Ultimate Bearing Capacity of Soil under Long Footing at Surface of Soil Calculator

✖Prandtls Cohesion is the component of shear strength of a rock or soil that is independent of interparticle friction.ⓘ Prandtls Cohesion [C]			+10% -10%
✖Angle of Internal Friction of Soil is a measure of the soil's resistance to shear stress. It represents the angle at which soil particles resist sliding over each other.ⓘ Angle of Internal Friction of Soil [Φ_i]			+10% -10%
✖The Dry Unit Weight of Soil is the weight of soil solids per unit of total volume of soil mass.ⓘ Dry Unit Weight of Soil [γ_d]			+10% -10%
✖Width of Footing is the shorter dimension of the footing.ⓘ Width of Footing [B]			+10% -10%
✖Coefficient of Passive Pressure is the ratio of lateral earth pressure exerted by soil when it is in a passive state, meaning the soil is being pushed or compacted laterally.ⓘ Coefficient of Passive Pressure [K_P]			+10% -10%

✖Ultimate Bearing Capacity is defined as the minimum gross pressure intensity at the base of the foundation at which the soil fails in shear.ⓘ Ultimate Bearing Capacity of Soil under Long Footing at Surface of Soil [q_f]

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Formula

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Ultimate Bearing Capacity of Soil under Long Footing at Surface of Soil

Formula

q f = ((\frac{C}{\tan (Φ i)}) + (0.5 \cdot γ d \cdot B \cdot \sqrt{K P}) \cdot (K P \cdot \exp (π \cdot \tan (Φ i)) - 1))

Example

60.65884 kPa = ((\frac{3 kgf/m²}{\tan (82.87 °)}) + (0.5 \cdot 0.073 kN/m³ \cdot 0.23 m \cdot \sqrt{2E-5}) \cdot (2E-5 \cdot \exp (π \cdot \tan (82.87 °)) - 1))

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Ultimate Bearing Capacity of Soil under Long Footing at Surface of Soil Solution

STEP 0: Pre-Calculation Summary

Formula Used

Ultimate Bearing Capacity = ((Prandtls Cohesion/tan(Angle of Internal Friction of Soil))+(0.5*Dry Unit Weight of Soil*Width of Footing*sqrt(Coefficient of Passive Pressure))*(Coefficient of Passive Pressure*exp(pi*tan(Angle of Internal Friction of Soil))-1))
q_f = ((C/tan(Φ_i))+(0.5*γ_d*B*sqrt(K_P))*(K_P*exp(pi*tan(Φ_i))-1))
This formula uses 1 Constants, 3 Functions, 6 Variables

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Functions Used

tan - The tangent of an angle is a trigonometric ratio of the length of the side opposite an angle to the length of the side adjacent to an angle in a right triangle., tan(Angle)
exp - n an exponential function, the value of the function changes by a constant factor for every unit change in the independent variable., exp(Number)
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., sqrt(Number)

Variables Used

Ultimate Bearing Capacity - (Measured in Pascal) - Ultimate Bearing Capacity is defined as the minimum gross pressure intensity at the base of the foundation at which the soil fails in shear.
Prandtls Cohesion - (Measured in Pascal) - Prandtls Cohesion is the component of shear strength of a rock or soil that is independent of interparticle friction.
Angle of Internal Friction of Soil - (Measured in Radian) - Angle of Internal Friction of Soil is a measure of the soil's resistance to shear stress. It represents the angle at which soil particles resist sliding over each other.
Dry Unit Weight of Soil - (Measured in Newton per Cubic Meter) - The Dry Unit Weight of Soil is the weight of soil solids per unit of total volume of soil mass.
Width of Footing - (Measured in Meter) - Width of Footing is the shorter dimension of the footing.
Coefficient of Passive Pressure - Coefficient of Passive Pressure is the ratio of lateral earth pressure exerted by soil when it is in a passive state, meaning the soil is being pushed or compacted laterally.

STEP 1: Convert Input(s) to Base Unit

Prandtls Cohesion: 3 Kilogram-Force per Square Meter --> 29.4199499999979 Pascal (Check conversion here)
Angle of Internal Friction of Soil: 82.87 Degree --> 1.44635435112743 Radian (Check conversion here)
Dry Unit Weight of Soil: 0.073 Kilonewton per Cubic Meter --> 73 Newton per Cubic Meter (Check conversion here)
Width of Footing: 0.23 Meter --> 0.23 Meter No Conversion Required
Coefficient of Passive Pressure: 2E-05 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

q_f = ((C/tan(Φ_i))+(0.5*γ_d*B*sqrt(K_P))*(K_P*exp(pi*tan(Φ_i))-1)) --> ((29.4199499999979/tan(1.44635435112743))+(0.5*73*0.23*sqrt(2E-05))*(2E-05*exp(pi*tan(1.44635435112743))-1))

Evaluating ... ...

q_f = 60658.8391394019

STEP 3: Convert Result to Output's Unit

60658.8391394019 Pascal -->60.6588391394019 Kilopascal (Check conversion here)

FINAL ANSWER

60.6588391394019 ≈ 60.65884 Kilopascal <-- Ultimate Bearing Capacity

(Calculation completed in 00.004 seconds)

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Home » Engineering » Civil » Geotechnical Engineering » Bearing Capacity of Soils » Ultimate Bearing Capacity of Soil under Long Footing at Surface of Soil

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Birsa Institute of Technology (BIT), Sindri

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< Bearing Capacity of Soils Calculators

Ultimate Bearing Capacity of Soil under Long Footing at Surface of Soil

Go Ultimate Bearing Capacity = ((Prandtls Cohesion/tan(Angle of Internal Friction of Soil))+(0.5*Dry Unit Weight of Soil*Width of Footing*sqrt(Coefficient of Passive Pressure))*(Coefficient of Passive Pressure*exp(pi*tan(Angle of Internal Friction of Soil))-1))

Net Ultimate Bearing Capacity given Ultimate Bearing Capacity

Go Net Ultimate Bearing Capacity of Soil = Ultimate Bearing Capacity-Effective Surcharge in Kilo Pascal

Ultimate Bearing Capacity

Go Ultimate Bearing Capacity = Net Ultimate Bearing Capacity of Soil+Effective Surcharge in Kilo Pascal

Effective Surcharge given Depth of Footing

Go Effective Surcharge in Kilo Pascal = Unit Weight of Soil*Depth of Footing

Ultimate Bearing Capacity of Soil under Long Footing at Surface of Soil Formula

What is Bearing Capacity of Soil?

In geotechnical engineering, bearing capacity is the capacity of soil to support the loads applied to the ground. The bearing capacity of soil is the maximum average contact pressure between the foundation and the soil which should not produce shear failure in the soil.

How to Calculate Ultimate Bearing Capacity of Soil under Long Footing at Surface of Soil?

Ultimate Bearing Capacity of Soil under Long Footing at Surface of Soil calculator uses Ultimate Bearing Capacity = ((Prandtls Cohesion/tan(Angle of Internal Friction of Soil))+(0.5*Dry Unit Weight of Soil*Width of Footing*sqrt(Coefficient of Passive Pressure))*(Coefficient of Passive Pressure*exp(pi*tan(Angle of Internal Friction of Soil))-1)) to calculate the Ultimate Bearing Capacity, The Ultimate Bearing Capacity of Soil under Long Footing at Surface of Soil formula is defined as the maximum load per unit area that a soil foundation can support without undergoing shear failure. Ultimate Bearing Capacity is denoted by q_f symbol.

How to calculate Ultimate Bearing Capacity of Soil under Long Footing at Surface of Soil using this online calculator? To use this online calculator for Ultimate Bearing Capacity of Soil under Long Footing at Surface of Soil, enter Prandtls Cohesion (C), Angle of Internal Friction of Soil (Φ_i), Dry Unit Weight of Soil (γ_d), Width of Footing (B) & Coefficient of Passive Pressure (K_P) and hit the calculate button. Here is how the Ultimate Bearing Capacity of Soil under Long Footing at Surface of Soil calculation can be explained with given input values -> 0.060659 = ((29.4199499999979/tan(1.44635435112743))+(0.5*73*0.23*sqrt(2E-05))*(2E-05*exp(pi*tan(1.44635435112743))-1)).

FAQ

What is Ultimate Bearing Capacity of Soil under Long Footing at Surface of Soil?

The Ultimate Bearing Capacity of Soil under Long Footing at Surface of Soil formula is defined as the maximum load per unit area that a soil foundation can support without undergoing shear failure and is represented as q_f = ((C/tan(Φ_i))+(0.5*γ_d*B*sqrt(K_P))*(K_P*exp(pi*tan(Φ_i))-1)) or Ultimate Bearing Capacity = ((Prandtls Cohesion/tan(Angle of Internal Friction of Soil))+(0.5*Dry Unit Weight of Soil*Width of Footing*sqrt(Coefficient of Passive Pressure))*(Coefficient of Passive Pressure*exp(pi*tan(Angle of Internal Friction of Soil))-1)). Prandtls Cohesion is the component of shear strength of a rock or soil that is independent of interparticle friction, Angle of Internal Friction of Soil is a measure of the soil's resistance to shear stress. It represents the angle at which soil particles resist sliding over each other, The Dry Unit Weight of Soil is the weight of soil solids per unit of total volume of soil mass, Width of Footing is the shorter dimension of the footing & Coefficient of Passive Pressure is the ratio of lateral earth pressure exerted by soil when it is in a passive state, meaning the soil is being pushed or compacted laterally.

How to calculate Ultimate Bearing Capacity of Soil under Long Footing at Surface of Soil?

The Ultimate Bearing Capacity of Soil under Long Footing at Surface of Soil formula is defined as the maximum load per unit area that a soil foundation can support without undergoing shear failure is calculated using Ultimate Bearing Capacity = ((Prandtls Cohesion/tan(Angle of Internal Friction of Soil))+(0.5*Dry Unit Weight of Soil*Width of Footing*sqrt(Coefficient of Passive Pressure))*(Coefficient of Passive Pressure*exp(pi*tan(Angle of Internal Friction of Soil))-1)). To calculate Ultimate Bearing Capacity of Soil under Long Footing at Surface of Soil, you need Prandtls Cohesion (C), Angle of Internal Friction of Soil (Φ_i), Dry Unit Weight of Soil (γ_d), Width of Footing (B) & Coefficient of Passive Pressure (K_P). With our tool, you need to enter the respective value for Prandtls Cohesion, Angle of Internal Friction of Soil, Dry Unit Weight of Soil, Width of Footing & Coefficient of Passive Pressure 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 Ultimate Bearing Capacity?

In this formula, Ultimate Bearing Capacity uses Prandtls Cohesion, Angle of Internal Friction of Soil, Dry Unit Weight of Soil, Width of Footing & Coefficient of Passive Pressure. We can use 2 other way(s) to calculate the same, which is/are as follows -

Ultimate Bearing Capacity = Net Ultimate Bearing Capacity of Soil+Effective Surcharge in Kilo Pascal
Ultimate Bearing Capacity = Net Ultimate Bearing Capacity+(Unit Weight of Soil*Depth of Footing in Soil)

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