Road Design Concepts When setting out a road design which incorporates either horizontal or vertical curves (or both), there are many considerations that must be undertaken. 

Some things to consider before beginning are: What is the road to be used for?What vehicle types will be using the road?What terrain will the road be traversing?What speed limit will the road be rated at?

 All of these considerations will affect the way that horizontal and vertical curves will be applied to final design.  The Road Design Module in Surpac will assist you to create a centreline for a road which will store other information related to the curves within the description fields.

 Curve Types

 There are many types of curves all of which can be used in road design.

 Simple Curve

 

 

A simple curve is a curve of constant radius from one tangent line to another.  This curve type does not allow for transitions from the straight to the maximum curvature and should only be used in situations where vehicle velocity is at a minimum.

 

Broken Back Curve

A broken back curve is essentially two simple curves in the same direction with a tangent line in between them.  The two curves to not need to be of the same radius of curvature.  Again, this shows an instant transition from the tangent to the maximum curvature.

 

Reverse Curve

 

 

A reverse curve goes from one simple curve to a second simple curve turning in the opposite direction without a tangent line between them.  The tangent point of the first curve coincides with a tangent point of the second curve.

 Compound Curve

A compound curve is two or more curves turning in the same direction where each curve has a different radius.  Again there is no transition from the tangent to the maximum curvature and in the above example the maximum curvature increases at some point along the curve.

 Spiral Between Tangent and Circular Curve

 

 

This is the most common form of curve creation in Road Design.  A spiral (or transition) exists between the tangent and the circular curve.  This allows the vehicle to gradually increase its radius of curvature as it travels around the corner until it reaches maximum curvature.

 

Double Spiral

 

 The double spiral is similar to the previous example however there is no circular curve between the two transitions.  This means that the curve will gradually increase in curvature until it reaches maximum curvature at which point it starts to gradually decrease in curvature until the tangent is

reached.

 

Vertical Curves

 

 

All of the above mentioned curve types can exist in the vertical plane to traverse across undulating terrain.

 

Further Road Design Terminology

 Line of Sight

 

Safety requirements dictate minimum sight distances in zones where passing is permitted and in non-passing zones to allow adequate stopping distance if there is an obstruction on the roadway.  From the picture above, the sight distance AS (or C) can be summarised in the following equation.

This is a practical equation and is not the exact equation.  This assumes that the value of m is usually small in comparison to R, however C is not the true stopping distance given that cars travel on either the inner or the outer lane.  The result of this equation errs on the side of safety and is commonly used in Road Design.

 

Superelevation

The effect of centrifugal force on a vehicle as it passes through a curve must be countered by raising the outer edge.  This process is known as superelevation.  The outer edge is raised incrementally through the transition curve until the beginning of the circular curve where it remains constant until the exit transition curve where the outer edge is incrementally lowered.  Roads are slightly more complicated that railway conditions and a road normally does not have a level cross section to allow water to drain away to road edge.  However, it is common practice to raise the outer lane to level (with the centreline) before beginning the superelevation.

 The calculation of supereleveation takes into account a number of factors including vehicle velocity, weight of the vehicle and a coefficient of friction between the tyres and the road surface.  The general equation for approximating the superelevation is:

 

Where V is the velocity in metres per second

            R is the radius of the curve in metres            g is gravity = 9.8m/sec2

            e is the superelevation in radians

and      f is the coefficient of friction (nominally 0.35 on bitumen for 50km/h, 0.25 for 80km/h and 0.12 for 100km/h).

 

Exercise

 Design and compare 3 road design options

 The boss has asked you to design and compare the costs of building a road from the mine at point A to the processing plant at point B in the picture below.  As can be seen, the terrain is very mountainous.

 

 

After careful consideration, three possible paths were chosen that might be suitable.

 1.                  Drag the file topography1.dtm into graphics and then drag the file 3choices1.str into graphics.

 Three road choices exist, the first road takes us in a direct line from the mine to the processing plant.  Another takes us out to the west along a valley and the third option attempts to follow a contour and minimise the hills involved.  We will first look at the direct route.

 

 

Vertical Alignments

 We will first  separate the roads into different files for convenience.  Using the string numbers as a guide we will call them Road1, Road2 and Road3.

1. Reset the graphics2. Drag the file 3choices1.str into the Viewport3. Go to File >> Save >> String/DTM File and save the file as Road1 making sure the

range field has string 1 only in it as shown below.

 

4. Save the file again for Road2.str with string range 2 and Road3.str with string range 3

5. Reset the Graphics and drag the file Topography1.dtm into the Viewport.6. Drag the file Road1.str into the Viewport and rotate the view similar to that shown

below.

 

We need to rotate into this orientation to make it easier to select the road alignment in graphics.

 As this is a straight line road, there is no need to do any horizontal alignment on the centreline.  The Horizontal alignment tools are related to horizontal curves only and will be explored on the other two alignments.

7. Select Road Design >> Drape Segment over DTM and graphically select the road alignment string.

The form will ask which layer you the DTM you wish to drape the string over lies in and gives the option of whether or not to interpolate new points into the string.  This must be done as this will ensure that all of the string will match the exact DTM surface.  When you drape a string over a DTM a new point is created wherever the string crosses a triangle boundary.  Apply this form.

 The result should look something like the following (note that the DTM has been re-coloured to make the image clearer).

 

We can now get rid of the topography file.

 

8.                  Select Edit >> Layer >> Delete and delete the topography1.dtm layer.

 The next step is to create a longitudinal profile of the string.  This is like generating a section of the draped string except the horizontal axis is taken as the distance from the starting point (or chainage).  This way it does not matter how the string bends in the horizontal plane.

 9.             Select Road Design >> Create Longitudinal Profile and select the road centreline.  Fill in the form as shown below.

The result is a split screen showing the original string and its associated profile.

 

As can be seen the profile undulates considerably and the road we wish to create needs to be smoother than these undulations.  While this is an extreme example, cut and fill will be required to smooth the road out.  By this we need to determine where the best points will be for creating the vertical curves.  This decision is usually based on the factors of safety and minimising earthworks.

In Surpac, the Vertical inflection points can be defined by clicking on the screen or selecting points on the screen or they can be imported in from an existing string file.  In this example we will use an existing design.

 10.              Select Road Design >> Design Vertical Inflection Points >> Open File Containing Existing Design.  Fill in the form as follows.

 

 

 

Once the inflection points have been defined, we must now determine the radius of curvature for each vertical curve.

 11.              Select Road Design >> Design Vertical Alignment and select the white line indicated in the diagram below.

 

 

You will be presented with a table that outlines the properties of your inflection points.

 

 

Once you input a string number, the screen will be updated with that string and each inflection point is numbered.  The numbers correspond to entries in the table.  All you need to do is add radii of curvature for each of the inflection points to describe your alignment.  As you enter the values, the screen will automatically update the centreline.  By adjusting the values through the table you can get the curve of best fit for the road alignment.  The values in the table shown below give a reasonable curve.

 

 

Once you have filled in the table as above, Press Apply.

The next step is to apply that vertical alignment to the horizontal alignment.  Surpac requires that you identify each alignment in their respective Viewports.

 12.              Select Road Design >> Apply Longitudinal Profile.  Click in the bottom viewport, then select the smooth curved line we created in that viewport.  Now click in the upper viewport and select your horizontal alignment.

 

Once you have selected the alignments, a form will appear giving a summary of the segments you have selected.  Make sure they are correct and press Apply.

The result in the top portion of your screen is the final centreline design.  The road width can be added to this to give a final design.  Due to the mathematical nature of the way the points are interpolated.  A few areas of the centreline may need a little cleaning.  Duplicate Points can occur as well as the occasional spike or “foldback.”

 13.              Select Edit >> Layer >> Clean and fill in the form as shown below to remove any duplicate points from the road centreline.

Once we have removed the duplicate points in the string, we should now remove any spikes.

 14.              Select Edit >> Layer >> Clean and fill in the form as shown below.

 

 

The centreline is now ready to use.  The first thing we want to do is create a road from the centreline.

 

15.              Select Road Design >> Create Road Outline.  Click on the horizontal design of your road centreline and fill in the for as shown below.

 

 

The road will now be filled out to a full width of 40m.  The description fields are not important in this example because while there are no horizontal curves, there is no superelevation to take into account.

 

The final result should look similar to this.

 

 

16.              Select File >> Save >> String/DTM File and save the Road Design.

 

 

 

Horizontal Road Design

 

Designing horizontal Curves is similar to vertical curves, the main difference being that superelevation needs to be taken into account.  This means we need to work with a vehicle speed in mind.  Vehicle speeds are usually rated by type of vehicle, safety concerns, sight distances, road surfaces and environmental conditions.  The vehicle speed must be input in metres per second or feet per second, depending on the units you have set in your Surpac defaults.  Below is a brief conversion table.

 

km/h m/s mph ft/s       

10 2.78 10 14.6715 4.17 15 22.0020 5.56 20 29.3325 6.94 25 36.6730 8.33 30 44.0040 11.11 35 51.3350 13.89 40 58.6760 16.67 50 73.3370 19.44 55 80.6780 22.22 60 88.00

90 25.00 70 102.67100 27.78 80 117.33

 

Lets look at how we can apply this to our horizontal alignments.

 

1.                  Drag in the file road2.str that we saved earlier.

 

 

2.                  Select Road Design >> Design Horizontal Alignment and click on the string in the viewport.

 

When you select the string each Intersection Point will be numbered on the screen and a corresponding record will appear in the table on the form.

 

 

The form allows you to choose a new string number, chainage intervals and a vehicle velocity.  There is a table at the bottom of the form with one entry for each Intersection point in the alignment.  Based on the radius of curvature and the vehicle speed, the transition length and the superelevation will be automatically calculated.  Where you do not wish to have a curve at the Intersection point, you can tick the “Fixed” box in the table and no values will be calculated.  Once calculated the software will indicate a valid or invalid curve depending on the values generated.  For instance trying to create a curve of 10m radius to be driven at 100 metres per second will result in an invalid curve.  You will not be able to Apply the form until all curves are valid.  Similarly you will not be able to apply the form if the transition lengths are not compatible with the tangent lengths.  For example the transition length may calculate to be 700m, however the length from Intersection Point to Intersection Point may be 500m and although the curve

itself is valid, the road design is not.  You will be required to fix all of these before the form is able to be applied.

 

3.                  Fill in the form as shown below and press Apply.

 

 

4.                  Select Edit >> Segment >> Delete and click on the blue segment.  This is no longer required.

 

Once the horizontal alignment is complete, the vertical alignment must needs to be undertaken.  This is similar to the method we used before, except this time we will generate our own inflection points.

 

5.                  Drag the file Topography1.dtm into graphics

6.                  Change your active layer from topography1.dtm to road2.str

 

 

7.                  Rotate the image around so you can exclusively select the road design string and then go to Road Design >> Drape Segment Over DTM and click on the string an press Apply to the form that pops up.

8.                  Go to Edit >> Layer >> Delete and delete the topography layer.

9.                  Select Road Design >> Create Longitudinal Profile and click on the horizontal alignment string and fill in the form as shown below.

 

 

Your screen should look like that shown below.  The Longitudinal profile has the effect of straightening the road and showing the relief, even though we know that the road curves around corners.

 

 

The road generally follows a contour around the mountain so it is more or less flat, however, some vertical alignment is required.

 

In this case we will digitise our own vertical inflection points.

 

10.              Select Road Design >> Design Vertical Inflection Points >> Digitise Points at Cursor Location and digitise a string similar to that shown below.  Note that each point will become an inflection point.

 

 

11.              Once you are happy with your inflection points select Road Design >> Design Vertical Alignment and click on the string you just digitised.

 

Depending on how many inflection points you digitised and where you digitised them, the entries in your form may differ from those shown here.  Fill in the radii until you are happy with the curve as seen on screen.

 

 

If your curves are quite small, you may need to window in to see them behind your inflection points.

 

 

12.              Select Road Design >> Apply Longitudinal Profile.  Remember that this is a four click process.  You must first select the lower viewport, then the vertical alignment in that viewport, then select the upper viewport and then select your horizontal alignment in that viewport.  Confirm that you have selected the correct strings and then press Apply.

 

Your vertical alignment must now be cleaned of extraneous data before we can build the road outline.

 

13.              Select Edit >> Layer >> Clean and fill in the form as shown below.

 

 

14.              Select Edit >> Layer >> Clean and fill in the form as shown below.

 

 

15.              Now select Road Design >> Create Road Outline and choose your horizontal alignment and fill in the form as shown below.

 

 

The results should look similar to this.

 

 

This time, superelevation was relevant because we had some horizontal curves.  The amount of superelevation in a transition is written to the D4 field of the string.  This value is used to compute the z value of each point in the transition zone of a curve.  This effect is shown below.

 

 

16.              Select File >> Save >> String/DTM File and save the road design.

 

 

Option 3 Road Design

 

1.                  Create a Road Design Using Road3.str in the same manner as above.  Horizontal Curve properties are shown below.

 

 

2.                  An example of a vertical alignment is shown below.

 

 

In the example above, the results given would look like this.

 

 

3.                  Save the file as shown below.

 

 

Further Exercise

 

The contractor responsible for constructing the road submitted the following costs.

 

Base rate:                    $1,000,000 per kilometre.

Additional Rate:           $1,000,000 per kilometre extra where the gradient is steeper than 1 in 10

 

Based on these simple costs, which option is most expensive?  Which option is cheapest?  Which option is viable?

 

Answers

 

 

Changes to Curve Creation

 

The algorithms for curve creation have also been added to the existing functionality in Surpac.  Now when you create curves from tangents or curves at the end of segments, the option to add transitions is given.

 

Create >> Curve From Tangents

 

 

 

 

Create >> Curve At Segment End

 

 

 

Answers

 

Note:  The numbers in your answers may differ from those shown below due to free hand digitising of inflection points.  The methodology is the same.

 

The contractor responsible for constructing the road submitted the following costs.

 

Base rate:                    $1,000,000 per kilometre.

Additional Rate:          $1,000,000 per kilometre extra where the gradient is steeper than 1 in 10

 

Based on these simple costs, which option is most expensive?  Which option is cheapest?  Which option is most viable?

 

 

Treat each road separately.

 

1.                  Using Inquire >> Segment Properties, the total length of the road can be established.

 

Road Option 1:             Length –          18,198.5m

                                    Base Cost –     $18,198,500

 

Road Option 2:             Length –          25,316m

                                    Base Cost –     $25,316,000

 

Road Option 3:             Length –          25,338.7m

                                    Base Cost –     $25,338,700

 

Calculate The penalty Costs for terrain road building.

 

Using string maths, the slope of the segments of roads can be calculated.  Using these slopes we can calculate the costs of construction.

 

2.                  Drag in the File finished_road1.str

3.                  Window in closely to the centerline and using Edit >> Segment >> Delete, delete the two road edges.

4.                  Go to Edit >> Layer >> Maths and fill in the form as shown below.

 

The partially obscured expression is

“_tmp1 + iif(_next_slope > 10, _next_3dlen * 1000,iif(_next_slope < -10, _next_3dlen * 1000, 0))”

In words, this can be said as, if the slope from one point to the next point is greater that 10% then add the 3d length of that line multiplied by $1000 to the aggregation, otherwise if the slope from one point to the next point is less than -10% then add the 3d length of that line multiplied by $1000 to the aggregation, otherwise (if it is close to horizontal) add zero to the aggregation.  Then format the resulting numbers to zero decimal places.

 

 

The result of that string maths can be seen by displaying the D1 field for each point.  Each point carries an accumulation of cost along the road.  The last point on the string will have the total cost.  The D2 field for each point will also hold the total cost of the penalty construction costs.

 

 

 

Adding these values for each road to their base costs:

 

Option 1:                     Base Cost -      $18,198,500

                                    Penalties -        $15,798,282                                    Total -                $33,996,782

 

Option 2:                     Base Cost -      $25,316,000                                    Penalties -          $9,746,187                                    Total -                $35,062,187

 

Option 3:                     Base Cost -      $25,338,700                                    Penalties -        $17,943,496                                    Total -                $43,282,196

Based on these figures, the direct route (Option 1) is the cheapest option and Option 3 is the most expensive.

 The most viable option would be Option 2 because areas along the other two options have gradients in excess of 37 degrees and this may not make it possible to drive on these roads.