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Received: 16.11.2015 Accepted: 17.02.2016 Published: 30.06.2018 The paper describes the methodology of fractal dimension definition for deformation curves on the basis of the minimal covering method. The methodology allows to obtain the integral quantitative estimation of fracture of structural composite materials under compression and define the location of the fracture path parametric point. We compared the offered method to the algorithms for definition of the Hurst exponent and fractal dimension by the square covering method. The work shows the advantage of the methodology based on definition of the fractal dimension using the minimal covering method. To perform the mechanical testing of dispersal reinforced fine-grained concrete compositions, we used the WilleGeotechnik® hardware and software system additionally equipped with a climatic chamber allowing for temperature (from –40 to +100 °С) and humidity (from 10 to 96 %) adjustment during the loading. The change of stress and deformations of the samples during the loading was registered spaced at 0.01 sec. We used the following materials as the main components of disperse reinforced fine-grained concrete: CEM I 42.5B concrete, gravel sand, condensed and densified microsilicasuspension MKU-85, polycarboxylate superplasticizing agent Melflux 1641 F. Dispersed reinforcement of concrete was ensured by a separate adding of three types of fiber, i.e. the polypropylene multifilament fiber, polyacrylonitrile synthetic fiber FibARM Fiber WВ and astralene modified basalt microfiber Astroflex-MBM. We defined the values of indices of fractality and fractal dimension of stress incrementation and deformations of deformation curves for fine-grained concrete using the minimal covering method. On the basis of the fractal analysis of dynamic series, we defined the location and vicinity of the point of transition from the quiescent condition to the apparent trend for the concrete sample. We revealed the change of location of the parametric point and fractal dimension values depending on the type of fiber. It was discovered that the incorporation of 1 % of the polypropylene multifilament fiber or 5 % of the astralene modified basalt microfiber Astroflex-MBM resulted in the substantial increase of the first critical level, up to 54 and 47 % accordingly, both in the stress incrementation and deformation analyses compared to 19 and 28 % for the compositions containing 1.5 % of the polyacrylonitrile synthetic fiber. The proposed methodology of the fractal analysis of deformation curves on the basis of the minimal covering method allows to obtain valuable information about the fracturing process of different composite materials. © PNRPU

FRACTAL ANALYSIS OF DEFORMATION CURVES OF FIBER-REINFORCED FINE-GRAINED CONCRETES UNDER COMPRESSION