Case Study 6 - Balanced Volumes

Links for the needed files: https://www.dropbox.com/s/erjc11xlb34cdo7/Case%206%20-%20Balanced%20Vols%20%28May%202020%29.sdb?dl=0 

There are many situations where earthworks are carried out with balanced balance cut and fill quantities.

This exercise deals with such a situation and introduces you to two possible solutions.  One using a trend surface but not necessarily to produce an exact balanced volume quantity and the other to generate a horizontal plane with balanced volume quantities, making allowances for batter intercepts and bulking factors, if required.

In this example the situation is complicated since the required outline of the preferred surface (purple) does not fall wholly within the original ground surface (triangles).  We will use tools to extend the original survey, so the design is fully encapsulated.

Ground Survey with Platform Backcloth

Case 1 – Best Fit Plane

The platform we wish to create is 130x70m in size.  In this case, we need a plane surface but not necessarily horizontal.  This is best achieved using a Trend surface.  This uses the List option to identify points used to define this best-fit plane surface.

Note: List is a useful tool that normally works in conjunction with the Pick option.  In graphics, points on the List will be identified with a blue or yellow blob, depending upon background colour and greenish in the project grid (spreadsheet).  The latter turn red when selected.  Also note the List point count in graphics, bottom right (151 selected below).

We can be more selective in adding points to the List but here we will use all the points in the Ground Survey model.  The easiest way to do this is to use List-->Invert.

Now select Design --> DM --> Advanced -->Trending Create.  This will use the listed points to create a best-fit height offset plane passing through listed points.  A summary of the fitted surface will appear.

Note Each model can have its own Trend Surface, which is only accessible within that model.

Trend Surface Create

Best Fit Trend parameters

The trend surface created will depend upon the density and location of the points on the List, with greater influence coming from clustered points.  There may be local highs and/or lows that will be smoothed to the trend surface.  There is no visual to the Trend apart from our “old” 3D viewer, which is still available.  You need to hold down the shift key when selecting the yellow cube icon.  Use the fourth icon to display the Trend.

Old 3D Viewer Showing the Trend (Hold Shift when Selecting the Yellow Cube Icon)

It is now possible to use this Trend for point interpolation.  You will note that the platform extends beyond the ground survey, which deemed satisfactory. 

We now wish to move the four Platform points to this trend surface.  Since the trend surface only works with the current model, we will have to copy these four points from the Platform model to the Ground Survey model, then after interpolation copy them back, replacing the original Platform points.  The easiest way to do this is from the Project grid.

Copying Platform Points

After copying the fours platform points, they are pasted into the Ground Survey model, where the trend has been formed.  Remove listed points from the original survey, then add the four platform points to the list, as shown below.

Adding Four Copied Platform Points to the List

We can now go into graphics and move the listed points to the Trend.  Remove the Platform backcloth, revealing the copy of the platform points.  Now use the Points --> Move --> Heights to Trend to interpolate the copied platform points onto the trend.  This can be done individually (Pick Element) or after putting the points on a new List (Pick List), as shown here.

Moving points onto the Trend

Note, since the platform coding is FE (a string) an alternative option for copying points from one model to another, graphically, is to use the backcloths option.  Add Platform as a backcloth to the Ground Survey model, then use Lines --> Copy Backcloth, selecting the Platform feature string in the backcloth.

Now replace the original Platform points with the copies.  This is best done in the Project grid, as shown previously, using cut and paste from Ground Survey to the Platform, deleting the original four FE corner points.  Enter graphics on Platform.  We now need to create a DTM.

Note: When generating a DTM, there are various settings including colour, layer, boundary filtering and max side length.

DTM (left) and Height Shading (right) Settings

Select Settings --> DTM Settings.  If the Boundary Filter by Length is set to 100m the DTM will not create as the long length of the boundary is 130m.  Uncheck it, then create a DTM-->Normal DTM.

Add Ground Survey as a backcloth then select the 3D yellow cube icon.  Use the Properties panel to show the Ground Survey as a blue wireframe and the Platform to shaded.

Platform as a Best Fit Plane

If we want to see how the volumes would be affected using this platform, use the DTM --> Volumes Prisms to a Projected Surface and generate cut and fill volumes to the Ground Survey model.

Prismoidal Volumes

You will be expected to identify the reference surface for comparison.  In this case, it will be Ground Survey.  An outline of both models will be displayed, as shown here.

Selecting a Reference Surface

The results will appear in a rich text editor, and if selected as a plotted table.

Report on Volume Calculations - Rich Text Editor

The plotted table has options for selecting what is being displayed in the table.  The table will be plotted in this model's dedicated CAD backcloth.

Plotted Table Definitions

Ideally, we are looking for a balance of zero.  This is NOT the case here as there is a balance of 158m³.  As an additional exercise, you may wish to raise the platform points, and hence the DTM, by small margins and recalculate the volume.  You can start by taking half the balance divided by the plan area.

But of course, the platform has taken the slope of the trend, which was not horizontal.  The next Case will look at balancing quantities with a horizontal platform.

Case 2 – Balance Volumes

For whatever reason, the original survey did not cover the area of interest, so before we go any further we must update the original survey and identify new points so we can encapsulate the platform which currently extends beyond the survey.  These gaps are mainly at the eastern and western parts of the Ground Survey model.

The plan here is to use representative points, close to where we need to extend the model.  We have two choices.  Firstly, to use near neighbour inserts for heights or secondly to identify a trend surface from sampled points and use this trend to provide heights to new points.  These additional points can then be added to the existing DTM.  We will use List here.

Selecting Points to be added to the List

First, we have to select representative points to form the trend surface using the List Add-->Inside --> Polygon option here.  These points can now be used to generate the trend surface, found in the Design menu (see above in Case 1 to see how).

Use the Points --> Insert option, select Model Trend for reference surface and add additional points outside the Platform model extents, shown here in the backcloth. 

Note In this case you may select a Trend from another model.  This was not the case for Move points, which had to be the current model. (v4.30a)

Extending Points in the Model using the Trend Surface

The Trend created here is only appropriate for this side of the model.  You will have to clear the List and repeat the process for the top and right sides of the model.

Note:  Make sure you select representative points to form the Trend.  Do not select points forming a single line feature as the Trend may not form as you expect it!  In cases like this, it would be better to use the Near Neighbour option when Inserting points.

Once these external points have been created, it's now possible to add them to an existing DTM, without having to delete and reform the DTM or stitch them in manually.  The new external points are added to the List, then use the DTM-->Extend option.

Extending a DTM Using Listed Point

Note If the points to be added fall inside the current DTM, it's possible to stitch these in using the DTM-->Edit-->Apex Include option.  The pick options Element, Rectangle and List are used here.

Now, return to the Platform model and set temporally set all the heights at 20m in the Point grid, defining our horizontal plane.  You could leave it inclined from the previous exercise and the plane will be retained, but we are looking for a level platform here, with batter slopes.

With the Platform model in graphics, use Lines-->Densify --> All to add additional points to the platform at 10m spacing.  This will make it more stable for what is about to follow.

Note: As a general principle try and avoid long thin triangles when modelling.  Use this densify option along long spaced strings to add more points.

Densify Platform String at 10m Intervals

Densify Using Linear Interpolation

We will now use this modified string to generate a horizontal plane with balanced cut/fill quantities.  We are able to include batter intercept strings and take account of bulking factors.

Use the option Design-->Strings Balancing to the modified Ground Survey model, as shown below.

Balancing String – Selecting Reference Model

Selecting Balancing Properties

This option will move the Platform model string up and down until the volume of cut/fill is balanced.  Batter strings and bulking factors can be introduced.  For this exercise, we have added batters at 1 in 10.  You will also notice that a Fan angle of 15degs has been introduced.  This will smooth off the corners.  Also, the platform has been kept level at 18.4601.

We can now create the DTM and view the Platform and modified Ground Survey models in 3D.

3D View of Horizontally Balanced Platform

To check the volume quantified, go to DTM --> Prismoidal Volumes, using the modified Ground Survey as the reference surface.  This time plot out the table.  It should look something like this, with zero material to import or export from site!

Balanced Volume Table

Summary

This exercise identifies how ⁿ4ce can be used to calculate balance quantities.  Two methods were examined.  The first was based on a best-fit plane passing through ground points.  It was shown that simply using offsets from this plane did not generate balanced quantities.  And of course, the plane was not horizontal.

The second method used the original base string, with batter strings to create an outline model that is moved up/down until the volumes are balanced.  The original plane of the original string is retained, thus allowing surfaces to remain horizontal if required.

The two options have resulted in different volumes.  In the first case within an inclined surface, we saw a movement of around 158m³ of cut.  In the second case where we opted for a horizontal plane, there was a potential movement of 1159m³ (cut/fill) material.  Which is right for you?