Depth of Prism for Cohesive Soil given Submerged Slope 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%
✖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%

✖Depth of Prism is the length of prism along z direction.ⓘ Depth of Prism for Cohesive Soil given Submerged Slope [z]

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Depth of Prism for Cohesive Soil given Submerged Slope Solution

STEP 0: Pre-Calculation Summary

Formula Used

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))))
z = (C_s/((f_s-(tan((φ))/tan((i))))*γ^'*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

Depth of Prism - (Measured in Meter) - Depth of Prism is the length of prism along z direction.
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.
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.

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)
Submerged Unit Weight: 5.01 Newton per Cubic Meter --> 5.01 Newton per Cubic Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

z = (C_s/((f_s-(tan((φ))/tan((i))))*γ^'*cos((i))*sin((i)))) --> (5/((2.8-(tan((0.802851455917241))/tan((1.11701072127616))))*5.01*cos((1.11701072127616))*sin((1.11701072127616))))

Evaluating ... ...

z = 1.10372060476287

STEP 3: Convert Result to Output's Unit

1.10372060476287 Meter --> No Conversion Required

FINAL ANSWER

1.10372060476287 ≈ 1.103721 Meter <-- Depth of Prism

(Calculation completed in 00.022 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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< Stability Analysis of Submerged Slopes Calculators

Shear Stress Component given Submerged Unit Weight

LaTeX 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 Normal Stress Component

LaTeX 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

LaTeX 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

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

Depth of Prism for Cohesive Soil given Submerged Slope Formula

LaTeX Go

What is Finite Slope?

A finite slope is one with a base and top surface, the height being limited. The inclined. faces of earth dams, embankments and excavation and the like are all finite slopes.

How to Calculate Depth of Prism for Cohesive Soil given Submerged Slope?

Depth of Prism for Cohesive Soil given Submerged Slope calculator uses 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)))) to calculate the Depth of Prism, The Depth of Prism for Cohesive Soil given Submerged Slope is defined as critical to stability, influencing slope angle, pore pressures, and equilibrium. Depth of Prism is denoted by z symbol.

How to calculate Depth of Prism for Cohesive Soil given Submerged Slope using this online calculator? To use this online calculator for Depth of Prism for Cohesive Soil given Submerged Slope, enter Cohesion of Soil (C_s), Factor of Safety (f_s), Angle of Internal Friction (φ), Angle of Inclination to Horizontal in Soil (i) & Submerged Unit Weight (γ^') and hit the calculate button. Here is how the Depth of Prism for Cohesive Soil given Submerged Slope calculation can be explained with given input values -> 1.105928 = (5000/((2.8-(tan((0.802851455917241))/tan((1.11701072127616))))*5.01*cos((1.11701072127616))*sin((1.11701072127616)))).

FAQ

What is Depth of Prism for Cohesive Soil given Submerged Slope?

The Depth of Prism for Cohesive Soil given Submerged Slope is defined as critical to stability, influencing slope angle, pore pressures, and equilibrium and is represented as z = (C_s/((f_s-(tan((φ))/tan((i))))*γ^'*cos((i))*sin((i)))) or 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)))). 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 & Submerged Unit Weight is the unit weight of weight of soil as observed underwater in a saturated condition of course.

How to calculate Depth of Prism for Cohesive Soil given Submerged Slope?

The Depth of Prism for Cohesive Soil given Submerged Slope is defined as critical to stability, influencing slope angle, pore pressures, and equilibrium is calculated using 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)))). To calculate Depth of Prism for Cohesive Soil given Submerged Slope, 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) & Submerged Unit Weight (γ^'). 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 & Submerged Unit Weight 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 Cohesion of Soil, Factor of Safety, Angle of Internal Friction, Angle of Inclination to Horizontal in Soil & Submerged Unit Weight. We can use 2 other way(s) to calculate the same, which is/are as follows -

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

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