Multidisciplinary approach to the assessment of historic structures based on the case of a masonry bridge in Galicia (Spain)
Introduction
The Cernadela Bridge is a masonry structure (Fig. 1), which is an important element of the Spanish heritage. It is located on the Tea River in the Council of Mondariz, in the Northwest of the Iberian Peninsula. It was probably constructed during the 15th century on the foundations of an old Roman bridge. A channel circulates under one of the five arches, whose design was aimed at water transportation to the mills nearby. This area of the Cernadela Bridge, together with the forest along the shore, is a tourist site with valuable historical interest.
Masonry bridge structures built centuries ago are still working as parts of roads and must operate under different load conditions than those for which they were originally designed. The much higher load level of modern transport and intensive vibrations can cause damage to these historic structures [1], which are integral parts of rural architecture. An important task for engineers and scientists is to find a way to prevent structural damage using methods that will not change the historic character of the structure (e.g., [2]). Because of the age of the structures, their design documentation is usually not available. As a consequence, their location is more difficult and heritage protection is more complicated. Furthermore, the geometry of old and degraded structures is usually difficult to measure.
Given the advances in computer graphics hardware, three-dimensional (3D) modelling software tools, and 3D display capabilities, there is an increasing interest in virtually reconstructing real world objects and scenes for further analysis in several fields: heritage [3], medicine [4], and computer vision [5], among others. Specifically, photogrammetry and laser scanning techniques have earned the interest of researchers in the structure inspection and computation fields (e.g., [6], [7], [8], [9]). Photogrammetric techniques have proved to be especially useful since they are more balanced, in terms of cost and accuracy. In this study the authors use digital close range photogrammetry to generate a geometric model of the analysed structure.
Another difficulty arises when the material used to build the bridge is not completely known especially inside the walls and structural members. However, in this particular case, we can assume that certain materials were used taking as a basis other known Roman structures. Thus, ground probing radar is used to characterise layers with specific material properties.
The information obtained from photogrammetry and radar is used to prepare a 3D model of the bridge that matches the static analysis using the finite element method (cf., [10], [11]). The authors decided to focus on static analysis of the bridge to indicate the high tensile stress zones that can lead to the damage of arches. Two different approaches to modelling the internal composition of the bridge with finite elements were developed. Due to the lack of data regarding the previous state of the structure, sensitivity analysis is applied to study the influence of the geometric changes of the bridge foundations on the structural stress level that affect damage zones. The proposed methodology is shown to be useful in the design of the process of restoration for this type of historic bridge structure.
The main goal of the study is to present an overall methodology to the assessment of historic structure joining photogrammetry, radar and finite element modelling that can help to indicate possible reasons of structural damage but the analysis is performed in the linear field and the authors do not introduce any specific damage models. Since the cracking process can be history dependent and certain factors like damage accumulation or material properties degradation can considerably affect it, as shown in e.g., [12], the following study presents only some estimation of potential damage causes.
Section snippets
Mathematical principles of photogrammetry
Photogrammetry is a technique that allows the 3D metric reconstruction of an object from photographs. A series of mathematical procedures are involved in the achievement of the final 3D: interior orientation and external orientation (relative and absolute).
The interior orientation refers to the process of assessment of the internal geometric camera configuration in order to reconstruct its perspective system. This configuration is defined by the parameters (principal distance and principal
Fundamental principles
Although close range photogrammetry allows achieving high accuracy in the 3D reconstruction of the external faces of stones, it does not permit the geometric modelling of inner materials.
Ground probing radar (GPR) is a remote sensing and geophysical method that is based on the emission of very short electromagnetic pulses (1–20 ns) in the frequency band of 10 MHz–5 GHz. By moving the antennas over the ground, an image of the shallow subsurface under the displacement line is obtained. These images,
Methodology
The geometry of the Cernadela Bridge based on the photogrammetry survey described in Section 2 was applied to develop a 3D finite element model of the structure which was then used to mechanical analysis of the bridge. There are different strategies when modelling masonry structures. The most important components of a typical masonry bridge, such as vaults, piers and filling, can be considered to be simple, one- or two-dimensional structural members modelled as beam, truss or shell. Ideally,
Conclusions
In this paper, some problems encountered when modelling historic masonry bridges have been presented. The mechanical model was based on optometric methods and ground probing radar tests to prepare a relatively accurate finite element model of the Cernadela Bridge. The model was applied to assess the structural behaviour under different types of load and the possible cause of the structural damage. Two finite element models were prepared and their results were compared. The first model using two
Acknowledgements
The financial support of the Ministry of Science and Education (Spain) for Scientific Research under Grant No BIA2009-08012 (Title: “Observatory for masonry arch bridges. Management system”) and AP2006-04663 (“National Program for creating faculty staff, FPU”) is gratefully acknowledged. Computations were done at the TASK Computer Science Centre, Gdańsk, Poland.
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