Minimum Unit Weight of Soil given Relative Density Calculator

✖Dry Unit Weight of soil is the weight of soil solids per unit of total volume of soil mass.ⓘ Dry Unit Weight [γ_dry]			+10% -10%
✖Maximum Unit Weight of soil is ratio of weight of soil to minimum volume of soil.ⓘ Maximum Unit Weight [γ_max]			+10% -10%
✖Relative Density is density of an object in terms of the density of another reference object.ⓘ Relative Density [R]			+10% -10%

✖Minimum Unit Weight of soil is ratio of weight of soil to maximum volume of soil.ⓘ Minimum Unit Weight of Soil given Relative Density [γ_min]

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Minimum Unit Weight of Soil given Relative Density

Formula

`"γ"_{"min"} = (("γ"_{"dry"}*"γ"_{"max"}*("R"-1))/(("R"*"γ"_{"dry"})-"γ"_{"max"}))`

Example

`"10.6769kN/m³"=(("6.12kN/m³"*"10kN/m³"*("11"-1))/(("11"*"6.12kN/m³")-"10kN/m³"))`

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Download Soil Origin and Its Properties Formulas PDF

Minimum Unit Weight of Soil given Relative Density Solution

STEP 0: Pre-Calculation Summary

Formula Used

Minimum Unit Weight = ((Dry Unit Weight*Maximum Unit Weight*(Relative Density-1))/((Relative Density*Dry Unit Weight)-Maximum Unit Weight))
γ_min = ((γ_dry*γ_max*(R-1))/((R*γ_dry)-γ_max))
This formula uses 4 Variables

Variables Used

Minimum Unit Weight - (Measured in Newton per Cubic Meter) - Minimum Unit Weight of soil is ratio of weight of soil to maximum volume of soil.
Dry Unit Weight - (Measured in Newton per Cubic Meter) - Dry Unit Weight of soil is the weight of soil solids per unit of total volume of soil mass.
Maximum Unit Weight - (Measured in Newton per Cubic Meter) - Maximum Unit Weight of soil is ratio of weight of soil to minimum volume of soil.
Relative Density - Relative Density is density of an object in terms of the density of another reference object.

STEP 1: Convert Input(s) to Base Unit

Dry Unit Weight: 6.12 Kilonewton per Cubic Meter --> 6120 Newton per Cubic Meter (Check conversion here)
Maximum Unit Weight: 10 Kilonewton per Cubic Meter --> 10000 Newton per Cubic Meter (Check conversion here)
Relative Density: 11 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

γ_min = ((γ_dry*γ_max*(R-1))/((R*γ_dry)-γ_max)) --> ((6120*10000*(11-1))/((11*6120)-10000))

Evaluating ... ...

γ_min = 10676.9016050244

STEP 3: Convert Result to Output's Unit

10676.9016050244 Newton per Cubic Meter -->10.6769016050244 Kilonewton per Cubic Meter (Check conversion here)

FINAL ANSWER

10.6769016050244 ≈ 10.6769 Kilonewton per Cubic Meter <-- Minimum Unit Weight

(Calculation completed in 00.004 seconds)

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Home » Engineering » Civil » Geotechnical Engineering » Soil Origin and Its Properties » Minimum Unit Weight of Soil given Relative Density

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Created by Suraj Kumar

Birsa Institute of Technology (BIT), Sindri

Suraj Kumar has created this Calculator and 2200+ more calculators!

Verified by Ishita Goyal

Meerut Institute of Engineering and Technology (MIET), Meerut

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< 24 Soil Origin and Its Properties Calculators

Porosity Given Relative Density in Porosity

Go Porosity of Soil = (Maximum Porosity*(1-Minimum Porosity-Relative Density in Soil Mechanics)+Relative Density in Soil Mechanics*Minimum Porosity)/(1-Minimum Porosity+Relative Density in Soil Mechanics*Minimum Porosity-Relative Density in Soil Mechanics*Maximum Porosity)

Minimum Porosity given Relative Density in Porosity

Go Minimum Porosity = Maximum Porosity*(1+(Porosity of Soil*Relative Density)-Porosity of Soil-Relative Density)/(Maximum Porosity-Porosity of Soil-Relative Density+(Porosity of Soil*Relative Density))

Maximum Porosity given Relative Density in Porosity

Go Maximum Porosity = Minimum Porosity*(Relative Density-(Porosity of Soil*Relative Density)-Porosity of Soil+1)/(Relative Density-(Porosity of Soil*Relative Density)+Minimum Porosity-1)

Dry Unit Weight of Soil given Relative Density

Go Dry Unit Weight = ((Minimum Unit Weight*Maximum Unit Weight)/(Maximum Unit Weight-Relative Density in Soil Mechanics*(Maximum Unit Weight-Minimum Unit Weight)))

Relative density given porosity

Go Relative Density in Soil Mechanics = ((Maximum Porosity-Porosity of Soil)*(1-Minimum Porosity))/((Maximum Porosity-Minimum Porosity)*(1-Porosity of Soil))

Minimum Unit Weight of Soil given Relative Density

Go Minimum Unit Weight = ((Dry Unit Weight*Maximum Unit Weight*(Relative Density-1))/((Relative Density*Dry Unit Weight)-Maximum Unit Weight))

Maximum Unit Weight of Soil given Relative Density

Go Maximum Unit Weight = ((Minimum Unit Weight*Dry Unit Weight*Relative Density)/(Dry Unit Weight*(Relative Density-1)+Minimum Unit Weight))

Dry Unit Weight of Soil with any Degree of Saturation

Go Dry Unit Weight = ((Unit Weight of Water*Specific Gravity of Soil*Degree of Saturation)/(1+(Water Content of Soil from Pycnometer*Specific Gravity of Soil)))

Natural Void Ratio of Soil given Relative Density

Go Natural Void Ratio = (Maximum Void Ratio*(1-Relative Density in Soil Mechanics)+(Relative Density in Soil Mechanics*Minimum Void Ratio))

Relative Density of Cohesionless Soil given Unit Weight of Soil

Go Relative Density in Soil Mechanics = ((1/Minimum Unit Weight)-(1/Dry Unit Weight))/((1/Minimum Unit Weight)-(1/Maximum Unit Weight))

Degree of Saturation given Dry Unit Weight of Soil

Go Degree of Saturation = ((Dry Unit Weight/Unit Weight of Water)*((1/Specific Gravity of Soil)+Water Content of Soil from Pycnometer))

Relative Density of Cohesionless Soil given Void Ratio

Go Relative Density in Soil Mechanics = ((Maximum Void Ratio-Natural Void Ratio)/(Maximum Void Ratio-Minimum Void Ratio))

Maximum Void Ratio of Soil given Relative Density

Go Maximum Void Ratio = (Natural Void Ratio-(Relative Density*Minimum Void Ratio))/(1-Relative Density)

Minimum Void Ratio of Soil given Relative Density

Go Minimum Void Ratio = (Maximum Void Ratio-((Maximum Void Ratio-Natural Void Ratio)/Relative Density))

Specific Gravity of Soil given Degree of Saturation

Go Specific Gravity of Soil = ((Degree of Saturation*Void Ratio of Soil)/Water Content of Soil from Pycnometer)

Water Content of Soil given Degree of Saturation

Go Water Content of Soil from Pycnometer = ((Degree of Saturation*Void Ratio of Soil)/Specific Gravity of Soil)

Void Ratio of Soil given Degree of Saturation

Go Void Ratio of Soil = ((Water Content of Soil from Pycnometer*Specific Gravity of Soil)/Degree of Saturation)

Degree of Saturation of Soil

Go Degree of Saturation = ((Water Content of Soil from Pycnometer*Specific Gravity of Soil)/Void Ratio of Soil)

Porosity of Soil given Void Ratio

Go Porosity of Soil = (Void Ratio of Soil/(1+Void Ratio of Soil))

Void Ratio of Soil given Porosity

Go Void Ratio of Soil = (Porosity of Soil/(1-Porosity of Soil))

Total Volume of Soil using Porosity

Go Volume of Soil = (Volume of Voids/Porosity of Soil)

Volume of Voids using Porosity

Go Volume of Voids = (Porosity of Soil*Volume of Soil)

Void ratio of soil

Go Void Ratio of Soil = (Volume of Voids/Solid Volume)

Porosity of soil

Go Porosity of Soil = (Volume of Voids/Volume of Soil)

Minimum Unit Weight of Soil given Relative Density Formula

Minimum Unit Weight = ((Dry Unit Weight*Maximum Unit Weight*(Relative Density-1))/((Relative Density*Dry Unit Weight)-Maximum Unit Weight))
γ_min = ((γ_dry*γ_max*(R-1))/((R*γ_dry)-γ_max))

What is Relative Density of Soil?

Relative density or density index is the ratio of the difference between the void ratios of a cohesionless soil in its loosest state and existing natural state to the difference between its void ratio in the loosest and densest states.

How to Calculate Minimum Unit Weight of Soil given Relative Density?

Minimum Unit Weight of Soil given Relative Density calculator uses Minimum Unit Weight = ((Dry Unit Weight*Maximum Unit Weight*(Relative Density-1))/((Relative Density*Dry Unit Weight)-Maximum Unit Weight)) to calculate the Minimum Unit Weight, The Minimum Unit Weight of Soil given Relative Density formula is defined as the ratio of the weight of soil to a maximum volume of soil. Minimum Unit Weight is denoted by γ_min symbol.

How to calculate Minimum Unit Weight of Soil given Relative Density using this online calculator? To use this online calculator for Minimum Unit Weight of Soil given Relative Density, enter Dry Unit Weight (γ_dry), Maximum Unit Weight (γ_max) & Relative Density (R) and hit the calculate button. Here is how the Minimum Unit Weight of Soil given Relative Density calculation can be explained with given input values -> 0.010677 = ((6120*10000*(11-1))/((11*6120)-10000)).

FAQ

What is Minimum Unit Weight of Soil given Relative Density?

The Minimum Unit Weight of Soil given Relative Density formula is defined as the ratio of the weight of soil to a maximum volume of soil and is represented as γ_min = ((γ_dry*γ_max*(R-1))/((R*γ_dry)-γ_max)) or Minimum Unit Weight = ((Dry Unit Weight*Maximum Unit Weight*(Relative Density-1))/((Relative Density*Dry Unit Weight)-Maximum Unit Weight)). Dry Unit Weight of soil is the weight of soil solids per unit of total volume of soil mass, Maximum Unit Weight of soil is ratio of weight of soil to minimum volume of soil & Relative Density is density of an object in terms of the density of another reference object.

How to calculate Minimum Unit Weight of Soil given Relative Density?

The Minimum Unit Weight of Soil given Relative Density formula is defined as the ratio of the weight of soil to a maximum volume of soil is calculated using Minimum Unit Weight = ((Dry Unit Weight*Maximum Unit Weight*(Relative Density-1))/((Relative Density*Dry Unit Weight)-Maximum Unit Weight)). To calculate Minimum Unit Weight of Soil given Relative Density, you need Dry Unit Weight (γ_dry), Maximum Unit Weight (γ_max) & Relative Density (R). With our tool, you need to enter the respective value for Dry Unit Weight, Maximum Unit Weight & Relative Density and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

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