The first design stage is modeling of the site generally obtained by triangulation of points and lines. This is an essential stage, leading to the creation of a digital ground model (MNT), to be used as a basis for calculation of measurements.
The second stage is the creation of the project lines: as a priority, creation of the horizontal axis and longitudinal section. This method is common to all software. We thus have two modeling types:
• construction of project cross sections from a tabulation (Piste, Autopiste, etc.);
• construction of lines deduced from the red line, describing items on the platform, earthworks slopes and road structures (Macao, Mxroad, etc.).
The third stage is actual calculation of the measurements and publishing of results.
A.5.6.1 – The Digital Ground Model
The MNT (digital ground model) is a virtual representation of the natural ground for calculation of the point’s elevation (z) for all x/y coordinates. The most common form of MNT is triangulation. There are other models:
skew surfaces from a quadrilateral (BDZ IGN file) and ruled surfaces obtained from interpolation between two lines (contour lines, existing carriageway verges, etc.).
S p r e a d o f p o i n t s
The spread of points is composed of points and lines. We must select the points and lines belonging to the natural ground, excluding points which have no altitude (municipal boundaries), but also contour lines which have often been calculated from the basic spread. We must work with the most accurate spread possible, excluding points and lines which are unrelated to the description of the ground.
The spread forms the basis for, but under no circumstances constitutes an MNT (Figure 3).
Software Distributor (last known)
Covadis Geomedia - Immeuble “La Vigie” - 20 quai Malbert – BP 50701 – 29607 Brest Cedex Macao A Bentley product distributed by Graphland
Mensura Cobra Integra Finance - Rue Louis Blériot – BP75 – Forum d’Orvault – 44702 Orvault Cedex Mx Road (ex Moss) Bentley Système France – Cnit – BP 424 – 92053 Paris-La-Défense
Piste + Sétra - 46 Avenue Aristide Briand – BP 100 – 92225 Bagneux Cedex
T r i a n g u l a t i o n
This operation consists of creating triangles by joining up points without crossing the lines.
The main method used is the Delaunay triangulation method, selecting the most equilateral triangles possible. It should be noted that triangulation from the same spread of points may be different, depending on the programs used (Figure 4).
G e o l o g y
Geological layers are generally defined from the ground’s longitudinal section, and this means they are not so accurate in terms of measurements. Their 3D modeling is barely recognized or not recognized at all by design tools, and more accurate assessments are often assigned to experts.
A.5.6.2 – Project modeling
There are two main product families:
• construction of project cross sections based on a tabulation – a traditional method, but difficult to use in the case of junctions;
• construction of lines deduced from the red line, describing items on the platform, earthworks slopes and road structures – a more complex method which nevertheless obtains more accurate volume calculations.
B y c r o s s s e c t i o n s
The planner initially defines a horizontal axis and a project longitudinal section, and then a tabulation based on equidistance or imposed sections.
He then “interpolates” the cross sections by calculating points in accordance with the digital ground model (MNT) (Figure 5).
He may then apply type cross sections (Figure 6).
The Terrain [Ground] line represents the unstripped natural ground.
The Projet [Project] line consists of carriageways and perhaps the central reservation, hard shoulders, embankments and slopes.
The Assise [Earthworks Base] line represents the earthworks section prior to construction of the road structure.
It is used to construct other lines.
The Forme [Capping Layer] line is the intermediate line between the Earthworks Base and Project lines (this line may be used to mark out the capping layer or any other part of the road structure).
The Base [Road Base] line is the intermediate line between the Capping Layer and Project lines (this line may be used to mark out the base layer or any other part of the road structure).
Figure 3 Figure 4
Figure 5 Figure 6
Figure 5
Largeur gauche Left width
Largeur droite Right width
profil en travers cross-section
point terrain calculé calculated point on ground
Axe du fichier projet Axis of project file
Figure 6
LES LIGNES LINES
Terrain naturel Existing natural ground
Décapage Stripping
Projet Proposed road
Base Road base
Couche de forme Capping layer
Assise des terrassements Base of earthworks
B y l i n e s
Moss or Macao use line modeling.
A.5.6.3 – Calculation of measurements
When the modeling of the project and the ground has been completed, we can calculate the measurements.
L i n e a r a n d G u l d e n The linear method This is the classic method.
Sections and widths calculated for each project profile are multiplied by the application length to obtain volumes and surfaces.
The application length is taken at the project axis at the “inter-half-distance” between each profile.
The Gulden method
This method calculates sections and widths in classical fashion, but the application lengths differ from the lengths in the linear method.
The center of gravity is calculated for each surface.
The application lengths are calculated for each entity to be estimated (from the center of gravity), and take account of the radius of curvature.
Where the Gulden method is used, the “Application Length” has no meaning.
The Gulden method makes for better accuracy in the case of projects with considerable curvature:
• alignment with a large number of small radii (mountain roads with hairpin bends, etc.);
• roundabout ring, etc. (Figure 7).