Predicting the Change in Natural Period of Building due to Damage
The automation of the visual detection of structural elements and cracks have the potential in the future to greatly improve the post-earthquake safety evaluation of buildings in terms of time and accuracy. In addition, models could be combined with these methods in order to link the damage patterns to structural properties such as the residual stiffness and strength. It has been proposed that the concept of fractal dimension could be used to quantify the extent of cracking in a structural element and that the fractal dimension of the element can be linked to a certain loss in stiffness and strength. So far, this concept has only been applied to tests on isolated reinforced concrete and unreinforced masonry walls. The objective of this study is to investigate whether it can be extended to an entire building. First, a program based on the box-counting method is developed in order to compute the values of the fractal dimension of reinforced concrete and unreinforced masonry walls. Then, the program is tested on half-scale unreinforced masonry walls subjected to quasi-static cyclic loading. An approached based on the fractal dimension to estimate the residual stiffness of the specimens is analyzed and improved. Finally, the fundamental period of a four-storey building subjected to shake-table tests is predicted by means of a linear elastic model. The objective is determine whether or not the approach based on the fractal dimension can accurately capture the period elongation of the building. It is observed that the fractal dimension can indeed provide a tool to estimate the stiffness degradation of unreinforced masonry walls. However, the box-counting method includes many limitations that influence the results. Consequently, some adaptations are needed to improve the accuracy of the approach. At last, it is shown that the predicted period computed by means of the model can partially capture the damage propagation in the building.
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