Depth of Prism given Submerged Unit Weight Calculator

✖Normal stress is defined as the stress produced by the perpendicular action of a force on a given area.ⓘ Normal Stress [σ_Normal]			+10% -10%
✖Submerged Unit Weight is the unit weight of weight of soil as observed underwater in a saturated condition of course.ⓘ Submerged Unit Weight [γ^']			+10% -10%
✖Angle of Inclination to Horizontal in Soil is defined as the angle measured from the horizontal surface of the wall or any object.ⓘ Angle of Inclination to Horizontal in Soil [i]			+10% -10%

✖Depth of Prism is the length of prism along z direction.ⓘ Depth of Prism given Submerged Unit Weight [z]

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Formula

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Depth of Prism given Submerged Unit Weight

Formula

`"z" = "σ"_{"Normal"}/("γ"^{"'"}*(cos(("i")))^2)`

Example

`"0.830937m"="0.8Pa"/("5.01N/m³"*(cos(("64°")))^2)`

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Depth of Prism given Submerged Unit Weight Solution

STEP 0: Pre-Calculation Summary

Formula Used

Depth of Prism = Normal Stress/(Submerged Unit Weight*(cos((Angle of Inclination to Horizontal in Soil)))^2)
z = σ_Normal/(γ^'*(cos((i)))^2)
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

Depth of Prism - (Measured in Meter) - Depth of Prism is the length of prism along z direction.
Normal Stress - (Measured in Pascal) - Normal stress is defined as the stress produced by the perpendicular action of a force on a given area.
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.
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

Normal Stress: 0.8 Pascal --> 0.8 Pascal No Conversion Required
Submerged Unit Weight: 5.01 Newton per Cubic Meter --> 5.01 Newton per Cubic Meter 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

z = σ_Normal/(γ^'*(cos((i)))^2) --> 0.8/(5.01*(cos((1.11701072127616)))^2)

Evaluating ... ...

z = 0.830937459926598

STEP 3: Convert Result to Output's Unit

0.830937459926598 Meter --> No Conversion Required

FINAL ANSWER

0.830937459926598 ≈ 0.830937 Meter <-- Depth of Prism

(Calculation completed in 00.004 seconds)

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Home » Engineering » Civil » Geotechnical Engineering » Stability Analysis Of Submerged Slopes » Depth of Prism given Submerged Unit Weight

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Created by Suraj Kumar

Birsa Institute of Technology (BIT), Sindri

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Meerut Institute of Engineering and Technology (MIET), Meerut

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< 14 Stability Analysis Of Submerged Slopes Calculators

Cohesion given Submerged Unit Weight

Go Cohesion of Soil = (Factor of Safety-(tan((Angle of Internal Friction*pi)/180)/tan((Angle of Inclination to Horizontal in Soil))))*(Submerged Unit Weight*Depth of Prism*cos((Angle of Inclination to Horizontal in Soil))*sin((Angle of Inclination to Horizontal in Soil)))

Submerged Unit Weight given Factor of Safety for Cohesive Soil

Go Submerged Unit Weight = (Cohesion of Soil/((Factor of Safety-(tan((Angle of Internal Friction))/tan((Angle of Inclination to Horizontal in Soil))))*Depth of Prism*cos((Angle of Inclination to Horizontal in Soil))*sin((Angle of Inclination to Horizontal in Soil))))

Depth of Prism for Cohesive Soil given Submerged Slope

Go Depth of Prism = (Cohesion of Soil/((Factor of Safety-(tan((Angle of Internal Friction))/tan((Angle of Inclination to Horizontal in Soil))))*Submerged Unit Weight*cos((Angle of Inclination to Horizontal in Soil))*sin((Angle of Inclination to Horizontal in Soil))))

Factor of Safety for Cohesive Soil given Depth of Prism

Go Factor of Safety = (Cohesion of Soil/(Submerged Unit Weight*Depth of Prism*cos((Angle of Inclination to Horizontal in Soil))*sin((Angle of Inclination to Horizontal in Soil))))+(tan((Angle of Internal Friction))/tan((Angle of Inclination to Horizontal in Soil)))

Angle of Internal Friction given Factor of Safety for Submerged Slope

Go Angle of Internal Friction of Soil = atan(tan((Angle of Inclination to Horizontal in Soil))*(Factor of Safety-(Cohesion in Soil as Kilopascal/(Submerged Unit Weight*cos((Angle of Inclination to Horizontal in Soil))*sin((Angle of Inclination to Horizontal in Soil))))))

Cohesion of Soil given Submerged Unit Weight

Go Cohesion of Soil = Critical Depth/(((sec((Angle of Inclination to Horizontal in Soil)))^2)/(Submerged Unit Weight*(tan((Angle of Inclination to Horizontal in Soil))-tan((Angle of Internal Friction)))))

Critical Depth given Submerged Unit Weight

Go Critical Depth = (Cohesion of Soil*(sec((Angle of Inclination to Horizontal in Soil)))^2)/(Submerged Unit Weight*(tan((Angle of Inclination to Horizontal in Soil))-tan((Angle of Internal Friction))))

Submerged Unit Weight given Critical Depth

Go Submerged Unit Weight = (Cohesion of Soil*(sec((Angle of Inclination to Horizontal in Soil)))^2)/(Critical Depth*(tan((Angle of Inclination to Horizontal in Soil))-tan((Angle of Internal Friction))))

Depth of Prism given Submerged Unit Weight and Shear Stress

Go Depth of Prism = Shear Stress for Submerged Slopes/(Submerged Unit Weight*cos((Angle of Inclination to Horizontal in Soil))*sin((Angle of Inclination to Horizontal in Soil)))

Shear Stress Component given Submerged Unit Weight

Go Shear Stress for Submerged Slopes = (Submerged Unit Weight*Depth of Prism*cos((Angle of Inclination to Horizontal in Soil))*sin((Angle of Inclination to Horizontal in Soil)))

Submerged Unit Weight given Shear Stress Component

Go Submerged Unit Weight = Shear Stress for Submerged Slopes/(Depth of Prism*cos((Angle of Inclination to Horizontal in Soil))*sin((Angle of Inclination to Horizontal in Soil)))

Submerged Unit Weight given Normal Stress Component

Go Submerged Unit Weight = Normal Stress/(Depth of Prism*(cos((Angle of Inclination to Horizontal in Soil)))^2)

Depth of Prism given Submerged Unit Weight

Go Depth of Prism = Normal Stress/(Submerged Unit Weight*(cos((Angle of Inclination to Horizontal in Soil)))^2)

Normal Stress Component given Submerged Unit Weight

Go Normal Stress = Submerged Unit Weight*Depth of Prism*(cos((Angle of Inclination to Horizontal in Soil)))^2

Depth of Prism given Submerged Unit Weight Formula

Depth of Prism = Normal Stress/(Submerged Unit Weight*(cos((Angle of Inclination to Horizontal in Soil)))^2)
z = σ_Normal/(γ^'*(cos((i)))^2)

What is Submerged Unit Weight?

Submerged density or buoyant density is the density of a mass of soil as observed under water in a saturated condition of course.

How to Calculate Depth of Prism given Submerged Unit Weight?

Depth of Prism given Submerged Unit Weight calculator uses Depth of Prism = Normal Stress/(Submerged Unit Weight*(cos((Angle of Inclination to Horizontal in Soil)))^2) to calculate the Depth of Prism, The Depth of Prism given Submerged Unit Weight is defined as its weight per unit volume, expressed as submerged unit weight. Depth of Prism is denoted by z symbol.

How to calculate Depth of Prism given Submerged Unit Weight using this online calculator? To use this online calculator for Depth of Prism given Submerged Unit Weight, enter Normal Stress (σ_Normal), Submerged Unit Weight (γ^') & Angle of Inclination to Horizontal in Soil (i) and hit the calculate button. Here is how the Depth of Prism given Submerged Unit Weight calculation can be explained with given input values -> 0.832599 = 0.8/(5.01*(cos((1.11701072127616)))^2).

FAQ

What is Depth of Prism given Submerged Unit Weight?

The Depth of Prism given Submerged Unit Weight is defined as its weight per unit volume, expressed as submerged unit weight and is represented as z = σ_Normal/(γ^'*(cos((i)))^2) or Depth of Prism = Normal Stress/(Submerged Unit Weight*(cos((Angle of Inclination to Horizontal in Soil)))^2). Normal stress is defined as the stress produced by the perpendicular action of a force on a given area, Submerged Unit Weight is the unit weight of weight of soil as observed underwater in a saturated condition of course & 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 Depth of Prism given Submerged Unit Weight?

The Depth of Prism given Submerged Unit Weight is defined as its weight per unit volume, expressed as submerged unit weight is calculated using Depth of Prism = Normal Stress/(Submerged Unit Weight*(cos((Angle of Inclination to Horizontal in Soil)))^2). To calculate Depth of Prism given Submerged Unit Weight, you need Normal Stress (σ_Normal), Submerged Unit Weight (γ^') & Angle of Inclination to Horizontal in Soil (i). With our tool, you need to enter the respective value for Normal Stress, Submerged Unit Weight & 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 Depth of Prism?

In this formula, Depth of Prism uses Normal Stress, Submerged Unit Weight & Angle of Inclination to Horizontal in Soil. We can use 2 other way(s) to calculate the same, which is/are as follows -

Depth of Prism = Shear Stress for Submerged Slopes/(Submerged Unit Weight*cos((Angle of Inclination to Horizontal in Soil))*sin((Angle of Inclination to Horizontal in Soil)))
Depth of Prism = (Cohesion of Soil/((Factor of Safety-(tan((Angle of Internal Friction))/tan((Angle of Inclination to Horizontal in Soil))))*Submerged Unit Weight*cos((Angle of Inclination to Horizontal in Soil))*sin((Angle of Inclination to Horizontal in Soil))))

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