Fracture Energy of High-Performance Concrete (HPC) and Ultra-High Performance Concrete (UHPC): A Comprehensive State-of-the-Art Review from Micromechanisms to Structural Applications

Fracture energy, denoted as G_F, stands as the most fundamental intrinsic parameter within the nonlinear fracture mechanics framework for cementitious materials, quantitatively defined as the energy dissipated per unit area of crack surface and encompassing all microscale mechanisms including chemical decohesion, frictional sliding, plastic deformation, and fiber bridging [۱, ۲]. This parameter fundamentally governs the post-peak constitutive response of concrete—whether strain softening or strain hardening—and therefore dictates structural behavior ranging from crack width evolution to ductility and size dependency [۳]. High performance concrete (HPC) and ultra high performance concrete (UHPC), characterized by their ultra-dense microstructures achieved through low water to cement ratios, pozzolanic reactivity, and often substantial steel fiber reinforcement, exhibit fracture behavior that deviates radically from that of conventional concrete [۴, ۵]. This paper presents a state-of-the-art systematic review of advances in the fracture energy of HPC and UHPC over the three-decade period from ۱۹۹۵ to ۲۰۲۵, synthesized from a critical analysis of more than ۲۰۰ peer-reviewed journal papers indexed in Scopus, Web of Science, and the ASCE library. The review begins by revisiting the theoretical foundations of fracture mechanics as applied to quasi-brittle materials, including the strain energy release rate (G), plane strain fracture toughness (K_IC), the path-independent J-integral, and the fracture process zone (FPZ) concept [۶, ۷], with explicit discussion of why these formulations deviate from linear elastic fracture mechanics when applied to HPC and UHPC. Standard experimental protocols, namely RILEM TC ۵۰, RILEM TC ۸۹, and JCI S-۰۰۱, are critically examined alongside alternative test setups such as the wedge splitting test and non-destructive techniques [۸, ۹, ۱۰], with particular attention to the unique measurement challenges posed by UHPC including its strain hardening response and fiber-dominated post-cracking behavior [۱۱]. The most influential material and processing parameters are systematically analyzed: fiber characteristics including type, geometry, length, diameter, aspect ratio, and volume fraction with emphasis on bridging stress and pull-out energy [۱۲, ۱۳]; water to cement ratio [۱۴]; type and dosage of pozzolanic supplementary materials [۱۵]; aggregate size and gradation [۱۶]; curing regime (standard, heat, or autoclave) [۱۷]; strain rate sensitivity [۱۸]; and long-term aging effects [۱۹]. Recent advances in analytical and numerical modeling are introduced, encompassing cohesive zone models with parabolic, exponential, and tri-linear softening laws [۲۰], the extended finite element method (XFEM) for mesh-independent crack propagation [۲۱], and the concrete damaged plasticity model (CDPM) adapted for UHPC [۲۲]. Quantitative synthesis of the reviewed literature reveals that HPC without fibers exhibits G_F values typically in the range of ۱۰۰ to ۲۰۰ J/m² [۲۳], the addition of steel fibers to HPC raises this value to approximately ۵۰۰ J/m² [۲۴], and UHPC containing ۲ to ۳ percent steel fibers by volume displays fracture energies ranging from ۱,۰۰۰ to over ۲۵,۰۰۰ J/m² depending critically on test methodology, specimen geometry, and fiber architecture [۲۵, ۲۶]. The review concludes by identifying persistent research gaps including the absence of a unified, internationally accepted standard for fracture energy measurement in UHPC [۲۷], the unacceptably high scatter in reported values across laboratories [۲۸], the severe shortage of long-term environmental durability studies [۲۹], and the largely untapped potential of machine learning and nanomaterials for predictive modeling and property enhancement [۳۰]. This paper serves as a comprehensive reference for both researchers and practicing engineers engaged in fracture energy-based design, performance assessment, and life-cycle evaluation of HPC and UHPC structures.

کلیدواژه ها:

Fracture energy (G_F) ، High performance concrete (HPC) ، Ultra high performance concrete (UHPC) ، Size effect ، Fiber reinforcement ، R-curve ، Cohesive zone model (CZM)