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International audience; This paper provides multi-level modeling of microcracked viscoelastic masonries generally present in historical masonries or refractory linings. It is an extension of the Cecchi and Tralli (2012) or Cecchi & Barbieri (2008) and Cecchi & Taliercio (2013) works for the typical Burgers and Modified Maxwell models followed by both undamaged and microcracked masonries. For the sake of simplicity and in order to provide rigorous analytical global estimates, only the mortar is assumed to be viscoelastic and microcracked. Bricks are assumed to be undamaged, elastic or quasi-rigid. The distribution of microcracks is assumed to be isotropic. The effective behavior of the viscoelastic microcracked masonry is provided by two steps. The first one relies on the coupling between the Griffith’s brittle fracture theory and linear mean-field homogenization scheme in order to account for the effect of microcracks on the macroscopic deformation of the mortar and establishes a linear relation between apparent macroscopic stress and strain. This step allows to easily and fast determine the effective creep function of the microcracked mortar without recourse to ’complex’ or heavy numerical inversion of the Laplace–Carson transform. The second step is based on the coupling between asymptotic analysis and homogenization theory applied for a periodic masonry. The proposed models provide analytical solutions - explicit functions of the crack density parameter - for the effective orthotropic behavior of a microcracked viscoelastic periodic masonry cell. This study proves that the Cecchi & Tralli’s and Cecchi & Taliercio’s extension estimates are close and that the later are softer. Such overall properties are used to perform finite element computations on a compressed masonry panel as a first application. These models allow then the prediction of mostly stressed and deformed areas in microcracked masonry structures. This study demonstrates that modeling a mortar (at its undamaged or microcracked state) with this Burgers formulation is only suitable for a masonry with too high values of the Maxwell’s relaxation time otherwise it yields to vanishing effective properties with the increase of time and crack density leading thus to a premature collapse of the masonry. On the other hand, the Modified Maxwell model permits the masonry to preserve a certain resistance for every range value of Maxwell’s relaxation time. These conclusions are valid for masonry either with elastic or quasi-rigid undamaged bricks.

International audience; In order to support the optimization of mortarless brick linings of steel producing furnaces it is proposed in this paper to investigate only the compressibility of dry refractory joints. To this end, optical measurements based on the Digital Image Correlation method were carried out during compression of Magnesia-Carbon brick samples with dry joints. The second main objective is to assess the accuracy of the secant linearization schemes (the classical secant procedure and its modified extension) to reproduce the reference local and global behaviour of refractory mortarless linings accounting for the identified inelastic convex powerlaw behaviour of the Magnesia-Carbon dry joint. The reference nonlinear solution is obtained by means of finite elements method. Under normal compressive loading, unlike for usual (concave) power-law viscoplastic composites for which the secant schemes are known to provide too stiff results, it was found that the modified secant scheme leads to good overall predictions. The classical secant procedure underestimates the reference local and overall behaviour. To improve the latter result, an empirical improved secant formulation was proposed and implemented. It leads to better estimates at local and global levels.