Stability Number given Factor of Safety with Respect to Cohesion Calculator

✖Cohesion of Soil is the ability of like particles within soil to hold onto each other. It is the shear strength or force that binds together like particles in the structure of a soil.ⓘ Cohesion of Soil [c]			+10% -10%
✖Factor of Safety with respect to Cohesion is the ratio of material's shear strength to applied shear stress, ensuring stability against sliding.ⓘ Factor of Safety with respect to Cohesion [F_c]			+10% -10%
✖Unit Weight of Soil mass is the ratio of the total weight of soil to the total volume of soil.ⓘ Unit Weight of Soil [γ]			+10% -10%
✖Depth at Mobilised Cohesion in Stability Number is soil layer thickness where effective cohesion is reached, impacting slope stability.ⓘ Depth at Mobilised Cohesion in Stability Number [H_Mobilised]			+10% -10%

✖Stability Number is a theoretical number given by Taylor.ⓘ Stability Number given Factor of Safety with Respect to Cohesion [S_n]

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Formula

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Stability Number given Factor of Safety with Respect to Cohesion

Formula

`"S"_{"n"} = ("c"/("F"_{"c"}*"γ"*"H"_{"Mobilised"}))`

Example

`"2.200292"=("3.01kPa"/("1.9"*"18kN/m³"*"0.04m"))`

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Stability Number given Factor of Safety with Respect to Cohesion Solution

STEP 0: Pre-Calculation Summary

Formula Used

Stability Number = (Cohesion of Soil/(Factor of Safety with respect to Cohesion*Unit Weight of Soil*Depth at Mobilised Cohesion in Stability Number))
S_n = (c/(F_c*γ*H_Mobilised))
This formula uses 5 Variables

Variables Used

Stability Number - Stability Number is a theoretical number given by Taylor.
Cohesion of Soil - (Measured in Kilopascal) - Cohesion of Soil is the ability of like particles within soil to hold onto each other. It is the shear strength or force that binds together like particles in the structure of a soil.
Factor of Safety with respect to Cohesion - Factor of Safety with respect to Cohesion is the ratio of material's shear strength to applied shear stress, ensuring stability against sliding.
Unit Weight of Soil - (Measured in Kilonewton per Cubic Meter) - Unit Weight of Soil mass is the ratio of the total weight of soil to the total volume of soil.
Depth at Mobilised Cohesion in Stability Number - (Measured in Meter) - Depth at Mobilised Cohesion in Stability Number is soil layer thickness where effective cohesion is reached, impacting slope stability.

STEP 1: Convert Input(s) to Base Unit

Cohesion of Soil: 3.01 Kilopascal --> 3.01 Kilopascal No Conversion Required
Factor of Safety with respect to Cohesion: 1.9 --> No Conversion Required
Unit Weight of Soil: 18 Kilonewton per Cubic Meter --> 18 Kilonewton per Cubic Meter No Conversion Required
Depth at Mobilised Cohesion in Stability Number: 0.04 Meter --> 0.04 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

S_n = (c/(F_c*γ*H_Mobilised)) --> (3.01/(1.9*18*0.04))

Evaluating ... ...

S_n = 2.20029239766082

STEP 3: Convert Result to Output's Unit

2.20029239766082 --> No Conversion Required

FINAL ANSWER

2.20029239766082 ≈ 2.200292 <-- Stability Number

(Calculation completed in 00.004 seconds)

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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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< 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 in Soil Mechanics*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 in Soil Mechanics*tan((Angle of Internal Friction)))

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 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

Shear Strength of Soil given Angle of Internal Friction

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

Shear Stress of Soil given Angle of Internal Friction

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

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 given Angle of Internal Friction

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

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))

Unit Weight of Soil given Mobilised Cohesion

Go Unit Weight of Soil = (Mobilised Cohesion/(Stability Number*Depth at Mobilised Cohesion))

Depth at Mobilised Cohesion

Go Depth at Mobilised Cohesion = (Mobilised Cohesion/(Unit Weight of Soil*Stability Number))

Mobilised Cohesion given Stability Number for Cohesive Soil

Go Mobilised Cohesion = (Stability Number*Unit Weight of Soil*Depth at Mobilised Cohesion)

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 Mobilised Cohesion

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

Mobilised Cohesion

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

Stability Number given Factor of Safety with Respect to Cohesion Formula

Stability Number = (Cohesion of Soil/(Factor of Safety with respect to Cohesion*Unit Weight of Soil*Depth at Mobilised Cohesion in Stability Number))
S_n = (c/(F_c*γ*H_Mobilised))

What is Stability Number?

It is the method used to evaluate slope stability for homogeneous soils having cohesion. This method is proposed by the Taylor.

How to Calculate Stability Number given Factor of Safety with Respect to Cohesion?

Stability Number given Factor of Safety with Respect to Cohesion calculator uses Stability Number = (Cohesion of Soil/(Factor of Safety with respect to Cohesion*Unit Weight of Soil*Depth at Mobilised Cohesion in Stability Number)) to calculate the Stability Number, The Stability Number given Factor of Safety with Respect to Cohesion is defined as ratio of cohesion to applied stress, ensuring safety in geotechnical engineering; higher values indicate increased stability. Stability Number is denoted by S_n symbol.

How to calculate Stability Number given Factor of Safety with Respect to Cohesion using this online calculator? To use this online calculator for Stability Number given Factor of Safety with Respect to Cohesion, enter Cohesion of Soil (c), Factor of Safety with respect to Cohesion (F_c), Unit Weight of Soil (γ) & Depth at Mobilised Cohesion in Stability Number (H_Mobilised) and hit the calculate button. Here is how the Stability Number given Factor of Safety with Respect to Cohesion calculation can be explained with given input values -> 2.200292 = (3010/(1.9*18000*0.04)).

FAQ

What is Stability Number given Factor of Safety with Respect to Cohesion?

The Stability Number given Factor of Safety with Respect to Cohesion is defined as ratio of cohesion to applied stress, ensuring safety in geotechnical engineering; higher values indicate increased stability and is represented as S_n = (c/(F_c*γ*H_Mobilised)) or Stability Number = (Cohesion of Soil/(Factor of Safety with respect to Cohesion*Unit Weight of Soil*Depth at Mobilised Cohesion in Stability Number)). Cohesion of Soil is the ability of like particles within soil to hold onto each other. It is the shear strength or force that binds together like particles in the structure of a soil, Factor of Safety with respect to Cohesion is the ratio of material's shear strength to applied shear stress, ensuring stability against sliding, Unit Weight of Soil mass is the ratio of the total weight of soil to the total volume of soil & Depth at Mobilised Cohesion in Stability Number is soil layer thickness where effective cohesion is reached, impacting slope stability.

How to calculate Stability Number given Factor of Safety with Respect to Cohesion?

The Stability Number given Factor of Safety with Respect to Cohesion is defined as ratio of cohesion to applied stress, ensuring safety in geotechnical engineering; higher values indicate increased stability is calculated using Stability Number = (Cohesion of Soil/(Factor of Safety with respect to Cohesion*Unit Weight of Soil*Depth at Mobilised Cohesion in Stability Number)). To calculate Stability Number given Factor of Safety with Respect to Cohesion, you need Cohesion of Soil (c), Factor of Safety with respect to Cohesion (F_c), Unit Weight of Soil (γ) & Depth at Mobilised Cohesion in Stability Number (H_Mobilised). With our tool, you need to enter the respective value for Cohesion of Soil, Factor of Safety with respect to Cohesion, Unit Weight of Soil & Depth at Mobilised Cohesion in Stability Number 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 Stability Number?

In this formula, Stability Number uses Cohesion of Soil, Factor of Safety with respect to Cohesion, Unit Weight of Soil & Depth at Mobilised Cohesion in Stability Number. We can use 2 other way(s) to calculate the same, which is/are as follows -

Stability Number = (Cohesion of Soil/(Unit Weight of Soil*Critical Depth for Stability Number))
Stability Number = (Mobilised Cohesion/(Unit Weight of Soil*Depth at Mobilised Cohesion))

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