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Submerged Unit Weight given Factor of Safety with respect to Shear Strength Formula

GoSubmerged Unit Weight given Weighted and Mobilised Friction Angle Formula

GoSubmerged Unit Weight given Weighted and Effective Friction Angle Formula

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Submerged Unit Weight is the effective weight of the soil per unit volume when it is submerged in water. Check FAQs

γ' = \frac{\tan (\frac{φ w \cdot π}{180})}{(\frac{1}{γ sat}) \cdot (\frac{\tan (\frac{Φ i \cdot π}{180})}{f s})}

γ^' - Submerged Unit Weight?φ_w - Weighted Friction Angle?γ_sat - Saturated Unit Weight?Φ_i - Angle of Internal Friction of Soil?f_s - Factor of Safety?π - Archimedes' constant?

Submerged Unit Weight given Factor of Safety with respect to Shear Strength Example

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Here is how the Submerged Unit Weight given Factor of Safety with respect to Shear Strength equation looks like with Values.

Here is how the Submerged Unit Weight given Factor of Safety with respect to Shear Strength equation looks like with Units.

Here is how the Submerged Unit Weight given Factor of Safety with respect to Shear Strength equation looks like.

43.85 = \frac{\tan (\frac{130 \cdot 3.1416}{180})}{(\frac{1}{9.98}) \cdot (\frac{\tan (\frac{82.87 \cdot 3.1416}{180})}{2.8})}

43.85N/m³ = \frac{\tan (\frac{130° \cdot 3.1416}{180})}{(\frac{1}{9.98N/m³}) \cdot (\frac{\tan (\frac{82.87° \cdot 3.1416}{180})}{2.8})}

43.85 = \frac{\tan (\frac{130 \cdot 3.1416}{180})}{(\frac{1}{9.98}) \cdot (\frac{\tan (\frac{82.87 \cdot 3.1416}{180})}{2.8})}

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Submerged Unit Weight given Factor of Safety with respect to Shear Strength Solution

Follow our step by step solution on how to calculate Submerged Unit Weight given Factor of Safety with respect to Shear Strength?

FIRST Step Consider the formula

γ' = \frac{\tan (\frac{φ w \cdot π}{180})}{(\frac{1}{γ sat}) \cdot (\frac{\tan (\frac{Φ i \cdot π}{180})}{f s})}

Next Step Substitute values of Variables

∴

γ' = \frac{\tan (\frac{130° \cdot π}{180})}{(\frac{1}{9.98N/m³}) \cdot (\frac{\tan (\frac{82.87° \cdot π}{180})}{2.8})}

Next Step Substitute values of Constants

∴

γ' = \frac{\tan (\frac{130° \cdot 3.1416}{180})}{(\frac{1}{9.98N/m³}) \cdot (\frac{\tan (\frac{82.87° \cdot 3.1416}{180})}{2.8})}

Next Step Convert Units

∴

γ' = \frac{\tan (\frac{2.2689rad \cdot 3.1416}{180})}{(\frac{1}{9.98N/m³}) \cdot (\frac{\tan (\frac{1.4464rad \cdot 3.1416}{180})}{2.8})}

Next Step Prepare to Evaluate

∴

γ' = \frac{\tan (\frac{2.2689 \cdot 3.1416}{180})}{(\frac{1}{9.98}) \cdot (\frac{\tan (\frac{1.4464 \cdot 3.1416}{180})}{2.8})}

Next Step Evaluate

∴

γ' = 43.8499823350497N/m³

LAST Step Rounding Answer

∴

γ' = 43.85N/m³

Submerged Unit Weight given Factor of Safety with respect to Shear Strength Formula Elements

Variables

Constants

Functions

Submerged Unit Weight

Submerged Unit Weight is the effective weight of the soil per unit volume when it is submerged in water.

Symbol: γ^'

Measurement: Specific WeightUnit: N/m³

Note: Value should be greater than 0.

Formulas to find Submerged Unit Weight

Weighted Friction Angle

Weighted Friction Angle is an effective measure combining materials' friction properties and their relative contributions in geotechnical engineering for stability analysis.

Symbol: φ_w

Measurement: AngleUnit: °

Note: Value should be greater than 0.

Formulas to find Weighted Friction Angle

Saturated Unit Weight

Saturated Unit Weight is the value of the unit weight of the soil when the soil is completely saturated with water that is all the soil pores are completely filled with water.

Symbol: γ_sat

Measurement: Specific WeightUnit: N/m³

Note: Value should be greater than 0.

Formulas to find Saturated Unit Weight

Angle of Internal Friction of Soil

Angle of Internal Friction of Soil is a measure of the shear strength of soil due to friction.

Symbol: Φ_i

Measurement: AngleUnit: °

Note: Value should be between -180 to 180.

Formulas to find Angle of Internal Friction of Soil

Factor of Safety

Factor of Safety is a measure of the load-carrying capacity of a structure or material compared to the actual load or stress that is applied to it.

Symbol: f_s

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Factor of Safety

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

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 Weighted and Mobilised Friction Angle

γ' = \frac{γ sat \cdot φ w}{φ m}

Go Submerged Unit Weight given Weighted and Effective Friction Angle

γ' = \frac{φ IF \cdot (\frac{180}{π})}{\frac{φ' \cdot (\frac{180}{π})}{f s \cdot γ sat}}

Go Submerged Unit Weight given Weighted Friction Angle

γ' = \frac{φ w \cdot γ sat}{φ iw}

Other formulas in Taylor's Stability Number and Stability Curves category

Go Weighted Friction Angle given Factor of Safety with respect to Shear Strength

φ w = a \tan ((\frac{γ'}{γ sat}) \cdot (\frac{\tan ((Φ i))}{f s}))

Go Factor of Safety with respect to Shear Strength

f s = ((\frac{γ'}{γ sat}) \cdot (\frac{\tan ((φ))}{\tan ((φ IF))}))

Go Saturated Unit Weight given Factor of Safety with respect to Shear Strength

γ sat = ((\frac{γ'}{\tan ((φ IF))}) \cdot (\frac{\tan ((φ))}{f s}))

Go Angle of Internal Friction given Factor of Safety

φ = a \tan (\frac{f s \cdot γ sat \cdot \tan ((φ IF))}{γ'})

How to Evaluate Submerged Unit Weight given Factor of Safety with respect to Shear Strength?

Submerged Unit Weight given Factor of Safety with respect to Shear Strength evaluator uses Submerged Unit Weight = tan((Weighted Friction Angle*pi)/180)/((1/Saturated Unit Weight)*(tan((Angle of Internal Friction of Soil*pi)/180)/Factor of Safety)) to evaluate the Submerged Unit Weight, The Submerged Unit Weight given Factor of Safety with respect to Shear Strength is defined as the weight of a material under water, ensuring stability with a safety factor over shear strength. Submerged Unit Weight is denoted by γ^' symbol.

How to evaluate Submerged Unit Weight given Factor of Safety with respect to Shear Strength using this online evaluator? To use this online evaluator for Submerged Unit Weight given Factor of Safety with respect to Shear Strength, enter Weighted Friction Angle (φ_w), Saturated Unit Weight (γ_sat), Angle of Internal Friction of Soil (Φ_i) & Factor of Safety (f_s) and hit the calculate button.

FAQs on Submerged Unit Weight given Factor of Safety with respect to Shear Strength

What is the formula to find Submerged Unit Weight given Factor of Safety with respect to Shear Strength?

The formula of Submerged Unit Weight given Factor of Safety with respect to Shear Strength is expressed as Submerged Unit Weight = tan((Weighted Friction Angle*pi)/180)/((1/Saturated Unit Weight)*(tan((Angle of Internal Friction of Soil*pi)/180)/Factor of Safety)). Here is an example- 43.84998 = tan((2.2689280275922*pi)/180)/((1/9.98)*(tan((1.44635435112743*pi)/180)/2.8)).

How to calculate Submerged Unit Weight given Factor of Safety with respect to Shear Strength?

With Weighted Friction Angle (φ_w), Saturated Unit Weight (γ_sat), Angle of Internal Friction of Soil (Φ_i) & Factor of Safety (f_s) we can find Submerged Unit Weight given Factor of Safety with respect to Shear Strength using the formula - Submerged Unit Weight = tan((Weighted Friction Angle*pi)/180)/((1/Saturated Unit Weight)*(tan((Angle of Internal Friction of Soil*pi)/180)/Factor of Safety)). This formula also uses Archimedes' constant and 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=(Saturated Unit Weight*Weighted Friction Angle)/Angle of Mobilized Friction
Submerged Unit Weight=(Weighted Friction Angle for Internal Friction*(180/pi))/((Effective Angle of Internal Friction*(180/pi))/(Factor of Safety*Saturated Unit Weight))
Submerged Unit Weight=(Weighted Friction Angle*Saturated Unit Weight)/(Internal Friction Angle with Weighted Frict. Angle)

Can the Submerged Unit Weight given Factor of Safety with respect to Shear Strength be negative?

No, the Submerged Unit Weight given Factor of Safety with respect to Shear Strength, measured in Specific Weight cannot be negative.

Which unit is used to measure Submerged Unit Weight given Factor of Safety with respect to Shear Strength?

Submerged Unit Weight given Factor of Safety with respect to Shear Strength 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 with respect to Shear Strength can be measured.

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Submerged Unit Weight given Factor of Safety with respect to Shear Strength Formula

​GoSubmerged Unit Weight given Weighted and Mobilised Friction Angle Formula

​GoSubmerged Unit Weight given Weighted and Effective Friction Angle Formula

Submerged Unit Weight given Factor of Safety with respect to Shear Strength Example

Submerged Unit Weight given Factor of Safety with respect to Shear Strength Solution

Submerged Unit Weight given Factor of Safety with respect to Shear Strength Formula Elements

Other Formulas to find Submerged Unit Weight

Other formulas in Taylor's Stability Number and Stability Curves category

How to Evaluate Submerged Unit Weight given Factor of Safety with respect to Shear Strength?

FAQs on Submerged Unit Weight given Factor of Safety with respect to Shear Strength

Variable Name

GoSubmerged Unit Weight given Weighted and Mobilised Friction Angle Formula

GoSubmerged Unit Weight given Weighted and Effective Friction Angle Formula