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Unit Weight of Soil given Total Thrust from Soil that are Free to Move Formula

GoUnit Weight of Soil given Total Thrust from Soil for Level Surface behind Wall Formula

GoUnit Weight of Soil given Total Thrust from Soil that are Completely Restrained Formula

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Unit Weight of Soil mass is the ratio of the total weight of soil to the total volume of soil. Check FAQs

γ = \frac{2 \cdot P}{{(h w)}^{2} \cdot \cos (i)} \cdot (\frac{\cos (i) - \sqrt{{(\cos (i))}^{2} - {(\cos (φ))}^{2}}}{\cos (i) + \sqrt{{(\cos (i))}^{2} - {(\cos (φ))}^{2}}})

γ - Unit Weight of Soil?P - Total Thrust of Soil?h_w - Total Height of Wall?i - Angle of Inclination?φ - Angle of Internal Friction?

Unit Weight of Soil given Total Thrust from Soil that are Free to Move Example

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Here is how the Unit Weight of Soil given Total Thrust from Soil that are Free to Move equation looks like with Values.

Here is how the Unit Weight of Soil given Total Thrust from Soil that are Free to Move equation looks like with Units.

Here is how the Unit Weight of Soil given Total Thrust from Soil that are Free to Move equation looks like.

0.6061 = \frac{2 \cdot 10}{{(3.1)}^{2} \cdot \cos (30)} \cdot (\frac{\cos (30) - \sqrt{{(\cos (30))}^{2} - {(\cos (46))}^{2}}}{\cos (30) + \sqrt{{(\cos (30))}^{2} - {(\cos (46))}^{2}}})

0.6061kN/m³ = \frac{2 \cdot 10kN/m}{{(3.1m)}^{2} \cdot \cos (30°)} \cdot (\frac{\cos (30°) - \sqrt{{(\cos (30°))}^{2} - {(\cos (46°))}^{2}}}{\cos (30°) + \sqrt{{(\cos (30°))}^{2} - {(\cos (46°))}^{2}}})

0.6061 = \frac{2 \cdot 10}{{(3.1)}^{2} \cdot \cos (30)} \cdot (\frac{\cos (30) - \sqrt{{(\cos (30))}^{2} - {(\cos (46))}^{2}}}{\cos (30) + \sqrt{{(\cos (30))}^{2} - {(\cos (46))}^{2}}})

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Unit Weight of Soil given Total Thrust from Soil that are Free to Move Solution

Follow our step by step solution on how to calculate Unit Weight of Soil given Total Thrust from Soil that are Free to Move?

FIRST Step Consider the formula

γ = \frac{2 \cdot P}{{(h w)}^{2} \cdot \cos (i)} \cdot (\frac{\cos (i) - \sqrt{{(\cos (i))}^{2} - {(\cos (φ))}^{2}}}{\cos (i) + \sqrt{{(\cos (i))}^{2} - {(\cos (φ))}^{2}}})

Next Step Substitute values of Variables

∴

γ = \frac{2 \cdot 10kN/m}{{(3.1m)}^{2} \cdot \cos (30°)} \cdot (\frac{\cos (30°) - \sqrt{{(\cos (30°))}^{2} - {(\cos (46°))}^{2}}}{\cos (30°) + \sqrt{{(\cos (30°))}^{2} - {(\cos (46°))}^{2}}})

Next Step Convert Units

∴

γ = \frac{2 \cdot 10000N/m}{{(3.1m)}^{2} \cdot \cos (0.5236rad)} \cdot (\frac{\cos (0.5236rad) - \sqrt{{(\cos (0.5236rad))}^{2} - {(\cos (0.8029rad))}^{2}}}{\cos (0.5236rad) + \sqrt{{(\cos (0.5236rad))}^{2} - {(\cos (0.8029rad))}^{2}}})

Next Step Prepare to Evaluate

∴

γ = \frac{2 \cdot 10000}{{(3.1)}^{2} \cdot \cos (0.5236)} \cdot (\frac{\cos (0.5236) - \sqrt{{(\cos (0.5236))}^{2} - {(\cos (0.8029))}^{2}}}{\cos (0.5236) + \sqrt{{(\cos (0.5236))}^{2} - {(\cos (0.8029))}^{2}}})

Next Step Evaluate

∴

γ = 606.122759839706N/m³

Next Step Convert to Output's Unit

∴

γ = 0.606122759839706kN/m³

LAST Step Rounding Answer

∴

γ = 0.6061kN/m³

Unit Weight of Soil given Total Thrust from Soil that are Free to Move Formula Elements

Variables

Functions

Unit Weight of Soil

Unit Weight of Soil mass is the ratio of the total weight of soil to the total volume of soil.

Symbol: γ

Measurement: Specific WeightUnit: kN/m³

Note: Value should be greater than 0.

Formulas to find Unit Weight of Soil

Total Thrust of Soil

Total Thrust of Soil is the force acting on unit length of soil.

Symbol: P

Measurement: Surface TensionUnit: kN/m

Note: Value should be greater than 0.

Formulas to find Total Thrust of Soil

Total Height of Wall

Total height of wall which is under the consideration.

Symbol: h_w

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Total Height of Wall

Angle of Inclination

Angle of Inclination of ground surface behind wall with horizontal.

Symbol: i

Measurement: AngleUnit: °

Note: Value should be greater than 0.

Formulas to find Angle of Inclination

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

cos

Cosine of an angle is the ratio of the side adjacent to the angle to the hypotenuse of the triangle.

Syntax: cos(Angle)

sqrt

A square root function is a function that takes a non-negative number as an input and returns the square root of the given input number.

Syntax: sqrt(Number)

Other Formulas to find Unit Weight of Soil

Go Unit Weight of Soil given Total Thrust from Soil for Level Surface behind Wall

γ = \frac{2 \cdot P}{{(h w)}^{2} \cdot K A}

Go Unit Weight of Soil given Total Thrust from Soil that are Completely Restrained

γ = \frac{2 \cdot P}{{(h w)}^{2} \cdot \cos (i)} \cdot (\frac{\cos (i) + \sqrt{{(\cos (i))}^{2} - {(\cos (φ))}^{2}}}{\cos (i) - \sqrt{{(\cos (i))}^{2} - {(\cos (φ))}^{2}}})

Go Unit Weight of Soil given Thrust of Soil that are Completely Restrained and Surface is Level

γ = \frac{2 \cdot P}{{(h w)}^{2} \cdot K P}

Go Unit Weight of Soil given Total Thrust from Soil with Small Angles of Internal Friction

γ = ((2 \cdot \frac{P}{{(h w)}^{2}}) + (4 \cdot \frac{C}{h w}))

Other formulas in Lateral Pressure for Cohesive and Non Cohesive Soil category

Go Total Thrust from Soil that are Free to Move

P = (0.5 \cdot γ \cdot {(h w)}^{2} \cdot \cos (i)) \cdot (\frac{\cos (i) - \sqrt{{(\cos (i))}^{2} - {(\cos (φ))}^{2}}}{\cos (i) + \sqrt{{(\cos (i))}^{2} - {(\cos (φ))}^{2}}})

Go Total Height of Wall given Total Thrust from Soil that are Free to move

h w = \sqrt{\frac{2 \cdot P}{γ \cdot \cos (i) \cdot (\frac{\cos (i) - \sqrt{{(\cos (i))}^{2} - {(\cos (φ))}^{2}}}{\cos (i) + \sqrt{{(\cos (i))}^{2} - {(\cos (φ))}^{2}}})}}

Go Total Thrust from Soil when Surface behind Wall is Level

P = (0.5 \cdot γ \cdot {(h w)}^{2} \cdot K A)

Go Total Height of Wall given Total Thrust from Soil for Level Surface behind Wall

h w = \sqrt{\frac{2 \cdot P}{γ \cdot K A}}

How to Evaluate Unit Weight of Soil given Total Thrust from Soil that are Free to Move?

Unit Weight of Soil given Total Thrust from Soil that are Free to Move evaluator uses Unit Weight of Soil = (2*Total Thrust of Soil)/((Total Height of Wall)^2*cos(Angle of Inclination))*((cos(Angle of Inclination)-sqrt((cos(Angle of Inclination))^2-(cos(Angle of Internal Friction))^2))/(cos(Angle of Inclination)+sqrt((cos(Angle of Inclination))^2-(cos(Angle of Internal Friction))^2))) to evaluate the Unit Weight of Soil, The Unit Weight of Soil given Total Thrust from Soil that are Free to Move is defined as the ratio of weight of the soil to volume of the soil. Unit Weight of Soil is denoted by γ symbol.

How to evaluate Unit Weight of Soil given Total Thrust from Soil that are Free to Move using this online evaluator? To use this online evaluator for Unit Weight of Soil given Total Thrust from Soil that are Free to Move, enter Total Thrust of Soil (P), Total Height of Wall (h_w), Angle of Inclination (i) & Angle of Internal Friction (φ) and hit the calculate button.

FAQs on Unit Weight of Soil given Total Thrust from Soil that are Free to Move

What is the formula to find Unit Weight of Soil given Total Thrust from Soil that are Free to Move?

The formula of Unit Weight of Soil given Total Thrust from Soil that are Free to Move is expressed as Unit Weight of Soil = (2*Total Thrust of Soil)/((Total Height of Wall)^2*cos(Angle of Inclination))*((cos(Angle of Inclination)-sqrt((cos(Angle of Inclination))^2-(cos(Angle of Internal Friction))^2))/(cos(Angle of Inclination)+sqrt((cos(Angle of Inclination))^2-(cos(Angle of Internal Friction))^2))). Here is an example- 0.000606 = (2*10000)/((3.1)^2*cos(0.5235987755982))*((cos(0.5235987755982)-sqrt((cos(0.5235987755982))^2-(cos(0.802851455917241))^2))/(cos(0.5235987755982)+sqrt((cos(0.5235987755982))^2-(cos(0.802851455917241))^2))).

How to calculate Unit Weight of Soil given Total Thrust from Soil that are Free to Move?

With Total Thrust of Soil (P), Total Height of Wall (h_w), Angle of Inclination (i) & Angle of Internal Friction (φ) we can find Unit Weight of Soil given Total Thrust from Soil that are Free to Move using the formula - Unit Weight of Soil = (2*Total Thrust of Soil)/((Total Height of Wall)^2*cos(Angle of Inclination))*((cos(Angle of Inclination)-sqrt((cos(Angle of Inclination))^2-(cos(Angle of Internal Friction))^2))/(cos(Angle of Inclination)+sqrt((cos(Angle of Inclination))^2-(cos(Angle of Internal Friction))^2))). This formula also uses Cosine (cos), Square Root (sqrt) function(s).

What are the other ways to Calculate Unit Weight of Soil?

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

Unit Weight of Soil=(2*Total Thrust of Soil)/((Total Height of Wall)^2*Coefficient of Active Pressure)
Unit Weight of Soil=(2*Total Thrust of Soil)/((Total Height of Wall)^2*cos(Angle of Inclination))*((cos(Angle of Inclination)+sqrt((cos(Angle of Inclination))^2-(cos(Angle of Internal Friction))^2))/(cos(Angle of Inclination)-sqrt((cos(Angle of Inclination))^2-(cos(Angle of Internal Friction))^2)))
Unit Weight of Soil=(2*Total Thrust of Soil)/((Total Height of Wall)^2*Coefficient of Passive Pressure)

Can the Unit Weight of Soil given Total Thrust from Soil that are Free to Move be negative?

No, the Unit Weight of Soil given Total Thrust from Soil that are Free to Move, measured in Specific Weight cannot be negative.

Which unit is used to measure Unit Weight of Soil given Total Thrust from Soil that are Free to Move?

Unit Weight of Soil given Total Thrust from Soil that are Free to Move 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 Unit Weight of Soil given Total Thrust from Soil that are Free to Move can be measured.

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Unit Weight of Soil given Total Thrust from Soil that are Free to Move Formula

​GoUnit Weight of Soil given Total Thrust from Soil for Level Surface behind Wall Formula

​GoUnit Weight of Soil given Total Thrust from Soil that are Completely Restrained Formula

Unit Weight of Soil given Total Thrust from Soil that are Free to Move Example

Unit Weight of Soil given Total Thrust from Soil that are Free to Move Solution

Unit Weight of Soil given Total Thrust from Soil that are Free to Move Formula Elements

Other Formulas to find Unit Weight of Soil

Other formulas in Lateral Pressure for Cohesive and Non Cohesive Soil category

How to Evaluate Unit Weight of Soil given Total Thrust from Soil that are Free to Move?

FAQs on Unit Weight of Soil given Total Thrust from Soil that are Free to Move

Variable Name

GoUnit Weight of Soil given Total Thrust from Soil for Level Surface behind Wall Formula

GoUnit Weight of Soil given Total Thrust from Soil that are Completely Restrained Formula