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Factor of Safety for Cohesive Soil given Saturated Unit Weight Formula

GoFactor of Safety given Effective Normal Stress Formula

GoFactor of Safety given Submerged 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{c' + (γ' \cdot z \cdot \tan ((φ)) \cdot {(\cos ((i)))}^{2})}{γ sat \cdot z \cdot \cos ((i)) \cdot \sin ((i))}

F_s - Factor of Safety in Soil Mechanics?c' - Effective Cohesion?γ^' - Submerged Unit Weight?z - Depth of Prism?φ - Angle of Internal Friction?i - Angle of Inclination to Horizontal in Soil?γ_sat - Saturated Unit Weight in Newton per Cubic Meter?

Factor of Safety for Cohesive Soil given Saturated Unit Weight Example

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

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

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

0.1834 = \frac{4 + (5.01 \cdot 3 \cdot \tan ((46)) \cdot {(\cos ((64)))}^{2})}{32.24 \cdot 3 \cdot \cos ((64)) \cdot \sin ((64))}

0.1834 = \frac{4Pa + (5.01N/m³ \cdot 3m \cdot \tan ((46°)) \cdot {(\cos ((64°)))}^{2})}{32.24N/m³ \cdot 3m \cdot \cos ((64°)) \cdot \sin ((64°))}

0.1834 = \frac{4 + (5.01 \cdot 3 \cdot \tan ((46)) \cdot {(\cos ((64)))}^{2})}{32.24 \cdot 3 \cdot \cos ((64)) \cdot \sin ((64))}

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Factor of Safety for Cohesive Soil given Saturated Unit Weight Solution

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

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

F s = \frac{4Pa + (5.01N/m³ \cdot 3m \cdot \tan ((46°)) \cdot {(\cos ((64°)))}^{2})}{32.24N/m³ \cdot 3m \cdot \cos ((64°)) \cdot \sin ((64°))}

Next Step Convert Units

∴

F s = \frac{4Pa + (5.01N/m³ \cdot 3m \cdot \tan ((0.8029rad)) \cdot {(\cos ((1.117rad)))}^{2})}{32.24N/m³ \cdot 3m \cdot \cos ((1.117rad)) \cdot \sin ((1.117rad))}

Next Step Prepare to Evaluate

∴

F s = \frac{4 + (5.01 \cdot 3 \cdot \tan ((0.8029)) \cdot {(\cos ((1.117)))}^{2})}{32.24 \cdot 3 \cdot \cos ((1.117)) \cdot \sin ((1.117))}

Next Step Evaluate

∴

F s = 0.183449398100144

LAST Step Rounding Answer

∴

F s = 0.1834

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

Variables

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 Cohesion

Effective Cohesion is the consistency of soft to hard defined on the basis of the standard CSN 73 1001 for different states of consistency and degree of saturation.

Symbol: c'

Measurement: PressureUnit: Pa

Note: Value should be greater than 0.

Formulas to find Effective Cohesion

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

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

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

Saturated Unit Weight in Newton per Cubic Meter

Saturated Unit Weight in Newton per Cubic Meter is the value of the unit weight of the saturated soil in Newton per Cubic Meter.

Symbol: γ_sat

Measurement: Specific WeightUnit: N/m³

Note: Value should be greater than 0.

Formulas to find Saturated Unit Weight in Newton per Cubic Meter

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 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 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})}

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})}

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

Factor of Safety for Cohesive Soil given Saturated Unit Weight evaluator uses 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))) to evaluate the Factor of Safety in Soil Mechanics, The Factor of Safety for Cohesive Soil given Saturated 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 for Cohesive Soil given Saturated Unit Weight using this online evaluator? To use this online evaluator for Factor of Safety for Cohesive Soil given Saturated Unit Weight, enter Effective Cohesion (c'), Submerged Unit Weight (γ^'), Depth of Prism (z), Angle of Internal Friction (φ), Angle of Inclination to Horizontal in Soil (i) & Saturated Unit Weight in Newton per Cubic Meter (γ_sat) and hit the calculate button.

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

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

The formula of Factor of Safety for Cohesive Soil given Saturated Unit Weight is expressed as 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))). Here is an example- 0.183293 = (4+(5.01*3*tan((0.802851455917241))*(cos((1.11701072127616)))^2))/(32.24*3*cos((1.11701072127616))*sin((1.11701072127616))).

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

With Effective Cohesion (c'), Submerged Unit Weight (γ^'), Depth of Prism (z), Angle of Internal Friction (φ), Angle of Inclination to Horizontal in Soil (i) & Saturated Unit Weight in Newton per Cubic Meter (γ_sat) we can find Factor of Safety for Cohesive Soil given Saturated Unit Weight using the formula - 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))). This formula also uses Sine (sin)Cosine (cos), 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=(Effective Normal Stress in Soil Mechanics*tan((Angle of Internal Friction*pi)/180))/Shear Stress 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))

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Factor of Safety for Cohesive Soil given Saturated Unit Weight Formula

​GoFactor of Safety given Effective Normal Stress Formula

​GoFactor of Safety given Submerged Unit Weight Formula

Factor of Safety for Cohesive Soil given Saturated Unit Weight Example

Factor of Safety for Cohesive Soil given Saturated Unit Weight Solution

Factor of Safety for Cohesive Soil given Saturated 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 for Cohesive Soil given Saturated Unit Weight?

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

Variable Name

GoFactor of Safety given Effective Normal Stress Formula

GoFactor of Safety given Submerged Unit Weight Formula