Unit Weight of Soil given Vertical Stress on Surface of Prism Calculator

✖Vertical Stress at a Point in Pascal is the stress acting perpendicular to the surface.ⓘ Vertical Stress at a Point in Pascal [σ_vertical]			+10% -10%
✖Depth of Prism is the length of prism along z direction.ⓘ Depth of Prism [z]			+10% -10%
✖Angle of Inclination is defined as the angle measured from the horizontal surface of the wall or any object.ⓘ Angle of Inclination [I]			+10% -10%

✖Unit Weight of Soil mass is the ratio of the total weight of soil to the total volume of soil.ⓘ Unit Weight of Soil given Vertical Stress on Surface of Prism [γ]

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Formula

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Unit Weight of Soil given Vertical Stress on Surface of Prism

Formula

`"γ" = "σ"_{"vertical"}/("z"*cos(("I")))`

Example

`"19.1959kN/m³"="10Pa"/("3m"*cos(("80°")))`

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Download Stability Analysis of Infinite Slopes in Prism Formulas PDF

Unit Weight of Soil given Vertical Stress on Surface of Prism Solution

STEP 0: Pre-Calculation Summary

Formula Used

Unit Weight of Soil = Vertical Stress at a Point in Pascal/(Depth of Prism*cos((Angle of Inclination)))
γ = σ_vertical/(z*cos((I)))
This formula uses 1 Functions, 4 Variables

Functions Used

cos - Cosine of an angle is the ratio of the side adjacent to the angle to the hypotenuse of the triangle., cos(Angle)

Variables Used

Unit Weight of Soil - (Measured in Kilonewton per Cubic Meter) - Unit Weight of Soil mass is the ratio of the total weight of soil to the total volume of soil.
Vertical Stress at a Point in Pascal - (Measured in Pascal) - Vertical Stress at a Point in Pascal is the stress acting perpendicular to the surface.
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.

STEP 1: Convert Input(s) to Base Unit

Vertical Stress at a Point in Pascal: 10 Pascal --> 10 Pascal No Conversion Required
Depth of Prism: 3 Meter --> 3 Meter No Conversion Required
Angle of Inclination: 80 Degree --> 1.3962634015952 Radian (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

γ = σ_vertical/(z*cos((I))) --> 10/(3*cos((1.3962634015952)))

Evaluating ... ...

γ = 19.1959016104501

STEP 3: Convert Result to Output's Unit

19195.9016104501 Newton per Cubic Meter -->19.1959016104501 Kilonewton per Cubic Meter (Check conversion here)

FINAL ANSWER

19.1959016104501 ≈ 19.1959 Kilonewton per Cubic Meter <-- Unit Weight of Soil

(Calculation completed in 00.006 seconds)

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Created by Suraj Kumar

Birsa Institute of Technology (BIT), Sindri

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Verified by Ishita Goyal

Meerut Institute of Engineering and Technology (MIET), Meerut

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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 Vertical Stress on Surface of Prism Formula

Unit Weight of Soil = Vertical Stress at a Point in Pascal/(Depth of Prism*cos((Angle of Inclination)))
γ = σ_vertical/(z*cos((I)))

What is Unit Weight of Soil?

Unit weight for a soil is a property of a soil which is used to solve the problems related to the earthwork. Unit weight is also known by the name specific weight. Unit weight of the soil is the total weight of the soil divided by total volume. Total weight of soil also includes weight of water.

How to Calculate Unit Weight of Soil given Vertical Stress on Surface of Prism?

Unit Weight of Soil given Vertical Stress on Surface of Prism calculator uses Unit Weight of Soil = Vertical Stress at a Point in Pascal/(Depth of Prism*cos((Angle of Inclination))) to calculate the Unit Weight of Soil, The Unit Weight of Soil given Vertical Stress on Surface of Prism is defined as the ratio of vertical stress on the surface of a prism to its volume. Unit Weight of Soil is denoted by γ symbol.

How to calculate Unit Weight of Soil given Vertical Stress on Surface of Prism using this online calculator? To use this online calculator for Unit Weight of Soil given Vertical Stress on Surface of Prism, enter Vertical Stress at a Point in Pascal (σ_vertical), Depth of Prism (z) & Angle of Inclination (I) and hit the calculate button. Here is how the Unit Weight of Soil given Vertical Stress on Surface of Prism calculation can be explained with given input values -> 0.002304 = 10/(3*cos((1.3962634015952))).

FAQ

What is Unit Weight of Soil given Vertical Stress on Surface of Prism?

The Unit Weight of Soil given Vertical Stress on Surface of Prism is defined as the ratio of vertical stress on the surface of a prism to its volume and is represented as γ = σ_vertical/(z*cos((I))) or Unit Weight of Soil = Vertical Stress at a Point in Pascal/(Depth of Prism*cos((Angle of Inclination))). Vertical Stress at a Point in Pascal is the stress acting perpendicular to the surface, 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.

How to calculate Unit Weight of Soil given Vertical Stress on Surface of Prism?

The Unit Weight of Soil given Vertical Stress on Surface of Prism is defined as the ratio of vertical stress on the surface of a prism to its volume is calculated using Unit Weight of Soil = Vertical Stress at a Point in Pascal/(Depth of Prism*cos((Angle of Inclination))). To calculate Unit Weight of Soil given Vertical Stress on Surface of Prism, you need Vertical Stress at a Point in Pascal (σ_vertical), Depth of Prism (z) & Angle of Inclination (I). With our tool, you need to enter the respective value for Vertical Stress at a Point in Pascal, Depth of Prism & Angle of Inclination 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 Vertical Stress at a Point in Pascal, Depth of Prism & Angle of Inclination. 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 = 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))

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