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Factor of Safety given Effective Normal Stress Formula

GoFactor of Safety given Submerged Unit Weight 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{σ' \cdot \tan (\frac{φ \cdot π}{180})}{ζ soil}

F_s - Factor of Safety in Soil Mechanics?σ^' - Effective Normal Stress in Soil Mechanics?φ - Angle of Internal Friction?ζ_soil - Shear Stress in Soil Mechanics?π - Archimedes' constant?

Factor of Safety given Effective Normal Stress Example

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Here is how the Factor of Safety given Effective Normal Stress equation looks like with Values.

Here is how the Factor of Safety given Effective Normal Stress equation looks like with Units.

Here is how the Factor of Safety given Effective Normal Stress equation looks like.

0.4869 = \frac{24.67 \cdot \tan (\frac{46 \cdot 3.1416}{180})}{0.71}

0.4869 = \frac{24.67kN/m² \cdot \tan (\frac{46° \cdot 3.1416}{180})}{0.71kN/m²}

0.4869 = \frac{24.67 \cdot \tan (\frac{46 \cdot 3.1416}{180})}{0.71}

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Factor of Safety given Effective Normal Stress Solution

Follow our step by step solution on how to calculate Factor of Safety given Effective Normal Stress?

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

F s = \frac{24.67kN/m² \cdot \tan (\frac{46° \cdot π}{180})}{0.71kN/m²}

Next Step Substitute values of Constants

∴

F s = \frac{24.67kN/m² \cdot \tan (\frac{46° \cdot 3.1416}{180})}{0.71kN/m²}

Next Step Convert Units

∴

F s = \frac{24670Pa \cdot \tan (\frac{0.8029rad \cdot 3.1416}{180})}{710Pa}

Next Step Prepare to Evaluate

∴

F s = \frac{24670 \cdot \tan (\frac{0.8029 \cdot 3.1416}{180})}{710}

Next Step Evaluate

∴

F s = 0.486913474568258

LAST Step Rounding Answer

∴

F s = 0.4869

Factor of Safety given Effective Normal Stress 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

Effective Normal Stress in Soil Mechanics

Effective Normal Stress in Soil Mechanics is related to total stress and pore pressure.

Symbol: σ^'

Measurement: PressureUnit: kN/m²

Note: Value should be greater than 0.

Formulas to find Effective Normal Stress in Soil Mechanics

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

Shear Stress in Soil Mechanics

Shear Stress in Soil Mechanics is force tending to cause deformation of a material by slippage along a plane or planes parallel to the imposed stress.

Symbol: ζ_soil

Measurement: StressUnit: kN/m²

Note: Value should be greater than 0.

Formulas to find Shear Stress in Soil Mechanics

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 Submerged Unit Weight

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

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 Effective Normal Stress?

Factor of Safety given Effective Normal Stress evaluator uses Factor of Safety in Soil Mechanics = (Effective Normal Stress in Soil Mechanics*tan((Angle of Internal Friction*pi)/180))/Shear Stress in Soil Mechanics to evaluate the Factor of Safety in Soil Mechanics, The Factor of Safety given Effective Normal Stress 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 Effective Normal Stress using this online evaluator? To use this online evaluator for Factor of Safety given Effective Normal Stress, enter Effective Normal Stress in Soil Mechanics (σ^'), Angle of Internal Friction (φ) & Shear Stress in Soil Mechanics (ζ_soil) and hit the calculate button.

FAQs on Factor of Safety given Effective Normal Stress

What is the formula to find Factor of Safety given Effective Normal Stress?

The formula of Factor of Safety given Effective Normal Stress is expressed as Factor of Safety in Soil Mechanics = (Effective Normal Stress in Soil Mechanics*tan((Angle of Internal Friction*pi)/180))/Shear Stress in Soil Mechanics. Here is an example- 1.895956 = (24670*tan((0.802851455917241*pi)/180))/710.

How to calculate Factor of Safety given Effective Normal Stress?

With Effective Normal Stress in Soil Mechanics (σ^'), Angle of Internal Friction (φ) & Shear Stress in Soil Mechanics (ζ_soil) we can find Factor of Safety given Effective Normal Stress using the formula - Factor of Safety in Soil Mechanics = (Effective Normal Stress in Soil Mechanics*tan((Angle of Internal Friction*pi)/180))/Shear Stress in Soil Mechanics. This formula also uses Archimedes' constant and Tangent (tan) 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=(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))
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 Effective Normal Stress Formula

​GoFactor of Safety given Submerged Unit Weight Formula

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

Factor of Safety given Effective Normal Stress Example

Factor of Safety given Effective Normal Stress Solution

Factor of Safety given Effective Normal Stress 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 Effective Normal Stress?

FAQs on Factor of Safety given Effective Normal Stress

Variable Name

GoFactor of Safety given Submerged Unit Weight Formula

GoFactor of Safety for Cohesive Soil given Saturated Unit Weight Formula