Modeling the apparent and intrinsic viscoelastic relaxation of hydrating cement paste
Introduction
Previously, a model implementing the finite element method (FEM) was used to successfully predict the elastic properties of cement paste based on the elastic properties of the microscopic phases and their evolving spatial structure [1]. However, it is widely known that cement paste exhibits viscoelastic/viscoplastic (VE/VP) effects in addition to the instantaneous elastic effects; such time-dependent VE/VP effects have a significant impact on the stress and strain fields in cementitious materials [2]. Theoretically predicting the VE/VP relaxation moduli of cement paste is a difficult task. In addition to its complex, random, composite matrix arrangement at the micrometer scale, the microstructure evolution of cement paste during the hydration process is an additional important complexity, as its response to load critically depends on loading histories relative to the time the new components are formed.
The VE/VP behavior of cement paste has been traditionally attributed to the inherent VE/VP behavior of the calcium silicate hydrate (C-S-H) phase [2], and based on this understanding, many mechanisms towards C-S-H VE/VP behavior have been proposed, such as the seepage theory [3], [4] and the viscous shear theory [3], [5]. Besides inherent C-S-H VE/VP effects, researchers have also suggested other mechanisms leading to time-dependent deformation of cement paste, including poromechanical effects (see, e.g., [6], [7], [8], [9], [10], [11]) and dissolution of load bearing phases [12], [13]. Poromechanical effects manifest as a time-dependent transfer of stress from the pore fluid phase to the solid skeleton inside saturated cementitious materials, which leads to an effective relaxation of the moduli [14], [15]. Similarly, an effective relaxation of the moduli, shown in preliminary results of the model described in this present paper, may also occur due to the redistribution of stress generated by the dissolution of load bearing solid phases [16]. Since the effect of poromechanics is apparently only substantial when the material is fully saturated, in this paper, the main VE/VP mechanisms considered are the intrinsic VE/VP behavior of C-S-H and the time-dependent dissolution of cement grains. While it is well known that drying of cementitious materials while under load enhances deformation (i.e., the so-called “drying creep” or “Pickett effect”), the consideration of drying is outside the scope of the present paper and thus will not be addressed.
The objective of this research is to develop a model using computational methods to predict the evolution of VE/VP properties of hydrating cement paste based on the aforementioned mechanisms. By carrying out virtual experiments using the model, the contribution of each mechanism towards the overall VE/VP behavior of cementitious materials can be evaluated.
Section snippets
Microstructure modeling
The previously referenced prediction of cement paste elastic moduli involved utilizing the microstructure model CEMHYD3D (CEMent HYDration in 3D) [17], which generated lattice-based 3D digital microstructure images of specific cement pastes at specific degrees of hydration. Each voxel in the 3D microstructure was treated as an eight-node tri-linear cubic element in a finite element solver at the micrometer scale. By assigning individual phase elastic moduli to each voxel (depending on which
Viscoelasticity/viscoplasticity due to microstructure evolution
To evaluate the apparent VE/VP behavior occurring strictly due to microstructure evolution, microstructures of cement composites with pure elastic phases (no inherent viscoelasticity) at different ages (from 1 d to 56 d) were first considered. Fig. 4 shows the predicted apparent VE/VP Young’s modulus of 0.40 w/c cement paste under constant periodic strain boundary condition applied at different ages of 1 d and 7 d. The relaxation shown in Fig. 4 was due entirely to the time-dependent dissolution of
Conclusions
A computational scheme that couples a microstructure evolution model and a time-stepping finite element method capable of tracking phase formation is developed in this paper to predict the apparent VE/VP properties of cement paste as a function of time-evolving microstructures. From the model simulations, the apparent VE/VP behavior of hydrating cement paste due to dissolution of cement grains is a significant factor in the overall early-age creep and relaxation of the paste. The main reasons
Acknowledgments
This research was supported by the National Science Foundation under grant numbers 0843979 and 1327314. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.
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