Linear Homogenization and Mechanical Characterization of Strengthened Masonry Elements with Concrete Overlay

Vulnerability of masonry buildings to seismic activities has been observed during the past earthquakes. A large number of these structures in Iran are residential buildings, hospitals and schools, and their damage ends to massive human being causalities. Therefore, seismic evaluation and strengthening of masonry structures is crucial in seismic regions. Coating the walls with thin reinforced concrete layer(s) is an ordinary technique in retrofitting the masonry buildings in Iran. However, due to the lack of appropriate design guidelines, the rehabilitation procedures are mostly carried out following empirical procedures.
Mechanical continuum elastic properties of a masonry wall are needed for modeling it as a continuum media in the elastic range. These properties can be achieved through the homogenization techniques. The homogenization theory for periodic media allows derivation of global behavior of masonry from the behavior of the constitutive materials (brick and mortar). In other words homogenization is the technique of describing the composite behavior of masonry in terms of macro or average stresses and strains. Homogenization techniques can be done in two main directions called experimental homogenization and analytical homogenization. Experimental homogenization needs so many costly tests and the obtained results are limited to the tests conditions. Analytical homogenizations have been used by many authors in different frame works (elastic, plastic, limit states and …) and with a variety of methods like single step homogenization, two-step homogenization and engineering methods and in most cases only in plane behavior in a two dimensional framework is considered. Single-step homogenization needs numerical solution that can be obtained through finite element analysis and it contains a great number of computations, also the results are not in close-form.
In this paper the elastic properties of bare and retrofitted masonry walls, which can be used in linear seismic evaluation procedures, are derived from a simple analytical homogenization method. The adopted homogenization method can be used easily in any kind of bond patterns, the solution is in closed-form and the results are in good agreement with the complex homogenization procedures used by other authors. The obtained relations for computing the orthotropic elastic properties of the bare and retrofitted masonry wall are presented. The accuracy of the proposed relations for bare masonry walls are verified by comparing the results with the results obtained with a more complex homogenization method. Moreover, the verification for both bare and retrofitted masonry wall is conducted by comparing the elastic behavior of masonry walls following macro and micro modeling approaches.