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 is the angle measured between the normal force and resultant force .ⓘ Angle of Internal Friction [φ]			+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 defined as the ratio of the horizontal to vertical stress.ⓘ Coefficient of Passive Pressure [K_P]			+10% -10%

✖The 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"} = (("C"/tan("φ"))+(0.5*"γ"_{"d"}*"B"*sqrt("K"_{"P"}))*("K"_{"P"}*exp(pi*tan("φ"))-1))`

Example

`"119.3385kPa"=(("3kgf/m²"/tan("46°"))+(0.5*"95kN/m³"*"2m"*sqrt("0.16"))*("0.16"*exp(pi*tan("46°"))-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))+(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))-1))
q_f = ((C/tan(φ))+(0.5*γ_d*B*sqrt(K_P))*(K_P*exp(pi*tan(φ))-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) - The 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 - (Measured in Radian) - Angle of Internal Friction is the angle measured between the normal force and resultant force .
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 defined as the ratio of the horizontal to vertical stress.

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: 46 Degree --> 0.802851455917241 Radian (Check conversion here)
Dry Unit Weight of Soil: 95 Kilonewton per Cubic Meter --> 95000 Newton per Cubic Meter (Check conversion here)
Width of Footing: 2 Meter --> 2 Meter No Conversion Required
Coefficient of Passive Pressure: 0.16 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

q_f = ((C/tan(φ))+(0.5*γ_d*B*sqrt(K_P))*(K_P*exp(pi*tan(φ))-1)) --> ((29.4199499999979/tan(0.802851455917241))+(0.5*95000*2*sqrt(0.16))*(0.16*exp(pi*tan(0.802851455917241))-1))

Evaluating ... ...

q_f = 119338.527163501

STEP 3: Convert Result to Output's Unit

119338.527163501 Pascal -->119.338527163501 Kilopascal (Check conversion here)

FINAL ANSWER

119.338527163501 ≈ 119.3385 Kilopascal <-- Ultimate Bearing Capacity

(Calculation completed in 00.004 seconds)

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Created by Suraj Kumar

Birsa Institute of Technology (BIT), Sindri

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< 16 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))+(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))-1))

Safe Bearing Capacity given Net Ultimate Bearing Capacity

Go Safe Bearing Capacity = (Net Ultimate Bearing Capacity in Soil/Factor of Safety in Bearing Capacity of Soil)+(Unit Weight of Soil*Depth of Footing in Soil)

Bearing Capacity Factor Dependent on Unit Weight by Vesic's Analysis

Go Bearing Capacity Factor dependent on Unit Weight = 2*(Bearing Capacity Factor dependent on Surcharge+1)*tan((Angle of Internal Friction of Soil*pi)/180)

Net Safe Bearing Capacity given Ultimate Bearing Capacity

Go Net Safe Bearing Capacity in Soil = (Ultimate Bearing Capacity in Soil-Effective Surcharge in KiloPascal)/Factor of Safety in Bearing Capacity of Soil

Ultimate Bearing Capacity given Factor of Safety

Go Ultimate Bearing Capacity = (Net Safe Bearing Capacity in Soil*Factor of Safety in Bearing Capacity of Soil)+Effective Surcharge in KiloPascal

Angle of Internal Friction given Bearing Capacity by by Vesic's Analysis

Go Angle of Internal Friction = atan(Bearing Capacity Factor dependent on Unit Weight/(2*(Bearing Capacity Factor dependent on Surcharge+1)))

Ultimate Bearing Capacity given Depth of Footing

Go Ultimate Bearing Capacity = Net Ultimate Bearing Capacity in Soil+(Unit Weight of Soil*Depth of Footing in Soil)

Safe Bearing Capacity

Go Safe Bearing Capacity = Net Safe Bearing Capacity in Soil+(Unit Weight of Soil*Depth of Footing in Soil)

Depth of Footing given Safe Bearing Capacity

Go Depth of Footing = (Safe Bearing Capacity-Net Safe Bearing Capacity in Soil)/Unit Weight of Soil

Net Ultimate Bearing Capacity given Net Safe Bearing Capacity

Go Net Ultimate Bearing Capacity in Soil = Net Safe Bearing Capacity in Soil*Factor of Safety in Bearing Capacity of Soil

Net Safe Bearing Capacity

Go Net Safe Bearing Capacity in Soil = Net Ultimate Bearing Capacity in Soil/Factor of Safety in Bearing Capacity of Soil

Net Ultimate Bearing Capacity given Ultimate Bearing Capacity

Go Net Ultimate Bearing Capacity in Soil = Ultimate Bearing Capacity in Soil-Effective Surcharge in KiloPascal

Ultimate Bearing Capacity

Go Ultimate Bearing Capacity = Net Ultimate Bearing Capacity in Soil+Effective Surcharge in KiloPascal

Effective Surcharge given Depth of Footing

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

Effective Surcharge given Net Pressure Intensity

Go Effective Surcharge in KiloPascal = Gross Pressure-Net Pressure

Net Pressure Intensity

Go Net Pressure = Gross Pressure-Effective Surcharge in KiloPascal

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))+(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))-1)) to calculate the Ultimate Bearing Capacity, The Ultimate Bearing Capacity of Soil under Long Footing at Surface of Soil is defined as the capacity of soil to support the loads applied to the ground. 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 (φ), 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 -> 0.119339 = ((29.4199499999979/tan(0.802851455917241))+(0.5*95000*2*sqrt(0.16))*(0.16*exp(pi*tan(0.802851455917241))-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 is defined as the capacity of soil to support the loads applied to the ground and is represented as q_f = ((C/tan(φ))+(0.5*γ_d*B*sqrt(K_P))*(K_P*exp(pi*tan(φ))-1)) or Ultimate Bearing Capacity = ((Prandtls Cohesion/tan(Angle of Internal Friction))+(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))-1)). Prandtls Cohesion is the component of shear strength of a rock or soil that is independent of interparticle friction, Angle of Internal Friction is the angle measured between the normal force and resultant force , 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 defined as the ratio of the horizontal to vertical stress.

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 is defined as the capacity of soil to support the loads applied to the ground is calculated using Ultimate Bearing Capacity = ((Prandtls Cohesion/tan(Angle of Internal Friction))+(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))-1)). To calculate Ultimate Bearing Capacity of Soil under Long Footing at Surface of Soil, you need Prandtls Cohesion (C), Angle of Internal Friction (φ), 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, 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, Dry Unit Weight of Soil, Width of Footing & Coefficient of Passive Pressure. We can use 3 other way(s) to calculate the same, which is/are as follows -

Ultimate Bearing Capacity = Net Ultimate Bearing Capacity in Soil+Effective Surcharge in KiloPascal
Ultimate Bearing Capacity = Net Ultimate Bearing Capacity in Soil+(Unit Weight of Soil*Depth of Footing in Soil)
Ultimate Bearing Capacity = (Net Safe Bearing Capacity in Soil*Factor of Safety in Bearing Capacity of Soil)+Effective Surcharge in KiloPascal

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