Shear Strength along Slip Plane Calculator

✖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%
✖Length of Slip Plane is the length of plane along which failure may occur.ⓘ Length of Slip Plane [L]			+10% -10%
✖Weight of Wedge is defined as the weight of total soil which is in the form of wedge.ⓘ Weight of Wedge [W]			+10% -10%
✖Slope Angle is defined as the angle measured between a horizontal plane at a given point on the land surface.ⓘ Slope Angle [θ]			+10% -10%
✖Angle of Internal Friction is the angle measured between the normal force and resultant force .ⓘ Angle of Internal Friction [φ]			+10% -10%

✖Shear Strength of Soil is the strength of a material against the structural failure when the material fails in shear.ⓘ Shear Strength along Slip Plane [ζ _soil]

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Formula

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Shear Strength along Slip Plane

Formula

`"ζ "_{"soil"} = ("C"_{"s"}*"L")+("W"*cos(("θ"*pi)/180)*tan(("φ"*pi)/180))`

Example

`"0.025MPa"=("5.0kPa"*"5m")+("10.01kg"*cos(("25°"*pi)/180)*tan(("46°"*pi)/180))`

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Shear Strength along Slip Plane Solution

STEP 0: Pre-Calculation Summary

Formula Used

Shear Strength = (Cohesion of Soil*Length of Slip Plane)+(Weight of Wedge*cos((Slope Angle*pi)/180)*tan((Angle of Internal Friction*pi)/180))
ζ _soil = (C_s*L)+(W*cos((θ*pi)/180)*tan((φ*pi)/180))
This formula uses 1 Constants, 2 Functions, 6 Variables

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Functions Used

cos - Cosine of an angle is the ratio of the side adjacent to the angle to the hypotenuse of the triangle., cos(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)

Variables Used

Shear Strength - (Measured in Pascal) - Shear Strength of Soil is the strength of a material against the structural failure when the material fails in shear.
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.
Length of Slip Plane - (Measured in Meter) - Length of Slip Plane is the length of plane along which failure may occur.
Weight of Wedge - (Measured in Kilogram) - Weight of Wedge is defined as the weight of total soil which is in the form of wedge.
Slope Angle - (Measured in Radian) - Slope Angle is defined as the angle measured between a horizontal plane at a given point on the land surface.
Angle of Internal Friction - (Measured in Radian) - Angle of Internal Friction is the angle measured between the normal force and resultant force .

STEP 1: Convert Input(s) to Base Unit

Cohesion of Soil: 5 Kilopascal --> 5000 Pascal (Check conversion here)
Length of Slip Plane: 5 Meter --> 5 Meter No Conversion Required
Weight of Wedge: 10.01 Kilogram --> 10.01 Kilogram No Conversion Required
Slope Angle: 25 Degree --> 0.4363323129985 Radian (Check conversion here)
Angle of Internal Friction: 46 Degree --> 0.802851455917241 Radian (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

ζ _soil = (C_s*L)+(W*cos((θ*pi)/180)*tan((φ*pi)/180)) --> (5000*5)+(10.01*cos((0.4363323129985*pi)/180)*tan((0.802851455917241*pi)/180))

Evaluating ... ...

ζ _soil = 25000.1402692505

STEP 3: Convert Result to Output's Unit

25000.1402692505 Pascal -->0.0250001402692505 Megapascal (Check conversion here)

FINAL ANSWER

0.0250001402692505 ≈ 0.025 Megapascal <-- Shear Strength

(Calculation completed in 00.020 seconds)

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Home » Engineering » Civil » Geotechnical Engineering » Slope Stability Analysis using Culman's Method » Shear Strength along Slip Plane

Credits

Created by Suraj Kumar

Birsa Institute of Technology (BIT), Sindri

Suraj Kumar has created this Calculator and 2200+ more calculators!

Verified by Ishita Goyal

Meerut Institute of Engineering and Technology (MIET), Meerut

Ishita Goyal has verified this Calculator and 2600+ more calculators!

< 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

Shear Strength along Slip Plane Formula

Shear Strength = (Cohesion of Soil*Length of Slip Plane)+(Weight of Wedge*cos((Slope Angle*pi)/180)*tan((Angle of Internal Friction*pi)/180))
ζ _soil = (C_s*L)+(W*cos((θ*pi)/180)*tan((φ*pi)/180))

What is Shear Strength?

Shear strength is the strength of a material or component against the type of yield or structural failure when the material or component fails in shear. A shear load is a force that tends to produce a sliding failure on a material along a plane that is parallel to the direction of the force.

How to Calculate Shear Strength along Slip Plane?

Shear Strength along Slip Plane calculator uses Shear Strength = (Cohesion of Soil*Length of Slip Plane)+(Weight of Wedge*cos((Slope Angle*pi)/180)*tan((Angle of Internal Friction*pi)/180)) to calculate the Shear Strength, The Shear Strength along Slip Plane is defined as the value of shear strength when we have prior information of other parameters used. Shear Strength is denoted by ζ _soil symbol.

How to calculate Shear Strength along Slip Plane using this online calculator? To use this online calculator for Shear Strength along Slip Plane, enter Cohesion of Soil (C_s), Length of Slip Plane (L), Weight of Wedge (W), Slope Angle (θ) & Angle of Internal Friction (φ) and hit the calculate button. Here is how the Shear Strength along Slip Plane calculation can be explained with given input values -> 2.5E-8 = (5000*5)+(10.01*cos((0.4363323129985*pi)/180)*tan((0.802851455917241*pi)/180)).

FAQ

What is Shear Strength along Slip Plane?

The Shear Strength along Slip Plane is defined as the value of shear strength when we have prior information of other parameters used and is represented as ζ _soil = (C_s*L)+(W*cos((θ*pi)/180)*tan((φ*pi)/180)) or Shear Strength = (Cohesion of Soil*Length of Slip Plane)+(Weight of Wedge*cos((Slope Angle*pi)/180)*tan((Angle of Internal Friction*pi)/180)). 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, Length of Slip Plane is the length of plane along which failure may occur, Weight of Wedge is defined as the weight of total soil which is in the form of wedge, Slope Angle is defined as the angle measured between a horizontal plane at a given point on the land surface & Angle of Internal Friction is the angle measured between the normal force and resultant force .

How to calculate Shear Strength along Slip Plane?

The Shear Strength along Slip Plane is defined as the value of shear strength when we have prior information of other parameters used is calculated using Shear Strength = (Cohesion of Soil*Length of Slip Plane)+(Weight of Wedge*cos((Slope Angle*pi)/180)*tan((Angle of Internal Friction*pi)/180)). To calculate Shear Strength along Slip Plane, you need Cohesion of Soil (C_s), Length of Slip Plane (L), Weight of Wedge (W), Slope Angle (θ) & Angle of Internal Friction (φ). With our tool, you need to enter the respective value for Cohesion of Soil, Length of Slip Plane, Weight of Wedge, Slope Angle & Angle of Internal 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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