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Unit Weight of Soil given Factor of Safety for Cohesive Soil Formula

GoUnit Weight of Soil given Weight of Soil Prism Formula

GoUnit Weight of Soil given Vertical Stress on Surface of Prism 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}{(f s - (\frac{\tan (\frac{φ \cdot π}{180})}{\tan (\frac{I \cdot π}{180})})) \cdot z \cdot \cos (\frac{I \cdot π}{180}) \cdot \sin (\frac{I \cdot π}{180})}

γ - Unit Weight of Soil?c - Cohesion of Soil?f_s - Factor of Safety?φ - Angle of Internal Friction?I - Angle of Inclination?z - Depth of Prism?π - Archimedes' constant?

Unit Weight of Soil given Factor of Safety for Cohesive Soil Example

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Here is how the Unit Weight of Soil given Factor of Safety for Cohesive Soil equation looks like with Values.

Here is how the Unit Weight of Soil given Factor of Safety for Cohesive Soil equation looks like with Units.

Here is how the Unit Weight of Soil given Factor of Safety for Cohesive Soil equation looks like.

18.5109 = \frac{3.01}{(2.8 - (\frac{\tan (\frac{46 \cdot 3.1416}{180})}{\tan (\frac{80 \cdot 3.1416}{180})})) \cdot 3 \cdot \cos (\frac{80 \cdot 3.1416}{180}) \cdot \sin (\frac{80 \cdot 3.1416}{180})}

18.5109kN/m³ = \frac{3.01kPa}{(2.8 - (\frac{\tan (\frac{46° \cdot 3.1416}{180})}{\tan (\frac{80° \cdot 3.1416}{180})})) \cdot 3m \cdot \cos (\frac{80° \cdot 3.1416}{180}) \cdot \sin (\frac{80° \cdot 3.1416}{180})}

18.5109 = \frac{3.01}{(2.8 - (\frac{\tan (\frac{46 \cdot 3.1416}{180})}{\tan (\frac{80 \cdot 3.1416}{180})})) \cdot 3 \cdot \cos (\frac{80 \cdot 3.1416}{180}) \cdot \sin (\frac{80 \cdot 3.1416}{180})}

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Unit Weight of Soil given Factor of Safety for Cohesive Soil Solution

Follow our step by step solution on how to calculate Unit Weight of Soil given Factor of Safety for Cohesive Soil?

FIRST Step Consider the formula

γ = \frac{c}{(f s - (\frac{\tan (\frac{φ \cdot π}{180})}{\tan (\frac{I \cdot π}{180})})) \cdot z \cdot \cos (\frac{I \cdot π}{180}) \cdot \sin (\frac{I \cdot π}{180})}

Next Step Substitute values of Variables

∴

γ = \frac{3.01kPa}{(2.8 - (\frac{\tan (\frac{46° \cdot π}{180})}{\tan (\frac{80° \cdot π}{180})})) \cdot 3m \cdot \cos (\frac{80° \cdot π}{180}) \cdot \sin (\frac{80° \cdot π}{180})}

Next Step Substitute values of Constants

∴

γ = \frac{3.01kPa}{(2.8 - (\frac{\tan (\frac{46° \cdot 3.1416}{180})}{\tan (\frac{80° \cdot 3.1416}{180})})) \cdot 3m \cdot \cos (\frac{80° \cdot 3.1416}{180}) \cdot \sin (\frac{80° \cdot 3.1416}{180})}

Next Step Convert Units

∴

γ = \frac{3010Pa}{(2.8 - (\frac{\tan (\frac{0.8029rad \cdot 3.1416}{180})}{\tan (\frac{1.3963rad \cdot 3.1416}{180})})) \cdot 3m \cdot \cos (\frac{1.3963rad \cdot 3.1416}{180}) \cdot \sin (\frac{1.3963rad \cdot 3.1416}{180})}

Next Step Prepare to Evaluate

∴

γ = \frac{3010}{(2.8 - (\frac{\tan (\frac{0.8029 \cdot 3.1416}{180})}{\tan (\frac{1.3963 \cdot 3.1416}{180})})) \cdot 3 \cdot \cos (\frac{1.3963 \cdot 3.1416}{180}) \cdot \sin (\frac{1.3963 \cdot 3.1416}{180})}

Next Step Evaluate

∴

γ = 18510.9021894337N/m³

Next Step Convert to Output's Unit

∴

γ = 18.5109021894337kN/m³

LAST Step Rounding Answer

∴

γ = 18.5109kN/m³

Unit Weight of Soil given Factor of Safety for Cohesive Soil 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

Cohesion of Soil

Cohesion of Soil is the ability of like particles within soil to hold onto each other. It is the shear strength or force that binds together like particles in the structure of a soil.

Symbol: c

Measurement: PressureUnit: kPa

Note: Value should be greater than 0.

Formulas to find Cohesion of Soil

Factor of Safety

Factor of Safety 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

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

Angle of Inclination

Angle of Inclination 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

Depth of Prism

Depth of Prism is the length of prism along z direction.

Symbol: z

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Depth of Prism

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)

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 Unit Weight of Soil

Go Unit Weight of Soil given Weight of Soil Prism

γ = \frac{W}{z \cdot b \cdot \cos ((I))}

Go Unit Weight of Soil given Vertical Stress on Surface of Prism

γ = \frac{σ vertical}{z \cdot \cos ((I))}

Other formulas in Stability Analysis of Infinite Slopes in Prism category

Go Weight of Soil Prism in Stability Analysis

W = (γ \cdot z \cdot b \cdot \cos ((I)))

Go Inclined Length along Slope given Weight of Soil Prism

b = \frac{W}{γ \cdot z \cdot \cos ((I))}

Go Depth of Prism given Weight of Soil Prism

z = \frac{W}{γ \cdot b \cdot \cos ((I))}

Go Angle of Inclination given Weight of Soil Prism

I = a \cos (\frac{W}{γ \cdot z \cdot b})

How to Evaluate Unit Weight of Soil given Factor of Safety for Cohesive Soil?

Unit Weight of Soil given Factor of Safety for Cohesive Soil evaluator uses Unit Weight of Soil = Cohesion of Soil/((Factor of Safety-(tan((Angle of Internal Friction*pi)/180)/tan((Angle of Inclination*pi)/180)))*Depth of Prism*cos((Angle of Inclination*pi)/180)*sin((Angle of Inclination*pi)/180)) to evaluate the Unit Weight of Soil, The Unit Weight of Soil given Factor of Safety for Cohesive Soil is defined as the weight per unit volume, adjusted for safety, in cohesive soil to ensure stability in construction. Unit Weight of Soil is denoted by γ symbol.

How to evaluate Unit Weight of Soil given Factor of Safety for Cohesive Soil using this online evaluator? To use this online evaluator for Unit Weight of Soil given Factor of Safety for Cohesive Soil, enter Cohesion of Soil (c), Factor of Safety (f_s), Angle of Internal Friction (φ), Angle of Inclination (I) & Depth of Prism (z) and hit the calculate button.

FAQs on Unit Weight of Soil given Factor of Safety for Cohesive Soil

What is the formula to find Unit Weight of Soil given Factor of Safety for Cohesive Soil?

The formula of Unit Weight of Soil given Factor of Safety for Cohesive Soil is expressed as Unit Weight of Soil = Cohesion of Soil/((Factor of Safety-(tan((Angle of Internal Friction*pi)/180)/tan((Angle of Inclination*pi)/180)))*Depth of Prism*cos((Angle of Inclination*pi)/180)*sin((Angle of Inclination*pi)/180)). Here is an example- 0.018449 = 3010/((2.8-(tan((0.802851455917241*pi)/180)/tan((1.3962634015952*pi)/180)))*3*cos((1.3962634015952*pi)/180)*sin((1.3962634015952*pi)/180)).

How to calculate Unit Weight of Soil given Factor of Safety for Cohesive Soil?

With Cohesion of Soil (c), Factor of Safety (f_s), Angle of Internal Friction (φ), Angle of Inclination (I) & Depth of Prism (z) we can find Unit Weight of Soil given Factor of Safety for Cohesive Soil using the formula - Unit Weight of Soil = Cohesion of Soil/((Factor of Safety-(tan((Angle of Internal Friction*pi)/180)/tan((Angle of Inclination*pi)/180)))*Depth of Prism*cos((Angle of Inclination*pi)/180)*sin((Angle of Inclination*pi)/180)). This formula also uses Archimedes' constant and , Sine (sin), Cosine (cos), Tangent (tan) 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 Prism/(Depth of Prism*Inclined Length*cos((Angle of Inclination)))
Unit Weight of Soil=Vertical Stress at a Point in Pascal/(Depth of Prism*cos((Angle of Inclination)))

Can the Unit Weight of Soil given Factor of Safety for Cohesive Soil be negative?

No, the Unit Weight of Soil given Factor of Safety for Cohesive Soil, measured in Specific Weight cannot be negative.

Which unit is used to measure Unit Weight of Soil given Factor of Safety for Cohesive Soil?

Unit Weight of Soil given Factor of Safety for Cohesive Soil 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 Factor of Safety for Cohesive Soil can be measured.

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Unit Weight of Soil given Factor of Safety for Cohesive Soil Formula

​GoUnit Weight of Soil given Weight of Soil Prism Formula

​GoUnit Weight of Soil given Vertical Stress on Surface of Prism Formula

Unit Weight of Soil given Factor of Safety for Cohesive Soil Example

Unit Weight of Soil given Factor of Safety for Cohesive Soil Solution

Unit Weight of Soil given Factor of Safety for Cohesive Soil Formula Elements

Other Formulas to find Unit Weight of Soil

Other formulas in Stability Analysis of Infinite Slopes in Prism category

How to Evaluate Unit Weight of Soil given Factor of Safety for Cohesive Soil?

FAQs on Unit Weight of Soil given Factor of Safety for Cohesive Soil

Variable Name

GoUnit Weight of Soil given Weight of Soil Prism Formula

GoUnit Weight of Soil given Vertical Stress on Surface of Prism Formula