Non-dimensionalization and scaling of fracture processes in concrete and rock

Many types of engineering structures may fracture, due to extreme external loads or due to inherent damages arising while in service or during their manufacturing/creation. The fractures may form at various scales, particularly within geological or cementitious materials like rock and concrete. Understanding and simulating accurately the fracturing processes at different scales, from laboratory to field, assists with the optimization of structural design and enhances reliability. This paper proposes novel non-dimensional scaling laws for fracture mechanics problems. They improve the prediction and interpretation of crack initiation and evolution and the subsequent mechanical response of structures. They have direct applicability in advanced numerical models like phase field models, where the governing parameters and mesh sizes can be appropriately scaled prior to conducting the numerical simulation. This leads to a unique dimensionless model output for any given loading configuration. Rescaling the unique non-dimensional output, which may incorporate varying pre-peak and post-peak fracture resistances, allows for the fracture behavior of a structure at any scale to be determined. The non-dimensionalization and rescaling techniques are demonstrated and validated against independent analytical and experimental benchmark problems. The scaling laws enable the adoption of coarse meshes in numerical models, significantly reducing computational cost while maintaining accuracy and capturing the fundamental mechanics. It is shown that the challenges associated with modeling fracture processes across scales can be mitigated as long as the problem is appropriately scaled.