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

GoHeight from Toe of Wedge to Top of Wedge Formula

GoHeight from Toe of Wedge to Top of Wedge given Weight of Wedge Formula

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Height from Toe of Wedge to Top of Wedge of soil. Check FAQs

H = \frac{c m}{0.5 \cdot \cos e c (\frac{i \cdot π}{180}) \cdot \sec (\frac{φ mob \cdot π}{180}) \cdot \sin (\frac{(i - θ) \cdot π}{180}) \cdot \sin (\frac{(θ slope - φ mob) \cdot π}{180}) \cdot γ}

H - Height from Toe of Wedge to Top of Wedge?c_m - Mobilized Cohesion in Soil Mechanics?i - Angle of Inclination to Horizontal in Soil?φ_mob - Angle of Mobilized Friction in Soil Mechanics?θ - Slope Angle?θ_slope - Slope Angle in Soil Mechanics?γ - Unit Weight of Soil?π - Archimedes' constant?

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

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Here is how the Height from Toe to Top of Wedge given Angle of Mobilized Friction equation looks like with Values.

Here is how the Height from Toe to Top of Wedge given Angle of Mobilized Friction equation looks like with Units.

Here is how the Height from Toe to Top of Wedge given Angle of Mobilized Friction equation looks like.

7.3113 = \frac{0.3}{0.5 \cdot \cos e c (\frac{64 \cdot 3.1416}{180}) \cdot \sec (\frac{12.33 \cdot 3.1416}{180}) \cdot \sin (\frac{(64 - 25) \cdot 3.1416}{180}) \cdot \sin (\frac{(36.89 - 12.33) \cdot 3.1416}{180}) \cdot 18}

7.3113m = \frac{0.3kN/m²}{0.5 \cdot \cos e c (\frac{64° \cdot 3.1416}{180}) \cdot \sec (\frac{12.33° \cdot 3.1416}{180}) \cdot \sin (\frac{(64° - 25°) \cdot 3.1416}{180}) \cdot \sin (\frac{(36.89° - 12.33°) \cdot 3.1416}{180}) \cdot 18kN/m³}

7.3113 = \frac{0.3}{0.5 \cdot \cos e c (\frac{64 \cdot 3.1416}{180}) \cdot \sec (\frac{12.33 \cdot 3.1416}{180}) \cdot \sin (\frac{(64 - 25) \cdot 3.1416}{180}) \cdot \sin (\frac{(36.89 - 12.33) \cdot 3.1416}{180}) \cdot 18}

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Home » Engineering » Civil » Geotechnical Engineering » Height from Toe to Top of Wedge given Angle of Mobilized Friction

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

Follow our step by step solution on how to calculate Height from Toe to Top of Wedge given Angle of Mobilized Friction?

FIRST Step Consider the formula

H = \frac{c m}{0.5 \cdot \cos e c (\frac{i \cdot π}{180}) \cdot \sec (\frac{φ mob \cdot π}{180}) \cdot \sin (\frac{(i - θ) \cdot π}{180}) \cdot \sin (\frac{(θ slope - φ mob) \cdot π}{180}) \cdot γ}

Next Step Substitute values of Variables

∴

H = \frac{0.3kN/m²}{0.5 \cdot \cos e c (\frac{64° \cdot π}{180}) \cdot \sec (\frac{12.33° \cdot π}{180}) \cdot \sin (\frac{(64° - 25°) \cdot π}{180}) \cdot \sin (\frac{(36.89° - 12.33°) \cdot π}{180}) \cdot 18kN/m³}

Next Step Substitute values of Constants

∴

H = \frac{0.3kN/m²}{0.5 \cdot \cos e c (\frac{64° \cdot 3.1416}{180}) \cdot \sec (\frac{12.33° \cdot 3.1416}{180}) \cdot \sin (\frac{(64° - 25°) \cdot 3.1416}{180}) \cdot \sin (\frac{(36.89° - 12.33°) \cdot 3.1416}{180}) \cdot 18kN/m³}

Next Step Convert Units

∴

H = \frac{300Pa}{0.5 \cdot \cos e c (\frac{1.117rad \cdot 3.1416}{180}) \cdot \sec (\frac{0.2152rad \cdot 3.1416}{180}) \cdot \sin (\frac{(1.117rad - 0.4363rad) \cdot 3.1416}{180}) \cdot \sin (\frac{(0.6439rad - 0.2152rad) \cdot 3.1416}{180}) \cdot 18000N/m³}

Next Step Prepare to Evaluate

∴

H = \frac{300}{0.5 \cdot \cos e c (\frac{1.117 \cdot 3.1416}{180}) \cdot \sec (\frac{0.2152 \cdot 3.1416}{180}) \cdot \sin (\frac{(1.117 - 0.4363) \cdot 3.1416}{180}) \cdot \sin (\frac{(0.6439 - 0.2152) \cdot 3.1416}{180}) \cdot 18000}

Next Step Evaluate

∴

H = 7.31130173327608m

LAST Step Rounding Answer

∴

H = 7.3113m

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

Variables

Constants

Functions

Height from Toe of Wedge to Top of Wedge

Height from Toe of Wedge to Top of Wedge of soil.

Symbol: H

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Mobilized Cohesion in Soil Mechanics

Mobilized Cohesion in Soil Mechanics is the amount of cohesion that is resisting the shear stress.

Symbol: c_m

Measurement: PressureUnit: kN/m²

Note: Value should be between 0 to 10.

Angle of Inclination to Horizontal in Soil

Angle of Inclination to Horizontal in Soil is defined as the angle measured from the horizontal surface of the wall or any object.

Symbol: i

Measurement: AngleUnit: °

Note: Value should be greater than 0.

Angle of Mobilized Friction in Soil Mechanics

Angle of Mobilized Friction in Soil Mechanics is the slope angle at which an object starts sliding due to applied force.

Symbol: φ_mob

Measurement: AngleUnit: °

Note: Value should be between -180 to 180.

Slope Angle

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

Symbol: θ

Measurement: AngleUnit: °

Note: Value should be greater than 0.

Slope Angle in Soil Mechanics

Slope Angle in Soil Mechanics is defined as the angle measured between a horizontal plane at a given point on the land surface.

Symbol: θ_slope

Measurement: AngleUnit: °

Note: Value should be between -45 to 180.

Unit Weight of Soil

Unit Weight of Soil mass is the ratio of the total weight of soil to the total volume of soil.

Symbol: γ

Measurement: Specific WeightUnit: kN/m³

Note: Value should be greater than 0.

Archimedes' constant

Archimedes' constant is a mathematical constant that represents the ratio of the circumference of a circle to its diameter.

Symbol: π

Value: 3.14159265358979323846264338327950288

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.

Syntax: 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.

Syntax: sec(Angle)

cosec

The cosecant function is a trigonometric function that is the reciprocal of the sine function.

Syntax: cosec(Angle)

Credits

Created by Suraj Kumar

Birsa Institute of Technology (BIT), Sindri

Suraj Kumar has created this Formula and 2100+ more formulas!

Verified by Ishita Goyal

Meerut Institute of Engineering and Technology (MIET), Meerut

Ishita Goyal has verified this Formula and 2600+ more formulas!

Other Formulas to find Height from Toe of Wedge to Top of Wedge

Go Height from Toe of Wedge to Top of Wedge

H = \frac{h}{\frac{\sin (\frac{(θ i - θ) \cdot π}{180})}{\sin (\frac{θ i \cdot π}{180})}}

Go Height from Toe of Wedge to Top of Wedge given Weight of Wedge

H = \frac{W we}{\frac{γ \cdot L \cdot (\sin (\frac{(θ i - θ) \cdot π}{180}))}{2 \cdot \sin (\frac{θ i \cdot π}{180})}}

Other formulas in Slope Stability Analysis using Culman's Method category

Go Height of Wedge of Soil given Weight of Wedge

h = \frac{W we}{\frac{L \cdot γ}{2}}

Go Cohesive Force along Slip Plane

F c = c m \cdot L

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

Height from Toe to Top of Wedge given Angle of Mobilized Friction evaluator 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 evaluate 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 evaluate Height from Toe to Top of Wedge given Angle of Mobilized Friction using this online evaluator? To use this online evaluator 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.

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

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

The formula of Height from Toe to Top of Wedge given Angle of Mobilized Friction is expressed as 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). Here is an example- 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).

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

With 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) we can find Height from Toe to Top of Wedge given Angle of Mobilized Friction using the formula - 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). This formula also uses Archimedes' constant and , Sine (sin), Secant (sec), Cosecant (cosec) function(s).

What are the other ways to Calculate Height from Toe of Wedge to Top of Wedge?

Here are the different ways to Calculate Height from Toe of Wedge to Top of Wedge-

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)))

Can the Height from Toe to Top of Wedge given Angle of Mobilized Friction be negative?

No, the Height from Toe to Top of Wedge given Angle of Mobilized Friction, measured in Length cannot be negative.

Which unit is used to measure Height from Toe to Top of Wedge given Angle of Mobilized Friction?

Height from Toe to Top of Wedge given Angle of Mobilized Friction is usually measured using the Meter[m] for Length. Millimeter[m], Kilometer[m], Decimeter[m] are the few other units in which Height from Toe to Top of Wedge given Angle of Mobilized Friction can be measured.

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

​GoHeight from Toe of Wedge to Top of Wedge Formula

​GoHeight from Toe of Wedge to Top of Wedge given Weight of Wedge Formula

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

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

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

Credits

Other Formulas to find Height from Toe of Wedge to Top of Wedge

Other formulas in Slope Stability Analysis using Culman's Method category

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

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

Variable Name

GoHeight from Toe of Wedge to Top of Wedge Formula

GoHeight from Toe of Wedge to Top of Wedge given Weight of Wedge Formula