Saturated Unit Weight given Factor of Safety Solution

STEP 0: Pre-Calculation Summary
Formula Used
Saturated Unit Weight of Soil = (Submerged Unit Weight in KN per Cubic Meter*tan((Angle of Internal Friction of Soil*pi)/180))/(Factor of Safety in Soil Mechanics*tan((Angle of Inclination to Horizontal in Soil*pi)/180))
γsaturated = (yS*tan((Φi*pi)/180))/(Fs*tan((i*pi)/180))
This formula uses 1 Constants, 1 Functions, 5 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
Saturated Unit Weight of Soil - (Measured in Newton per Cubic Meter) - Saturated Unit Weight of Soil is the ratio of mass of saturated soil sample to total volume.
Submerged Unit Weight in KN per Cubic Meter - (Measured in Newton per Cubic Meter) - Submerged Unit Weight in KN per Cubic Meter is the unit weight of a weight of soil as observed under water in a saturated condition of course.
Angle of Internal Friction of Soil - (Measured in Radian) - Angle of Internal Friction of Soil is a shear strength parameter of soils.
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 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.
STEP 1: Convert Input(s) to Base Unit
Submerged Unit Weight in KN per Cubic Meter: 5 Kilonewton per Cubic Meter --> 5000 Newton per Cubic Meter (Check conversion here)
Angle of Internal Friction of Soil: 82.87 Degree --> 1.44635435112743 Radian (Check conversion here)
Factor of Safety in Soil Mechanics: 2.8 --> No Conversion Required
Angle of Inclination to Horizontal in Soil: 64 Degree --> 1.11701072127616 Radian (Check conversion here)
STEP 2: Evaluate Formula
Substituting Input Values in Formula
γsaturated = (yS*tan((Φi*pi)/180))/(Fs*tan((i*pi)/180)) --> (5000*tan((1.44635435112743*pi)/180))/(2.8*tan((1.11701072127616*pi)/180))
Evaluating ... ...
γsaturated = 2312.41924632733
STEP 3: Convert Result to Output's Unit
2312.41924632733 Newton per Cubic Meter -->2.31241924632733 Kilonewton per Cubic Meter (Check conversion here)
FINAL ANSWER
2.31241924632733 2.312419 Kilonewton per Cubic Meter <-- Saturated Unit Weight of Soil
(Calculation completed in 00.004 seconds)

Credits

Created by Suraj Kumar
Birsa Institute of Technology (BIT), Sindri
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18 Factor of Steady Seepage Along the Slope Calculators

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

Saturated Unit Weight given Factor of Safety Formula

Saturated Unit Weight of Soil = (Submerged Unit Weight in KN per Cubic Meter*tan((Angle of Internal Friction of Soil*pi)/180))/(Factor of Safety in Soil Mechanics*tan((Angle of Inclination to Horizontal in Soil*pi)/180))
γsaturated = (yS*tan((Φi*pi)/180))/(Fs*tan((i*pi)/180))

What is Saturated Unit Weight?

Saturated unit weight is equal to the bulk density when the total voids is filled up with water.Buoyant unit weight or submerged unit weight is the effective mass per unit volume when the soil is submerged below standing water or below the ground water table.

How to Calculate Saturated Unit Weight given Factor of Safety?

Saturated Unit Weight given Factor of Safety calculator uses Saturated Unit Weight of Soil = (Submerged Unit Weight in KN per Cubic Meter*tan((Angle of Internal Friction of Soil*pi)/180))/(Factor of Safety in Soil Mechanics*tan((Angle of Inclination to Horizontal in Soil*pi)/180)) to calculate the Saturated Unit Weight of Soil, The Saturated Unit Weight given Factor of Safety is defined as the value of saturated unit weight when we have prior information of other parameters used. Saturated Unit Weight of Soil is denoted by γsaturated symbol.

How to calculate Saturated Unit Weight given Factor of Safety using this online calculator? To use this online calculator for Saturated Unit Weight given Factor of Safety, enter Submerged Unit Weight in KN per Cubic Meter (yS), Angle of Internal Friction of Soil i), Factor of Safety in Soil Mechanics (Fs) & Angle of Inclination to Horizontal in Soil (i) and hit the calculate button. Here is how the Saturated Unit Weight given Factor of Safety calculation can be explained with given input values -> 0.002312 = (5000*tan((1.44635435112743*pi)/180))/(2.8*tan((1.11701072127616*pi)/180)).

FAQ

What is Saturated Unit Weight given Factor of Safety?
The Saturated Unit Weight given Factor of Safety is defined as the value of saturated unit weight when we have prior information of other parameters used and is represented as γsaturated = (yS*tan((Φi*pi)/180))/(Fs*tan((i*pi)/180)) or Saturated Unit Weight of Soil = (Submerged Unit Weight in KN per Cubic Meter*tan((Angle of Internal Friction of Soil*pi)/180))/(Factor of Safety in Soil Mechanics*tan((Angle of Inclination to Horizontal in Soil*pi)/180)). Submerged Unit Weight in KN per Cubic Meter is the unit weight of a weight of soil as observed under water in a saturated condition of course, Angle of Internal Friction of Soil is a shear strength parameter of soils, Factor of Safety in Soil Mechanics expresses how much stronger a system is than it needs to be for an intended load & Angle of Inclination to Horizontal in Soil is defined as the angle measured from the horizontal surface of the wall or any object.
How to calculate Saturated Unit Weight given Factor of Safety?
The Saturated Unit Weight given Factor of Safety is defined as the value of saturated unit weight when we have prior information of other parameters used is calculated using Saturated Unit Weight of Soil = (Submerged Unit Weight in KN per Cubic Meter*tan((Angle of Internal Friction of Soil*pi)/180))/(Factor of Safety in Soil Mechanics*tan((Angle of Inclination to Horizontal in Soil*pi)/180)). To calculate Saturated Unit Weight given Factor of Safety, you need Submerged Unit Weight in KN per Cubic Meter (yS), Angle of Internal Friction of Soil i), Factor of Safety in Soil Mechanics (Fs) & Angle of Inclination to Horizontal in Soil (i). With our tool, you need to enter the respective value for Submerged Unit Weight in KN per Cubic Meter, Angle of Internal Friction of Soil, Factor of Safety in Soil Mechanics & Angle of Inclination to Horizontal in Soil 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 Saturated Unit Weight of Soil?
In this formula, Saturated Unit Weight of Soil uses Submerged Unit Weight in KN per Cubic Meter, Angle of Internal Friction of Soil, Factor of Safety in Soil Mechanics & Angle of Inclination to Horizontal in Soil. We can use 6 other way(s) to calculate the same, which is/are as follows -
  • Saturated Unit Weight of Soil = Weight of Prism in Soil Mechanics/(Depth of Prism*Inclined Length of Prism*cos((Angle of Inclination to Horizontal in Soil*pi)/180))
  • Saturated Unit Weight of Soil = Vertical Stress at a Point in Kilopascal/(Depth of Prism*cos((Angle of Inclination to Horizontal in Soil*pi)/180))
  • Saturated Unit Weight of Soil = Normal Stress in Soil Mechanics/(Depth of Prism*(cos((Angle of Inclination to Horizontal in Soil*pi)/180))^2)
  • Saturated Unit Weight of Soil = Shear Stress in Soil Mechanics/(Depth of Prism*cos((Angle of Inclination to Horizontal in Soil*pi)/180)*sin((Angle of Inclination to Horizontal in Soil*pi)/180))
  • Saturated Unit Weight of Soil = Unit Weight of Water+(Effective Normal Stress in Soil Mechanics/(Depth of Prism*(cos((Angle of Inclination to Horizontal in Soil*pi)/180))^2))
  • Saturated Unit Weight of Soil = (Submerged Unit Weight in KN per Cubic Meter*Shear Stress in Soil Mechanics*tan((Angle of Internal Friction of Soil*pi)/180))/(Shear Strength in KN per Cubic Meter*tan((Angle of Inclination to Horizontal in Soil*pi)/180))
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