Bridging behavior and fracture mechanisms of UHPC revealed by inverse analysis and micromechanical modeling

Ultra-high-performance concrete (UHPC) is a dense cementitious composite with outstanding mechanical properties and durability. However, its ultra-high-strength cementitious matrix remains intrinsically brittle in tension in the absence of fiber bridging. Steel fibers are therefore commonly incorporated to enhance crack resistance, post-cracking load-carrying capacity, and fracture energy. Steel fibers are widely introduced to enhance fracture resistance, yet the quantitative relationship between fiber parameters and fracture behavior, particularly the evolution of the fracture process zone (FPZ), remains insufficiently understood. This study presents a combined experimental and numerical investigation into the fracture performance of UHPC with systematically varied steel fiber volume fraction, length, and diameter. Three-point bending tests on notched beams were conducted to obtain load-crack mouth opening displacement (CMOD) responses, double-K fracture parameters, and fracture energy. A finite element framework using a cohesive zone model (CZM) and a three-stage bond-slip law was developed to simulate the effective fiber-bridging response and pull-out process. The identified bridging relationship is interpreted as an energy-equivalent effective law representing the net additional fracture resistance induced by steel fibers relative to plain UHPC. Results demonstrate that fiber volume fraction and length significantly enhance fracture energy and unstable fracture toughness, by increasing crack-bridging capacity and energy dissipation. Fiber diameter shows a limited macroscopic effect, due to the competing mechanisms of single-fiber resistance and fiber number density. The numerical model accurately reproduces the full fracture process, capturing the transition from brittle to quasi-ductile behavior. Furthermore, the evolution characteristics of the FPZ are quantified, revealing that fiber parameters govern both its spatial extent and energy dissipation capacity. This study provides mechanistic insights into fiber-matrix interaction, provides an exploratory framework for interpreting the combined effects of fiber parameters on UHPC fracture behavior within the investigated mixtures through fiber parameter design.