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Saturated Unit Weight given Effective Normal Stress Formula

GoSaturated Unit Weight given Weight of Soil Prism Formula

GoSaturated Unit Weight given Vertical Stress on Prism Formula

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

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

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

Saturated Unit Weight given Effective Normal Stress Example

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Here is how the Saturated Unit Weight given Effective Normal Stress equation looks like with Values.

Here is how the Saturated Unit Weight given Effective Normal Stress equation looks like with Units.

Here is how the Saturated Unit Weight given Effective Normal Stress equation looks like.

18.0365 = 9.81 + (\frac{24.67}{3 \cdot {(\cos (\frac{64 \cdot 3.1416}{180}))}^{2}})

18.0365kN/m³ = 9.81kN/m³ + (\frac{24.67kN/m²}{3m \cdot {(\cos (\frac{64° \cdot 3.1416}{180}))}^{2}})

18.0365 = 9.81 + (\frac{24.67}{3 \cdot {(\cos (\frac{64 \cdot 3.1416}{180}))}^{2}})

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Saturated Unit Weight given Effective Normal Stress Solution

Follow our step by step solution on how to calculate Saturated Unit Weight given Effective Normal Stress?

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

γ saturated = 9.81kN/m³ + (\frac{24.67kN/m²}{3m \cdot {(\cos (\frac{64° \cdot π}{180}))}^{2}})

Next Step Substitute values of Constants

∴

γ saturated = 9.81kN/m³ + (\frac{24.67kN/m²}{3m \cdot {(\cos (\frac{64° \cdot 3.1416}{180}))}^{2}})

Next Step Convert Units

∴

γ saturated = 9810N/m³ + (\frac{24670Pa}{3m \cdot {(\cos (\frac{1.117rad \cdot 3.1416}{180}))}^{2}})

Next Step Prepare to Evaluate

∴

γ saturated = 9810 + (\frac{24670}{3 \cdot {(\cos (\frac{1.117 \cdot 3.1416}{180}))}^{2}})

Next Step Evaluate

∴

γ saturated = 18036.459609688N/m³

Next Step Convert to Output's Unit

∴

γ saturated = 18.036459609688kN/m³

LAST Step Rounding Answer

∴

γ saturated = 18.0365kN/m³

Saturated Unit Weight given Effective Normal Stress Formula Elements

Variables

Constants

Functions

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

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

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

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 Saturated Unit Weight of Soil

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 Saturated Unit Weight given Vertical Stress on Prism

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

Go Saturated Unit Weight given Normal Stress Component

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

Go Saturated Unit Weight given Shear Stress Component

γ saturated = \frac{ζ soil}{z \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 Depth of Prism given Saturated Unit Weight

z = \frac{W prism}{γ sat \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 Depth of Prism given Vertical Stress and Saturated Unit Weight

z = \frac{σ zkp}{γ saturated \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 Saturated Unit Weight given Effective Normal Stress?

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

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

FAQs on Saturated Unit Weight given Effective Normal Stress

What is the formula to find Saturated Unit Weight given Effective Normal Stress?

The formula of Saturated Unit Weight given Effective Normal Stress is expressed as Saturated Unit Weight of Soil = Unit Weight of Water+(Effective Normal Stress in Soil Mechanics/(Depth of Prism*(cos((Angle of Inclination to Horizontal in Soil*pi)/180))^2)). Here is an example- 0.018036 = 9810+(24670/(3*(cos((1.11701072127616*pi)/180))^2)).

How to calculate Saturated Unit Weight given Effective Normal Stress?

With Unit Weight of Water (γ_water), Effective Normal Stress in Soil Mechanics (σ^'), Depth of Prism (z) & Angle of Inclination to Horizontal in Soil (i) we can find Saturated Unit Weight given Effective Normal Stress using the formula - Saturated Unit Weight of Soil = Unit Weight of Water+(Effective Normal Stress in Soil Mechanics/(Depth of Prism*(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 Saturated Unit Weight of Soil?

Here are the different ways to Calculate Saturated Unit Weight of Soil-

Saturated Unit Weight of Soil=Weight of Prism in Soil Mechanics/(Depth of Prism*Inclined Length of Prism*cos((Angle of Inclination to Horizontal in Soil*pi)/180))
Saturated Unit Weight of Soil=Vertical Stress at a Point in Kilopascal/(Depth of Prism*cos((Angle of Inclination to Horizontal in Soil*pi)/180))
Saturated Unit Weight of Soil=Normal Stress in Soil Mechanics/(Depth of Prism*(cos((Angle of Inclination to Horizontal in Soil*pi)/180))^2)

Can the Saturated Unit Weight given Effective Normal Stress be negative?

No, the Saturated Unit Weight given Effective Normal Stress, measured in Specific Weight cannot be negative.

Which unit is used to measure Saturated Unit Weight given Effective Normal Stress?

Saturated Unit Weight given Effective Normal Stress is usually measured using the Kilonewton per Cubic Meter[kN/m³] for Specific Weight. Newton per Cubic Meter[kN/m³], Newton per Cubic Centimeter[kN/m³], Newton per Cubic Millimeter[kN/m³] are the few other units in which Saturated Unit Weight given Effective Normal Stress can be measured.

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Saturated Unit Weight given Effective Normal Stress Formula

​GoSaturated Unit Weight given Weight of Soil Prism Formula

​GoSaturated Unit Weight given Vertical Stress on Prism Formula

Saturated Unit Weight given Effective Normal Stress Example

Saturated Unit Weight given Effective Normal Stress Solution

Saturated Unit Weight given Effective Normal Stress Formula Elements

Other Formulas to find Saturated Unit Weight of Soil

Other formulas in Factor of Steady Seepage Along the Slope category

How to Evaluate Saturated Unit Weight given Effective Normal Stress?

FAQs on Saturated Unit Weight given Effective Normal Stress

Variable Name

GoSaturated Unit Weight given Weight of Soil Prism Formula

GoSaturated Unit Weight given Vertical Stress on Prism Formula