Improving Theoretical Concepts of Composition Design of Dispersedly-Reinforced Concretes

Introduction. Obtaining the dispersedly-reinforced concretes with given properties is an important objective of materials science in civil engineering. Today, a great deal of experimental and theoretical research in the field of designing the compositions of dispersedly-reinforced concretes is being held. The majority of the existing works solve mainly the problems of modeling the structure of dispersedly-reinforced systems from perspective of fracture mechanics. However, an important objective is to determine a minimum reinforcement volume ratio of the composite material. The models developed by different researchers can be reproduced only for the limited recipe and technological factors. The aim of the present research is to improve the theoretical approaches and develop an analytical model for determining the volume of fiber in a composite. The paper proposes to investigate the properties of dispersedly-reinforced concrete from perspective of the percolation theory and fractal geometry.

Materials and Methods. Literature analysis of a significant amount of experimental data from information sources on the topic of dispersed reinforcement of concrete was carried out in the article. The statistical analysis and approximation of the obtained data was made within the research. Based on the obtained functions, the graphs of the dependencies of the fractal dimension of fiber on the analysed factors were plotted.

Results. The paper presents the theoretical grounds for determining the volume ratio of fiber concrete reinforcement using provisions of the percolation theory. The analysis and comparison of the experimental values of the reinforcement ratio with the theoretical values obtained by solving a problem involving spheres was carried out. A model for determining the fractal dimension of fibers in dispersedly-reinforced concrete was proposed. The available experimental data of different researchers was analysed to establish the degree of influence of the specific surface area of fibers on the fractal dimension parameter. Dependencies obtained by approximating the data using the least squares method were presented for the different types of fibers sorted by material.

Discussion and Conclusion. It is proposed to determine the fractal dimension of the composite material by the analytical method. The influence of the relative length of the fibers and their specific surface area on the fractal dimension parameter was shown. The research in this direction may be of certain scientific interest in terms of forecasting the properties of dispersedly-reinforced concretes and design of their compositions. This, undoubtedly, will contribute to further development of the theoretical concepts of creating the fiber reinforced concrete composites.

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