a. The use of continuum based numerical models to simulate discontinuous structures, such as masonry, is fraught with difficulty. The introduction of discontinuities such as cracks during the loading event, or because of loading history, has to
be wholly or partly predetermined. The use of gap elements allows cracks to open and maintain normal and shear force connection when closed but the crack locations have to be known in advance. Another approach is to avoid explicit representation
of discontinuities but instead smear their effect by using a brittle non-linear material model. However, these models fail to predict mechanisms where, for example, initially isolated parts react dynamically together. Continuum methods can give
satisfactory results but generally fail to provide a practical method of analysis for masonry.
b. As an alternative to the traditional finite element continuum approach, a discrete element (DE) formulation has been employed to simulate masonry with and without strengthening. So far, the results of the analyses have been applied to parts
of buildings and used to help develop remedial design philosophies by providing simulations under ground excitations and explosive effects. A separate project where the engineering analysis has been based on the DE technique has involved the
successful strengthening of over sixty masonry arches in Europe, Australia and USA. Predictive verification of full-scale tests underlies this work and has involved calculated collapse loads of masonry arch bridges as well as supplementary load
tests on in-service bridges. Results have been shown to correlate very closely with tests (Brookes, Tilly 1999). As the technique is developed it is hoped that the performance of whole buildings can be checked before strengthening systems have
been installed.
In order to represent masonry with or without retrofitted reinforcement, particularly in seismic engineering where non-linear structural performance defines how ductility and energy absorption characteristics are exhibited, the following types of
fundamental behaviour need to be included in the model.
