## Sloping surface area of embankment Solution

STEP 0: Pre-Calculation Summary
Formula Used
Sloping surface area = Length of road section*Mean height*sqrt((Side slope)^2+1)
Asloping = Lsection*dmean*sqrt((S)^2+1)
This formula uses 1 Functions, 4 Variables
Functions Used
sqrt - Squre root function, sqrt(Number)
Variables Used
Sloping surface area - (Measured in Square Meter) - Sloping surface area is defined as area of sloping face of embankment.
Length of road section - (Measured in Meter) - Length of road section is the total extent /stretch of road.
Mean height - (Measured in Meter) - Mean height is defined as sum total of all the heights divided by total number of heights given.
Side slope - Side slope is the graded area immediately adjacent to the graded roadway shoulder. Side slopes are provided on embankments and fills to provide stability for earthworks.
STEP 1: Convert Input(s) to Base Unit
Length of road section: 20 Meter --> 20 Meter No Conversion Required
Mean height: 5 Meter --> 5 Meter No Conversion Required
Side slope: 2 --> No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
Asloping = Lsection*dmean*sqrt((S)^2+1) --> 20*5*sqrt((2)^2+1)
Evaluating ... ...
Asloping = 223.606797749979
STEP 3: Convert Result to Output's Unit
223.606797749979 Square Meter --> No Conversion Required
223.606797749979 Square Meter <-- Sloping surface area
(Calculation completed in 00.016 seconds)
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## Credits

Created by Smriti Singh
MIT Academy of engineering, Pune (MITAOE), Alandi, Pune
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Verified by Ayush Singh
Gautam Buddha University (GBU), Greater Noida
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## < 5 Quantity of earthwork for embankments Calculators

Mean sectional area method

## Mean sectional area method

Formula
"V"_{"earthwork "} = "L"_{"section"}*(("B"*"d"_{"1"})+("S"*"d"_{"1"}^2)+("B"*"d"_{"2"})+("S"*"d"_{"2"}^2))/2

Example
"360m³"="20m"*(("10m"*"1.2m")+("2"*"1.2m"^2)+("10m"*"1.6m")+("2"*"1.6m"^2))/2

Calculator
LaTeX
Volume of earthwork = Length of road section*((Width of formation level*Height of bank at start portion of embankment)+(Side slope*Height of bank at start portion of embankment^2)+(Width of formation level*Height of bank at end portion of embankment)+(Side slope*Height of bank at end portion of embankment^2))/2
Mid sectional area method

## Mid sectional area method

Formula
"V"_{"earthwork "} = "L"_{"section"}*("B"*(("d"_{"1"}+"d"_{"2"})/2))+"L"_{"section"}*("S"*(("d"_{"1"}+"d"_{"2"})/2)^2)

Example
"358.4m³"="20m"*("10m"*(("1.2m"+"1.6m")/2))+"20m"*("2"*(("1.2m"+"1.6m")/2)^2)

Calculator
LaTeX
Volume of earthwork = Length of road section*(Width of formation level*((Height of bank at start portion of embankment+Height of bank at end portion of embankment)/2))+Length of road section*(Side slope*((Height of bank at start portion of embankment+Height of bank at end portion of embankment)/2)^2)
Prizmoidal Formula for series of cross sections of road

## Prizmoidal Formula for series of cross sections of road

Formula
"V"_{"earthwork "} = "D"_{"consecutive c/s"}/3*("A"_{"1st"}+"A"_{"last"}+4*("Σ Odd areas")+2*("Σ Even areas"))

Example
"5472m³"="9m"/3*("7m²"+"17m²"+4*("250m²")+2*("400m²"))

Calculator
LaTeX
Volume of earthwork = Distance between consecutive sections/3*(Area of first section+Area of last section+4*(Odd areas sum)+2*(Even areas sum))
Trapezoidal Formula for series of cross sections of road

## Trapezoidal Formula for series of cross sections of road

Formula
"V"_{"earthwork "} = "D"_{"consecutive c/s"}*("A"_{"1st"}+"A"_{"last"}+2*("Σ Remaining areas"))/2

Example
"324m³"="9m"*("7m²"+"17m²"+2*("24m²"))/2

Calculator
LaTeX
Volume of earthwork = Distance between consecutive sections*(Area of first section+Area of last section+2*(Remaining areas))/2
Sloping surface area of embankment

## Sloping surface area of embankment

Formula
"A"_{"sloping"} = "L"_{"section"}*"d"_{""mean""}*sqrt(("S")^2+1)

Example
"223.6068m²"="20m"*"5m"*sqrt(("2")^2+1)

Calculator
LaTeX
Sloping surface area = Length of road section*Mean height*sqrt((Side slope)^2+1)

## Sloping surface area of embankment Formula

Sloping surface area = Length of road section*Mean height*sqrt((Side slope)^2+1)
Asloping = Lsection*dmean*sqrt((S)^2+1)

## About formula for sloping surface area of embankment

This formula is used to calculate area of sloping surface of embankment of road, dam, canal in order to make a estimate that how much material would be needed for stone pitching, concreting, short-creating etc.

## How to Calculate Sloping surface area of embankment?

Sloping surface area of embankment calculator uses Sloping surface area = Length of road section*Mean height*sqrt((Side slope)^2+1) to calculate the Sloping surface area, The Sloping surface area of embankment formula is used to calculate the area of sloping face of embankment for a given length. Sloping surface area is denoted by Asloping symbol.

How to calculate Sloping surface area of embankment using this online calculator? To use this online calculator for Sloping surface area of embankment, enter Length of road section (Lsection), Mean height (dmean) & Side slope (S) and hit the calculate button. Here is how the Sloping surface area of embankment calculation can be explained with given input values -> 223.6068 = 20*5*sqrt((2)^2+1).

### FAQ

What is Sloping surface area of embankment?
The Sloping surface area of embankment formula is used to calculate the area of sloping face of embankment for a given length and is represented as Asloping = Lsection*dmean*sqrt((S)^2+1) or Sloping surface area = Length of road section*Mean height*sqrt((Side slope)^2+1). Length of road section is the total extent /stretch of road, Mean height is defined as sum total of all the heights divided by total number of heights given & Side slope is the graded area immediately adjacent to the graded roadway shoulder. Side slopes are provided on embankments and fills to provide stability for earthworks.
How to calculate Sloping surface area of embankment?
The Sloping surface area of embankment formula is used to calculate the area of sloping face of embankment for a given length is calculated using Sloping surface area = Length of road section*Mean height*sqrt((Side slope)^2+1). To calculate Sloping surface area of embankment, you need Length of road section (Lsection), Mean height (dmean) & Side slope (S). With our tool, you need to enter the respective value for Length of road section, Mean height & Side slope and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.
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