Cellular automaton simulations of cement hydration and microstructure development

Abstract

Cellular automaton algorithms, which operate on a starting digital image of a water-cement suspension, are described. The algorithms simulate the microstructure development process due to hydration reactions that occurs between cement and water. This paper describes the evolution of the cement model from a simple model, which treated the cement particles as single-phase materials, with a greatly simplified hydration chemistry, into a model which has many more chemical species and includes numerous reactions which eventually convert the viscous water-cement suspension into a rigid porous solid. Methods are presented for generating two- and three-dimensional images representing suspension initial conditions; these are derived from both micrographs of real cements and computer-based algorithms. The 2D initial images are based on the processing of backscattered electron and x-ray images of real cement suspensions. The 3D images employ either spheres to represent cement particles, or more realistic randomly shaped particles via an algorithm which smooths and thresholds a 3D lattice whose sites are initially populated with random white noise. A convenient measure of the point at which the initial paste turns into a solid material is the percolation threshold of the solids. Consideration of these models has already led to the prediction and subsequent experimental observation of a sharply defined onset of shear wave propagation, from ultrasonic measurements through hydrating cement slurries. The amount of hydration needed to reach the percolation threshold can be determined in the present simulations, and our results are compared with time of shear wave onset in actual cement slurries. Variants of the basic model provide insight into both early-time behaviour that is of primary interest to oil well cementing and the later-time microstructural properties that are of interest in the construction industry.

Multi-scale interaction potentials (F − r) for describing fracture of brittle disordered materials like cement and concrete

“…The lattice structure is the computational 'back-bone', whereas in Vonk's model, for example, or the 'numerical concrete' model by Roelfstra et al (1985) the two-or three-dimensional finite elements have to be fitted to the complex material structure, which is particularly tedious in three dimensions. Independent generation of lattice and particle structure also opens the way to Examples of computer generated material structure intended to mimic the structure of concrete at the meso-level: (a) Burt and Dougill (1977), (b) Vonk et al (1991) and (c) Schlangen and Van Mier (1992) use real aggregate shapes, as was demonstrated by Schlangen and Garboczi (1997), in a way similar to the generation of computational cement hydration models pioneered at NIST by Bentz et al (1994).…”

“…The reaction with water is called hydration and proceeds only controlled when gypsum is included. The emerging structure is rather complicated, and for a good overview of the matter, the reader is referred to the various publications dealing with cement hydration, for example Bentz et al (1994) and Bentz (1997) and more recently Pignat et al (2005). The hydration starts at places where cement comes into contact with water, and results in a complicated microstructure, like the one visible in Fig.…”

“…The model developed at NIST by Bentz et al (1994), Bentz (1997) is a cellular automaton which 2 In cement chemistry, abbreviated nomenclature is used: C stands for CaO, S for SiO 2 , H for H 2 O and A for Al 2 O 3 . includes direct geometrical and chemical information obtained on un-hydrated cement grains.…”

“…Note that when the shape of the particles changes, for example, take the shape of M&M candies, the number of contacts increases substantially (Donev et al 2004), but again, one has to investigate what happens to the water phase. Simulations including realistic grain sizes and grain contacts, like in the NIST Model (Bentz et al 1994), are considered essential to derive valid behavioural laws.…”

Modelling cement microstructure: Pixels, particles, and property prediction

“…After execution of each cycle of the model, digital image processing techniques may be employed to determine the new phase volume fractions, etc. In addition to the present model for cement hydration [5,20], CA-type models have been developed for sintering [21], dendritic growth [22], and the carbonation of cement [23].…”