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Unit Weight of Soil given Safe Height from Toe to Top of Wedge Formula

GoUnit Weight of Soil given Weight of Wedge Formula

GoUnit Weight of Soil given Angle of Mobilized Friction Formula

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

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

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

Unit Weight of Soil given Safe Height from Toe to Top of Wedge Example

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

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

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

18.8859 = \frac{4 \cdot 0.3 \cdot \sin (\frac{64 \cdot 3.1416}{180}) \cdot \cos (\frac{12.33 \cdot 3.1416}{180})}{10 \cdot (1 - \cos (\frac{(64 - 12.33) \cdot 3.1416}{180}))}

18.8859kN/m³ = \frac{4 \cdot 0.3kN/m² \cdot \sin (\frac{64° \cdot 3.1416}{180}) \cdot \cos (\frac{12.33° \cdot 3.1416}{180})}{10m \cdot (1 - \cos (\frac{(64° - 12.33°) \cdot 3.1416}{180}))}

18.8859 = \frac{4 \cdot 0.3 \cdot \sin (\frac{64 \cdot 3.1416}{180}) \cdot \cos (\frac{12.33 \cdot 3.1416}{180})}{10 \cdot (1 - \cos (\frac{(64 - 12.33) \cdot 3.1416}{180}))}

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Unit Weight of Soil given Safe Height from Toe to Top of Wedge Solution

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

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

γ = \frac{4 \cdot 0.3kN/m² \cdot \sin (\frac{64° \cdot π}{180}) \cdot \cos (\frac{12.33° \cdot π}{180})}{10m \cdot (1 - \cos (\frac{(64° - 12.33°) \cdot π}{180}))}

Next Step Substitute values of Constants

∴

γ = \frac{4 \cdot 0.3kN/m² \cdot \sin (\frac{64° \cdot 3.1416}{180}) \cdot \cos (\frac{12.33° \cdot 3.1416}{180})}{10m \cdot (1 - \cos (\frac{(64° - 12.33°) \cdot 3.1416}{180}))}

Next Step Convert Units

∴

γ = \frac{4 \cdot 300Pa \cdot \sin (\frac{1.117rad \cdot 3.1416}{180}) \cdot \cos (\frac{0.2152rad \cdot 3.1416}{180})}{10m \cdot (1 - \cos (\frac{(1.117rad - 0.2152rad) \cdot 3.1416}{180}))}

Next Step Prepare to Evaluate

∴

γ = \frac{4 \cdot 300 \cdot \sin (\frac{1.117 \cdot 3.1416}{180}) \cdot \cos (\frac{0.2152 \cdot 3.1416}{180})}{10 \cdot (1 - \cos (\frac{(1.117 - 0.2152) \cdot 3.1416}{180}))}

Next Step Evaluate

∴

γ = 18885.9114391667N/m³

Next Step Convert to Output's Unit

∴

γ = 18.8859114391667kN/m³

LAST Step Rounding Answer

∴

γ = 18.8859kN/m³

Unit Weight of Soil given Safe Height from Toe to Top of Wedge Formula Elements

Variables

Constants

Functions

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

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

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

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 Unit Weight of Soil

Go Unit Weight of Soil given Weight of Wedge

γ = \frac{W we}{\frac{L \cdot h}{2}}

Go Unit Weight of Soil given Angle of Mobilized Friction

γ = \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 slope) \cdot π}{180}) \cdot \sin (\frac{(θ slope - φ mob) \cdot π}{180}) \cdot H}

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 Unit Weight of Soil given Safe Height from Toe to Top of Wedge?

Unit Weight of Soil given Safe Height from Toe to Top of Wedge evaluator uses Unit Weight of Soil = (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))/(Height from Toe of Wedge to Top of Wedge*(1-cos(((Angle of Inclination to Horizontal in Soil-Angle of Mobilized Friction in Soil Mechanics)*pi)/180))) to evaluate the Unit Weight of Soil, The Unit Weight of Soil given Safe Height from Toe to Top of Wedge is defined as the value of unit weight of soil when we have prior information of other parameters used. Unit Weight of Soil is denoted by γ symbol.

How to evaluate Unit Weight of Soil given Safe Height from Toe to Top of Wedge using this online evaluator? To use this online evaluator for Unit Weight of Soil given 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) & Height from Toe of Wedge to Top of Wedge (H) and hit the calculate button.

FAQs on Unit Weight of Soil given Safe Height from Toe to Top of Wedge

What is the formula to find Unit Weight of Soil given Safe Height from Toe to Top of Wedge?

The formula of Unit Weight of Soil given Safe Height from Toe to Top of Wedge is expressed as Unit Weight of Soil = (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))/(Height from Toe of Wedge to Top of Wedge*(1-cos(((Angle of Inclination to Horizontal in Soil-Angle of Mobilized Friction in Soil Mechanics)*pi)/180))). Here is an example- 0.018886 = (4*300*sin((1.11701072127616*pi)/180)*cos((0.21519909677086*pi)/180))/(10*(1-cos(((1.11701072127616-0.21519909677086)*pi)/180))).

How to calculate Unit Weight of Soil given 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) & Height from Toe of Wedge to Top of Wedge (H) we can find Unit Weight of Soil given Safe Height from Toe to Top of Wedge using the formula - Unit Weight of Soil = (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))/(Height from Toe of Wedge to Top of Wedge*(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, Cosine function(s).

What are the other ways to Calculate Unit Weight of Soil?

Here are the different ways to Calculate Unit Weight of Soil-

Unit Weight of Soil=Weight of Wedge in Kilonewton/((Length of Slip Plane*Height of Wedge)/2)
Unit Weight of Soil=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)*Height from Toe of Wedge to Top of Wedge)

Can the Unit Weight of Soil given Safe Height from Toe to Top of Wedge be negative?

No, the Unit Weight of Soil given Safe Height from Toe to Top of Wedge, measured in Specific Weight cannot be negative.

Which unit is used to measure Unit Weight of Soil given Safe Height from Toe to Top of Wedge?

Unit Weight of Soil given Safe Height from Toe to Top of Wedge is usually measured using the Kilonewton per Cubic Meter[kN/m³] for Specific Weight. Newton per Cubic Meter[kN/m³], Newton per Cubic Centimeter[kN/m³], Newton per Cubic Millimeter[kN/m³] are the few other units in which Unit Weight of Soil given Safe Height from Toe to Top of Wedge can be measured.

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Unit Weight of Soil given Safe Height from Toe to Top of Wedge Formula

​GoUnit Weight of Soil given Weight of Wedge Formula

​GoUnit Weight of Soil given Angle of Mobilized Friction Formula

Unit Weight of Soil given Safe Height from Toe to Top of Wedge Example

Unit Weight of Soil given Safe Height from Toe to Top of Wedge Solution

Unit Weight of Soil given Safe Height from Toe to Top of Wedge Formula Elements

Other Formulas to find Unit Weight of Soil

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

How to Evaluate Unit Weight of Soil given Safe Height from Toe to Top of Wedge?

FAQs on Unit Weight of Soil given Safe Height from Toe to Top of Wedge

Variable Name

GoUnit Weight of Soil given Weight of Wedge Formula

GoUnit Weight of Soil given Angle of Mobilized Friction Formula