Angle of Internal Friction given Shear Strength of Soil Calculator

✖Shear Strength is the strength of a material against structural failure when the material fails in shear.ⓘ Shear Strength [τ_s]			+10% -10%
✖Shear Stress is force tending to cause deformation of a material by slippage along a plane or planes parallel to the imposed stress.ⓘ Shear Stress [𝜏]			+10% -10%
✖Angle of Inclination is defined as the angle measured from the horizontal surface of the wall or any object.ⓘ Angle of Inclination [I]			+10% -10%

✖Angle of Internal Friction of Soil is a shear strength parameter of soils.ⓘ Angle of Internal Friction given Shear Strength of Soil [Φ_i]

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Formula

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Angle of Internal Friction given Shear Strength of Soil

Formula

`"Φ"_{"i"} = atan(("τ"_{"s"}/"𝜏")*tan(("I")))`

Example

`"89.99949°"=atan(("1.2MPa"/"61Pa")*tan(("80°")))`

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Angle of Internal Friction given Shear Strength of Soil Solution

STEP 0: Pre-Calculation Summary

Formula Used

Angle of Internal Friction of Soil = atan((Shear Strength/Shear Stress)*tan((Angle of Inclination)))
Φ_i = atan((τ_s/𝜏)*tan((I)))
This formula uses 2 Functions, 4 Variables

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)
atan - Inverse tan is used to calculate the angle by applying the tangent ratio of the angle, which is the opposite side divided by the adjacent side of the right triangle., atan(Number)

Variables Used

Angle of Internal Friction of Soil - (Measured in Radian) - Angle of Internal Friction of Soil is a shear strength parameter of soils.
Shear Strength - (Measured in Pascal) - Shear Strength is the strength of a material against structural failure when the material fails in shear.
Shear Stress - (Measured in Pascal) - Shear Stress is force tending to cause deformation of a material by slippage along a plane or planes parallel to the imposed stress.
Angle of Inclination - (Measured in Radian) - Angle of Inclination is defined as the angle measured from the horizontal surface of the wall or any object.

STEP 1: Convert Input(s) to Base Unit

Shear Strength: 1.2 Megapascal --> 1200000 Pascal (Check conversion here)
Shear Stress: 61 Pascal --> 61 Pascal No Conversion Required
Angle of Inclination: 80 Degree --> 1.3962634015952 Radian (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

Φ_i = atan((τ_s/𝜏)*tan((I))) --> atan((1200000/61)*tan((1.3962634015952)))

Evaluating ... ...

Φ_i = 1.57078736350671

STEP 3: Convert Result to Output's Unit

1.57078736350671 Radian -->89.9994864414333 Degree (Check conversion here)

FINAL ANSWER

89.9994864414333 ≈ 89.99949 Degree <-- Angle of Internal Friction of Soil

(Calculation completed in 00.004 seconds)

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Created by Suraj Kumar

Birsa Institute of Technology (BIT), Sindri

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Verified by Ishita Goyal

Meerut Institute of Engineering and Technology (MIET), Meerut

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< 25 Stability Analysis of Infinite Slopes Calculators

Unit Weight of Soil given Critical Depth for Cohesive Soil

Go Unit Weight of Soil = Cohesion of Soil/(Critical Depth*(tan((Angle of Inclination))-tan((Angle of Internal Friction)))*(cos((Angle of Inclination)))^2)

Cohesion given Critical Depth for Cohesive Soil

Go Cohesion of Soil = (Critical Depth*Unit Weight of Soil*(tan((Angle of Inclination))-tan((Angle of Internal Friction)))*(cos((Angle of Inclination)))^2)

Critical Depth for Cohesive Soil

Go Critical Depth = Cohesion of Soil/(Unit Weight of Soil*(tan((Angle of Inclination))-tan((Angle of Internal Friction)))*(cos((Angle of Inclination)))^2)

Cohesion given Shear Strength of Cohesive Soil

Go Cohesion of Soil = Shear Strength in KN per Cubic Meter-(Normal Stress in Soil Mechanics*tan((Angle of Internal Friction of Soil*pi)/180))

Cohesion of Soil given Factor of Safety for Cohesive Soil

Go Cohesion of Soil = (Shear Stress in Cohesive Soil*Factor of Safety)-(Normal Stress in Soil Mechanics*tan((Angle of Internal Friction)))

Normal Stress given Factor of Safety for Cohesive Soil

Go Normal Stress = ((Shear Stress for Factor of Safety*Factor of Safety)-Unit Cohesion)/tan((Angle of Internal Friction of Soil))

Shear Stress given Factor of Safety for Cohesive Soil

Go Shear Stress for Factor of Safety = (Unit Cohesion+(Normal Stress*tan((Angle of Internal Friction of Soil))))/Factor of Safety

Shear Strength of Soil given Angle of Internal Friction

Go Shear Strength = (Shear Stress for Factor of Safety*(tan(Angle of Internal Friction of Soil)/tan(Angle of Inclination)))

Shear Stress of Soil given Angle of Internal Friction

Go Shear Stress for Factor of Safety = Shear Strength/(tan((Angle of Internal Friction))/tan((Angle of Inclination)))

Angle of Internal Friction given Shear Strength of Soil

Go Angle of Internal Friction of Soil = atan((Shear Strength/Shear Stress)*tan((Angle of Inclination)))

Normal Stress given Shear Strength of Cohesive Soil

Go Normal Stress in Mega Pascal = (Shear Strength-Cohesion of Soil)/tan((Angle of Internal Friction))

Shear Strength of Cohesive Soil

Go Shear Strength = Cohesion of Soil+(Normal Stress in Mega Pascal*tan((Angle of Internal Friction)))

Factor of Safety against Sliding given Angle of Internal Friction

Go Factor of Safety = (tan((Angle of Internal Friction of Soil))/tan((Angle of Inclination)))

Unit Weight of Soil given Stability Number for Cohesive Soil

Go Unit Weight of Soil = (Cohesion of Soil/(Stability Number*Critical Depth for Stability Number))

Critical Depth given Stability Number for Cohesive Soil

Go Critical Depth for Stability Number = (Cohesion of Soil/(Unit Weight of Soil*Stability Number))

Cohesion given Stability Number for Cohesive Soil

Go Cohesion of Soil = Stability Number*(Unit Weight of Soil*Critical Depth for Stability Number)

Normal Stress given Shear Stress of Cohesionless Soil

Go Normal Stress in Mega Pascal = Shear Stress for Factor of Safety*cot((Angle of Inclination))

Unit Weight of Soil given Mobilised Cohesion

Go Unit Weight of Soil = (Mobilised Cohesion/(Stability Number*Depth at Mobilised Cohesion))

Depth at Mobilised Cohesion

Go Depth at Mobilised Cohesion = (Mobilised Cohesion/(Unit Weight of Soil*Stability Number))

Mobilised Cohesion given Stability Number for Cohesive Soil

Go Mobilised Cohesion = (Stability Number*Unit Weight of Soil*Depth at Mobilised Cohesion)

Normal Stress given Shear Strength of Cohesionless Soil

Go Normal Stress in Mega Pascal = Shear Strength/tan((Angle of Internal Friction))

Shear Strength of Cohesionless Soil

Go Shear Strength = Normal Stress in Mega Pascal*tan((Angle of Internal Friction))

Angle of Internal Friction given Shear Strength of Cohesionless Soil

Go Angle of Internal Friction = atan(Shear Strength/Normal Stress in Mega Pascal)

Cohesion of Soil given Mobilised Cohesion

Go Cohesion of Soil = Mobilised Cohesion*Factor of Safety with respect to Cohesion

Mobilised Cohesion

Go Mobilised Cohesion = Cohesion of Soil/Factor of Safety with respect to Cohesion

Angle of Internal Friction given Shear Strength of Soil Formula

Angle of Internal Friction of Soil = atan((Shear Strength/Shear Stress)*tan((Angle of Inclination)))
Φ_i = atan((τ_s/𝜏)*tan((I)))

What is Angle of Internal Friction?

The angle of internal friction is a physical property of earth materials or the slope of a linear representation of the shear strength of earth materials.

How to Calculate Angle of Internal Friction given Shear Strength of Soil?

Angle of Internal Friction given Shear Strength of Soil calculator uses Angle of Internal Friction of Soil = atan((Shear Strength/Shear Stress)*tan((Angle of Inclination))) to calculate the Angle of Internal Friction of Soil, The Angle of Internal Friction given Shear Strength of Soil is defined as the measure of soil's resistance to shear stress, defining its shear strength behavior. Angle of Internal Friction of Soil is denoted by Φ_i symbol.

How to calculate Angle of Internal Friction given Shear Strength of Soil using this online calculator? To use this online calculator for Angle of Internal Friction given Shear Strength of Soil, enter Shear Strength (τ_s), Shear Stress (𝜏) & Angle of Inclination (I) and hit the calculate button. Here is how the Angle of Internal Friction given Shear Strength of Soil calculation can be explained with given input values -> 5156.606 = atan((1200000/61)*tan((1.3962634015952))).

FAQ

What is Angle of Internal Friction given Shear Strength of Soil?

The Angle of Internal Friction given Shear Strength of Soil is defined as the measure of soil's resistance to shear stress, defining its shear strength behavior and is represented as Φ_i = atan((τ_s/𝜏)*tan((I))) or Angle of Internal Friction of Soil = atan((Shear Strength/Shear Stress)*tan((Angle of Inclination))). Shear Strength is the strength of a material against structural failure when the material fails in shear, Shear Stress is force tending to cause deformation of a material by slippage along a plane or planes parallel to the imposed stress & Angle of Inclination is defined as the angle measured from the horizontal surface of the wall or any object.

How to calculate Angle of Internal Friction given Shear Strength of Soil?

The Angle of Internal Friction given Shear Strength of Soil is defined as the measure of soil's resistance to shear stress, defining its shear strength behavior is calculated using Angle of Internal Friction of Soil = atan((Shear Strength/Shear Stress)*tan((Angle of Inclination))). To calculate Angle of Internal Friction given Shear Strength of Soil, you need Shear Strength (τ_s), Shear Stress (𝜏) & Angle of Inclination (I). With our tool, you need to enter the respective value for Shear Strength, Shear Stress & Angle of Inclination 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 Angle of Internal Friction of Soil?

In this formula, Angle of Internal Friction of Soil uses Shear Strength, Shear Stress & Angle of Inclination. We can use 2 other way(s) to calculate the same, which is/are as follows -

Angle of Internal Friction of Soil = atan((Shear Strength-Unit Cohesion)/Normal Stress)
Angle of Internal Friction of Soil = atan(((Shear Stress for Factor of Safety*Factor of Safety)-Unit Cohesion)/Normal Stress)

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