ slope = a \cos (\frac{25000 - (5000 \cdot 5)}{267 \cdot \tan (\frac{0.8029 \cdot 3.1416}{180})})

Next Step Evaluate

∴

θ slope = 1.5707963267949rad

Next Step Convert to Output's Unit

∴

θ slope = 90.0000000000169°

LAST Step Rounding Answer

∴

θ slope = 90°

Slope Angle given Shear Strength along Slip Plane Formula Elements

Variables

Constants

Functions

Slope Angle in Soil Mechanics

Slope Angle in Soil Mechanics is defined as the angle measured between a horizontal plane at a given point on the land surface.

Symbol: θ_slope

Measurement: AngleUnit: °

Note: Value should be between -45 to 180.

Formulas to find Slope Angle in Soil Mechanics

Shear Strength

Shear Strength of Soil is the strength of a material against the structural failure when the material fails in shear.

Symbol: ζ _soil

Measurement: PressureUnit: MPa