Materiales de Construcción, Vol 60, No 300 (2010)

A numerical-statistical approach to determining the representative elementary volume (REV) of cement paste for measuring diffusivity

M. Z. Zhang
Delft University,

G. Ye
Delft University,

K. van Breugel
Delft University,


Concrete diffusivity is a function of its microstructure on many scales, ranging from nanometres to millimetres. Multi-scale techniques are therefore needed to model this parameter. Representative elementary volume (REV), in conjunction with the homogenization principle, is one of the most common multi-scale approaches. This study aimed to establish a procedure for establishing the REV required to determine cement paste diffusivity based on a three-step, numerical-statistical approach. First, several series of 3D cement paste microstructures were generated with HYMOSTRUC3D, a cement hydration and microstructure model, for different volumes of cement paste and w/c ratios ranging from 0.30 to 0.60. Second, the finite element method was used to simulate the diffusion of tritiated water through these microstructures. Effective cement paste diffusivity values for different REVs were obtained by applying Fick’s law. Finally, statistical analysis was used to find the fluctuation in effective diffusivity with cement paste volume, from which the REV was then determined. The conclusion drawn was that the REV for measuring diffusivity in cement paste is 100x100x100 μm3.


representative elementary volume (REV); cement paste; diffusivity; microstructure; HYMOSTRUC3D

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