Keywords: masonry modelling, quasi-brittle material, interfacial transition zone, experimental verification, ATENA computer code.

This paper is a continuation of our previous contributions [1,2,3] devoted to material modeling of natural stone masonry with regular and irregular mesostructure as well as quarry masonry. To achieve effective material properties on the macroscopic level both components, i.e. stone blocks and mortar beds, are treated as quasi-brittle materials, characterized by strain softening. The phenomenon manifests itself by the localization of inelastic strains prevailing into the mortar beds between stones. The geometry of both basic materials is discretized using finite elements.

The novelty of the proposed model consists in the fact that the mortar is still discretized by finite elements but the contact elements with the Mohr-Coulomb material model are used to express the impaired material properties of the interfacial transition zone (ITZ) between the mortar and stones.

All computational simulations are performed similarly to our preceding works with the aid of the ATENA commercial software [4] utilizing a plastic-fracturing non-linear cementitious model exploiting the mesh-adjusted softening modulus in the smeared-crack approach to address the behavior of individual stone block and mortar phases.

Calibration of the model is a very important task from both the theoretical and practical point of view. An experimentally tested quarry masonry sample renders suitable sources for optimizing the material data, especially for contact elements in the ITZ. Loading in compression was selected because in this particular case the satisfactory correspondence of the computationally obtained results with experimental outputs is rather difficult to reach.

There is a variety of techniques to optimize the input data. One approach is very simple and starts from a set of input parameters based on the "trial and error" procedure. The calculated loading path is obtained by utilizing the simplified model with the stone blocks expanded up to the middle surface of the mortar beds. To calibrate the material data the least square method is applied to minimize the difference between the calculated and measured loading force (if the test is controlled by the displacement). Another way stands to benefit from a set of randomly generated input data, of course under the assumption that probability density distributions of individual input parameters can be well estimated. Standard simulation techniques, such as the Monte Carlo or Latin Hypercube Sampling methods, are very suitable tools for data generation. Combination of above approaches with neuron networks is also desirable. The best choice of optimized input data is again established with the help of the least square method.

The simplified FE model with contact elements of zero thickness between the stone blocks was subjected to the same numerical tests as the proposed improved model. The improved model exhibits certain merits for which it should be preferred to the simplified one, namely

• Better agreement of the calculated loading path with that obtained experimentally and not only in the elastic region but also in the region corresponding to fully developed cracks (the plateau of the diagram before the sample collapses)
• When calibrating the improved model the back analysis is based on a set of only slightly scattered loading paths
• The pattern of cracks predicted by the improved model reminds much better the real distribution of cracks found experimentally than that calculated by the simplified model.

To conclude, recall that both models are suitable for the application with first-order homogenization schemes. In comparison with the simplified model, the results predicted by the improved model comply much better with the results obtained experimentally.

1

J. Novák, J. Zeman and M. Šejnoha. "Multiscale-based constitutive modeling of regular natural stone masonry". In B.H.V. Topping and C.A. Mota Soares, editors. Proceedings of the Seventh International Conference on Computational Structures Technology. Stirling, Scotland 2004, Civil-Comp Press. Paper 197. doi:10.4203/ccp.79.197

2

M. Šejnoha, V. Blazek, J. Zeman and J. Šejnoha. "Non-linear homogenization of quarry masonry". In B.H.V. Topping and C.A. Mota Soares, editors. Proceedings of the Seventh International Conference on Computational Structures Technology. Stirling, Scotland 2004, Civil-Comp Press. Paper 196. doi:10.4203/ccp.79.196

3

J. Zeman, M. Šejnoha and J. Šejnoha. "Homogenization of stone masonry with irregular geometry". In B.H.V. Topping and C.A. Mota Soares, editors. Proceedings of the Seventh International Conference on Computational Structures Technology. Stirling, Scotland 2004, Civil-Comp Press. Paper 200. doi:10.4203/ccp.79.200

4

V. Cervenka, L. Jendele and J. Cervenka, ATENA Program Documentation - Part I: Theory, Cervenka Consulting Company, Prague 2002.

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