A Modified Trilinear Post-Cracking Model for Fiber-Reinforced Concrete to Improve the Evaluation of the Serviceability Limit State Performance

An accurate constitutive model for fiber-reinforced concrete (FRC) is fundamental for analyzing and designing FRC structures. The recently released fib Model Code 2020 (MC2020) includes significant modifications to the tensile constitutive model for FRC, enhancing its accuracy. However, it has been observed that the applicability of this model for certain types of FRC is limited due to its overly simplified post-cracking mechanical assumptions. This is particularly evident in structural FRC, where the fiber pull-out force reaches its maximum at a large fiber slip, resulting in a load decrease before increasing again after the notched beam cracks. In that case, the bilinear assumption in the stress–strain model of MC2020 for post-cracking is insufficient to reflect the fiber mechanism and the mechanical properties of FRC at small crack widths. Therefore, based on the characteristics of fiber pull-out in structural FRC, this paper proposes a trilinear post-cracking stress–strain model to reflect the fiber pull-out mechanism more accurately and better analyze the performance of FRC structures in the serviceability limit state. Through an analysis of experimental data and numerical simulation studies on steel fiber-reinforced concrete (SFRC) notched beams, the parameters for the proposed trilinear constitutive model are determined and validated, and the results indicate that the stress value at the new inflection point in the post-cracking trilinear model should be 0.8fFts (the serviceability residual strength of the FRC). Although the proposed trilinear model seems similar to the trilinear model provided in MC2020, it is developed based on fiber pull-out behavior, whereas the trilinear model in MC2020 was mainly developed to eliminate numerical singularities. Finally, while the models in MC2020 perform well in evaluating the ultimate limit state performance, the proposed constitutive model can serve as a supplement, especially when serviceability limit state performance is considered.