This study presents test results and in-depth discussion regarding the measurement of the fracture mechanics parameters of new concrete composites based on quaternary blended cements (QBC). A composition of the two most commonly used mineral additives, i.e., fly ash (FA) and silica fume (SF), in combination with nanosilica (nS), has been proposed as a partial replacement for ordinary Portland cement (OPC) binder. Four series of concrete were made, one of which was the reference concrete (REF) and the remaining three were QBC. During the research, the main mechanical parameters of compressive strength (fcm) and splitting tensile strength (fctm), as well as fracture mechanics parameters and the critical stress intensity factor (KIcS), along with critical crack-tip opening displacements (CTODc) were investigated. Based on the tests, it was found that the total addition of siliceous materials, i.e., SF + nS without FA, increases the strength and fracture parameters of concrete by approximately 40%. On the other hand, supplementing the composition of the binder with SF and nS with 5% of FA additive causes an increase in all mechanical parameters by approximately 10%, whereas an increase by another 10% in the FA content in the concrete mix causes a significant decrease in all the analyzed factors by 10%, compared to the composite with the addition of silica modifiers only.