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

✖Weighted Friction Angle is an effective measure combining materials' friction properties and their relative contributions in geotechnical engineering for stability analysis.ⓘ Weighted Friction Angle [φ_w]			+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 measure of the shear strength of soil due to friction.ⓘ Angle of Internal Friction of Soil [Φ_i]			+10% -10%
✖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%

✖Submerged Unit Weight is the effective weight of the soil per unit volume when it is submerged in water.ⓘ Submerged Unit Weight given Factor of Safety with respect to Shear Strength [γ^']

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Formula

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

Formula

γ' = \frac{\tan (\frac{φ w \cdot π}{180})}{(\frac{1}{γ sat}) \cdot (\frac{\tan (\frac{Φ i \cdot π}{180})}{f s})}

Example

43.84998 N/m³ = \frac{\tan (\frac{130 ° \cdot π}{180})}{(\frac{1}{9.98 N/m³}) \cdot (\frac{\tan (\frac{82.87 ° \cdot π}{180})}{2.8})}

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

STEP 0: Pre-Calculation Summary

Formula Used

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))
γ^' = tan((φ_w*pi)/180)/((1/γ_sat)*(tan((Φ_i*pi)/180)/f_s))
This formula uses 1 Constants, 1 Functions, 5 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)

Variables Used

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.
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.
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 measure of the shear strength of soil due to friction.
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.

STEP 1: Convert Input(s) to Base Unit

Weighted Friction Angle: 130 Degree --> 2.2689280275922 Radian (Check conversion here)
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

γ^' = tan((φ_w*pi)/180)/((1/γ_sat)*(tan((Φ_i*pi)/180)/f_s)) --> tan((2.2689280275922*pi)/180)/((1/9.98)*(tan((1.44635435112743*pi)/180)/2.8))

Evaluating ... ...

γ^' = 43.8499823350497

STEP 3: Convert Result to Output's Unit

43.8499823350497 Newton per Cubic Meter --> No Conversion Required

FINAL ANSWER

43.8499823350497 ≈ 43.84998 Newton per Cubic Meter <-- Submerged Unit Weight

(Calculation completed in 00.020 seconds)

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Home » Engineering » Civil » Geotechnical Engineering » Stability of Slopes In Earthen Dams » Taylor's Stability Number and Stability Curves » Submerged Unit Weight given Factor of Safety with respect to Shear Strength

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Birsa Institute of Technology (BIT), Sindri

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< 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))

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))))

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))

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

What is Submerged Unit Weight?

Buoyant unit weight or submerged unit weight is the effective mass per unit volume when the soil is submerged below standing water or below the ground water table.

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

Submerged Unit Weight given Factor of Safety with respect to Shear Strength calculator uses 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)) to calculate the Submerged Unit Weight, The Submerged Unit Weight given Factor of Safety with respect to Shear Strength is defined as the weight of a material under water, ensuring stability with a safety factor over shear strength. Submerged Unit Weight is denoted by γ^' symbol.

How to calculate Submerged Unit Weight given Factor of Safety with respect to Shear Strength using this online calculator? To use this online calculator for Submerged Unit Weight given Factor of Safety with respect to Shear Strength, enter Weighted Friction Angle (φ_w), 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 Submerged Unit Weight given Factor of Safety with respect to Shear Strength calculation can be explained with given input values -> 43.84998 = tan((2.2689280275922*pi)/180)/((1/9.98)*(tan((1.44635435112743*pi)/180)/2.8)).

FAQ

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

The Submerged Unit Weight given Factor of Safety with respect to Shear Strength is defined as the weight of a material under water, ensuring stability with a safety factor over shear strength and is represented as γ^' = tan((φ_w*pi)/180)/((1/γ_sat)*(tan((Φ_i*pi)/180)/f_s)) or 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)). Weighted Friction Angle is an effective measure combining materials' friction properties and their relative contributions in geotechnical engineering for stability analysis, 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 measure of the shear strength of soil due to friction & 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.

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

The Submerged Unit Weight given Factor of Safety with respect to Shear Strength is defined as the weight of a material under water, ensuring stability with a safety factor over shear strength is calculated using 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)). To calculate Submerged Unit Weight given Factor of Safety with respect to Shear Strength, you need Weighted Friction Angle (φ_w), 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 Weighted Friction Angle, 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 Submerged Unit Weight?

In this formula, Submerged Unit Weight uses Weighted Friction Angle, Saturated Unit Weight, Angle of Internal Friction of Soil & Factor of Safety. We can use 3 other way(s) to calculate the same, which is/are as follows -

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

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