Factor of Safety for Cohesive Soil given Cohesion Solution

STEP 0: Pre-Calculation Summary
Formula Used
Factor of Safety = (Unit Cohesion/(Unit Weight of Soil*Depth of Prism*cos((Angle of Inclination))*sin((Angle of Inclination))))+(tan((Angle of Internal Friction of Soil))/tan((Angle of Inclination)))
fs = (cu/(γ*z*cos((I))*sin((I))))+(tan((Φi))/tan((I)))
This formula uses 3 Functions, 6 Variables
Functions Used
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., sin(Angle)
cos - Cosine of an angle is the ratio of the side adjacent to the angle to the hypotenuse of the triangle., 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., tan(Angle)
Variables Used
Factor of Safety - Factor of Safety expresses how much stronger a system is than it needs to be for an intended load.
Unit Cohesion - (Measured in Pascal) - Unit Cohesion is the force that holds together molecules or like particles within a soil.
Unit Weight of Soil - (Measured in Newton per Cubic Meter) - Unit Weight of Soil mass is the ratio of the total weight of soil to the total volume of soil.
Depth of Prism - (Measured in Meter) - Depth of Prism is the length of prism along z direction.
Angle of Inclination - (Measured in Radian) - Angle of Inclination is defined as the angle measured from the horizontal surface of the wall or any object.
Angle of Internal Friction of Soil - (Measured in Radian) - Angle of Internal Friction of Soil is a shear strength parameter of soils.
STEP 1: Convert Input(s) to Base Unit
Unit Cohesion: 10 Pascal --> 10 Pascal No Conversion Required
Unit Weight of Soil: 18 Kilonewton per Cubic Meter --> 18000 Newton per Cubic Meter (Check conversion here)
Depth of Prism: 3 Meter --> 3 Meter No Conversion Required
Angle of Inclination: 80 Degree --> 1.3962634015952 Radian (Check conversion here)
Angle of Internal Friction of Soil: 82.87 Degree --> 1.44635435112743 Radian (Check conversion here)
STEP 2: Evaluate Formula
Substituting Input Values in Formula
fs = (cu/(γ*z*cos((I))*sin((I))))+(tan((Φi))/tan((I))) --> (10/(18000*3*cos((1.3962634015952))*sin((1.3962634015952))))+(tan((1.44635435112743))/tan((1.3962634015952)))
Evaluating ... ...
fs = 1.41070251670873
STEP 3: Convert Result to Output's Unit
1.41070251670873 --> No Conversion Required
FINAL ANSWER
1.41070251670873 1.410703 <-- Factor of Safety
(Calculation completed in 00.004 seconds)

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23 Stability Analysis of Infinite Slopes in Prism Calculators

Unit Weight of Soil given Factor of Safety for Cohesive Soil
Go Unit Weight of Soil = Cohesion of Soil/((Factor of Safety-(tan((Angle of Internal Friction*pi)/180)/tan((Angle of Inclination*pi)/180)))*Depth of Prism*cos((Angle of Inclination*pi)/180)*sin((Angle of Inclination*pi)/180))
Cohesion given Factor of Safety for Cohesive Soil
Go Cohesion of Soil = (Factor of Safety-(tan((Angle of Internal Friction*pi)/180)/tan((Angle of Inclination*pi)/180)))*(Unit Weight of Soil*Depth of Prism*cos((Angle of Inclination*pi)/180)*sin((Angle of Inclination*pi)/180))
Depth of Prism given Factor of Safety for Cohesive Soil
Go Depth of Prism = Unit Cohesion/((Factor of Safety-(tan((Angle of Internal Friction of Soil))/tan((Angle of Inclination))))*Unit Weight of Soil*cos((Angle of Inclination))*sin((Angle of Inclination)))
Factor of Safety for Cohesive Soil given Cohesion
Go Factor of Safety = (Unit Cohesion/(Unit Weight of Soil*Depth of Prism*cos((Angle of Inclination))*sin((Angle of Inclination))))+(tan((Angle of Internal Friction of Soil))/tan((Angle of Inclination)))
Inclined Length along Slope given Weight of Soil Prism
Go Inclined Length = Weight of Prism/(Unit Weight of Soil*Depth of Prism*cos((Angle of Inclination)))
Unit Weight of Soil given Weight of Soil Prism
Go Unit Weight of Soil = Weight of Prism/(Depth of Prism*Inclined Length*cos((Angle of Inclination)))
Weight of Soil Prism in Stability Analysis
Go Weight of Prism = (Unit Weight of Soil*Depth of Prism*Inclined Length*cos((Angle of Inclination)))
Depth of Prism given Weight of Soil Prism
Go Depth of Prism = Weight of Prism/(Unit Weight of Soil*Inclined Length*cos((Angle of Inclination)))
Angle of Inclination given Weight of Soil Prism
Go Angle of Inclination = acos(Weight of Prism/(Unit Weight of Soil*Depth of Prism*Inclined Length))
Unit Weight of Soil given Vertical Stress on Surface of Prism
Go Unit Weight of Soil = Vertical Stress at a Point in Pascal/(Depth of Prism*cos((Angle of Inclination)))
Depth of Prism given Vertical Stress on Surface of Prism
Go Depth of Prism = Vertical Stress at a Point in Pascal/(Unit Weight of Soil*cos((Angle of Inclination)))
Angle of Inclination given Vertical Stress on Surface of Prism
Go Angle of Inclination = acos(Vertical Stress at a Point in Pascal/(Depth of Prism*Unit Weight of Soil))
Inclined Length along Slope given Volume Per Unit Length of Prism
Go Inclined Length = Volume per unit length of prism/(Depth of Prism*cos((Angle of Inclination)))
Depth of Prism given Volume per Unit Length of Prism
Go Depth of Prism = Volume per unit length of prism/(Inclined Length*cos((Angle of Inclination)))
Volume Per Unit Length of Prism
Go Volume per unit length of prism = (Depth of Prism*Inclined Length*cos((Angle of Inclination)))
Vertical Stress on Surface of Prism given Unit Weight of Soil
Go Vertical Stress at a Point = (Depth of Prism*Unit Weight of Soil*cos((Angle of Inclination)))
Angle of Inclination given Volume per Unit Length of Prism
Go Angle of Inclination = acos(Volume per unit length of prism/(Depth of Prism*Inclined Length))
Inclined Length along Slope given Horizontal Length of Prism
Go Inclined Length = Horizontal Length of Prism/cos((Angle of Inclination))
Horizontal Length of Prism
Go Horizontal Length of Prism = Inclined Length*cos((Angle of Inclination))
Angle of Inclination given Horizontal Length of Prism
Go Angle of Inclination = acos(Horizontal Length of Prism/Inclined Length)
Weight of Soil Prism given Vertical Stress on Surface of Prism
Go Weight of Prism = Vertical Stress at a Point in Pascal*Inclined Length
Inclined Length along Slope given Vertical Stress on Surface of Prism
Go Inclined Length = Weight of Prism/Vertical Stress at a Point*5
Vertical Stress on Surface of Prism
Go Vertical Stress at a Point = Weight of Prism/Inclined Length

Factor of Safety for Cohesive Soil given Cohesion Formula

Factor of Safety = (Unit Cohesion/(Unit Weight of Soil*Depth of Prism*cos((Angle of Inclination))*sin((Angle of Inclination))))+(tan((Angle of Internal Friction of Soil))/tan((Angle of Inclination)))
fs = (cu/(γ*z*cos((I))*sin((I))))+(tan((Φi))/tan((I)))

What is Factor of Safety?

The ratio of a structure's absolute strength (structural capability) to actual applied load; this is a measure of the reliability of a particular design.

How to Calculate Factor of Safety for Cohesive Soil given Cohesion?

Factor of Safety for Cohesive Soil given Cohesion calculator uses Factor of Safety = (Unit Cohesion/(Unit Weight of Soil*Depth of Prism*cos((Angle of Inclination))*sin((Angle of Inclination))))+(tan((Angle of Internal Friction of Soil))/tan((Angle of Inclination))) to calculate the Factor of Safety, The Factor of Safety for Cohesive Soil given Cohesion is defined as ratio of soil's shear strength to applied stress, ensuring stability in cohesive soil, preventing failure or deformation. Factor of Safety is denoted by fs symbol.

How to calculate Factor of Safety for Cohesive Soil given Cohesion using this online calculator? To use this online calculator for Factor of Safety for Cohesive Soil given Cohesion, enter Unit Cohesion (cu), Unit Weight of Soil (γ), Depth of Prism (z), Angle of Inclination (I) & Angle of Internal Friction of Soil i) and hit the calculate button. Here is how the Factor of Safety for Cohesive Soil given Cohesion calculation can be explained with given input values -> 1.410703 = (10/(18000*3*cos((1.3962634015952))*sin((1.3962634015952))))+(tan((1.44635435112743))/tan((1.3962634015952))).

FAQ

What is Factor of Safety for Cohesive Soil given Cohesion?
The Factor of Safety for Cohesive Soil given Cohesion is defined as ratio of soil's shear strength to applied stress, ensuring stability in cohesive soil, preventing failure or deformation and is represented as fs = (cu/(γ*z*cos((I))*sin((I))))+(tan((Φi))/tan((I))) or Factor of Safety = (Unit Cohesion/(Unit Weight of Soil*Depth of Prism*cos((Angle of Inclination))*sin((Angle of Inclination))))+(tan((Angle of Internal Friction of Soil))/tan((Angle of Inclination))). Unit Cohesion is the force that holds together molecules or like particles within a soil, Unit Weight of Soil mass is the ratio of the total weight of soil to the total volume of soil, Depth of Prism is the length of prism along z direction, Angle of Inclination is defined as the angle measured from the horizontal surface of the wall or any object & Angle of Internal Friction of Soil is a shear strength parameter of soils.
How to calculate Factor of Safety for Cohesive Soil given Cohesion?
The Factor of Safety for Cohesive Soil given Cohesion is defined as ratio of soil's shear strength to applied stress, ensuring stability in cohesive soil, preventing failure or deformation is calculated using Factor of Safety = (Unit Cohesion/(Unit Weight of Soil*Depth of Prism*cos((Angle of Inclination))*sin((Angle of Inclination))))+(tan((Angle of Internal Friction of Soil))/tan((Angle of Inclination))). To calculate Factor of Safety for Cohesive Soil given Cohesion, you need Unit Cohesion (cu), Unit Weight of Soil (γ), Depth of Prism (z), Angle of Inclination (I) & Angle of Internal Friction of Soil i). With our tool, you need to enter the respective value for Unit Cohesion, Unit Weight of Soil, Depth of Prism, Angle of Inclination & Angle of Internal Friction of Soil and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.
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