Distribution of relaxation time analysis for stage-resolved flexural damage sensing in carbon black-modified ultra-high-performance concrete

Self-sensing cement composites convert mechanical deformation and cracking into measurable electrical responses. However, the conductive-network evolution underlying resistance variation and their ability to track loading-induced damage remain insufficiently understood. Here, we used electrical impedance spectroscopy and distribution of relaxation times (DRT) with digital image correlation (DIC) and fractional change in resistance (FCR) measurements to elucidate how carbon black (CB) reorganizes the hybrid conductive-network and how flexural cracking perturbs its relaxation domains in ultra-high-performance concrete. Increasing CB content induced a marked conductive transition between 1.5 and 2.0 vol%, accompanied by redistribution of relaxation responses across short, intermediate, and long timescales. The mixture containing 2.0 vol% CB exhibited the stress sensitivities of 1.00%/MPa at the limit of proportionality and 3.88%/MPa at the modulus of rupture, with a signal-to-noise ratio reaching 37.0 dB at the modulus of rupture. During flexural loading, DIC-detectable crack initiation produced only limited changes in the DRT spectra, whereas dominant crack formation generated substantially stronger and broader intermediate- and long-timescale responses. These changes are consistent with progressive disruption and redistribution of contact and tunneling pathways, interfacial polarization, and ionic transport. Our findings demonstrate that DRT captures the progressive redistribution of electrical transport as cracking evolves from initiation to localization, establishing a stage-resolved link between conductive-network evolution and flexural damage.