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Saturated Unit Weight given Factor of Safety for Cohesive Soil Formula

GoSaturated Unit Weight given Critical Depth 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{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})}

γ_saturated - Saturated Unit Weight of Soil?C_eff - Effective Cohesion in Geotech as Kilopascal?y_S - Submerged Unit Weight in KN per Cubic Meter?z - Depth of Prism?Φ_i - Angle of Internal Friction of Soil?i - Angle of Inclination to Horizontal in Soil?F_s - Factor of Safety in Soil Mechanics?π - Archimedes' constant?

Saturated Unit Weight given Factor of Safety for Cohesive Soil Example

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Here is how the Saturated Unit Weight given Factor of Safety for Cohesive Soil equation looks like with Values.

Here is how the Saturated Unit Weight given Factor of Safety for Cohesive Soil equation looks like with Units.

Here is how the Saturated Unit Weight given Factor of Safety for Cohesive Soil equation looks like.

4.267 = \frac{0.32 + (5 \cdot 3 \cdot \tan (\frac{82.87 \cdot 3.1416}{180}) \cdot {(\cos (\frac{64 \cdot 3.1416}{180}))}^{2})}{2.8 \cdot 3 \cdot \cos (\frac{64 \cdot 3.1416}{180}) \cdot \sin (\frac{64 \cdot 3.1416}{180})}

4.267kN/m³ = \frac{0.32kPa + (5kN/m³ \cdot 3m \cdot \tan (\frac{82.87° \cdot 3.1416}{180}) \cdot {(\cos (\frac{64° \cdot 3.1416}{180}))}^{2})}{2.8 \cdot 3m \cdot \cos (\frac{64° \cdot 3.1416}{180}) \cdot \sin (\frac{64° \cdot 3.1416}{180})}

4.267 = \frac{0.32 + (5 \cdot 3 \cdot \tan (\frac{82.87 \cdot 3.1416}{180}) \cdot {(\cos (\frac{64 \cdot 3.1416}{180}))}^{2})}{2.8 \cdot 3 \cdot \cos (\frac{64 \cdot 3.1416}{180}) \cdot \sin (\frac{64 \cdot 3.1416}{180})}

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Saturated Unit Weight given Factor of Safety for Cohesive Soil Solution

Follow our step by step solution on how to calculate Saturated Unit Weight given Factor of Safety for Cohesive Soil?

FIRST Step Consider the formula

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})}

Next Step Substitute values of Variables

∴

γ saturated = \frac{0.32kPa + (5kN/m³ \cdot 3m \cdot \tan (\frac{82.87° \cdot π}{180}) \cdot {(\cos (\frac{64° \cdot π}{180}))}^{2})}{2.8 \cdot 3m \cdot \cos (\frac{64° \cdot π}{180}) \cdot \sin (\frac{64° \cdot π}{180})}

Next Step Substitute values of Constants

∴

γ saturated = \frac{0.32kPa + (5kN/m³ \cdot 3m \cdot \tan (\frac{82.87° \cdot 3.1416}{180}) \cdot {(\cos (\frac{64° \cdot 3.1416}{180}))}^{2})}{2.8 \cdot 3m \cdot \cos (\frac{64° \cdot 3.1416}{180}) \cdot \sin (\frac{64° \cdot 3.1416}{180})}

Next Step Convert Units

∴

γ saturated = \frac{320Pa + (5000N/m³ \cdot 3m \cdot \tan (\frac{1.4464rad \cdot 3.1416}{180}) \cdot {(\cos (\frac{1.117rad \cdot 3.1416}{180}))}^{2})}{2.8 \cdot 3m \cdot \cos (\frac{1.117rad \cdot 3.1416}{180}) \cdot \sin (\frac{1.117rad \cdot 3.1416}{180})}

Next Step Prepare to Evaluate

∴

γ saturated = \frac{320 + (5000 \cdot 3 \cdot \tan (\frac{1.4464 \cdot 3.1416}{180}) \cdot {(\cos (\frac{1.117 \cdot 3.1416}{180}))}^{2})}{2.8 \cdot 3 \cdot \cos (\frac{1.117 \cdot 3.1416}{180}) \cdot \sin (\frac{1.117 \cdot 3.1416}{180})}

Next Step Evaluate

∴

γ saturated = 4266.96585716475N/m³

Next Step Convert to Output's Unit

∴

γ saturated = 4.26696585716475kN/m³

LAST Step Rounding Answer

∴

γ saturated = 4.267kN/m³

Saturated Unit Weight given Factor of Safety for Cohesive Soil 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.

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.

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.

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.

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.

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.

Factor of Safety in Soil Mechanics

Factor of Safety in Soil Mechanics 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.

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

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)

Credits

Created by Suraj Kumar

Birsa Institute of Technology (BIT), Sindri

Suraj Kumar has created this Formula and 2100+ more formulas!

Verified by Ishita Goyal

Meerut Institute of Engineering and Technology (MIET), Meerut

Ishita Goyal has verified this Formula and 2600+ more formulas!

Other Formulas to find Saturated Unit Weight of Soil

Go Saturated Unit Weight given Critical Depth

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}}

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})}

How to Evaluate Saturated Unit Weight given Factor of Safety for Cohesive Soil?

Saturated Unit Weight given Factor of Safety for Cohesive Soil evaluator uses 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)) to evaluate the Saturated Unit Weight of Soil, The Saturated Unit Weight given Factor of Safety for Cohesive Soil 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 Factor of Safety for Cohesive Soil using this online evaluator? To use this online evaluator for Saturated Unit Weight given Factor of Safety for Cohesive Soil, enter Effective Cohesion in Geotech as Kilopascal (C_eff), Submerged Unit Weight in KN per Cubic Meter (y_S), Depth of Prism (z), Angle of Internal Friction of Soil (Φ_i), Angle of Inclination to Horizontal in Soil (i) & Factor of Safety in Soil Mechanics (F_s) and hit the calculate button.

FAQs on Saturated Unit Weight given Factor of Safety for Cohesive Soil

What is the formula to find Saturated Unit Weight given Factor of Safety for Cohesive Soil?

The formula of Saturated Unit Weight given Factor of Safety for Cohesive Soil is expressed as 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)). Here is an example- 0.004267 = (320+(5000*3*tan((1.44635435112743*pi)/180)*(cos((1.11701072127616*pi)/180))^2))/(2.8*3*cos((1.11701072127616*pi)/180)*sin((1.11701072127616*pi)/180)).

How to calculate Saturated Unit Weight given Factor of Safety for Cohesive Soil?

With Effective Cohesion in Geotech as Kilopascal (C_eff), Submerged Unit Weight in KN per Cubic Meter (y_S), Depth of Prism (z), Angle of Internal Friction of Soil (Φ_i), Angle of Inclination to Horizontal in Soil (i) & Factor of Safety in Soil Mechanics (F_s) we can find Saturated Unit Weight given Factor of Safety for Cohesive Soil using the formula - 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)). This formula also uses Archimedes' constant and , Sine (sin), Cosine (cos), 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=((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)

Can the Saturated Unit Weight given Factor of Safety for Cohesive Soil be negative?

No, the Saturated Unit Weight given Factor of Safety for Cohesive Soil, measured in Specific Weight cannot be negative.

Which unit is used to measure Saturated Unit Weight given Factor of Safety for Cohesive Soil?

Saturated Unit Weight given Factor of Safety for Cohesive Soil 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 Factor of Safety for Cohesive Soil can be measured.

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Saturated Unit Weight given Factor of Safety for Cohesive Soil Formula

​GoSaturated Unit Weight given Critical Depth Formula

Saturated Unit Weight given Factor of Safety for Cohesive Soil Example

Saturated Unit Weight given Factor of Safety for Cohesive Soil Solution

Saturated Unit Weight given Factor of Safety for Cohesive Soil Formula Elements

Credits

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 Factor of Safety for Cohesive Soil?

FAQs on Saturated Unit Weight given Factor of Safety for Cohesive Soil

Variable Name

GoSaturated Unit Weight given Critical Depth Formula