Keywords: unreinforced masonry, finite element method, macro modelling, strengthening, textile.

Unreinforced masonry is a brittle building material with only marginal tensile strength and low ductility. As a result of these properties its capability to dissipate energy is not sufficient to resist strong dynamic excitation. However in many earthquake vulnerable regions, like Romania, Greece or Turkey, masonry is the predominant construction type. To enlarge the brickwork's capacity against seismic action appropriate strengthening techniques are necessary. Textile strengthening has proved to be a very effective method to increase the ductility and tensile strength of masonry without charging the building with additional weight. Although the effectiveness of textile strengthening methods is well known up to now neither reliable analytical nor numerical models are available to calculate the capacity of masonry shear walls strengthened with textiles. Hence there is a requirement for the development of models which allow the capacity calculation of textile strengthened masonry walls with a reasonable computational effort.

The present paper introduces a new smeared numerical model of unreinforced masonry strengthened with an arbitrary oriented bidirectional textile net inlaid in a cementitious matrix. The brittle nonlinear behaviour of the masonry is described by a cyclic two-dimensional non-linear macro-model based on the concept of equivalent uniaxial strain introduced by Darwin and Pecknold [1]. The main idea of this concept is the decoupled formulation of the biaxial stress-strain-relationships for each principal stress direction. Therefore the actual stress state depends on both the present strain state and the load history. The basic advantages of this formulation are the applicability for cyclic loading and the use of parameters and stress-strain relationships which can be obtained from simple uniaxial experiments. The integrated failure criterion [2,3] defines the tensile and compressive strength as functions of the principal stress relation for several bed joint orientations. If the strengthened masonry fails in tension, the tension stiffening effect due to participation of the masonry between the cracks is modelled by a modified textile characteristic curve. The nonlinear curve is approximated by a multi-linear model whose anchor points are defined by the average textile strain between two cracks and the corresponding textile stress within the crack for different states of crack formations. The average crack spacing is calculated in relation to the transfer length under consideration of the scatter of the tensile strength for a certain degree of crack formation according to Kreller [4]. The resulting textile stress within the crack is calculated by means of the equilibrium of forces of a crack element taken into account the angle between the reinforcement direction and crack orientation.

The application of the model, which was implemented into the finite element package ANSYS, is shown for the simulation of masonry shear walls, with and without strengthening methods. The walls are subjected to horizontal and vertical loading and the simulations are carried out for different geometries. Finally the simulation results are discussed and compared with experimental results.

1

Darwin, D.; Pecknold, D.A.: Inelastic model for cyclic biaxial loading of reinforced concrete, University of Illinois at Urbana-Champaign, 1974

2

Page, A.W.: The biaxial compressive strength of brick masonry, Proc. Intsn. Civ. Engrs., Part 2, 71, p. 893-906, 1981. doi:10.1680/iicep.1981.1825

3

Page, A.W.: The strength of brick masonry under biaxial compression-tension, Int. J. Masonry Constr., 3(1), p. 26-31, 1983.

4

Kreller, H.: Zum nichtlinearen Trag- und Verformungsverhalten von Stahlbetontragwerken unter Last- und Zwangseinwirkung, Deutscher Ausschuss für Stahlbeton, Heft 409, Beuth Verlag GmbH, 1990

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