Uncertainty propagation of a multiscale poromechanics-hydration model for poroelastic properties of cement paste at early-age

Abstract

The durability of concrete materials with regard to early-age volume changes and cracking phenomena depends on the evolution of the poroelastic properties of cement paste. The ability of engineers to control the uncertainty of the percolation threshold and the evolution of the elastic modulus, the Biot-Willis parameter and the skeleton Biot modulus is key for minimizing the vulnerability of concrete structures at early-age. This work presents original results on the uncertainty propagation and the sensitivity analysis of a multiscale poromechanics-hydration model applied to cement pastes of water-to-cement ratio of 0.40, 0.50 and 0.60. Notably, the proposed approach provides poroelastic properties required to model the behavior of partially saturated aging cement pastes (e.g. autogenous shrinkage) and it predicts the percolation threshold and undrained elastic modulus in good agreement with experimental data. The development of a stochastic metamodel using polynomial chaos expansions allows to propagate the uncertainties of kinetic parameters of hydration, cement phase composition, elastic moduli and morphological parameters of the microstructure. The presented results show that the propagation does not magnify the uncertainty of the single poroelastic properties although, their correlation may amplify the variability of the estimates obtained from poroelastic state equations. In order to reduce the uncertainty of the percolation threshold and that of the poroelastic properties at early-age, engineers need to assess more accurately the apparent activation energy of calcium aluminate and, later on, of the elastic modulus of low density calcium-silicate-hydrate.

Unloading‐Based Stiffness Characterisation of Cement Pastes During the Second, Third and Fourth Day After Production

“…As far as the early‐age stiffness evolution is concerned, we draw the following conclusions: Early‐age stiffness of pure and blended cement pastes increases practically linearly with increasing hydration degree, in the investigated regime of hydration degrees ranging from 40 to 60%. The ultrasound‐related dynamic Young's moduli are, 24 h after production, by 21% ( w / c = w / s = 0.42), by 25% ( w / c = 0.5 and w / s = 0.42), and by 29% ( w / c = w / c = 0.5) larger than the corresponding unloading moduli. The described ratio reduces monotonously with increasing age of the materials and reaches typical values of 11–12%, 4 days after production. The difference between dynamic Young's moduli and unloading moduli is likely related to the behaviour of water, including the activation of pore pressures in ultrasound testing . This underlines the complexity of cementitious materials, because a similar effect is typically unknown for other media, including tissue engineering scaffolds . The stiffness evolution of a fly ash‐blended cement paste with initial water‐to‐solid mass ratio w / s = 0.42 and initial water‐to‐cement mass ratio w / c = 0.50 falls between the stiffness evolution of a pure cement paste exhibiting w / c = w / s = 0.42 and the one of a pure cement paste exhibiting w / c = w / s = 0.50.…”

Hybrid Fixed-Point Fixed-Stress Splitting Method for Linear Poroelasticity

“…The accuracy of these stresses via prior or empirical approximations of material parameters and source term variability [17] depends on the representations of the elastic moduli and permeability factors [18]. However, a bias toward non-intrusive uncertainty quantification methods such as Collocation [19,20] and Monte Carlo [21][22][23] methods in many engineering applications [19,20,[24][25][26][27], including poroelasticity [28,29]. These methods only require weighted sums of solutions to a problem at specific points in the random space [19].…”

Assessment of a Continuum Micromechanics-Based Multiscale Model for Concrete by Means of Sensitivity Analysis and Uncertainty Propagation

“…Particularly, approaches for independent as well as for correlated input parameters were introduced. Uncertainties in the multiscale modeling of concrete were investigated by Berveiller [10] and Venkovic et al [11]. Berveiller in [10] discussed the variability of the Young's modulus of cement paste using polynomial chaos expansions.…”

“…Berveiller in [10] discussed the variability of the Young's modulus of cement paste using polynomial chaos expansions. Venkovic et al [11] computed the uncertainty propagation of a multiscale poromechanics-hydration model for concrete by means of stochastic meta-models and polynomial chaos expansions.…”