Submerged Unit Weight for Steady Seepage along Slope Calculator

✖Factor of Safety in Soil Mechanics expresses how much stronger a system is than it needs to be for an intended load.ⓘ Factor of Safety in Soil Mechanics [F_s]			+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%
✖Depth of Prism is the length of prism along z direction.ⓘ Depth of Prism [z]			+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%
✖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%
✖Angle of Internal Friction of Soil is a shear strength parameter of soils.ⓘ Angle of Internal Friction of Soil [Φ_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 for Steady Seepage along Slope [y_S]

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Submerged Unit Weight for Steady Seepage along Slope

Formula

`"y"_{"S"} = (("F"_{"s"}*"γ"_{"saturated"}*"z"*cos(("i"*pi)/180)*sin(("i"*pi)/180))-"C")/("z"*tan(("Φ"_{"i"}*pi)/180)*(cos(("i"*pi)/180))^2)`

Example

`"8.936297kN/m³"= (("2.8"*"11.89kN/m³"*"3m"*cos(("64°"*pi)/180)*sin(("64°"*pi)/180))-"1.27kPa")/("3m"*tan(("82.87°"*pi)/180)*(cos(("64°"*pi)/180))^2)`

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Submerged Unit Weight for Steady Seepage along Slope Solution

STEP 0: Pre-Calculation Summary

Formula Used

Submerged Unit Weight in KN per Cubic Meter = ((Factor of Safety 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))-Cohesion in Soil as Kilopascal)/(Depth of Prism*tan((Angle of Internal Friction of Soil*pi)/180)*(cos((Angle of Inclination to Horizontal in Soil*pi)/180))^2)
y_S = ((F_s*γ_saturated*z*cos((i*pi)/180)*sin((i*pi)/180))-C)/(z*tan((Φ_i*pi)/180)*(cos((i*pi)/180))^2)
This formula uses 1 Constants, 3 Functions, 7 Variables

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Functions Used

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., sin(Angle)
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

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.
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.
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.
Depth of Prism - (Measured in Meter) - Depth of Prism is the length of prism along z direction.
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.
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.
Angle of Internal Friction of Soil - (Measured in Radian) - Angle of Internal Friction of Soil is a shear strength parameter of soils.

STEP 1: Convert Input(s) to Base Unit

Factor of Safety in Soil Mechanics: 2.8 --> No Conversion Required
Saturated Unit Weight of Soil: 11.89 Kilonewton per Cubic Meter --> 11890 Newton per Cubic Meter (Check conversion here)
Depth of Prism: 3 Meter --> 3 Meter No Conversion Required
Angle of Inclination to Horizontal in Soil: 64 Degree --> 1.11701072127616 Radian (Check conversion here)
Cohesion in Soil as Kilopascal: 1.27 Kilopascal --> 1270 Pascal (Check conversion here)
Angle of Internal Friction of Soil: 82.87 Degree --> 1.44635435112743 Radian (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

y_S = ((F_s*γ_saturated*z*cos((i*pi)/180)*sin((i*pi)/180))-C)/(z*tan((Φ_i*pi)/180)*(cos((i*pi)/180))^2) --> ((2.8*11890*3*cos((1.11701072127616*pi)/180)*sin((1.11701072127616*pi)/180))-1270)/(3*tan((1.44635435112743*pi)/180)*(cos((1.11701072127616*pi)/180))^2)

Evaluating ... ...

y_S = 8936.29722379064

STEP 3: Convert Result to Output's Unit

8936.29722379064 Newton per Cubic Meter -->8.93629722379064 Kilonewton per Cubic Meter (Check conversion here)

FINAL ANSWER

8.93629722379064 ≈ 8.936297 Kilonewton per Cubic Meter <-- Submerged Unit Weight in KN per Cubic Meter

(Calculation completed in 00.020 seconds)

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Created by Suraj Kumar

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

Submerged Unit Weight for Steady Seepage along Slope Formula

What is Submerged Unit Weight?

The weight of the solids in air minus the weight of water displaced by the solids per unit of volume of soil mass; the saturated unit weight minus the unit weight of water.

How to Calculate Submerged Unit Weight for Steady Seepage along Slope?

Submerged Unit Weight for Steady Seepage along Slope calculator uses Submerged Unit Weight in KN per Cubic Meter = ((Factor of Safety 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))-Cohesion in Soil as Kilopascal)/(Depth of Prism*tan((Angle of Internal Friction of Soil*pi)/180)*(cos((Angle of Inclination to Horizontal in Soil*pi)/180))^2) to calculate the Submerged Unit Weight in KN per Cubic Meter, The Submerged Unit Weight for Steady Seepage along Slope is defined as the value of submerged unit weight when we have prior information of other parameters used. Submerged Unit Weight in KN per Cubic Meter is denoted by y_S symbol.

How to calculate Submerged Unit Weight for Steady Seepage along Slope using this online calculator? To use this online calculator for Submerged Unit Weight for Steady Seepage along Slope, enter Factor of Safety in Soil Mechanics (F_s), Saturated Unit Weight of Soil (γ_saturated), Depth of Prism (z), Angle of Inclination to Horizontal in Soil (i), Cohesion in Soil as Kilopascal (C) & Angle of Internal Friction of Soil (Φ_i) and hit the calculate button. Here is how the Submerged Unit Weight for Steady Seepage along Slope calculation can be explained with given input values -> 0.008936 = ((2.8*11890*3*cos((1.11701072127616*pi)/180)*sin((1.11701072127616*pi)/180))-1270)/(3*tan((1.44635435112743*pi)/180)*(cos((1.11701072127616*pi)/180))^2).

FAQ

What is Submerged Unit Weight for Steady Seepage along Slope?

The Submerged Unit Weight for Steady Seepage along Slope is defined as the value of submerged unit weight when we have prior information of other parameters used and is represented as y_S = ((F_s*γ_saturated*z*cos((i*pi)/180)*sin((i*pi)/180))-C)/(z*tan((Φ_i*pi)/180)*(cos((i*pi)/180))^2) or Submerged Unit Weight in KN per Cubic Meter = ((Factor of Safety 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))-Cohesion in Soil as Kilopascal)/(Depth of Prism*tan((Angle of Internal Friction of Soil*pi)/180)*(cos((Angle of Inclination to Horizontal in Soil*pi)/180))^2). Factor of Safety in Soil Mechanics expresses how much stronger a system is than it needs to be for an intended load, Saturated Unit Weight of Soil is the ratio of mass of saturated soil sample to total volume, Depth of Prism is the length of prism along z direction, Angle of Inclination to Horizontal in Soil is defined as the angle measured from the horizontal surface of the wall or any object, 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 & Angle of Internal Friction of Soil is a shear strength parameter of soils.

How to calculate Submerged Unit Weight for Steady Seepage along Slope?

The Submerged Unit Weight for Steady Seepage along Slope is defined as the value of submerged unit weight when we have prior information of other parameters used is calculated using Submerged Unit Weight in KN per Cubic Meter = ((Factor of Safety 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))-Cohesion in Soil as Kilopascal)/(Depth of Prism*tan((Angle of Internal Friction of Soil*pi)/180)*(cos((Angle of Inclination to Horizontal in Soil*pi)/180))^2). To calculate Submerged Unit Weight for Steady Seepage along Slope, you need Factor of Safety in Soil Mechanics (F_s), Saturated Unit Weight of Soil (γ_saturated), Depth of Prism (z), Angle of Inclination to Horizontal in Soil (i), Cohesion in Soil as Kilopascal (C) & Angle of Internal Friction of Soil (Φ_i). With our tool, you need to enter the respective value for Factor of Safety in Soil Mechanics, Saturated Unit Weight of Soil, Depth of Prism, Angle of Inclination to Horizontal in Soil, Cohesion in Soil as Kilopascal & Angle of Internal Friction of Soil and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

How many ways are there to calculate Submerged Unit Weight in KN per Cubic Meter?

In this formula, Submerged Unit Weight in KN per Cubic Meter uses Factor of Safety in Soil Mechanics, Saturated Unit Weight of Soil, Depth of Prism, Angle of Inclination to Horizontal in Soil, Cohesion in Soil as Kilopascal & Angle of Internal Friction of Soil. We can use 5 other way(s) to calculate the same, which is/are as follows -

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)
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)
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)))
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))))
Submerged Unit Weight in KN per Cubic Meter = ((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)-(Cohesion in Soil as Kilopascal/Critical Depth))/(-tan((Angle of Internal Friction of Soil*pi)/180)*(cos((Angle of Inclination to Horizontal in Soil*pi)/180))^2)

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