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Saturated Unit Weight given Shear Strength 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 = \frac{y S \cdot ζ soil \cdot \tan (\frac{Φ i \cdot π}{180})}{τ f \cdot \tan (\frac{i \cdot π}{180})}

γ_saturated - Saturated Unit Weight of Soil?y_S - Submerged Unit Weight in KN per Cubic Meter?ζ_soil - Shear Stress in Soil Mechanics?Φ_i - Angle of Internal Friction of Soil?τ_f - Shear Strength in KN per Cubic Meter?i - Angle of Inclination to Horizontal in Soil?π - Archimedes' constant?

Saturated Unit Weight given Shear Strength Example

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Here is how the Saturated Unit Weight given Shear Strength equation looks like with Values.

Here is how the Saturated Unit Weight given Shear Strength equation looks like with Units.

Here is how the Saturated Unit Weight given Shear Strength equation looks like.

0.9344 = \frac{5 \cdot 0.71 \cdot \tan (\frac{82.87 \cdot 3.1416}{180})}{4.92 \cdot \tan (\frac{64 \cdot 3.1416}{180})}

0.9344kN/m³ = \frac{5kN/m³ \cdot 0.71kN/m² \cdot \tan (\frac{82.87° \cdot 3.1416}{180})}{4.92kN/m² \cdot \tan (\frac{64° \cdot 3.1416}{180})}

0.9344 = \frac{5 \cdot 0.71 \cdot \tan (\frac{82.87 \cdot 3.1416}{180})}{4.92 \cdot \tan (\frac{64 \cdot 3.1416}{180})}

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Saturated Unit Weight given Shear Strength Solution

Follow our step by step solution on how to calculate Saturated Unit Weight given Shear Strength?

FIRST Step Consider the formula

γ saturated = \frac{y S \cdot ζ soil \cdot \tan (\frac{Φ i \cdot π}{180})}{τ f \cdot \tan (\frac{i \cdot π}{180})}

Next Step Substitute values of Variables

∴

γ saturated = \frac{5kN/m³ \cdot 0.71kN/m² \cdot \tan (\frac{82.87° \cdot π}{180})}{4.92kN/m² \cdot \tan (\frac{64° \cdot π}{180})}

Next Step Substitute values of Constants

∴

γ saturated = \frac{5kN/m³ \cdot 0.71kN/m² \cdot \tan (\frac{82.87° \cdot 3.1416}{180})}{4.92kN/m² \cdot \tan (\frac{64° \cdot 3.1416}{180})}

Next Step Convert Units

∴

γ saturated = \frac{5000N/m³ \cdot 710Pa \cdot \tan (\frac{1.4464rad \cdot 3.1416}{180})}{4920Pa \cdot \tan (\frac{1.117rad \cdot 3.1416}{180})}

Next Step Prepare to Evaluate

∴

γ saturated = \frac{5000 \cdot 710 \cdot \tan (\frac{1.4464 \cdot 3.1416}{180})}{4920 \cdot \tan (\frac{1.117 \cdot 3.1416}{180})}

Next Step Evaluate

∴

γ saturated = 934.367776768035N/m³

Next Step Convert to Output's Unit

∴

γ saturated = 0.934367776768035kN/m³

LAST Step Rounding Answer

∴

γ saturated = 0.9344kN/m³

Saturated Unit Weight given Shear Strength 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

Submerged Unit Weight in KN per Cubic Meter

Submerged Unit Weight in KN per Cubic Meter is the unit weight of a weight of soil as observed under water in a saturated condition of course.

Symbol: y_S

Measurement: Specific WeightUnit: kN/m³

Note: Value should be greater than 0.

Formulas to find Submerged Unit Weight in KN per Cubic Meter

Shear Stress in Soil Mechanics

Shear Stress in Soil Mechanics is force tending to cause deformation of a material by slippage along a plane or planes parallel to the imposed stress.

Symbol: ζ_soil

Measurement: StressUnit: kN/m²

Note: Value should be greater than 0.

Formulas to find Shear Stress in Soil Mechanics

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

Shear Strength in KN per Cubic Meter

Shear Strength in KN per Cubic Meter is the strength of a material against structural failure when the material fails in shear.

Symbol: τ_f

Measurement: StressUnit: kN/m²

Note: Value should be greater than 0.

Formulas to find Shear Strength in KN per Cubic Meter

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

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 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 Shear Strength?

Saturated Unit Weight given Shear Strength evaluator uses Saturated Unit Weight of Soil = (Submerged Unit Weight in KN per Cubic Meter*Shear Stress in Soil Mechanics*tan((Angle of Internal Friction of Soil*pi)/180))/(Shear Strength in KN per Cubic Meter*tan((Angle of Inclination to Horizontal in Soil*pi)/180)) to evaluate the Saturated Unit Weight of Soil, The Saturated Unit Weight given Shear Strength 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 Shear Strength using this online evaluator? To use this online evaluator for Saturated Unit Weight given Shear Strength, enter Submerged Unit Weight in KN per Cubic Meter (y_S), Shear Stress in Soil Mechanics (ζ_soil), Angle of Internal Friction of Soil (Φ_i), Shear Strength in KN per Cubic Meter (τ_f) & Angle of Inclination to Horizontal in Soil (i) and hit the calculate button.

FAQs on Saturated Unit Weight given Shear Strength

What is the formula to find Saturated Unit Weight given Shear Strength?

The formula of Saturated Unit Weight given Shear Strength is expressed as Saturated Unit Weight of Soil = (Submerged Unit Weight in KN per Cubic Meter*Shear Stress in Soil Mechanics*tan((Angle of Internal Friction of Soil*pi)/180))/(Shear Strength in KN per Cubic Meter*tan((Angle of Inclination to Horizontal in Soil*pi)/180)). Here is an example- 0.000934 = (5000*710*tan((1.44635435112743*pi)/180))/(4920*tan((1.11701072127616*pi)/180)).

How to calculate Saturated Unit Weight given Shear Strength?

With Submerged Unit Weight in KN per Cubic Meter (y_S), Shear Stress in Soil Mechanics (ζ_soil), Angle of Internal Friction of Soil (Φ_i), Shear Strength in KN per Cubic Meter (τ_f) & Angle of Inclination to Horizontal in Soil (i) we can find Saturated Unit Weight given Shear Strength using the formula - Saturated Unit Weight of Soil = (Submerged Unit Weight in KN per Cubic Meter*Shear Stress in Soil Mechanics*tan((Angle of Internal Friction of Soil*pi)/180))/(Shear Strength in KN per Cubic Meter*tan((Angle of Inclination to Horizontal in Soil*pi)/180)). This formula also uses Archimedes' constant and Tangent (tan) 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 Shear Strength be negative?

No, the Saturated Unit Weight given Shear Strength, measured in Specific Weight cannot be negative.

Which unit is used to measure Saturated Unit Weight given Shear Strength?

Saturated Unit Weight given Shear Strength 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 Shear Strength can be measured.

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Saturated Unit Weight given Shear Strength Formula

​GoSaturated Unit Weight given Weight of Soil Prism Formula

​GoSaturated Unit Weight given Vertical Stress on Prism Formula

Saturated Unit Weight given Shear Strength Example

Saturated Unit Weight given Shear Strength Solution

Saturated Unit Weight given Shear Strength 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 Shear Strength?

FAQs on Saturated Unit Weight given Shear Strength

Variable Name

GoSaturated Unit Weight given Weight of Soil Prism Formula

GoSaturated Unit Weight given Vertical Stress on Prism Formula