Critical Depth given Saturated Unit Weight Calculator

✖Cohesion in Soil as Kilopascal 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 in Soil as Kilopascal [C]			+10% -10%
✖Saturated Unit Weight of Soil is the ratio of mass of saturated soil sample to total volume.ⓘ Saturated Unit Weight of Soil [γ_saturated]			+10% -10%
✖Angle of Inclination to Horizontal in Soil is defined as the angle measured from the horizontal surface of the wall or any object.ⓘ Angle of Inclination to Horizontal in Soil [i]			+10% -10%
✖Submerged Unit Weight in KN per Cubic Meter is the unit weight of a weight of soil as observed under water in a saturated condition of course.ⓘ Submerged Unit Weight in KN per Cubic Meter [y_S]			+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 given Saturated Unit Weight [h_c]

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Formula

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Critical Depth given Saturated Unit Weight

Formula

`"h"_{"c"} = "C"/(("γ"_{"saturated"}*tan(("i"*pi)/180)*(cos(("i"*pi)/180))^2)-("y"_{"S"}*tan(("φ"*pi)/180)*(cos(("i"*pi)/180))^2))`

Example

`"7.853906m"="1.27kPa"/(("11.89kN/m³"*tan(("64°"*pi)/180)*(cos(("64°"*pi)/180))^2)-("5.00kN/m³"*tan(("46°"*pi)/180)*(cos(("64°"*pi)/180))^2))`

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Critical Depth given Saturated Unit Weight Solution

STEP 0: Pre-Calculation Summary

Formula Used

Critical Depth = Cohesion in Soil as Kilopascal/((Saturated Unit Weight of Soil*tan((Angle of Inclination to Horizontal in Soil*pi)/180)*(cos((Angle of Inclination to Horizontal in Soil*pi)/180))^2)-(Submerged Unit Weight in KN per Cubic Meter*tan((Angle of Internal Friction*pi)/180)*(cos((Angle of Inclination to Horizontal in Soil*pi)/180))^2))
h_c = C/((γ_saturated*tan((i*pi)/180)*(cos((i*pi)/180))^2)-(y_S*tan((φ*pi)/180)*(cos((i*pi)/180))^2))
This formula uses 1 Constants, 2 Functions, 6 Variables

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

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 in Soil as Kilopascal - (Measured in Pascal) - Cohesion in Soil as Kilopascal 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.
Saturated Unit Weight of Soil - (Measured in Newton per Cubic Meter) - Saturated Unit Weight of Soil is the ratio of mass of saturated soil sample to total volume.
Angle of Inclination to Horizontal in Soil - (Measured in Radian) - Angle of Inclination to Horizontal in Soil is defined as the angle measured from the horizontal surface of the wall or any object.
Submerged Unit Weight in KN per Cubic Meter - (Measured in Newton per Cubic Meter) - Submerged Unit Weight in KN per Cubic Meter is the unit weight of a weight of soil as observed under water in a saturated condition of course.
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 in Soil as Kilopascal: 1.27 Kilopascal --> 1270 Pascal (Check conversion here)
Saturated Unit Weight of Soil: 11.89 Kilonewton per Cubic Meter --> 11890 Newton per Cubic Meter (Check conversion here)
Angle of Inclination to Horizontal in Soil: 64 Degree --> 1.11701072127616 Radian (Check conversion here)
Submerged Unit Weight in KN per Cubic Meter: 5 Kilonewton per Cubic Meter --> 5000 Newton per Cubic Meter (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_saturated*tan((i*pi)/180)*(cos((i*pi)/180))^2)-(y_S*tan((φ*pi)/180)*(cos((i*pi)/180))^2)) --> 1270/((11890*tan((1.11701072127616*pi)/180)*(cos((1.11701072127616*pi)/180))^2)-(5000*tan((0.802851455917241*pi)/180)*(cos((1.11701072127616*pi)/180))^2))

Evaluating ... ...

h_c = 7.85390614906757

STEP 3: Convert Result to Output's Unit

7.85390614906757 Meter --> No Conversion Required

FINAL ANSWER

7.85390614906757 ≈ 7.853906 Meter <-- Critical Depth

(Calculation completed in 00.004 seconds)

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Home » Engineering » Civil » Geotechnical Engineering » Seepage Analysis » Steady State Seepage Analysis Along The Slopes » Critical Depth given Saturated Unit Weight

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Birsa Institute of Technology (BIT), Sindri

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< 25 Steady State Seepage Analysis Along The Slopes Calculators

Factor of Safety for Cohesive Soil given Saturated Unit Weight

Go Factor of Safety in Soil Mechanics = (Effective Cohesion+(Submerged Unit Weight*Depth of Prism*tan((Angle of Internal Friction))*(cos((Angle of Inclination to Horizontal in Soil)))^2))/(Saturated Unit Weight in Newton per Cubic Meter*Depth of Prism*cos((Angle of Inclination to Horizontal in Soil))*sin((Angle of Inclination to Horizontal in Soil)))

Shear Strength given Submerged Unit Weight

Go Shear Strength in KN per Cubic Meter = (Shear Stress in Soil Mechanics*Submerged Unit Weight in KN per Cubic Meter*tan((Angle of Internal Friction*pi)/180))/(Saturated Unit Weight of Soil*tan((Angle of Inclination to Horizontal in Soil*pi)/180))

Submerged Unit Weight given Factor of Safety

Go Submerged Unit Weight in KN per Cubic Meter = Factor of Safety in Soil Mechanics/((tan((Angle of Internal Friction of Soil*pi)/180))/(Saturated Unit Weight of Soil*tan((Angle of Inclination to Horizontal in Soil*pi)/180)))

Factor of Safety given Submerged Unit Weight

Go Factor of Safety in Soil Mechanics = (Submerged Unit Weight in KN per Cubic Meter*tan((Angle of Internal Friction of Soil*pi)/180))/(Saturated Unit Weight of Soil*tan((Angle of Inclination to Horizontal in Soil*pi)/180))

Submerged Unit Weight given Shear Strength

Go Submerged Unit Weight in KN per Cubic Meter = (Shear Strength in KN per Cubic Meter/Shear Stress in Soil Mechanics)/((tan((Angle of Internal Friction of Soil)))/(Saturated Unit Weight of Soil*tan((Angle of Inclination to Horizontal in Soil))))

Shear Stress given Submerged Unit Weight

Go Shear Stress in Soil Mechanics = Shear Strength in KN per Cubic Meter/((Submerged Unit Weight in KN per Cubic Meter*tan((Angle of Internal Friction)))/(Saturated Unit Weight of Soil*tan((Angle of Inclination to Horizontal in Soil))))

Shear Stress Component given Saturated Unit Weight

Go Shear Stress in Soil Mechanics = (Saturated Unit Weight of Soil*Depth of Prism*cos((Angle of Inclination to Horizontal in Soil*pi)/180)*sin((Angle of Inclination to Horizontal in Soil*pi)/180))

Submerged Unit Weight given Upward Force

Go Submerged Unit Weight in KN per Cubic Meter = (Normal Stress in Soil Mechanics-Upward Force in Seepage Analysis)/(Depth of Prism*(cos((Angle of Inclination to Horizontal in Soil*pi)/180))^2)

Normal Stress Component given Submerged Unit Weight and Depth of Prism

Go Normal Stress in Soil Mechanics = Upward Force in Seepage Analysis+(Submerged Unit Weight in KN per Cubic Meter*Depth of Prism*(cos((Angle of Inclination to Horizontal in Soil*pi)/180))^2)

Upward Force due to Seepage Water given Submerged Unit Weight

Go Upward Force in Seepage Analysis = Normal Stress in Soil Mechanics-(Submerged Unit Weight in KN per Cubic Meter*Depth of Prism*(cos((Angle of Inclination to Horizontal in Soil*pi)/180))^2)

Effective Normal Stress given Saturated Unit Weight

Go Effective Normal Stress in Soil Mechanics = ((Saturated Unit Weight of Soil-Unit Weight of Water)*Depth of Prism*(cos((Angle of Inclination to Horizontal in Soil*pi)/180))^2)

Unit Weight of Water given Effective Normal Stress

Go Unit Weight of Water = Saturated Unit Weight of Soil-(Effective Normal Stress in Soil Mechanics/(Depth of Prism*(cos((Angle of Inclination to Horizontal in Soil*pi)/180))^2))

Inclined Length of Prism given Saturated Unit Weight

Go Inclined Length of Prism = Weight of Prism in Soil Mechanics/(Saturated Unit Weight of Soil*Depth of Prism*cos((Angle of Inclination to Horizontal in Soil*pi)/180))

Weight of Soil Prism given Saturated Unit Weight

Go Weight of Prism in Soil Mechanics = (Saturated Unit Weight of Soil*Depth of Prism*Inclined Length of Prism*cos((Angle of Inclination to Horizontal in Soil*pi)/180))

Effective Normal Stress given Submerged Unit Weight

Go Effective Normal Stress in Soil Mechanics = (Submerged Unit Weight in KN per Cubic Meter*Depth of Prism*(cos((Angle of Inclination to Horizontal in Soil*pi)/180))^2)

Submerged Unit Weight given Effective Normal Stress

Go Submerged Unit Weight in KN per Cubic Meter = Effective Normal Stress in Soil Mechanics/(Depth of Prism*(cos((Angle of Inclination to Horizontal in Soil*pi)/180))^2)

Effective Normal Stress given Factor of Safety

Go Effective Normal Stress in Soil Mechanics = Factor of Safety in Soil Mechanics/((tan((Angle of Internal Friction of Soil*pi)/180))/Shear Stress in Soil Mechanics)

Factor of Safety given Effective Normal Stress

Go Factor of Safety in Soil Mechanics = (Effective Normal Stress in Soil Mechanics*tan((Angle of Internal Friction*pi)/180))/Shear Stress in Soil Mechanics

Vertical Stress on Prism given Saturated Unit Weight

Go Vertical Stress at a Point in Kilopascal = (Saturated Unit Weight of Soil*Depth of Prism*cos((Angle of Inclination to Horizontal in Soil*pi)/180))

Normal Stress Component given Saturated Unit Weight

Go Normal Stress in Soil Mechanics = (Saturated Unit Weight of Soil*Depth of Prism*(cos((Angle of Inclination to Horizontal in Soil*pi)/180))^2)

Unit Weight of Water given Upward Force due to Seepage Water

Go Unit Weight of Water = Upward Force in Seepage Analysis/(Depth of Prism*(cos((Angle of Inclination to Horizontal in Soil*pi)/180))^2)

Upward Force due to Seepage Water

Go Upward Force in Seepage Analysis = (Unit Weight of Water*Depth of Prism*(cos((Angle of Inclination to Horizontal in Soil*pi)/180))^2)

Effective Normal Stress given Upward Force due to Seepage Water

Go Effective Normal Stress in Soil Mechanics = Normal Stress in Soil Mechanics-Upward Force in Seepage Analysis

Upward Force due to Seepage Water given Effective Normal Stress

Go Upward Force in Seepage Analysis = Normal Stress in Soil Mechanics-Effective Normal Stress in Soil Mechanics

Normal Stress Component given Effective Normal Stress

Go Normal Stress in Soil Mechanics = Effective Normal Stress in Soil Mechanics+Upward Force in Seepage Analysis

Critical Depth given Saturated Unit Weight Formula

What is Saturated Unit Weight?

Saturated unit weight is equal to the bulk density when the total voids is filled up with water.Buoyant unit weight or submerged unit weight is the effective mass per unit volume when the soil is submerged below standing water or below the ground water table.

How to Calculate Critical Depth given Saturated Unit Weight?

Critical Depth given Saturated Unit Weight calculator uses Critical Depth = Cohesion in Soil as Kilopascal/((Saturated Unit Weight of Soil*tan((Angle of Inclination to Horizontal in Soil*pi)/180)*(cos((Angle of Inclination to Horizontal in Soil*pi)/180))^2)-(Submerged Unit Weight in KN per Cubic Meter*tan((Angle of Internal Friction*pi)/180)*(cos((Angle of Inclination to Horizontal in Soil*pi)/180))^2)) to calculate the Critical Depth, The Critical Depth given Saturated Unit Weight is defined as the value of critical depth when we have prior information of other parameters used. Critical Depth is denoted by h_c symbol.

How to calculate Critical Depth given Saturated Unit Weight using this online calculator? To use this online calculator for Critical Depth given Saturated Unit Weight, enter Cohesion in Soil as Kilopascal (C), Saturated Unit Weight of Soil (γ_saturated), Angle of Inclination to Horizontal in Soil (i), Submerged Unit Weight in KN per Cubic Meter (y_S) & Angle of Internal Friction (φ) and hit the calculate button. Here is how the Critical Depth given Saturated Unit Weight calculation can be explained with given input values -> 7.853906 = 1270/((11890*tan((1.11701072127616*pi)/180)*(cos((1.11701072127616*pi)/180))^2)-(5000*tan((0.802851455917241*pi)/180)*(cos((1.11701072127616*pi)/180))^2)).

FAQ

What is Critical Depth given Saturated Unit Weight?

The Critical Depth given Saturated Unit Weight is defined as the value of critical depth when we have prior information of other parameters used and is represented as h_c = C/((γ_saturated*tan((i*pi)/180)*(cos((i*pi)/180))^2)-(y_S*tan((φ*pi)/180)*(cos((i*pi)/180))^2)) or Critical Depth = Cohesion in Soil as Kilopascal/((Saturated Unit Weight of Soil*tan((Angle of Inclination to Horizontal in Soil*pi)/180)*(cos((Angle of Inclination to Horizontal in Soil*pi)/180))^2)-(Submerged Unit Weight in KN per Cubic Meter*tan((Angle of Internal Friction*pi)/180)*(cos((Angle of Inclination to Horizontal in Soil*pi)/180))^2)). Cohesion in Soil as Kilopascal 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, Saturated Unit Weight of Soil is the ratio of mass of saturated soil sample to total volume, Angle of Inclination to Horizontal in Soil is defined as the angle measured from the horizontal surface of the wall or any object, Submerged Unit Weight in KN per Cubic Meter is the unit weight of a weight of soil as observed under water in a saturated condition of course & Angle of Internal Friction is the angle measured between the normal force and resultant force .

How to calculate Critical Depth given Saturated Unit Weight?

The Critical Depth given Saturated Unit Weight is defined as the value of critical depth when we have prior information of other parameters used is calculated using Critical Depth = Cohesion in Soil as Kilopascal/((Saturated Unit Weight of Soil*tan((Angle of Inclination to Horizontal in Soil*pi)/180)*(cos((Angle of Inclination to Horizontal in Soil*pi)/180))^2)-(Submerged Unit Weight in KN per Cubic Meter*tan((Angle of Internal Friction*pi)/180)*(cos((Angle of Inclination to Horizontal in Soil*pi)/180))^2)). To calculate Critical Depth given Saturated Unit Weight, you need Cohesion in Soil as Kilopascal (C), Saturated Unit Weight of Soil (γ_saturated), Angle of Inclination to Horizontal in Soil (i), Submerged Unit Weight in KN per Cubic Meter (y_S) & Angle of Internal Friction (φ). With our tool, you need to enter the respective value for Cohesion in Soil as Kilopascal, Saturated Unit Weight of Soil, Angle of Inclination to Horizontal in Soil, Submerged Unit Weight in KN per Cubic Meter & 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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