Effects of layered accretion on the mechanics of masonry structures

Masonry constructions are built up in successive layers of bricks or blocks that may have considerable effect on the deformation and equilibrium of these structures when they are statically indeterminate and when gravity loads are predominant. This problem is analyzed by referring to a thick arch that reaches its final shape by means of a continuous deposition of heavy brick layers in stress free condition. The brick/block units of the accreting layer are assumed to have a negligible size in comparison to the structural size and the resulting continuous deposition is described taking into account their possible sliding on the current extrados at the instant of deposition. The kinematics of the growing body is described by the superposition of the displacement resulting from the continuing addition of heavy layers to the initial displacement at the considered point when it is attached to the current extrados, i.e., on the accreting layer. The two corresponding strain tensor fields do not satisfy the equations of compatibility, while the total strain field results to be compatible. The stress field is the cumulative effect of the incremental stress induced by the weight of the added layers during the growing process with residual stresses, which are shown to be independent of the initial strain field. Two examples are analyzed to show the effects of the growing process on the stress field and the properties of the strain field are discussed. The first example concerns a masonry wall supported at periodic points while the second example concerns a segmental multileaf thick arch in which the growing process begins from a thin arch resting on its own weight. In both cases a remarkable increase of the stress field is observed in comparison to the solution where the gravity loads are applied on the final domain.