Unit Weight of Soil given Factor of Safety for Cohesive Soil Solution

STEP 0: Pre-Calculation Summary
Formula Used
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))
γ = c/((fs-(tan((φ*pi)/180)/tan((I*pi)/180)))*z*cos((I*pi)/180)*sin((I*pi)/180))
This formula uses 1 Constants, 3 Functions, 6 Variables
Constants Used
pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288
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
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.
Cohesion of Soil - (Measured in Pascal) - Cohesion of Soil is the ability of like particles within soil to hold onto each other. It is the shear strength or force that binds together like particles in the structure of a soil.
Factor of Safety - Factor of Safety expresses how much stronger a system is than it needs to be for an intended load.
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 - (Measured in Radian) - Angle of Inclination is defined as the angle measured from the horizontal surface of the wall or any object.
Depth of Prism - (Measured in Meter) - Depth of Prism is the length of prism along z direction.
STEP 1: Convert Input(s) to Base Unit
Cohesion of Soil: 3.01 Kilopascal --> 3010 Pascal (Check conversion here)
Factor of Safety: 2.8 --> No Conversion Required
Angle of Internal Friction: 46 Degree --> 0.802851455917241 Radian (Check conversion here)
Angle of Inclination: 80 Degree --> 1.3962634015952 Radian (Check conversion here)
Depth of Prism: 3 Meter --> 3 Meter No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
γ = c/((fs-(tan((φ*pi)/180)/tan((I*pi)/180)))*z*cos((I*pi)/180)*sin((I*pi)/180)) --> 3010/((2.8-(tan((0.802851455917241*pi)/180)/tan((1.3962634015952*pi)/180)))*3*cos((1.3962634015952*pi)/180)*sin((1.3962634015952*pi)/180))
Evaluating ... ...
γ = 18510.9021894337
STEP 3: Convert Result to Output's Unit
18510.9021894337 Newton per Cubic Meter -->18.5109021894337 Kilonewton per Cubic Meter (Check conversion here)
FINAL ANSWER
18.5109021894337 18.5109 Kilonewton per Cubic Meter <-- Unit Weight of Soil
(Calculation completed in 00.020 seconds)

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Birsa Institute of Technology (BIT), Sindri
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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

Unit Weight of Soil given Factor of Safety for Cohesive Soil Formula

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))
γ = c/((fs-(tan((φ*pi)/180)/tan((I*pi)/180)))*z*cos((I*pi)/180)*sin((I*pi)/180))

What is Unit Weight of Soil?

The mass of solid particles is usually expressed in terms of their particle unit weight or specific gravity (Gs) of the soil grain solids . For most inorganic soils, the value of Gs lies between 2.60 and 2.80.

How to Calculate Unit Weight of Soil given Factor of Safety for Cohesive Soil?

Unit Weight of Soil given Factor of Safety for Cohesive Soil calculator uses 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)) to calculate the Unit Weight of Soil, The Unit Weight of Soil given Factor of Safety for Cohesive Soil is defined as the weight per unit volume, adjusted for safety, in cohesive soil to ensure stability in construction. Unit Weight of Soil is denoted by γ symbol.

How to calculate Unit Weight of Soil given Factor of Safety for Cohesive Soil using this online calculator? To use this online calculator for Unit Weight of Soil given Factor of Safety for Cohesive Soil, enter Cohesion of Soil (c), Factor of Safety (fs), Angle of Internal Friction (φ), Angle of Inclination (I) & Depth of Prism (z) and hit the calculate button. Here is how the Unit Weight of Soil given Factor of Safety for Cohesive Soil calculation can be explained with given input values -> 0.018449 = 3010/((2.8-(tan((0.802851455917241*pi)/180)/tan((1.3962634015952*pi)/180)))*3*cos((1.3962634015952*pi)/180)*sin((1.3962634015952*pi)/180)).

FAQ

What is Unit Weight of Soil given Factor of Safety for Cohesive Soil?
The Unit Weight of Soil given Factor of Safety for Cohesive Soil is defined as the weight per unit volume, adjusted for safety, in cohesive soil to ensure stability in construction and is represented as γ = c/((fs-(tan((φ*pi)/180)/tan((I*pi)/180)))*z*cos((I*pi)/180)*sin((I*pi)/180)) or 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 of Soil is the ability of like particles within soil to hold onto each other. It is the shear strength or force that binds together like particles in the structure of a soil, Factor of Safety expresses how much stronger a system is than it needs to be for an intended load, Angle of Internal Friction is the angle measured between the normal force and resultant force , Angle of Inclination is defined as the angle measured from the horizontal surface of the wall or any object & Depth of Prism is the length of prism along z direction.
How to calculate Unit Weight of Soil given Factor of Safety for Cohesive Soil?
The Unit Weight of Soil given Factor of Safety for Cohesive Soil is defined as the weight per unit volume, adjusted for safety, in cohesive soil to ensure stability in construction is calculated using 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)). To calculate Unit Weight of Soil given Factor of Safety for Cohesive Soil, you need Cohesion of Soil (c), Factor of Safety (fs), Angle of Internal Friction (φ), Angle of Inclination (I) & Depth of Prism (z). With our tool, you need to enter the respective value for Cohesion of Soil, Factor of Safety, Angle of Internal Friction, Angle of Inclination & Depth of Prism 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 Unit Weight of Soil?
In this formula, Unit Weight of Soil uses Cohesion of Soil, Factor of Safety, Angle of Internal Friction, Angle of Inclination & Depth of Prism. We can use 2 other way(s) to calculate the same, which is/are as follows -
  • Unit Weight of Soil = Weight of Prism/(Depth of Prism*Inclined Length*cos((Angle of Inclination)))
  • Unit Weight of Soil = Vertical Stress at a Point in Pascal/(Depth of Prism*cos((Angle of Inclination)))
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