engleski

Numerical analysis of masonry structures by combined finite-discrete element method

Building construction using stone or clay bricks that are held together by mortar is one of the oldest building techniques that is still in use today. Among the oldest construction are masonry stone huts in a form of a circle found nearby lake Hullen in Israel that come from a period between 9.000 and 8.000 BC [1]. The first masonry structures were amazing piles of natural stone. As humans became more skilled and began using tools, masonry structures began to be more symmetrical. Later humans learned to make bricks moulding them from mud or clay leaving them to dry in the air and later baking them in ovens. Bricks were strong, uniform and easy to make. In addition to improving the techniques of making blocks various cultures began to use architectural features such as pillars to obtain the height or beams, arches and domes for bridging over the spans of distance. Masonry has a long worldwide tradition of use in construction due to its simplicity. The durability of masonry structures is evident in the number of structures that are still in use after hundreds or even several thousands of years. A few examples of structures that have become symbols of certain cultures are the Egyptian pyramids that have their origin from a period between 2800.-2000. BC, the Parthenon in Greece from the fifth century BC, The Great Wall of China whose construction began in fifth century before Christ and the Colosseum in Rome from first century. In spite of the simplicity that is manifested during the construction of masonry structures, understanding and describing mechanical behaviour of those structures, especially in conditions of seismic loading, represents a true challenge due to the nature of masonry structure which due to the presence of joints among blocks that can but don’t have to be filled in with mortar shows a complex and particular nonlinear behavior. Various methods and numerical models are used for analysis of dry-stone masonry structures, based upon the degree of complexity, volume of input data and accuracy of required solution. There are two basic approaches in numerical modelling of masonry structures: idealization using continuum, and discontinuum. The most commonly used numerical tool in continuum approach is finite element method [1], where different modelling strategies at micro, meso and macro scale have been developed to model masonry structure with desired accuracy. Although the great number of numerical models based on finite element method, the need for modelling the discontinuities and mutual mechanical interaction, finite displacement and rotation including complete detachment of the structure, which is especially expressed in the masonry structures under dynamic loading conditions, led to the development of numerous discontinuum models represented through the framework of discrete element method. The main idea behind the application of the discrete element method to masonry refers to the idealisation of the structure as a discontinuum, where the blocks are represented by rigid discrete elements, while the joints are modelled as contact surfaces between different blocks. In recent times, a number of numerical models combine the advantages of discrete and finite element methods. One of the methods which combine the advantages of continuum and discontinuum approach is a combined finite- discrete element method (FDEM) pioneered by Munjiza [3, 4]. FDEM was developed mainly for the simulation of fracturing problems considering deformable blocks that may split and separate during the analysis. Within the framework of this method, the blocks are discretised by triangular (2D) or tetrahedral (3D) finite elements. The material model in the finite elements is linear elastic, while the material nonlinearity, fracture and fragmentation of discrete elements are considered through displacement-based contact elements implemented within a finite element mesh. The interaction between discrete elements is considered through the contact interaction algorithm for normal forces, which is based on potential contact forces. The method uses an explicit numerical integration of the motion equation. The purpose of this paper is to present the application of combined finite-discrete element method in analysis of dry stone masonry structures [5-7], masonry structures with mortar joints [9] and confined masonry structures [9]. For the purpose of validation of the method in analysis of dry stone masonry structures, experimental analysis [10] were conducted and compared with numerical results.

Masonry structures ; Combined finite-discrete element method

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