Factor of Safety for Cohesive Soil given Depth of Prism 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%
✖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 [z]			+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%
✖Angle of Internal Friction is the angle measured between the normal force and resultant force .ⓘ Angle of Internal Friction [φ]			+10% -10%

✖Factor of Safety expresses how much stronger a system is than it needs to be for an intended load.ⓘ Factor of Safety for Cohesive Soil given Depth of Prism [f_s]

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Formula

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Factor of Safety for Cohesive Soil given Depth of Prism

Formula

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

Example

`"1.349385"=("5.0kPa"/("5.01N/m³"*"3m"*cos(("64°"))*sin(("64°"))))+(tan(("46°"))/tan(("64°")))`

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Factor of Safety for Cohesive Soil given Depth of Prism Solution

STEP 0: Pre-Calculation Summary

Formula Used

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)))
f_s = (C_s/(γ^'*z*cos((i))*sin((i))))+(tan((φ))/tan((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

Factor of Safety - Factor of Safety expresses how much stronger a system is than it needs to be for an intended load.
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.
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.
Depth of Prism - (Measured in Meter) - Depth of Prism is the length of prism along z direction.
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.
Angle of Internal Friction - (Measured in Radian) - Angle of Internal Friction is the angle measured between the normal force and resultant force .

STEP 1: Convert Input(s) to Base Unit

Cohesion of Soil: 5 Kilopascal --> 5 Kilopascal No Conversion Required
Submerged Unit Weight: 5.01 Newton per Cubic Meter --> 5.01 Newton per Cubic Meter No Conversion Required
Depth of Prism: 3 Meter --> 3 Meter No Conversion Required
Angle of Inclination to Horizontal in Soil: 64 Degree --> 1.11701072127616 Radian (Check conversion here)
Angle of Internal Friction: 46 Degree --> 0.802851455917241 Radian (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

f_s = (C_s/(γ^'*z*cos((i))*sin((i))))+(tan((φ))/tan((i))) --> (5/(5.01*3*cos((1.11701072127616))*sin((1.11701072127616))))+(tan((0.802851455917241))/tan((1.11701072127616)))

Evaluating ... ...

f_s = 1.34938537687227

STEP 3: Convert Result to Output's Unit

1.34938537687227 --> No Conversion Required

FINAL ANSWER

1.34938537687227 ≈ 1.349385 <-- Factor of Safety

(Calculation completed in 00.004 seconds)

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

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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

Factor of Safety for Cohesive Soil given Depth of Prism Formula

What is Factor of Safety?

The ratio of a structure's absolute strength (structural capability) to actual applied load; this is a measure of the reliability of a particular design.

How to Calculate Factor of Safety for Cohesive Soil given Depth of Prism?

Factor of Safety for Cohesive Soil given Depth of Prism calculator uses 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))) to calculate the Factor of Safety, The Factor of Safety for Cohesive Soil given Depth of Prism is defined as the ratio of soil's shear strength to applied stress. Critical for stability in construction. Factor of Safety is denoted by f_s symbol.

How to calculate Factor of Safety for Cohesive Soil given Depth of Prism using this online calculator? To use this online calculator for Factor of Safety for Cohesive Soil given Depth of Prism, enter Cohesion of Soil (C_s), Submerged Unit Weight (γ^'), Depth of Prism (z), Angle of Inclination to Horizontal in Soil (i) & Angle of Internal Friction (φ) and hit the calculate button. Here is how the Factor of Safety for Cohesive Soil given Depth of Prism calculation can be explained with given input values -> 1.351074 = (5000/(5.01*3*cos((1.11701072127616))*sin((1.11701072127616))))+(tan((0.802851455917241))/tan((1.11701072127616))).

FAQ

What is Factor of Safety for Cohesive Soil given Depth of Prism?

The Factor of Safety for Cohesive Soil given Depth of Prism is defined as the ratio of soil's shear strength to applied stress. Critical for stability in construction and is represented as f_s = (C_s/(γ^'*z*cos((i))*sin((i))))+(tan((φ))/tan((i))) or 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))). 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, Submerged Unit Weight is the unit weight of weight of soil as observed underwater in a saturated condition of course, Depth of Prism is the length of prism along z direction, 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 Internal Friction is the angle measured between the normal force and resultant force .

How to calculate Factor of Safety for Cohesive Soil given Depth of Prism?

The Factor of Safety for Cohesive Soil given Depth of Prism is defined as the ratio of soil's shear strength to applied stress. Critical for stability in construction is calculated using 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))). To calculate Factor of Safety for Cohesive Soil given Depth of Prism, you need Cohesion of Soil (C_s), Submerged Unit Weight (γ^'), Depth of Prism (z), Angle of Inclination to Horizontal in Soil (i) & Angle of Internal Friction (φ). With our tool, you need to enter the respective value for Cohesion of Soil, Submerged Unit Weight, Depth of Prism, Angle of Inclination to Horizontal in Soil & Angle of Internal Friction and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

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