Height from Toe of Wedge to Top of Wedge given Factor of Safety Calculator

✖Effective Cohesion in Geotech as Kilopascal is the consistency of soft to hard defined on the basis of the standard CSN 73 1001 for different states of consistency and degree of saturation.ⓘ Effective Cohesion in Geotech as Kilopascal [C_eff]			+10% -10%
✖Factor of Safety in Soil Mechanics expresses how much stronger a system is than it needs to be for an intended load.ⓘ Factor of Safety in Soil Mechanics [F_s]			+10% -10%
✖Angle of Internal Friction is the angle measured between the normal force and resultant force .ⓘ Angle of Internal Friction [φ]			+10% -10%
✖Critical Slope Angle in Soil Mechanics is the angle formed by most dangerous plane.ⓘ Critical Slope Angle in Soil Mechanics [θ_cr]			+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%
✖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%

✖Height from Toe of Wedge to Top of Wedge of soil.ⓘ Height from Toe of Wedge to Top of Wedge given Factor of Safety [H]

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Height from Toe of Wedge to Top of Wedge given Factor of Safety Solution

STEP 0: Pre-Calculation Summary

Formula Used

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)))
H = (C_eff/((1/2)*(F_s-(tan((φ*pi)/180)/tan((θ_cr*pi)/180)))*γ*(sin(((i-θ_cr)*pi)/180)/sin((i*pi)/180))*sin((θ_cr*pi)/180)))
This formula uses 1 Constants, 2 Functions, 7 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)
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)

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.
Effective Cohesion in Geotech as Kilopascal - (Measured in Pascal) - Effective Cohesion in Geotech as Kilopascal is the consistency of soft to hard defined on the basis of the standard CSN 73 1001 for different states of consistency and degree of saturation.
Factor of Safety in Soil Mechanics - Factor of Safety in Soil Mechanics expresses how much stronger a system is than it needs to be for an intended load.
Angle of Internal Friction - (Measured in Radian) - Angle of Internal Friction is the angle measured between the normal force and resultant force .
Critical Slope Angle in Soil Mechanics - (Measured in Radian) - Critical Slope Angle in Soil Mechanics is the angle formed by most dangerous plane.
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.
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

Effective Cohesion in Geotech as Kilopascal: 0.32 Kilopascal --> 320 Pascal (Check conversion here)
Factor of Safety in Soil Mechanics: 2.8 --> No Conversion Required
Angle of Internal Friction: 46 Degree --> 0.802851455917241 Radian (Check conversion here)
Critical Slope Angle in Soil Mechanics: 52.1 Degree --> 0.909316540288875 Radian (Check conversion here)
Unit Weight of Soil: 18 Kilonewton per Cubic Meter --> 18000 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

H = (C_eff/((1/2)*(F_s-(tan((φ*pi)/180)/tan((θ_cr*pi)/180)))*γ*(sin(((i-θ_cr)*pi)/180)/sin((i*pi)/180))*sin((θ_cr*pi)/180))) --> (320/((1/2)*(2.8-(tan((0.802851455917241*pi)/180)/tan((0.909316540288875*pi)/180)))*18000*(sin(((1.11701072127616-0.909316540288875)*pi)/180)/sin((1.11701072127616*pi)/180))*sin((0.909316540288875*pi)/180)))

Evaluating ... ...

H = 6.28485383153865

STEP 3: Convert Result to Output's Unit

6.28485383153865 Meter --> No Conversion Required

FINAL ANSWER

6.28485383153865 ≈ 6.284854 Meter <-- Height from Toe of Wedge to Top of Wedge

(Calculation completed in 00.004 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

LaTeX 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

LaTeX 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

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

Cohesive Force along Slip Plane

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

Height from Toe of Wedge to Top of Wedge given Factor of Safety Formula

LaTeX Go

What is Angle of Internal Friction?

A measure of the ability of a unit of rock or soil to withstand a shear stress. It is the angle (φ), measured between the normal force (N) and resultant force (R), that is attained when failure just occurs in response to a shearing stress (S).

How to Calculate Height from Toe of Wedge to Top of Wedge given Factor of Safety?

Height from Toe of Wedge to Top of Wedge given Factor of Safety calculator uses 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))) to calculate the Height from Toe of Wedge to Top of Wedge, The Height from Toe of Wedge to Top of Wedge given Factor of Safety is defined as the the value of height from toe to top of wedge 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 Height from Toe of Wedge to Top of Wedge given Factor of Safety using this online calculator? To use this online calculator for Height from Toe of Wedge to Top of Wedge given Factor of Safety, enter Effective Cohesion in Geotech as Kilopascal (C_eff), Factor of Safety in Soil Mechanics (F_s), Angle of Internal Friction (φ), Critical Slope Angle in Soil Mechanics (θ_cr), Unit Weight of Soil (γ) & Angle of Inclination to Horizontal in Soil (i) and hit the calculate button. Here is how the Height from Toe of Wedge to Top of Wedge given Factor of Safety calculation can be explained with given input values -> 6.284854 = (320/((1/2)*(2.8-(tan((0.802851455917241*pi)/180)/tan((0.909316540288875*pi)/180)))*18000*(sin(((1.11701072127616-0.909316540288875)*pi)/180)/sin((1.11701072127616*pi)/180))*sin((0.909316540288875*pi)/180))).

FAQ

What is Height from Toe of Wedge to Top of Wedge given Factor of Safety?

The Height from Toe of Wedge to Top of Wedge given Factor of Safety is defined as the the value of height from toe to top of wedge when we have prior information of other parameters used and is represented as H = (C_eff/((1/2)*(F_s-(tan((φ*pi)/180)/tan((θ_cr*pi)/180)))*γ*(sin(((i-θ_cr)*pi)/180)/sin((i*pi)/180))*sin((θ_cr*pi)/180))) or 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))). Effective Cohesion in Geotech as Kilopascal is the consistency of soft to hard defined on the basis of the standard CSN 73 1001 for different states of consistency and degree of saturation, Factor of Safety in Soil Mechanics expresses how much stronger a system is than it needs to be for an intended load, Angle of Internal Friction is the angle measured between the normal force and resultant force , Critical Slope Angle in Soil Mechanics is the angle formed by most dangerous plane, Unit Weight of Soil mass is the ratio of the total weight of soil to the total volume of soil & 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 Height from Toe of Wedge to Top of Wedge given Factor of Safety?

The Height from Toe of Wedge to Top of Wedge given Factor of Safety is defined as the the value of height from toe to top of wedge when we have prior information of other parameters used is calculated using 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))). To calculate Height from Toe of Wedge to Top of Wedge given Factor of Safety, you need Effective Cohesion in Geotech as Kilopascal (C_eff), Factor of Safety in Soil Mechanics (F_s), Angle of Internal Friction (φ), Critical Slope Angle in Soil Mechanics (θ_cr), Unit Weight of Soil (γ) & Angle of Inclination to Horizontal in Soil (i). With our tool, you need to enter the respective value for Effective Cohesion in Geotech as Kilopascal, Factor of Safety in Soil Mechanics, Angle of Internal Friction, Critical Slope Angle in Soil Mechanics, 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 Height from Toe of Wedge to Top of Wedge?

In this formula, Height from Toe of Wedge to Top of Wedge uses Effective Cohesion in Geotech as Kilopascal, Factor of Safety in Soil Mechanics, Angle of Internal Friction, Critical Slope Angle in Soil Mechanics, Unit Weight of Soil & Angle of Inclination to Horizontal in 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 = 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)*pi)/180)*sin(((Slope Angle in Soil Mechanics-Angle of Mobilized Friction in Soil Mechanics)*pi)/180)*Unit Weight of Soil)

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