Angle of Inclination given Shear Strength and Submerged Unit Weight Calculator

✖Submerged Unit Weight is the unit weight of weight of soil as observed underwater in a saturated condition of course.ⓘ Submerged Unit Weight [γ^']			+10% -10%
✖Angle of Internal Friction is the angle measured between the normal force and resultant force .ⓘ Angle of Internal Friction [φ]			+10% -10%
✖Saturated Unit Weight in Newton per Cubic Meter is the value of the unit weight of the saturated soil in Newton per Cubic Meter.ⓘ Saturated Unit Weight in Newton per Cubic Meter [γ_sat]			+10% -10%
✖Shear strength of soil is the strength of a material against the structural failure when the material fails in shear.ⓘ Shear Strength of Soil [T_f]			+10% -10%
✖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%

✖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 Shear Strength and Submerged Unit Weight [i]

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Formula

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Angle of Inclination given Shear Strength and Submerged Unit Weight

Formula

`"i" = atan(("γ"^{"'"}*tan(("φ")))/("γ"_{"sat"}*("T"_{"f"}/"ζ"_{"soil"})))`

Example

`"80.07088°"=atan(("5.01N/m³"*tan(("46°")))/("32.24N/m³"*("20Pa"/"0.71kN/m²")))`

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Angle of Inclination given Shear Strength and Submerged Unit Weight Solution

STEP 0: Pre-Calculation Summary

Formula Used

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)))
i = atan((γ^'*tan((φ)))/(γ_sat*(T_f/ζ_soil)))
This formula uses 2 Functions, 6 Variables

Functions Used

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)
atan - Inverse tan is used to calculate the angle by applying the tangent ratio of the angle, which is the opposite side divided by the adjacent side of the right triangle., atan(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.
Submerged Unit Weight - (Measured in Newton per Cubic Meter) - Submerged Unit Weight is the unit weight of weight of soil as observed underwater 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 .
Saturated Unit Weight in Newton per Cubic Meter - (Measured in Newton per Cubic Meter) - Saturated Unit Weight in Newton per Cubic Meter is the value of the unit weight of the saturated soil in Newton per Cubic Meter.
Shear Strength of Soil - (Measured in Pascal) - Shear strength of soil is the strength of a material against the structural failure when the material fails in shear.
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.

STEP 1: Convert Input(s) to Base Unit

Submerged Unit Weight: 5.01 Newton per Cubic Meter --> 5.01 Newton per Cubic Meter No Conversion Required
Angle of Internal Friction: 46 Degree --> 0.802851455917241 Radian (Check conversion here)
Saturated Unit Weight in Newton per Cubic Meter: 32.24 Newton per Cubic Meter --> 32.24 Newton per Cubic Meter No Conversion Required
Shear Strength of Soil: 20 Pascal --> 20 Pascal No Conversion Required
Shear Stress in Soil Mechanics: 0.71 Kilonewton per Square Meter --> 710 Pascal (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

i = atan((γ^'*tan((φ)))/(γ_sat*(T_f/ζ_soil))) --> atan((5.01*tan((0.802851455917241)))/(32.24*(20/710)))

Evaluating ... ...

i = 1.39750057344301

STEP 3: Convert Result to Output's Unit

1.39750057344301 Radian -->80.0708847254121 Degree (Check conversion here)

FINAL ANSWER

80.0708847254121 ≈ 80.07088 Degree <-- Angle of Inclination to Horizontal in Soil

(Calculation completed in 00.004 seconds)

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Home » Engineering » Civil » Geotechnical Engineering » Seepage Analysis » Factor of Steady Seepage Along the Slope » Angle of Inclination given Shear Strength and Submerged Unit Weight

Credits

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 Shear Strength and Submerged Unit Weight Formula

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 Shear Strength and Submerged Unit Weight?

Angle of Inclination given Shear Strength and Submerged Unit Weight calculator uses 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))) to calculate the Angle of Inclination to Horizontal in Soil, The Angle of Inclination given Shear Strength and Submerged Unit Weight is defined as the value of angle of inclination with horizontal 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 Shear Strength and Submerged Unit Weight using this online calculator? To use this online calculator for Angle of Inclination given Shear Strength and Submerged Unit Weight, enter Submerged Unit Weight (γ^'), Angle of Internal Friction (φ), Saturated Unit Weight in Newton per Cubic Meter (γ_sat), Shear Strength of Soil (T_f) & Shear Stress in Soil Mechanics (ζ_soil) and hit the calculate button. Here is how the Angle of Inclination given Shear Strength and Submerged Unit Weight calculation can be explained with given input values -> 4586.609 = atan((5.01*tan((0.802851455917241)))/(32.24*(20/710))).

FAQ

What is Angle of Inclination given Shear Strength and Submerged Unit Weight?

The Angle of Inclination given Shear Strength and Submerged Unit Weight is defined as the value of angle of inclination with horizontal when we have prior information of other parameters used and is represented as i = atan((γ^'*tan((φ)))/(γ_sat*(T_f/ζ_soil))) or 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))). Submerged Unit Weight is the unit weight of weight of soil as observed underwater in a saturated condition of course, Angle of Internal Friction is the angle measured between the normal force and resultant force , Saturated Unit Weight in Newton per Cubic Meter is the value of the unit weight of the saturated soil in Newton per Cubic Meter, Shear strength of soil is the strength of a material against the structural failure when the material fails in shear & 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.

How to calculate Angle of Inclination given Shear Strength and Submerged Unit Weight?

The Angle of Inclination given Shear Strength and Submerged Unit Weight is defined as the value of angle of inclination with horizontal when we have prior information of other parameters used is calculated using 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))). To calculate Angle of Inclination given Shear Strength and Submerged Unit Weight, you need Submerged Unit Weight (γ^'), Angle of Internal Friction (φ), Saturated Unit Weight in Newton per Cubic Meter (γ_sat), Shear Strength of Soil (T_f) & Shear Stress in Soil Mechanics (ζ_soil). With our tool, you need to enter the respective value for Submerged Unit Weight, Angle of Internal Friction, Saturated Unit Weight in Newton per Cubic Meter, Shear Strength of Soil & Shear Stress in Soil Mechanics 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 Submerged Unit Weight, Angle of Internal Friction, Saturated Unit Weight in Newton per Cubic Meter, Shear Strength of Soil & Shear Stress in Soil Mechanics. 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 = acos(Vertical Stress at Point/(Unit Weight of Soil*Depth of Prism))

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