Progressive development of cracks in biochar–cement composites through multiscale analysis

The intrinsic brittleness of the cement matrix limits its synergy with steel reinforcement bars, constraining energy dissipation and crack control capacity of concrete. Enhancing the ductility of cementitious materials is, therefore, essential for improving structural resilience. A porous carbon material, for example, biochar, offers a sustainable alternative that can improve ductility and energy dissipation capacity, while simultaneously contributing to carbon sequestration. Despite promising experimental observation, the fracture mechanisms underlying this toughening effect remain insufficiently understood. This study addresses this knowledge gap by developing a multi-scale voxel-based modeling framework for biochar–cement composites, linking microscale mechanical heterogeneity to macroscale fracture behavior. The elastic modulus of biochar–cement paste was first quantified across nanoscale (∼nm and ∼µm) to mesoscale (∼mm and ∼cm) through nano- and micro-indentation, providing scale-bridged inputs for the model. The framework explicitly resolves aggregates, interfacial transition zones, and biochar particles within a concurrent multi-scale domain, enabling simulation of localized fracture while retaining computational efficiency. The simulation results were validated through a three-point bending test and digital image correlation. These findings demonstrated that biochar could alter the crack propagation by redistributing interfacial stress and promoting multi-layered crack deflection, which significantly enhanced the energy dissipation by up to 90%. This study elucidates the multi-scale mechanisms by which the pore architecture of biochar enhances ductility, providing a scalable framework for the design of high-ductile, sustainable cementitious materials.