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Factor of Safety given Length of Slip Plane Formula

GoFactor of Safety given Angle of Mobilized Friction 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 \cdot L}{W wedge \cdot \sin (\frac{θ cr \cdot π}{180})}) + (\frac{\tan (\frac{φ \cdot π}{180})}{\tan (\frac{θ cr \cdot π}{180})})

F_s - Factor of Safety in Soil Mechanics?c - Cohesion in Soil?L - Length of Slip Plane?W_wedge - Weight of Wedge in Newton?θ_cr - Critical Slope Angle in Soil Mechanics?φ - Angle of Internal Friction?π - Archimedes' constant?

Factor of Safety given Length of Slip Plane Example

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Here is how the Factor of Safety given Length of Slip Plane equation looks like with Values.

Here is how the Factor of Safety given Length of Slip Plane equation looks like with Units.

Here is how the Factor of Safety given Length of Slip Plane equation looks like.

3.3019 = (\frac{2.05 \cdot 5}{267 \cdot \sin (\frac{52.1 \cdot 3.1416}{180})}) + (\frac{\tan (\frac{46 \cdot 3.1416}{180})}{\tan (\frac{52.1 \cdot 3.1416}{180})})

3.3019 = (\frac{2.05Pa \cdot 5m}{267N \cdot \sin (\frac{52.1° \cdot 3.1416}{180})}) + (\frac{\tan (\frac{46° \cdot 3.1416}{180})}{\tan (\frac{52.1° \cdot 3.1416}{180})})

3.3019 = (\frac{2.05 \cdot 5}{267 \cdot \sin (\frac{52.1 \cdot 3.1416}{180})}) + (\frac{\tan (\frac{46 \cdot 3.1416}{180})}{\tan (\frac{52.1 \cdot 3.1416}{180})})

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Factor of Safety given Length of Slip Plane Solution

Follow our step by step solution on how to calculate Factor of Safety given Length of Slip Plane?

FIRST Step Consider the formula

F s = (\frac{c \cdot L}{W wedge \cdot \sin (\frac{θ cr \cdot π}{180})}) + (\frac{\tan (\frac{φ \cdot π}{180})}{\tan (\frac{θ cr \cdot π}{180})})

Next Step Substitute values of Variables

∴

F s = (\frac{2.05Pa \cdot 5m}{267N \cdot \sin (\frac{52.1° \cdot π}{180})}) + (\frac{\tan (\frac{46° \cdot π}{180})}{\tan (\frac{52.1° \cdot π}{180})})

Next Step Substitute values of Constants

∴

F s = (\frac{2.05Pa \cdot 5m}{267N \cdot \sin (\frac{52.1° \cdot 3.1416}{180})}) + (\frac{\tan (\frac{46° \cdot 3.1416}{180})}{\tan (\frac{52.1° \cdot 3.1416}{180})})

Next Step Convert Units

∴

F s = (\frac{2.05Pa \cdot 5m}{267N \cdot \sin (\frac{0.9093rad \cdot 3.1416}{180})}) + (\frac{\tan (\frac{0.8029rad \cdot 3.1416}{180})}{\tan (\frac{0.9093rad \cdot 3.1416}{180})})

Next Step Prepare to Evaluate

∴

F s = (\frac{2.05 \cdot 5}{267 \cdot \sin (\frac{0.9093 \cdot 3.1416}{180})}) + (\frac{\tan (\frac{0.8029 \cdot 3.1416}{180})}{\tan (\frac{0.9093 \cdot 3.1416}{180})})

Next Step Evaluate

∴

F s = 3.30191509589154

LAST Step Rounding Answer

∴

F s = 3.3019

Factor of Safety given Length of Slip Plane 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

Cohesion in Soil

Cohesion in Soil is the ability of like particles within soil to hold onto each other. It is the shear strength or force that binds together like particles in the structure of a soil.

Symbol: c

Measurement: PressureUnit: Pa

Note: Value should be greater than 0.

Formulas to find Cohesion in Soil

Length of Slip Plane

Length of Slip Plane is the length of plane along which failure may occur.

Symbol: L

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Length of Slip Plane

Weight of Wedge in Newton

Weight of Wedge in Newton is defined as the weight of total soil which is in the form of wedge.

Symbol: W_wedge

Measurement: ForceUnit: N

Note: Value should be greater than 0.

Formulas to find Weight of Wedge in Newton

Critical Slope Angle in Soil Mechanics

Critical Slope Angle in Soil Mechanics is the angle formed by most dangerous plane.

Symbol: θ_cr

Measurement: AngleUnit: °

Note: Value should be between -180 to 180.

Formulas to find Critical Slope Angle 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

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

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)

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 Angle of Mobilized Friction

F s = \frac{\tan (\frac{Φ i \cdot π}{180})}{\tan (\frac{φ m \cdot π}{180})}

Other formulas in Slope Stability Analysis using Culman's Method category

Go Height of Wedge of Soil given Weight of Wedge

h = \frac{W we}{\frac{L \cdot γ}{2}}

Go Cohesive Force along Slip Plane

F c = c m \cdot L

Go Mobilized Cohesion given Cohesive Force along Slip Plane

c m = \frac{F c}{L}

Go Height of Wedge of Soil given Angle of Inclination and Slope angle

h = \frac{H \cdot \sin (\frac{(θ i - θ) \cdot π}{180})}{\sin (\frac{θ i \cdot π}{180})}

How to Evaluate Factor of Safety given Length of Slip Plane?

Factor of Safety given Length of Slip Plane evaluator uses Factor of Safety in Soil Mechanics = ((Cohesion in Soil*Length of Slip Plane)/(Weight of Wedge in Newton*sin((Critical Slope Angle in Soil Mechanics*pi)/180)))+(tan((Angle of Internal Friction*pi)/180)/tan((Critical Slope Angle in Soil Mechanics*pi)/180)) to evaluate the Factor of Safety in Soil Mechanics, The Factor of Safety given Length of Slip Plane 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 Length of Slip Plane using this online evaluator? To use this online evaluator for Factor of Safety given Length of Slip Plane, enter Cohesion in Soil (c), Length of Slip Plane (L), Weight of Wedge in Newton (W_wedge), Critical Slope Angle in Soil Mechanics (θ_cr) & Angle of Internal Friction (φ) and hit the calculate button.

FAQs on Factor of Safety given Length of Slip Plane

What is the formula to find Factor of Safety given Length of Slip Plane?

The formula of Factor of Safety given Length of Slip Plane is expressed as Factor of Safety in Soil Mechanics = ((Cohesion in Soil*Length of Slip Plane)/(Weight of Wedge in Newton*sin((Critical Slope Angle in Soil Mechanics*pi)/180)))+(tan((Angle of Internal Friction*pi)/180)/tan((Critical Slope Angle in Soil Mechanics*pi)/180)). Here is an example- 7.341668 = ((2.05*5)/(267*sin((0.909316540288875*pi)/180)))+(tan((0.802851455917241*pi)/180)/tan((0.909316540288875*pi)/180)).

How to calculate Factor of Safety given Length of Slip Plane?

With Cohesion in Soil (c), Length of Slip Plane (L), Weight of Wedge in Newton (W_wedge), Critical Slope Angle in Soil Mechanics (θ_cr) & Angle of Internal Friction (φ) we can find Factor of Safety given Length of Slip Plane using the formula - Factor of Safety in Soil Mechanics = ((Cohesion in Soil*Length of Slip Plane)/(Weight of Wedge in Newton*sin((Critical Slope Angle in Soil Mechanics*pi)/180)))+(tan((Angle of Internal Friction*pi)/180)/tan((Critical Slope Angle in Soil Mechanics*pi)/180)). This formula also uses Archimedes' constant and , Sine (sin), 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=tan((Angle of Internal Friction of Soil*pi)/180)/tan((Angle of Mobilized Friction*pi)/180)

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Factor of Safety given Length of Slip Plane Formula

​GoFactor of Safety given Angle of Mobilized Friction Formula

Factor of Safety given Length of Slip Plane Example

Factor of Safety given Length of Slip Plane Solution

Factor of Safety given Length of Slip Plane Formula Elements

Other Formulas to find Factor of Safety in Soil Mechanics

Other formulas in Slope Stability Analysis using Culman's Method category

How to Evaluate Factor of Safety given Length of Slip Plane?

FAQs on Factor of Safety given Length of Slip Plane

Variable Name

GoFactor of Safety given Angle of Mobilized Friction Formula