Stability Number for Failure on Slope with Seepage of Water Calculator

✖Slope of Ground surface is the rise or fall of the land surface.ⓘ Slope of Ground [δ]			+10% -10%
✖Buoyant unit weight is the effective mass per unit volume when the soil is submerged below standing water or below the ground water table.ⓘ Buoyant Unit Weight [γ_b]			+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%
✖Saturated Unit Weight of Soil is the ratio of mass of saturated soil sample to total volume.ⓘ Saturated Unit Weight of Soil [γ_saturated]			+10% -10%

✖Stability Number is a theoretical number given by Taylor.ⓘ Stability Number for Failure on Slope with Seepage of Water [S_n]

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Formula

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Stability Number for Failure on Slope with Seepage of Water

Formula

`"S"_{"n"} = (cos("δ"))^2*(tan("δ")-(("γ"_{"b"}*tan("Φ"_{"i"}))/"γ"_{"saturated"}))`

Example

`"0.041214"=(cos("87°"))^2*(tan("87°")-(("6kN/m³"*tan("82.87°"))/"11.89kN/m³"))`

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Stability Number for Failure on Slope with Seepage of Water Solution

STEP 0: Pre-Calculation Summary

Formula Used

Stability Number = (cos(Slope of Ground))^2*(tan(Slope of Ground)-((Buoyant Unit Weight*tan(Angle of Internal Friction of Soil))/Saturated Unit Weight of Soil))
S_n = (cos(δ))^2*(tan(δ)-((γ_b*tan(Φ_i))/γ_saturated))
This formula uses 2 Functions, 5 Variables

Functions Used

cos - Cosine of an angle is the ratio of the side adjacent to the angle to the hypotenuse of the triangle., cos(Angle)
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

Stability Number - Stability Number is a theoretical number given by Taylor.
Slope of Ground - (Measured in Radian) - Slope of Ground surface is the rise or fall of the land surface.
Buoyant Unit Weight - (Measured in Newton per Cubic Meter) - Buoyant unit weight is the effective mass per unit volume when the soil is submerged below standing water or below the ground water table.
Angle of Internal Friction of Soil - (Measured in Radian) - Angle of Internal Friction of Soil is a shear strength parameter of soils.
Saturated Unit Weight of Soil - (Measured in Newton per Cubic Meter) - Saturated Unit Weight of Soil is the ratio of mass of saturated soil sample to total volume.

STEP 1: Convert Input(s) to Base Unit

Slope of Ground: 87 Degree --> 1.51843644923478 Radian (Check conversion here)
Buoyant Unit Weight: 6 Kilonewton per Cubic Meter --> 6000 Newton per Cubic Meter (Check conversion here)
Angle of Internal Friction of Soil: 82.87 Degree --> 1.44635435112743 Radian (Check conversion here)
Saturated Unit Weight of Soil: 11.89 Kilonewton per Cubic Meter --> 11890 Newton per Cubic Meter (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

S_n = (cos(δ))^2*(tan(δ)-((γ_b*tan(Φ_i))/γ_saturated)) --> (cos(1.51843644923478))^2*(tan(1.51843644923478)-((6000*tan(1.44635435112743))/11890))

Evaluating ... ...

S_n = 0.0412144704990858

STEP 3: Convert Result to Output's Unit

0.0412144704990858 --> No Conversion Required

FINAL ANSWER

0.0412144704990858 ≈ 0.041214 <-- Stability Number

(Calculation completed in 00.004 seconds)

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Home » Engineering » Civil » Geotechnical Engineering » Seepage Analysis » Steady State Seepage Analysis Along The Slopes » Stability Number for Failure on Slope with Seepage of Water

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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 Steady State Seepage Analysis Along The Slopes Calculators

Factor of Safety for Cohesive Soil given Saturated Unit Weight

Go Factor of Safety in Soil Mechanics = (Effective Cohesion+(Submerged Unit Weight*Depth of Prism*tan((Angle of Internal Friction))*(cos((Angle of Inclination to Horizontal in Soil)))^2))/(Saturated Unit Weight in Newton per Cubic Meter*Depth of Prism*cos((Angle of Inclination to Horizontal in Soil))*sin((Angle of Inclination to Horizontal in Soil)))

Shear Strength given Submerged Unit Weight

Go Shear Strength in KN per Cubic Meter = (Shear Stress in Soil Mechanics*Submerged Unit Weight in KN per Cubic Meter*tan((Angle of Internal Friction*pi)/180))/(Saturated Unit Weight of Soil*tan((Angle of Inclination to Horizontal in Soil*pi)/180))

Submerged Unit Weight given Factor of Safety

Go Submerged Unit Weight in KN per Cubic Meter = Factor of Safety in Soil Mechanics/((tan((Angle of Internal Friction of Soil*pi)/180))/(Saturated Unit Weight of Soil*tan((Angle of Inclination to Horizontal in Soil*pi)/180)))

Factor of Safety given Submerged Unit Weight

Go Factor of Safety in Soil Mechanics = (Submerged Unit Weight in KN per Cubic Meter*tan((Angle of Internal Friction of Soil*pi)/180))/(Saturated Unit Weight of Soil*tan((Angle of Inclination to Horizontal in Soil*pi)/180))

Submerged Unit Weight given Shear Strength

Go Submerged Unit Weight in KN per Cubic Meter = (Shear Strength in KN per Cubic Meter/Shear Stress in Soil Mechanics)/((tan((Angle of Internal Friction of Soil)))/(Saturated Unit Weight of Soil*tan((Angle of Inclination to Horizontal in Soil))))

Shear Stress given Submerged Unit Weight

Go Shear Stress in Soil Mechanics = Shear Strength in KN per Cubic Meter/((Submerged Unit Weight in KN per Cubic Meter*tan((Angle of Internal Friction)))/(Saturated Unit Weight of Soil*tan((Angle of Inclination to Horizontal in Soil))))

Shear Stress Component given Saturated Unit Weight

Go Shear Stress in Soil Mechanics = (Saturated Unit Weight of Soil*Depth of Prism*cos((Angle of Inclination to Horizontal in Soil*pi)/180)*sin((Angle of Inclination to Horizontal in Soil*pi)/180))

Submerged Unit Weight given Upward Force

Go Submerged Unit Weight in KN per Cubic Meter = (Normal Stress in Soil Mechanics-Upward Force in Seepage Analysis)/(Depth of Prism*(cos((Angle of Inclination to Horizontal in Soil*pi)/180))^2)

Normal Stress Component given Submerged Unit Weight and Depth of Prism

Go Normal Stress in Soil Mechanics = Upward Force in Seepage Analysis+(Submerged Unit Weight in KN per Cubic Meter*Depth of Prism*(cos((Angle of Inclination to Horizontal in Soil*pi)/180))^2)

Upward Force due to Seepage Water given Submerged Unit Weight

Go Upward Force in Seepage Analysis = Normal Stress in Soil Mechanics-(Submerged Unit Weight in KN per Cubic Meter*Depth of Prism*(cos((Angle of Inclination to Horizontal in Soil*pi)/180))^2)

Effective Normal Stress given Saturated Unit Weight

Go Effective Normal Stress in Soil Mechanics = ((Saturated Unit Weight of Soil-Unit Weight of Water)*Depth of Prism*(cos((Angle of Inclination to Horizontal in Soil*pi)/180))^2)

Unit Weight of Water given Effective Normal Stress

Go Unit Weight of Water = Saturated Unit Weight of Soil-(Effective Normal Stress in Soil Mechanics/(Depth of Prism*(cos((Angle of Inclination to Horizontal in Soil*pi)/180))^2))

Inclined Length of Prism given Saturated Unit Weight

Go Inclined Length of Prism = Weight of Prism in Soil Mechanics/(Saturated Unit Weight of Soil*Depth of Prism*cos((Angle of Inclination to Horizontal in Soil*pi)/180))

Weight of Soil Prism given Saturated Unit Weight

Go Weight of Prism in Soil Mechanics = (Saturated Unit Weight of Soil*Depth of Prism*Inclined Length of Prism*cos((Angle of Inclination to Horizontal in Soil*pi)/180))

Effective Normal Stress given Submerged Unit Weight

Go Effective Normal Stress in Soil Mechanics = (Submerged Unit Weight in KN per Cubic Meter*Depth of Prism*(cos((Angle of Inclination to Horizontal in Soil*pi)/180))^2)

Submerged Unit Weight given Effective Normal Stress

Go Submerged Unit Weight in KN per Cubic Meter = Effective Normal Stress in Soil Mechanics/(Depth of Prism*(cos((Angle of Inclination to Horizontal in Soil*pi)/180))^2)

Effective Normal Stress given Factor of Safety

Go Effective Normal Stress in Soil Mechanics = Factor of Safety in Soil Mechanics/((tan((Angle of Internal Friction of Soil*pi)/180))/Shear Stress in Soil Mechanics)

Factor of Safety given Effective Normal Stress

Go Factor of Safety in Soil Mechanics = (Effective Normal Stress in Soil Mechanics*tan((Angle of Internal Friction*pi)/180))/Shear Stress in Soil Mechanics

Vertical Stress on Prism given Saturated Unit Weight

Go Vertical Stress at a Point in Kilopascal = (Saturated Unit Weight of Soil*Depth of Prism*cos((Angle of Inclination to Horizontal in Soil*pi)/180))

Normal Stress Component given Saturated Unit Weight

Go Normal Stress in Soil Mechanics = (Saturated Unit Weight of Soil*Depth of Prism*(cos((Angle of Inclination to Horizontal in Soil*pi)/180))^2)

Unit Weight of Water given Upward Force due to Seepage Water

Go Unit Weight of Water = Upward Force in Seepage Analysis/(Depth of Prism*(cos((Angle of Inclination to Horizontal in Soil*pi)/180))^2)

Upward Force due to Seepage Water

Go Upward Force in Seepage Analysis = (Unit Weight of Water*Depth of Prism*(cos((Angle of Inclination to Horizontal in Soil*pi)/180))^2)

Effective Normal Stress given Upward Force due to Seepage Water

Go Effective Normal Stress in Soil Mechanics = Normal Stress in Soil Mechanics-Upward Force in Seepage Analysis

Upward Force due to Seepage Water given Effective Normal Stress

Go Upward Force in Seepage Analysis = Normal Stress in Soil Mechanics-Effective Normal Stress in Soil Mechanics

Normal Stress Component given Effective Normal Stress

Go Normal Stress in Soil Mechanics = Effective Normal Stress in Soil Mechanics+Upward Force in Seepage Analysis

Stability Number for Failure on Slope with Seepage of Water Formula

What is Stability Number?

Taylor proposed an analyzing method to find the stability of slope with the possible greatest angle of slope and angle of internal friction. This method represents the result using a theoretical number, which is called the stability number.

How to Calculate Stability Number for Failure on Slope with Seepage of Water?

Stability Number for Failure on Slope with Seepage of Water calculator uses Stability Number = (cos(Slope of Ground))^2*(tan(Slope of Ground)-((Buoyant Unit Weight*tan(Angle of Internal Friction of Soil))/Saturated Unit Weight of Soil)) to calculate the Stability Number, The Stability Number for Failure on Slope with Seepage of Water is defined as a theoretical number given by taylor to find out stability of slopes. Stability Number is denoted by S_n symbol.

How to calculate Stability Number for Failure on Slope with Seepage of Water using this online calculator? To use this online calculator for Stability Number for Failure on Slope with Seepage of Water, enter Slope of Ground (δ), Buoyant Unit Weight (γ_b), Angle of Internal Friction of Soil (Φ_i) & Saturated Unit Weight of Soil (γ_saturated) and hit the calculate button. Here is how the Stability Number for Failure on Slope with Seepage of Water calculation can be explained with given input values -> 0.041214 = (cos(1.51843644923478))^2*(tan(1.51843644923478)-((6000*tan(1.44635435112743))/11890)).

FAQ

What is Stability Number for Failure on Slope with Seepage of Water?

The Stability Number for Failure on Slope with Seepage of Water is defined as a theoretical number given by taylor to find out stability of slopes and is represented as S_n = (cos(δ))^2*(tan(δ)-((γ_b*tan(Φ_i))/γ_saturated)) or Stability Number = (cos(Slope of Ground))^2*(tan(Slope of Ground)-((Buoyant Unit Weight*tan(Angle of Internal Friction of Soil))/Saturated Unit Weight of Soil)). Slope of Ground surface is the rise or fall of the land surface, Buoyant unit weight is the effective mass per unit volume when the soil is submerged below standing water or below the ground water table, Angle of Internal Friction of Soil is a shear strength parameter of soils & Saturated Unit Weight of Soil is the ratio of mass of saturated soil sample to total volume.

How to calculate Stability Number for Failure on Slope with Seepage of Water?

The Stability Number for Failure on Slope with Seepage of Water is defined as a theoretical number given by taylor to find out stability of slopes is calculated using Stability Number = (cos(Slope of Ground))^2*(tan(Slope of Ground)-((Buoyant Unit Weight*tan(Angle of Internal Friction of Soil))/Saturated Unit Weight of Soil)). To calculate Stability Number for Failure on Slope with Seepage of Water, you need Slope of Ground (δ), Buoyant Unit Weight (γ_b), Angle of Internal Friction of Soil (Φ_i) & Saturated Unit Weight of Soil (γ_saturated). With our tool, you need to enter the respective value for Slope of Ground, Buoyant Unit Weight, Angle of Internal Friction of Soil & Saturated Unit Weight of Soil 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 Slope of Ground, Buoyant Unit Weight, Angle of Internal Friction of Soil & Saturated Unit Weight of Soil. We can use 1 other way(s) to calculate the same, which is/are as follows -

Stability Number = (cos(Slope of Ground))^2*(tan(Slope of Ground)-tan(Angle of Internal Friction of Soil))

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