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Factor of Safety given Submerged Unit Weight Formula

GoFactor of Safety given Effective Normal Stress Formula

GoFactor of Safety for Cohesive Soil given Saturated Unit Weight Formula

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Factor of Safety in Soil Mechanics expresses how much stronger a system is than it needs to be for an intended load. Check FAQs

F s = \frac{y S \cdot \tan (\frac{Φ i \cdot π}{180})}{γ saturated \cdot \tan (\frac{i \cdot π}{180})}

F_s - Factor of Safety in Soil Mechanics?y_S - Submerged Unit Weight in KN per Cubic Meter?Φ_i - Angle of Internal Friction of Soil?γ_saturated - Saturated Unit Weight of Soil?i - Angle of Inclination to Horizontal in Soil?π - Archimedes' constant?

Factor of Safety given Submerged Unit Weight Example

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

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

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

0.5446 = \frac{5 \cdot \tan (\frac{82.87 \cdot 3.1416}{180})}{11.89 \cdot \tan (\frac{64 \cdot 3.1416}{180})}

0.5446 = \frac{5kN/m³ \cdot \tan (\frac{82.87° \cdot 3.1416}{180})}{11.89kN/m³ \cdot \tan (\frac{64° \cdot 3.1416}{180})}

0.5446 = \frac{5 \cdot \tan (\frac{82.87 \cdot 3.1416}{180})}{11.89 \cdot \tan (\frac{64 \cdot 3.1416}{180})}

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Factor of Safety given Submerged Unit Weight Solution

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

FIRST Step Consider the formula

F s = \frac{y S \cdot \tan (\frac{Φ i \cdot π}{180})}{γ saturated \cdot \tan (\frac{i \cdot π}{180})}

Next Step Substitute values of Variables

∴

F s = \frac{5kN/m³ \cdot \tan (\frac{82.87° \cdot π}{180})}{11.89kN/m³ \cdot \tan (\frac{64° \cdot π}{180})}

Next Step Substitute values of Constants

∴

F s = \frac{5kN/m³ \cdot \tan (\frac{82.87° \cdot 3.1416}{180})}{11.89kN/m³ \cdot \tan (\frac{64° \cdot 3.1416}{180})}

Next Step Convert Units

∴

F s = \frac{5000N/m³ \cdot \tan (\frac{1.4464rad \cdot 3.1416}{180})}{11890N/m³ \cdot \tan (\frac{1.117rad \cdot 3.1416}{180})}

Next Step Prepare to Evaluate

∴

F s = \frac{5000 \cdot \tan (\frac{1.4464 \cdot 3.1416}{180})}{11890 \cdot \tan (\frac{1.117 \cdot 3.1416}{180})}

Next Step Evaluate

∴

F s = 0.544556256494241

LAST Step Rounding Answer

∴

F s = 0.5446

Factor of Safety given Submerged Unit Weight Formula Elements

Variables

Constants

Functions

Factor of Safety in Soil Mechanics

Factor of Safety in Soil Mechanics 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 in Soil Mechanics

Submerged Unit Weight in KN per Cubic Meter

Submerged Unit Weight in KN per Cubic Meter is the unit weight of a weight of soil as observed under water in a saturated condition of course.

Symbol: y_S

Measurement: Specific WeightUnit: kN/m³

Note: Value should be greater than 0.

Formulas to find Submerged Unit Weight in KN per Cubic Meter

Angle of Internal Friction of Soil

Angle of Internal Friction of Soil is 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

Saturated Unit Weight of Soil

Saturated Unit Weight of Soil is the ratio of mass of saturated soil sample to total volume.

Symbol: γ_saturated

Measurement: Specific WeightUnit: kN/m³

Note: Value should be greater than 0.

Formulas to find Saturated Unit Weight of Soil

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

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 Factor of Safety in Soil Mechanics

Go Factor of Safety given Effective Normal Stress

F s = \frac{σ' \cdot \tan (\frac{φ \cdot π}{180})}{ζ soil}

Go Factor of Safety for Cohesive Soil given Saturated Unit Weight

F s = \frac{c' + (γ' \cdot z \cdot \tan ((φ)) \cdot {(\cos ((i)))}^{2})}{γ sat \cdot z \cdot \cos ((i)) \cdot \sin ((i))}

Other formulas in Steady State Seepage Analysis Along The Slopes category

Go Weight of Soil Prism given Saturated Unit Weight

W prism = (γ saturated \cdot z \cdot b \cdot \cos (\frac{i \cdot π}{180}))

Go Inclined Length of Prism given Saturated Unit Weight

b = \frac{W prism}{γ saturated \cdot z \cdot \cos (\frac{i \cdot π}{180})}

Go Vertical Stress on Prism given Saturated Unit Weight

σ zkp = (γ saturated \cdot z \cdot \cos (\frac{i \cdot π}{180}))

Go Normal Stress Component given Saturated Unit Weight

σ n = (γ saturated \cdot z \cdot {(\cos (\frac{i \cdot π}{180}))}^{2})

How to Evaluate Factor of Safety given Submerged Unit Weight?

Factor of Safety given Submerged Unit Weight evaluator uses Factor of Safety in Soil Mechanics = (Submerged Unit Weight in KN per Cubic Meter*tan((Angle of Internal Friction of Soil*pi)/180))/(Saturated Unit Weight of Soil*tan((Angle of Inclination to Horizontal in Soil*pi)/180)) to evaluate the Factor of Safety in Soil Mechanics, The Factor of Safety given Submerged Unit Weight is defined as the value of factor of safety when we have prior information of other parameters used. Factor of Safety in Soil Mechanics is denoted by F_s symbol.

How to evaluate Factor of Safety given Submerged Unit Weight using this online evaluator? To use this online evaluator for Factor of Safety given Submerged Unit Weight, enter Submerged Unit Weight in KN per Cubic Meter (y_S), Angle of Internal Friction of Soil (Φ_i), Saturated Unit Weight of Soil (γ_saturated) & Angle of Inclination to Horizontal in Soil (i) and hit the calculate button.

FAQs on Factor of Safety given Submerged Unit Weight

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

The formula of Factor of Safety given Submerged Unit Weight is expressed as Factor of Safety in Soil Mechanics = (Submerged Unit Weight in KN per Cubic Meter*tan((Angle of Internal Friction of Soil*pi)/180))/(Saturated Unit Weight of Soil*tan((Angle of Inclination to Horizontal in Soil*pi)/180)). Here is an example- 0.544556 = (5000*tan((1.44635435112743*pi)/180))/(11890*tan((1.11701072127616*pi)/180)).

How to calculate Factor of Safety given Submerged Unit Weight?

With Submerged Unit Weight in KN per Cubic Meter (y_S), Angle of Internal Friction of Soil (Φ_i), Saturated Unit Weight of Soil (γ_saturated) & Angle of Inclination to Horizontal in Soil (i) we can find Factor of Safety given Submerged Unit Weight using the formula - Factor of Safety in Soil Mechanics = (Submerged Unit Weight in KN per Cubic Meter*tan((Angle of Internal Friction of Soil*pi)/180))/(Saturated Unit Weight of Soil*tan((Angle of Inclination to Horizontal in Soil*pi)/180)). This formula also uses Archimedes' constant and Tangent function(s).

What are the other ways to Calculate Factor of Safety in Soil Mechanics?

Here are the different ways to Calculate Factor of Safety in Soil Mechanics-

Factor of Safety in Soil Mechanics=(Effective Normal Stress in Soil Mechanics*tan((Angle of Internal Friction*pi)/180))/Shear Stress in Soil Mechanics
Factor of Safety in Soil Mechanics=(Effective Cohesion+(Submerged Unit Weight*Depth of Prism*tan((Angle of Internal Friction))*(cos((Angle of Inclination to Horizontal in Soil)))^2))/(Saturated Unit Weight in Newton per Cubic Meter*Depth of Prism*cos((Angle of Inclination to Horizontal in Soil))*sin((Angle of Inclination to Horizontal in Soil)))

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Factor of Safety given Submerged Unit Weight Formula

​GoFactor of Safety given Effective Normal Stress Formula

​GoFactor of Safety for Cohesive Soil given Saturated Unit Weight Formula

Factor of Safety given Submerged Unit Weight Example

Factor of Safety given Submerged Unit Weight Solution

Factor of Safety given Submerged Unit Weight Formula Elements

Other Formulas to find Factor of Safety in Soil Mechanics

Other formulas in Steady State Seepage Analysis Along The Slopes category

How to Evaluate Factor of Safety given Submerged Unit Weight?

FAQs on Factor of Safety given Submerged Unit Weight

Variable Name

GoFactor of Safety given Effective Normal Stress Formula

GoFactor of Safety for Cohesive Soil given Saturated Unit Weight Formula