Research On Masonry Homogenization Theory And Application

Security guarantees of masonry structures are obtained through proper analyses and calculations of existing and new-built masonry buildings. Masonry structures are composed of blocks and mortar regularly which are completely different in the properties. Due to the different characteristics of the blocks and mortar, which determine the complexity of accurately analyzing masonry’s mechanical performances. There are many difficulties in making basic theoretical researches to masonry structures, and also having some faultiness. Therefore, the current masonry codes are mainly based on empirical formulae by tests, which resulting theory researches behind engineering practice. It is emerging as countries all over the world concerning issues to establish accurate and complete masonry structure theory through physical and mathematical models, by further studying of mechanical properties and failure mechanisms of masonry structures. It is clear that researches in the basic theories and application of the basic theories of masonry structures are very necessary.In this paper, masonry homogenized theory and application were researched in-depth. Masonry was deemed continuous media materials according to a certain way. The common performances of blocks and mortar were considered and their geometry and material information were integrated into a representative volume element(RVE).Then the representative volume element(RVE) with the same nature of masonry was applied to the mechanical performance analyses of the overall structure. References for theoretical researches and engineering designs of masonry structures could be provided by research results in the paper, the main research results were as follows:(1) Masonry structures were considered as two-dimensional periodic material and three-dimensional periodic material respectively and corresponding basic equations and homogenization relationships were established. Theoretical bases for the study of in-plane and out-of-plane mechanical properties of homogenized masonry were provided in here.(2) The calculation formulae of equivalent elastic modulus to three-dimensional homogenization element were established. The influences to equivalent elastic modulus produced by elastic modulus and Poisson’s ratio of block and mortar, the ratio of horizontal mortar joint thickness to block height, the ratio of vertical mortar joint thickness to block length were discussed in detail. Then the feasibility of the formulae was verified by comparing with the measured values and calculated values of codes and common formulae to masonry with different passes, different materials and different sizes of block.(3) The calculation formulae of equivalent bending stiffness to three-dimensional homogenization element were established. The influences to equivalent bending stiffness produced by elastic modulus and Poisson’s ratio of block and mortar, the ratio of horizontal mortar joint thickness to block height, the ratio of vertical mortar joint thickness to block length were considered. And the influence degree of each factor was attained by massive calculation conversed different factors.(4) Based on homogenization theory, a different angles failure surface of masonry wall in shear-compression action was assumed. Shear strength was analyzed using rigid plastic limit analysis method with energy principle for homogenization masonry. Uniform shear strength formula of the masonry wall was obtained. The three failure models about shear-friction, shear-compression, diagonal compression could completely be expressed with this formula. And provides a better way to solve the problems in the shearing strength calculating method about "code for seismic design of buildings"(GB 50011-2010) based on the principal tensile stress strength theory and "code for design of masonry structures"(GB 50003-2011) based on Coulomb theory, which were urgently to be solved in engineering designs.(5) Homogenization models with theory of thin plates and theory of medium and heavy plates were given respectively and the calculation formulae of deflection of homogenization masonry walls were deduced. Deflections of 120mm,180mm,240mm and 370mm masonry walls in fixed and different ratio of height to width were analyzed. The applicability of two kinds of plate theories of homogenization masonry walls of different sizes was obtained.(6) Meanwhile for the defects of "code for design of masonry structures"(GB 50003-2011) about inconsistencies of computing models, which for derivation of allowable ratio of height to thickness correction coefficient was inconsistent with derivation of Calculation of height of the wall. High thickness ratio limits of the hole walls were studied detailedly. Massive calculations were executed to different hole size walls with height to width aspect ratio 0.5,1.0,1.5. It was obtained that allowable ratio of height to thickness of hole wall need to consider both the sizes of the hole and the wall.