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Saturated Unit Weight given Critical Depth Formula

GoSaturated Unit Weight given Factor of Safety for Cohesive Soil 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{(\frac{C eff}{h c}) - (y S \cdot \tan (\frac{φ \cdot π}{180}) \cdot {(\cos (\frac{i \cdot π}{180}))}^{2})}{\tan (\frac{i \cdot π}{180}) \cdot {(\cos (\frac{i \cdot π}{180}))}^{2}}

γ_saturated - Saturated Unit Weight of Soil?C_eff - Effective Cohesion in Geotech as Kilopascal?h_c - Critical Depth?y_S - Submerged Unit Weight in KN per Cubic Meter?φ - Angle of Internal Friction?i - Angle of Inclination to Horizontal in Soil?π - Archimedes' constant?

Saturated Unit Weight given Critical Depth Example

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Here is how the Saturated Unit Weight given Critical Depth equation looks like with Values.

Here is how the Saturated Unit Weight given Critical Depth equation looks like with Units.

Here is how the Saturated Unit Weight given Critical Depth equation looks like.

12.6621 = \frac{(\frac{0.32}{1.01}) - (5 \cdot \tan (\frac{46 \cdot 3.1416}{180}) \cdot {(\cos (\frac{64 \cdot 3.1416}{180}))}^{2})}{\tan (\frac{64 \cdot 3.1416}{180}) \cdot {(\cos (\frac{64 \cdot 3.1416}{180}))}^{2}}

12.6621kN/m³ = \frac{(\frac{0.32kPa}{1.01m}) - (5kN/m³ \cdot \tan (\frac{46° \cdot 3.1416}{180}) \cdot {(\cos (\frac{64° \cdot 3.1416}{180}))}^{2})}{\tan (\frac{64° \cdot 3.1416}{180}) \cdot {(\cos (\frac{64° \cdot 3.1416}{180}))}^{2}}

12.6621 = \frac{(\frac{0.32}{1.01}) - (5 \cdot \tan (\frac{46 \cdot 3.1416}{180}) \cdot {(\cos (\frac{64 \cdot 3.1416}{180}))}^{2})}{\tan (\frac{64 \cdot 3.1416}{180}) \cdot {(\cos (\frac{64 \cdot 3.1416}{180}))}^{2}}

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Saturated Unit Weight given Critical Depth Solution

Follow our step by step solution on how to calculate Saturated Unit Weight given Critical Depth?

FIRST Step Consider the formula

γ saturated = \frac{(\frac{C eff}{h c}) - (y S \cdot \tan (\frac{φ \cdot π}{180}) \cdot {(\cos (\frac{i \cdot π}{180}))}^{2})}{\tan (\frac{i \cdot π}{180}) \cdot {(\cos (\frac{i \cdot π}{180}))}^{2}}

Next Step Substitute values of Variables

∴

γ saturated = \frac{(\frac{0.32kPa}{1.01m}) - (5kN/m³ \cdot \tan (\frac{46° \cdot π}{180}) \cdot {(\cos (\frac{64° \cdot π}{180}))}^{2})}{\tan (\frac{64° \cdot π}{180}) \cdot {(\cos (\frac{64° \cdot π}{180}))}^{2}}

Next Step Substitute values of Constants

∴

γ saturated = \frac{(\frac{0.32kPa}{1.01m}) - (5kN/m³ \cdot \tan (\frac{46° \cdot 3.1416}{180}) \cdot {(\cos (\frac{64° \cdot 3.1416}{180}))}^{2})}{\tan (\frac{64° \cdot 3.1416}{180}) \cdot {(\cos (\frac{64° \cdot 3.1416}{180}))}^{2}}

Next Step Convert Units

∴

γ saturated = \frac{(\frac{320Pa}{1.01m}) - (5000N/m³ \cdot \tan (\frac{0.8029rad \cdot 3.1416}{180}) \cdot {(\cos (\frac{1.117rad \cdot 3.1416}{180}))}^{2})}{\tan (\frac{1.117rad \cdot 3.1416}{180}) \cdot {(\cos (\frac{1.117rad \cdot 3.1416}{180}))}^{2}}

Next Step Prepare to Evaluate

∴

γ saturated = \frac{(\frac{320}{1.01}) - (5000 \cdot \tan (\frac{0.8029 \cdot 3.1416}{180}) \cdot {(\cos (\frac{1.117 \cdot 3.1416}{180}))}^{2})}{\tan (\frac{1.117 \cdot 3.1416}{180}) \cdot {(\cos (\frac{1.117 \cdot 3.1416}{180}))}^{2}}

Next Step Evaluate

∴

γ saturated = 12662.1052925916N/m³

Next Step Convert to Output's Unit

∴

γ saturated = 12.6621052925916kN/m³

LAST Step Rounding Answer

∴

γ saturated = 12.6621kN/m³

Saturated Unit Weight given Critical Depth 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

Effective Cohesion in Geotech as Kilopascal

Effective Cohesion in Geotech as Kilopascal is the consistency of soft to hard defined on the basis of the standard CSN 73 1001 for different states of consistency and degree of saturation.

Symbol: C_eff

Measurement: PressureUnit: kPa

Note: Value should be greater than 0.

Formulas to find Effective Cohesion in Geotech as Kilopascal

Critical Depth

The Critical Depth is defined as the depth of flow where energy is at a minimum for a particular discharge.

Symbol: h_c

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Critical Depth

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

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

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)

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 Factor of Safety for Cohesive Soil

γ saturated = \frac{C eff + (y S \cdot z \cdot \tan (\frac{Φ i \cdot π}{180}) \cdot {(\cos (\frac{i \cdot π}{180}))}^{2})}{F s \cdot z \cdot \cos (\frac{i \cdot π}{180}) \cdot \sin (\frac{i \cdot π}{180})}

Other formulas in Steady State Seepage Analysis Along The Slopes category

Go Weight of Soil Prism given Saturated Unit Weight

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

Go Inclined Length of Prism given Saturated Unit Weight

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

Go Vertical Stress on Prism given Saturated Unit Weight

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

Go Normal Stress Component given Saturated Unit Weight

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

How to Evaluate Saturated Unit Weight given Critical Depth?

Saturated Unit Weight given Critical Depth evaluator uses Saturated Unit Weight of Soil = ((Effective Cohesion in Geotech as Kilopascal/Critical Depth)-(Submerged Unit Weight in KN per Cubic Meter*tan((Angle of Internal Friction*pi)/180)*(cos((Angle of Inclination to Horizontal in Soil*pi)/180))^2))/(tan((Angle of Inclination to Horizontal in Soil*pi)/180)*(cos((Angle of Inclination to Horizontal in Soil*pi)/180))^2) to evaluate the Saturated Unit Weight of Soil, The Saturated Unit Weight given Critical Depth 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 Critical Depth using this online evaluator? To use this online evaluator for Saturated Unit Weight given Critical Depth, enter Effective Cohesion in Geotech as Kilopascal (C_eff), Critical Depth (h_c), Submerged Unit Weight in KN per Cubic Meter (y_S), Angle of Internal Friction (φ) & Angle of Inclination to Horizontal in Soil (i) and hit the calculate button.

FAQs on Saturated Unit Weight given Critical Depth

What is the formula to find Saturated Unit Weight given Critical Depth?

The formula of Saturated Unit Weight given Critical Depth is expressed as Saturated Unit Weight of Soil = ((Effective Cohesion in Geotech as Kilopascal/Critical Depth)-(Submerged Unit Weight in KN per Cubic Meter*tan((Angle of Internal Friction*pi)/180)*(cos((Angle of Inclination to Horizontal in Soil*pi)/180))^2))/(tan((Angle of Inclination to Horizontal in Soil*pi)/180)*(cos((Angle of Inclination to Horizontal in Soil*pi)/180))^2). Here is an example- 0.012662 = ((320/1.01)-(5000*tan((0.802851455917241*pi)/180)*(cos((1.11701072127616*pi)/180))^2))/(tan((1.11701072127616*pi)/180)*(cos((1.11701072127616*pi)/180))^2).

How to calculate Saturated Unit Weight given Critical Depth?

With Effective Cohesion in Geotech as Kilopascal (C_eff), Critical Depth (h_c), Submerged Unit Weight in KN per Cubic Meter (y_S), Angle of Internal Friction (φ) & Angle of Inclination to Horizontal in Soil (i) we can find Saturated Unit Weight given Critical Depth using the formula - Saturated Unit Weight of Soil = ((Effective Cohesion in Geotech as Kilopascal/Critical Depth)-(Submerged Unit Weight in KN per Cubic Meter*tan((Angle of Internal Friction*pi)/180)*(cos((Angle of Inclination to Horizontal in Soil*pi)/180))^2))/(tan((Angle of Inclination to Horizontal in Soil*pi)/180)*(cos((Angle of Inclination to Horizontal in Soil*pi)/180))^2). This formula also uses Archimedes' constant and , Cosine, Tangent 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=(Effective Cohesion in Geotech as Kilopascal+(Submerged Unit Weight in KN per Cubic Meter*Depth of Prism*tan((Angle of Internal Friction of Soil*pi)/180)*(cos((Angle of Inclination to Horizontal in Soil*pi)/180))^2))/(Factor of Safety in Soil Mechanics*Depth of Prism*cos((Angle of Inclination to Horizontal in Soil*pi)/180)*sin((Angle of Inclination to Horizontal in Soil*pi)/180))

Can the Saturated Unit Weight given Critical Depth be negative?

No, the Saturated Unit Weight given Critical Depth, measured in Specific Weight cannot be negative.

Which unit is used to measure Saturated Unit Weight given Critical Depth?

Saturated Unit Weight given Critical Depth 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 Critical Depth can be measured.

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Saturated Unit Weight given Critical Depth Formula

​GoSaturated Unit Weight given Factor of Safety for Cohesive Soil Formula

Saturated Unit Weight given Critical Depth Example

Saturated Unit Weight given Critical Depth Solution

Saturated Unit Weight given Critical Depth Formula Elements

Other Formulas to find Saturated Unit Weight of Soil

Other formulas in Steady State Seepage Analysis Along The Slopes category

How to Evaluate Saturated Unit Weight given Critical Depth?

FAQs on Saturated Unit Weight given Critical Depth

Variable Name

GoSaturated Unit Weight given Factor of Safety for Cohesive Soil Formula