Unit Weight of Soil given Bearing Capacity Factor, Depth and Width of Footing Calculator

✖Net Ultimate Bearing Capacity is the minimum net pressure intensity causing shear failure.ⓘ Net Ultimate Bearing Capacity [q_nf]			+10% -10%
✖Cohesion of Soil is the ability of like particles within soil to hold onto each other. It is the shear strength or force that binds together like particles in the structure of a soil.ⓘ Cohesion of Soil [C_s]			+10% -10%
✖Bearing Capacity Factor dependent on Cohesion is a constant whose value depends upon the cohesion of soil.ⓘ Bearing Capacity Factor dependent on Cohesion [N_c]			+10% -10%
✖Width of Footing is the shorter dimension of the footing.ⓘ Width of Footing [B]			+10% -10%
✖Bearing Capacity Factor dependent on Unit Weight is a constant whose value depends upon unit weight of soil.ⓘ Bearing Capacity Factor dependent on Unit Weight [N_γ]			+10% -10%
✖Depth of Footing is the longer dimension of the footing.ⓘ Depth of Footing [D]			+10% -10%
✖Bearing Capacity Factor dependent on Surcharge is a constant whose value depends upon surcharge.ⓘ Bearing Capacity Factor dependent on Surcharge [N_q]			+10% -10%

✖Unit Weight of Soil mass is the ratio of the total weight of soil to the total volume of soil.ⓘ Unit Weight of Soil given Bearing Capacity Factor, Depth and Width of Footing [γ]

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Formula

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Unit Weight of Soil given Bearing Capacity Factor, Depth and Width of Footing

Formula

`"γ" = ("q"_{"nf"}-("C"_{"s"}*"N"_{"c"}))/((0.5*"B"*"N"_{"γ"})+("D"*("N"_{"q"}-1)))`

Example

`"0.040075kN/m³"=("150kN/m²"-("5.0kPa"*"9"))/((0.5*"2m"*"1.6")+("1.01m"*("2.01"-1)))`

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Download Terzaghi's Analysis: Water Table is Below the Base of Footing Formulas PDF

Unit Weight of Soil given Bearing Capacity Factor, Depth and Width of Footing Solution

STEP 0: Pre-Calculation Summary

Formula Used

Unit Weight of Soil = (Net Ultimate Bearing Capacity-(Cohesion of Soil*Bearing Capacity Factor dependent on Cohesion))/((0.5*Width of Footing*Bearing Capacity Factor dependent on Unit Weight)+(Depth of Footing*(Bearing Capacity Factor dependent on Surcharge-1)))
γ = (q_nf-(C_s*N_c))/((0.5*B*N_γ)+(D*(N_q-1)))
This formula uses 8 Variables

Variables Used

Unit Weight of Soil - (Measured in Newton per Cubic Meter) - Unit Weight of Soil mass is the ratio of the total weight of soil to the total volume of soil.
Net Ultimate Bearing Capacity - (Measured in Kilonewton per Square Meter) - Net Ultimate Bearing Capacity is the minimum net pressure intensity causing shear failure.
Cohesion of Soil - (Measured in Kilonewton per Square Meter) - Cohesion of Soil is the ability of like particles within soil to hold onto each other. It is the shear strength or force that binds together like particles in the structure of a soil.
Bearing Capacity Factor dependent on Cohesion - Bearing Capacity Factor dependent on Cohesion is a constant whose value depends upon the cohesion of soil.
Width of Footing - (Measured in Meter) - Width of Footing is the shorter dimension of the footing.
Bearing Capacity Factor dependent on Unit Weight - Bearing Capacity Factor dependent on Unit Weight is a constant whose value depends upon unit weight of soil.
Depth of Footing - (Measured in Meter) - Depth of Footing is the longer dimension of the footing.
Bearing Capacity Factor dependent on Surcharge - Bearing Capacity Factor dependent on Surcharge is a constant whose value depends upon surcharge.

STEP 1: Convert Input(s) to Base Unit

Net Ultimate Bearing Capacity: 150 Kilonewton per Square Meter --> 150 Kilonewton per Square Meter No Conversion Required
Cohesion of Soil: 5 Kilopascal --> 5 Kilonewton per Square Meter (Check conversion here)
Bearing Capacity Factor dependent on Cohesion: 9 --> No Conversion Required
Width of Footing: 2 Meter --> 2 Meter No Conversion Required
Bearing Capacity Factor dependent on Unit Weight: 1.6 --> No Conversion Required
Depth of Footing: 1.01 Meter --> 1.01 Meter No Conversion Required
Bearing Capacity Factor dependent on Surcharge: 2.01 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

γ = (q_nf-(C_s*N_c))/((0.5*B*N_γ)+(D*(N_q-1))) --> (150-(5*9))/((0.5*2*1.6)+(1.01*(2.01-1)))

Evaluating ... ...

γ = 40.0748063051029

STEP 3: Convert Result to Output's Unit

40.0748063051029 Newton per Cubic Meter -->0.0400748063051029 Kilonewton per Cubic Meter (Check conversion here)

FINAL ANSWER

0.0400748063051029 ≈ 0.040075 Kilonewton per Cubic Meter <-- Unit Weight of Soil

(Calculation completed in 00.004 seconds)

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Home » Engineering » Civil » Geotechnical Engineering » Terzaghi's Analysis: Shear Failure Theories » Terzaghi's Analysis: Water Table is Below the Base of Footing » Unit Weight of Soil given Bearing Capacity Factor, Depth and Width of Footing

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< 25 Terzaghi's Analysis: Water Table is Below the Base of Footing Calculators

Width of Footing given Factor of Safety and Safe Bearing Capacity

Go Width of Footing = (((Safe Bearing Capacity*Factor of Safety)-(Factor of Safety*(Unit Weight of Soil*Depth of Footing)))-((Cohesion of Soil*Bearing Capacity Factor dependent on Cohesion)+((Unit Weight of Soil*Depth of Footing)*(Bearing Capacity Factor dependent on Surcharge-1))))/(0.5*Unit Weight of Soil*Bearing Capacity Factor dependent on Unit Weight)

Safe Bearing Capacity given Depth and Width of Footing

Go Safe Bearing Capacity = (((Cohesion of Soil*Bearing Capacity Factor dependent on Cohesion)+((Unit Weight of Soil*Depth of Footing)*(Bearing Capacity Factor dependent on Surcharge-1))+(0.5*Unit Weight of Soil*Width of Footing*Bearing Capacity Factor dependent on Unit Weight))/Factor of Safety)+(Unit Weight of Soil*Depth of Footing)

Factor of Safety given Depth and Width of Footing

Go Factor of Safety = ((Cohesion of Soil*Bearing Capacity Factor dependent on Cohesion)+((Unit Weight of Soil*Depth of Footing)*(Bearing Capacity Factor dependent on Surcharge-1))+(0.5*Unit Weight of Soil*Width of Footing*Bearing Capacity Factor dependent on Unit Weight))/(Safe Bearing Capacity-(Unit Weight of Soil*Depth of Footing))

Unit Weight of Soil given Safe Bearing Capacity

Go Unit Weight of Soil = (((Safe Bearing Capacity*Factor of Safety)-(Factor of Safety*Effective Surcharge in KiloPascal))-((Cohesion in Soil as Kilopascal*Bearing Capacity Factor dependent on Cohesion)+(Effective Surcharge in KiloPascal*(Bearing Capacity Factor dependent on Surcharge-1))))/(0.5*Width of Footing*Bearing Capacity Factor dependent on Unit Weight)

Width of Footing given Safe Bearing Capacity

Go Width of Footing = (((Safe Bearing Capacity*Factor of Safety)-(Factor of Safety*Effective Surcharge in KiloPascal))-((Cohesion in Soil as Kilopascal*Bearing Capacity Factor dependent on Cohesion)+(Effective Surcharge in KiloPascal*(Bearing Capacity Factor dependent on Surcharge-1))))/(0.5*Unit Weight of Soil*Bearing Capacity Factor dependent on Unit Weight)

Cohesion of Soil given Safe Bearing Capacity

Go Cohesion of Soil = (((Safe Bearing Capacity*Factor of Safety)-(Factor of Safety*Effective Surcharge))-((Effective Surcharge in KiloPascal*(Bearing Capacity Factor dependent on Surcharge-1))+(0.5*Unit Weight of Soil*Width of Footing*Bearing Capacity Factor dependent on Unit Weight)))/Bearing Capacity Factor dependent on Cohesion

Safe Bearing Capacity given Bearing Capacity Factor

Go Safe Bearing Capacity = (((Cohesion of Soil*Bearing Capacity Factor dependent on Cohesion)+(Effective Surcharge in KiloPascal*(Bearing Capacity Factor dependent on Surcharge-1))+(0.5*Unit Weight of Soil*Width of Footing*Bearing Capacity Factor dependent on Unit Weight))/Factor of Safety)+Effective Surcharge in KiloPascal

Factor of Safety given Bearing Capacity Factor

Go Factor of Safety = ((Cohesion of Soil*Bearing Capacity Factor dependent on Cohesion)+(Effective Surcharge in KiloPascal*(Bearing Capacity Factor dependent on Surcharge-1))+(0.5*Unit Weight of Soil*Width of Footing*Bearing Capacity Factor dependent on Unit Weight))/(Safe Bearing Capacity-Effective Surcharge in KiloPascal)

Effective Surcharge given Safe Bearing Capacity

Go Effective Surcharge in KiloPascal = ((Safe Bearing Capacity*Factor of Safety)-((Cohesion of Soil*Bearing Capacity Factor dependent on Cohesion)+(0.5*Unit Weight of Soil*Width of Footing*Bearing Capacity Factor dependent on Unit Weight)))/(Factor of Safety+Bearing Capacity Factor dependent on Surcharge-1)

Depth of Footing given Factor of Safety and Safe Bearing Capacity

Go Depth of Footing = ((Safe Bearing Capacity*Factor of Safety)-((Cohesion of Soil*Bearing Capacity Factor dependent on Cohesion)+(0.5*Unit Weight of Soil*Width of Footing*Bearing Capacity Factor dependent on Unit Weight)))/(Unit Weight of Soil*Bearing Capacity Factor dependent on Surcharge)

Width of Footing given Ultimate Bearing Capacity

Go Width of Footing = (Ultimate Bearing Capacity in Soil-((Cohesion in Soil as Kilopascal*Bearing Capacity Factor dependent on Cohesion)+(Unit Weight of Soil*Depth of Footing in Soil*Bearing Capacity Factor dependent on Surcharge)))/(0.5*Unit Weight of Soil*Bearing Capacity Factor dependent on Unit Weight)

Depth of Footing given Bearing Capacity Factor

Go Depth of Footing in Soil = (Ultimate Bearing Capacity in Soil-((Cohesion in Soil as Kilopascal*Bearing Capacity Factor dependent on Cohesion)+(0.5*Unit Weight of Soil*Width of Footing*Bearing Capacity Factor dependent on Unit Weight)))/(Unit Weight of Soil*Bearing Capacity Factor dependent on Surcharge)

Cohesion of Soil given Depth and Width of Footing

Go Cohesion in Soil as Kilopascal = (Ultimate Bearing Capacity in Soil-((Unit Weight of Soil*Depth of Footing in Soil*Bearing Capacity Factor dependent on Surcharge)+(0.5*Unit Weight of Soil*Width of Footing*Bearing Capacity Factor dependent on Unit Weight)))/Bearing Capacity Factor dependent on Cohesion

Depth of Footing given Bearing Capacity Factor and Width of Footing

Go Depth of Footing = (Net Ultimate Bearing Capacity-((Cohesion of Soil*Bearing Capacity Factor dependent on Cohesion)+(0.5*Unit Weight of Soil*Width of Footing*Bearing Capacity Factor dependent on Unit Weight)))/(Unit Weight of Soil* (Bearing Capacity Factor dependent on Surcharge-1))

Width of Footing given Bearing Capacity Factor and Depth of Footing

Go Width of Footing = (Net Ultimate Bearing Capacity-((Cohesion of Soil*Bearing Capacity Factor dependent on Cohesion)+((Unit Weight of Soil*Depth of Footing)*(Bearing Capacity Factor dependent on Surcharge-1))))/(0.5*Unit Weight of Soil*Bearing Capacity Factor dependent on Unit Weight)

Net Ultimate Bearing Capacity given Depth and Width of Footing

Go Net Ultimate Bearing Capacity = ((Cohesion of Soil*Bearing Capacity Factor dependent on Cohesion)+((Unit Weight of Soil*Depth of Footing)*(Bearing Capacity Factor dependent on Surcharge-1))+(0.5*Unit Weight of Soil*Width of Footing*Bearing Capacity Factor dependent on Unit Weight))

Unit Weight of Soil given Factor of Safety and Safe Bearing Capacity

Go Unit Weight of Soil = ((Safe Bearing Capacity*Factor of Safety)-((Cohesion of Soil*Bearing Capacity Factor dependent on Cohesion)))/((Bearing Capacity Factor dependent on Surcharge*Depth of Footing)+(0.5*Width of Footing*Bearing Capacity Factor dependent on Unit Weight))

Ultimate Bearing Capacity given Bearing Capacity Factor

Go Ultimate Bearing Capacity = (Cohesion of Soil*Bearing Capacity Factor dependent on Cohesion)+(Unit Weight of Soil*Depth of Footing*Bearing Capacity Factor dependent on Surcharge)+(0.5*Unit Weight of Soil*Width of Footing*Bearing Capacity Factor dependent on Unit Weight)

Unit Weight of Soil given Net Ultimate Bearing Capacity

Go Unit Weight of Soil = (Net Ultimate Bearing Capacity-((Cohesion of Soil*Bearing Capacity Factor dependent on Cohesion)+(Effective Surcharge in KiloPascal*(Bearing Capacity Factor dependent on Surcharge-1))))/(0.5*Width of Footing*Bearing Capacity Factor dependent on Unit Weight)

Width of Footing given Effective Surcharge

Go Width of Footing = (Net Ultimate Bearing Capacity-((Cohesion of Soil*Bearing Capacity Factor dependent on Cohesion)+(Effective Surcharge in KiloPascal*(Bearing Capacity Factor dependent on Surcharge-1))))/(0.5*Unit Weight of Soil*Bearing Capacity Factor dependent on Unit Weight)

Cohesion of Soil given Net Ultimate Bearing Capacity

Go Cohesion of Soil = (Net Ultimate Bearing Capacity-((Effective Surcharge in KiloPascal*(Bearing Capacity Factor dependent on Surcharge-1))+(0.5*Unit Weight of Soil*Width of Footing*Bearing Capacity Factor dependent on Unit Weight)))/Bearing Capacity Factor dependent on Cohesion

Effective Surcharge given Bearing Capacity Factor

Go Effective Surcharge in KiloPascal = (Net Ultimate Bearing Capacity-((Cohesion of Soil*Bearing Capacity Factor dependent on Cohesion)+(0.5*Unit Weight of Soil*Width of Footing*Bearing Capacity Factor dependent on Unit Weight)))/(Bearing Capacity Factor dependent on Surcharge-1)

Net Ultimate Bearing Capacity given Bearing Capacity Factor

Go Net Ultimate Bearing Capacity = (Cohesion of Soil*Bearing Capacity Factor dependent on Cohesion)+(Effective Surcharge in KiloPascal*(Bearing Capacity Factor dependent on Surcharge-1))+(0.5*Unit Weight of Soil*Width of Footing*Bearing Capacity Factor dependent on Unit Weight)

Unit Weight of Soil given Bearing Capacity Factor, Depth and Width of Footing

Go Unit Weight of Soil = (Net Ultimate Bearing Capacity-(Cohesion of Soil*Bearing Capacity Factor dependent on Cohesion))/((0.5*Width of Footing*Bearing Capacity Factor dependent on Unit Weight)+(Depth of Footing*(Bearing Capacity Factor dependent on Surcharge-1)))

Unit Weight of Soil given Depth and Width of Footing

Go Unit Weight of Soil = (Ultimate Bearing Capacity-(Cohesion of Soil*Bearing Capacity Factor dependent on Cohesion))/((Depth of Footing*Bearing Capacity Factor dependent on Surcharge)+(0.5*Width of Footing*Bearing Capacity Factor dependent on Unit Weight))

Unit Weight of Soil given Bearing Capacity Factor, Depth and Width of Footing Formula

What is Unit Weight of Soil?

Unit weight of the soil is the total weight of the soil divided by total volume. Total weight of soil also includes weight of water. Total volume occupied includes the volume of water as well as the volume of air along with the soil volume.

How to Calculate Unit Weight of Soil given Bearing Capacity Factor, Depth and Width of Footing?

Unit Weight of Soil given Bearing Capacity Factor, Depth and Width of Footing calculator uses Unit Weight of Soil = (Net Ultimate Bearing Capacity-(Cohesion of Soil*Bearing Capacity Factor dependent on Cohesion))/((0.5*Width of Footing*Bearing Capacity Factor dependent on Unit Weight)+(Depth of Footing*(Bearing Capacity Factor dependent on Surcharge-1))) to calculate the Unit Weight of Soil, The Unit Weight of Soil given Bearing Capacity Factor, Depth and Width of Footing is defined as the weight per unit volume, determined by bearing capacity factor, depth, and width of the footing. Unit Weight of Soil is denoted by γ symbol.

How to calculate Unit Weight of Soil given Bearing Capacity Factor, Depth and Width of Footing using this online calculator? To use this online calculator for Unit Weight of Soil given Bearing Capacity Factor, Depth and Width of Footing, enter Net Ultimate Bearing Capacity (q_nf), Cohesion of Soil (C_s), Bearing Capacity Factor dependent on Cohesion (N_c), Width of Footing (B), Bearing Capacity Factor dependent on Unit Weight (N_γ), Depth of Footing (D) & Bearing Capacity Factor dependent on Surcharge (N_q) and hit the calculate button. Here is how the Unit Weight of Soil given Bearing Capacity Factor, Depth and Width of Footing calculation can be explained with given input values -> 4E-5 = (150000-(5000*9))/((0.5*2*1.6)+(1.01*(2.01-1))).

FAQ

What is Unit Weight of Soil given Bearing Capacity Factor, Depth and Width of Footing?

The Unit Weight of Soil given Bearing Capacity Factor, Depth and Width of Footing is defined as the weight per unit volume, determined by bearing capacity factor, depth, and width of the footing and is represented as γ = (q_nf-(C_s*N_c))/((0.5*B*N_γ)+(D*(N_q-1))) or Unit Weight of Soil = (Net Ultimate Bearing Capacity-(Cohesion of Soil*Bearing Capacity Factor dependent on Cohesion))/((0.5*Width of Footing*Bearing Capacity Factor dependent on Unit Weight)+(Depth of Footing*(Bearing Capacity Factor dependent on Surcharge-1))). Net Ultimate Bearing Capacity is the minimum net pressure intensity causing shear failure, Cohesion of Soil is the ability of like particles within soil to hold onto each other. It is the shear strength or force that binds together like particles in the structure of a soil, Bearing Capacity Factor dependent on Cohesion is a constant whose value depends upon the cohesion of soil, Width of Footing is the shorter dimension of the footing, Bearing Capacity Factor dependent on Unit Weight is a constant whose value depends upon unit weight of soil, Depth of Footing is the longer dimension of the footing & Bearing Capacity Factor dependent on Surcharge is a constant whose value depends upon surcharge.

How to calculate Unit Weight of Soil given Bearing Capacity Factor, Depth and Width of Footing?

The Unit Weight of Soil given Bearing Capacity Factor, Depth and Width of Footing is defined as the weight per unit volume, determined by bearing capacity factor, depth, and width of the footing is calculated using Unit Weight of Soil = (Net Ultimate Bearing Capacity-(Cohesion of Soil*Bearing Capacity Factor dependent on Cohesion))/((0.5*Width of Footing*Bearing Capacity Factor dependent on Unit Weight)+(Depth of Footing*(Bearing Capacity Factor dependent on Surcharge-1))). To calculate Unit Weight of Soil given Bearing Capacity Factor, Depth and Width of Footing, you need Net Ultimate Bearing Capacity (q_nf), Cohesion of Soil (C_s), Bearing Capacity Factor dependent on Cohesion (N_c), Width of Footing (B), Bearing Capacity Factor dependent on Unit Weight (N_γ), Depth of Footing (D) & Bearing Capacity Factor dependent on Surcharge (N_q). With our tool, you need to enter the respective value for Net Ultimate Bearing Capacity, Cohesion of Soil, Bearing Capacity Factor dependent on Cohesion, Width of Footing, Bearing Capacity Factor dependent on Unit Weight, Depth of Footing & Bearing Capacity Factor dependent on Surcharge and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

How many ways are there to calculate Unit Weight of Soil?

In this formula, Unit Weight of Soil uses Net Ultimate Bearing Capacity, Cohesion of Soil, Bearing Capacity Factor dependent on Cohesion, Width of Footing, Bearing Capacity Factor dependent on Unit Weight, Depth of Footing & Bearing Capacity Factor dependent on Surcharge. We can use 4 other way(s) to calculate the same, which is/are as follows -

Unit Weight of Soil = (Ultimate Bearing Capacity-(Cohesion of Soil*Bearing Capacity Factor dependent on Cohesion))/((Depth of Footing*Bearing Capacity Factor dependent on Surcharge)+(0.5*Width of Footing*Bearing Capacity Factor dependent on Unit Weight))
Unit Weight of Soil = (Net Ultimate Bearing Capacity-((Cohesion of Soil*Bearing Capacity Factor dependent on Cohesion)+(Effective Surcharge in KiloPascal*(Bearing Capacity Factor dependent on Surcharge-1))))/(0.5*Width of Footing*Bearing Capacity Factor dependent on Unit Weight)
Unit Weight of Soil = (((Safe Bearing Capacity*Factor of Safety)-(Factor of Safety*Effective Surcharge in KiloPascal))-((Cohesion in Soil as Kilopascal*Bearing Capacity Factor dependent on Cohesion)+(Effective Surcharge in KiloPascal*(Bearing Capacity Factor dependent on Surcharge-1))))/(0.5*Width of Footing*Bearing Capacity Factor dependent on Unit Weight)
Unit Weight of Soil = ((Safe Bearing Capacity*Factor of Safety)-((Cohesion of Soil*Bearing Capacity Factor dependent on Cohesion)))/((Bearing Capacity Factor dependent on Surcharge*Depth of Footing)+(0.5*Width of Footing*Bearing Capacity Factor dependent on Unit Weight))

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