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

✖Factor of Safety in Soil Mechanics expresses how much stronger a system is than it needs to be for an intended load.ⓘ Factor of Safety in Soil Mechanics [F_s]			+10% -10%
✖Cohesion of Soil is the ability of like particles within soil to hold onto each other. It is the shear strength or force that binds together like particles in the structure of a soil.ⓘ Cohesion of Soil [C_s]			+10% -10%
✖Unit Weight of Soil mass is the ratio of the total weight of soil to the total volume of soil.ⓘ Unit Weight of Soil [γ]			+10% -10%
✖Height from Toe of Wedge to Top of Wedge of soil.ⓘ Height from Toe of Wedge to Top of Wedge [H]			+10% -10%
✖Angle of Inclination in Soil Mechanics the angle formed by the x-axis and a given line (measured counterclockwise from the positive half of the x-axis).ⓘ Angle of Inclination in Soil Mechanics [θ_i]			+10% -10%
✖Slope Angle in Soil Mechanics is defined as the angle measured between a horizontal plane at a given point on the land surface.ⓘ Slope Angle in Soil Mechanics [θ_slope]			+10% -10%

✖Angle of Internal Friction of Soil is is a measure of the shear strength of soil due to friction.ⓘ Angle of Internal Friction given Angle of Inclination and Slope Angle [Φ_i]

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Formula

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Angle of Internal Friction given Angle of Inclination and Slope Angle

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}))

Example

88.88139 ° = a \tan ((2.8 - (\frac{5.0 kPa}{(\frac{1}{2}) \cdot 18 kN/m³ \cdot 10 m \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}))

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

STEP 0: Pre-Calculation Summary

Formula Used

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))
Φ_i = atan((F_s-(C_s/((1/2)*γ*H*(sin(((θ_i-θ_slope)*pi)/180)/sin((θ_i*pi)/180))*sin((θ_slope*pi)/180))))*tan((θ_slope*pi)/180))
This formula uses 1 Constants, 3 Functions, 7 Variables

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Functions Used

sin - Sine is a trigonometric function that describes the ratio of the length of the opposite side of a right triangle to the length of the hypotenuse., sin(Angle)
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., 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., atan(Number)

Variables Used

Angle of Internal Friction of Soil - (Measured in Radian) - Angle of Internal Friction of Soil is is a measure of the shear strength of soil due to friction.
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.
Cohesion of Soil - (Measured in Pascal) - Cohesion of Soil is the ability of like particles within soil to hold onto each other. It is the shear strength or force that binds together like particles in the structure of a soil.
Unit Weight of Soil - (Measured in Newton per Cubic Meter) - Unit Weight of Soil mass is the ratio of the total weight of soil to the total volume of soil.
Height from Toe of Wedge to Top of Wedge - (Measured in Meter) - Height from Toe of Wedge to Top of Wedge of soil.
Angle of Inclination in Soil Mechanics - (Measured in Radian) - Angle of Inclination in Soil Mechanics the angle formed by the x-axis and a given line (measured counterclockwise from the positive half of the x-axis).
Slope Angle in Soil Mechanics - (Measured in Radian) - Slope Angle in Soil Mechanics is defined as the angle measured between a horizontal plane at a given point on the land surface.

STEP 1: Convert Input(s) to Base Unit

Factor of Safety in Soil Mechanics: 2.8 --> No Conversion Required
Cohesion of Soil: 5 Kilopascal --> 5000 Pascal (Check conversion here)
Unit Weight of Soil: 18 Kilonewton per Cubic Meter --> 18000 Newton per Cubic Meter (Check conversion here)
Height from Toe of Wedge to Top of Wedge: 10 Meter --> 10 Meter No Conversion Required
Angle of Inclination in Soil Mechanics: 36.85 Degree --> 0.643153829359789 Radian (Check conversion here)
Slope Angle in Soil Mechanics: 36.89 Degree --> 0.643851961060587 Radian (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

Φ_i = atan((F_s-(C_s/((1/2)*γ*H*(sin(((θ_i-θ_slope)*pi)/180)/sin((θ_i*pi)/180))*sin((θ_slope*pi)/180))))*tan((θ_slope*pi)/180)) --> atan((2.8-(5000/((1/2)*18000*10*(sin(((0.643153829359789-0.643851961060587)*pi)/180)/sin((0.643153829359789*pi)/180))*sin((0.643851961060587*pi)/180))))*tan((0.643851961060587*pi)/180))

Evaluating ... ...

Φ_i = 1.55127296474477

STEP 3: Convert Result to Output's Unit

1.55127296474477 Radian -->88.8813937526386 Degree (Check conversion here)

FINAL ANSWER

88.8813937526386 ≈ 88.88139 Degree <-- Angle of Internal Friction of Soil

(Calculation completed in 00.020 seconds)

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< Slope Stability Analysis using Culman's Method Calculators

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

Go Height of Wedge = (Height from Toe of Wedge to Top of Wedge*sin(((Angle of Inclination in Soil Mechanics-Slope Angle)*pi)/180))/sin((Angle of Inclination in Soil Mechanics*pi)/180)

Height of Wedge of Soil given Weight of Wedge

Go Height of Wedge = Weight of Wedge in Kilonewton/((Length of Slip Plane*Unit Weight of Soil)/2)

Mobilized Cohesion given Cohesive Force along Slip Plane

Go Mobilized Cohesion in Soil Mechanics = Cohesive Force in KN/Length of Slip Plane

Cohesive Force along Slip Plane

Go Cohesive Force in KN = Mobilized Cohesion in Soil Mechanics*Length of Slip Plane

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

What is Angle of Internal Friction?

A measure of the ability of a unit of rock or soil to withstand a shear stress. It is the angle (φ), measured between the normal force (N) and resultant force (R), that is attained when failure just occurs in response to a shearing stress (S).

How to Calculate Angle of Internal Friction given Angle of Inclination and Slope Angle?

Angle of Internal Friction given Angle of Inclination and Slope Angle calculator uses 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)) to calculate the Angle of Internal Friction of Soil, The Angle of Internal Friction given Angle of Inclination and Slope Angle 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 calculate Angle of Internal Friction given Angle of Inclination and Slope Angle using this online calculator? To use this online calculator for Angle of Internal Friction given Angle of Inclination and Slope Angle, enter Factor of Safety in Soil Mechanics (F_s), Cohesion of Soil (C_s), Unit Weight of Soil (γ), Height from Toe of Wedge to Top of Wedge (H), Angle of Inclination in Soil Mechanics (θ_i) & Slope Angle in Soil Mechanics (θ_slope) and hit the calculate button. Here is how the Angle of Internal Friction given Angle of Inclination and Slope Angle calculation can be explained with given input values -> 5092.529 = atan((2.8-(5000/((1/2)*18000*10*(sin(((0.643153829359789-0.643851961060587)*pi)/180)/sin((0.643153829359789*pi)/180))*sin((0.643851961060587*pi)/180))))*tan((0.643851961060587*pi)/180)).

FAQ

What is Angle of Internal Friction given Angle of Inclination and Slope Angle?

The Angle of Internal Friction given Angle of Inclination and Slope Angle is defined as the value of angle of internal friction when we have prior information of other parameters used and is represented as Φ_i = atan((F_s-(C_s/((1/2)*γ*H*(sin(((θ_i-θ_slope)*pi)/180)/sin((θ_i*pi)/180))*sin((θ_slope*pi)/180))))*tan((θ_slope*pi)/180)) or 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)). Factor of Safety in Soil Mechanics expresses how much stronger a system is than it needs to be for an intended load, Cohesion of Soil is the ability of like particles within soil to hold onto each other. It is the shear strength or force that binds together like particles in the structure of a soil, Unit Weight of Soil mass is the ratio of the total weight of soil to the total volume of soil, Height from Toe of Wedge to Top of Wedge of soil, Angle of Inclination in Soil Mechanics the angle formed by the x-axis and a given line (measured counterclockwise from the positive half of the x-axis) & Slope Angle in Soil Mechanics is defined as the angle measured between a horizontal plane at a given point on the land surface.

How to calculate Angle of Internal Friction given Angle of Inclination and Slope Angle?

The Angle of Internal Friction given Angle of Inclination and Slope Angle is defined as the value of angle of internal friction when we have prior information of other parameters used is calculated using 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)). To calculate Angle of Internal Friction given Angle of Inclination and Slope Angle, you need Factor of Safety in Soil Mechanics (F_s), Cohesion of Soil (C_s), Unit Weight of Soil (γ), Height from Toe of Wedge to Top of Wedge (H), Angle of Inclination in Soil Mechanics (θ_i) & Slope Angle in Soil Mechanics (θ_slope). With our tool, you need to enter the respective value for Factor of Safety in Soil Mechanics, Cohesion of Soil, Unit Weight of Soil, Height from Toe of Wedge to Top of Wedge, Angle of Inclination in Soil Mechanics & Slope Angle in Soil Mechanics and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

How many ways are there to calculate Angle of Internal Friction of Soil?

In this formula, Angle of Internal Friction of Soil uses Factor of Safety in Soil Mechanics, Cohesion of Soil, Unit Weight of Soil, Height from Toe of Wedge to Top of Wedge, Angle of Inclination in Soil Mechanics & Slope Angle in Soil Mechanics. We can use 1 other way(s) to calculate the same, which is/are as follows -

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)

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