Keywords: masonry, concrete, elastic analysis, reliability, Monte Carlo, parallelization.

In some cases a numerical analysis of a building structure with some input data described as random variables is required. For our research we have created tools that allows us to include random input data (material properties, loads and boundary conditions, as well as some geometry properties) to the finite element analysis. The results obtained from using these tools are used (with results obtained from experimental research) for an analysis of behaviour of historical structures.

The work presented is restricted to a linear static analysis with some possibilities of an analysis of a state. The finite element method has been used for a static analysis of structures and the random aspects of the problem heve been solved through the usual Monte Carlo - based simulation process [1].

The algorithm prepared is based on a plain Monte Carlo procedure and includes the possibility to make a statistical correlation between input data [2] though in a basic formulation that can effectively only be used in a limited set of situations, as described in [3].

In the problems where an assessment of a material status is requested a failure criteria is used. The Chen-Chen [4] failure condition for concrete is used in the form of two functions (one for the compression-compression state of stress, one for all other states).

A very simple approach for the homogenization of material properties of masonry models has been utilised: the models of specimens with individually modelled bricks and mortar have been used in a computational simulation of simple material tests (uniaxial stress tests and shear tests). In most cases it has been assumed that resulting homogenized material properties are orthotropic.

In two-dimensional cases the model with homogenized properties (that were obtained from the procedure discussed above) can lead to results that are very close to the results obtained from models with individually modelled bricks and mortar. In three-dimensional cases the situation is more complicated because of the larger number of material properties required. Also the precision of the computed Young's modulli is much better than the precision of the Poisson's ratios.

For these reasons in most cases an iterative process of improving the homogenized material properties has to be used. In current state of the works the iteration is done by hand but a software is developed for this task.

1

I.M. Sobolj, "Metod Monte-Karlo" (in Russian: "The Monte Carlo Method"), Nauka, Moscow, 1968.

2

P. Konecný, "Reliability of Reinforced Concrete Bridge Decks with Respect to Ingress of Chlorides", Ph.D. thesis, VSB - Technical University of Ostrava, Ostrava, Czech Republic, 2007.

3

K.K. Phoon, S.T. Quek, H. Huang, "Simulation of non-Gaussian processes using fractile correlation Probabilistic Engineering Mechanics", Volume 19, 4, 2004, 287-292 doi:10.1016/j.probengmech.2003.09.001

4

A.C.T. Chen, W.F. Chen, "Constitutive Relations for Concrete", Journal of the Engineering Mechanics Division ASCE, 1975. <

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