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))
Φi = atan((Fs-(Cs/((1/2)*γ*H*(sin(((θi-θslope)*pi)/180)/sin((θi*pi)/180))*sin((θslope*pi)/180))))*tan((θslope*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 a shear strength parameter of soils.
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
Φi = atan((Fs-(Cs/((1/2)*γ*H*(sin(((θislope)*pi)/180)/sin((θi*pi)/180))*sin((θslope*pi)/180))))*tan((θslope*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 ... ...
Φi = 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 00.004 seconds)

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25 Slope Stability Analysis using Culman's Method Calculators

Height from Toe of Wedge to Top of Wedge given Factor of Safety
Go Height from Toe of Wedge to Top of Wedge = (Effective Cohesion in Geotech as Kilopascal/((1/2)*(Factor of Safety in Soil Mechanics-(tan((Angle of Internal Friction*pi)/180)/tan((Critical Slope Angle in Soil Mechanics*pi)/180)))* Unit Weight of Soil*(sin(((Angle of Inclination to Horizontal in Soil-Critical Slope Angle in Soil Mechanics)*pi)/180)/sin((Angle of Inclination to Horizontal in Soil*pi)/180))*sin((Critical Slope Angle in Soil Mechanics*pi)/180)))
Cohesion of Soil given Angle of Inclination and Slope angle
Go Effective Cohesion in Geotech as Kilopascal = (Factor of Safety in Soil Mechanics-(tan((Angle of Internal Friction*pi)/180)/tan((Slope Angle*pi)/180)))*((1/2)*Unit Weight of Soil*Height from Toe of Wedge to Top of Wedge*(sin(((Angle of Inclination to Horizontal in Soil-Slope Angle)*pi)/180)/sin((Angle of Inclination to Horizontal in Soil*pi)/180))*sin((Slope Angle*pi)/180))
Mobilized Cohesion given Angle of Mobilized Friction
Go Mobilized Cohesion in Soil Mechanics = (0.5*cosec((Angle of Inclination to Horizontal in Soil*pi)/180)*sec((Angle of Mobilized Friction in Soil Mechanics*pi)/180)*sin(((Angle of Inclination to Horizontal in Soil-Slope Angle in Soil Mechanics)*pi)/180)*sin(((Slope Angle in Soil Mechanics-Angle of Mobilized Friction in Soil Mechanics)*pi)/180))*(Unit Weight of Soil*Height from Toe of Wedge to Top of Wedge)
Height from Toe to Top of Wedge given Angle of Mobilized Friction
Go Height from Toe of Wedge to Top of Wedge = Mobilized Cohesion in Soil Mechanics/(0.5*cosec((Angle of Inclination to Horizontal in Soil*pi)/180)*sec((Angle of Mobilized Friction in Soil Mechanics*pi)/180)*sin(((Angle of Inclination to Horizontal in Soil-Slope Angle)*pi)/180)*sin(((Slope Angle in Soil Mechanics-Angle of Mobilized Friction in Soil Mechanics)*pi)/180)*Unit Weight of Soil)
Mobilized Cohesion given Safe Height from Toe to Top of Wedge
Go Mobilized Cohesion in Kilopascal = Height from Toe of Wedge to Top of Wedge/(4*sin((Angle of Inclination in Soil Mechanics*pi)/180)*cos((Angle of Mobilized Friction in Soil Mechanics*pi)/180))/(Unit Weight of Water in Soil Mechanics*(1-cos(((Angle of Inclination in Soil Mechanics-Angle of Mobilized Friction in Soil Mechanics)*pi)/180)))
Safe Height from Toe to Top of Wedge
Go Height from Toe of Wedge to Top of Wedge = (4*Mobilized Cohesion in Soil Mechanics*sin((Angle of Inclination to Horizontal in Soil*pi)/180)*cos((Angle of Mobilized Friction in Soil Mechanics*pi)/180))/(Unit Weight of Soil*(1-cos(((Angle of Inclination to Horizontal in Soil-Angle of Mobilized Friction in Soil Mechanics)*pi)/180)))
Factor of Safety given Length of Slip Plane
Go Factor of Safety in Soil Mechanics = ((Cohesion in Soil*Length of Slip Plane)/(Weight of Wedge in Newton*sin((Critical Slope Angle in Soil Mechanics*pi)/180)))+(tan((Angle of Internal Friction*pi)/180)/tan((Critical Slope Angle in Soil Mechanics*pi)/180))
Height from Toe of Wedge to Top of Wedge given Weight of Wedge
Go Height from Toe of Wedge to Top of Wedge = Weight of Wedge in Kilonewton/((Unit Weight of Soil*Length of Slip Plane*(sin(((Angle of Inclination in Soil Mechanics-Slope Angle)*pi)/180)))/(2*sin((Angle of Inclination in Soil Mechanics*pi)/180)))
Length of Slip Plane given Shear Strength along Slip Plane
Go Length of Slip Plane = (Shear Strength of Soil-(Weight of Wedge*cos((Slope Angle in Soil Mechanics*pi)/180)*tan((Angle of Internal Friction*pi)/180)))/Cohesion in Soil
Height from Toe of Wedge to Top of Wedge
Go Height from Toe of Wedge to Top of Wedge = Height 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 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)
Shear Strength along Slip Plane
Go Shear Strength = (Cohesion of Soil*Length of Slip Plane)+(Weight of Wedge*cos((Slope Angle*pi)/180)*tan((Angle of Internal Friction*pi)/180))
Slope Angle given Shear Strength along Slip Plane
Go Slope Angle in Soil Mechanics = acos((Shear Strength-(Cohesion of Soil*Length of Slip Plane))/(Weight of Wedge in Newton*tan((Angle of Internal Friction*pi)/180)))
Angle of Internal Friction given Effective Normal Stress
Go 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)
Slope Angle given Shear Stress along Slip Plane
Go Slope Angle in Soil Mechanics = asin(Average Shear Stress on Shear Plane in Soil Mech/Weight of Wedge in Newton)
Length of Slip Plane given Weight of Wedge of Soil
Go Length of Slip Plane = Weight of Wedge in Kilonewton/((Height of Wedge*Unit Weight of Soil)/2)
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)
Unit Weight of Soil given Weight of Wedge
Go Unit Weight of Soil = Weight of Wedge in Kilonewton/((Length of Slip Plane*Height of Wedge)/2)
Weight of Wedge of Soil
Go Weight of Wedge in Kilonewton = (Length of Slip Plane*Height of Wedge*Unit Weight of Soil)/2
Angle of Mobilized Friction given Critical Slope Angle
Go Angle of Mobilized Friction = (2*Critical Slope Angle in Soil Mechanics)-Angle of Inclination to Horizontal in Soil
Critical Slope Angle given Angle of Inclination
Go Critical Slope Angle in Soil Mechanics = (Angle of Inclination to Horizontal in Soil+Angle of Mobilized Friction)/2
Angle of Inclination given Critical Slope Angle
Go Angle of Inclination to Horizontal in Soil = (2*Critical Slope Angle in Soil Mechanics)-Angle of Mobilized Friction
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
Length of Slip Plane given Cohesive Force along Slip Plane
Go Length of Slip Plane = Cohesive Force in KN/Mobilized Cohesion in Kilopascal

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

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))
Φi = atan((Fs-(Cs/((1/2)*γ*H*(sin(((θi-θslope)*pi)/180)/sin((θi*pi)/180))*sin((θslope*pi)/180))))*tan((θslope*pi)/180))

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 Φi 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 (Fs), Cohesion of Soil (Cs), Unit Weight of Soil (γ), Height from Toe of Wedge to Top of Wedge (H), Angle of Inclination in Soil Mechanics i) & Slope Angle in Soil Mechanics 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 Φi = atan((Fs-(Cs/((1/2)*γ*H*(sin(((θislope)*pi)/180)/sin((θi*pi)/180))*sin((θslope*pi)/180))))*tan((θslope*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 (Fs), Cohesion of Soil (Cs), Unit Weight of Soil (γ), Height from Toe of Wedge to Top of Wedge (H), Angle of Inclination in Soil Mechanics i) & Slope Angle in Soil Mechanics 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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