Fractal analysis of deformation curves of fiber-reinforced fine-grained concretes under compression

The authors set out the methodology of determining the fractal dimension of deformation curves based on the minimum coverage method, allowing to obtain an integral quantitative estimation of destruction process of building composites under compression; and determine the position of the parametric point of destruction curve. The proposed method was compared with the algorithms of the Hurst exponent determination and fractal dimension by the coverage squares method. It became possible to show the advantage of the method based on the determination of the fractal dimension by the minimum coverage method. For the realization of mechanical tests of compositions of fine-grained fiber-reinforced concretes we used hardware-software complex WilleGeotechnik®, which was additionally equipped by a climatic chamber with the possibility of adjusting the temperature (from - 40 to + 100 °C) and humidity (10 to 96 %) in the process of loading. The change of stresses and deformations of samples in the process of load was fixed with a step of 0.01 sec. The following components were used as basic ones in fiber-reinforced fine-grained concretes: cement of CEM I 42,5R class, river sand, densified condensed microsilica DCM-85, polycarboxylate superplasticizer Melflux 1641 F. The dispersed reinforcement of concretes was provided by a separate injection of three types of fibers: polypropylene multifilament fiber, polyacrylonitrile synthetic fiber FibARM Fiber WВ and basalt microfiber “Astroflex-MBM” modified by astralene. As a result, we defined values of fractality index and fractal dimension of the growth stress and strain curves of deformation of fine-grained concrete by the minimal cover method. Based on fractal analysis of time series, the position and neighborhood of the point of transition of the concrete sample from the resting state to the state of the pronounced trend were determined. The position change of parametric point was detected using the dependence of types in the applied fibers. It was established that the introduction of 1 % polypropylene multifilament fiber or 5 % modified astralene basalt microfiber “Astroflex-MBM” leads to a significant increase of the first “critical” level, respectively, to 54 and 47 % as in the analysis of growth stresses and deformations compared with 19 and 28 % for the formulations containing 1,5 % polyacrylonitrile synthetic fiber. The suggested method of fractal analysis of deformation curves based on the method of minimal coverage allows obtaining valuable information about the process related to destruction of composite materials of different natures.