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Factor of Safety given Angle of Mobilized Friction Formula

GoFactor of Safety given Length of Slip Plane 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{\tan (\frac{Φ i \cdot π}{180})}{\tan (\frac{φ m \cdot π}{180})}

F_s - Factor of Safety in Soil Mechanics?Φ_i - Angle of Internal Friction of Soil?φ_m - Angle of Mobilized Friction?π - Archimedes' constant?

Factor of Safety given Angle of Mobilized Friction Example

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Here is how the Factor of Safety given Angle of Mobilized Friction equation looks like with Values.

Here is how the Factor of Safety given Angle of Mobilized Friction equation looks like with Units.

Here is how the Factor of Safety given Angle of Mobilized Friction equation looks like.

2.0721 = \frac{\tan (\frac{82.87 \cdot 3.1416}{180})}{\tan (\frac{40 \cdot 3.1416}{180})}

2.0721 = \frac{\tan (\frac{82.87° \cdot 3.1416}{180})}{\tan (\frac{40° \cdot 3.1416}{180})}

2.0721 = \frac{\tan (\frac{82.87 \cdot 3.1416}{180})}{\tan (\frac{40 \cdot 3.1416}{180})}

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Factor of Safety given Angle of Mobilized Friction Solution

Follow our step by step solution on how to calculate Factor of Safety given Angle of Mobilized Friction?

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

F s = \frac{\tan (\frac{82.87° \cdot π}{180})}{\tan (\frac{40° \cdot π}{180})}

Next Step Substitute values of Constants

∴

F s = \frac{\tan (\frac{82.87° \cdot 3.1416}{180})}{\tan (\frac{40° \cdot 3.1416}{180})}

Next Step Convert Units

∴

F s = \frac{\tan (\frac{1.4464rad \cdot 3.1416}{180})}{\tan (\frac{0.6981rad \cdot 3.1416}{180})}

Next Step Prepare to Evaluate

∴

F s = \frac{\tan (\frac{1.4464 \cdot 3.1416}{180})}{\tan (\frac{0.6981 \cdot 3.1416}{180})}

Next Step Evaluate

∴

F s = 2.07208762913669

LAST Step Rounding Answer

∴

F s = 2.0721

Factor of Safety given Angle of Mobilized Friction 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

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

Angle of Mobilized Friction

Angle of Mobilized Friction is the slope angle at which an object starts sliding due to applied force.

Symbol: φ_m

Measurement: AngleUnit: °

Note: Value should be greater than 0.

Formulas to find Angle of Mobilized 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

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 Length of Slip Plane

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})})

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 Angle of Mobilized Friction?

Factor of Safety given Angle of Mobilized Friction evaluator uses Factor of Safety in Soil Mechanics = tan((Angle of Internal Friction of Soil*pi)/180)/tan((Angle of Mobilized Friction*pi)/180) to evaluate the Factor of Safety in Soil Mechanics, Factor of Safety given Angle of Mobilized Friction 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 Angle of Mobilized Friction using this online evaluator? To use this online evaluator for Factor of Safety given Angle of Mobilized Friction, enter Angle of Internal Friction of Soil (Φ_i) & Angle of Mobilized Friction (φ_m) and hit the calculate button.

FAQs on Factor of Safety given Angle of Mobilized Friction

What is the formula to find Factor of Safety given Angle of Mobilized Friction?

The formula of Factor of Safety given Angle of Mobilized Friction is expressed as Factor of Safety in Soil Mechanics = tan((Angle of Internal Friction of Soil*pi)/180)/tan((Angle of Mobilized Friction*pi)/180). Here is an example- 2.072088 = tan((1.44635435112743*pi)/180)/tan((0.698131700797601*pi)/180).

How to calculate Factor of Safety given Angle of Mobilized Friction?

With Angle of Internal Friction of Soil (Φ_i) & Angle of Mobilized Friction (φ_m) we can find Factor of Safety given Angle of Mobilized Friction using the formula - Factor of Safety in Soil Mechanics = tan((Angle of Internal Friction of Soil*pi)/180)/tan((Angle of Mobilized Friction*pi)/180). 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=((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))

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