Factor of Safety for Cohesive Soil given Cohesion Calculator

✖Unit Cohesion is the force that holds together molecules or like particles within a soil.ⓘ Unit Cohesion [c_u]			+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 [γ]			+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%
✖Angle of Internal Friction of Soil is is a measure of the shear strength of soil due to friction.ⓘ Angle of Internal Friction of Soil [Φ_i]			+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 Cohesion [f_s]

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Formula

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Factor of Safety for Cohesive Soil given Cohesion

Formula

f s = (\frac{c u}{γ \cdot z \cdot \cos ((I)) \cdot \sin ((I))}) + (\frac{\tan ((Φ i))}{\tan ((I))})

Example

1.410703 = (\frac{10 Pa}{18 kN/m³ \cdot 3 m \cdot \cos ((80 °)) \cdot \sin ((80 °))}) + (\frac{\tan ((82.87 °))}{\tan ((80 °))})

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Factor of Safety for Cohesive Soil given Cohesion Solution

STEP 0: Pre-Calculation Summary

Formula Used

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)))
f_s = (c_u/(γ*z*cos((I))*sin((I))))+(tan((Φ_i))/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.
Unit Cohesion - (Measured in Pascal) - Unit Cohesion is the force that holds together molecules or like particles within a soil.
Unit Weight of Soil - (Measured in Newton per Cubic Meter) - Unit Weight of Soil mass is the ratio of the total weight of soil to the total volume of soil.
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.
Angle of Internal Friction of Soil - (Measured in Radian) - Angle of Internal Friction of Soil is is a measure of the shear strength of soil due to friction.

STEP 1: Convert Input(s) to Base Unit

Unit Cohesion: 10 Pascal --> 10 Pascal No Conversion Required
Unit Weight of Soil: 18 Kilonewton per Cubic Meter --> 18000 Newton per Cubic Meter (Check conversion here)
Depth of Prism: 3 Meter --> 3 Meter No Conversion Required
Angle of Inclination: 80 Degree --> 1.3962634015952 Radian (Check conversion here)
Angle of Internal Friction of Soil: 82.87 Degree --> 1.44635435112743 Radian (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

f_s = (c_u/(γ*z*cos((I))*sin((I))))+(tan((Φ_i))/tan((I))) --> (10/(18000*3*cos((1.3962634015952))*sin((1.3962634015952))))+(tan((1.44635435112743))/tan((1.3962634015952)))

Evaluating ... ...

f_s = 1.41070251670873

STEP 3: Convert Result to Output's Unit

1.41070251670873 --> No Conversion Required

FINAL ANSWER

1.41070251670873 ≈ 1.410703 <-- Factor of Safety

(Calculation completed in 00.004 seconds)

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Home » Engineering » Civil » Geotechnical Engineering » Stability Analysis of Infinite Slopes in Prism » Factor of Safety for Cohesive Soil given Cohesion

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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 Infinite Slopes in Prism Calculators

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)))

Factor of Safety for Cohesive Soil given Cohesion 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 Cohesion?

Factor of Safety for Cohesive Soil given Cohesion calculator uses 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))) to calculate the Factor of Safety, The Factor of Safety for Cohesive Soil given Cohesion is defined as ratio of soil's shear strength to applied stress, ensuring stability in cohesive soil, preventing failure or deformation. Factor of Safety is denoted by f_s symbol.

How to calculate Factor of Safety for Cohesive Soil given Cohesion using this online calculator? To use this online calculator for Factor of Safety for Cohesive Soil given Cohesion, enter Unit Cohesion (c_u), Unit Weight of Soil (γ), Depth of Prism (z), Angle of Inclination (I) & Angle of Internal Friction of Soil (Φ_i) and hit the calculate button. Here is how the Factor of Safety for Cohesive Soil given Cohesion calculation can be explained with given input values -> 1.410703 = (10/(18000*3*cos((1.3962634015952))*sin((1.3962634015952))))+(tan((1.44635435112743))/tan((1.3962634015952))).

FAQ

What is Factor of Safety for Cohesive Soil given Cohesion?

The Factor of Safety for Cohesive Soil given Cohesion is defined as ratio of soil's shear strength to applied stress, ensuring stability in cohesive soil, preventing failure or deformation and is represented as f_s = (c_u/(γ*z*cos((I))*sin((I))))+(tan((Φ_i))/tan((I))) or 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))). Unit Cohesion is the force that holds together molecules or like particles within a soil, Unit Weight of Soil mass is the ratio of the total weight of soil to the total volume of soil, 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 & Angle of Internal Friction of Soil is is a measure of the shear strength of soil due to friction.

How to calculate Factor of Safety for Cohesive Soil given Cohesion?

The Factor of Safety for Cohesive Soil given Cohesion is defined as ratio of soil's shear strength to applied stress, ensuring stability in cohesive soil, preventing failure or deformation is calculated using 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))). To calculate Factor of Safety for Cohesive Soil given Cohesion, you need Unit Cohesion (c_u), Unit Weight of Soil (γ), Depth of Prism (z), Angle of Inclination (I) & Angle of Internal Friction of Soil (Φ_i). With our tool, you need to enter the respective value for Unit Cohesion, Unit Weight of Soil, Depth of Prism, Angle of Inclination & Angle of Internal Friction of Soil 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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