Steel fibre-reinforced concrete (SFRC) is generally modelled for compressive strength; nevertheless, almost all published models assume fibres are added to a fixed mix and stop at predicting mean strength, neglecting both the cement-replacement scenario and reliability-based design. This study develops a mechanistic, interpretable model for SFRC in which steel fibres replace cement by mass, a composition that raises the effective water-to-cement ratio while incorporating crack-bridging benefit. Compressive strength is expressed as the sum of a paste-weakening term decaying with the surviving cement fraction and a Rayleigh-type bridging term that peaks before balling degrades dispersion. Across seven fibre dosages (0–12% of cement mass) at two curing ages (224 specimens), the model reproduced the non-monotonic strength response with R² = 0.887 at 28 days and independently recovered the bridging optimum near 6–7% fibre without that value being imposed, indicating that it demonstrates the governing physics rather than merely fitting the data. Hardened density showed no reliable dosage trend and stayed within the normal-weight band. Extending the study to characteristic strength and reliability indices, the model showed that only the control mix cleared the design target, every fibre mix falling below it. The framework links predictive accuracy to structural usability, with external validation identified as the priority next step.