Submerged Unit Weight given Factor of Safety for Cohesive Soil Calculator

✖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.ⓘ Cohesion of Soil [C_s]			+10% -10%
✖Factor of Safety expresses how much stronger a system is than it needs to be for an intended load.ⓘ Factor of Safety [f_s]			+10% -10%
✖Angle of Internal Friction is the angle measured between the normal force and resultant force .ⓘ Angle of Internal Friction [φ]			+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 [z]			+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 given Factor of Safety for Cohesive Soil [γ^']

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Formula

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Submerged Unit Weight given Factor of Safety for Cohesive Soil

Formula

`"γ"^{"'"} = ("C"_{"s"}/(("f"_{"s"}-(tan(("φ"))/tan(("i"))))*"z"*cos(("i"))*sin(("i"))))`

Example

`"1.843213N/m³"=("5.0kPa"/(("2.8"-(tan(("46°"))/tan(("64°"))))*"3m"*cos(("64°"))*sin(("64°"))))`

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Submerged Unit Weight given Factor of Safety for Cohesive Soil Solution

STEP 0: Pre-Calculation Summary

Formula Used

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))))
γ^' = (C_s/((f_s-(tan((φ))/tan((i))))*z*cos((i))*sin((i))))
This formula uses 3 Functions, 6 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

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.
Cohesion of Soil - (Measured in Kilopascal) - 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 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.
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: 5 Kilopascal --> 5 Kilopascal No Conversion Required
Factor of Safety: 2.8 --> 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)
Depth of Prism: 3 Meter --> 3 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

γ^' = (C_s/((f_s-(tan((φ))/tan((i))))*z*cos((i))*sin((i)))) --> (5/((2.8-(tan((0.802851455917241))/tan((1.11701072127616))))*3*cos((1.11701072127616))*sin((1.11701072127616))))

Evaluating ... ...

γ^' = 1.84321340995399

STEP 3: Convert Result to Output's Unit

1.84321340995399 Newton per Cubic Meter --> No Conversion Required

FINAL ANSWER

1.84321340995399 ≈ 1.843213 Newton per Cubic Meter <-- Submerged Unit Weight

(Calculation completed in 00.020 seconds)

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Home » Engineering » Civil » Geotechnical Engineering » Stability Analysis Of Submerged Slopes » Submerged Unit Weight given Factor of Safety for Cohesive Soil

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Created by Suraj Kumar

Birsa Institute of Technology (BIT), Sindri

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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

Submerged Unit Weight given Factor of Safety for Cohesive Soil Formula

What is Submerged Unit Weight?

The weight of the solids in air minus the weight of water displaced by the solids per unit of volume of soil mass; the saturated unit weight minus the unit weight of water.

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

Submerged Unit Weight given Factor of Safety for Cohesive Soil calculator uses 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)))) to calculate the Submerged Unit Weight, The Submerged Unit Weight given Factor of Safety for Cohesive Soil is defined as the weight per unit volume of cohesive soil submerged in water, considering a safety factor. Submerged Unit Weight is denoted by γ^' symbol.

How to calculate Submerged Unit Weight given Factor of Safety for Cohesive Soil using this online calculator? To use this online calculator for Submerged Unit Weight given Factor of Safety for Cohesive Soil, enter Cohesion of Soil (C_s), Factor of Safety (f_s), Angle of Internal Friction (φ), Angle of Inclination to Horizontal in Soil (i) & Depth of Prism (z) and hit the calculate button. Here is how the Submerged Unit Weight given Factor of Safety for Cohesive Soil calculation can be explained with given input values -> 1.843213 = (5000/((2.8-(tan((0.802851455917241))/tan((1.11701072127616))))*3*cos((1.11701072127616))*sin((1.11701072127616)))).

FAQ

What is Submerged Unit Weight given Factor of Safety for Cohesive Soil?

The Submerged Unit Weight given Factor of Safety for Cohesive Soil is defined as the weight per unit volume of cohesive soil submerged in water, considering a safety factor and is represented as γ^' = (C_s/((f_s-(tan((φ))/tan((i))))*z*cos((i))*sin((i)))) or 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)))). 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 to Horizontal in Soil 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 Submerged Unit Weight given Factor of Safety for Cohesive Soil?

The Submerged Unit Weight given Factor of Safety for Cohesive Soil is defined as the weight per unit volume of cohesive soil submerged in water, considering a safety factor is calculated using 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)))). To calculate Submerged Unit Weight given Factor of Safety for Cohesive Soil, you need Cohesion of Soil (C_s), Factor of Safety (f_s), Angle of Internal Friction (φ), Angle of Inclination to Horizontal in Soil (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 to Horizontal in Soil & 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 Submerged Unit Weight?

In this formula, Submerged Unit Weight uses Cohesion of Soil, Factor of Safety, Angle of Internal Friction, Angle of Inclination to Horizontal in Soil & Depth of Prism. We can use 3 other way(s) to calculate the same, which is/are as follows -

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

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