Depth of Prism given Shear Stress and Saturated Unit Weight Calculator

✖Shear Stress in Soil Mechanics is force tending to cause deformation of a material by slippage along a plane or planes parallel to the imposed stress.ⓘ Shear Stress in Soil Mechanics [ζ_soil]			+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%

✖Depth of Prism is the length of prism along z direction.ⓘ Depth of Prism given Shear Stress and Saturated Unit Weight [z]

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Formula

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Depth of Prism given Shear Stress and Saturated Unit Weight

Formula

`"z" = "ζ"_{"soil"}/("γ"_{"saturated"}*cos(("i"*pi)/180)*sin(("i"*pi)/180))`

Example

`"3.063739m"="0.71kN/m²"/("11.89kN/m³"*cos(("64°"*pi)/180)*sin(("64°"*pi)/180))`

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Depth of Prism given Shear Stress and Saturated Unit Weight Solution

STEP 0: Pre-Calculation Summary

Formula Used

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))
z = ζ_soil/(γ_saturated*cos((i*pi)/180)*sin((i*pi)/180))
This formula uses 1 Constants, 2 Functions, 4 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)

Variables Used

Depth of Prism - (Measured in Meter) - Depth of Prism is the length of prism along z direction.
Shear Stress in Soil Mechanics - (Measured in Pascal) - Shear Stress in Soil Mechanics is force tending to cause deformation of a material by slippage along a plane or planes parallel to the imposed stress.
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.

STEP 1: Convert Input(s) to Base Unit

Shear Stress in Soil Mechanics: 0.71 Kilonewton per Square Meter --> 710 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)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

z = ζ_soil/(γ_saturated*cos((i*pi)/180)*sin((i*pi)/180)) --> 710/(11890*cos((1.11701072127616*pi)/180)*sin((1.11701072127616*pi)/180))

Evaluating ... ...

z = 3.06373948355613

STEP 3: Convert Result to Output's Unit

3.06373948355613 Meter --> No Conversion Required

FINAL ANSWER

3.06373948355613 ≈ 3.063739 Meter <-- Depth of Prism

(Calculation completed in 00.004 seconds)

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Home » Engineering » Civil » Geotechnical Engineering » Seepage Analysis » Factor of Steady Seepage Along the Slope » Depth of Prism given Shear Stress and Saturated Unit Weight

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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!

< 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 Shear Stress and Saturated Unit Weight Formula

What is shear stress ?

Shear stress, often denoted by τ (Greek: tau), is the component of stress coplanar with a material cross section. It arises from the shear force, the component of force vector parallel to the material cross section. Normal stress, on the other hand.

How to Calculate Depth of Prism given Shear Stress and Saturated Unit Weight?

Depth of Prism given Shear Stress and Saturated Unit Weight calculator uses 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)) to calculate the Depth of Prism, Depth of Prism given Shear Stress and Saturated Unit Weight calculates value of depth of prism when we have prior information of other parameters used. Depth of Prism is denoted by z symbol.

How to calculate Depth of Prism given Shear Stress and Saturated Unit Weight using this online calculator? To use this online calculator for Depth of Prism given Shear Stress and Saturated Unit Weight, enter Shear Stress in Soil Mechanics (ζ_soil), Saturated Unit Weight of Soil (γ_saturated) & Angle of Inclination to Horizontal in Soil (i) and hit the calculate button. Here is how the Depth of Prism given Shear Stress and Saturated Unit Weight calculation can be explained with given input values -> 3.063739 = 710/(11890*cos((1.11701072127616*pi)/180)*sin((1.11701072127616*pi)/180)).

FAQ

What is Depth of Prism given Shear Stress and Saturated Unit Weight?

Depth of Prism given Shear Stress and Saturated Unit Weight calculates value of depth of prism when we have prior information of other parameters used and is represented as z = ζ_soil/(γ_saturated*cos((i*pi)/180)*sin((i*pi)/180)) or 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)). Shear Stress in Soil Mechanics is force tending to cause deformation of a material by slippage along a plane or planes parallel to the imposed stress, 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.

How to calculate Depth of Prism given Shear Stress and Saturated Unit Weight?

Depth of Prism given Shear Stress and Saturated Unit Weight calculates value of depth of prism when we have prior information of other parameters used is calculated using 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)). To calculate Depth of Prism given Shear Stress and Saturated Unit Weight, you need Shear Stress in Soil Mechanics (ζ_soil), Saturated Unit Weight of Soil (γ_saturated) & Angle of Inclination to Horizontal in Soil (i). With our tool, you need to enter the respective value for Shear Stress in Soil Mechanics, Saturated Unit Weight of Soil & 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 Shear Stress in Soil Mechanics, Saturated Unit Weight of Soil & 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 = 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 = 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)
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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