Unfortunately, most of the previous work studying the fracture toughness of fibrous composites has deliberately ignored bridging the fiber onto the pre-crack/notch surfaces by creating such a crack as a through-thickness crack (TTC). Furthermore, no standard specifications for measuring the fracture toughness of fibrous composites have considered the fiber bridging through the pre-notch. Only a few pieces of research, no more than fingers on one hand, have addressed this problem by creating an actual crack, i.e., a matrix crack (MC) instead of a TTC. The challenge these researchers face is the inability to calculate the fracture toughness directly through the stress intensity factor (SIF) relationship because there is no geometry correction factor equation, f(a/d), for an MC. The main objective of the present work is to calculate f(a/d) and ascertain a relationship between the SIF and crack mouth opening displacement (CMOD) for an MC numerically using 3-D finite element analysis. An experimental program was also conducted to measure the fracture toughness of three types of concrete beams: high-strength concrete (HSC) beams with a TTC, HSC beams with an MC, and fiber-reinforced concrete (FRC) beams with an MC. The results showed that FRC beams with an MC have the highest fracture toughness and, subsequently, the highest resistance to crack growth. The numerical results revealed a suggested relationship between the SIF and CMOD of FRC beams with an MC. This relation was used to predict the fracture toughness of FRC with an MC by the critical value of CMOD measured experimentally.

This study presents an innovative approach by combining magnetized water (MW) with Bacillus megaterium to improve the sustainability of concrete under various curing conditions. These enhancements contribute directly to reduced cement use and improved durability, both essential factors in sustainable construction. An experimental program with 27 distinct mixes analyzed variables such as the type of water (tap water/TW and two magnetization sequences/MW1 and MW2), bacterial dosage (0%, 2.5%, and 5% relative to cement weight), and curing methods (traditional water curing/C1, thermal shock/C2, freeze–thaw/C3). The primary discovery is a synergistic relationship between MW and bacteria: the MW1 treatment (1.5 T followed by 0.9 T) paired with a 2.5% bacterial dosage significantly improved the mechanical and self-healing properties of the concrete. This combination led to significant improvements in workability and compressive strength, achieving an increase of as much as 46.5% compared to the control. There was also an impressive recovery of strength in pre-cracked specimens, particularly under thermal shock curing (C2), where some healed cubes exceeded the strength of the uncracked ones. On the other hand, a 5% bacterial dosage was less effective, often resulting in reduced returns due to variations in microstructure. SEM and XRD analyses confirmed a more compact matrix and increased calcite precipitation with 2.5% bacteria, illustrating the combined effects of microbial activity and microwave treatment for sustainable concrete.