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 situations where you may wish to carry out earthworks without the need to introduce or remove materials from the site, to balance cut and fill volumes.

This exercise deals with such a situation and introduces you to two possible solutions.  One using a trend surface to balance offsets 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 level is 130x70m in size.  In this case, we need a plane surface but not necessarily horizontal.  Here we will use the Trend surface found in the Design menu.  This uses the List option to identify points used to define the trend surface.

Note: A list is a useful tool which 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 (191 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 ListàInvert.

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.

Trend Surface Summary

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 which will be smoothed to the trend surface.  There is no visual to the Trend apart from our “old” 3D viewer, which is still available.

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, but for this case, it will be 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.  We will use a copy from backcloth tool first.

Moving points onto the Trend

Add Platform as a backcloth, then use Lines --> Copy Backcloth and select the Platform feature string in the backcloth.

Note: An alternative option is to simply copy the Platform points in the Project grid pasting them into the Ground Survey grid.  These points are coded FE as opposed to the survey which are all SL.

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).

Now replace the original Platform points with the copies.  This is best done in the project grid using cut and paste from Ground Survey to the Platform, deleting the original 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 Normal DTM.

Add Ground Survey as a backcloth then select the 3D 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

Use the DTM --> Volumes Prisms to a Projected Surface and generate cut and fill volumes to the Ground Survey model.

Prismoidal Volumes

Report on Volume Calculations

Ideally, we are looking for a balance of zero.  This is NOT the case here as there is a balance of 185m³.  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

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 that can be used in the trend surface using the List option.  We can use the Inside --> Polygon option here.  These points can now be used to generate the trend surface, found in Design menu (see above in Case 1 to see how).

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

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 you would be better to use the Near Neighbour option when Inserting points.

Due to the way we create and save the DTM, its not currently possible to automatically add these boundary points to the Ground Survey model.

Manually Stitching Points into the DTM

Two options are available possible.  Firstly, delete the DTM and reform it which will include the new points.  But this may be a problem if you have already carried out editing on the current DTM, as this editing will be lost.  You may wish to add the new points manually using one of the Insert options found in the DTM --> Edit options.  We will delete the DTM and recreate it.

Note: If the new points fall within the current DTM it's possible to add them automatically.  The list is particularly useful here.

Return to the Platform model and set all the heights at 20m in the grid, defining our horizontal plane.  You could leave it inclined from the previous exercise and the plane will be retained.

With the Platform model in graphics, use LinesàDensify --> All to add additional points to the platform at 10m spacing.  This will add additional points along each side of the platform making it more stable for what is about to follow.

Densify Strings at 10m Intervals

Densify Using Linear Interpolation

Note: As a general principle try and avoid long thin triangles when modelling.  Use this densify option along long space strings.

We will now use the densified Platform string to generate a horizontal plane with balanced cut/fill quantities.  With this option, we are able to include batter intercept strings and take account of bulking factors.

Use the option DesignàStrings Balancing to balance the string to the modified Ground Survey model.

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.

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

3D View of Horizontallt Balanced Platform

To check the volume quantified, go to DTM --> Prismoidal Volumes, using the modified Ground Survey as the reference surface.

Prismoidal Volumes

Volume Report Results

If you’ve been following this exercise you will have noted that there are two ways of displaying volume results.  We’ve only been showing the report, but an option to plot a table will have been offered.  If plotted this appears in the dedicated CAD backcloth on the layer nominated you’re your chosen colours.

Table of Volumes

• 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 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 400m³ (cut/fill).  In the second case where we opted for a horizontal plane, there was a movement of 1159m³ (cut/fill) material.  Which is right for you?