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Depth of Footing given Factor of Safety and Safe Bearing Capacity Formula

GoDepth of Footing given Bearing Capacity Factor and Width of Footing Formula

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Depth of Footing is the longer dimension of the footing. Check FAQs

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

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

Depth of Footing given Factor of Safety and Safe Bearing Capacity Example

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Here is how the Depth of Footing given Factor of Safety and Safe Bearing Capacity equation looks like with Values.

Here is how the Depth of Footing given Factor of Safety and Safe Bearing Capacity equation looks like with Units.

Here is how the Depth of Footing given Factor of Safety and Safe Bearing Capacity equation looks like.

3.3776 = \frac{(70 \cdot 2.8) - ((5 \cdot 9) + (0.5 \cdot 18 \cdot 2 \cdot 1.6))}{18 \cdot 2.01}

3.3776m = \frac{(70kN/m² \cdot 2.8) - ((5kPa \cdot 9) + (0.5 \cdot 18kN/m³ \cdot 2m \cdot 1.6))}{18kN/m³ \cdot 2.01}

3.3776 = \frac{(70 \cdot 2.8) - ((5 \cdot 9) + (0.5 \cdot 18 \cdot 2 \cdot 1.6))}{18 \cdot 2.01}

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Depth of Footing given Factor of Safety and Safe Bearing Capacity Solution

Follow our step by step solution on how to calculate Depth of Footing given Factor of Safety and Safe Bearing Capacity?

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

D = \frac{(70kN/m² \cdot 2.8) - ((5kPa \cdot 9) + (0.5 \cdot 18kN/m³ \cdot 2m \cdot 1.6))}{18kN/m³ \cdot 2.01}

Next Step Convert Units

∴

D = \frac{(70000Pa \cdot 2.8) - ((5000Pa \cdot 9) + (0.5 \cdot 18000N/m³ \cdot 2m \cdot 1.6))}{18000N/m³ \cdot 2.01}

Next Step Prepare to Evaluate

∴

D = \frac{(70000 \cdot 2.8) - ((5000 \cdot 9) + (0.5 \cdot 18000 \cdot 2 \cdot 1.6))}{18000 \cdot 2.01}

Next Step Evaluate

∴

D = 3.37755666113875m

LAST Step Rounding Answer

∴

D = 3.3776m

Depth of Footing given Factor of Safety and Safe Bearing Capacity Formula Elements

Variables

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

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

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

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

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

Other Formulas to find Depth of Footing

Go Depth of Footing given Bearing Capacity Factor and Width of Footing

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

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 Depth of Footing given Factor of Safety and Safe Bearing Capacity?

Depth of Footing given Factor of Safety and Safe Bearing Capacity evaluator uses 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) to evaluate the Depth of Footing, The Depth of Footing given Factor of Safety and Safe Bearing Capacity is defined as the safe bearing capacity by the factor of safety for stability. Depth of Footing is denoted by D symbol.

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

FAQs on Depth of Footing given Factor of Safety and Safe Bearing Capacity

What is the formula to find Depth of Footing given Factor of Safety and Safe Bearing Capacity?

The formula of Depth of Footing given Factor of Safety and Safe Bearing Capacity is expressed as 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). Here is an example- 3.394444 = ((70000*2.8)-((5000*9)+(0.5*18000*2*1.6)))/(18000*2.01).

How to calculate Depth of Footing 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), Unit Weight of Soil (γ), Width of Footing (B), Bearing Capacity Factor dependent on Unit Weight (N_γ) & Bearing Capacity Factor dependent on Surcharge (N_q) we can find Depth of Footing given Factor of Safety and Safe Bearing Capacity using the formula - 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).

What are the other ways to Calculate Depth of Footing?

Here are the different ways to Calculate Depth of Footing-

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))

Can the Depth of Footing given Factor of Safety and Safe Bearing Capacity be negative?

No, the Depth of Footing given Factor of Safety and Safe Bearing Capacity, measured in Length cannot be negative.

Which unit is used to measure Depth of Footing given Factor of Safety and Safe Bearing Capacity?

Depth of Footing given Factor of Safety and Safe Bearing Capacity is usually measured using the Meter[m] for Length. Millimeter[m], Kilometer[m], Decimeter[m] are the few other units in which Depth of Footing given Factor of Safety and Safe Bearing Capacity can be measured.

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Depth of Footing given Factor of Safety and Safe Bearing Capacity Formula

​GoDepth of Footing given Bearing Capacity Factor and Width of Footing Formula

Depth of Footing given Factor of Safety and Safe Bearing Capacity Example

Depth of Footing given Factor of Safety and Safe Bearing Capacity Solution

Depth of Footing given Factor of Safety and Safe Bearing Capacity Formula Elements

Other Formulas to find Depth of Footing

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

How to Evaluate Depth of Footing given Factor of Safety and Safe Bearing Capacity?

FAQs on Depth of Footing given Factor of Safety and Safe Bearing Capacity

Variable Name

GoDepth of Footing given Bearing Capacity Factor and Width of Footing Formula