Issue 78

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

were used to produce fiber-reinforced concrete (FRC) at a volume fraction of 1.0%. Specimens of both cubic and cylindrical shapes were cast in metal molds and removed after 24 hours. The specimens were then cured under controlled conditions at 23 °C and 100% relative humidity for 56 days [2].

Property

Results

Color

Light Gray

Specific Gravity Bulk Density

2.20

350 kg/m 3 Specific surface area 16.7 m 2 /gm Table 2: Properties of silica fume as given by the producer.

A compressive strength test was performed in accordance with [16] using cubic specimens measuring 150 mm. The indirect tensile strength was assessed based on the method outlined in [17], using cylindrical specimens with a diameter of 150 mm and a height of 300 mm. The quantities of materials needed for producing 1 cubic meter of each concrete mix are presented in Tab. 3.

Concrete type Cement content Coarse (kg) Fine (kg) w/c ratio Silica (kg)Fiber (kg) Admixtures (kg) (NC) 450 916 762 0.36 50 0.0 10 FRC 450 916 762 0.36 50 79 10 Table 3: Material quantities (kg/m 3 ) for producing NC and FRC.

Experimental program and specimen geometry The experimental study involved 14 beam specimens, representing a variety of configurations using Fiber-Reinforced Concrete (FRC), Normal-Strength Concrete (NC), and Reinforced Concrete (RC) materials. The specimens included matrix cracked (MC), through-thickness cracked (TTC), and uncracked beams, all standardized to a width of 150 mm. The investigation focused on samples with a span-to-depth ratio (L/d) of 5, exploring both MC and uncracked scenarios. The MC specimens were categorized into three crack-slenderness classes: 0, 0.25, and 0.5, defined by the ratio of notch depth to beam depth (a/d). The research was organized into three primary groups based on the crack configuration. The first group included four uncracked specimens with an a/d ratio of 0, which comprised both FRC, RC, and NC variants. The second group included five specimens with an a/d ratio of 0.25, while the third group contained five specimens with an a/d ratio of 0.5. Two distinct beam cross-sections were deliberately adopted within the test matrix, as summarized in Tab. 4. A cross-section of b × d = 150 × 300 mm was used for every specimen containing main longitudinal steel reinforcement, namely the RC, RC FRC, MC-RC-FRC, TTC-RC-FRC and TTC-RC beams. This larger depth was required to accommodate the two 8 mm top bars, the two 10 mm bottom bars, the corresponding concrete cover, and the 5 mm stirrups specified for these specimens. A smaller cross-section of b × d = 150 × 180 mm was used for the unreinforced, fiber-only matrix-cracked specimens that contained no main steel bars, namely FRC and NC (a/d = 0), MC-NC and MC-FRC (a/d = 0.25 and 0.5). This section size follows the specimen geometry previously validated by the authors for matrix-crack fracture-toughness testing of plain FRC and functionally graded concrete beams without main reinforcement [13–15], and was retained here so that the present unreinforced results remain directly comparable with that earlier body of work. For all Reinforced Concrete specimens, longitudinal reinforcement consisted of two 8 mm-diameter bars positioned at the top and two 10 mm-diameter bars at the bottom. Shear reinforcement was implemented using 6-mm-diameter stirrups spaced 7 per meter. Detailed information on the test matrix and dimensional data can be found in Tab. 4, and the schematic diagrams of the beam geometries, along with relevant dimensions in millimeters, are illustrated in Fig. 1. Although the two series differ in absolute cross-sectional dimensions, the span-to-depth ratio (L/d = 5) and the notch depth-to-beam-depth ratio (a/d) were kept identical between them, so that geometric similarity is preserved within each series. The fracture energy was, moreover, normalized per unit crack-surface area ( Δ G = Δ W/(2 × a × b)), and the corresponding stress intensity factor was obtained from this normalized energy release rate together with each specimen’s own elastic modulus, so that the reported fracture parameters remain physically consistent within each series individually. Because of the difference in absolute specimen size between the two series, all quantitative comparisons presented in the results and discussion section are restricted to specimens of the same cross-section i.e., RC versus RC-FRC (150 × 300 mm, reinforced series) and MC-NC versus MC-FRC at a given a/d ratio (150 × 180 mm, unreinforced series) and no percentage change is reported between specimens belonging to the two different cross-section series.

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