✖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%
✖Angle of Inclination is the angle measured from the horizontal surface of the wall or any object.ⓘ Angle of Inclination [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 against Sliding [f_s]

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Formula

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Factor of Safety against Sliding

Formula

`"f"_{"s"} = (tan(("Φ"_{"i"}))/tan(("I")))`

Example

`"0.88163"=(tan(("78.69°"))/tan(("80°")))`

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Factor of Safety against Sliding Solution

STEP 0: Pre-Calculation Summary

Formula Used

Factor of Safety = (tan((Angle of Internal Friction of Soil))/tan((Angle of Inclination)))
f_s = (tan((Φ_i))/tan((I)))
This formula uses 1 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)

Variables Used

Factor of Safety - Factor of Safety expresses how much stronger a system is than it needs to be for an intended load.
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.
Angle of Inclination - (Measured in Radian) - Angle of Inclination is the angle measured from the horizontal surface of the wall or any object.

STEP 1: Convert Input(s) to Base Unit

Angle of Internal Friction of Soil: 78.69 Degree --> 1.37339958839408 Radian (Check conversion here)
Angle of Inclination: 80 Degree --> 1.3962634015952 Radian (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

f_s = (tan((Φ_i))/tan((I))) --> (tan((1.37339958839408))/tan((1.3962634015952)))

Evaluating ... ...

f_s = 0.881629500506991

STEP 3: Convert Result to Output's Unit

0.881629500506991 --> No Conversion Required

FINAL ANSWER

0.881629500506991 ≈ 0.88163 <-- Factor of Safety

(Calculation completed in 00.004 seconds)

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Birsa Institute of Technology (BIT), Sindri

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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 at a Point in Soil*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 at a Point in Soil*tan((Angle of Internal Friction)))

Shear Strength of Soil given Angle of Internal Friction

Go Shear Strength of Soil = (Shear Stress for Factor of Safety*(tan(Angle of Internal Friction of Soil)/tan(Angle of Inclination)))

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 of Soil given Angle of Internal Friction

Go Shear Stress given Angle of Internal Friction = Shear Strength/(tan((Angle of Internal Friction))/tan((Angle of Inclination)))

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

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

Go Factor of Safety = (tan((Angle of Internal Friction of Soil))/tan((Angle of Inclination)))

Unit Weight of Soil given Mobilized Cohesion

Go Unit Weight of Soil = (Mobilized Cohesion for Cohesive Soil/(Stability Number*Depth at Mobilized Cohesion))

Depth at Mobilized Cohesion

Go Depth at Mobilized Cohesion = (Mobilized Cohesion for Cohesive Soil/(Unit Weight of Soil*Stability Number))

Mobilized Cohesion given Stability Number for Cohesive Soil

Go Mobilized Cohesion for Cohesive Soil = (Stability Number*Unit Weight of Soil*Depth at Mobilized Cohesion)

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))

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 Mobilized Cohesion

Go Cohesion of Soil = Mobilized Cohesion*Factor of Safety with respect to Cohesion

Mobilized Cohesion

Go Mobilized Cohesion = Cohesion of Soil/Factor of Safety with respect to Cohesion

Factor of Safety against Sliding Formula

Factor of Safety = (tan((Angle of Internal Friction of Soil))/tan((Angle of Inclination)))
f_s = (tan((Φ_i))/tan((I)))

What is Factor of Safety?

The ratio of a structure's absolute strength (structural capability) to actual applied load; this is a measure of the reliability of a particular design.

How to Calculate Factor of Safety against Sliding?

Factor of Safety against Sliding calculator uses Factor of Safety = (tan((Angle of Internal Friction of Soil))/tan((Angle of Inclination))) to calculate the Factor of Safety, The Factor of Safety against Sliding formula is defined as the measure of safety margin used to assess the stability of slopes or structures on slopes against sliding failure. Factor of Safety is denoted by f_s symbol.

How to calculate Factor of Safety against Sliding using this online calculator? To use this online calculator for Factor of Safety against Sliding, enter Angle of Internal Friction of Soil (Φ_i) & Angle of Inclination (I) and hit the calculate button. Here is how the Factor of Safety against Sliding calculation can be explained with given input values -> 0.88163 = (tan((1.37339958839408))/tan((1.3962634015952))).

FAQ

What is Factor of Safety against Sliding?

The Factor of Safety against Sliding formula is defined as the measure of safety margin used to assess the stability of slopes or structures on slopes against sliding failure and is represented as f_s = (tan((Φ_i))/tan((I))) or Factor of Safety = (tan((Angle of Internal Friction of Soil))/tan((Angle of Inclination))). Angle of Internal Friction of Soil is a measure of the shear strength of soil due to friction & Angle of Inclination is the angle measured from the horizontal surface of the wall or any object.

How to calculate Factor of Safety against Sliding?

The Factor of Safety against Sliding formula is defined as the measure of safety margin used to assess the stability of slopes or structures on slopes against sliding failure is calculated using Factor of Safety = (tan((Angle of Internal Friction of Soil))/tan((Angle of Inclination))). To calculate Factor of Safety against Sliding, you need Angle of Internal Friction of Soil (Φ_i) & Angle of Inclination (I). With our tool, you need to enter the respective value for Angle of Internal Friction of Soil & Angle of Inclination 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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