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 is the angle measured between the normal force and resultant force .ⓘ Angle of Internal Friction [φ]			+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%

✖Factor of Safety expresses how much stronger a system is than it needs to be for an intended load.ⓘ Factor of Safety with respect to Shear Strength [f_s]

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Formula

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Factor of Safety with respect to Shear Strength

Formula

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

Example

`"16.54785"=(("31N/m³"/"9.98N/m³")*(tan(("46°"))/tan(("11°"))))`

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Factor of Safety with respect to Shear Strength Solution

STEP 0: Pre-Calculation Summary

Formula Used

Factor of Safety = ((Submerged Unit Weight/Saturated Unit Weight)*(tan((Angle of Internal Friction))/tan((Weighted Friction Angle for Internal Friction))))
f_s = ((γ^'/γ_sat)*(tan((φ))/tan((φ_IF))))
This formula uses 1 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)

Variables Used

Factor of Safety - Factor of Safety expresses how much stronger a system is than it needs to be for an intended load.
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 - (Measured in Radian) - Angle of Internal Friction is the angle measured between the normal force and resultant force .
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.

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: 46 Degree --> 0.802851455917241 Radian (Check conversion here)
Weighted Friction Angle for Internal Friction: 11 Degree --> 0.19198621771934 Radian (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

f_s = ((γ^'/γ_sat)*(tan((φ))/tan((φ_IF)))) --> ((31/9.98)*(tan((0.802851455917241))/tan((0.19198621771934))))

Evaluating ... ...

f_s = 16.5478547764089

STEP 3: Convert Result to Output's Unit

16.5478547764089 --> No Conversion Required

FINAL ANSWER

16.5478547764089 ≈ 16.54785 <-- Factor of Safety

(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 » 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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Verified by Ishita Goyal

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

Factor of Safety with respect to Shear Strength Formula

What is Factor of Safety?

Factor of safety (FoS) is ability of a system's structural capacity to be viable beyond its expected or actual loads.For example, a safety factor of 2 does not mean that a structure can carry twice as much load as it was designed for. The safety factor depends on the materials and use of an item.

How to Calculate Factor of Safety with respect to Shear Strength?

Factor of Safety with respect to Shear Strength calculator uses Factor of Safety = ((Submerged Unit Weight/Saturated Unit Weight)*(tan((Angle of Internal Friction))/tan((Weighted Friction Angle for Internal Friction)))) to calculate the Factor of Safety, The Factor of Safety with respect to Shear Strength is defined as the value of factor of safety when we have prior information of other parameters used. Factor of Safety is denoted by f_s symbol.

How to calculate Factor of Safety with respect to Shear Strength using this online calculator? To use this online calculator for Factor of Safety with respect to Shear Strength, enter Submerged Unit Weight (γ^'), Saturated Unit Weight (γ_sat), Angle of Internal Friction (φ) & Weighted Friction Angle for Internal Friction (φ_IF) and hit the calculate button. Here is how the Factor of Safety with respect to Shear Strength calculation can be explained with given input values -> 16.51476 = ((31/9.98)*(tan((0.802851455917241))/tan((0.19198621771934)))).

FAQ

What is Factor of Safety with respect to Shear Strength?

The Factor of Safety with respect to Shear Strength is defined as the value of factor of safety when we have prior information of other parameters used and is represented as f_s = ((γ^'/γ_sat)*(tan((φ))/tan((φ_IF)))) or Factor of Safety = ((Submerged Unit Weight/Saturated Unit Weight)*(tan((Angle of Internal Friction))/tan((Weighted Friction Angle for Internal Friction)))). 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 is the angle measured between the normal force and resultant force & Weighted Friction Angle for Internal Friction is an effective measure combining materials' friction properties and their relative contributions in geotechnical engineering for stability analysis.

How to calculate Factor of Safety with respect to Shear Strength?

The Factor of Safety with respect to Shear Strength is defined as the value of factor of safety when we have prior information of other parameters used is calculated using Factor of Safety = ((Submerged Unit Weight/Saturated Unit Weight)*(tan((Angle of Internal Friction))/tan((Weighted Friction Angle for Internal Friction)))). To calculate Factor of Safety with respect to Shear Strength, you need Submerged Unit Weight (γ^'), Saturated Unit Weight (γ_sat), Angle of Internal Friction (φ) & Weighted Friction Angle for Internal Friction (φ_IF). With our tool, you need to enter the respective value for Submerged Unit Weight, Saturated Unit Weight, Angle of Internal Friction & Weighted Friction Angle for Internal Friction 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 Factor of Safety?

In this formula, Factor of Safety uses Submerged Unit Weight, Saturated Unit Weight, Angle of Internal Friction & Weighted Friction Angle for Internal Friction. We can use 1 other way(s) to calculate the same, which is/are as follows -

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

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