Critical Depth for Cohesive Soil Calculator

✖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.ⓘ Cohesion of Soil [c]			+10% -10%
✖Unit Weight of Soil mass is the ratio of the total weight of soil to the total volume of soil.ⓘ Unit Weight of Soil [γ]			+10% -10%
✖Angle of Inclination is defined as the angle measured from the horizontal surface of the wall or any object.ⓘ Angle of Inclination [I]			+10% -10%
✖Angle of Internal Friction is the angle measured between the normal force and resultant force .ⓘ Angle of Internal Friction [φ]			+10% -10%

✖The Critical Depth is defined as the depth of flow where energy is at a minimum for a particular discharge.ⓘ Critical Depth for Cohesive Soil [h_c]

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Formula

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Critical Depth for Cohesive Soil

Formula

`"h"_{"c"} = "c"/("γ"*(tan(("I"))-tan(("φ")))*(cos(("I")))^2)`

Example

`"1.196281m"="3.01kPa"/("18kN/m³"*(tan(("80°"))-tan(("46°")))*(cos(("80°")))^2)`

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Critical Depth for Cohesive Soil Solution

STEP 0: Pre-Calculation Summary

Formula Used

Critical Depth = Cohesion of Soil/(Unit Weight of Soil*(tan((Angle of Inclination))-tan((Angle of Internal Friction)))*(cos((Angle of Inclination)))^2)
h_c = c/(γ*(tan((I))-tan((φ)))*(cos((I)))^2)
This formula uses 2 Functions, 5 Variables

Functions Used

cos - Cosine of an angle is the ratio of the side adjacent to the angle to the hypotenuse of the triangle., 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., tan(Angle)

Variables Used

Critical Depth - (Measured in Meter) - The Critical Depth is defined as the depth of flow where energy is at a minimum for a particular discharge.
Cohesion of Soil - (Measured in Pascal) - 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.
Unit Weight of Soil - (Measured in Newton per Cubic Meter) - Unit Weight of Soil mass is the ratio of the total weight of soil to the total volume of soil.
Angle of Inclination - (Measured in Radian) - Angle of Inclination is defined as the angle measured from the horizontal surface of the wall or any object.
Angle of Internal Friction - (Measured in Radian) - Angle of Internal Friction is the angle measured between the normal force and resultant force .

STEP 1: Convert Input(s) to Base Unit

Cohesion of Soil: 3.01 Kilopascal --> 3010 Pascal (Check conversion here)
Unit Weight of Soil: 18 Kilonewton per Cubic Meter --> 18000 Newton per Cubic Meter (Check conversion here)
Angle of Inclination: 80 Degree --> 1.3962634015952 Radian (Check conversion here)
Angle of Internal Friction: 46 Degree --> 0.802851455917241 Radian (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

h_c = c/(γ*(tan((I))-tan((φ)))*(cos((I)))^2) --> 3010/(18000*(tan((1.3962634015952))-tan((0.802851455917241)))*(cos((1.3962634015952)))^2)

Evaluating ... ...

h_c = 1.19628148845819

STEP 3: Convert Result to Output's Unit

1.19628148845819 Meter --> No Conversion Required

FINAL ANSWER

1.19628148845819 ≈ 1.196281 Meter <-- Critical Depth

(Calculation completed in 00.020 seconds)

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Home » Engineering » Civil » Geotechnical Engineering » Stability Analysis of Infinite Slopes » Critical Depth for Cohesive Soil

Credits

Created by Suraj Kumar

Birsa Institute of Technology (BIT), Sindri

Suraj Kumar has created this Calculator and 2200+ more calculators!

Verified by Ishita Goyal

Meerut Institute of Engineering and Technology (MIET), Meerut

Ishita Goyal has verified this Calculator and 2600+ more calculators!

< 25 Stability Analysis of Infinite Slopes Calculators

Unit Weight of Soil given Critical Depth for Cohesive Soil

Go Unit Weight of Soil = Cohesion of Soil/(Critical Depth*(tan((Angle of Inclination))-tan((Angle of Internal Friction)))*(cos((Angle of Inclination)))^2)

Cohesion given Critical Depth for Cohesive Soil

Go Cohesion of Soil = (Critical Depth*Unit Weight of Soil*(tan((Angle of Inclination))-tan((Angle of Internal Friction)))*(cos((Angle of Inclination)))^2)

Critical Depth for Cohesive Soil

Go Critical Depth = Cohesion of Soil/(Unit Weight of Soil*(tan((Angle of Inclination))-tan((Angle of Internal Friction)))*(cos((Angle of Inclination)))^2)

Cohesion given Shear Strength of Cohesive Soil

Go Cohesion of Soil = Shear Strength in KN per Cubic Meter-(Normal Stress in Soil Mechanics*tan((Angle of Internal Friction of Soil*pi)/180))

Cohesion of Soil given Factor of Safety for Cohesive Soil

Go Cohesion of Soil = (Shear Stress in Cohesive Soil*Factor of Safety)-(Normal Stress in Soil Mechanics*tan((Angle of Internal Friction)))

Normal Stress given Factor of Safety for Cohesive Soil

Go Normal Stress = ((Shear Stress for Factor of Safety*Factor of Safety)-Unit Cohesion)/tan((Angle of Internal Friction of Soil))

Shear Stress given Factor of Safety for Cohesive Soil

Go Shear Stress for Factor of Safety = (Unit Cohesion+(Normal Stress*tan((Angle of Internal Friction of Soil))))/Factor of Safety

Shear Strength of Soil given Angle of Internal Friction

Go Shear Strength = (Shear Stress for Factor of Safety*(tan(Angle of Internal Friction of Soil)/tan(Angle of Inclination)))

Shear Stress of Soil given Angle of Internal Friction

Go Shear Stress for Factor of Safety = Shear Strength/(tan((Angle of Internal Friction))/tan((Angle of Inclination)))

Angle of Internal Friction given Shear Strength of Soil

Go Angle of Internal Friction of Soil = atan((Shear Strength/Shear Stress)*tan((Angle of Inclination)))

Normal Stress given Shear Strength of Cohesive Soil

Go Normal Stress in Mega Pascal = (Shear Strength-Cohesion of Soil)/tan((Angle of Internal Friction))

Shear Strength of Cohesive Soil

Go Shear Strength = Cohesion of Soil+(Normal Stress in Mega Pascal*tan((Angle of Internal Friction)))

Factor of Safety against Sliding given Angle of Internal Friction

Go Factor of Safety = (tan((Angle of Internal Friction of Soil))/tan((Angle of Inclination)))

Unit Weight of Soil given Stability Number for Cohesive Soil

Go Unit Weight of Soil = (Cohesion of Soil/(Stability Number*Critical Depth for Stability Number))

Critical Depth given Stability Number for Cohesive Soil

Go Critical Depth for Stability Number = (Cohesion of Soil/(Unit Weight of Soil*Stability Number))

Cohesion given Stability Number for Cohesive Soil

Go Cohesion of Soil = Stability Number*(Unit Weight of Soil*Critical Depth for Stability Number)

Normal Stress given Shear Stress of Cohesionless Soil

Go Normal Stress in Mega Pascal = Shear Stress for Factor of Safety*cot((Angle of Inclination))

Unit Weight of Soil given Mobilised Cohesion

Go Unit Weight of Soil = (Mobilised Cohesion/(Stability Number*Depth at Mobilised Cohesion))

Depth at Mobilised Cohesion

Go Depth at Mobilised Cohesion = (Mobilised Cohesion/(Unit Weight of Soil*Stability Number))

Mobilised Cohesion given Stability Number for Cohesive Soil

Go Mobilised Cohesion = (Stability Number*Unit Weight of Soil*Depth at Mobilised Cohesion)

Normal Stress given Shear Strength of Cohesionless Soil

Go Normal Stress in Mega Pascal = Shear Strength/tan((Angle of Internal Friction))

Shear Strength of Cohesionless Soil

Go Shear Strength = Normal Stress in Mega Pascal*tan((Angle of Internal Friction))

Angle of Internal Friction given Shear Strength of Cohesionless Soil

Go Angle of Internal Friction = atan(Shear Strength/Normal Stress in Mega Pascal)

Cohesion of Soil given Mobilised Cohesion

Go Cohesion of Soil = Mobilised Cohesion*Factor of Safety with respect to Cohesion

Mobilised Cohesion

Go Mobilised Cohesion = Cohesion of Soil/Factor of Safety with respect to Cohesion

Critical Depth for Cohesive Soil Formula

Critical Depth = Cohesion of Soil/(Unit Weight of Soil*(tan((Angle of Inclination))-tan((Angle of Internal Friction)))*(cos((Angle of Inclination)))^2)
h_c = c/(γ*(tan((I))-tan((φ)))*(cos((I)))^2)

What is Critical Depth?

When the specific energy is minimum for a given discharge flow will be critical flow and depth of flow will be called as critical depth of flow (y) and velocity of flow will be called as critical velocity.

How to Calculate Critical Depth for Cohesive Soil?

Critical Depth for Cohesive Soil calculator 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 calculate the Critical Depth, The Critical Depth for Cohesive Soil is defined as the depth at which soil strength equals applied stress, leading to slope instability or failure. Critical Depth is denoted by h_c symbol.

How to calculate Critical Depth for Cohesive Soil using this online calculator? To use this online calculator 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. Here is how the Critical Depth for Cohesive Soil calculation can be explained with given input values -> 1.192307 = 3010/(18000*(tan((1.3962634015952))-tan((0.802851455917241)))*(cos((1.3962634015952)))^2).

FAQ

What is Critical Depth for Cohesive Soil?

The Critical Depth for Cohesive Soil is defined as the depth at which soil strength equals applied stress, leading to slope instability or failure and is represented as h_c = c/(γ*(tan((I))-tan((φ)))*(cos((I)))^2) or Critical Depth = Cohesion of Soil/(Unit Weight of Soil*(tan((Angle of Inclination))-tan((Angle of Internal Friction)))*(cos((Angle of Inclination)))^2). 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, Unit Weight of Soil mass is the ratio of the total weight of soil to the total volume of soil, Angle of Inclination is defined as the angle measured from the horizontal surface of the wall or any object & Angle of Internal Friction is the angle measured between the normal force and resultant force .

How to calculate Critical Depth for Cohesive Soil?

The Critical Depth for Cohesive Soil is defined as the depth at which soil strength equals applied stress, leading to slope instability or failure is calculated using Critical Depth = Cohesion of Soil/(Unit Weight of Soil*(tan((Angle of Inclination))-tan((Angle of Internal Friction)))*(cos((Angle of Inclination)))^2). To calculate Critical Depth for Cohesive Soil, you need Cohesion of Soil (c), Unit Weight of Soil (γ), Angle of Inclination (I) & Angle of Internal Friction (φ). With our tool, you need to enter the respective value for Cohesion of Soil, Unit Weight of Soil, Angle of Inclination & Angle of Internal Friction and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

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