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Safe Height from Toe to Top of Wedge 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{4 \cdot c m \cdot \sin (\frac{i \cdot π}{180}) \cdot \cos (\frac{φ mob \cdot π}{180})}{γ \cdot (1 - \cos (\frac{(i - φ mob) \cdot π}{180}))}

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?γ - Unit Weight of Soil?π - Archimedes' constant?

Safe Height from Toe to Top of Wedge Example

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Here is how the Safe Height from Toe to Top of Wedge equation looks like with Values.

Here is how the Safe Height from Toe to Top of Wedge equation looks like with Units.

Here is how the Safe Height from Toe to Top of Wedge equation looks like.

10.4922 = \frac{4 \cdot 0.3 \cdot \sin (\frac{64 \cdot 3.1416}{180}) \cdot \cos (\frac{12.33 \cdot 3.1416}{180})}{18 \cdot (1 - \cos (\frac{(64 - 12.33) \cdot 3.1416}{180}))}

10.4922m = \frac{4 \cdot 0.3kN/m² \cdot \sin (\frac{64° \cdot 3.1416}{180}) \cdot \cos (\frac{12.33° \cdot 3.1416}{180})}{18kN/m³ \cdot (1 - \cos (\frac{(64° - 12.33°) \cdot 3.1416}{180}))}

10.4922 = \frac{4 \cdot 0.3 \cdot \sin (\frac{64 \cdot 3.1416}{180}) \cdot \cos (\frac{12.33 \cdot 3.1416}{180})}{18 \cdot (1 - \cos (\frac{(64 - 12.33) \cdot 3.1416}{180}))}

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Safe Height from Toe to Top of Wedge Solution

Follow our step by step solution on how to calculate Safe Height from Toe to Top of Wedge?

FIRST Step Consider the formula

H = \frac{4 \cdot c m \cdot \sin (\frac{i \cdot π}{180}) \cdot \cos (\frac{φ mob \cdot π}{180})}{γ \cdot (1 - \cos (\frac{(i - φ mob) \cdot π}{180}))}

Next Step Substitute values of Variables

∴

H = \frac{4 \cdot 0.3kN/m² \cdot \sin (\frac{64° \cdot π}{180}) \cdot \cos (\frac{12.33° \cdot π}{180})}{18kN/m³ \cdot (1 - \cos (\frac{(64° - 12.33°) \cdot π}{180}))}

Next Step Substitute values of Constants

∴

H = \frac{4 \cdot 0.3kN/m² \cdot \sin (\frac{64° \cdot 3.1416}{180}) \cdot \cos (\frac{12.33° \cdot 3.1416}{180})}{18kN/m³ \cdot (1 - \cos (\frac{(64° - 12.33°) \cdot 3.1416}{180}))}

Next Step Convert Units

∴

H = \frac{4 \cdot 300Pa \cdot \sin (\frac{1.117rad \cdot 3.1416}{180}) \cdot \cos (\frac{0.2152rad \cdot 3.1416}{180})}{18000N/m³ \cdot (1 - \cos (\frac{(1.117rad - 0.2152rad) \cdot 3.1416}{180}))}

Next Step Prepare to Evaluate

∴

H = \frac{4 \cdot 300 \cdot \sin (\frac{1.117 \cdot 3.1416}{180}) \cdot \cos (\frac{0.2152 \cdot 3.1416}{180})}{18000 \cdot (1 - \cos (\frac{(1.117 - 0.2152) \cdot 3.1416}{180}))}

Next Step Evaluate

∴

H = 10.4921730217593m

LAST Step Rounding Answer

∴

H = 10.4922m

Safe Height from Toe to Top of Wedge 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.

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

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.

Formulas to find Mobilized Cohesion in Soil Mechanics

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.

Formulas to find Angle of Inclination to Horizontal in Soil

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.

Formulas to find Angle of Mobilized Friction in Soil Mechanics

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.

Formulas to find Unit Weight of Soil

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)

cos

Cosine of an angle is the ratio of the side adjacent to the angle to the hypotenuse of the triangle.

Syntax: cos(Angle)

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})}}

Go Height from Toe of Wedge to Top of Wedge given Factor of Safety

H = (\frac{C eff}{(\frac{1}{2}) \cdot (F s - (\frac{\tan (\frac{φ \cdot π}{180})}{\tan (\frac{θ cr \cdot π}{180})})) \cdot γ \cdot (\frac{\sin (\frac{(i - θ cr) \cdot π}{180})}{\sin (\frac{i \cdot π}{180})}) \cdot \sin (\frac{θ cr \cdot π}{180})})

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

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}

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

Go Mobilized Cohesion given Cohesive Force along Slip Plane

c m = \frac{F c}{L}

Go Height of Wedge of Soil given Angle of Inclination and Slope angle

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

How to Evaluate Safe Height from Toe to Top of Wedge?

Safe Height from Toe to Top of Wedge evaluator uses 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))) to evaluate the Height from Toe of Wedge to Top of Wedge, The Safe Height from Toe to Top of Wedge is defined as the value of safe height from toe to top of the wedge of soil 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 Safe Height from Toe to Top of Wedge using this online evaluator? To use this online evaluator for Safe Height from Toe to Top of Wedge, 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) & Unit Weight of Soil (γ) and hit the calculate button.

FAQs on Safe Height from Toe to Top of Wedge

What is the formula to find Safe Height from Toe to Top of Wedge?

The formula of Safe Height from Toe to Top of Wedge is expressed as 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))). Here is an example- 10.49217 = (4*300*sin((1.11701072127616*pi)/180)*cos((0.21519909677086*pi)/180))/(18000*(1-cos(((1.11701072127616-0.21519909677086)*pi)/180))).

How to calculate Safe Height from Toe to Top of Wedge?

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) & Unit Weight of Soil (γ) we can find Safe Height from Toe to Top of Wedge using the formula - 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))). This formula also uses Archimedes' constant and , Sine (sin), Cosine (cos) 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 Safe Height from Toe to Top of Wedge be negative?

No, the Safe Height from Toe to Top of Wedge, measured in Length cannot be negative.

Which unit is used to measure Safe Height from Toe to Top of Wedge?

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

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Safe Height from Toe to Top of Wedge 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

Safe Height from Toe to Top of Wedge Example

Safe Height from Toe to Top of Wedge Solution

Safe Height from Toe to Top of Wedge Formula Elements

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 Safe Height from Toe to Top of Wedge?

FAQs on Safe Height from Toe to Top of Wedge

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