Keywords: geodetic measurement, solar radiation, heat transfer, numerical models, finite element method.

The Prague Castle ranks among the most important historical landmarks of the Czech nation and is one of the greatest buildings in the capital. The major component of the Castle is Saint Vitus' Cathedral with its oldest part built in the 14th century. Geodetic monitoring of such a historically important building helps to detect early signs of structural degradation, facilitating thus repair [1]. It can also help to identify how and why the building is degrading so it can be prevented from worsening. This paper reports on the geodetic monitoring of Saint Vitus' Cathedral and determines whether the measured displacements were caused by temperature extensibility or by other influences.

Two programs of the finite elements method: Feat and Adina, were used for the numerical analysis. Feat is a program for calculating displacements and internal forces caused by temperature differences (static linear analysis). However, this program cannot simulate the transient heat transfer. Therefore, the Adina system (which can simulate the transient heat transfer by solving appropriate partial differential equations using the finite element method) was applied to calculate the average temperatures inside the various parts of the structure (such as columns, walls, and ribs). The outputs of Adina served as inputs for the simulation in the program Feat. The numerical model of the old part of the Cathedral was created using the Feat software. It was a 3-D model consisting of 2-D (walls, shells) and 1-D elements (beams) and this model described one bay of the structure.

When comparing the theoretical and geodetically measured deformations, the best possible approximation of the temperature distribution inside the structure of the Cathedral during the measurements is necessary. The influence of solar radiation (inclusive the shadow-casting effect of other parts of the Cathedral) cannot be omitted if we want to achieve the most realistic distribution of the temperature field in the external parts of the structure of Saint Vitus' Cathedral. We have also to consider how the temperature field depends on the temperature of the air around the structure. The verification of the temperature analysis of Saint Vitus' Cathedral by comparing the computed and measured values of surface temperatures of the structure proved the analysis to be realistic.

The most exact results of the theoretical analysis were achieved in the variant considering also the influence of solar radiation. This analysis showed that the measured deformations are cyclic in nature and are mainly caused by the periodical changes of temperature. Geodetic measurements and the simulation analysis described in this paper did not prove any degradation for the Saint Vitus' Cathedral.

1

Procházka J., Voborilová, "Displacements and Deformation Measurement of Historical Buildings with Geodetical Methods", Stavebníobzor: Civil Engineering Journal, 8, 232-238, 2003.

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