Fractal-Chaos-Theory-Based Research on Mesoscopic Analytical Method for Concrete
Supervisor:wang feng lai
Concrete is widely applied in field of civil engineering as a construction and building material,which plays a significant role.The relationship between the structure and properties of concrete has been a topic of common interest.An understanding of the composite mechanical behavior of concrete is useful for concrete mix design and damage prediction.The research about concrete mechanical behavior should be combined with the latest research of physics,mechanics,materials and information technology,in order to promote the development of scientific research,achieve precise design and control,minimize security risks and economic cost.Since the meso-theory could explain the internal mechanism of concrete macroscopic phenomenon and mechanical behavior,the importance of the meso-scale analysis of concrete has been a controversial topic.In this paper,several means of complexity science study were applied to analyze the geometrical properties of concrete meso-structure quantitatively and its influence to mechanical behavior.The main research contents and the results were as follows:(1)The structure and components of concrete in multi-scale were clearly defined.as well as the extension of meso-model of concrete.Based on the essential nature of aggregates and cement paste,the fractal dimension ranges of each set were derived theoretically.The definition of fractal dimension of concrete was given,which was implemented to describe mathematically the geometrical property of concrete.(2)According to various analysis object,the measurements of concrete fractal dimension,such as based on the definition of similarity dimension,sieving test and Box-counting method were discussed.On the basis of Box-counting dimension,the determination of fractal dimension for binarization matrix was introduced.Meanwhile,mining the determination data as much as possible,a modified box-counting method with lower memory consumption and higher operating efficiency was presented,which was used to analyze the results of CT.The fractal dimension of concrete samples was then obtained,the values proved the theoretical derivation.(3)A versatile random-fractal-geometry-based modelling method that can generate a numerical aggregates model with stable geometrical property was presented.as well as the manner of shape and quantity and shape modification for meso-simulation.Several numerical meso-models were generated in order to detail the application of this modeling method.Using the sampling statistical analysis and algorithm complexity,the effect of modeling was evaluated.(4)By applying the analytical,numerical method and mechanical experiments,the linear and nonlinear behavior of concrete was discussed qualitatively and quantitatively.The influence of concrete fractal dimension and coarse aggregates content to the elasticity modulus,axial compressive strength and ultimate strain was identified and explained,which demonstrated that the meso-structure of concrete had a direct impact on its macroscopic behavior.Furthermore,the chaotic behavior of concrete under load was studied.The initial value sensitivity of chaos in concrete was described by Lyapunov exponent.The major factor caused chaos was discussed.A predict method of mechanical behavior was as well introduced.