Issue 78

M. Adel et.al, Frattura ed Integrità Strutturale, 78 (2026) 168-185; DOI: 10.3221/IGF-ESIS.78.10

Fig. 17 illustrates the behavior of K IC in steel-reinforced concrete beams as the a/d ratio increases from 0.25 to 0.5, showing an increase in K 1C of approximately 25.69%. In reinforced concrete beams, the presence of reinforcing steel bars enhances the closing effect caused by the compressive forces generated by these bars. This effect becomes more pronounced with increasing crack depth. Consequently, two opposing influences are at play in reinforced concrete beams, ultimately affecting the overall fracture toughness, which increases in this analysis. The experimental findings indicate that cracked reinforced concrete beams demonstrate lower maximum load capacities and higher maximum deflection compared to uncracked beams. This behavior contributes to a rise in the total fracture toughness of the cracked beams as the a/d ratio increases. The observed enhancement in fracture toughness can be linked to the formation of microcracks ahead of the primary crack tip, which occurs due to stress concentration within the crack process zone during loading. However, for a group of beams reinforced with fibers, K IC decreased as the a/d ratio increased, according to [25]. The effect of the crack depth-to-beam depth ratio (a/d) on the critical stress intensity factor (K IC ) in fiber-reinforced concrete beams indicates that an increase in the a/d ratio leads to a decrease in K IC . In other words, as the crack length increases, the beam's ability to resist fracture diminishes. Although the fibers initially improve performance, their effect diminishes as the a/d ratio increases.

Figure 17: K IC against a/d for different groups, (Group 1 = MC-RC-FRC, Group 2 = TTC-RC, Group 3 = TTC-RC-FRC, Group 4 = MC-FRC).

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his study experimentally examines the fracture behavior of reinforced concrete (RC) beams incorporating steel fibers (SF) by employing a matrix-crack (MC) methodology to accurately ascertain the true mode I fracture toughness (K IC ). This is contrasted with conventional through-thickness cracked (TTC) beams. The findings are summarized as follows: 1. The addition of steel fibers (SF) significantly improved the flexural fracture behavior of unreinforced matrix-cracked concrete and of reinforced concrete beams. The maximum load capacity of the matrix-cracked (a/d = 0.25) unreinforced specimens increased by about 32% (MC-NC to MC-FRC), while the maximum load capacity of cracked reinforced concrete beams increased by up to 50% with the addition of steel fibers . 2. The addition of steel fibers increased the stiffness, fracture strength, and modulus of toughness (MOT) by 13.3%, 69.7%, and 94.4%, respectively, in uncracked beams as compared with the plain reinforced concrete (RC) beam. 3. At the same a/d ratio, for RC-FRC beams, the matrix-crack (MC) approach gives higher first-cracking loads and improved post-cracking ductility and toughness compared to the through-thickness cracked (TTC) approach, indicating that the MC method accounts for fiber-bridging effects in reinforced beams more realistically. 4. For conventionally reinforced beams without fibers, the critical stress intensity factor (K IC ) increased by about 25.6– 25.7% when the notch-depth-to-beam-depth ratio (a/d) increased from 0.25 to 0.5 due to the increasing moment arm of the steel closing force.

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