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Factor of Safety for Cohesive Soil given Cohesion Formula

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Factor of Safety expresses how much stronger a system is than it needs to be for an intended load. Check FAQs

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

f_s - Factor of Safety?c_u - Unit Cohesion?γ - Unit Weight of Soil?z - Depth of Prism?I - Angle of Inclination?Φ_i - Angle of Internal Friction of Soil?

Factor of Safety for Cohesive Soil given Cohesion Example

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Here is how the Factor of Safety for Cohesive Soil given Cohesion equation looks like with Values.

Here is how the Factor of Safety for Cohesive Soil given Cohesion equation looks like with Units.

Here is how the Factor of Safety for Cohesive Soil given Cohesion equation looks like.

1.4107 = (\frac{10}{18 \cdot 3 \cdot \cos ((80)) \cdot \sin ((80))}) + (\frac{\tan ((82.87))}{\tan ((80))})

1.4107 = (\frac{10Pa}{18kN/m³ \cdot 3m \cdot \cos ((80°)) \cdot \sin ((80°))}) + (\frac{\tan ((82.87°))}{\tan ((80°))})

1.4107 = (\frac{10}{18 \cdot 3 \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

Follow our step by step solution on how to calculate Factor of Safety for Cohesive Soil given Cohesion?

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

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

Next Step Convert Units

∴

f s = (\frac{10Pa}{18000N/m³ \cdot 3m \cdot \cos ((1.3963rad)) \cdot \sin ((1.3963rad))}) + (\frac{\tan ((1.4464rad))}{\tan ((1.3963rad))})

Next Step Prepare to Evaluate

∴

f s = (\frac{10}{18000 \cdot 3 \cdot \cos ((1.3963)) \cdot \sin ((1.3963))}) + (\frac{\tan ((1.4464))}{\tan ((1.3963))})

Next Step Evaluate

∴

f s = 1.41070251670873

LAST Step Rounding Answer

∴

f s = 1.4107

Factor of Safety for Cohesive Soil given Cohesion Formula Elements

Variables

Functions

Factor of Safety

Factor of Safety expresses how much stronger a system is than it needs to be for an intended load.

Symbol: f_s

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Factor of Safety

Unit Cohesion

Unit Cohesion is the force that holds together molecules or like particles within a soil.

Symbol: c_u

Measurement: PressureUnit: Pa

Note: Value should be greater than 0.

Formulas to find Unit Cohesion

Unit Weight of Soil

Unit Weight of Soil mass is the ratio of the total weight of soil to the total volume of soil.

Symbol: γ

Measurement: Specific WeightUnit: kN/m³

Note: Value should be greater than 0.

Formulas to find Unit Weight of Soil

Depth of Prism

Depth of Prism is the length of prism along z direction.

Symbol: z

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Depth of Prism

Angle of Inclination

Angle of Inclination is defined as the angle measured from the horizontal surface of the wall or any object.

Symbol: I

Measurement: AngleUnit: °

Note: Value should be greater than 0.

Formulas to find Angle of Inclination

Angle of Internal Friction of Soil

Angle of Internal Friction of Soil is is a measure of the shear strength of soil due to friction.

Symbol: Φ_i

Measurement: AngleUnit: °

Note: Value should be between -180 to 180.

Formulas to find Angle of Internal Friction of Soil

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.

Syntax: sin(Angle)

cos

Cosine of an angle is the ratio of the side adjacent to the angle to the hypotenuse of the triangle.

Syntax: 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.

Syntax: tan(Angle)

Other formulas in Stability Analysis of Infinite Slopes in Prism category

Go Weight of Soil Prism in Stability Analysis

W = (γ \cdot z \cdot b \cdot \cos ((I)))

Go Unit Weight of Soil given Weight of Soil Prism

γ = \frac{W}{z \cdot b \cdot \cos ((I))}

Go Inclined Length along Slope given Weight of Soil Prism

b = \frac{W}{γ \cdot z \cdot \cos ((I))}

Go Depth of Prism given Weight of Soil Prism

z = \frac{W}{γ \cdot b \cdot \cos ((I))}

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

Factor of Safety for Cohesive Soil given Cohesion evaluator 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 evaluate 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 evaluate Factor of Safety for Cohesive Soil given Cohesion using this online evaluator? To use this online evaluator 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.

FAQs on Factor of Safety for Cohesive Soil given Cohesion

What is the formula to find Factor of Safety for Cohesive Soil given Cohesion?

The formula of Factor of Safety for Cohesive Soil given Cohesion is expressed as 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))). Here is an example- 1.410703 = (10/(18000*3*cos((1.3962634015952))*sin((1.3962634015952))))+(tan((1.44635435112743))/tan((1.3962634015952))).

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

With 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) we can find Factor of Safety for Cohesive Soil given Cohesion using the formula - 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))). This formula also uses Sine (sin)Cosine (cos), Tangent (tan) function(s).

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Factor of Safety for Cohesive Soil given Cohesion Formula

Factor of Safety for Cohesive Soil given Cohesion Example

Factor of Safety for Cohesive Soil given Cohesion Solution

Factor of Safety for Cohesive Soil given Cohesion Formula Elements

Other formulas in Stability Analysis of Infinite Slopes in Prism category

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

FAQs on Factor of Safety for Cohesive Soil given Cohesion

Variable Name