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Submerged Unit Weight given Factor of Safety for Cohesive Soil Formula

GoSubmerged Unit Weight given Normal Stress Component Formula

GoSubmerged Unit Weight given Shear Stress Component Formula

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Submerged Unit Weight is the unit weight of weight of soil as observed underwater in a saturated condition of course. Check FAQs

γ' = (\frac{C s}{(f s - (\frac{\tan ((φ))}{\tan ((i))})) \cdot z \cdot \cos ((i)) \cdot \sin ((i))})

γ^' - Submerged Unit Weight?C_s - Cohesion of Soil?f_s - Factor of Safety?φ - Angle of Internal Friction?i - Angle of Inclination to Horizontal in Soil?z - Depth of Prism?

Submerged Unit Weight given Factor of Safety for Cohesive Soil Example

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

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

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

1.8432 = (\frac{5}{(2.8 - (\frac{\tan ((46))}{\tan ((64))})) \cdot 3 \cdot \cos ((64)) \cdot \sin ((64))})

1.8432N/m³ = (\frac{5kPa}{(2.8 - (\frac{\tan ((46°))}{\tan ((64°))})) \cdot 3m \cdot \cos ((64°)) \cdot \sin ((64°))})

1.8432 = (\frac{5}{(2.8 - (\frac{\tan ((46))}{\tan ((64))})) \cdot 3 \cdot \cos ((64)) \cdot \sin ((64))})

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Submerged Unit Weight given Factor of Safety for Cohesive Soil Solution

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

FIRST Step Consider the formula

γ' = (\frac{C s}{(f s - (\frac{\tan ((φ))}{\tan ((i))})) \cdot z \cdot \cos ((i)) \cdot \sin ((i))})

Next Step Substitute values of Variables

∴

γ' = (\frac{5kPa}{(2.8 - (\frac{\tan ((46°))}{\tan ((64°))})) \cdot 3m \cdot \cos ((64°)) \cdot \sin ((64°))})

Next Step Convert Units

∴

γ' = (\frac{5kPa}{(2.8 - (\frac{\tan ((0.8029rad))}{\tan ((1.117rad))})) \cdot 3m \cdot \cos ((1.117rad)) \cdot \sin ((1.117rad))})

Next Step Prepare to Evaluate

∴

γ' = (\frac{5}{(2.8 - (\frac{\tan ((0.8029))}{\tan ((1.117))})) \cdot 3 \cdot \cos ((1.117)) \cdot \sin ((1.117))})

Next Step Evaluate

∴

γ' = 1.84321340995399N/m³

LAST Step Rounding Answer

∴

γ' = 1.8432N/m³

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

Variables

Functions

Submerged Unit Weight

Submerged Unit Weight is the unit weight of weight of soil as observed underwater in a saturated condition of course.

Symbol: γ^'

Measurement: Specific WeightUnit: N/m³

Note: Value should be greater than 0.

Formulas to find Submerged Unit Weight

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_s

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 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

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

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 Submerged Unit Weight

Go Submerged Unit Weight given Normal Stress Component

γ' = \frac{σ Normal}{z \cdot {(\cos ((i)))}^{2}}

Go Submerged Unit Weight given Shear Stress Component

γ' = \frac{𝜏}{z \cdot \cos ((i)) \cdot \sin ((i))}

Go Submerged Unit Weight given Critical Depth

γ' = \frac{C s \cdot {(\sec ((i)))}^{2}}{h c \cdot (\tan ((i)) - \tan ((φ)))}

Other formulas in Stability Analysis of Submerged Slopes category

Go Normal Stress Component given Submerged Unit Weight

σ Normal = γ' \cdot z \cdot {(\cos ((i)))}^{2}

Go Depth of Prism given Submerged Unit Weight

z = \frac{σ Normal}{γ' \cdot {(\cos ((i)))}^{2}}

Go Shear Stress Component given Submerged Unit Weight

𝜏 = (γ' \cdot z \cdot \cos ((i)) \cdot \sin ((i)))

Go Depth of Prism given Submerged Unit Weight and Shear Stress

z = \frac{𝜏}{γ' \cdot \cos ((i)) \cdot \sin ((i))}

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

Submerged Unit Weight given Factor of Safety for Cohesive Soil evaluator uses Submerged Unit Weight = (Cohesion of Soil/((Factor of Safety-(tan((Angle of Internal Friction))/tan((Angle of Inclination to Horizontal in Soil))))*Depth of Prism*cos((Angle of Inclination to Horizontal in Soil))*sin((Angle of Inclination to Horizontal in Soil)))) to evaluate the Submerged Unit Weight, The Submerged Unit Weight given Factor of Safety for Cohesive Soil is defined as the weight per unit volume of cohesive soil submerged in water, considering a safety factor. Submerged Unit Weight is denoted by γ^' symbol.

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

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

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

The formula of Submerged Unit Weight given Factor of Safety for Cohesive Soil is expressed as Submerged Unit Weight = (Cohesion of Soil/((Factor of Safety-(tan((Angle of Internal Friction))/tan((Angle of Inclination to Horizontal in Soil))))*Depth of Prism*cos((Angle of Inclination to Horizontal in Soil))*sin((Angle of Inclination to Horizontal in Soil)))). Here is an example- 1.843213 = (5000/((2.8-(tan((0.802851455917241))/tan((1.11701072127616))))*3*cos((1.11701072127616))*sin((1.11701072127616)))).

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

With Cohesion of Soil (C_s), Factor of Safety (f_s), Angle of Internal Friction (φ), Angle of Inclination to Horizontal in Soil (i) & Depth of Prism (z) we can find Submerged Unit Weight given Factor of Safety for Cohesive Soil using the formula - Submerged Unit Weight = (Cohesion of Soil/((Factor of Safety-(tan((Angle of Internal Friction))/tan((Angle of Inclination to Horizontal in Soil))))*Depth of Prism*cos((Angle of Inclination to Horizontal in Soil))*sin((Angle of Inclination to Horizontal in Soil)))). This formula also uses Sine (sin)Cosine (cos), Tangent (tan) function(s).

What are the other ways to Calculate Submerged Unit Weight?

Here are the different ways to Calculate Submerged Unit Weight-

Submerged Unit Weight=Normal Stress/(Depth of Prism*(cos((Angle of Inclination to Horizontal in Soil)))^2)
Submerged Unit Weight=Shear Stress for Submerged Slopes/(Depth of Prism*cos((Angle of Inclination to Horizontal in Soil))*sin((Angle of Inclination to Horizontal in Soil)))
Submerged Unit Weight=(Cohesion of Soil*(sec((Angle of Inclination to Horizontal in Soil)))^2)/(Critical Depth*(tan((Angle of Inclination to Horizontal in Soil))-tan((Angle of Internal Friction))))

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

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

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

Submerged Unit Weight given Factor of Safety for Cohesive Soil is usually measured using the Newton per Cubic Meter[N/m³] for Specific Weight. Newton per Cubic Centimeter[N/m³], Newton per Cubic Millimeter[N/m³], Kilonewton per Cubic Meter[N/m³] are the few other units in which Submerged Unit Weight given Factor of Safety for Cohesive Soil can be measured.

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Submerged Unit Weight given Factor of Safety for Cohesive Soil Formula

​GoSubmerged Unit Weight given Normal Stress Component Formula

​GoSubmerged Unit Weight given Shear Stress Component Formula

Submerged Unit Weight given Factor of Safety for Cohesive Soil Example

Submerged Unit Weight given Factor of Safety for Cohesive Soil Solution

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

Other Formulas to find Submerged Unit Weight

Other formulas in Stability Analysis of Submerged Slopes category

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

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

Variable Name

GoSubmerged Unit Weight given Normal Stress Component Formula

GoSubmerged Unit Weight given Shear Stress Component Formula