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%
✖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%

✖Height from Toe of Wedge to Top of Wedge of soil.ⓘ Safe Height from Toe to Top of Wedge [H]

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Formula

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Safe Height from Toe to Top of Wedge

Formula

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

Example

10.49217 m = \frac{4 \cdot 0.30 kN/m² \cdot \sin (\frac{64 ° \cdot π}{180}) \cdot \cos (\frac{12.33 ° \cdot π}{180})}{18 kN/m³ \cdot (1 - \cos (\frac{(64 ° - 12.33 °) \cdot π}{180}))}

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Download Slope Stability Analysis using Culman's Method Formulas PDF PDF Image

Safe Height from Toe to Top of Wedge Solution

STEP 0: Pre-Calculation Summary

Formula Used

Height from Toe of Wedge to Top of Wedge = (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))/(Unit Weight of Soil*(1-cos(((Angle of Inclination to Horizontal in Soil-Angle of Mobilized Friction in Soil Mechanics)*pi)/180)))
H = (4*c_m*sin((i*pi)/180)*cos((φ_mob*pi)/180))/(γ*(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

Height from Toe of Wedge to Top of Wedge - (Measured in Meter) - Height from Toe of Wedge to Top of Wedge 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.
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.

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)
Unit Weight of Soil: 18 Kilonewton per Cubic Meter --> 18000 Newton per Cubic Meter (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

H = (4*c_m*sin((i*pi)/180)*cos((φ_mob*pi)/180))/(γ*(1-cos(((i-φ_mob)*pi)/180))) --> (4*300*sin((1.11701072127616*pi)/180)*cos((0.21519909677086*pi)/180))/(18000*(1-cos(((1.11701072127616-0.21519909677086)*pi)/180)))

Evaluating ... ...

H = 10.4921730217593

STEP 3: Convert Result to Output's Unit

10.4921730217593 Meter --> No Conversion Required

FINAL ANSWER

10.4921730217593 ≈ 10.49217 Meter <-- Height from Toe of Wedge to Top of Wedge

(Calculation completed in 00.004 seconds)

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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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< 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

Safe Height from Toe to Top of Wedge Formula

What is Angle of Internal Friction?

The angle of internal friction is a physical property of earth materials or the slope of a linear representation of the shear strength of earth materials.

How to Calculate Safe Height from Toe to Top of Wedge?

Safe Height from Toe to Top of Wedge calculator uses Height from Toe of Wedge to Top of Wedge = (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))/(Unit Weight of Soil*(1-cos(((Angle of Inclination to Horizontal in Soil-Angle of Mobilized Friction in Soil Mechanics)*pi)/180))) to calculate the Height from Toe of Wedge to Top of Wedge, The Safe Height from Toe to Top of Wedge is defined as the value of safe height from toe to top of the wedge of soil when we have prior information of other parameters used. Height from Toe of Wedge to Top of Wedge is denoted by H symbol.

How to calculate Safe Height from Toe to Top of Wedge using this online calculator? To use this online calculator for 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) & Unit Weight of Soil (γ) and hit the calculate button. Here is how the Safe Height from Toe to Top of Wedge calculation can be explained with given input values -> 10.49217 = (4*300*sin((1.11701072127616*pi)/180)*cos((0.21519909677086*pi)/180))/(18000*(1-cos(((1.11701072127616-0.21519909677086)*pi)/180))).

FAQ

What is Safe Height from Toe to Top of Wedge?

The Safe Height from Toe to Top of Wedge is defined as the value of safe height from toe to top of the wedge of soil when we have prior information of other parameters used and is represented as H = (4*c_m*sin((i*pi)/180)*cos((φ_mob*pi)/180))/(γ*(1-cos(((i-φ_mob)*pi)/180))) or Height from Toe of Wedge to Top of Wedge = (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))/(Unit Weight of Soil*(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 & Unit Weight of Soil mass is the ratio of the total weight of soil to the total volume of soil.

How to calculate Safe Height from Toe to Top of Wedge?

The Safe Height from Toe to Top of Wedge is defined as the value of safe height from toe to top of the wedge of soil when we have prior information of other parameters used is calculated using Height from Toe of Wedge to Top of Wedge = (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))/(Unit Weight of Soil*(1-cos(((Angle of Inclination to Horizontal in Soil-Angle of Mobilized Friction in Soil Mechanics)*pi)/180))). To calculate 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) & Unit Weight of Soil (γ). 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 & Unit Weight of 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 Height from Toe of Wedge to Top of Wedge?

In this formula, Height from Toe of Wedge to Top of Wedge uses Mobilized Cohesion in Soil Mechanics, Angle of Inclination to Horizontal in Soil, Angle of Mobilized Friction in Soil Mechanics & Unit Weight of Soil. We can use 3 other way(s) to calculate the same, which is/are as follows -

Height from Toe of Wedge to Top of Wedge = Height of Wedge/((sin(((Angle of Inclination in Soil Mechanics-Slope Angle)*pi)/180))/sin((Angle of Inclination in Soil Mechanics*pi)/180))
Height from Toe of Wedge to Top of Wedge = Weight of Wedge in Kilonewton/((Unit Weight of Soil*Length of Slip Plane*(sin(((Angle of Inclination in Soil Mechanics-Slope Angle)*pi)/180)))/(2*sin((Angle of Inclination in Soil Mechanics*pi)/180)))
Height from Toe of Wedge to Top of Wedge = (Effective Cohesion in Geotech as Kilopascal/((1/2)*(Factor of Safety in Soil Mechanics-(tan((Angle of Internal Friction*pi)/180)/tan((Critical Slope Angle in Soil Mechanics*pi)/180)))*Unit Weight of Soil*(sin(((Angle of Inclination to Horizontal in Soil-Critical Slope Angle in Soil Mechanics)*pi)/180)/sin((Angle of Inclination to Horizontal in Soil*pi)/180))*sin((Critical Slope Angle in Soil Mechanics*pi)/180)))

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