Depth of Prism given Effective Normal Stress Solution

STEP 0: Pre-Calculation Summary
Formula Used
Depth of Prism = Effective Normal Stress in Soil Mechanics/((Saturated Unit Weight of Soil-Unit Weight of Water)*(cos((Angle of Inclination to Horizontal in Soil*pi)/180))^2)
z = σ'/((γsaturated-γwater)*(cos((i*pi)/180))^2)
This formula uses 1 Constants, 1 Functions, 5 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)
Variables Used
Depth of Prism - (Measured in Meter) - Depth of Prism is the length of prism along z direction.
Effective Normal Stress in Soil Mechanics - (Measured in Pascal) - Effective Normal Stress in Soil Mechanics is related to total stress and pore pressure.
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.
Unit Weight of Water - (Measured in Newton per Cubic Meter) - Unit Weight of Water is mass per unit of water.
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 Normal Stress in Soil Mechanics: 24.67 Kilonewton per Square Meter --> 24670 Pascal (Check conversion here)
Saturated Unit Weight of Soil: 11.89 Kilonewton per Cubic Meter --> 11890 Newton per Cubic Meter (Check conversion here)
Unit Weight of Water: 9.81 Kilonewton per Cubic Meter --> 9810 Newton per Cubic Meter (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
z = σ'/((γsaturatedwater)*(cos((i*pi)/180))^2) --> 24670/((11890-9810)*(cos((1.11701072127616*pi)/180))^2)
Evaluating ... ...
z = 11.8650859755115
STEP 3: Convert Result to Output's Unit
11.8650859755115 Meter --> No Conversion Required
FINAL ANSWER
11.8650859755115 11.86509 Meter <-- Depth of Prism
(Calculation completed in 00.020 seconds)

Credits

Created by Suraj Kumar
Birsa Institute of Technology (BIT), Sindri
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Meerut Institute of Engineering and Technology (MIET), Meerut
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18 Factor of Steady Seepage Along the Slope Calculators

Saturated Unit Weight given Shear Strength
Go Saturated Unit Weight of Soil = (Submerged Unit Weight in KN per Cubic Meter*Shear Stress in Soil Mechanics*tan((Angle of Internal Friction of Soil*pi)/180))/(Shear Strength in KN per Cubic Meter*tan((Angle of Inclination to Horizontal in Soil*pi)/180))
Saturated Unit Weight given Factor of Safety
Go Saturated Unit Weight of Soil = (Submerged Unit Weight in KN per Cubic Meter*tan((Angle of Internal Friction of Soil*pi)/180))/(Factor of Safety in Soil Mechanics*tan((Angle of Inclination to Horizontal in Soil*pi)/180))
Depth of Prism given Shear Stress and Saturated Unit Weight
Go Depth of Prism = Shear Stress in Soil Mechanics/(Saturated Unit Weight of Soil*cos((Angle of Inclination to Horizontal in Soil*pi)/180)*sin((Angle of Inclination to Horizontal in Soil*pi)/180))
Saturated Unit Weight given Shear Stress Component
Go Saturated Unit Weight of Soil = Shear Stress 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))
Angle of Inclination given Shear Strength and Submerged Unit Weight
Go Angle of Inclination to Horizontal in Soil = atan((Submerged Unit Weight*tan((Angle of Internal Friction)))/(Saturated Unit Weight in Newton per Cubic Meter*(Shear Strength of Soil/Shear Stress in Soil Mechanics)))
Depth of Prism given Upward Force
Go Depth of Prism = (Normal Stress in Soil Mechanics-Upward Force in Seepage Analysis)/(Submerged Unit Weight in KN per Cubic Meter*(cos((Angle of Inclination to Horizontal in Soil*pi)/180))^2)
Depth of Prism given Saturated Unit Weight
Go Depth of Prism = Weight of Prism in Soil Mechanics/(Saturated Unit Weight in Newton per Cubic Meter*Inclined Length of Prism*cos((Angle of Inclination to Horizontal in Soil*pi)/180))
Saturated Unit Weight given Effective Normal Stress
Go Saturated Unit Weight of Soil = Unit Weight of Water+(Effective Normal Stress in Soil Mechanics/(Depth of Prism*(cos((Angle of Inclination to Horizontal in Soil*pi)/180))^2))
Depth of Prism given Effective Normal Stress
Go Depth of Prism = Effective Normal Stress in Soil Mechanics/((Saturated Unit Weight of Soil-Unit Weight of Water)*(cos((Angle of Inclination to Horizontal in Soil*pi)/180))^2)
Saturated Unit Weight given Weight of Soil Prism
Go Saturated Unit Weight of Soil = Weight of Prism in Soil Mechanics/(Depth of Prism*Inclined Length of Prism*cos((Angle of Inclination to Horizontal in Soil*pi)/180))
Depth of Prism given Submerged Unit Weight and Effective Normal Stress
Go Depth of Prism = Effective Normal Stress in Soil Mechanics/(Submerged Unit Weight in KN per Cubic Meter*(cos((Angle of Inclination to Horizontal in Soil*pi)/180))^2)
Depth of Prism given Vertical Stress and Saturated Unit Weight
Go Depth of Prism = Vertical Stress at a Point in Kilopascal/(Saturated Unit Weight of Soil*cos((Angle of Inclination to Horizontal in Soil*pi)/180))
Saturated Unit Weight given Vertical Stress on Prism
Go Saturated Unit Weight of Soil = Vertical Stress at a Point in Kilopascal/(Depth of Prism*cos((Angle of Inclination to Horizontal in Soil*pi)/180))
Angle of Inclination given Saturated Unit Weight
Go Angle of Inclination to Horizontal in Soil = acos(Weight of Prism in Soil Mechanics/(Unit Weight of Soil*Depth of Prism*Inclined Length of Prism))
Depth of Prism given Normal Stress and Saturated Unit Weight
Go Depth of Prism = Normal Stress in Soil Mechanics/(Saturated Unit Weight of Soil*(cos((Angle of Inclination to Horizontal in Soil*pi)/180))^2)
Saturated Unit Weight given Normal Stress Component
Go Saturated Unit Weight of Soil = Normal Stress in Soil Mechanics/(Depth of Prism*(cos((Angle of Inclination to Horizontal in Soil*pi)/180))^2)
Depth of Prism given Upward Force due to Seepage Water
Go Depth of Prism = Upward Force in Seepage Analysis/(Unit Weight of Water*(cos((Angle of Inclination to Horizontal in Soil*pi)/180))^2)
Angle of Inclination given Vertical Stress and Saturated Unit Weight
Go Angle of Inclination to Horizontal in Soil = acos(Vertical Stress at Point/(Unit Weight of Soil*Depth of Prism))

Depth of Prism given Effective Normal Stress Formula

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

What is Normal Stress?

A normal stress is a stress that occurs when a member is loaded by an axial force. The value of the normal force for any prismatic section is simply the force divided by the cross sectional area.

How to Calculate Depth of Prism given Effective Normal Stress?

Depth of Prism given Effective Normal Stress calculator uses Depth of Prism = Effective Normal Stress in Soil Mechanics/((Saturated Unit Weight of Soil-Unit Weight of Water)*(cos((Angle of Inclination to Horizontal in Soil*pi)/180))^2) to calculate the Depth of Prism, The Depth of Prism given Effective Normal Stress is defined as the value of depth of soil prism considered when we have prior information of other parameters used. Depth of Prism is denoted by z symbol.

How to calculate Depth of Prism given Effective Normal Stress using this online calculator? To use this online calculator for Depth of Prism given Effective Normal Stress, enter Effective Normal Stress in Soil Mechanics '), Saturated Unit Weight of Soil saturated), Unit Weight of Water water) & Angle of Inclination to Horizontal in Soil (i) and hit the calculate button. Here is how the Depth of Prism given Effective Normal Stress calculation can be explained with given input values -> 3.013355 = 24670/((11890-9810)*(cos((1.11701072127616*pi)/180))^2).

FAQ

What is Depth of Prism given Effective Normal Stress?
The Depth of Prism given Effective Normal Stress is defined as the value of depth of soil prism considered when we have prior information of other parameters used and is represented as z = σ'/((γsaturatedwater)*(cos((i*pi)/180))^2) or Depth of Prism = Effective Normal Stress in Soil Mechanics/((Saturated Unit Weight of Soil-Unit Weight of Water)*(cos((Angle of Inclination to Horizontal in Soil*pi)/180))^2). Effective Normal Stress in Soil Mechanics is related to total stress and pore pressure, Saturated Unit Weight of Soil is the ratio of mass of saturated soil sample to total volume, Unit Weight of Water is mass per unit of water & 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 Depth of Prism given Effective Normal Stress?
The Depth of Prism given Effective Normal Stress is defined as the value of depth of soil prism considered when we have prior information of other parameters used is calculated using Depth of Prism = Effective Normal Stress in Soil Mechanics/((Saturated Unit Weight of Soil-Unit Weight of Water)*(cos((Angle of Inclination to Horizontal in Soil*pi)/180))^2). To calculate Depth of Prism given Effective Normal Stress, you need Effective Normal Stress in Soil Mechanics '), Saturated Unit Weight of Soil saturated), Unit Weight of Water water) & Angle of Inclination to Horizontal in Soil (i). With our tool, you need to enter the respective value for Effective Normal Stress in Soil Mechanics, Saturated Unit Weight of Soil, Unit Weight of Water & 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 Depth of Prism?
In this formula, Depth of Prism uses Effective Normal Stress in Soil Mechanics, Saturated Unit Weight of Soil, Unit Weight of Water & Angle of Inclination to Horizontal in Soil. We can use 7 other way(s) to calculate the same, which is/are as follows -
  • Depth of Prism = Weight of Prism in Soil Mechanics/(Saturated Unit Weight in Newton per Cubic Meter*Inclined Length of Prism*cos((Angle of Inclination to Horizontal in Soil*pi)/180))
  • Depth of Prism = Vertical Stress at a Point in Kilopascal/(Saturated Unit Weight of Soil*cos((Angle of Inclination to Horizontal in Soil*pi)/180))
  • Depth of Prism = Normal Stress in Soil Mechanics/(Saturated Unit Weight of Soil*(cos((Angle of Inclination to Horizontal in Soil*pi)/180))^2)
  • Depth of Prism = Shear Stress in Soil Mechanics/(Saturated Unit Weight of Soil*cos((Angle of Inclination to Horizontal in Soil*pi)/180)*sin((Angle of Inclination to Horizontal in Soil*pi)/180))
  • Depth of Prism = Upward Force in Seepage Analysis/(Unit Weight of Water*(cos((Angle of Inclination to Horizontal in Soil*pi)/180))^2)
  • Depth of Prism = Effective Normal Stress in Soil Mechanics/(Submerged Unit Weight in KN per Cubic Meter*(cos((Angle of Inclination to Horizontal in Soil*pi)/180))^2)
  • Depth of Prism = (Normal Stress in Soil Mechanics-Upward Force in Seepage Analysis)/(Submerged Unit Weight in KN per Cubic Meter*(cos((Angle of Inclination to Horizontal in Soil*pi)/180))^2)
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