Estimation of cement paste stiffness and UHPC elastic modulus through measured phase-property upscaling

The elastic stiffness of bulk concrete materials results from the complex interaction of aggregates, voids, and hydrated cement (which can have multiple hardened phases at multiple length scales). Given the complexities associated with understanding the arrangement of these particles within bulk concrete volumes, estimations for elastic modulus often rely on empirical correlations with unit weight and compressive strength. Such estimations are inherently scale-dependent and fail to capture variability in mix designs, particularly the variability found in specialty concrete mixes. To develop a scale-independent method for estimating elastic modulus from mix-design volume fraction information, this study explores a novel bottom-up approach using cement paste phase stiffness values determined through micro-mechanical experimentation and randomized Monte-Carlo spring arrangement simulations. Statistical representations of cement paste phase stiffness distributions and bulk volume fraction data are combined to provide estimations for elastic stiffness in both the composite cement paste and bulk concrete containing fine aggregate and fibers. Resulting a priori estimations of UHPC cement paste stiffness from the micro-mechanical upscaling simulations were within 4% of measured values (based on mix-design and void volume fraction information alone) for a selected sample of mix proportions. When applied to the two UHPC mixes containing fibers and fine aggregate, upscaling simulations consistently overpredicted the measured elastic modulus, likely due to the aggregate-cement interfacial transition zone (ITZ) properties that were not captured in the micro-mechanical testing.