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Depth of Prism for Cohesive Soil given Submerged Slope Formula

GoDepth of Prism given Submerged Unit Weight Formula

GoDepth of Prism given Submerged Unit Weight and Shear Stress Formula

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

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

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

Depth of Prism for Cohesive Soil given Submerged Slope Example

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

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

Here is how the Depth of Prism for Cohesive Soil given Submerged Slope equation looks like.

1.1037 = (\frac{5}{(2.8 - (\frac{\tan ((46))}{\tan ((64))})) \cdot 5.01 \cdot \cos ((64)) \cdot \sin ((64))})

1.1037m = (\frac{5kPa}{(2.8 - (\frac{\tan ((46°))}{\tan ((64°))})) \cdot 5.01N/m³ \cdot \cos ((64°)) \cdot \sin ((64°))})

1.1037 = (\frac{5}{(2.8 - (\frac{\tan ((46))}{\tan ((64))})) \cdot 5.01 \cdot \cos ((64)) \cdot \sin ((64))})

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Depth of Prism for Cohesive Soil given Submerged Slope Solution

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

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

z = (\frac{5kPa}{(2.8 - (\frac{\tan ((46°))}{\tan ((64°))})) \cdot 5.01N/m³ \cdot \cos ((64°)) \cdot \sin ((64°))})

Next Step Convert Units

∴

z = (\frac{5kPa}{(2.8 - (\frac{\tan ((0.8029rad))}{\tan ((1.117rad))})) \cdot 5.01N/m³ \cdot \cos ((1.117rad)) \cdot \sin ((1.117rad))})

Next Step Prepare to Evaluate

∴

z = (\frac{5}{(2.8 - (\frac{\tan ((0.8029))}{\tan ((1.117))})) \cdot 5.01 \cdot \cos ((1.117)) \cdot \sin ((1.117))})

Next Step Evaluate

∴

z = 1.10372060476287m

LAST Step Rounding Answer

∴

z = 1.1037m

Depth of Prism for Cohesive Soil given Submerged Slope Formula Elements

Variables

Functions

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

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

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

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

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

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

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 to find Depth of Prism

Go Depth of Prism given Submerged Unit Weight

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

Go Depth of Prism given Submerged Unit Weight and Shear Stress

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

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 Shear Stress Component given Submerged Unit Weight

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

Go Submerged Unit Weight given Shear Stress Component

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

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

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

FAQs on Depth of Prism for Cohesive Soil given Submerged Slope

What is the formula to find Depth of Prism for Cohesive Soil given Submerged Slope?

The formula of Depth of Prism for Cohesive Soil given Submerged Slope is expressed as 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)))). Here is an example- 1.105928 = (5000/((2.8-(tan((0.802851455917241))/tan((1.11701072127616))))*5.01*cos((1.11701072127616))*sin((1.11701072127616)))).

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

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

What are the other ways to Calculate Depth of Prism?

Here are the different ways to Calculate Depth of Prism-

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)))

Can the Depth of Prism for Cohesive Soil given Submerged Slope be negative?

No, the Depth of Prism for Cohesive Soil given Submerged Slope, measured in Length cannot be negative.

Which unit is used to measure Depth of Prism for Cohesive Soil given Submerged Slope?

Depth of Prism for Cohesive Soil given Submerged Slope is usually measured using the Meter[m] for Length. Millimeter[m], Kilometer[m], Decimeter[m] are the few other units in which Depth of Prism for Cohesive Soil given Submerged Slope can be measured.

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Depth of Prism for Cohesive Soil given Submerged Slope Formula

​GoDepth of Prism given Submerged Unit Weight Formula

​GoDepth of Prism given Submerged Unit Weight and Shear Stress Formula

Depth of Prism for Cohesive Soil given Submerged Slope Example

Depth of Prism for Cohesive Soil given Submerged Slope Solution

Depth of Prism for Cohesive Soil given Submerged Slope Formula Elements

Other Formulas to find Depth of Prism

Other formulas in Stability Analysis of Submerged Slopes category

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

FAQs on Depth of Prism for Cohesive Soil given Submerged Slope

Variable Name

GoDepth of Prism given Submerged Unit Weight Formula

GoDepth of Prism given Submerged Unit Weight and Shear Stress Formula