Angle of Internal Friction given Shear Strength of Cohesionless 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%
✖Normal Stress in Mega Pascal is a stress that occurs when a member is loaded by an axial force.ⓘ Normal Stress in Mega Pascal [σ_nm]			+10% -10%

✖Angle of Internal Friction is the angle measured between the normal force and resultant force .ⓘ Angle of Internal Friction given Shear Strength of Cohesionless Soil [φ]

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Formula

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Angle of Internal Friction given Shear Strength of Cohesionless Soil

Formula

`"φ" = atan("τ"_{"s"}/"σ"_{"nm"})`

Example

`"47.48955°"=atan("1.2MPa"/"1.1MPa")`

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Angle of Internal Friction given Shear Strength of Cohesionless Soil Solution

STEP 0: Pre-Calculation Summary

Formula Used

Angle of Internal Friction = atan(Shear Strength/Normal Stress in Mega Pascal)
φ = atan(τ_s/σ_nm)
This formula uses 2 Functions, 3 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 - (Measured in Radian) - Angle of Internal Friction is the angle measured between the normal force and resultant force .
Shear Strength - (Measured in Megapascal) - Shear Strength is the strength of a material against structural failure when the material fails in shear.
Normal Stress in Mega Pascal - (Measured in Megapascal) - Normal Stress in Mega Pascal is a stress that occurs when a member is loaded by an axial force.

STEP 1: Convert Input(s) to Base Unit

Shear Strength: 1.2 Megapascal --> 1.2 Megapascal No Conversion Required
Normal Stress in Mega Pascal: 1.1 Megapascal --> 1.1 Megapascal No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

φ = atan(τ_s/σ_nm) --> atan(1.2/1.1)

Evaluating ... ...

φ = 0.828849058788979

STEP 3: Convert Result to Output's Unit

0.828849058788979 Radian -->47.4895529220081 Degree (Check conversion here)

FINAL ANSWER

47.4895529220081 ≈ 47.48955 Degree <-- Angle of Internal Friction

(Calculation completed in 00.004 seconds)

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Home » Engineering » Civil » Geotechnical Engineering » Stability Analysis of Infinite Slopes » Angle of Internal Friction given Shear Strength of Cohesionless Soil

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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 Cohesionless Soil Formula

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

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 Cohesionless Soil?

Angle of Internal Friction given Shear Strength of Cohesionless Soil calculator uses Angle of Internal Friction = atan(Shear Strength/Normal Stress in Mega Pascal) to calculate the Angle of Internal Friction, The Angle of Internal Friction given Shear Strength of Cohesionless Soil is defined as the measure of resistance to shear in cohesionless soil, reflecting its shear strength. Angle of Internal Friction is denoted by φ symbol.

How to calculate Angle of Internal Friction given Shear Strength of Cohesionless Soil using this online calculator? To use this online calculator for Angle of Internal Friction given Shear Strength of Cohesionless Soil, enter Shear Strength (τ_s) & Normal Stress in Mega Pascal (σ_nm) and hit the calculate button. Here is how the Angle of Internal Friction given Shear Strength of Cohesionless Soil calculation can be explained with given input values -> 4737.617 = atan(1200000/1100000).

FAQ

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

The Angle of Internal Friction given Shear Strength of Cohesionless Soil is defined as the measure of resistance to shear in cohesionless soil, reflecting its shear strength and is represented as φ = atan(τ_s/σ_nm) or Angle of Internal Friction = atan(Shear Strength/Normal Stress in Mega Pascal). Shear Strength is the strength of a material against structural failure when the material fails in shear & Normal Stress in Mega Pascal is a stress that occurs when a member is loaded by an axial force.

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

The Angle of Internal Friction given Shear Strength of Cohesionless Soil is defined as the measure of resistance to shear in cohesionless soil, reflecting its shear strength is calculated using Angle of Internal Friction = atan(Shear Strength/Normal Stress in Mega Pascal). To calculate Angle of Internal Friction given Shear Strength of Cohesionless Soil, you need Shear Strength (τ_s) & Normal Stress in Mega Pascal (σ_nm). With our tool, you need to enter the respective value for Shear Strength & Normal Stress in Mega Pascal and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

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