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Stability Number for Failure on Slope with Seepage of Water Formula

GoStability Number for Failure on Slope without Seepage Water Formula

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Stability Number is a theoretical number given by Taylor. Check FAQs

S n = {(\cos (δ))}^{2} \cdot (\tan (δ) - (\frac{γ b \cdot \tan (Φ i)}{γ saturated}))

S_n - Stability Number?δ - Slope of Ground?γ_b - Buoyant Unit Weight?Φ_i - Angle of Internal Friction of Soil?γ_saturated - Saturated Unit Weight of Soil?

Stability Number for Failure on Slope with Seepage of Water Example

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Here is how the Stability Number for Failure on Slope with Seepage of Water equation looks like with Values.

Here is how the Stability Number for Failure on Slope with Seepage of Water equation looks like with Units.

Here is how the Stability Number for Failure on Slope with Seepage of Water equation looks like.

0.0412 = {(\cos (87))}^{2} \cdot (\tan (87) - (\frac{6 \cdot \tan (82.87)}{11.89}))

0.0412 = {(\cos (87°))}^{2} \cdot (\tan (87°) - (\frac{6kN/m³ \cdot \tan (82.87°)}{11.89kN/m³}))

0.0412 = {(\cos (87))}^{2} \cdot (\tan (87) - (\frac{6 \cdot \tan (82.87)}{11.89}))

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Stability Number for Failure on Slope with Seepage of Water Solution

Follow our step by step solution on how to calculate Stability Number for Failure on Slope with Seepage of Water?

FIRST Step Consider the formula

S n = {(\cos (δ))}^{2} \cdot (\tan (δ) - (\frac{γ b \cdot \tan (Φ i)}{γ saturated}))

Next Step Substitute values of Variables

∴

S n = {(\cos (87°))}^{2} \cdot (\tan (87°) - (\frac{6kN/m³ \cdot \tan (82.87°)}{11.89kN/m³}))

Next Step Convert Units

∴

S n = {(\cos (1.5184rad))}^{2} \cdot (\tan (1.5184rad) - (\frac{6000N/m³ \cdot \tan (1.4464rad)}{11890N/m³}))

Next Step Prepare to Evaluate

∴

S n = {(\cos (1.5184))}^{2} \cdot (\tan (1.5184) - (\frac{6000 \cdot \tan (1.4464)}{11890}))

Next Step Evaluate

∴

S n = 0.0412144704990858

LAST Step Rounding Answer

∴

S n = 0.0412

Stability Number for Failure on Slope with Seepage of Water Formula Elements

Variables

Functions

Stability Number

Stability Number is a theoretical number given by Taylor.

Symbol: S_n

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Slope of Ground

Slope of Ground surface is the rise or fall of the land surface.

Symbol: δ

Measurement: AngleUnit: °

Note: Value should be greater than 0.

Buoyant Unit Weight

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

Symbol: γ_b

Measurement: Specific WeightUnit: kN/m³

Note: Value should be greater than 0.

Angle of Internal Friction of Soil

Angle of Internal Friction of Soil is is a measure of the shear strength of soil due to friction.

Symbol: Φ_i

Measurement: AngleUnit: °

Note: Value should be between -180 to 180.

Saturated Unit Weight of Soil

Saturated Unit Weight of Soil is the ratio of mass of saturated soil sample to total volume.

Symbol: γ_saturated

Measurement: Specific WeightUnit: kN/m³

Note: Value should be greater than 0.

cos

Cosine of an angle is the ratio of the side adjacent to the angle to the hypotenuse of the triangle.

Syntax: 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.

Syntax: tan(Angle)

Credits

Created by Suraj Kumar

Birsa Institute of Technology (BIT), Sindri

Suraj Kumar has created this Formula and 2100+ more formulas!

Verified by Ishita Goyal

Meerut Institute of Engineering and Technology (MIET), Meerut

Ishita Goyal has verified this Formula and 2600+ more formulas!

Other Formulas to find Stability Number

Go Stability Number for Failure on Slope without Seepage Water

S n = {(\cos (δ))}^{2} \cdot (\tan (δ) - \tan (Φ i))

Other formulas in Steady State Seepage Analysis Along The Slopes category

Go Weight of Soil Prism given Saturated Unit Weight

W prism = (γ saturated \cdot z \cdot b \cdot \cos (\frac{i \cdot π}{180}))

Go Inclined Length of Prism given Saturated Unit Weight

b = \frac{W prism}{γ saturated \cdot z \cdot \cos (\frac{i \cdot π}{180})}

Go Vertical Stress on Prism given Saturated Unit Weight

σ zkp = (γ saturated \cdot z \cdot \cos (\frac{i \cdot π}{180}))

Go Normal Stress Component given Saturated Unit Weight

σ n = (γ saturated \cdot z \cdot {(\cos (\frac{i \cdot π}{180}))}^{2})

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

Stability Number for Failure on Slope with Seepage of Water evaluator 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 evaluate 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 evaluate Stability Number for Failure on Slope with Seepage of Water using this online evaluator? To use this online evaluator 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.

FAQs on Stability Number for Failure on Slope with Seepage of Water

What is the formula to find Stability Number for Failure on Slope with Seepage of Water?

The formula of Stability Number for Failure on Slope with Seepage of Water is expressed as 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)). Here is an example- 0.041214 = (cos(1.51843644923478))^2*(tan(1.51843644923478)-((6000*tan(1.44635435112743))/11890)).

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

With Slope of Ground (δ), Buoyant Unit Weight (γ_b), Angle of Internal Friction of Soil (Φ_i) & Saturated Unit Weight of Soil (γ_saturated) we can find Stability Number for Failure on Slope with Seepage of Water using the formula - 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)). This formula also uses Cosine (cos), Tangent (tan) function(s).

What are the other ways to Calculate Stability Number?

Here are the different ways to Calculate Stability Number-

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

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Stability Number for Failure on Slope with Seepage of Water Formula

​GoStability Number for Failure on Slope without Seepage Water Formula

Stability Number for Failure on Slope with Seepage of Water Example

Stability Number for Failure on Slope with Seepage of Water Solution

Stability Number for Failure on Slope with Seepage of Water Formula Elements

Credits

Other Formulas to find Stability Number

Other formulas in Steady State Seepage Analysis Along The Slopes category

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

FAQs on Stability Number for Failure on Slope with Seepage of Water

Variable Name

GoStability Number for Failure on Slope without Seepage Water Formula