Factor of Safety given Angle of Mobilized Friction Calculator

✖Angle of Internal Friction of Soil is a shear strength parameter of soils.ⓘ Angle of Internal Friction of Soil [Φ_i]			+10% -10%
✖Angle of Mobilized Friction is the slope angle at which an object starts sliding due to applied force.ⓘ Angle of Mobilized Friction [φ_m]			+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 Angle of Mobilized Friction [F_s]

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Formula

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Factor of Safety given Angle of Mobilized Friction

Formula

`"F"_{"s"} = tan(("Φ"_{"i"}*pi)/180)/tan(("φ"_{"m"}*pi)/180)`

Example

`"2.072088"=tan(("82.87°"*pi)/180)/tan(("40°"*pi)/180)`

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Download Slope Stability Analysis using Culman's Method Formulas PDF

Factor of Safety given Angle of Mobilized Friction Solution

STEP 0: Pre-Calculation Summary

Formula Used

Factor of Safety in Soil Mechanics = tan((Angle of Internal Friction of Soil*pi)/180)/tan((Angle of Mobilized Friction*pi)/180)
F_s = tan((Φ_i*pi)/180)/tan((φ_m*pi)/180)
This formula uses 1 Constants, 1 Functions, 3 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.
Angle of Internal Friction of Soil - (Measured in Radian) - Angle of Internal Friction of Soil is a shear strength parameter of soils.
Angle of Mobilized Friction - (Measured in Radian) - Angle of Mobilized Friction is the slope angle at which an object starts sliding due to applied force.

STEP 1: Convert Input(s) to Base Unit

Angle of Internal Friction of Soil: 82.87 Degree --> 1.44635435112743 Radian (Check conversion here)
Angle of Mobilized Friction: 40 Degree --> 0.698131700797601 Radian (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

F_s = tan((Φ_i*pi)/180)/tan((φ_m*pi)/180) --> tan((1.44635435112743*pi)/180)/tan((0.698131700797601*pi)/180)

Evaluating ... ...

F_s = 2.07208762913669

STEP 3: Convert Result to Output's Unit

2.07208762913669 --> No Conversion Required

FINAL ANSWER

2.07208762913669 ≈ 2.072088 <-- Factor of Safety in Soil Mechanics

(Calculation completed in 00.004 seconds)

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Created by Suraj Kumar

Birsa Institute of Technology (BIT), Sindri

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Meerut Institute of Engineering and Technology (MIET), Meerut

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< 25 Slope Stability Analysis using Culman's Method Calculators

Height from Toe of Wedge to Top of Wedge given Factor of Safety

Go Height from Toe of Wedge to Top of Wedge = (Effective Cohesion in Geotech as Kilopascal/((1/2)*(Factor of Safety in Soil Mechanics-(tan((Angle of Internal Friction*pi)/180)/tan((Critical Slope Angle in Soil Mechanics*pi)/180)))*Unit Weight of Soil*(sin(((Angle of Inclination to Horizontal in Soil-Critical Slope Angle in Soil Mechanics)*pi)/180)/sin((Angle of Inclination to Horizontal in Soil*pi)/180))*sin((Critical Slope Angle in Soil Mechanics*pi)/180)))

Cohesion of Soil given Angle of Inclination and Slope angle

Go Effective Cohesion in Geotech as Kilopascal = (Factor of Safety in Soil Mechanics-(tan((Angle of Internal Friction*pi)/180)/tan((Slope Angle*pi)/180)))*((1/2)*Unit Weight of Soil*Height from Toe of Wedge to Top of Wedge*(sin(((Angle of Inclination to Horizontal in Soil-Slope Angle)*pi)/180)/sin((Angle of Inclination to Horizontal in Soil*pi)/180))*sin((Slope Angle*pi)/180))

Mobilized Cohesion given Angle of Mobilized Friction

Go Mobilized Cohesion in Soil Mechanics = (0.5*cosec((Angle of Inclination to Horizontal in Soil*pi)/180)*sec((Angle of Mobilized Friction in Soil Mechanics*pi)/180)*sin(((Angle of Inclination to Horizontal in Soil-Slope Angle in Soil Mechanics)*pi)/180)*sin(((Slope Angle in Soil Mechanics-Angle of Mobilized Friction in Soil Mechanics)*pi)/180))*(Unit Weight of Soil*Height from Toe of Wedge to Top of Wedge)

Height from Toe to Top of Wedge given Angle of Mobilized Friction

Go Height from Toe of Wedge to Top of Wedge = Mobilized Cohesion in Soil Mechanics/(0.5*cosec((Angle of Inclination to Horizontal in Soil*pi)/180)*sec((Angle of Mobilized Friction in Soil Mechanics*pi)/180)*sin(((Angle of Inclination to Horizontal in Soil-Slope Angle)*pi)/180)*sin(((Slope Angle in Soil Mechanics-Angle of Mobilized Friction in Soil Mechanics)*pi)/180)*Unit Weight of Soil)

Mobilized Cohesion given Safe Height from Toe to Top of Wedge

Go Mobilized Cohesion in Kilopascal = Height from Toe of Wedge to Top of Wedge/(4*sin((Angle of Inclination in Soil Mechanics*pi)/180)*cos((Angle of Mobilized Friction in Soil Mechanics*pi)/180))/(Unit Weight of Water in Soil Mechanics*(1-cos(((Angle of Inclination in Soil Mechanics-Angle of Mobilized Friction in Soil Mechanics)*pi)/180)))

Safe Height from Toe to Top of Wedge

Go Height from Toe of Wedge to Top of Wedge = (4*Mobilized Cohesion in Soil Mechanics*sin((Angle of Inclination to Horizontal in Soil*pi)/180)*cos((Angle of Mobilized Friction in Soil Mechanics*pi)/180))/(Unit Weight of Soil*(1-cos(((Angle of Inclination to Horizontal in Soil-Angle of Mobilized Friction in Soil Mechanics)*pi)/180)))

Factor of Safety given Length of Slip Plane

Go 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))

Height from Toe of Wedge to Top of Wedge given Weight of Wedge

Go Height from Toe of Wedge to Top of Wedge = Weight of Wedge in Kilonewton/((Unit Weight of Soil*Length of Slip Plane*(sin(((Angle of Inclination in Soil Mechanics-Slope Angle)*pi)/180)))/(2*sin((Angle of Inclination in Soil Mechanics*pi)/180)))

Length of Slip Plane given Shear Strength along Slip Plane

Go Length of Slip Plane = (Shear Strength of Soil-(Weight of Wedge*cos((Slope Angle in Soil Mechanics*pi)/180)*tan((Angle of Internal Friction*pi)/180)))/Cohesion in Soil

Height from Toe of Wedge to Top of Wedge

Go Height from Toe of Wedge to Top of Wedge = Height of Wedge/((sin(((Angle of Inclination in Soil Mechanics-Slope Angle)*pi)/180))/sin((Angle of Inclination in Soil Mechanics*pi)/180))

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

Go Height of Wedge = (Height from Toe of Wedge to Top of Wedge*sin(((Angle of Inclination in Soil Mechanics-Slope Angle)*pi)/180))/sin((Angle of Inclination in Soil Mechanics*pi)/180)

Shear Strength along Slip Plane

Go Shear Strength = (Cohesion of Soil*Length of Slip Plane)+(Weight of Wedge*cos((Slope Angle*pi)/180)*tan((Angle of Internal Friction*pi)/180))

Slope Angle given Shear Strength along Slip Plane

Go Slope Angle in Soil Mechanics = acos((Shear Strength-(Cohesion of Soil*Length of Slip Plane))/(Weight of Wedge in Newton*tan((Angle of Internal Friction*pi)/180)))

Angle of Internal Friction given Effective Normal Stress

Go Angle of Internal Friction of Soil = atan((Factor of Safety in Soil Mechanics*Shear Stress of Soil in Megapascal)/Effective Normal Stress of Soil in Megapascal)

Slope Angle given Shear Stress along Slip Plane

Go Slope Angle in Soil Mechanics = asin(Average Shear Stress on Shear Plane in Soil Mech/Weight of Wedge in Newton)

Length of Slip Plane given Weight of Wedge of Soil

Go Length of Slip Plane = Weight of Wedge in Kilonewton/((Height of Wedge*Unit Weight of Soil)/2)

Height of Wedge of Soil given Weight of Wedge

Go Height of Wedge = Weight of Wedge in Kilonewton/((Length of Slip Plane*Unit Weight of Soil)/2)

Unit Weight of Soil given Weight of Wedge

Go Unit Weight of Soil = Weight of Wedge in Kilonewton/((Length of Slip Plane*Height of Wedge)/2)

Weight of Wedge of Soil

Go Weight of Wedge in Kilonewton = (Length of Slip Plane*Height of Wedge*Unit Weight of Soil)/2

Angle of Mobilized Friction given Critical Slope Angle

Go Angle of Mobilized Friction = (2*Critical Slope Angle in Soil Mechanics)-Angle of Inclination to Horizontal in Soil

Critical Slope Angle given Angle of Inclination

Go Critical Slope Angle in Soil Mechanics = (Angle of Inclination to Horizontal in Soil+Angle of Mobilized Friction)/2

Angle of Inclination given Critical Slope Angle

Go Angle of Inclination to Horizontal in Soil = (2*Critical Slope Angle in Soil Mechanics)-Angle of Mobilized Friction

Mobilized Cohesion given Cohesive Force along Slip Plane

Go Mobilized Cohesion in Soil Mechanics = Cohesive Force in KN/Length of Slip Plane

Cohesive Force along Slip Plane

Go Cohesive Force in KN = Mobilized Cohesion in Soil Mechanics*Length of Slip Plane

Length of Slip Plane given Cohesive Force along Slip Plane

Go Length of Slip Plane = Cohesive Force in KN/Mobilized Cohesion in Kilopascal

Factor of Safety given Angle of Mobilized Friction Formula

Factor of Safety in Soil Mechanics = tan((Angle of Internal Friction of Soil*pi)/180)/tan((Angle of Mobilized Friction*pi)/180)
F_s = tan((Φ_i*pi)/180)/tan((φ_m*pi)/180)

What is Factor of Safety?

It is defined as the ratio between the strength of the material and the maximum stress in the part. What it tells us basically is that in a specific area of the model, the stress is higher than the strength the material can bear.

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

Factor of Safety given Angle of Mobilized Friction calculator uses Factor of Safety in Soil Mechanics = tan((Angle of Internal Friction of Soil*pi)/180)/tan((Angle of Mobilized Friction*pi)/180) to calculate 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 calculate Factor of Safety given Angle of Mobilized Friction using this online calculator? To use this online calculator 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. Here is how the Factor of Safety given Angle of Mobilized Friction calculation can be explained with given input values -> 2.072088 = tan((1.44635435112743*pi)/180)/tan((0.698131700797601*pi)/180).

FAQ

What is Factor of Safety given Angle of Mobilized Friction?

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 and is represented as F_s = tan((Φ_i*pi)/180)/tan((φ_m*pi)/180) or Factor of Safety in Soil Mechanics = tan((Angle of Internal Friction of Soil*pi)/180)/tan((Angle of Mobilized Friction*pi)/180). Angle of Internal Friction of Soil is a shear strength parameter of soils & Angle of Mobilized Friction is the slope angle at which an object starts sliding due to applied force.

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

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 is calculated using Factor of Safety in Soil Mechanics = tan((Angle of Internal Friction of Soil*pi)/180)/tan((Angle of Mobilized Friction*pi)/180). To calculate Factor of Safety given Angle of Mobilized Friction, you need Angle of Internal Friction of Soil (Φ_i) & Angle of Mobilized Friction (φ_m). With our tool, you need to enter the respective value for Angle of Internal Friction of Soil & Angle of Mobilized Friction 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 Angle of Internal Friction of Soil & Angle of Mobilized Friction. We can use 1 other way(s) to calculate the same, which is/are as follows -

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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