Factor of Safety for Cohesive Soil given Saturated Unit Weight Solution

STEP 0: Pre-Calculation Summary
Formula Used
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)))
Fs = (c'+(γ'*z*tan((φ))*(cos((i)))^2))/(γsat*z*cos((i))*sin((i)))
This formula uses 3 Functions, 7 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 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.
Effective Cohesion - (Measured in Pascal) - 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.
Submerged Unit Weight - (Measured in Newton per Cubic Meter) - Submerged Unit Weight is the unit weight of weight of soil as observed underwater in a saturated condition of course.
Depth of Prism - (Measured in Meter) - Depth of Prism is the length of prism along z direction.
Angle of Internal Friction - (Measured in Radian) - Angle of Internal Friction is the angle measured between the normal force and resultant force .
Angle of Inclination to Horizontal in Soil - (Measured in Radian) - Angle of Inclination to Horizontal in Soil is defined as the angle measured from the horizontal surface of the wall or any object.
Saturated Unit Weight in Newton per Cubic Meter - (Measured 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.
STEP 1: Convert Input(s) to Base Unit
Effective Cohesion: 4 Pascal --> 4 Pascal No Conversion Required
Submerged Unit Weight: 5.01 Newton per Cubic Meter --> 5.01 Newton per Cubic Meter No Conversion Required
Depth of Prism: 3 Meter --> 3 Meter No Conversion Required
Angle of Internal Friction: 46 Degree --> 0.802851455917241 Radian (Check conversion here)
Angle of Inclination to Horizontal in Soil: 64 Degree --> 1.11701072127616 Radian (Check conversion here)
Saturated Unit Weight in Newton per Cubic Meter: 32.24 Newton per Cubic Meter --> 32.24 Newton per Cubic Meter No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
Fs = (c'+(γ'*z*tan((φ))*(cos((i)))^2))/(γsat*z*cos((i))*sin((i))) --> (4+(5.01*3*tan((0.802851455917241))*(cos((1.11701072127616)))^2))/(32.24*3*cos((1.11701072127616))*sin((1.11701072127616)))
Evaluating ... ...
Fs = 0.183449398100144
STEP 3: Convert Result to Output's Unit
0.183449398100144 --> No Conversion Required
FINAL ANSWER
0.183449398100144 0.183449 <-- Factor of Safety in Soil Mechanics
(Calculation completed in 00.004 seconds)

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Birsa Institute of Technology (BIT), Sindri
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Factor of Safety for Cohesive Soil given Saturated Unit Weight
Go 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)))
Shear Strength given Submerged Unit Weight
Go Shear Strength in KN per Cubic Meter = (Shear Stress in Soil Mechanics*Submerged Unit Weight in KN per Cubic Meter*tan((Angle of Internal Friction*pi)/180))/(Saturated Unit Weight of Soil*tan((Angle of Inclination to Horizontal in Soil*pi)/180))
Submerged Unit Weight given Factor of Safety
Go Submerged Unit Weight in KN per Cubic Meter = Factor of Safety in Soil Mechanics/((tan((Angle of Internal Friction of Soil*pi)/180))/(Saturated Unit Weight of Soil*tan((Angle of Inclination to Horizontal in Soil*pi)/180)))
Factor of Safety given Submerged Unit Weight
Go 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))
Submerged Unit Weight given Shear Strength
Go Submerged Unit Weight in KN per Cubic Meter = (Shear Strength in KN per Cubic Meter/Shear Stress in Soil Mechanics)/((tan((Angle of Internal Friction of Soil)))/(Saturated Unit Weight of Soil*tan((Angle of Inclination to Horizontal in Soil))))
Shear Stress given Submerged Unit Weight
Go Shear Stress in Soil Mechanics = Shear Strength in KN per Cubic Meter/((Submerged Unit Weight in KN per Cubic Meter*tan((Angle of Internal Friction)))/(Saturated Unit Weight of Soil*tan((Angle of Inclination to Horizontal in Soil))))
Shear Stress Component given Saturated Unit Weight
Go Shear Stress in Soil Mechanics = (Saturated Unit Weight of Soil*Depth of Prism*cos((Angle of Inclination to Horizontal in Soil*pi)/180)*sin((Angle of Inclination to Horizontal in Soil*pi)/180))
Submerged Unit Weight given Upward Force
Go Submerged Unit Weight in KN per Cubic Meter = (Normal Stress in Soil Mechanics-Upward Force in Seepage Analysis)/(Depth of Prism*(cos((Angle of Inclination to Horizontal in Soil*pi)/180))^2)
Normal Stress Component given Submerged Unit Weight and Depth of Prism
Go Normal Stress in Soil Mechanics = Upward Force in Seepage Analysis+(Submerged Unit Weight in KN per Cubic Meter*Depth of Prism*(cos((Angle of Inclination to Horizontal in Soil*pi)/180))^2)
Upward Force due to Seepage Water given Submerged Unit Weight
Go Upward Force in Seepage Analysis = Normal Stress in Soil Mechanics-(Submerged Unit Weight in KN per Cubic Meter*Depth of Prism*(cos((Angle of Inclination to Horizontal in Soil*pi)/180))^2)
Effective Normal Stress given Saturated Unit Weight
Go Effective Normal Stress in Soil Mechanics = ((Saturated Unit Weight of Soil-Unit Weight of Water)*Depth of Prism*(cos((Angle of Inclination to Horizontal in Soil*pi)/180))^2)
Unit Weight of Water given Effective Normal Stress
Go Unit Weight of Water = Saturated Unit Weight of Soil-(Effective Normal Stress in Soil Mechanics/(Depth of Prism*(cos((Angle of Inclination to Horizontal in Soil*pi)/180))^2))
Inclined Length of Prism given Saturated Unit Weight
Go Inclined Length of Prism = Weight of Prism in Soil Mechanics/(Saturated Unit Weight of Soil*Depth of Prism*cos((Angle of Inclination to Horizontal in Soil*pi)/180))
Weight of Soil Prism given Saturated Unit Weight
Go Weight of Prism in Soil Mechanics = (Saturated Unit Weight of Soil*Depth of Prism*Inclined Length of Prism*cos((Angle of Inclination to Horizontal in Soil*pi)/180))
Effective Normal Stress given Submerged Unit Weight
Go Effective Normal Stress in Soil Mechanics = (Submerged Unit Weight in KN per Cubic Meter*Depth of Prism*(cos((Angle of Inclination to Horizontal in Soil*pi)/180))^2)
Submerged Unit Weight given Effective Normal Stress
Go Submerged Unit Weight in KN per Cubic Meter = Effective Normal Stress in Soil Mechanics/(Depth of Prism*(cos((Angle of Inclination to Horizontal in Soil*pi)/180))^2)
Effective Normal Stress given Factor of Safety
Go Effective Normal Stress in Soil Mechanics = Factor of Safety in Soil Mechanics/((tan((Angle of Internal Friction of Soil*pi)/180))/Shear Stress in Soil Mechanics)
Factor of Safety given Effective Normal Stress
Go Factor of Safety in Soil Mechanics = (Effective Normal Stress in Soil Mechanics*tan((Angle of Internal Friction*pi)/180))/Shear Stress in Soil Mechanics
Vertical Stress on Prism given Saturated Unit Weight
Go Vertical Stress at a Point in Kilopascal = (Saturated Unit Weight of Soil*Depth of Prism*cos((Angle of Inclination to Horizontal in Soil*pi)/180))
Normal Stress Component given Saturated Unit Weight
Go Normal Stress in Soil Mechanics = (Saturated Unit Weight of Soil*Depth of Prism*(cos((Angle of Inclination to Horizontal in Soil*pi)/180))^2)
Unit Weight of Water given Upward Force due to Seepage Water
Go Unit Weight of Water = Upward Force in Seepage Analysis/(Depth of Prism*(cos((Angle of Inclination to Horizontal in Soil*pi)/180))^2)
Upward Force due to Seepage Water
Go Upward Force in Seepage Analysis = (Unit Weight of Water*Depth of Prism*(cos((Angle of Inclination to Horizontal in Soil*pi)/180))^2)
Effective Normal Stress given Upward Force due to Seepage Water
Go Effective Normal Stress in Soil Mechanics = Normal Stress in Soil Mechanics-Upward Force in Seepage Analysis
Upward Force due to Seepage Water given Effective Normal Stress
Go Upward Force in Seepage Analysis = Normal Stress in Soil Mechanics-Effective Normal Stress in Soil Mechanics
Normal Stress Component given Effective Normal Stress
Go Normal Stress in Soil Mechanics = Effective Normal Stress in Soil Mechanics+Upward Force in Seepage Analysis

Factor of Safety for Cohesive Soil given Saturated Unit Weight 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)))
Fs = (c'+(γ'*z*tan((φ))*(cos((i)))^2))/(γsat*z*cos((i))*sin((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 Saturated Unit Weight?

Factor of Safety for Cohesive Soil given Saturated Unit Weight calculator 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 calculate 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 Fs symbol.

How to calculate Factor of Safety for Cohesive Soil given Saturated Unit Weight using this online calculator? To use this online calculator for Factor of Safety for Cohesive Soil given Saturated Unit Weight, enter Effective Cohesion (c'), Submerged Unit Weight '), 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 sat) and hit the calculate button. Here is how the Factor of Safety for Cohesive Soil given Saturated Unit Weight calculation can be explained with given input values -> 0.183293 = (4+(5.01*3*tan((0.802851455917241))*(cos((1.11701072127616)))^2))/(32.24*3*cos((1.11701072127616))*sin((1.11701072127616))).

FAQ

What is Factor of Safety for Cohesive Soil given Saturated Unit Weight?
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 and is represented as Fs = (c'+(γ'*z*tan((φ))*(cos((i)))^2))/(γsat*z*cos((i))*sin((i))) or 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))). 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, Submerged Unit Weight is the unit weight of weight of soil as observed underwater in a saturated condition of course, Depth of Prism is the length of prism along z direction, Angle of Internal Friction is the angle measured between the normal force and resultant force , Angle of Inclination to Horizontal in Soil is defined as the angle measured from the horizontal surface of the wall or any object & Saturated Unit Weight in Newton per Cubic Meter is the value of the unit weight of the saturated soil in Newton per Cubic Meter.
How to calculate Factor of Safety for Cohesive Soil given Saturated Unit Weight?
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 is calculated using 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 calculate Factor of Safety for Cohesive Soil given Saturated Unit Weight, you need Effective Cohesion (c'), Submerged Unit Weight '), 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 sat). With our tool, you need to enter the respective value for Effective Cohesion, Submerged Unit Weight, Depth of Prism, Angle of Internal Friction, Angle of Inclination to Horizontal in Soil & Saturated Unit Weight in Newton per Cubic Meter 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 Effective Cohesion, Submerged Unit Weight, Depth of Prism, Angle of Internal Friction, Angle of Inclination to Horizontal in Soil & Saturated Unit Weight in Newton per Cubic Meter. We can use 2 other way(s) to calculate the same, which is/are as follows -
  • 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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