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Depth of Prism given Factor of Safety for Cohesive Soil Formula

GoDepth of Prism given Weight of Soil Prism Formula

GoDepth of Prism given Volume per Unit Length of Prism Formula

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Depth of Prism is the length of prism along z direction. Check FAQs

z = \frac{c u}{(f s - (\frac{\tan ((Φ i))}{\tan ((I))})) \cdot γ \cdot \cos ((I)) \cdot \sin ((I))}

z - Depth of Prism?c_u - Unit Cohesion?f_s - Factor of Safety?Φ_i - Angle of Internal Friction of Soil?I - Angle of Inclination?γ - Unit Weight of Soil?

Depth of Prism given Factor of Safety for Cohesive Soil Example

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Here is how the Depth of Prism given Factor of Safety for Cohesive Soil equation looks like with Values.

Here is how the Depth of Prism given Factor of Safety for Cohesive Soil equation looks like with Units.

Here is how the Depth of Prism given Factor of Safety for Cohesive Soil equation looks like.

2.3365 = \frac{10}{(2.8 - (\frac{\tan ((82.87))}{\tan ((80))})) \cdot 18 \cdot \cos ((80)) \cdot \sin ((80))}

2.3365m = \frac{10Pa}{(2.8 - (\frac{\tan ((82.87°))}{\tan ((80°))})) \cdot 18kN/m³ \cdot \cos ((80°)) \cdot \sin ((80°))}

2.3365 = \frac{10}{(2.8 - (\frac{\tan ((82.87))}{\tan ((80))})) \cdot 18 \cdot \cos ((80)) \cdot \sin ((80))}

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Depth of Prism given Factor of Safety for Cohesive Soil Solution

Follow our step by step solution on how to calculate Depth of Prism given Factor of Safety for Cohesive Soil?

FIRST Step Consider the formula

z = \frac{c u}{(f s - (\frac{\tan ((Φ i))}{\tan ((I))})) \cdot γ \cdot \cos ((I)) \cdot \sin ((I))}

Next Step Substitute values of Variables

∴

z = \frac{10Pa}{(2.8 - (\frac{\tan ((82.87°))}{\tan ((80°))})) \cdot 18kN/m³ \cdot \cos ((80°)) \cdot \sin ((80°))}

Next Step Convert Units

∴

z = \frac{10Pa}{(2.8 - (\frac{\tan ((1.4464rad))}{\tan ((1.3963rad))})) \cdot 18kN/m³ \cdot \cos ((1.3963rad)) \cdot \sin ((1.3963rad))}

Next Step Prepare to Evaluate

∴

z = \frac{10}{(2.8 - (\frac{\tan ((1.4464))}{\tan ((1.3963))})) \cdot 18 \cdot \cos ((1.3963)) \cdot \sin ((1.3963))}

Next Step Evaluate

∴

z = 2.3365343879461m

LAST Step Rounding Answer

∴

z = 2.3365m

Depth of Prism given Factor of Safety for Cohesive Soil Formula Elements

Variables

Functions

Depth of Prism

Depth of Prism is the length of prism along z direction.

Symbol: z

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Depth of Prism

Unit Cohesion

Unit Cohesion is the force that holds together molecules or like particles within a soil.

Symbol: c_u

Measurement: PressureUnit: Pa

Note: Value should be greater than 0.

Formulas to find Unit Cohesion

Factor of Safety

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

Symbol: f_s

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Factor of Safety

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.

Formulas to find Angle of Internal Friction of Soil

Angle of Inclination

Angle of Inclination is defined as the angle measured from the horizontal surface of the wall or any object.

Symbol: I

Measurement: AngleUnit: °

Note: Value should be greater than 0.

Formulas to find Angle of Inclination

Unit Weight of Soil

Unit Weight of Soil mass is the ratio of the total weight of soil to the total volume of soil.

Symbol: γ

Measurement: Specific WeightUnit: kN/m³

Note: Value should be greater than 0.

Formulas to find Unit Weight of Soil

sin

Sine is a trigonometric function that describes the ratio of the length of the opposite side of a right triangle to the length of the hypotenuse.

Syntax: sin(Angle)

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)

Other Formulas to find Depth of Prism

Go Depth of Prism given Weight of Soil Prism

z = \frac{W}{γ \cdot b \cdot \cos ((I))}

Go Depth of Prism given Volume per Unit Length of Prism

z = \frac{V l}{b \cdot \cos ((I))}

Go Depth of Prism given Vertical Stress on Surface of Prism

z = \frac{σ vertical}{γ \cdot \cos ((I))}

Other formulas in Stability Analysis of Infinite Slopes in Prism category

Go Weight of Soil Prism in Stability Analysis

W = (γ \cdot z \cdot b \cdot \cos ((I)))

Go Unit Weight of Soil given Weight of Soil Prism

γ = \frac{W}{z \cdot b \cdot \cos ((I))}

Go Inclined Length along Slope given Weight of Soil Prism

b = \frac{W}{γ \cdot z \cdot \cos ((I))}

Go Angle of Inclination given Weight of Soil Prism

I = a \cos (\frac{W}{γ \cdot z \cdot b})

How to Evaluate Depth of Prism given Factor of Safety for Cohesive Soil?

Depth of Prism given Factor of Safety for Cohesive Soil evaluator uses Depth of Prism = Unit Cohesion/((Factor of Safety-(tan((Angle of Internal Friction of Soil))/tan((Angle of Inclination))))*Unit Weight of Soil*cos((Angle of Inclination))*sin((Angle of Inclination))) to evaluate the Depth of Prism, The Depth of Prism given Factor of Safety for Cohesive Soil is defined as the minimum depth required to prevent slope failure in cohesive soil with a specified factor of safety. Depth of Prism is denoted by z symbol.

How to evaluate Depth of Prism given Factor of Safety for Cohesive Soil using this online evaluator? To use this online evaluator for Depth of Prism given Factor of Safety for Cohesive Soil, enter Unit Cohesion (c_u), Factor of Safety (f_s), Angle of Internal Friction of Soil (Φ_i), Angle of Inclination (I) & Unit Weight of Soil (γ) and hit the calculate button.

FAQs on Depth of Prism given Factor of Safety for Cohesive Soil

What is the formula to find Depth of Prism given Factor of Safety for Cohesive Soil?

The formula of Depth of Prism given Factor of Safety for Cohesive Soil is expressed as Depth of Prism = Unit Cohesion/((Factor of Safety-(tan((Angle of Internal Friction of Soil))/tan((Angle of Inclination))))*Unit Weight of Soil*cos((Angle of Inclination))*sin((Angle of Inclination))). Here is an example- 2.336534 = 10/((2.8-(tan((1.44635435112743))/tan((1.3962634015952))))*18000*cos((1.3962634015952))*sin((1.3962634015952))).

How to calculate Depth of Prism given Factor of Safety for Cohesive Soil?

With Unit Cohesion (c_u), Factor of Safety (f_s), Angle of Internal Friction of Soil (Φ_i), Angle of Inclination (I) & Unit Weight of Soil (γ) we can find Depth of Prism given Factor of Safety for Cohesive Soil using the formula - Depth of Prism = Unit Cohesion/((Factor of Safety-(tan((Angle of Internal Friction of Soil))/tan((Angle of Inclination))))*Unit Weight of Soil*cos((Angle of Inclination))*sin((Angle of Inclination))). This formula also uses Sine (sin)Cosine (cos), Tangent (tan) function(s).

What are the other ways to Calculate Depth of Prism?

Here are the different ways to Calculate Depth of Prism-

Depth of Prism=Weight of Prism/(Unit Weight of Soil*Inclined Length*cos((Angle of Inclination)))
Depth of Prism=Volume per unit length of prism/(Inclined Length*cos((Angle of Inclination)))
Depth of Prism=Vertical Stress at a Point in Pascal/(Unit Weight of Soil*cos((Angle of Inclination)))

Can the Depth of Prism given Factor of Safety for Cohesive Soil be negative?

No, the Depth of Prism given Factor of Safety for Cohesive Soil, measured in Length cannot be negative.

Which unit is used to measure Depth of Prism given Factor of Safety for Cohesive Soil?

Depth of Prism given Factor of Safety for Cohesive Soil is usually measured using the Meter[m] for Length. Millimeter[m], Kilometer[m], Decimeter[m] are the few other units in which Depth of Prism given Factor of Safety for Cohesive Soil can be measured.

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Depth of Prism given Factor of Safety for Cohesive Soil Formula

​GoDepth of Prism given Weight of Soil Prism Formula

​GoDepth of Prism given Volume per Unit Length of Prism Formula

Depth of Prism given Factor of Safety for Cohesive Soil Example

Depth of Prism given Factor of Safety for Cohesive Soil Solution

Depth of Prism given Factor of Safety for Cohesive Soil Formula Elements

Other Formulas to find Depth of Prism

Other formulas in Stability Analysis of Infinite Slopes in Prism category

How to Evaluate Depth of Prism given Factor of Safety for Cohesive Soil?

FAQs on Depth of Prism given Factor of Safety for Cohesive Soil

Variable Name

GoDepth of Prism given Weight of Soil Prism Formula

GoDepth of Prism given Volume per Unit Length of Prism Formula