FormulaDen.com

Physics Chemistry Math Chemical Engineering Civil Electrical Electronics Electronics and Instrumentation Materials Science Mechanical Production Engineering Financial Health

Factor of Safety for Cohesive Soil given Depth of Prism Formula

Fx Copy

LaTeX Copy

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 s}{γ' \cdot z \cdot \cos ((i)) \cdot \sin ((i))}) + (\frac{\tan ((φ))}{\tan ((i))})

f_s - Factor of Safety?C_s - Cohesion of Soil?γ^' - Submerged Unit Weight?z - Depth of Prism?i - Angle of Inclination to Horizontal in Soil?φ - Angle of Internal Friction?

Factor of Safety for Cohesive Soil given Depth of Prism Example

With values

With units

Only example

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

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

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

1.3494 = (\frac{5}{5.01 \cdot 3 \cdot \cos ((64)) \cdot \sin ((64))}) + (\frac{\tan ((46))}{\tan ((64))})

1.3494 = (\frac{5kPa}{5.01N/m³ \cdot 3m \cdot \cos ((64°)) \cdot \sin ((64°))}) + (\frac{\tan ((46°))}{\tan ((64°))})

1.3494 = (\frac{5}{5.01 \cdot 3 \cdot \cos ((64)) \cdot \sin ((64))}) + (\frac{\tan ((46))}{\tan ((64))})

Tip: Use pencil ( Pencil

) icon above to edit Input Values and Units.

Calculate

Recalculate

Solution

Copy

Reset

You are here -

Home » Category

Engineering » Category

Civil » Category

Geotechnical Engineering » fx Factor of Safety for Cohesive Soil given Depth of Prism

Factor of Safety for Cohesive Soil given Depth of Prism Solution

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

FIRST Step Consider the formula

f s = (\frac{C s}{γ' \cdot z \cdot \cos ((i)) \cdot \sin ((i))}) + (\frac{\tan ((φ))}{\tan ((i))})

Next Step Substitute values of Variables

∴

f s = (\frac{5kPa}{5.01N/m³ \cdot 3m \cdot \cos ((64°)) \cdot \sin ((64°))}) + (\frac{\tan ((46°))}{\tan ((64°))})

Next Step Convert Units

∴

f s = (\frac{5kPa}{5.01N/m³ \cdot 3m \cdot \cos ((1.117rad)) \cdot \sin ((1.117rad))}) + (\frac{\tan ((0.8029rad))}{\tan ((1.117rad))})

Next Step Prepare to Evaluate

∴

f s = (\frac{5}{5.01 \cdot 3 \cdot \cos ((1.117)) \cdot \sin ((1.117))}) + (\frac{\tan ((0.8029))}{\tan ((1.117))})

Next Step Evaluate

∴

f s = 1.34938537687227

LAST Step Rounding Answer

∴

f s = 1.3494

Factor of Safety for Cohesive Soil given Depth of Prism 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

Cohesion of 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.

Symbol: C_s

Measurement: PressureUnit: kPa

Note: Value should be greater than 0.

Formulas to find Cohesion of Soil

Submerged Unit Weight

Submerged Unit Weight is the unit weight of weight of soil as observed underwater in a saturated condition of course.

Symbol: γ^'

Measurement: Specific WeightUnit: N/m³

Note: Value should be greater than 0.

Formulas to find Submerged Unit Weight

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 to Horizontal in Soil

Angle of Inclination to Horizontal in Soil 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 to Horizontal in Soil

Angle of Internal Friction

Angle of Internal Friction is the angle measured between the normal force and resultant force .

Symbol: φ

Measurement: AngleUnit: °

Note: Value should be greater than 0.

Formulas to find Angle of Internal Friction

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 Submerged Slopes category

Go Normal Stress Component given Submerged Unit Weight

σ Normal = γ' \cdot z \cdot {(\cos ((i)))}^{2}

Go Submerged Unit Weight given Normal Stress Component

γ' = \frac{σ Normal}{z \cdot {(\cos ((i)))}^{2}}

Go Depth of Prism given Submerged Unit Weight

z = \frac{σ Normal}{γ' \cdot {(\cos ((i)))}^{2}}

Go Shear Stress Component given Submerged Unit Weight

𝜏 = (γ' \cdot z \cdot \cos ((i)) \cdot \sin ((i)))

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

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

FAQs on Factor of Safety for Cohesive Soil given Depth of Prism

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

The formula of Factor of Safety for Cohesive Soil given Depth of Prism is expressed as 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))). Here is an example- 1.351074 = (5000/(5.01*3*cos((1.11701072127616))*sin((1.11701072127616))))+(tan((0.802851455917241))/tan((1.11701072127616))).

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

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

Let Others Know

✖

Facebook

Twitter

Copied!

Factor of Safety for Cohesive Soil given Depth of Prism Formula

Factor of Safety for Cohesive Soil given Depth of Prism Example

Factor of Safety for Cohesive Soil given Depth of Prism Solution

Factor of Safety for Cohesive Soil given Depth of Prism Formula Elements

Other formulas in Stability Analysis of Submerged Slopes category

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

FAQs on Factor of Safety for Cohesive Soil given Depth of Prism

Variable Name