Keywords: corrector factor, cellular automata.

Laboratory experimental data is often erroneous. This error is more apparent in data obtained from testing of full size anisotropic composite materials such as masonry wall panels. In this paper methodologies for reducing (correcting) error in laboratory tested data are discussed. Research in the University of Plymouth by Zhou [1] and Rafiq et al [2], has proposed a novel approach for the analysis of masonry panels subjected to lateral loading, which gives a much closer prediction of both failure load and failure patterns. The research has introduced a new concept, "stiffness/strength corrector" Zhou [1], which quantifies panel boundaries effect and properly models the variation in masonry properties at various locations (zones) within a masonry wall panel. A cellular automata (CA) technique was used to model the boundary effects and establish stiffness/strength corrector values for unseen panels, using zone similarity techniques introduced by Zhou et al [3]. These stiffness/strength correctors are then used in a non-linear finite element analysis (FEA) to predict the failure load and failure pattern of these unseen panels. This paper demonstrates that methodologies for reducing error in experimental data can further improve the quality of corrector values and hence improve the predicted failure load and load deflection of the panels.

An in depth investigation was carried out to reduce the error in the laboratory data to reflect the real response of the panel under the uniformly distributed lateral load in order to be able to compare a like with like situation both for the FAE and experimental results. The first step was to carry out a regression analysis both on the 3D data and 2D linear data to find a better fit to the expected experimental data in order to minimise discrepancies in the measured experimental data. To further refine and improve the corrector values and to ensure a good fit between the FEA and the experimental load deflection results, the following methods were used:

1. Iteration method: Zhou's corrector values were based on a direct comparison (a single step) of the FEA and experimental deflection values. In order to further improve the accuracy of the corrector values a number iteration were carried out to refine these values.
2. The Genetic Algorithm approach: in this investigation corrector values at each location on the panel were treated as independent GA variables and the GA fitness was to minimise the error between the GA and experimental results.
3. Combing the GA and regression method: in this method the corrector values obtained by the GA were refined by regression method.

Based on this investigation the following conclusions can be drawn:

• The predicted failure load values were much closer to the experimental results.
• Load deflection curves at various locations on the panel were closely related to the experimental results.
• The failure pattern was similar to those of the experimental results and those of Zhou [1].
• The corrector values for new ('unseen') panels, which were determined by the Cellular Automata, using zone similarity concepts, greatly improved the prediction of failure load and load deflection values.
• Scaling rules proposed in this research was effective to model scaling effects due to changes in the size of any 'unseen' panel in comparison with the 'base panel'.

1

Zhou, G.C. (2002). Application of Stiffness/Strength Corrector and Cellular Automata in Predicting Response of Laterally Loaded Masonry Panels. School of Civil and Structural Engineering. Plymouth, University of Plymouth. PhD Thesis.

2

Rafiq, M.Y., Zhou, G.C., et al. (2003). "Analysis of brick wall panels subjected to lateral loading using correctors", Masonry International 16(2): 75-82.

3

Zhou, G.C., Rafiq, M.Y., et al. (2003). "Application of cellular automata in modelling laterally loaded masonry panel boundary effects", Masonry International (3): 104-114.

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