Critical Slope Angle given Angle of Inclination Calculator

✖Angle of Inclination to Horizontal in Soil is defined as the angle measured from the horizontal surface of the wall or any object.ⓘ Angle of Inclination to Horizontal in Soil [i]			+10% -10%
✖Angle of Mobilized Friction is the slope angle at which an object starts sliding due to applied force.ⓘ Angle of Mobilized Friction [φ_m]			+10% -10%

✖Critical Slope Angle in Soil Mechanics is the angle formed by most dangerous plane.ⓘ Critical Slope Angle given Angle of Inclination [θ_cr]

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Formula

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Critical Slope Angle given Angle of Inclination

Formula

`"θ"_{"cr"} = ("i"+"φ"_{"m"})/2`

Example

`"52°"=("64°"+"40°")/2`

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Download Slope Stability Analysis using Culman's Method Formulas PDF

Critical Slope Angle given Angle of Inclination Solution

STEP 0: Pre-Calculation Summary

Formula Used

Critical Slope Angle in Soil Mechanics = (Angle of Inclination to Horizontal in Soil+Angle of Mobilized Friction)/2
θ_cr = (i+φ_m)/2
This formula uses 3 Variables

Variables Used

Critical Slope Angle in Soil Mechanics - (Measured in Radian) - Critical Slope Angle in Soil Mechanics is the angle formed by most dangerous plane.
Angle of Inclination to Horizontal in Soil - (Measured in Radian) - Angle of Inclination to Horizontal in Soil is defined as the angle measured from the horizontal surface of the wall or any object.
Angle of Mobilized Friction - (Measured in Radian) - Angle of Mobilized Friction is the slope angle at which an object starts sliding due to applied force.

STEP 1: Convert Input(s) to Base Unit

Angle of Inclination to Horizontal in Soil: 64 Degree --> 1.11701072127616 Radian (Check conversion here)
Angle of Mobilized Friction: 40 Degree --> 0.698131700797601 Radian (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

θ_cr = (i+φ_m)/2 --> (1.11701072127616+0.698131700797601)/2

Evaluating ... ...

θ_cr = 0.907571211036881

STEP 3: Convert Result to Output's Unit

0.907571211036881 Radian -->52 Degree (Check conversion here)

FINAL ANSWER

52 Degree <-- Critical Slope Angle in Soil Mechanics

(Calculation completed in 00.004 seconds)

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Birsa Institute of Technology (BIT), Sindri

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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

Critical Slope Angle given Angle of Inclination Formula

Critical Slope Angle in Soil Mechanics = (Angle of Inclination to Horizontal in Soil+Angle of Mobilized Friction)/2
θ_cr = (i+φ_m)/2

What is Critical Angle?

The angle of repose, or critical angle of repose, of a granular material is the steepest angle of descent or dip relative to the horizontal plane to which a material can be piled without slumping. At this angle, the material on the slope face is on the verge of sliding. The angle of repose can range from 0° to 90°.

How to Calculate Critical Slope Angle given Angle of Inclination?

Critical Slope Angle given Angle of Inclination calculator uses Critical Slope Angle in Soil Mechanics = (Angle of Inclination to Horizontal in Soil+Angle of Mobilized Friction)/2 to calculate the Critical Slope Angle in Soil Mechanics, The Critical Slope Angle given Angle of Inclination is defined as the value of critical slope angle when we have prior information of other parameters used. Critical Slope Angle in Soil Mechanics is denoted by θ_cr symbol.

How to calculate Critical Slope Angle given Angle of Inclination using this online calculator? To use this online calculator for Critical Slope Angle given Angle of Inclination, enter Angle of Inclination to Horizontal in Soil (i) & Angle of Mobilized Friction (φ_m) and hit the calculate button. Here is how the Critical Slope Angle given Angle of Inclination calculation can be explained with given input values -> 2979.381 = (1.11701072127616+0.698131700797601)/2.

FAQ

What is Critical Slope Angle given Angle of Inclination?

The Critical Slope Angle given Angle of Inclination is defined as the value of critical slope angle when we have prior information of other parameters used and is represented as θ_cr = (i+φ_m)/2 or Critical Slope Angle in Soil Mechanics = (Angle of Inclination to Horizontal in Soil+Angle of Mobilized Friction)/2. Angle of Inclination to Horizontal in Soil is defined as the angle measured from the horizontal surface of the wall or any object & Angle of Mobilized Friction is the slope angle at which an object starts sliding due to applied force.

How to calculate Critical Slope Angle given Angle of Inclination?

The Critical Slope Angle given Angle of Inclination is defined as the value of critical slope angle when we have prior information of other parameters used is calculated using Critical Slope Angle in Soil Mechanics = (Angle of Inclination to Horizontal in Soil+Angle of Mobilized Friction)/2. To calculate Critical Slope Angle given Angle of Inclination, you need Angle of Inclination to Horizontal in Soil (i) & Angle of Mobilized Friction (φ_m). With our tool, you need to enter the respective value for Angle of Inclination to Horizontal in Soil & Angle of Mobilized Friction and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

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