Saturated Unit Weight given Critical Depth Solution

STEP 0: Pre-Calculation Summary
Formula Used
Saturated Unit Weight of Soil = ((Effective Cohesion in Geotech as Kilopascal/Critical Depth)-(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))/(tan((Angle of Inclination to Horizontal in Soil*pi)/180)*(cos((Angle of Inclination to Horizontal in Soil*pi)/180))^2)
γsaturated = ((Ceff/hc)-(yS*tan((φ*pi)/180)*(cos((i*pi)/180))^2))/(tan((i*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
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.
Effective Cohesion in Geotech as Kilopascal - (Measured in Pascal) - Effective Cohesion in Geotech as Kilopascal is the consistency of soft to hard defined on the basis of the standard CSN 73 1001 for different states of consistency and degree of saturation.
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.
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 .
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.
STEP 1: Convert Input(s) to Base Unit
Effective Cohesion in Geotech as Kilopascal: 0.32 Kilopascal --> 320 Pascal (Check conversion here)
Critical Depth: 1.01 Meter --> 1.01 Meter No Conversion Required
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)
Angle of Inclination to Horizontal in Soil: 64 Degree --> 1.11701072127616 Radian (Check conversion here)
STEP 2: Evaluate Formula
Substituting Input Values in Formula
γsaturated = ((Ceff/hc)-(yS*tan((φ*pi)/180)*(cos((i*pi)/180))^2))/(tan((i*pi)/180)*(cos((i*pi)/180))^2) --> ((320/1.01)-(5000*tan((0.802851455917241*pi)/180)*(cos((1.11701072127616*pi)/180))^2))/(tan((1.11701072127616*pi)/180)*(cos((1.11701072127616*pi)/180))^2)
Evaluating ... ...
γsaturated = 12662.1052925916
STEP 3: Convert Result to Output's Unit
12662.1052925916 Newton per Cubic Meter -->12.6621052925916 Kilonewton per Cubic Meter (Check conversion here)
FINAL ANSWER
12.6621052925916 12.66211 Kilonewton per Cubic Meter <-- Saturated Unit Weight of Soil
(Calculation completed in 00.035 seconds)

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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

Saturated Unit Weight given Critical Depth Formula

Saturated Unit Weight of Soil = ((Effective Cohesion in Geotech as Kilopascal/Critical Depth)-(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))/(tan((Angle of Inclination to Horizontal in Soil*pi)/180)*(cos((Angle of Inclination to Horizontal in Soil*pi)/180))^2)
γsaturated = ((Ceff/hc)-(yS*tan((φ*pi)/180)*(cos((i*pi)/180))^2))/(tan((i*pi)/180)*(cos((i*pi)/180))^2)

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 Saturated Unit Weight given Critical Depth?

Saturated Unit Weight given Critical Depth calculator uses Saturated Unit Weight of Soil = ((Effective Cohesion in Geotech as Kilopascal/Critical Depth)-(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))/(tan((Angle of Inclination to Horizontal in Soil*pi)/180)*(cos((Angle of Inclination to Horizontal in Soil*pi)/180))^2) to calculate the Saturated Unit Weight of Soil, The Saturated Unit Weight given Critical Depth is defined as the value of saturated unit weight when we have prior information of other parameters used. Saturated Unit Weight of Soil is denoted by γsaturated symbol.

How to calculate Saturated Unit Weight given Critical Depth using this online calculator? To use this online calculator for Saturated Unit Weight given Critical Depth, enter Effective Cohesion in Geotech as Kilopascal (Ceff), Critical Depth (hc), Submerged Unit Weight in KN per Cubic Meter (yS), Angle of Internal Friction (φ) & Angle of Inclination to Horizontal in Soil (i) and hit the calculate button. Here is how the Saturated Unit Weight given Critical Depth calculation can be explained with given input values -> 0.012662 = ((320/1.01)-(5000*tan((0.802851455917241*pi)/180)*(cos((1.11701072127616*pi)/180))^2))/(tan((1.11701072127616*pi)/180)*(cos((1.11701072127616*pi)/180))^2).

FAQ

What is Saturated Unit Weight given Critical Depth?
The Saturated Unit Weight given Critical Depth is defined as the value of saturated unit weight when we have prior information of other parameters used and is represented as γsaturated = ((Ceff/hc)-(yS*tan((φ*pi)/180)*(cos((i*pi)/180))^2))/(tan((i*pi)/180)*(cos((i*pi)/180))^2) or Saturated Unit Weight of Soil = ((Effective Cohesion in Geotech as Kilopascal/Critical Depth)-(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))/(tan((Angle of Inclination to Horizontal in Soil*pi)/180)*(cos((Angle of Inclination to Horizontal in Soil*pi)/180))^2). Effective Cohesion in Geotech as Kilopascal is the consistency of soft to hard defined on the basis of the standard CSN 73 1001 for different states of consistency and degree of saturation, The Critical Depth is defined as the depth of flow where energy is at a minimum for a particular discharge, 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 & Angle of Inclination to Horizontal in Soil is defined as the angle measured from the horizontal surface of the wall or any object.
How to calculate Saturated Unit Weight given Critical Depth?
The Saturated Unit Weight given Critical Depth is defined as the value of saturated unit weight when we have prior information of other parameters used is calculated using Saturated Unit Weight of Soil = ((Effective Cohesion in Geotech as Kilopascal/Critical Depth)-(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))/(tan((Angle of Inclination to Horizontal in Soil*pi)/180)*(cos((Angle of Inclination to Horizontal in Soil*pi)/180))^2). To calculate Saturated Unit Weight given Critical Depth, you need Effective Cohesion in Geotech as Kilopascal (Ceff), Critical Depth (hc), Submerged Unit Weight in KN per Cubic Meter (yS), Angle of Internal Friction (φ) & Angle of Inclination to Horizontal in Soil (i). With our tool, you need to enter the respective value for Effective Cohesion in Geotech as Kilopascal, Critical Depth, Submerged Unit Weight in KN per Cubic Meter, Angle of Internal Friction & Angle of Inclination to Horizontal in 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 Saturated Unit Weight of Soil?
In this formula, Saturated Unit Weight of Soil uses Effective Cohesion in Geotech as Kilopascal, Critical Depth, Submerged Unit Weight in KN per Cubic Meter, Angle of Internal Friction & Angle of Inclination to Horizontal in Soil. We can use 1 other way(s) to calculate the same, which is/are as follows -
  • Saturated Unit Weight of Soil = (Effective Cohesion in Geotech as Kilopascal+(Submerged Unit Weight in KN per Cubic Meter*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*Depth of Prism*cos((Angle of Inclination to Horizontal in Soil*pi)/180)*sin((Angle of Inclination to Horizontal in Soil*pi)/180))
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