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Height from Toe of Wedge to Top of Wedge given Factor of Safety 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 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})})

H - Height from Toe of Wedge to Top of Wedge?C_eff - Effective Cohesion in Geotech as Kilopascal?F_s - Factor of Safety in Soil Mechanics?φ - Angle of Internal Friction?θ_cr - Critical Slope Angle in Soil Mechanics?γ - Unit Weight of Soil?i - Angle of Inclination to Horizontal in Soil?π - Archimedes' constant?

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

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

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

Here is how the Height from Toe of Wedge to Top of Wedge given Factor of Safety equation looks like.

6.2849 = (\frac{0.32}{(\frac{1}{2}) \cdot (2.8 - (\frac{\tan (\frac{46 \cdot 3.1416}{180})}{\tan (\frac{52.1 \cdot 3.1416}{180})})) \cdot 18 \cdot (\frac{\sin (\frac{(64 - 52.1) \cdot 3.1416}{180})}{\sin (\frac{64 \cdot 3.1416}{180})}) \cdot \sin (\frac{52.1 \cdot 3.1416}{180})})

6.2849m = (\frac{0.32kPa}{(\frac{1}{2}) \cdot (2.8 - (\frac{\tan (\frac{46° \cdot 3.1416}{180})}{\tan (\frac{52.1° \cdot 3.1416}{180})})) \cdot 18kN/m³ \cdot (\frac{\sin (\frac{(64° - 52.1°) \cdot 3.1416}{180})}{\sin (\frac{64° \cdot 3.1416}{180})}) \cdot \sin (\frac{52.1° \cdot 3.1416}{180})})

6.2849 = (\frac{0.32}{(\frac{1}{2}) \cdot (2.8 - (\frac{\tan (\frac{46 \cdot 3.1416}{180})}{\tan (\frac{52.1 \cdot 3.1416}{180})})) \cdot 18 \cdot (\frac{\sin (\frac{(64 - 52.1) \cdot 3.1416}{180})}{\sin (\frac{64 \cdot 3.1416}{180})}) \cdot \sin (\frac{52.1 \cdot 3.1416}{180})})

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

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

FIRST Step Consider the formula

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})})

Next Step Substitute values of Variables

∴

H = (\frac{0.32kPa}{(\frac{1}{2}) \cdot (2.8 - (\frac{\tan (\frac{46° \cdot π}{180})}{\tan (\frac{52.1° \cdot π}{180})})) \cdot 18kN/m³ \cdot (\frac{\sin (\frac{(64° - 52.1°) \cdot π}{180})}{\sin (\frac{64° \cdot π}{180})}) \cdot \sin (\frac{52.1° \cdot π}{180})})

Next Step Substitute values of Constants

∴

H = (\frac{0.32kPa}{(\frac{1}{2}) \cdot (2.8 - (\frac{\tan (\frac{46° \cdot 3.1416}{180})}{\tan (\frac{52.1° \cdot 3.1416}{180})})) \cdot 18kN/m³ \cdot (\frac{\sin (\frac{(64° - 52.1°) \cdot 3.1416}{180})}{\sin (\frac{64° \cdot 3.1416}{180})}) \cdot \sin (\frac{52.1° \cdot 3.1416}{180})})

Next Step Convert Units

∴

H = (\frac{320Pa}{(\frac{1}{2}) \cdot (2.8 - (\frac{\tan (\frac{0.8029rad \cdot 3.1416}{180})}{\tan (\frac{0.9093rad \cdot 3.1416}{180})})) \cdot 18000N/m³ \cdot (\frac{\sin (\frac{(1.117rad - 0.9093rad) \cdot 3.1416}{180})}{\sin (\frac{1.117rad \cdot 3.1416}{180})}) \cdot \sin (\frac{0.9093rad \cdot 3.1416}{180})})

Next Step Prepare to Evaluate

∴

H = (\frac{320}{(\frac{1}{2}) \cdot (2.8 - (\frac{\tan (\frac{0.8029 \cdot 3.1416}{180})}{\tan (\frac{0.9093 \cdot 3.1416}{180})})) \cdot 18000 \cdot (\frac{\sin (\frac{(1.117 - 0.9093) \cdot 3.1416}{180})}{\sin (\frac{1.117 \cdot 3.1416}{180})}) \cdot \sin (\frac{0.9093 \cdot 3.1416}{180})})

Next Step Evaluate

∴

H = 6.28485383153865m

LAST Step Rounding Answer

∴

H = 6.2849m

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

Effective Cohesion in Geotech as Kilopascal

Effective Cohesion in Geotech as Kilopascal is the consistency of soft to hard defined on the basis of the standard CSN 73 1001 for different states of consistency and degree of saturation.

Symbol: C_eff

Measurement: PressureUnit: kPa

Note: Value should be greater than 0.

Formulas to find Effective Cohesion in Geotech as Kilopascal

Factor of Safety in Soil Mechanics

Factor of Safety in Soil Mechanics expresses how much stronger a system is than it needs to be for an intended load.

Symbol: F_s

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Factor of Safety in Soil Mechanics

Angle of Internal Friction

Angle of Internal Friction is the angle measured between the normal force and resultant force .

Symbol: φ

Measurement: AngleUnit: °

Note: Value should be greater than 0.

Formulas to find Angle of Internal Friction

Critical Slope Angle in Soil Mechanics

Critical Slope Angle in Soil Mechanics is the angle formed by most dangerous plane.

Symbol: θ_cr

Measurement: AngleUnit: °

Note: Value should be between -180 to 180.

Formulas to find Critical Slope Angle 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

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

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)

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.

Syntax: tan(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})}}

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 of Wedge to Top of Wedge given Factor of Safety?

Height from Toe of Wedge to Top of Wedge given Factor of Safety evaluator uses 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))) to evaluate the Height from Toe of Wedge to Top of Wedge, The Height from Toe of Wedge to Top of Wedge given Factor of Safety is defined as the 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 of Wedge to Top of Wedge given Factor of Safety using this online evaluator? To use this online evaluator for Height from Toe of Wedge to Top of Wedge given Factor of Safety, enter Effective Cohesion in Geotech as Kilopascal (C_eff), Factor of Safety in Soil Mechanics (F_s), Angle of Internal Friction (φ), Critical Slope Angle in Soil Mechanics (θ_cr), Unit Weight of Soil (γ) & Angle of Inclination to Horizontal in Soil (i) and hit the calculate button.

FAQs on Height from Toe of Wedge to Top of Wedge given Factor of Safety

What is the formula to find Height from Toe of Wedge to Top of Wedge given Factor of Safety?

The formula of Height from Toe of Wedge to Top of Wedge given Factor of Safety is expressed as 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))). Here is an example- 6.284854 = (320/((1/2)*(2.8-(tan((0.802851455917241*pi)/180)/tan((0.909316540288875*pi)/180)))*18000*(sin(((1.11701072127616-0.909316540288875)*pi)/180)/sin((1.11701072127616*pi)/180))*sin((0.909316540288875*pi)/180))).

How to calculate Height from Toe of Wedge to Top of Wedge given Factor of Safety?

With Effective Cohesion in Geotech as Kilopascal (C_eff), Factor of Safety in Soil Mechanics (F_s), Angle of Internal Friction (φ), Critical Slope Angle in Soil Mechanics (θ_cr), Unit Weight of Soil (γ) & Angle of Inclination to Horizontal in Soil (i) we can find Height from Toe of Wedge to Top of Wedge given Factor of Safety using the formula - 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))). This formula also uses Archimedes' constant and , Sine (sin), Tangent (tan) 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=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)

Can the Height from Toe of Wedge to Top of Wedge given Factor of Safety be negative?

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

Which unit is used to measure Height from Toe of Wedge to Top of Wedge given Factor of Safety?

Height from Toe of Wedge to Top of Wedge given Factor of Safety 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 of Wedge to Top of Wedge given Factor of Safety can be measured.

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

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

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

FAQs on Height from Toe of Wedge to Top of Wedge given Factor of Safety

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