The article describes a technique for the measurement of the level of complexity of fracture surfaces by the method of vertical sections, and a performed statistical analysis of the effect of profile lines on the fractographic and fractal parameters of fractures, i.e. the profile line development factor, $R_L$, and the fracture surface development factor, $R_S$, (as defined by the cycloid method), as well as the fractal dimension, $D_C$, (as determined by the chord method), and the fractal dimension, $D_{BC}$, (as determined by the box method). The above-mentioned parameters were determined for fracture surfaces of basalt and gravel concretes, respectively, which had previously been subjected to fracture toughness tests. The concretes were made from mixtures of a water/cement ratio ranging from 0.41 to 0.61 and with a variable fraction of coarse aggregate to fine aggregate, $C_{agg.}/F_{agg.}$, in the range from 1.5 to 3.5. Basalt and gravel aggregate of a fraction to maximum 16 mm were used to the tests. Based on the performed analysis it has been established that the necessary number of concrete fracture profile lines, which assures the reliability of obtained testing results, should amount to 12.