Keywords: masonry, first-order homogenization, heat transport, moisture transfer.

Applications of homogenization techniques to civil engineering problems have experienced a remarkable increase during last decades. This can be mainly attributed to the introduction of first-order numerical homogenization procedures to modeling of masonry structures. Examples of successful applications of homogenization-based modeling range from the determination of effective elastic parameters of masonry to the description of damage processes up to the point of failure using sophisticated material models [1]. So far, attention has been mainly paid to simulation of the mechanical behavior of masonry structures, which can be considered as the most important factor for the practical design of structures.

In addition, a number of other applications exist, where alternative sources of (non-mechanical) loading can be critical for the analysis of engineering structures. Examples include the analysis of masonry structures exposed to elevated temperatures, where heat exchange due to radiation and convection cannot be neglected in structural mechanical analysis. Recent inspection of various historical structures, e.g. the Charles Bridge in Prague [2], revealed an unfavorable impact of temperature and moisture on the mechanical response of such structures. Moreover, these effects may prove to be the crucial factor responsible for the appearance of cracks. The analysis of moisture and temperature fields for realistic boundary conditions and simulation times within the structure is thus of paramount importance.

A variety of sophisticated software tools exist, which allow the analysis of coupled transport processes of heterogeneous materials when individual phases are modeled separately, e.g. [3]. In this case, the direct application of such a code would require a detailed modeling of all material phases (blocks and mortar). Realizing that such an analysis might have to be performed for data collected over the time span of at least one year, it becomes clear that this approach is not computationally feasible even for dimensionally reduced 2D models. Therefore, the application of homogenization techniques to the analysis of transport processes in brick masonry seems to be inevitable.

For the case of linear transport processes, the determination of the effective macroscopic parameters such as thermal conductivity and moisture permeability is rather straightforward [4] since these parameters remain constant throughout the analysis. When limiting our attention to such a case, we may rely on a fully uncoupled modeling strategy to solve the macroscopic analysis separately with a certain constitutive model determined from the analysis on a meso-scale. It is well-known, however, that parameters of individual phases are highly nonlinear functions of the current temperature and moisture. Evidently, studying a nonstationary problem calls for an interactive and/or adaptive meso-macro analysis with storage of data related to every macroscopic material point.

The solution of the meso-scale problem assumes that the temperature and/or moisture gradient is expressed on the basis of temperatures and moisture content at the selected points in the unit cell. Unlike the mechanical analysis, however, the temperature and moisture dependence of the material parameters requires enrichment of information passed from macro- onto meso-scale. In particular, apart from gradients also the macroscopic (reference) temperature and/or moisture content must be introduced in the meso-scale analysis. These values, however, as they follow from a proper analysis on macro-scale, are generally not known a priori suggesting a full meso-macro analysis.

A certain simplification can be adopted when the distribution of individual fields on macro-scale can be estimated, e.g., on the basis of experimental measurements. In such a case the problem can be simplified by performing an appropriate parametric study for the reference macroscopic values of temperature and moisture content to form a table of homogenized coefficients thermal conductivity and moisture permeability. These parameters can be then used in independent macroscopic analyses with available commercial software. Comparing the predicted and assumed macroscopic thermal and moisture fields may serve to improve the estimates of the homogenized parameters from repetitive homogenization process on meso-scale. The resulting homogenized parameters including the predicted thermal and moisture fields are finally utilized in the mechanical part of the study. This approach is also employed in the present study.

1

T.J. Massart, "Multi-scale modeling of damage in masonry structures", Ph.D. thesis, Technische Universiteit Eindhoven, 2003.

2

J. Sejnoha, J. Zeman, J. Novak and Z. Janda, "Non-linear 3D analysis of Charles Bridge exposed to temperature impact", to be presented at The Tenth International Conference on Civil, Structural and Environmental Engineering Computing, Rome-Italy, 30.8.-2.9. 2005. doi:10.4203/ccp.81.187

3

J. Grunewald, DELPHIN 4.1 - Documentation, Theoretical fundamentals. Dresden: TU Dresden, 2000.

4

D. Cioranescu and P. Donato, "An introduction to homogenization", Oxford University Press, 1999.

purchase the full-text of this paper (price £20)

go to the previous paper
go to the next paper
return to the table of contents
return to the book description
purchase this book (price £135 +P&P)