Factor of Safety given Depth and Width of Footing Calculator

✖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%
✖Unit Weight of Soil mass is the ratio of the total weight of soil to the total volume of soil.ⓘ Unit Weight of Soil [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%
✖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%
✖Safe Bearing Capacity is the maximum pressure which the soil can carry safely without risk of shear failure.ⓘ Safe Bearing Capacity [q_sa]			+10% -10%

✖Factor of Safety expresses how much stronger a system is than it needs to be for an intended load.ⓘ Factor of Safety given Depth and Width of Footing [f_s]

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Factor of Safety given Depth and Width of Footing Solution

STEP 0: Pre-Calculation Summary

Formula Used

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))
f_s = ((C_s*N_c)+((γ*D)*(N_q-1))+(0.5*γ*B*N_γ))/(q_sa-(γ*D))
This formula uses 9 Variables

Variables Used

Factor of Safety - Factor of Safety expresses how much stronger a system is than it needs to be for an intended load.
Cohesion of Soil - (Measured in Pascal) - 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.
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.
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.
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.
Safe Bearing Capacity - (Measured in Pascal) - Safe Bearing Capacity is the maximum pressure which the soil can carry safely without risk of shear failure.

STEP 1: Convert Input(s) to Base Unit

Cohesion of Soil: 5 Kilopascal --> 5000 Pascal (Check conversion here)
Bearing Capacity Factor dependent on Cohesion: 9 --> No Conversion Required
Unit Weight of Soil: 18 Kilonewton per Cubic Meter --> 18000 Newton per Cubic Meter (Check conversion here)
Depth of Footing: 1.01 Meter --> 1.01 Meter No Conversion Required
Bearing Capacity Factor dependent on Surcharge: 2.01 --> 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
Safe Bearing Capacity: 70 Kilonewton per Square Meter --> 70000 Pascal (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

f_s = ((C_s*N_c)+((γ*D)*(N_q-1))+(0.5*γ*B*N_γ))/(q_sa-(γ*D)) --> ((5000*9)+((18000*1.01)*(2.01-1))+(0.5*18000*2*1.6))/(70000-(18000*1.01))

Evaluating ... ...

f_s = 1.7784986491702

STEP 3: Convert Result to Output's Unit

1.7784986491702 --> No Conversion Required

FINAL ANSWER

1.7784986491702 ≈ 1.778499 <-- Factor of Safety

(Calculation completed in 00.004 seconds)

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Home » Engineering » Civil » Geotechnical Engineering » Terzaghi's Analysis Shear Failure Theories » Terzaghi's Analysis in Water Table is Below the Base of Footing » Factor of Safety given Depth and Width of Footing

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

Depth of Footing given Bearing Capacity Factor

LaTeX 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

LaTeX 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

Ultimate Bearing Capacity given Bearing Capacity Factor

LaTeX 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 Depth and Width of Footing

LaTeX 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))

Factor of Safety given Depth and Width of Footing Formula

LaTeX Go

What is Factor of Safety?

The ratio of a structure's absolute strength (structural capability) to actual applied load; this is a measure of the reliability of a particular design.

How to Calculate Factor of Safety given Depth and Width of Footing?

Factor of Safety given Depth and Width of Footing calculator uses 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)) to calculate the Factor of Safety, The Factor of Safety given Depth and Width of Footing is defined as ratio of soil bearing capacity to actual load on footing, ensuring stability and preventing failure. Factor of Safety is denoted by f_s symbol.

How to calculate Factor of Safety given Depth and Width of Footing using this online calculator? To use this online calculator for Factor of Safety given Depth and Width of Footing, enter Cohesion of Soil (C_s), Bearing Capacity Factor dependent on Cohesion (N_c), Unit Weight of Soil (γ), Depth of Footing (D), Bearing Capacity Factor dependent on Surcharge (N_q), Width of Footing (B), Bearing Capacity Factor dependent on Unit Weight (N_γ) & Safe Bearing Capacity (q_sa) and hit the calculate button. Here is how the Factor of Safety given Depth and Width of Footing calculation can be explained with given input values -> 1.77499 = ((5000*9)+((18000*1.01)*(2.01-1))+(0.5*18000*2*1.6))/(70000-(18000*1.01)).

FAQ

What is Factor of Safety given Depth and Width of Footing?

The Factor of Safety given Depth and Width of Footing is defined as ratio of soil bearing capacity to actual load on footing, ensuring stability and preventing failure and is represented as f_s = ((C_s*N_c)+((γ*D)*(N_q-1))+(0.5*γ*B*N_γ))/(q_sa-(γ*D)) or 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)). 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, Unit Weight of Soil mass is the ratio of the total weight of soil to the total volume 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, 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 & Safe Bearing Capacity is the maximum pressure which the soil can carry safely without risk of shear failure.

How to calculate Factor of Safety given Depth and Width of Footing?

The Factor of Safety given Depth and Width of Footing is defined as ratio of soil bearing capacity to actual load on footing, ensuring stability and preventing failure is calculated using 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)). To calculate Factor of Safety given Depth and Width of Footing, you need Cohesion of Soil (C_s), Bearing Capacity Factor dependent on Cohesion (N_c), Unit Weight of Soil (γ), Depth of Footing (D), Bearing Capacity Factor dependent on Surcharge (N_q), Width of Footing (B), Bearing Capacity Factor dependent on Unit Weight (N_γ) & Safe Bearing Capacity (q_sa). With our tool, you need to enter the respective value for Cohesion of Soil, Bearing Capacity Factor dependent on Cohesion, Unit Weight of Soil, Depth of Footing, Bearing Capacity Factor dependent on Surcharge, Width of Footing, Bearing Capacity Factor dependent on Unit Weight & Safe Bearing Capacity 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 Factor of Safety?

In this formula, Factor of Safety uses Cohesion of Soil, Bearing Capacity Factor dependent on Cohesion, Unit Weight of Soil, Depth of Footing, Bearing Capacity Factor dependent on Surcharge, Width of Footing, Bearing Capacity Factor dependent on Unit Weight & Safe Bearing Capacity. We can use 1 other way(s) to calculate the same, which is/are as follows -

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)

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