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Unit Weight of Soil given Angle of Mobilized Friction Formula

GoUnit Weight of Soil given Weight of Wedge Formula

GoUnit Weight of Soil given Safe Height from Toe to Top of Wedge 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{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}

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?θ_slope - Slope Angle in Soil Mechanics?H - Height from Toe of Wedge to Top of Wedge?π - Archimedes' constant?

Unit Weight of Soil given Angle of Mobilized Friction Example

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Here is how the Unit Weight of Soil given Angle of Mobilized Friction equation looks like with Values.

Here is how the Unit Weight of Soil given Angle of Mobilized Friction equation looks like with Units.

Here is how the Unit Weight of Soil given Angle of Mobilized Friction equation looks like.

18.932 = \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 - 36.89) \cdot 3.1416}{180}) \cdot \sin (\frac{(36.89 - 12.33) \cdot 3.1416}{180}) \cdot 10}

18.932kN/m³ = \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° - 36.89°) \cdot 3.1416}{180}) \cdot \sin (\frac{(36.89° - 12.33°) \cdot 3.1416}{180}) \cdot 10m}

18.932 = \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 - 36.89) \cdot 3.1416}{180}) \cdot \sin (\frac{(36.89 - 12.33) \cdot 3.1416}{180}) \cdot 10}

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Unit Weight of Soil given Angle of Mobilized Friction Solution

Follow our step by step solution on how to calculate Unit Weight of Soil given Angle of Mobilized Friction?

FIRST Step Consider the formula

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}

Next Step Substitute values of Variables

∴

γ = \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° - 36.89°) \cdot π}{180}) \cdot \sin (\frac{(36.89° - 12.33°) \cdot π}{180}) \cdot 10m}

Next Step Substitute values of Constants

∴

γ = \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° - 36.89°) \cdot 3.1416}{180}) \cdot \sin (\frac{(36.89° - 12.33°) \cdot 3.1416}{180}) \cdot 10m}

Next Step Convert Units

∴

γ = \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 - 0.6439rad) \cdot 3.1416}{180}) \cdot \sin (\frac{(0.6439rad - 0.2152rad) \cdot 3.1416}{180}) \cdot 10m}

Next Step Prepare to Evaluate

∴

γ = \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 - 0.6439) \cdot 3.1416}{180}) \cdot \sin (\frac{(0.6439 - 0.2152) \cdot 3.1416}{180}) \cdot 10}

Next Step Evaluate

∴

γ = 18932.022955538N/m³

Next Step Convert to Output's Unit

∴

γ = 18.932022955538kN/m³

LAST Step Rounding Answer

∴

γ = 18.932kN/m³

Unit Weight of Soil given Angle of Mobilized Friction 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

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.

Formulas to find Slope Angle 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)

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)

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 Safe Height from Toe to Top of Wedge

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}))}

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 Angle of Mobilized Friction?

Unit Weight of Soil given Angle of Mobilized Friction evaluator uses 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) to evaluate the Unit Weight of Soil, The Unit Weight of Soil given Angle of Mobilized Friction 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 Angle of Mobilized Friction using this online evaluator? To use this online evaluator for Unit Weight of Soil 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 in Soil Mechanics (θ_slope) & Height from Toe of Wedge to Top of Wedge (H) and hit the calculate button.

FAQs on Unit Weight of Soil given Angle of Mobilized Friction

What is the formula to find Unit Weight of Soil given Angle of Mobilized Friction?

The formula of Unit Weight of Soil given Angle of Mobilized Friction is expressed as 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). Here is an example- 0.018932 = 300/(0.5*cosec((1.11701072127616*pi)/180)*sec((0.21519909677086*pi)/180)*sin(((1.11701072127616-0.643851961060587)*pi)/180)*sin(((0.643851961060587-0.21519909677086)*pi)/180)*10).

How to calculate Unit Weight of Soil 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 in Soil Mechanics (θ_slope) & Height from Toe of Wedge to Top of Wedge (H) we can find Unit Weight of Soil given Angle of Mobilized Friction using the formula - 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). This formula also uses Archimedes' constant and , Sine (sin), Secant (sec), Cosecant (cosec) 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=(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)))

Can the Unit Weight of Soil given Angle of Mobilized Friction be negative?

No, the Unit Weight of Soil given Angle of Mobilized Friction, measured in Specific Weight cannot be negative.

Which unit is used to measure Unit Weight of Soil given Angle of Mobilized Friction?

Unit Weight of Soil given Angle of Mobilized Friction 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 Angle of Mobilized Friction can be measured.

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Unit Weight of Soil given Angle of Mobilized Friction Formula

​GoUnit Weight of Soil given Weight of Wedge Formula

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

Unit Weight of Soil given Angle of Mobilized Friction Example

Unit Weight of Soil given Angle of Mobilized Friction Solution

Unit Weight of Soil given Angle of Mobilized Friction 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 Angle of Mobilized Friction?

FAQs on Unit Weight of Soil given Angle of Mobilized Friction

Variable Name

GoUnit Weight of Soil given Weight of Wedge Formula

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