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Factor of Safety of Earth Dam Formula

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GoFactor of Safety in Absence of Flow Net Formula

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Factor of Safety is a measure of the load-carrying capacity of a structure or material compared to the actual load or stress that is applied to it. Check FAQs

f s = \frac{(c' \cdot L') + ((ΣN - ΣU) \cdot \tan (\frac{φ' \cdot π}{180}))}{ΣT}

f_s - Factor of Safety?c' - Effective Cohesion?L^' - Length of Slip Arc?ΣN - Sum of all Normal Component?ΣU - Total Pore Pressure?φ' - Effective Angle of Internal Friction?ΣT - Sum of all Tangential Component?π - Archimedes' constant?

Factor of Safety of Earth Dam Example

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Here is how the Factor of Safety of Earth Dam equation looks like with Values.

Here is how the Factor of Safety of Earth Dam equation looks like with Units.

Here is how the Factor of Safety of Earth Dam equation looks like.

2.7971 = \frac{(4.64 \cdot 3.0001) + ((5.01 - 2) \cdot \tan (\frac{9.99 \cdot 3.1416}{180}))}{4.98}

2.7971 = \frac{(4.64Pa \cdot 3.0001m) + ((5.01N - 2N) \cdot \tan (\frac{9.99° \cdot 3.1416}{180}))}{4.98N}

2.7971 = \frac{(4.64 \cdot 3.0001) + ((5.01 - 2) \cdot \tan (\frac{9.99 \cdot 3.1416}{180}))}{4.98}

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Factor of Safety of Earth Dam Solution

Follow our step by step solution on how to calculate Factor of Safety of Earth Dam?

FIRST Step Consider the formula

f s = \frac{(c' \cdot L') + ((ΣN - ΣU) \cdot \tan (\frac{φ' \cdot π}{180}))}{ΣT}

Next Step Substitute values of Variables

∴

f s = \frac{(4.64Pa \cdot 3.0001m) + ((5.01N - 2N) \cdot \tan (\frac{9.99° \cdot π}{180}))}{4.98N}

Next Step Substitute values of Constants

∴

f s = \frac{(4.64Pa \cdot 3.0001m) + ((5.01N - 2N) \cdot \tan (\frac{9.99° \cdot 3.1416}{180}))}{4.98N}

Next Step Convert Units

∴

f s = \frac{(4.64Pa \cdot 3.0001m) + ((5.01N - 2N) \cdot \tan (\frac{0.1744rad \cdot 3.1416}{180}))}{4.98N}

Next Step Prepare to Evaluate

∴

f s = \frac{(4.64 \cdot 3.0001) + ((5.01 - 2) \cdot \tan (\frac{0.1744 \cdot 3.1416}{180}))}{4.98}

Next Step Evaluate

∴

f s = 2.79711322161176

LAST Step Rounding Answer

∴

f s = 2.7971

Factor of Safety of Earth Dam Formula Elements

Variables

Constants

Functions

Factor of Safety

Factor of Safety is a measure of the load-carrying capacity of a structure or material compared to the actual load or stress that is applied to it.

Symbol: f_s

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Effective Cohesion

Effective Cohesion is the cohesive strength of soil that is attributed to the soil's inherent properties, such as chemical bonding and other physicochemical forces between soil particles.

Symbol: c'

Measurement: PressureUnit: Pa

Note: Value should be greater than 0.

Length of Slip Arc

Length of Slip Arc is the length of the arc formed by slip circle.

Symbol: L^'

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Sum of all Normal Component

Sum of all Normal Component means total normal force on slip circle.

Symbol: ΣN

Measurement: ForceUnit: N

Note: Value should be greater than 0.

Total Pore Pressure

Total Pore Pressure is the total pressure of the fluid in the pore space of the rock, when it exceeds the hydrostatic pressure, over pressure situation occurs.

Symbol: ΣU

Measurement: ForceUnit: N

Note: Value should be greater than 0.

Effective Angle of Internal Friction

Effective Angle of Internal Friction is the shear strength of soil due to the friction between soil particles when subjected to effective stress.

Symbol: φ'

Measurement: AngleUnit: °

Note: Value should be greater than 0.

Sum of all Tangential Component

Sum of all Tangential Component means total tangential component.

Symbol: ΣT

Measurement: ForceUnit: N

Note: Value should be greater than 0.

Archimedes' constant

Archimedes' constant is a mathematical constant that represents the ratio of the circumference of a circle to its diameter.

Symbol: π

Value: 3.14159265358979323846264338327950288

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

Creator Image

Created by Suraj Kumar

Birsa Institute of Technology (BIT), Sindri

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

Verifier Image

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 Factor of Safety

Go Factor of Safety in Absence of Flow Net

f s = \frac{(c' \cdot L') + (ΣN \cdot \tan (\frac{φ' \cdot π}{180}))}{ΣT}

Other formulas in Stability of Slopes In Earthen Dams category

Go Sum of All Tangential Component given Factor of Safety of Earth Dam

ΣT = \frac{(c' \cdot L') + ((ΣN - ΣU) \cdot \tan (\frac{φ' \cdot π}{180}))}{f s}

Go Effective Cohesion given Factor of Safety of Earth Dam

c' = \frac{(f s \cdot ΣT) - ((ΣN - ΣU) \cdot \tan (\frac{φ' \cdot π}{180}))}{L'}

See More

How to Evaluate Factor of Safety of Earth Dam?

Factor of Safety of Earth Dam evaluator uses Factor of Safety = ((Effective Cohesion*Length of Slip Arc)+((Sum of all Normal Component-Total Pore Pressure)*tan((Effective Angle of Internal Friction*pi)/180)))/Sum of all Tangential Component to evaluate the Factor of Safety, The Factor of Safety of Earth Dam formula is defined as ratio of ultimate stress and working stress. It is also called as factor of ignorance. The factor of safety is dependent on the type of load. Factor of Safety is denoted by f_s symbol.

How to evaluate Factor of Safety of Earth Dam using this online evaluator? To use this online evaluator for Factor of Safety of Earth Dam, enter Effective Cohesion (c'), Length of Slip Arc (L^'), Sum of all Normal Component (ΣN), Total Pore Pressure (ΣU), Effective Angle of Internal Friction (φ') & Sum of all Tangential Component (ΣT) and hit the calculate button.

FAQs on Factor of Safety of Earth Dam

What is the formula to find Factor of Safety of Earth Dam?

The formula of Factor of Safety of Earth Dam is expressed as Factor of Safety = ((Effective Cohesion*Length of Slip Arc)+((Sum of all Normal Component-Total Pore Pressure)*tan((Effective Angle of Internal Friction*pi)/180)))/Sum of all Tangential Component. Here is an example- 1.734851 = ((4.64*3.0001)+((5.01-2)*tan((0.174358392274201*pi)/180)))/4.98.

How to calculate Factor of Safety of Earth Dam?

With Effective Cohesion (c'), Length of Slip Arc (L^'), Sum of all Normal Component (ΣN), Total Pore Pressure (ΣU), Effective Angle of Internal Friction (φ') & Sum of all Tangential Component (ΣT) we can find Factor of Safety of Earth Dam using the formula - Factor of Safety = ((Effective Cohesion*Length of Slip Arc)+((Sum of all Normal Component-Total Pore Pressure)*tan((Effective Angle of Internal Friction*pi)/180)))/Sum of all Tangential Component. This formula also uses Archimedes' constant and Tangent (tan) function(s).

What are the other ways to Calculate Factor of Safety?

Here are the different ways to Calculate Factor of Safety-

Factor of Safety=((Effective Cohesion*Length of Slip Arc)+(Sum of all Normal Component*tan((Effective Angle of Internal Friction*pi)/180)))/Sum of all Tangential Component

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