The case study is located in Marghera (Venice), Italy. Historical information has been gathered in two forms from private collections: design drawings and construction site annotation. The drawings are copied from a French-based design since the title blocks informed: “Refrigerant Hyperboliques – Procedure 17600 – Paris”. Refrigerant Hyperboliques was a French company, founded in 1927, among others, by two engineers Afred-Tony Guerritte and Marcel-Ernest Gérard (Association française du froid 1927). The annotation on the drawings reported 1938 as the date of design and construction.
The building and surrounding area have been digitally surveyed through Light Detection And Ranging (LiDAR) technique (Arayici and Hamilton 2005; Wang 2013), using a Leica C10 Scan Station. The representation as point cloud of the tower records the state of its conservation after structural renovation. Linking the digital survey with the generated parametric surfaces, a model is obtained that allows the representation of three surfaces, the internal, external, and median.
On design representation, the hyperbola is graphically described by a vertical radial section of the tower (Fig. 4). In the Ozx plane, it has been reported the x value – radius of any parallel – every unit meter in height, enumerated from the top to the base. Its correspondent asymmetrical hyperbola equation is:
$$\frac{{x}^{2}}{{\text{7,99}}^{2}}-\frac{{z}^{2} }{{\text{21,31}}^{2}}=1$$
The process highlights an issue in modeling the shape from the survey. The design is defined through a curve, which generates a surface by its revolution around the z-axis. To represent the final built surfaces, starting from the curve and along its normal direction, multiple values have been assigned, representing the thickness. During the design phase, this description answers technical purposes such as volume calculation and formwork manufacture. The thickness of the tower is reported variable: at the base parallel is 35 cm, becoming 8.8 cm at 22 m, from which it remains constant. Vice versa, the digital survey represents information about the outer surfaces. Consequently, the median surface must be calculated, and it does not represent an input. The scripting environment has been changed to fulfill this requirement. The internal and external surfaces are supposed to belong to one sheet hyperboloid type.
After setting all the parameters described above, by changing the value of the angle of rotation, it is possible to superimpose graphically the ideal hyperboloidical surface with the point cloud of the real building. In its original configuration, the tower had a total height of 50 m, it was supported by sloped columns at its base (7.10 m), with an underground fluid collection tank placed at -4.20 m. The hyperboloidical surface, not symmetrical, was 47.05 m in height (HH.hh), the base parallel inner radius was 13.56 m (HH.Ru), the top parallel radius was 10.02 m (HH.Ro), the throat section radius about 7.95 m (HH.Rt) placed at 30.60 m. The central angle of rotation of the generator is 91.7° (HH.ph).
Once set the values, the surface has been compared to the point cloud using deviance analysis. Since 58% of the points representing the internal surface are within the interval ± 3 cm, the modeling process is valid (Fig. 5).
Fig. 5Deviance analysis between the internal surface of the model and the point cloud
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The median surface has been built by using average values of the main parameters of the shape. Then it has been analyzed using a deviance analysis with the surface obtained from the design documentation and implemented with the formula stated above. This step makes evident the quality of the design-to-build process in 1938: the maximum distance is − 3.5 cm in the upper part and 5 cm in the lower part of the surface. This result demonstrates the ability of the construction operation to build these towers without pre-fabrication techniques.
Previous steps are performed within a BIM modeling tool, to semantically enrich the 3D model and operate in a design environment. The BIM model allows for the creation of a digital twin of the original design and the actual structure (4D model). First, the surface was completed at the top and bottom, as a closed surface, represented by a unique wall entity (IfcWall) (ISO 2018). Thus, it is possible to associate to it the designed rebars along the generatrixes of the hyperboloid, with alternatively positive and negative values of the angle HH.ph (Fig. 6). The model is then completed with other elements, which are design solutions particularly related to geometry or performance of the tower. For example, the tower included two openings for the plant water inlet. They have an elliptical profile to maximize the space between two consecutive circular and rectilinear reinforcements. Additionally, the tower presented small holes on the top to reduce precipitation and recover some water by condensation. They have been modeled as an object based on the wall (IfcOpening).
The top and bottom of the surface were later mapped with two circular structural objects (IfcBeam) that have their own reinforcements. The slanted columns (IfcColumn) at the ground floor, designed to support the tower and let the cooling fluid in, have a hexagonal section. Their analytical representations are congruent with the beam described above. The model is finally completed with the slabs and the retaining walls of the base water tank (Fig. 6). The median surface of the tower, fitting for FEM and CFD model, is defined as an instance of IfcWall with appropriate representation through NURBS surface.
Fig. 6On the left, the representation of the tower as point cloud. On the right, the analytical structural model and the BIM model presenting the geometric entities from the scripting environment
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