Angle of Inclination given Vertical Stress and Saturated Unit Weight Calculator

✖Vertical Stress at Point is the stress acting perpendicular to the surface.ⓘ Vertical Stress at Point [σ_z]			+10% -10%
✖Unit Weight of Soil mass is the ratio of the total weight of soil to the total volume of soil.ⓘ Unit Weight of Soil [γ]			+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 given Vertical Stress and Saturated Unit Weight [i]

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Angle of Inclination given Vertical Stress and Saturated Unit Weight

Formula

`"i" = acos("σ"_{"z"}/("γ"*"z"))`

Example

`"89.99873°"=acos("1.2Pa"/("18kN/m³"*"3m"))`

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Angle of Inclination given Vertical Stress and Saturated Unit Weight Solution

STEP 0: Pre-Calculation Summary

Formula Used

Angle of Inclination to Horizontal in Soil = acos(Vertical Stress at Point/(Unit Weight of Soil*Depth of Prism))
i = acos(σ_z/(γ*z))
This formula uses 2 Functions, 4 Variables

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)
acos - The inverse cosine function, is the inverse function of the cosine function. It is the function that takes a ratio as an input and returns the angle whose cosine is equal to that ratio., acos(Number)

Variables Used

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.
Vertical Stress at Point - (Measured in Pascal) - Vertical Stress at Point is the stress acting perpendicular to the surface.
Unit Weight of Soil - (Measured in Newton per Cubic Meter) - Unit Weight of Soil mass is the ratio of the total weight of soil to the total volume of soil.
Depth of Prism - (Measured in Meter) - Depth of Prism is the length of prism along z direction.

STEP 1: Convert Input(s) to Base Unit

Vertical Stress at Point: 1.2 Pascal --> 1.2 Pascal No Conversion Required
Unit Weight of Soil: 18 Kilonewton per Cubic Meter --> 18000 Newton per Cubic Meter (Check conversion here)
Depth of Prism: 3 Meter --> 3 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

i = acos(σ_z/(γ*z)) --> acos(1.2/(18000*3))

Evaluating ... ...

i = 1.57077410457267

STEP 3: Convert Result to Output's Unit

1.57077410457267 Radian -->89.9987267604721 Degree (Check conversion here)

FINAL ANSWER

89.9987267604721 ≈ 89.99873 Degree <-- Angle of Inclination to Horizontal in Soil

(Calculation completed in 00.004 seconds)

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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))

Angle of Inclination given Vertical Stress and Saturated Unit Weight Formula

Angle of Inclination to Horizontal in Soil = acos(Vertical Stress at Point/(Unit Weight of Soil*Depth of Prism))
i = acos(σ_z/(γ*z))

What is angle of inclination ?

The angle inclination of a line is the angle formed by the intersection of the line and the x-axis. Using a horizontal "run" of 1 and m for slope, the angle of inclination, theta=tan-1(m), or m=tan(theta).

How to Calculate Angle of Inclination given Vertical Stress and Saturated Unit Weight?

Angle of Inclination given Vertical Stress and Saturated Unit Weight calculator uses Angle of Inclination to Horizontal in Soil = acos(Vertical Stress at Point/(Unit Weight of Soil*Depth of Prism)) to calculate the Angle of Inclination to Horizontal in Soil, The Angle of Inclination given Vertical Stress and Saturated Unit Weight calculates the value of angle of inclination when we have prior information of other parameters used. Angle of Inclination to Horizontal in Soil is denoted by i symbol.

How to calculate Angle of Inclination given Vertical Stress and Saturated Unit Weight using this online calculator? To use this online calculator for Angle of Inclination given Vertical Stress and Saturated Unit Weight, enter Vertical Stress at Point (σ_z), Unit Weight of Soil (γ) & Depth of Prism (z) and hit the calculate button. Here is how the Angle of Inclination given Vertical Stress and Saturated Unit Weight calculation can be explained with given input values -> 5156.547 = acos(1.2/(18000*3)).

FAQ

What is Angle of Inclination given Vertical Stress and Saturated Unit Weight?

The Angle of Inclination given Vertical Stress and Saturated Unit Weight calculates the value of angle of inclination when we have prior information of other parameters used and is represented as i = acos(σ_z/(γ*z)) or Angle of Inclination to Horizontal in Soil = acos(Vertical Stress at Point/(Unit Weight of Soil*Depth of Prism)). Vertical Stress at Point is the stress acting perpendicular to the surface, Unit Weight of Soil mass is the ratio of the total weight of soil to the total volume of soil & Depth of Prism is the length of prism along z direction.

How to calculate Angle of Inclination given Vertical Stress and Saturated Unit Weight?

The Angle of Inclination given Vertical Stress and Saturated Unit Weight calculates the value of angle of inclination when we have prior information of other parameters used is calculated using Angle of Inclination to Horizontal in Soil = acos(Vertical Stress at Point/(Unit Weight of Soil*Depth of Prism)). To calculate Angle of Inclination given Vertical Stress and Saturated Unit Weight, you need Vertical Stress at Point (σ_z), Unit Weight of Soil (γ) & Depth of Prism (z). With our tool, you need to enter the respective value for Vertical Stress at Point, Unit Weight of Soil & Depth of Prism 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 Angle of Inclination to Horizontal in Soil?

In this formula, Angle of Inclination to Horizontal in Soil uses Vertical Stress at Point, Unit Weight of Soil & Depth of Prism. We can use 2 other way(s) to calculate the same, which is/are as follows -

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))
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)))

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