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

✖Submerged Unit Weight is the unit weight of weight of soil as observed underwater in a saturated condition of course.ⓘ Submerged Unit Weight [γ^']			+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%
✖Angle of Internal Friction of Soil is a shear strength parameter of soils.ⓘ Angle of Internal Friction of Soil [Φ_i]			+10% -10%
✖Factor of Safety expresses how much stronger a system is than it needs to be for an intended load.ⓘ Factor of Safety [f_s]			+10% -10%

✖Weighted Friction Angle is an effective measure combining materials' friction properties and their relative contributions in geotechnical engineering for stability analysis.ⓘ Weighted Friction Angle given Factor of Safety with respect to Shear Strength [φ_w]

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Formula

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

Formula

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

Example

`"83.56667°"=atan(("31N/m³"/"9.98N/m³")*(tan(("82.87°"))/"2.8"))`

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

STEP 0: Pre-Calculation Summary

Formula Used

Weighted Friction Angle = atan((Submerged Unit Weight/Saturated Unit Weight)*(tan((Angle of Internal Friction of Soil))/Factor of Safety))
φ_w = atan((γ^'/γ_sat)*(tan((Φ_i))/f_s))
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

Weighted Friction Angle - (Measured in Radian) - Weighted Friction Angle 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 unit weight of weight of soil as observed underwater in a saturated condition of course.
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.
Angle of Internal Friction of Soil - (Measured in Radian) - Angle of Internal Friction of Soil is a shear strength parameter of soils.
Factor of Safety - Factor of Safety expresses how much stronger a system is than it needs to be for an intended load.

STEP 1: Convert Input(s) to Base Unit

Submerged Unit Weight: 31 Newton per Cubic Meter --> 31 Newton per Cubic Meter No Conversion Required
Saturated Unit Weight: 9.98 Newton per Cubic Meter --> 9.98 Newton per Cubic Meter No Conversion Required
Angle of Internal Friction of Soil: 82.87 Degree --> 1.44635435112743 Radian (Check conversion here)
Factor of Safety: 2.8 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

φ_w = atan((γ^'/γ_sat)*(tan((Φ_i))/f_s)) --> atan((31/9.98)*(tan((1.44635435112743))/2.8))

Evaluating ... ...

φ_w = 1.45851353248699

STEP 3: Convert Result to Output's Unit

1.45851353248699 Radian -->83.566669774237 Degree (Check conversion here)

FINAL ANSWER

83.566669774237 ≈ 83.56667 Degree <-- Weighted Friction Angle

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

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Created by Suraj Kumar

Birsa Institute of Technology (BIT), Sindri

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Meerut Institute of Engineering and Technology (MIET), Meerut

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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*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 with respect to Shear Strength

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 Angle of Internal Friction = (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)/(Angle of Internal Friction)

Saturated Unit Weight given Weighted and Mobilised 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

Mobilised Friction Angle given Weighted Friction Angle

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

Weighted Friction Angle given Submerged Unit Weight

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

Saturated Unit Weight given Weighted Friction Angle

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

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

Weighted Friction Angle = atan((Submerged Unit Weight/Saturated Unit Weight)*(tan((Angle of Internal Friction of Soil))/Factor of Safety))
φ_w = atan((γ^'/γ_sat)*(tan((Φ_i))/f_s))

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

Weighted Friction Angle given Factor of Safety with respect to Shear Strength calculator uses Weighted Friction Angle = atan((Submerged Unit Weight/Saturated Unit Weight)*(tan((Angle of Internal Friction of Soil))/Factor of Safety)) to calculate the Weighted Friction Angle, The Weighted Friction Angle given Factor of Safety with respect to Shear Strength is defined as angle of internal friction adjusted for Factor of Safety, ensuring stability in structures against shear strength failure. Weighted Friction Angle is denoted by φ_w symbol.

How to calculate Weighted Friction Angle given Factor of Safety with respect to Shear Strength using this online calculator? To use this online calculator for Weighted Friction Angle given Factor of Safety with respect to Shear Strength, enter Submerged Unit Weight (γ^'), Saturated Unit Weight (γ_sat), Angle of Internal Friction of Soil (Φ_i) & Factor of Safety (f_s) and hit the calculate button. Here is how the Weighted Friction Angle given Factor of Safety with respect to Shear Strength calculation can be explained with given input values -> 4787.285 = atan((31/9.98)*(tan((1.44635435112743))/2.8)).

FAQ

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

The Weighted Friction Angle given Factor of Safety with respect to Shear Strength is defined as angle of internal friction adjusted for Factor of Safety, ensuring stability in structures against shear strength failure and is represented as φ_w = atan((γ^'/γ_sat)*(tan((Φ_i))/f_s)) or Weighted Friction Angle = atan((Submerged Unit Weight/Saturated Unit Weight)*(tan((Angle of Internal Friction of Soil))/Factor of Safety)). Submerged Unit Weight is the unit weight of weight of soil as observed underwater in a saturated condition of course, 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, Angle of Internal Friction of Soil is a shear strength parameter of soils & Factor of Safety expresses how much stronger a system is than it needs to be for an intended load.

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

The Weighted Friction Angle given Factor of Safety with respect to Shear Strength is defined as angle of internal friction adjusted for Factor of Safety, ensuring stability in structures against shear strength failure is calculated using Weighted Friction Angle = atan((Submerged Unit Weight/Saturated Unit Weight)*(tan((Angle of Internal Friction of Soil))/Factor of Safety)). To calculate Weighted Friction Angle given Factor of Safety with respect to Shear Strength, you need Submerged Unit Weight (γ^'), Saturated Unit Weight (γ_sat), Angle of Internal Friction of Soil (Φ_i) & Factor of Safety (f_s). With our tool, you need to enter the respective value for Submerged Unit Weight, Saturated Unit Weight, Angle of Internal Friction of Soil & Factor of Safety 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 Weighted Friction Angle?

In this formula, Weighted Friction Angle uses Submerged Unit Weight, Saturated Unit Weight, Angle of Internal Friction of Soil & Factor of Safety. We can use 2 other way(s) to calculate the same, which is/are as follows -

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

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