Deflection–crack mouth opening displacement relationship for concrete beams with and without fibres

The three-point bending (TPB) test of a notched beam is a method widely used to characterise the toughness of fibre reinforced concrete (FRC) in terms of fracture energy. However, since the measurement of deflection is significantly dependent on the test set-up, spurious deflections are sometimes obtained. Therefore, it is necessary to correlate deflection with crack mouth opening displacement (CMOD) so that the fracture energy can be evaluated from load–CMOD data. In this study, TPB tests were carried out on a series of beam specimens prepared with plain concrete, FRC and ultrahigh-performance concrete (UHPC). Load, deflection and CMOD were recorded. The results showed that a trilinear relationship could be established between deflection and CMOD. The FRC beams showed slightly higher deflection/CMOD ratios than the plain concrete beams, while a dependency of deflection/CMOD ratios on the fibre type or fibre content was not observed. Moreover, the trilinear relationship cannot apply to UHPC due to deflection-hardening and multiple-cracking behaviour.