Slope Angle given Shear Stress along Slip Plane Calculator

✖Average Shear Stress on Shear Plane in Soil Mech is the ratio of shear force on the shear plane to the area of shear plane.ⓘ Average Shear Stress on Shear Plane in Soil Mech [τ _s]			+10% -10%
✖Weight of Wedge in Newton is defined as the weight of total soil which is in the form of wedge.ⓘ Weight of Wedge in Newton [W_wedge]			+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 given Shear Stress along Slip Plane [θ_slope]

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Formula

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Slope Angle given Shear Stress along Slip Plane

Formula

`"θ"_{"slope"} = asin("τ "_{"s"}/"W"_{"wedge"})`

Example

`"36.81627°"=asin("160N/m²"/"267N")`

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Slope Angle given Shear Stress along Slip Plane Solution

STEP 0: Pre-Calculation Summary

Formula Used

Slope Angle in Soil Mechanics = asin(Average Shear Stress on Shear Plane in Soil Mech/Weight of Wedge in Newton)
θ_slope = asin(τ _s/W_wedge)
This formula uses 2 Functions, 3 Variables

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)
asin - The inverse sine function, is a trigonometric function that takes a ratio of two sides of a right triangle and outputs the angle opposite the side with the given ratio., asin(Number)

Variables Used

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.
Average Shear Stress on Shear Plane in Soil Mech - (Measured in Pascal) - Average Shear Stress on Shear Plane in Soil Mech is the ratio of shear force on the shear plane to the area of shear plane.
Weight of Wedge in Newton - (Measured in Newton) - Weight of Wedge in Newton is defined as the weight of total soil which is in the form of wedge.

STEP 1: Convert Input(s) to Base Unit

Average Shear Stress on Shear Plane in Soil Mech: 160 Newton per Square Meter --> 160 Pascal (Check conversion here)
Weight of Wedge in Newton: 267 Newton --> 267 Newton No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

θ_slope = asin(τ _s/W_wedge) --> asin(160/267)

Evaluating ... ...

θ_slope = 0.642565107605408

STEP 3: Convert Result to Output's Unit

0.642565107605408 Radian -->36.8162687281664 Degree (Check conversion here)

FINAL ANSWER

36.8162687281664 ≈ 36.81627 Degree <-- Slope Angle in Soil Mechanics

(Calculation completed in 00.004 seconds)

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Created by Suraj Kumar

Birsa Institute of Technology (BIT), Sindri

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Meerut Institute of Engineering and Technology (MIET), Meerut

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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

Slope Angle given Shear Stress along Slip Plane Formula

Slope Angle in Soil Mechanics = asin(Average Shear Stress on Shear Plane in Soil Mech/Weight of Wedge in Newton)
θ_slope = asin(τ _s/W_wedge)

What is Slope Angle?

Slope angle (degree) is defined as the angle measured between a horizontal plane at a given point on the land surface.

How to Calculate Slope Angle given Shear Stress along Slip Plane?

Slope Angle given Shear Stress along Slip Plane calculator uses Slope Angle in Soil Mechanics = asin(Average Shear Stress on Shear Plane in Soil Mech/Weight of Wedge in Newton) to calculate the Slope Angle in Soil Mechanics, The Slope Angle given Shear Stress along Slip Plane is defined as the value of slope angle when we have prior information of other parameters used. Slope Angle in Soil Mechanics is denoted by θ_slope symbol.

How to calculate Slope Angle given Shear Stress along Slip Plane using this online calculator? To use this online calculator for Slope Angle given Shear Stress along Slip Plane, enter Average Shear Stress on Shear Plane in Soil Mech (τ _s) & Weight of Wedge in Newton (W_wedge) and hit the calculate button. Here is how the Slope Angle given Shear Stress along Slip Plane calculation can be explained with given input values -> 2109.417 = asin(160/267).

FAQ

What is Slope Angle given Shear Stress along Slip Plane?

The Slope Angle given Shear Stress along Slip Plane is defined as the value of slope angle when we have prior information of other parameters used and is represented as θ_slope = asin(τ _s/W_wedge) or Slope Angle in Soil Mechanics = asin(Average Shear Stress on Shear Plane in Soil Mech/Weight of Wedge in Newton). Average Shear Stress on Shear Plane in Soil Mech is the ratio of shear force on the shear plane to the area of shear plane & Weight of Wedge in Newton is defined as the weight of total soil which is in the form of wedge.

How to calculate Slope Angle given Shear Stress along Slip Plane?

The Slope Angle given Shear Stress along Slip Plane is defined as the value of slope angle when we have prior information of other parameters used is calculated using Slope Angle in Soil Mechanics = asin(Average Shear Stress on Shear Plane in Soil Mech/Weight of Wedge in Newton). To calculate Slope Angle given Shear Stress along Slip Plane, you need Average Shear Stress on Shear Plane in Soil Mech (τ _s) & Weight of Wedge in Newton (W_wedge). With our tool, you need to enter the respective value for Average Shear Stress on Shear Plane in Soil Mech & Weight of Wedge in Newton 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 Slope Angle in Soil Mechanics?

In this formula, Slope Angle in Soil Mechanics uses Average Shear Stress on Shear Plane in Soil Mech & Weight of Wedge in Newton. We can use 1 other way(s) to calculate the same, which is/are as follows -

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)))

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