Keywords: capacity spectrum method, unreinforced masonry, multi-surface failure criterion, numerical simulation, seismic design.

The current reference method for the seismic design and safety verification of masonry buildings in Europe is based on linear-elastic response spectrum analysis. Two types of this method, a general and a simplified approach, can be distinguished. Whereas the simplified so-called "lateral force method" can be applied for masonry buildings in the most cases since the structural response is not significantly affected by contributions from higher modes of vibration. The basic input of the method is a linear-elastic response spectrum which characterises the seismic site hazard. For considering the ability of energy dissipation the linear-elastic spectrum is reduced by the so-called behaviour factor. The procedure is a simple approach for engineering practice in order to avoid time-consuming nonlinear time-history analyses. It is included in Eurocode 8 [1] and from the practical point of view this concept seems justified for material types with high ductility reserves.

But for quasi-brittle materials the behaviour factors given in the codes are too conservative and lie for many masonry buildings far beyond the safe side. This issue in combination with the significant increase of seismic loads in the European Standards leads to problems for the safety verification of masonry buildings, even for buildings which have been constructed years ago in seismic active regions and have already proven their stability in practice. Therefore, there is an urgent demand for the development of a design procedure which considers the construction type, material behaviour, geometry and distribution of the shear walls, as well as the state of stress in each of the walls. The procedure should be easily applicable in the engineering practise, yet precise enough to mirror the specific nonlinear masonry behaviour.

In the present paper the development of an innovative design procedure, which fully utilizes the nonlinear bearing reserves of masonry is presented. The basis of the procedure is the capacity spectrum method, in which the reduced response spectrum is superposed with the capacity curve of the structure considered. This curve has to be calculated iteratively using the capacity curves of the single shear walls [2]. The wall capacities are systematically stored in a database depending on the masonry type, geometry and loading state. The determination of the curves is based on cyclic shear wall tests in combination with numerical simulations using a multi surface elastoplastic-damage theory. The applied failure criteria corresponds to the theory of Mann-Müller [3], which forms also the basis of the German design code for masonry. According to this theory the anisotropic elastic and inelastic behaviour depends on the orientation of the masonry joints. On this basis, it is possible to simulate masonry-specific failure. Moreover, the damage mechanisms and progressions can be followed because of its failure mode dependent hardening and softening laws. The theory was implemented as a smeared continuum model with the return mapping procedure for local iteration at the integration point level into the finite element program ANSYS [4].

The application of the new design procedure will be demonstrated using the example of a typical three storey residential building in Germany. The calculation of the building capacity using the capacity curves of the single walls will be described in detail. Furthermore the correctness of the implemented smeared continuum model is shown by a comparison of experimental and numerical simulation results. Finally, the results of the new design procedure and the simplified response spectrum method are compared and discussed.

1

ENV 1998, Comité Européen de Normalisation, Eurocode 8 - Design of Structures for Earthquake Resistance, Brussels, 2004

2

Mistler, M: Seismisches Verhalten von Mauerwerksscheiben, DGEB-Publikation, No. 13, 2005.

3

Mann, W., Müller, H.: Schubtragfhigkeit von Mauerwerk. Berlin, Ernst & Sohn, 1978.

4

ANSYS, FE-Software, SAS IP Inc., 2005

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