Fractal patterns for failure modes of ultra-high performance concrete

From the perspective of fractal theory, the bridging effect of the fibres in ultra-high performance concrete (UHPC), may allow only volume cracks, rather than dominant fractures.Experimental tests are carried out to investigate the emitted energy and the fractal domain of the concrete specimens under compression.UHPC and plain concrete specimens with characteristic size equal to 75, 150, and 300 mm, and slenderness 0.5, 1, and 2, are fabricated.All the specimens are monitored using the acoustic emission (AE) sensors.The results indicate that compression strength and ductility of the block specimens exhibit a strong change by varying the sample size.As size and/or slenderness increase, the structural behaviour exhibits a ductile-to-brittle transition, and the final collapse shows a crushing-to-cracking transition.Moreover, the experimental fractal dimension of plain concrete is closer to 2, demonstrating that the fracture tends to occur on a plane (crack surface, 2-D).In contrast, the fractal dimension of fibre-reinforced concrete is close to 3 due to fibre bridging, which avoids the formation of crack surfaces, being the fractal domain very close to a volume (3-D).