Issue 78

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

finite element models using concrete damage-plasticity confirm. Findings like these led to the development of dedicated test procedures for measuring the intrinsic fracture toughness of fiber-reinforced and functionally graded concrete, using three point bending on pre-matrix-fractured specimens. Fracture energy in this approach follows Griffith's theory directly: it is the difference in area under the load-deflection curves of cracked and uncracked specimens, divided by the pre-crack surface area. Work using this framework has found that functionally graded concrete consistently outperforms conventional FRC, and a recent review confirms that even small changes in fiber distribution and orientation can shift the fracture response considerably [12]. One issue that sits at the heart of this study is how the notch itself is prepared. Two approaches are in common use: the matrix-crack (MC) approach and the through-thickness-cracked (TTC) approach. In the MC approach, the short steel fibers stay intact across the pre-cracked plane; in the TTC approach, cutting the notch severs these fibers, which removes the fiber-bridging closure stresses before the flexural test has even started. A crack that forms naturally in a real fiber-reinforced member grows through the matrix while leaving short fibers intact and bridging the crack faces, so the MC specimen is a much closer match to what actually happens in practice than the TTC specimen. As a result, the K IC value from MC testing reflects the real, intrinsic mode I fracture toughness of the fiber-reinforced material, while the TTC value tends to underestimate it. The MC concept itself is not new to the authors. Earlier work established and validated it for plain fiber-reinforced concrete and functionally graded concrete beams that had no main steel reinforcement [13,14,15]. Those studies could not address how the crack-closing effect of embedded longitudinal steel bars interacts with fiber bridging once the beam is matrix cracked, and how that interaction changes as the notch-depth ratio increases. That question is the starting point for the present study, which extends the MC methodology for the first time to steel-reinforced concrete beams that also contain dispersed short fibers, and tracks how the two mechanisms, steel closure and fiber bridging, interact as the notch-depth ratio (a/d) is varied. This is the specific contribution of the present work. With that gap in mind, the present study uses the matrix-crack methodology to determine the real mode I fracture toughness of steel-reinforced concrete beams containing dispersed steel fibers. The experimental program covers the combined effect of steel fiber volume fraction, reinforcement layout, and notch-depth-to-beam-depth ratio (a/d = 0.25 and 0.5) on crack propagation and load-deflection behavior. Conventional through-thickness-cracked beams were also cast and tested as a control group, so the two notch-preparation methods could be compared directly. Together, the results give a fuller picture of how matrix cracking in steel- and fiber-reinforced concrete differs from what conventional through-thickness testing captures, and offer some new insight into how these composite systems actually fail.

E XPERIMENTAL WORK

Materials he experimental study was carried out using materials obtained from local suppliers. The coarse aggregate consisted of a dolomite-based material with a maximum particle size of 12.5 mm, while the fine aggregate was ordinary siliceous sand. Normal strength concrete (NC) was produced with Type I Portland cement, designated with a strength class of 52.5 N, as the primary binder. The specific properties of the fine and coarse aggregates are detailed in Tab. 1 [1]. T

Coarse aggregate (dolomite)

Fine aggregate (sand)

Property

Measured Value

Property

Measured Value

2.67 1.560 0.6 % 21% 10.62

Specific gravity Unit weight, (t/m 3 ) Finess modulus

2.57 1.680

Specific gravity Unit weight, (t/m 3 ) Absorption, % Crushing value, % Impact value, % Los Angeles value, %

2.4

16.3 Table 1: Physical and mechanical properties of coarse and fine aggregates.

Silica fume, sourced from Sika company in Egypt, was incorporated as a partial cement replacement at 5% by weight to enhance the properties of the concrete. Tab. 2 outlines the properties of the silica fume. To achieve adequate workability, 2% by mass of the cement superplasticizer, Sicament-R2004 (from Sika company in Egypt), was added, particularly in mixtures containing steel fibers. The steel fibers were hooked-end, measuring 50 mm in length and 1 mm in diameter, and

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