Constitutive relationships for ultra-high-performance concrete at elevated temperatures

Ultra-high-performance concrete (UHPC) is known for its exceptional strength, durability, ductility, and toughness due to its dense cementitious matrix. However, its compact structure presents challenges when exposed to high temperatures, making it prone to strength deterioration and spalling. This study aims to develop reliable relationships to predict UHPC's mechanical properties at high temperatures, including compressive, tensile, and flexural strengths, modulus of elasticity, peak strain, and compressive stress-strain curves. The UHPCs considered in this study include UHPC without fibers (NF), UHPC with steel fibers (SF) only, UHPC with polypropylene fibers (PPF) only, and UHPC with a hybrid combination of SF and PPF. The proposed relationships have been validated against experimental data and existing equations. For compressive strength, bilinear and trilinear equations are used to model an initial slight increase in strength, followed by one or two stages of reduction before failure. Tensile strength is represented by bilinear equations, while flexural strength is modeled using both bilinear and trilinear equations. The modulus of elasticity and peak strain are described using linear and exponential combinations. The proposed compressive stress-strain relationships capture most data but may not accurately represent all cases. However, significant discrepancies exist in the proposed equations for certain UHPC specimens, particularly for compressive, tensile, and flexural strength in PPF specimens, compared to existing equations. The study suggests further testing to refine the constitutive relationships, including investigating different specimen sizes and shapes, varying heating durations, and exploring alternative curing methods.