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

GoUnit Weight of Soil given Depth and Width of Footing Formula

GoUnit Weight of Soil given Net Ultimate Bearing Capacity 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{(q sa \cdot f s) - ((C s \cdot N c))}{(N q \cdot D) + (0.5 \cdot B \cdot N γ)}

γ - Unit Weight of Soil?q_sa - Safe Bearing Capacity?f_s - Factor of Safety?C_s - Cohesion of Soil?N_c - Bearing Capacity Factor dependent on Cohesion?N_q - Bearing Capacity Factor dependent on Surcharge?D - Depth of Footing?B - Width of Footing?N_γ - Bearing Capacity Factor dependent on Unit Weight?

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

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Here is how the Unit Weight of Soil given Factor of Safety and Safe Bearing Capacity equation looks like with Values.

Here is how the Unit Weight of Soil given Factor of Safety and Safe Bearing Capacity equation looks like with Units.

Here is how the Unit Weight of Soil given Factor of Safety and Safe Bearing Capacity equation looks like.

41.5967 = \frac{(70 \cdot 2.8) - ((5 \cdot 9))}{(2.01 \cdot 1.01) + (0.5 \cdot 2 \cdot 1.6)}

41.5967kN/m³ = \frac{(70kN/m² \cdot 2.8) - ((5kPa \cdot 9))}{(2.01 \cdot 1.01m) + (0.5 \cdot 2m \cdot 1.6)}

41.5967 = \frac{(70 \cdot 2.8) - ((5 \cdot 9))}{(2.01 \cdot 1.01) + (0.5 \cdot 2 \cdot 1.6)}

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

Follow our step by step solution on how to calculate Unit Weight of Soil given Factor of Safety and Safe Bearing Capacity?

FIRST Step Consider the formula

γ = \frac{(q sa \cdot f s) - ((C s \cdot N c))}{(N q \cdot D) + (0.5 \cdot B \cdot N γ)}

Next Step Substitute values of Variables

∴

γ = \frac{(70kN/m² \cdot 2.8) - ((5kPa \cdot 9))}{(2.01 \cdot 1.01m) + (0.5 \cdot 2m \cdot 1.6)}

Next Step Convert Units

∴

γ = \frac{(70000Pa \cdot 2.8) - ((5000Pa \cdot 9))}{(2.01 \cdot 1.01m) + (0.5 \cdot 2m \cdot 1.6)}

Next Step Prepare to Evaluate

∴

γ = \frac{(70000 \cdot 2.8) - ((5000 \cdot 9))}{(2.01 \cdot 1.01) + (0.5 \cdot 2 \cdot 1.6)}

Next Step Evaluate

∴

γ = 41596.6502300212N/m³

Next Step Convert to Output's Unit

∴

γ = 41.5966502300212kN/m³

LAST Step Rounding Answer

∴

γ = 41.5967kN/m³

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

Variables

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

Safe Bearing Capacity

Safe Bearing Capacity is the maximum pressure which the soil can carry safely without risk of shear failure.

Symbol: q_sa

Measurement: PressureUnit: kN/m²

Note: Value should be greater than 0.

Formulas to find Safe Bearing Capacity

Factor of Safety

Factor of Safety 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.

Formulas to find Factor of Safety

Cohesion of Soil

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.

Symbol: C_s

Measurement: PressureUnit: kPa

Note: Value should be greater than 0.

Formulas to find Cohesion of Soil

Bearing Capacity Factor dependent on Cohesion

Bearing Capacity Factor dependent on Cohesion is a constant whose value depends upon the cohesion of soil.

Symbol: N_c

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Bearing Capacity Factor dependent on Cohesion

Bearing Capacity Factor dependent on Surcharge

Bearing Capacity Factor dependent on Surcharge is a constant whose value depends upon surcharge.

Symbol: N_q

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Bearing Capacity Factor dependent on Surcharge

Depth of Footing

Depth of Footing is the longer dimension of the footing.

Symbol: D

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Depth of Footing

Width of Footing

Width of Footing is the shorter dimension of the footing.

Symbol: B

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Width of 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.

Symbol: N_γ

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Bearing Capacity Factor dependent on Unit Weight

Other Formulas to find Unit Weight of Soil

Go Unit Weight of Soil given Depth and Width of Footing

γ = \frac{q f - (C s \cdot N c)}{(D \cdot N q) + (0.5 \cdot B \cdot N γ)}

Go Unit Weight of Soil given Net Ultimate Bearing Capacity

γ = \frac{q nf - ((C s \cdot N c) + (σ s \cdot (N q - 1)))}{0.5 \cdot B \cdot N γ}

Other formulas in Terzaghi's Analysis in Water Table is Below the Base of Footing category

Go Ultimate Bearing Capacity given Bearing Capacity Factor

q f = (C s \cdot N c) + (γ \cdot D \cdot N q) + (0.5 \cdot γ \cdot B \cdot N γ)

Go Cohesion of Soil given Depth and Width of Footing

C = \frac{q fc - ((γ \cdot D footing \cdot N q) + (0.5 \cdot γ \cdot B \cdot N γ))}{N c}

How to Evaluate Unit Weight of Soil given Factor of Safety and Safe Bearing Capacity?

Unit Weight of Soil given Factor of Safety and Safe Bearing Capacity evaluator uses 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)) to evaluate the Unit Weight of Soil, The Unit Weight of Soil given Factor of Safety and Safe Bearing Capacity is defined as the weight per unit volume; factor of safety relates to design strength and safe bearing capacity. Unit Weight of Soil is denoted by γ symbol.

How to evaluate Unit Weight of Soil given Factor of Safety and Safe Bearing Capacity using this online evaluator? To use this online evaluator for Unit Weight of Soil given Factor of Safety and Safe Bearing Capacity, enter Safe Bearing Capacity (q_sa), Factor of Safety (f_s), Cohesion of Soil (C_s), Bearing Capacity Factor dependent on Cohesion (N_c), Bearing Capacity Factor dependent on Surcharge (N_q), Depth of Footing (D), Width of Footing (B) & Bearing Capacity Factor dependent on Unit Weight (N_γ) and hit the calculate button.

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

What is the formula to find Unit Weight of Soil given Factor of Safety and Safe Bearing Capacity?

The formula of Unit Weight of Soil given Factor of Safety and Safe Bearing Capacity is expressed as 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)). Here is an example- 0.041713 = ((70000*2.8)-((5000*9)))/((2.01*1.01)+(0.5*2*1.6)).

How to calculate Unit Weight of Soil given Factor of Safety and Safe Bearing Capacity?

With Safe Bearing Capacity (q_sa), Factor of Safety (f_s), Cohesion of Soil (C_s), Bearing Capacity Factor dependent on Cohesion (N_c), Bearing Capacity Factor dependent on Surcharge (N_q), Depth of Footing (D), Width of Footing (B) & Bearing Capacity Factor dependent on Unit Weight (N_γ) we can find Unit Weight of Soil given Factor of Safety and Safe Bearing Capacity using the formula - 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)).

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=(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)

Can the Unit Weight of Soil given Factor of Safety and Safe Bearing Capacity be negative?

No, the Unit Weight of Soil given Factor of Safety and Safe Bearing Capacity, measured in Specific Weight cannot be negative.

Which unit is used to measure Unit Weight of Soil given Factor of Safety and Safe Bearing Capacity?

Unit Weight of Soil given Factor of Safety and Safe Bearing Capacity 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 Factor of Safety and Safe Bearing Capacity can be measured.

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

​GoUnit Weight of Soil given Depth and Width of Footing Formula

​GoUnit Weight of Soil given Net Ultimate Bearing Capacity Formula

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

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

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

Other Formulas to find Unit Weight of Soil

Other formulas in Terzaghi's Analysis in Water Table is Below the Base of Footing category

How to Evaluate Unit Weight of Soil given Factor of Safety and Safe Bearing Capacity?

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

Variable Name

GoUnit Weight of Soil given Depth and Width of Footing Formula

GoUnit Weight of Soil given Net Ultimate Bearing Capacity Formula