Factor of Safety for Cohesive Soil given Saturated Unit Weight Formula

GoFactor of Safety given Effective Normal Stress Formula

GoFactor of Safety given Submerged Unit Weight Formula

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Factor of Safety in Soil Mechanics expresses how much stronger a system is than it needs to be for an intended load. Check FAQs

F s = \frac{c' + (γ' \cdot z \cdot \tan ((φ)) \cdot {(\cos ((i)))}^{2})}{γ sat \cdot z \cdot \cos ((i)) \cdot \sin ((i))}

F_s - Factor of Safety in Soil Mechanics?c' - Effective Cohesion?γ^' - Submerged Unit Weight?z - Depth of Prism?φ - Angle of Internal Friction?i - Angle of Inclination to Horizontal in Soil?γ_sat - Saturated Unit Weight in Newton per Cubic Meter?

Factor of Safety for Cohesive Soil given Saturated Unit Weight Example

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Here is how the Factor of Safety for Cohesive Soil given Saturated Unit Weight equation looks like with Values.

Here is how the Factor of Safety for Cohesive Soil given Saturated Unit Weight equation looks like with Units.

Here is how the Factor of Safety for Cohesive Soil given Saturated Unit Weight equation looks like.

0.1834 = \frac{4 + (5.01 \cdot 3 \cdot \tan ((46)) \cdot {(\cos ((64)))}^{2})}{32.24 \cdot 3 \cdot \cos ((64)) \cdot \sin ((64))}

0.1834 = \frac{4Pa + (5.01N/m³ \cdot 3m \cdot \tan ((46°)) \cdot {(\cos ((64°)))}^{2})}{32.24N/m³ \cdot 3m \cdot \cos ((64°)) \cdot \sin ((64°))}

0.1834 = \frac{4 + (5.01 \cdot 3 \cdot \tan ((46)) \cdot {(\cos ((64)))}^{2})}{32.24 \cdot 3 \cdot \cos ((64)) \cdot \sin ((64))}

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Factor of Safety for Cohesive Soil given Saturated Unit Weight Solution

Follow our step by step solution on how to calculate Factor of Safety for Cohesive Soil given Saturated Unit Weight?

FIRST Step Consider the formula

F s = \frac{c' + (γ' \cdot z \cdot \tan ((φ)) \cdot {(\cos ((i)))}^{2})}{γ sat \cdot z \cdot \cos ((i)) \cdot \sin ((i))}

Next Step Substitute values of Variables

∴

F s = \frac{4Pa + (5.01N/m³ \cdot 3m \cdot \tan ((46°)) \cdot {(\cos ((64°)))}^{2})}{32.24N/m³ \cdot 3m \cdot \cos ((64°)) \cdot \sin ((64°))}

Next Step Convert Units

∴

F s = \frac{4Pa + (5.01N/m³ \cdot 3m \cdot \tan ((0.8029rad)) \cdot {(\cos ((1.117rad)))}^{2})}{32.24N/m³ \cdot 3m \cdot \cos ((1.117rad)) \cdot \sin ((1.117rad))}

Next Step Prepare to Evaluate

∴

F s = \frac{4 + (5.01 \cdot 3 \cdot \tan ((0.8029)) \cdot {(\cos ((1.117)))}^{2})}{32.24 \cdot 3 \cdot \cos ((1.117)) \cdot \sin ((1.117))}

Next Step Evaluate

∴

F s = 0.183449398100144

LAST Step Rounding Answer

∴

F s = 0.1834

Factor of Safety for Cohesive Soil given Saturated Unit Weight Formula Elements

Variables

Functions

Factor of Safety in Soil Mechanics

Factor of Safety in Soil Mechanics expresses how much stronger a system is than it needs to be for an intended load.

Symbol: F_s

Measurement: NAUnit: Unitless