Unit Weight of Soil given Safe Height from Toe to Top of Wedge Calculator

✖Mobilized Cohesion in Soil Mechanics is the amount of cohesion that is resisting the shear stress.ⓘ Mobilized Cohesion in Soil Mechanics [c_m]			+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%
✖Angle of Mobilized Friction in Soil Mechanics is the slope angle at which an object starts sliding due to applied force.ⓘ Angle of Mobilized Friction in Soil Mechanics [φ_mob]			+10% -10%
✖Height from Toe of Wedge to Top of Wedge of soil.ⓘ Height from Toe of Wedge to Top of Wedge [H]			+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 given Safe Height from Toe to Top of Wedge [γ]

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Formula

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Unit Weight of Soil given Safe Height from Toe to Top of Wedge

Formula

γ = \frac{4 \cdot c m \cdot \sin (\frac{i \cdot π}{180}) \cdot \cos (\frac{φ mob \cdot π}{180})}{H \cdot (1 - \cos (\frac{(i - φ mob) \cdot π}{180}))}

Example

18.88591 kN/m³ = \frac{4 \cdot 0.30 kN/m² \cdot \sin (\frac{64 ° \cdot π}{180}) \cdot \cos (\frac{12.33 ° \cdot π}{180})}{10 m \cdot (1 - \cos (\frac{(64 ° - 12.33 °) \cdot π}{180}))}

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Unit Weight of Soil given Safe Height from Toe to Top of Wedge Solution

STEP 0: Pre-Calculation Summary

Formula Used

Unit Weight of Soil = (4*Mobilized Cohesion in Soil Mechanics*sin((Angle of Inclination to Horizontal in Soil*pi)/180)*cos((Angle of Mobilized Friction in Soil Mechanics*pi)/180))/(Height from Toe of Wedge to Top of Wedge*(1-cos(((Angle of Inclination to Horizontal in Soil-Angle of Mobilized Friction in Soil Mechanics)*pi)/180)))
γ = (4*c_m*sin((i*pi)/180)*cos((φ_mob*pi)/180))/(H*(1-cos(((i-φ_mob)*pi)/180)))
This formula uses 1 Constants, 2 Functions, 5 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

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.
Mobilized Cohesion in Soil Mechanics - (Measured in Pascal) - Mobilized Cohesion in Soil Mechanics is the amount of cohesion that is resisting the shear stress.
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.
Angle of Mobilized Friction in Soil Mechanics - (Measured in Radian) - Angle of Mobilized Friction in Soil Mechanics is the slope angle at which an object starts sliding due to applied force.
Height from Toe of Wedge to Top of Wedge - (Measured in Meter) - Height from Toe of Wedge to Top of Wedge of soil.

STEP 1: Convert Input(s) to Base Unit

Mobilized Cohesion in Soil Mechanics: 0.3 Kilonewton per Square Meter --> 300 Pascal (Check conversion here)
Angle of Inclination to Horizontal in Soil: 64 Degree --> 1.11701072127616 Radian (Check conversion here)
Angle of Mobilized Friction in Soil Mechanics: 12.33 Degree --> 0.21519909677086 Radian (Check conversion here)
Height from Toe of Wedge to Top of Wedge: 10 Meter --> 10 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

γ = (4*c_m*sin((i*pi)/180)*cos((φ_mob*pi)/180))/(H*(1-cos(((i-φ_mob)*pi)/180))) --> (4*300*sin((1.11701072127616*pi)/180)*cos((0.21519909677086*pi)/180))/(10*(1-cos(((1.11701072127616-0.21519909677086)*pi)/180)))

Evaluating ... ...

γ = 18885.9114391667

STEP 3: Convert Result to Output's Unit

18885.9114391667 Newton per Cubic Meter -->18.8859114391667 Kilonewton per Cubic Meter (Check conversion here)

FINAL ANSWER

18.8859114391667 ≈ 18.88591 Kilonewton per Cubic Meter <-- Unit Weight of Soil

(Calculation completed in 00.020 seconds)

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< Slope Stability Analysis using Culman's Method Calculators

Height of Wedge of Soil given Angle of Inclination and Slope angle

Go Height of Wedge = (Height from Toe of Wedge to Top of Wedge*sin(((Angle of Inclination in Soil Mechanics-Slope Angle)*pi)/180))/sin((Angle of Inclination in Soil Mechanics*pi)/180)

Height of Wedge of Soil given Weight of Wedge

Go Height of Wedge = Weight of Wedge in Kilonewton/((Length of Slip Plane*Unit Weight of Soil)/2)

Mobilized Cohesion given Cohesive Force along Slip Plane

Go Mobilized Cohesion in Soil Mechanics = Cohesive Force in KN/Length of Slip Plane

Cohesive Force along Slip Plane

Go Cohesive Force in KN = Mobilized Cohesion in Soil Mechanics*Length of Slip Plane

Unit Weight of Soil given Safe Height from Toe to Top of Wedge Formula

What is Unit Weight of Soil?

The mass of solid particles is usually expressed in terms of their particle unit weight or specific gravity (Gs) of the soil grain solids . For most inorganic soils, the value of Gs lies between 2.60 and 2.80.

How to Calculate Unit Weight of Soil given Safe Height from Toe to Top of Wedge?

Unit Weight of Soil given Safe Height from Toe to Top of Wedge calculator uses Unit Weight of Soil = (4*Mobilized Cohesion in Soil Mechanics*sin((Angle of Inclination to Horizontal in Soil*pi)/180)*cos((Angle of Mobilized Friction in Soil Mechanics*pi)/180))/(Height from Toe of Wedge to Top of Wedge*(1-cos(((Angle of Inclination to Horizontal in Soil-Angle of Mobilized Friction in Soil Mechanics)*pi)/180))) to calculate the Unit Weight of Soil, The Unit Weight of Soil given Safe Height from Toe to Top of Wedge is defined as the value of unit weight of soil when we have prior information of other parameters used. Unit Weight of Soil is denoted by γ symbol.

How to calculate Unit Weight of Soil given Safe Height from Toe to Top of Wedge using this online calculator? To use this online calculator for Unit Weight of Soil given Safe Height from Toe to Top of Wedge, enter Mobilized Cohesion in Soil Mechanics (c_m), Angle of Inclination to Horizontal in Soil (i), Angle of Mobilized Friction in Soil Mechanics (φ_mob) & Height from Toe of Wedge to Top of Wedge (H) and hit the calculate button. Here is how the Unit Weight of Soil given Safe Height from Toe to Top of Wedge calculation can be explained with given input values -> 0.018886 = (4*300*sin((1.11701072127616*pi)/180)*cos((0.21519909677086*pi)/180))/(10*(1-cos(((1.11701072127616-0.21519909677086)*pi)/180))).

FAQ

What is Unit Weight of Soil given Safe Height from Toe to Top of Wedge?

The Unit Weight of Soil given Safe Height from Toe to Top of Wedge is defined as the value of unit weight of soil when we have prior information of other parameters used and is represented as γ = (4*c_m*sin((i*pi)/180)*cos((φ_mob*pi)/180))/(H*(1-cos(((i-φ_mob)*pi)/180))) or Unit Weight of Soil = (4*Mobilized Cohesion in Soil Mechanics*sin((Angle of Inclination to Horizontal in Soil*pi)/180)*cos((Angle of Mobilized Friction in Soil Mechanics*pi)/180))/(Height from Toe of Wedge to Top of Wedge*(1-cos(((Angle of Inclination to Horizontal in Soil-Angle of Mobilized Friction in Soil Mechanics)*pi)/180))). Mobilized Cohesion in Soil Mechanics is the amount of cohesion that is resisting the shear stress, 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 Mobilized Friction in Soil Mechanics is the slope angle at which an object starts sliding due to applied force & Height from Toe of Wedge to Top of Wedge of soil.

How to calculate Unit Weight of Soil given Safe Height from Toe to Top of Wedge?

The Unit Weight of Soil given Safe Height from Toe to Top of Wedge is defined as the value of unit weight of soil when we have prior information of other parameters used is calculated using Unit Weight of Soil = (4*Mobilized Cohesion in Soil Mechanics*sin((Angle of Inclination to Horizontal in Soil*pi)/180)*cos((Angle of Mobilized Friction in Soil Mechanics*pi)/180))/(Height from Toe of Wedge to Top of Wedge*(1-cos(((Angle of Inclination to Horizontal in Soil-Angle of Mobilized Friction in Soil Mechanics)*pi)/180))). To calculate Unit Weight of Soil given Safe Height from Toe to Top of Wedge, you need Mobilized Cohesion in Soil Mechanics (c_m), Angle of Inclination to Horizontal in Soil (i), Angle of Mobilized Friction in Soil Mechanics (φ_mob) & Height from Toe of Wedge to Top of Wedge (H). With our tool, you need to enter the respective value for Mobilized Cohesion in Soil Mechanics, Angle of Inclination to Horizontal in Soil, Angle of Mobilized Friction in Soil Mechanics & Height from Toe of Wedge to Top of Wedge 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 Unit Weight of Soil?

In this formula, Unit Weight of Soil uses Mobilized Cohesion in Soil Mechanics, Angle of Inclination to Horizontal in Soil, Angle of Mobilized Friction in Soil Mechanics & Height from Toe of Wedge to Top of Wedge. We can use 2 other way(s) to calculate the same, which is/are as follows -

Unit Weight of Soil = Weight of Wedge in Kilonewton/((Length of Slip Plane*Height of Wedge)/2)
Unit Weight of Soil = Mobilized Cohesion in Soil Mechanics/(0.5*cosec((Angle of Inclination to Horizontal in Soil*pi)/180)*sec((Angle of Mobilized Friction in Soil Mechanics*pi)/180)*sin(((Angle of Inclination to Horizontal in Soil-Slope Angle in Soil Mechanics)*pi)/180)*sin(((Slope Angle in Soil Mechanics-Angle of Mobilized Friction in Soil Mechanics)*pi)/180)*Height from Toe of Wedge to Top of Wedge)

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