Factor of Safety given Effective Normal Stress Calculator

✖Effective Normal Stress in Soil Mechanics is related to total stress and pore pressure.ⓘ Effective Normal Stress in Soil Mechanics [σ^']			+10% -10%
✖Angle of Internal Friction is the angle measured between the normal force and resultant force .ⓘ Angle of Internal Friction [φ]			+10% -10%
✖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.ⓘ Shear Stress in Soil Mechanics [ζ_soil]			+10% -10%

✖Factor of Safety in Soil Mechanics expresses how much stronger a system is than it needs to be for an intended load.ⓘ Factor of Safety given Effective Normal Stress [F_s]

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Formula

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Factor of Safety given Effective Normal Stress

Formula

`"F"_{"s"} = ("σ"^{"'"}*tan(("φ"*pi)/180))/"ζ"_{"soil"}`

Example

`"0.486913"=("24.67kN/m²"*tan(("46°"*pi)/180))/"0.71kN/m²"`

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Factor of Safety given Effective Normal Stress Solution

STEP 0: Pre-Calculation Summary

Formula Used

Factor of Safety in Soil Mechanics = (Effective Normal Stress in Soil Mechanics*tan((Angle of Internal Friction*pi)/180))/Shear Stress in Soil Mechanics
F_s = (σ^'*tan((φ*pi)/180))/ζ_soil
This formula uses 1 Constants, 1 Functions, 4 Variables

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Functions Used

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., tan(Angle)

Variables Used

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.
Effective Normal Stress in Soil Mechanics - (Measured in Pascal) - Effective Normal Stress in Soil Mechanics is related to total stress and pore pressure.
Angle of Internal Friction - (Measured in Radian) - Angle of Internal Friction is the angle measured between the normal force and resultant force .
Shear Stress in Soil Mechanics - (Measured in Pascal) - 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.

STEP 1: Convert Input(s) to Base Unit

Effective Normal Stress in Soil Mechanics: 24.67 Kilonewton per Square Meter --> 24670 Pascal (Check conversion here)
Angle of Internal Friction: 46 Degree --> 0.802851455917241 Radian (Check conversion here)
Shear Stress in Soil Mechanics: 0.71 Kilonewton per Square Meter --> 710 Pascal (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

F_s = (σ^'*tan((φ*pi)/180))/ζ_soil --> (24670*tan((0.802851455917241*pi)/180))/710

Evaluating ... ...

F_s = 0.486913474568258

STEP 3: Convert Result to Output's Unit

0.486913474568258 --> No Conversion Required

FINAL ANSWER

0.486913474568258 ≈ 0.486913 <-- Factor of Safety in Soil Mechanics

(Calculation completed in 00.004 seconds)

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Birsa Institute of Technology (BIT), Sindri

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< 25 Steady State Seepage Analysis Along The Slopes Calculators

Factor of Safety for Cohesive Soil given Saturated Unit Weight

Go 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)))

Shear Strength given Submerged Unit Weight

Go Shear Strength in KN per Cubic Meter = (Shear Stress in Soil Mechanics*Submerged Unit Weight in KN per Cubic Meter*tan((Angle of Internal Friction*pi)/180))/(Saturated Unit Weight of Soil*tan((Angle of Inclination to Horizontal in Soil*pi)/180))

Submerged Unit Weight given Factor of Safety

Go Submerged Unit Weight in KN per Cubic Meter = Factor of Safety in Soil Mechanics/((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 given Submerged Unit Weight

Go 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))

Submerged Unit Weight given Shear Strength

Go Submerged Unit Weight in KN per Cubic Meter = (Shear Strength in KN per Cubic Meter/Shear Stress in Soil Mechanics)/((tan((Angle of Internal Friction of Soil)))/(Saturated Unit Weight of Soil*tan((Angle of Inclination to Horizontal in Soil))))

Shear Stress given Submerged Unit Weight

Go Shear Stress in Soil Mechanics = Shear Strength in KN per Cubic Meter/((Submerged Unit Weight in KN per Cubic Meter*tan((Angle of Internal Friction)))/(Saturated Unit Weight of Soil*tan((Angle of Inclination to Horizontal in Soil))))

Shear Stress Component given Saturated Unit Weight

Go Shear Stress in Soil Mechanics = (Saturated Unit Weight of Soil*Depth of Prism*cos((Angle of Inclination to Horizontal in Soil*pi)/180)*sin((Angle of Inclination to Horizontal in Soil*pi)/180))

Submerged Unit Weight given Upward Force

Go Submerged Unit Weight in KN per Cubic Meter = (Normal Stress in Soil Mechanics-Upward Force in Seepage Analysis)/(Depth of Prism*(cos((Angle of Inclination to Horizontal in Soil*pi)/180))^2)

Normal Stress Component given Submerged Unit Weight and Depth of Prism

Go Normal Stress in Soil Mechanics = Upward Force in Seepage Analysis+(Submerged Unit Weight in KN per Cubic Meter*Depth of Prism*(cos((Angle of Inclination to Horizontal in Soil*pi)/180))^2)

Upward Force due to Seepage Water given Submerged Unit Weight

Go Upward Force in Seepage Analysis = Normal Stress in Soil Mechanics-(Submerged Unit Weight in KN per Cubic Meter*Depth of Prism*(cos((Angle of Inclination to Horizontal in Soil*pi)/180))^2)

Effective Normal Stress given Saturated Unit Weight

Go Effective Normal Stress in Soil Mechanics = ((Saturated Unit Weight of Soil-Unit Weight of Water)*Depth of Prism*(cos((Angle of Inclination to Horizontal in Soil*pi)/180))^2)

Unit Weight of Water given Effective Normal Stress

Go Unit Weight of Water = Saturated Unit Weight of Soil-(Effective Normal Stress in Soil Mechanics/(Depth of Prism*(cos((Angle of Inclination to Horizontal in Soil*pi)/180))^2))

Inclined Length of Prism given Saturated Unit Weight

Go Inclined Length of Prism = Weight of Prism in Soil Mechanics/(Saturated Unit Weight of Soil*Depth of Prism*cos((Angle of Inclination to Horizontal in Soil*pi)/180))

Weight of Soil Prism given Saturated Unit Weight

Go Weight of Prism in Soil Mechanics = (Saturated Unit Weight of Soil*Depth of Prism*Inclined Length of Prism*cos((Angle of Inclination to Horizontal in Soil*pi)/180))

Effective Normal Stress given Submerged Unit Weight

Go Effective Normal Stress in Soil Mechanics = (Submerged Unit Weight in KN per Cubic Meter*Depth of Prism*(cos((Angle of Inclination to Horizontal in Soil*pi)/180))^2)

Submerged Unit Weight given Effective Normal Stress

Go Submerged Unit Weight in KN per Cubic Meter = Effective Normal Stress in Soil Mechanics/(Depth of Prism*(cos((Angle of Inclination to Horizontal in Soil*pi)/180))^2)

Effective Normal Stress given Factor of Safety

Go Effective Normal Stress in Soil Mechanics = Factor of Safety in Soil Mechanics/((tan((Angle of Internal Friction of Soil*pi)/180))/Shear Stress in Soil Mechanics)

Factor of Safety given Effective Normal Stress

Go Factor of Safety in Soil Mechanics = (Effective Normal Stress in Soil Mechanics*tan((Angle of Internal Friction*pi)/180))/Shear Stress in Soil Mechanics

Vertical Stress on Prism given Saturated Unit Weight

Go Vertical Stress at a Point in Kilopascal = (Saturated Unit Weight of Soil*Depth of Prism*cos((Angle of Inclination to Horizontal in Soil*pi)/180))

Normal Stress Component given Saturated Unit Weight

Go Normal Stress in Soil Mechanics = (Saturated Unit Weight of Soil*Depth of Prism*(cos((Angle of Inclination to Horizontal in Soil*pi)/180))^2)

Unit Weight of Water given Upward Force due to Seepage Water

Go Unit Weight of Water = Upward Force in Seepage Analysis/(Depth of Prism*(cos((Angle of Inclination to Horizontal in Soil*pi)/180))^2)

Upward Force due to Seepage Water

Go Upward Force in Seepage Analysis = (Unit Weight of Water*Depth of Prism*(cos((Angle of Inclination to Horizontal in Soil*pi)/180))^2)

Effective Normal Stress given Upward Force due to Seepage Water

Go Effective Normal Stress in Soil Mechanics = Normal Stress in Soil Mechanics-Upward Force in Seepage Analysis

Upward Force due to Seepage Water given Effective Normal Stress

Go Upward Force in Seepage Analysis = Normal Stress in Soil Mechanics-Effective Normal Stress in Soil Mechanics

Normal Stress Component given Effective Normal Stress

Go Normal Stress in Soil Mechanics = Effective Normal Stress in Soil Mechanics+Upward Force in Seepage Analysis

Factor of Safety given Effective Normal Stress 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
F_s = (σ^'*tan((φ*pi)/180))/ζ_soil

What is Factor of Safety?

In engineering, a factor of safety, also known as safety factor, expresses how much stronger a system is than it needs to be for an intended load.

How to Calculate Factor of Safety given Effective Normal Stress?

Factor of Safety given Effective Normal Stress calculator 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 calculate 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 calculate Factor of Safety given Effective Normal Stress using this online calculator? To use this online calculator 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. Here is how the Factor of Safety given Effective Normal Stress calculation can be explained with given input values -> 1.895956 = (24670*tan((0.802851455917241*pi)/180))/710.

FAQ

What is Factor of Safety given Effective Normal Stress?

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 and is represented as F_s = (σ^'*tan((φ*pi)/180))/ζ_soil or Factor of Safety in Soil Mechanics = (Effective Normal Stress in Soil Mechanics*tan((Angle of Internal Friction*pi)/180))/Shear Stress in Soil Mechanics. Effective Normal Stress in Soil Mechanics is related to total stress and pore pressure, Angle of Internal Friction is the angle measured between the normal force and resultant force & 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.

How to calculate Factor of Safety given Effective Normal Stress?

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 is calculated using 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 calculate Factor of Safety given Effective Normal Stress, you need Effective Normal Stress in Soil Mechanics (σ^'), Angle of Internal Friction (φ) & Shear Stress in Soil Mechanics (ζ_soil). With our tool, you need to enter the respective value for Effective Normal Stress in Soil Mechanics, Angle of Internal Friction & Shear Stress in Soil Mechanics and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

How many ways are there to calculate Factor of Safety in Soil Mechanics?

In this formula, Factor of Safety in Soil Mechanics uses Effective Normal Stress in Soil Mechanics, Angle of Internal Friction & Shear Stress in Soil Mechanics. We can use 2 other way(s) to calculate the same, which is/are as follows -

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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