✖Factor of Safety is a measure of the load-carrying capacity of a structure or material compared to the actual load or stress that is applied to it.ⓘ Factor of Safety [f_s]			+10% -10%
✖Saturated Unit Weight is the value of the unit weight of the soil when the soil is completely saturated with water that is all the soil pores are completely filled with water.ⓘ Saturated Unit Weight [γ_sat]			+10% -10%
✖Weighted Friction Angle for Internal Friction is an effective measure combining materials' friction properties and their relative contributions in geotechnical engineering for stability analysis.ⓘ Weighted Friction Angle for Internal Friction [φ_IF]			+10% -10%
✖Submerged Unit Weight is the effective weight of the soil per unit volume when it is submerged in water.ⓘ Submerged Unit Weight [γ^']			+10% -10%

✖Angle of Internal Friction is the angle measured between the normal force and resultant force.ⓘ Angle of Internal Friction given Factor of Safety [φ]

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Formula

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Angle of Internal Friction given Factor of Safety

Formula

`"φ" = atan(("f"_{"s"}*"γ"_{"sat"}*tan(("φ"_{"IF"})))/"γ"^{"'"})`

Example

`"9.938374°"=atan(("2.8"*"9.98N/m³"*tan(("11°")))/"31N/m³")`

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Angle of Internal Friction given Factor of Safety Solution

STEP 0: Pre-Calculation Summary

Formula Used

Angle of Internal Friction = atan((Factor of Safety*Saturated Unit Weight*tan((Weighted Friction Angle for Internal Friction)))/Submerged Unit Weight)
φ = atan((f_s*γ_sat*tan((φ_IF)))/γ^')
This formula uses 2 Functions, 5 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.
Factor of Safety - Factor of Safety is a measure of the load-carrying capacity of a structure or material compared to the actual load or stress that is applied to it.
Saturated Unit Weight - (Measured in Newton per Cubic Meter) - Saturated Unit Weight is the value of the unit weight of the soil when the soil is completely saturated with water that is all the soil pores are completely filled with water.
Weighted Friction Angle for Internal Friction - (Measured in Radian) - Weighted Friction Angle for Internal Friction is an effective measure combining materials' friction properties and their relative contributions in geotechnical engineering for stability analysis.
Submerged Unit Weight - (Measured in Newton per Cubic Meter) - Submerged Unit Weight is the effective weight of the soil per unit volume when it is submerged in water.

STEP 1: Convert Input(s) to Base Unit

Factor of Safety: 2.8 --> No Conversion Required
Saturated Unit Weight: 9.98 Newton per Cubic Meter --> 9.98 Newton per Cubic Meter No Conversion Required
Weighted Friction Angle for Internal Friction: 11 Degree --> 0.19198621771934 Radian (Check conversion here)
Submerged Unit Weight: 31 Newton per Cubic Meter --> 31 Newton per Cubic Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

φ = atan((f_s*γ_sat*tan((φ_IF)))/γ^') --> atan((2.8*9.98*tan((0.19198621771934)))/31)

Evaluating ... ...

φ = 0.173457348461734

STEP 3: Convert Result to Output's Unit

0.173457348461734 Radian -->9.9383739923893 Degree (Check conversion here)

FINAL ANSWER

9.9383739923893 ≈ 9.938374 Degree <-- Angle of Internal Friction

(Calculation completed in 00.004 seconds)

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Home » Engineering » Civil » Geotechnical Engineering » Stability of Slopes In Earthen Dams » Taylor's Stability Number and Stability Curves » Angle of Internal Friction given Factor of Safety

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< 18 Taylor's Stability Number and Stability Curves Calculators

Submerged Unit Weight given Factor of Safety with respect to Shear Strength

Go Submerged Unit Weight = tan((Weighted Friction Angle*pi)/180)/((1/Saturated Unit Weight)*(tan((Angle of Internal Friction of Soil*pi)/180)/Factor of Safety))

Submerged Unit Weight given Weighted and Effective Friction Angle

Go Submerged Unit Weight = (Weighted Friction Angle for Internal Friction*(180/pi))/((Effective Angle of Internal Friction*(180/pi))/(Factor of Safety*Saturated Unit Weight))

Saturated Unit Weight given Factor of Safety with respect to Shear Strength

Go Saturated Unit Weight = ((Submerged Unit Weight/tan((Weighted Friction Angle for Internal Friction)))*(tan((Angle of Internal Friction))/Factor of Safety))

Factor of Safety with respect to Shear Strength

Go Factor of Safety = ((Submerged Unit Weight/Saturated Unit Weight)*(tan((Angle of Internal Friction))/tan((Weighted Friction Angle for Internal Friction))))

Angle of Internal Friction given Factor of Safety

Go Angle of Internal Friction = atan((Factor of Safety*Saturated Unit Weight*tan((Weighted Friction Angle for Internal Friction)))/Submerged Unit Weight)

Weighted Friction Angle given Factor of Safety with respect to Shear Strength

Go Weighted Friction Angle = atan((Submerged Unit Weight/Saturated Unit Weight)*(tan((Angle of Internal Friction of Soil))/Factor of Safety))

Effective Angle of Internal Friction given Weighted Friction Angle

Go Effective Angle of Internal Friction = Weighted Friction Angle for Internal Friction/((Submerged Unit Weight)/(Factor of Safety*Saturated Unit Weight))

Factor of Safety with respect to Shear Strength given Weighted Friction Angle

Go Factor of Safety = (Submerged Unit Weight*Effective Angle of Internal Friction)/(Weighted Friction Angle for Internal Friction*Saturated Unit Weight)

Weighted Friction Angle given Effective Angle of Internal Friction

Go Weighted Friction Angle for Internal Friction = (Submerged Unit Weight*Effective Angle of Internal Friction)/(Factor of Safety*Saturated Unit Weight)

Saturated Unit Weight given Weighted and Effective Friction Angle

Go Saturated Unit Weight = (Submerged Unit Weight*Effective Angle of Internal Friction)/(Weighted Friction Angle for Internal Friction*Factor of Safety)

Angle of Internal Friction given Weighted Friction Angle

Go Internal Friction Angle with Weighted Frict. Angle = (Weighted Friction Angle*Saturated Unit Weight)/(Submerged Unit Weight)

Submerged Unit Weight given Weighted Friction Angle

Go Submerged Unit Weight = (Weighted Friction Angle*Saturated Unit Weight)/(Internal Friction Angle with Weighted Frict. Angle)

Weighted Friction Angle given Submerged Unit Weight

Go Weighted Friction Angle = (Submerged Unit Weight*Internal Friction Angle with Weighted Frict. Angle)/Saturated Unit Weight

Saturated Unit Weight given Weighted Friction Angle

Go Saturated Unit Weight = (Submerged Unit Weight*Internal Friction Angle with Weighted Frict. Angle)/Weighted Friction Angle

Saturated Unit Weight given Weighted and Mobilized Friction Angle

Go Saturated Unit Weight = (Submerged Unit Weight*Angle of Mobilized Friction)/Weighted Friction Angle

Submerged Unit Weight given Weighted and Mobilised Friction Angle

Go Submerged Unit Weight = (Saturated Unit Weight*Weighted Friction Angle)/Angle of Mobilized Friction

Weighted Friction Angle given Mobilised Friction Angle

Go Weighted Friction Angle = (Submerged Unit Weight*Angle of Mobilized Friction)/Saturated Unit Weight

Mobilized Friction Angle given Weighted Friction Angle

Go Angle of Mobilized Friction = (Saturated Unit Weight*Weighted Friction Angle)/Submerged Unit Weight

Angle of Internal Friction given Factor of Safety Formula

Angle of Internal Friction = atan((Factor of Safety*Saturated Unit Weight*tan((Weighted Friction Angle for Internal Friction)))/Submerged Unit Weight)
φ = atan((f_s*γ_sat*tan((φ_IF)))/γ^')

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 Factor of Safety?

Angle of Internal Friction given Factor of Safety calculator uses Angle of Internal Friction = atan((Factor of Safety*Saturated Unit Weight*tan((Weighted Friction Angle for Internal Friction)))/Submerged Unit Weight) to calculate the Angle of Internal Friction, The Angle of Internal Friction given Factor of Safety formula is defined as the value of angle of internal friction with respect to shear strength. Angle of Internal Friction is denoted by φ symbol.

How to calculate Angle of Internal Friction given Factor of Safety using this online calculator? To use this online calculator for Angle of Internal Friction given Factor of Safety, enter Factor of Safety (f_s), Saturated Unit Weight (γ_sat), Weighted Friction Angle for Internal Friction (φ_IF) & Submerged Unit Weight (γ^') and hit the calculate button. Here is how the Angle of Internal Friction given Factor of Safety calculation can be explained with given input values -> 569.4269 = atan((2.8*9.98*tan((0.19198621771934)))/31).

FAQ

What is Angle of Internal Friction given Factor of Safety?

The Angle of Internal Friction given Factor of Safety formula is defined as the value of angle of internal friction with respect to shear strength and is represented as φ = atan((f_s*γ_sat*tan((φ_IF)))/γ^') or Angle of Internal Friction = atan((Factor of Safety*Saturated Unit Weight*tan((Weighted Friction Angle for Internal Friction)))/Submerged Unit Weight). Factor of Safety is a measure of the load-carrying capacity of a structure or material compared to the actual load or stress that is applied to it, Saturated Unit Weight is the value of the unit weight of the soil when the soil is completely saturated with water that is all the soil pores are completely filled with water, Weighted Friction Angle for Internal Friction is an effective measure combining materials' friction properties and their relative contributions in geotechnical engineering for stability analysis & Submerged Unit Weight is the effective weight of the soil per unit volume when it is submerged in water.

How to calculate Angle of Internal Friction given Factor of Safety?

The Angle of Internal Friction given Factor of Safety formula is defined as the value of angle of internal friction with respect to shear strength is calculated using Angle of Internal Friction = atan((Factor of Safety*Saturated Unit Weight*tan((Weighted Friction Angle for Internal Friction)))/Submerged Unit Weight). To calculate Angle of Internal Friction given Factor of Safety, you need Factor of Safety (f_s), Saturated Unit Weight (γ_sat), Weighted Friction Angle for Internal Friction (φ_IF) & Submerged Unit Weight (γ^'). With our tool, you need to enter the respective value for Factor of Safety, Saturated Unit Weight, Weighted Friction Angle for Internal Friction & Submerged Unit Weight 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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