Keywords: coefficient of thermal expansion, 3-D model, pit, filling material, transient heat transfer, finite element method.

Architectural and also sculptural stone monuments often suffer from deep surface deterioration due to spalling of the basic material and the appearance of deep pits. Artificial stone or mortar materials need to be used in the repair work to fill the defects. The filling material should have properties that are the same as or similar to those of the original material. However, it is almost impossible to obtain two distinct stones with the same properties in the real world. It is therefore necessary to find the maximum tolerable difference in the properties of the filling and the original materials. The aim of this paper is to show the effect of different thermal expansion coefficients of the filling and the original material that lead to an unacceptable increase in the stress in the filling material and its surroundings.

Numerical simulation was used to analyze the temperature field and the state of stress caused by different coefficients of thermal expansion. The simulation consisted of two stages: first, the temperature field was computed by solving a transient heat transfer problem described by a partial differential equation - see Jaluria [1]. Then, the resulting distribution of temperatures (temperature field) served as input data for the stress analysis, which used a static linear analysis to compute the state of stress.

Due to the different thermal expansion coefficients of the filling and the original material, the state of stress in the filling and its surroundings increases significantly. The magnitude of the stress depends on the difference of the thermal expansion coefficients of these two materials, on their Young Modulus values, on the shape and thickness of the filling, and on the temperature gradient.

Maximum effective and shear stress values occur at the pit edge, and at a distance of about 1 cm outwards from this edge, outside in the surrounding original material. An inappropriately chosen filling material can cause its own degradation and can increase the disruption of the structure. Therefore, the filling material should have physical properties identical or similar to those of the original material, especially the same value or a very similar value of the thermal expansion coefficient. If the coefficients of thermal expansion differ only slightly (less than 2*10^-6 approximately), the material can be considered as homogeneous, with no considerable increase in stress. However, if the coefficients of thermal expansion differ significantly, a corresponding increase in stress is inevitable. Due to the stress caused by periodic temperature changes, cracks can occur in the filling and in the original material in the surroundings of the repaired place. It is therefore necessary to consider material compatibility (especially coefficients of thermal expansion), when choosing a suitable filling material to repair the structures of historic buildings.

1

Jaluria Y., Torrance K.E., "Computational Heat Transfer", Taylor & Francis, 2nd ed., 2002.

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