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Critical Depth for Cohesive Soil Formula

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Critical Depth is the depth within a soil profile where the net pressure or stress acting on the soil particles is zero. Check FAQs

h c = \frac{c}{γ \cdot (\tan ((I)) - \tan ((φ))) \cdot {(\cos ((I)))}^{2}}

h_c - Critical Depth?c - Cohesion of Soil?γ - Unit Weight of Soil?I - Angle of Inclination?φ - Angle of Internal Friction?

Critical Depth for Cohesive Soil Example

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Here is how the Critical Depth for Cohesive Soil equation looks like with Values.

Here is how the Critical Depth for Cohesive Soil equation looks like with Units.

Here is how the Critical Depth for Cohesive Soil equation looks like.

1.0099 = \frac{2.511}{18 \cdot (\tan ((80)) - \tan ((47.48))) \cdot {(\cos ((80)))}^{2}}

1.0099m = \frac{2.511kPa}{18kN/m³ \cdot (\tan ((80°)) - \tan ((47.48°))) \cdot {(\cos ((80°)))}^{2}}

1.0099 = \frac{2.511}{18 \cdot (\tan ((80)) - \tan ((47.48))) \cdot {(\cos ((80)))}^{2}}

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Critical Depth for Cohesive Soil Solution

Follow our step by step solution on how to calculate Critical Depth for Cohesive Soil?

FIRST Step Consider the formula

h c = \frac{c}{γ \cdot (\tan ((I)) - \tan ((φ))) \cdot {(\cos ((I)))}^{2}}

Next Step Substitute values of Variables

∴

h c = \frac{2.511kPa}{18kN/m³ \cdot (\tan ((80°)) - \tan ((47.48°))) \cdot {(\cos ((80°)))}^{2}}

Next Step Convert Units

∴

h c = \frac{2511Pa}{18000N/m³ \cdot (\tan ((1.3963rad)) - \tan ((0.8287rad))) \cdot {(\cos ((1.3963rad)))}^{2}}

Next Step Prepare to Evaluate

∴

h c = \frac{2511}{18000 \cdot (\tan ((1.3963)) - \tan ((0.8287))) \cdot {(\cos ((1.3963)))}^{2}}

Next Step Evaluate

∴

h c = 1.00994637005937m

LAST Step Rounding Answer

∴

h c = 1.0099m

Critical Depth for Cohesive Soil Formula Elements

Variables

Functions

Critical Depth

Critical Depth is the depth within a soil profile where the net pressure or stress acting on the soil particles is zero.

Symbol: h_c

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Critical Depth

Cohesion of Soil

Cohesion of Soil is the ability of like particles within soil to hold onto each other. It is the shear strength or force that binds together like particles in the structure of a soil.

Symbol: c

Measurement: PressureUnit: kPa

Note: Value should be greater than 0.

Formulas to find Cohesion of Soil

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

Angle of Inclination

Angle of Inclination is 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

Angle of Internal Friction

Angle of Internal Friction is the angle measured between the normal force and resultant force.

Symbol: φ

Measurement: AngleUnit: °

Note: Value should be greater than 0.

Formulas to find Angle of Internal Friction

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 in Stability Analysis of Infinite Slopes category

Go Shear Strength of Cohesionless Soil

τ s = σ nm \cdot \tan ((φ))

Go Normal Stress given Shear Strength of Cohesionless Soil

σ nm = \frac{τ s}{\tan ((φ))}

Go Angle of Internal Friction given Shear Strength of Cohesionless Soil

φ = a \tan (\frac{τ s}{σ nm})

Go Normal Stress given Shear Stress of Cohesionless Soil

σ nm = 𝜏 Shearstress \cdot \cot ((I))

How to Evaluate Critical Depth for Cohesive Soil?

Critical Depth for Cohesive Soil evaluator uses Critical Depth = Cohesion of Soil/(Unit Weight of Soil*(tan((Angle of Inclination))-tan((Angle of Internal Friction)))*(cos((Angle of Inclination)))^2) to evaluate the Critical Depth, The Critical Depth for Cohesive Soil formula is defined as the measure of the value of depth at which soil strength equals applied stress, leading to slope instability or failure. Critical Depth is denoted by h_c symbol.

How to evaluate Critical Depth for Cohesive Soil using this online evaluator? To use this online evaluator for Critical Depth for Cohesive Soil, enter Cohesion of Soil (c), Unit Weight of Soil (γ), Angle of Inclination (I) & Angle of Internal Friction (φ) and hit the calculate button.

FAQs on Critical Depth for Cohesive Soil

What is the formula to find Critical Depth for Cohesive Soil?

The formula of Critical Depth for Cohesive Soil is expressed as Critical Depth = Cohesion of Soil/(Unit Weight of Soil*(tan((Angle of Inclination))-tan((Angle of Internal Friction)))*(cos((Angle of Inclination)))^2). Here is an example- 1.210649 = 2511/(18000*(tan((1.3962634015952))-tan((0.828682328846752)))*(cos((1.3962634015952)))^2).

How to calculate Critical Depth for Cohesive Soil?

With Cohesion of Soil (c), Unit Weight of Soil (γ), Angle of Inclination (I) & Angle of Internal Friction (φ) we can find Critical Depth for Cohesive Soil using the formula - Critical Depth = Cohesion of Soil/(Unit Weight of Soil*(tan((Angle of Inclination))-tan((Angle of Internal Friction)))*(cos((Angle of Inclination)))^2). This formula also uses Cosine (cos), Tangent (tan) function(s).

Can the Critical Depth for Cohesive Soil be negative?

No, the Critical Depth for Cohesive Soil, measured in Length cannot be negative.

Which unit is used to measure Critical Depth for Cohesive Soil?

Critical Depth 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 Critical Depth for Cohesive Soil can be measured.

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Critical Depth for Cohesive Soil Formula

Critical Depth for Cohesive Soil Example

Critical Depth for Cohesive Soil Solution

Critical Depth for Cohesive Soil Formula Elements

Other formulas in Stability Analysis of Infinite Slopes category

How to Evaluate Critical Depth for Cohesive Soil?

FAQs on Critical Depth for Cohesive Soil

Variable Name