Height from Toe to Top of Wedge given Angle of Mobilized Friction Calculator

✖Mobilized Cohesion in Soil Mechanics is the amount of cohesion that is resisting the shear stress.ⓘ Mobilized Cohesion in Soil Mechanics [c_m]			+10% -10%
✖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 in Soil Mechanics is the slope angle at which an object starts sliding due to applied force.ⓘ Angle of Mobilized Friction in Soil Mechanics [φ_mob]			+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%
✖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%
✖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 to Top of Wedge given Angle of Mobilized Friction [H]

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Formula

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Height from Toe to Top of Wedge given Angle of Mobilized Friction

Formula

`"H" = "c"_{"m"}/(0.5*cosec(("i"*pi)/180)*sec(("φ"_{"mob"}*pi)/180)*sin((("i"-"θ")*pi)/180)*sin((("θ"_{"slope"}-"φ"_{"mob"})*pi)/180)*"γ")`

Example

`"7.311302m"="0.30kN/m²"/(0.5*cosec(("64°"*pi)/180)*sec(("12.33°"*pi)/180)*sin((("64°"-"25°")*pi)/180)*sin((("36.89°"-"12.33°")*pi)/180)*"18kN/m³")`

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Height from Toe to Top of Wedge given Angle of Mobilized Friction Solution

STEP 0: Pre-Calculation Summary

Formula Used

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)
H = c_m/(0.5*cosec((i*pi)/180)*sec((φ_mob*pi)/180)*sin(((i-θ)*pi)/180)*sin(((θ_slope-φ_mob)*pi)/180)*γ)
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)
sec - Secant is a trigonometric function that is defined ratio of the hypotenuse to the shorter side adjacent to an acute angle (in a right-angled triangle); the reciprocal of a cosine., sec(Angle)
cosec - The cosecant function is a trigonometric function that is the reciprocal of the sine function., cosec(Angle)

Variables Used

Height from Toe of Wedge to Top of Wedge - (Measured in Meter) - Height from Toe of Wedge to Top of Wedge of soil.
Mobilized Cohesion in Soil Mechanics - (Measured in Pascal) - Mobilized Cohesion in Soil Mechanics is the amount of cohesion that is resisting the shear stress.
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 in Soil Mechanics - (Measured in Radian) - Angle of Mobilized Friction in Soil Mechanics is the slope angle at which an object starts sliding due to applied force.
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.
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.
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.

STEP 1: Convert Input(s) to Base Unit

Mobilized Cohesion in Soil Mechanics: 0.3 Kilonewton per Square Meter --> 300 Pascal (Check conversion here)
Angle of Inclination to Horizontal in Soil: 64 Degree --> 1.11701072127616 Radian (Check conversion here)
Angle of Mobilized Friction in Soil Mechanics: 12.33 Degree --> 0.21519909677086 Radian (Check conversion here)
Slope Angle: 25 Degree --> 0.4363323129985 Radian (Check conversion here)
Slope Angle in Soil Mechanics: 36.89 Degree --> 0.643851961060587 Radian (Check conversion here)
Unit Weight of Soil: 18 Kilonewton per Cubic Meter --> 18000 Newton per Cubic Meter (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

H = c_m/(0.5*cosec((i*pi)/180)*sec((φ_mob*pi)/180)*sin(((i-θ)*pi)/180)*sin(((θ_slope-φ_mob)*pi)/180)*γ) --> 300/(0.5*cosec((1.11701072127616*pi)/180)*sec((0.21519909677086*pi)/180)*sin(((1.11701072127616-0.4363323129985)*pi)/180)*sin(((0.643851961060587-0.21519909677086)*pi)/180)*18000)

Evaluating ... ...

H = 7.31130173327608

STEP 3: Convert Result to Output's Unit

7.31130173327608 Meter --> No Conversion Required

FINAL ANSWER

7.31130173327608 ≈ 7.311302 Meter <-- Height from Toe of Wedge to Top of Wedge

(Calculation completed in 00.004 seconds)

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Created by Suraj Kumar

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

Height from Toe to Top of Wedge given Angle of Mobilized Friction Formula

What is Friction?

Friction is a force between two surfaces that are sliding, or trying to slide, across each other. For example, when you try to push a book along the floor, friction makes this difficult. Friction always works in the direction opposite to the direction in which the object is moving, or trying to move.

How to Calculate Height from Toe to Top of Wedge given Angle of Mobilized Friction?

Height from Toe to Top of Wedge given Angle of Mobilized Friction calculator uses 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) to calculate the Height from Toe of Wedge to Top of Wedge, The Height from Toe to Top of Wedge given Angle of Mobilized Friction is defined as the value of height from toe to top of wedge when we have prior information of other parameters used. Height from Toe of Wedge to Top of Wedge is denoted by H symbol.

How to calculate Height from Toe to Top of Wedge given Angle of Mobilized Friction using this online calculator? To use this online calculator for Height from Toe to Top of Wedge given Angle of Mobilized Friction, enter Mobilized Cohesion in Soil Mechanics (c_m), Angle of Inclination to Horizontal in Soil (i), Angle of Mobilized Friction in Soil Mechanics (φ_mob), Slope Angle (θ), Slope Angle in Soil Mechanics (θ_slope) & Unit Weight of Soil (γ) and hit the calculate button. Here is how the Height from Toe to Top of Wedge given Angle of Mobilized Friction calculation can be explained with given input values -> 7.311302 = 300/(0.5*cosec((1.11701072127616*pi)/180)*sec((0.21519909677086*pi)/180)*sin(((1.11701072127616-0.4363323129985)*pi)/180)*sin(((0.643851961060587-0.21519909677086)*pi)/180)*18000).

FAQ

What is Height from Toe to Top of Wedge given Angle of Mobilized Friction?

The Height from Toe to Top of Wedge given Angle of Mobilized Friction is defined as the value of height from toe to top of wedge when we have prior information of other parameters used and is represented as H = c_m/(0.5*cosec((i*pi)/180)*sec((φ_mob*pi)/180)*sin(((i-θ)*pi)/180)*sin(((θ_slope-φ_mob)*pi)/180)*γ) or 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 in Soil Mechanics is the amount of cohesion that is resisting the shear stress, 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 in Soil Mechanics is the slope angle at which an object starts sliding due to applied force, Slope Angle is defined as the angle measured between a horizontal plane at a given point on the land surface, Slope Angle in Soil Mechanics is defined as the angle measured between a horizontal plane at a given point on the land surface & Unit Weight of Soil mass is the ratio of the total weight of soil to the total volume of soil.

How to calculate Height from Toe to Top of Wedge given Angle of Mobilized Friction?

The Height from Toe to Top of Wedge given Angle of Mobilized Friction is defined as the value of height from toe to top of wedge when we have prior information of other parameters used is calculated using 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). To calculate Height from Toe to Top of Wedge given Angle of Mobilized Friction, you need Mobilized Cohesion in Soil Mechanics (c_m), Angle of Inclination to Horizontal in Soil (i), Angle of Mobilized Friction in Soil Mechanics (φ_mob), Slope Angle (θ), Slope Angle in Soil Mechanics (θ_slope) & Unit Weight of Soil (γ). With our tool, you need to enter the respective value for Mobilized Cohesion in Soil Mechanics, Angle of Inclination to Horizontal in Soil, Angle of Mobilized Friction in Soil Mechanics, Slope Angle, Slope Angle in Soil Mechanics & Unit Weight of Soil 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 Height from Toe of Wedge to Top of Wedge?

In this formula, Height from Toe of Wedge to Top of Wedge uses Mobilized Cohesion in Soil Mechanics, Angle of Inclination to Horizontal in Soil, Angle of Mobilized Friction in Soil Mechanics, Slope Angle, Slope Angle in Soil Mechanics & Unit Weight of Soil. We can use 4 other way(s) to calculate the same, which is/are as follows -

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 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)))
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)))
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)))

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