Version use: 2.5.36.0 

Project file here

In MiTS 2, the cut fill volume can be calculated by the ‘End Area’ method.

The road end area calculation is calculated per road basis. The cut and fill volume is calculated in a way that the other platforms or road will not be included.

(Calculation is done as if there are no other platforms/roads) 

As per image below, the calculation shown is as per road basis.

The basis of earthwork volume will be dependent upon the road cross section as the road cross section solely depending upon the parameter set is the parameter dialog. 

If the slope is set to YES, hence the cut and fill volume will include the slope area and if NO then the cut and fill volume will exclude the slope area.

With slope  #

i.e; CH 0

Cross section CH 0 

Volume of fill = Fill area x chainage interval 

ஃ Volume of fill = 3.096m2 x 24.85m 

= 76.93m****3 

Without slope  #

i.e; CH 125

Cross section CH 125

Cross section CH 150

Volume of cut = (Cut area at CH 125 = Cut area at CH 150)/2 x chainage interval 

ஃ Volume of cut = (1.661m2 + 2.947m2)/2 x 25m 

= 57.60m****3 

Note:

• The cut and fill volume is solely dependent on the road cross section 
• While the road cross section slope is solely depending on a parameter in the parameter dialog

Curve-corrected road End Area volumes #

The standard End Area calculation uses the average of the two end-section areas over the distance between them, as described in Calculation of End Area Method in Earthwork. For each cut, fill, or topsoil component:

\displaystyle V=\frac{L}{2}\left(A_1+A_2\right)

where A_1 and A_2 are the component areas at the two chainages and L is the distance between the sections.

MiTS then applies the applicable material or boundary factors separately:

\displaystyle V_{\mathrm{factored,cut}}=S\,V_{\mathrm{cut}}

\displaystyle V_{\mathrm{factored,fill}}=\frac{V_{\mathrm{fill}}}{K}

where S is the swell factor and K is the shrink factor.

For a road curve, equal chainage intervals cover different arc lengths at different offsets from the curve centre. When Include curve-corrected volumes is enabled, MiTS evaluates the cut and fill polygons in radial strips between the two sections. For each strip, the correction is based on:

\displaystyle C=\frac{L}{2R}\left(A_1e_1+A_2e_2\right)

where R is the estimated radius to the section centre lines, and e_1 and e_2 are the strip centroids’ eccentricities from that radius. The cut and fill corrections are assigned to their respective material polygons and factored using the same swell and shrink factors before being added to the factored End Area volumes.

The plan-view part of the diagram shows why the sections are not parallel on a curve. The centroid-line follows a different radius from the road centreline, so it traces a different length over the same angle \theta . For an angular interval, the centreline length is L=R\theta ; a centroid at eccentricity e follows radius R+e and its path length differs by \Delta L=e\theta=Le/R . The section-view part shows the centroid used to measure that eccentricity.

From path-length difference to corrected volume #

\Delta L is an intermediate geometric quantity, not a separately reported volume. It expresses why an offset strip has a longer or shorter travel distance than the road centreline over the same angular interval. C is the resulting unfactored correction volume for the cut or fill strips in that End Area interval. MiTS adds its factored form to the standard factored volume:

\displaystyle V_{\mathrm{corrected,cut}}=V_{\mathrm{factored,cut}}+S\,C_{\mathrm{cut}}

\displaystyle V_{\mathrm{corrected,fill}}=V_{\mathrm{factored,fill}}+\frac{C_{\mathrm{fill}}}{K}

The corrected net volume is corrected cut minus corrected fill. These are the separate curve-corrected columns available in the report; they do not replace the report’s factored cumulative net-volume column.

How MiTS obtains the geometric terms #

• L is the End Area interval: the difference in road chainage between the two adjoining cross sections.
• MiTS extends the two cross-section lines until they intersect. That intersection is used as the estimated curve centre O .
• R is the average of the distances from O to the midpoints of the two cross-section lines. It is therefore an estimate of the road centreline radius for that interval.
• MiTS clips each cut or fill polygon into radial strips between the two section lines. For each strip, A_1 and A_2 are its areas at the first and second section, and e_1 and e_2 are the distances from the corresponding strip centroids to O , minus R .

How the eccentricity e is measured #

Each cross-section’s cut and fill polygons lie in the vertical plane that contains that cross-section’s line, so the horizontal position of any point on those polygons — including their centroid — falls on that same line. This means R and a strip’s e are just two different distances measured along the same straight line from O : R reaches the line’s own midpoint, while R+e reaches a particular strip’s centroid.

The diagram below is a plan (key-plan) view — looking straight down at that one cross-section line, not the vertical cut/fill shape itself. It also depicts the simplest possible case: one contiguous cut zone and one contiguous fill zone on either end of the line. A real cross-section can be less tidy — if the original ground is uneven across the section, cut and fill can alternate several times along the same line. MiTS handles that the same way: it treats every disjoint cut or fill polygon along the line as its own strip, each with its own centroid and its own e , and sums all of their contributions. The two-zone picture below is chosen only because it is the easiest way to see what e means geometrically.

Because cut and fill material typically sit on opposite ends of a cross-section — cut toward the inside of the curve, fill toward the outside, or vice versa — their centroids usually land on opposite sides of the section’s midpoint, giving them eccentricities of opposite sign relative to R . The same construction applies independently to the other cross-section (using its own line and midpoint, but the same O and R ) to get e_2 for that side.

Where the centroid itself comes from: a strip’s centroid is its ordinary area-weighted centre of mass — the same point you’d find by cutting the strip’s shape out of card and balancing it on a pin. A simple way to picture it:

• Slice the strip into many thin slivers along the line.
• Multiply each sliver’s area by its distance from O .
• Add all of those products up, and divide by the total area.

Slivers with more cut (or fill) area, or that sit farther from O , pull the centroid toward them. The result is a single distance that summarizes where the strip’s cut or fill area is “centred,” which is exactly the R+e used above. MiTS does not build the shape from slivers like this — it computes the same centroid directly from the clipped polygon’s geometry — but the sliver picture is a reasonable way to keep the idea in mind.

If the two section lines are parallel or do not produce a usable intersection, no curve correction is applied to that interval. The standard End Area volume remains valid.

The Cumulative Net Volume (Factored) column remains the running total of the standard factored cut minus factored fill. When curve correction is enabled, the report also includes separate curve-corrected cut, fill, and net-volume columns. The Mass Haul diagram uses the curve-corrected series when it is available.

Enable the option from Parameters > Detailing > End Area > Include curve-corrected volumes, then run End Area again. If MiTS cannot calculate a curve-corrected interval, it keeps the standard End Area result, omits the corrected columns, and reports a warning asking that the project be sent to MES Support for investigation.