Structural Engineering and Mechanics

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A fractal fracture model and application to concrete with different aggregate sizes and loading rates

  • Chang, Kug Kwan (Architectural Engineering Department, Seoul National University of Technology) ;
  • Xi, Yunping (Department of Civil, Environmental and Architectural Engineering, University of Colorado) ;
  • Roh, Y.S. (Architectural Engineering Department, Seoul National University of Technology)
  • Received : 2005.07.29
  • Accepted : 2006.02.03
  • Published : 2006.05.30
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Abstract

Recent developments in fractal theory suggest that fractal may provide a more realistic representation of characteristics of cementitious materials. In this paper, the roughness of fracture surfaces in cementitious material has been characterized by fractal theory. A systematic experimental investigation was carried out to examine the dependency of fracture parameters on the aggregate sizes as well as the loading rates. Three maximum aggregate sizes (4.76 mm, 12.7 mm, and 19.1 mm) and two loading rates (slow and fast loading rate) were used. A total of 25 compression tests and 25 tension tests were performed. All fracture parameters exhibited an increase, to varying degrees, when aggregates were added to the mortar matrix. The fracture surfaces of the specimens were digitized and analyzed. Results of the fractal analysis suggested that concrete fracture surfaces exhibit fractal characteristics, and the fractal geometry provide a useful tool for characterizing nonlinear fracture behavior of concrete. Fractal dimension D was monotonically increased as maximum aggregate sizes increase. A new fractal fracture model was developed which considers the size and shape of aggregate, and the crack paths in the constituent phases. Detailed analyses were given for four different types of fracture paths. The fractal fracture model can estimate fractal dimension for multiphase composites.

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References

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