Keywords: Charles bridge, historical structures, temperature impact, two-scale analysis, water flow-structure interaction.

The Charles bridge in Prague is one of listed monuments having a paramount historical importance. On 9th July 1357 in the morning, exactly at 5 hours and 31 minutes, which corresponds to the numerical sequence 135797531, Charles IV of the Louxenbourg Dynasty, King of Bohemia and Germany and Italy, Roman Emperor, laid the foundation stone and entrusted Peter Parlér and his stone mason's workshop to construct the bridge. Currently, a living discussion of two groups of specialists is underway on the concept of the bridge repair in the Czech Republic. The discussion mainly revolves around the function and performance of the reinforced concrete slab put in the bridge during the reconstruction in 1966-1975. It speaks for itself that the repair of the Charles Bridge is extremely demanding professionally, and, besides, carefully watched by the society as a whole. Therefore, detailed analyses of the response of the bridge to loading impact appears to be inevitable. It is obvious that they should be carried out on cogent material models and using progressive computational techniques.

This paper is a continuation of our previous works [1,2,3]. These papers deal with special material models related to quarry masonry and to natural stone masonry distinguished itself by regular and/or irregular geometry, respectively. The quarry masonry fills up the inner part, while the natural stone masonry forms the vertical surfaces and the vault of the bridge. In the framework of two-scale numerical homogenization, two different scales of analysis are considered - the mesoscopic (mesostructural) level, where a typical dimension is related to the size of the stone block, and the macroscopic level at which the bridge is analyzed as a whole.

The typical feature of the homogenization-based approach on the mesoscopic scale is that all the non-linear calculations are performed on a periodic unit cell (PUC). The present paper utilizes specific applications of these techniques to the evaluation of effective material properties described in the accompanying papers [4,5] and in references therein.

On macroscopic scale, the analysis is carried out on the three-dimensional segment of the bridge. The fracture energies are determined as areas under the loading curves derived on the mesoscopic scale and multiplied by the width of the localization band. This approach is of course a certain simplification of reality. Nevertheless, it can be realized immediately with the help of existing software ATENAWin [6] including the non-linear character of the problem linked to the evolution of cracks, which can be correctly represented.

The macroscopic calculations are conducted in two steps. In the first step, the non-stationary simultaneous moisture and heat transport is analyzed in a characteristic cross-sections of the bridge. The courses of the temperature calculated at individual material points complies well with the results of in situ measurements using temperature and moisture sensors. In the second step, the response of a bridge segment to temperature impact is analyzed under the assumption of periodic repetition of the bridge segments (vaults). Finally, incorporation of an additional load due to the bridge-water flow interaction is considered as a next logical step in moving the numerical model closer to reality.

1

J. Novák, J. Zeman, and M. Šejnoha. Multiscale-based constitutive modeling of regular natural stone masonry. In B. H. V. Topping and C. A. Mota Soares, editors, Proceedings of the Seventh International Conference on Computational Structures Technology, Civil-Comp Press, Stirling, United Kingdom, 2004. paper 197. doi:10.4203/ccp.79.197

2

M. Šejnoha, V. Blazek, J. Zeman, and J. Šejnoha. Non-linear homogenization of quarry masonry. In B. H. V. Topping and C. A. Mota Soares, editors, Proceedings of the Seventh International Conference on Computational Structures Technology, Civil-Comp Press, Stirling, United Kingdom, 2004. paper 196. doi:10.4203/ccp.79.196

3

J. Zeman, M. Šejnoha, and J. Šejnoha. Homogenization of stone masonry with irregular geometry. In B. H. V. Topping and C. A. Mota Soares, editors, Proceedings of the Seventh International Conference on Computational Structures Technology, Civil-Comp Press, Stirling, United Kingdom, 2004. paper 200. doi:10.4203/ccp.79.200

4

J. Novák, M. Šejnoha, and J. Zeman. On representative volume element size for analysis of masonry structures. In B. H. V. Topping, editor, Proceedings of the Tenth International Conference on Civil, Structural and Environmental Engineering Computing, Civil-Comp Press, Stirling, United Kingdom, 2005. doi:10.4203/ccp.81.188

5

J. Sýkora, J. Vorel, J. Šejnoha, and M. Šejnoha. Effective material parameters for transport processes in historical masonry structures. In B. H. V. Topping, editor, Proceedings of the Tenth International Conference on Civil, Structural and Environmental Engineering Computing, Civil-Comp Press, Stirling, United Kingdom, 2005. doi:10.4203/ccp.81.190

6

L. Jendele. ATENA Program Documentation. Part 7: AtenaWin description. Cervenka Consulting, Prague, 2003.

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