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Depth of Prism given Effective Normal Stress Formula

GoDepth of Prism given Saturated Unit Weight Formula

GoDepth of Prism given Vertical Stress and Saturated Unit Weight Formula

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

z = \frac{σ'}{(γ saturated - γ water) \cdot {(\cos (\frac{i \cdot π}{180}))}^{2}}

z - Depth of Prism?σ^' - Effective Normal Stress in Soil Mechanics?γ_saturated - Saturated Unit Weight of Soil?γ_water - Unit Weight of Water?i - Angle of Inclination to Horizontal in Soil?π - Archimedes' constant?

Depth of Prism given Effective Normal Stress Example

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Here is how the Depth of Prism given Effective Normal Stress equation looks like with Values.

Here is how the Depth of Prism given Effective Normal Stress equation looks like with Units.

Here is how the Depth of Prism given Effective Normal Stress equation looks like.

11.8651 = \frac{24.67}{(11.89 - 9.81) \cdot {(\cos (\frac{64 \cdot 3.1416}{180}))}^{2}}

11.8651m = \frac{24.67kN/m²}{(11.89kN/m³ - 9.81kN/m³) \cdot {(\cos (\frac{64° \cdot 3.1416}{180}))}^{2}}

11.8651 = \frac{24.67}{(11.89 - 9.81) \cdot {(\cos (\frac{64 \cdot 3.1416}{180}))}^{2}}

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Depth of Prism given Effective Normal Stress Solution

Follow our step by step solution on how to calculate Depth of Prism given Effective Normal Stress?

FIRST Step Consider the formula

z = \frac{σ'}{(γ saturated - γ water) \cdot {(\cos (\frac{i \cdot π}{180}))}^{2}}

Next Step Substitute values of Variables

∴

z = \frac{24.67kN/m²}{(11.89kN/m³ - 9.81kN/m³) \cdot {(\cos (\frac{64° \cdot π}{180}))}^{2}}

Next Step Substitute values of Constants

∴

z = \frac{24.67kN/m²}{(11.89kN/m³ - 9.81kN/m³) \cdot {(\cos (\frac{64° \cdot 3.1416}{180}))}^{2}}

Next Step Convert Units

∴

z = \frac{24670Pa}{(11890N/m³ - 9810N/m³) \cdot {(\cos (\frac{1.117rad \cdot 3.1416}{180}))}^{2}}

Next Step Prepare to Evaluate

∴

z = \frac{24670}{(11890 - 9810) \cdot {(\cos (\frac{1.117 \cdot 3.1416}{180}))}^{2}}

Next Step Evaluate

∴

z = 11.8650859755115m

LAST Step Rounding Answer

∴

z = 11.8651m

Depth of Prism given Effective Normal Stress Formula Elements

Variables

Constants

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

Effective Normal Stress in Soil Mechanics

Effective Normal Stress in Soil Mechanics is related to total stress and pore pressure.

Symbol: σ^'

Measurement: PressureUnit: kN/m²

Note: Value should be greater than 0.

Formulas to find Effective Normal Stress in Soil Mechanics

Saturated Unit Weight of Soil

Saturated Unit Weight of Soil is the ratio of mass of saturated soil sample to total volume.

Symbol: γ_saturated

Measurement: Specific WeightUnit: kN/m³

Note: Value should be greater than 0.

Formulas to find Saturated Unit Weight of Soil

Unit Weight of Water

Unit Weight of Water is mass per unit of water.

Symbol: γ_water

Measurement: Specific WeightUnit: kN/m³

Note: Value should be greater than 0.

Formulas to find Unit Weight of Water

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

Archimedes' constant

Archimedes' constant is a mathematical constant that represents the ratio of the circumference of a circle to its diameter.

Symbol: π

Value: 3.14159265358979323846264338327950288

cos

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

Syntax: cos(Angle)

Other Formulas to find Depth of Prism

Go Depth of Prism given Saturated Unit Weight

z = \frac{W prism}{γ sat \cdot b \cdot \cos (\frac{i \cdot π}{180})}

Go Depth of Prism given Vertical Stress and Saturated Unit Weight

z = \frac{σ zkp}{γ saturated \cdot \cos (\frac{i \cdot π}{180})}

Go Depth of Prism given Normal Stress and Saturated Unit Weight

z = \frac{σ n}{γ saturated \cdot {(\cos (\frac{i \cdot π}{180}))}^{2}}

Go Depth of Prism given Shear Stress and Saturated Unit Weight

z = \frac{ζ soil}{γ saturated \cdot \cos (\frac{i \cdot π}{180}) \cdot \sin (\frac{i \cdot π}{180})}

Other formulas in Factor of Steady Seepage Along the Slope category

Go Saturated Unit Weight given Weight of Soil Prism

γ saturated = \frac{W prism}{z \cdot b \cdot \cos (\frac{i \cdot π}{180})}

Go Angle of Inclination given Saturated Unit Weight

i = a \cos (\frac{W prism}{γ \cdot z \cdot b})

Go Saturated Unit Weight given Vertical Stress on Prism

γ saturated = \frac{σ zkp}{z \cdot \cos (\frac{i \cdot π}{180})}

Go Angle of Inclination given Vertical Stress and Saturated Unit Weight

i = a \cos (\frac{σ z}{γ \cdot z})

How to Evaluate Depth of Prism given Effective Normal Stress?

Depth of Prism given Effective Normal Stress evaluator uses Depth of Prism = Effective Normal Stress in Soil Mechanics/((Saturated Unit Weight of Soil-Unit Weight of Water)*(cos((Angle of Inclination to Horizontal in Soil*pi)/180))^2) to evaluate the Depth of Prism, The Depth of Prism given Effective Normal Stress is defined as the value of depth of soil prism considered when we have prior information of other parameters used. Depth of Prism is denoted by z symbol.

How to evaluate Depth of Prism given Effective Normal Stress using this online evaluator? To use this online evaluator for Depth of Prism given Effective Normal Stress, enter Effective Normal Stress in Soil Mechanics (σ^'), Saturated Unit Weight of Soil (γ_saturated), Unit Weight of Water (γ_water) & Angle of Inclination to Horizontal in Soil (i) and hit the calculate button.

FAQs on Depth of Prism given Effective Normal Stress

What is the formula to find Depth of Prism given Effective Normal Stress?

The formula of Depth of Prism given Effective Normal Stress is expressed as Depth of Prism = Effective Normal Stress in Soil Mechanics/((Saturated Unit Weight of Soil-Unit Weight of Water)*(cos((Angle of Inclination to Horizontal in Soil*pi)/180))^2). Here is an example- 3.013355 = 24670/((11890-9810)*(cos((1.11701072127616*pi)/180))^2).

How to calculate Depth of Prism given Effective Normal Stress?

With Effective Normal Stress in Soil Mechanics (σ^'), Saturated Unit Weight of Soil (γ_saturated), Unit Weight of Water (γ_water) & Angle of Inclination to Horizontal in Soil (i) we can find Depth of Prism given Effective Normal Stress using the formula - Depth of Prism = Effective Normal Stress in Soil Mechanics/((Saturated Unit Weight of Soil-Unit Weight of Water)*(cos((Angle of Inclination to Horizontal in Soil*pi)/180))^2). This formula also uses Archimedes' constant and Cosine (cos) 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=Weight of Prism in Soil Mechanics/(Saturated Unit Weight in Newton per Cubic Meter*Inclined Length of Prism*cos((Angle of Inclination to Horizontal in Soil*pi)/180))
Depth of Prism=Vertical Stress at a Point in Kilopascal/(Saturated Unit Weight of Soil*cos((Angle of Inclination to Horizontal in Soil*pi)/180))
Depth of Prism=Normal Stress in Soil Mechanics/(Saturated Unit Weight of Soil*(cos((Angle of Inclination to Horizontal in Soil*pi)/180))^2)

Can the Depth of Prism given Effective Normal Stress be negative?

No, the Depth of Prism given Effective Normal Stress, measured in Length cannot be negative.

Which unit is used to measure Depth of Prism given Effective Normal Stress?

Depth of Prism given Effective Normal Stress 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 given Effective Normal Stress can be measured.

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Depth of Prism given Effective Normal Stress Formula

​GoDepth of Prism given Saturated Unit Weight Formula

​GoDepth of Prism given Vertical Stress and Saturated Unit Weight Formula

Depth of Prism given Effective Normal Stress Example

Depth of Prism given Effective Normal Stress Solution

Depth of Prism given Effective Normal Stress Formula Elements

Other Formulas to find Depth of Prism

Other formulas in Factor of Steady Seepage Along the Slope category

How to Evaluate Depth of Prism given Effective Normal Stress?

FAQs on Depth of Prism given Effective Normal Stress

Variable Name

GoDepth of Prism given Saturated Unit Weight Formula

GoDepth of Prism given Vertical Stress and Saturated Unit Weight Formula