Existing Inverse Analysis Approaches for Tensile Stress–Strain Relationship of UHPC with Treated Steel Fibers

Based on the limited information on the tensile stress–strain relationship of ultra-high-performance concrete (UHPC) with treated fibers, the objective of the present research is to experimentally investigate the flexural behavior of UHPC with the treated fibers using a four-point flexural test. The steel fibers inside the UHPC matrix were aligned using an improved device and chemically treated using Zinc phosphate (ZnPh) simultaneously. Also, image analysis was used to obtain the fiber orientation factor with and without the fiber treatments. Two existing inverse analysis methods (namely point-by-point inverse analysis and a five-point inverse analysis) were used to derive tensile stress–strain relationships from the flexural test data. Then, comparisons between the predicted and experimental tensile response were conducted. The results showed that the flexural cracking strength, ultimate strength, and corresponding deflections were enhanced by 39.3%, 95.3%, and 124.5%, respectively, in UHPC with chemically treated and aligned fibers as compared to the reference specimen. The five-point inverse analysis cannot predict the tensile stress-stain relationship of UHPC with or without aligned fibers, while the predicted results from the point-by-point inverse analysis agree well with the experimental results for UHPC without fiber alignment. However, the testing tensile response of UHPC with aligned fibers can be predicted by the point-by-point inverse analysis after a ratio of fiber orientation factor of UHPC with fiber alignment to that without fiber alignment is incorporated to scale the tensile response.