15th International Congress on the Chemistry of Cement
Prague, Czech Republic, September 16–20, 2019
Development of pore structure and permeability during the
hydration of irregular shaped cement particles based on
simulation method
Zhiyong Liu1,2,a, Weiwei Chen 2,b, Yuncheng Wang2,c, Sen Gao 2,d, Yunsheng Zhang1,e
1Southeast University, Nanjing, China
2China University of Mining and Technology, Xuzhou, China
aliuzhiyong0728@163.com
bchnw_1125@126.com
c wangyc950902@foxmail.com
dsen-gao@qq.com
ezhangyunsheng2011@163.com
ABSTRACT
In this study, an irregular particle reconstruction rule is developed based on the principle of cellular
automata and the formation of irregular shapes is controlled by the selected eigenvectors. The
particles are then introduced into the CEMHYD3D model. Hydration is performed to extract the pore
structure from the microstructure. The algorithms (Combustion algorithm, random walk algorithm,
internal erosion method) are developed into programs to calculate the parameters of pore structure in
microstructure with different water cement ratio. The characteristic parameters of pore structure
include the total porosity (referred to as porosity), the porosity of continuous pore, isolated pore and
dead-end pore, connectivity, specific surface area, pore size distribution and tortuosity. Finally, based
on the microstructure of irregular particles, the permeability of the system is studied by boltzmann
method. By comparing with spherical particle reconstruction, it can be found that the initial system of
irregular particle remodeling in this study is closer to the real system. The parameters of the pore
structure parameters are more consistent with the relevant formulas and experimental data. At the
same time, the porosity of different kinds of pores are discussed with hydration time and the variation
curves of porosity, connectivity and specific surface area are analyzed. The time step and the number
of particles required for the calculation of tortuosity are discussed and the tortuosity of different
microstructures are counted. The permeability of different microstructures are calculated by boltzmann
method and the relationship between pore parameters and permeability is established.
15th International Congress on the Chemistry of Cement
Prague, Czech Republic, September 16–20, 2019
1. INTRODUCTION
At present, the rapid development of computer simulation for hydration of cement-based materials has
given birth to a large number of hydration models, such as HymoStruc model (Breugel KV 1992,
Breugel KV 1995, Koenders EAB & Breugel KV 1997, Pan F et al. 2014, Ye G et al. 2003), Ducom
model (Jiang Q 2012, Pommersheim JM & Clifton JR 1979, Ye G 2005), CEMHYD3D model (Bentz
DP 1997, Bentz DP 2000, Bentz DP 2008, Bentz DP & Garboczi EJ 1991, Garboczi EJ & Bentz DP
1992, Maekawa K et al. 2003), µic model (Bishnoi S & Scrivener KL 2009, Maekawa K et al.2003, Liu
C 2016)and HydratiCA model (Bullard JW 2007, Bullard JW 2007). It is found that they approximate
the simulated objects to spherical particles, which restrict the hydration accuracy of the model and limit
its application scope, through the study of the above models. Nevertheless, cement-based materials
are stacked by irregular-shaped particles according to a certain behavior. Obviously, the initial
stacking behavior of these particles determines the hydration process of cement-based materials and
the evolution of the microstructure of the paste, and then affects the macroscopic properties of the
system, such as the transport properties of moisture and ions.
Therefore, irregular cement particles were introduced to construct microstructure with different water-
cement ratios in this study. Then, the characteristic parameters of pore structure were studied through
the physical model. Finally, the transport properties under various saturation states was studied.
2. RECONSTRUCTION OF IRREGULAR CEMENT PARTICLES
A single irregular cement particle was constructed by a central growth method which was based on
discrete method and cellular automaton (Navi P & Pignat C 1996, Wolfram S 1983). In this method,
the center of space was chosen as the growing point, and the final shape of particle growth was
controlled by eigenvector. The specific idea in two-dimensional is as shown in Figure 1.: A random
value is assigned to each position by a random algorithm, and compared with the element values of
the eigenvector, which were corresponded to the adjacent positions of the center point respectively,
and the position where the random value was greater than the feature element value was activated as
the particle phase. This process was repeated until the volume of the particle was reached.
Figure 1. 2D schematic diagram of central growth law（Red pixels are activated cells）
15th International Congress on the Chemistry of Cement
Prague, Czech Republic, September 16–20, 2019
3. CONSTRUCTION OF IRREGULAR CEMENT PARTICLES HYDRATION MODEL
After rotating a randomly certain angle, Boolean operation, setting the periodic boundary condition,
overlap judgment and other processes, the irregular cement particles were put into the microstructure
system. And then the hydration model was constructed by using the phase separation and hydration
rules in the CEMHYD3D model. The initial microstructure, the phase-separated microstructure and the
microstructure in hydration when the water-cement ratio is 0.35 were constructed as shown in Figure
2.
4. CHARACTERIZATION OF PORE STRUCTURE CHARACTERISTIC PARAMETERS
The pores were divided into continuous pore, dead-end pore, and isolated pore according to the
connection between the pore and the surface of the microstructure. The CA (Cellular Automata)
distinguished three types of pore structures by marking adjacent pore voxels on opposite surfaces,
and counted the porosity and connectivity of the three pores. 3DIEM (Three-dimensional Internal
Erosion Method), which is based on internal erosion method (IEM) (Baldwin CA et al. 1996, Baxes GA
1994), obtained the pore size distribution by statistically counting the pore structure of the layer-by-
layer label. MIP simulation had considered about the pore effect of the "ink-bottle pore", and obtained
the pore size distribution by the erosion result of the maximum inscribed circle combined with pore
marked by CA. RWM obtained the pore tortuosity by calculating the mean square displacement of
particles after a certain step. Meanwhile, the specific surface area of the three types of pores were
obtained by the point-by-point scanning method of the pore structure after the connection judgment.
The pore structure characteristic parameters were characterized by the microstructure evolution
process with a water-cement ratio of 0.35, as shown in Figure 3-7.
Figure 2. Microstructure consisting of irregular cement particles when the water-cement
ratio is 0.35
Continuous pore
50 1.5
Dead-end pore
(39.82, 0.05 , 1.18) Isolated pore
40 Connectivity
Connectivity
1.0
Porosity (%)
(28.59, 0.18 , 3.47)
0.97003
30 0.88672
(14.40, 0.85, 8.76)
20 0.59959 0.5
10
0.0
0
0.20 0.35 0.50
Hydration degree (Non-spherical model)
15th International Congress on the Chemistry of Cement
Prague, Czech Republic, September 16–20, 2019
Figure 3. Porosity and connectivity of three types of pores
W35H20-Non-spherical model
W35H35-Non-spherical model 10
Differential porosity (%)
Cumulative porosity (%)
W35H50-Non-spherical model
40 W35H20-Non-spherical model
W35H35-Non-spherical model 8
W35H50-Non-spherical model
30
6
20
4
10
2
0
0
0 1 2 3 4 5 6
Pore size (um)
Figure 4. Pore size distribution obtained by 3DIEM
15
Cumulative porosity (%)
W35H20-continuous PSD
40
Differential porosity (%)
W35H20-continuous PSD W35H20-MIP simulation
12 W35H20-MIP simulation W35H35-continuous PSD
W35H35-continuous PSD 30 W35H35-MIP simulation
9 W35H35-MIP simulation W35H50-continuous PSD
W35H50-continuous PSD W35H50-MIP simulation
6 W35H50-MIP simulation 20
3 10
0
0
0 2 4 6 8 10 0 2 4 6 8 10
Pore size (um) Pore size (um)
Figure 5. Pore size distribution obtained by MIP simulation and continuous PSD
5.5
Hydration degree (um )
-1
5.0
4.5
4.0 W35-continuous pore
W35-dead-end pore
3.5 W35-isolated pore
3.0
2.5
2.0
0.20 0.35 0.50
Hydration degree
Figure 6. Specific surface area of three types of pores
15th International Congress on the Chemistry of Cement
Prague, Czech Republic, September 16–20, 2019
Mean square displacement (um2)
HD-20
6000 HD-35 y=-127.79+0.36x, =2.79
HD-50
Fitting curve of HD-20
Fitting curve of HD-35
4000 Fitting curve of HD-50
2000 y=-107.82+0.23x, =4.35
y=-12.29+0.10x, =10.0
0
0 5000 10000 15000
Time step (Non-spherical model)
Figure 7. Tortuosity obtained by RWM on different hydration degrees
The results show that as the hydration progresses, the continuous pores begin to decrease, and the
dead-end pores and the isolate pores begin to increase. The effect of "ink-bottle" pore and finer
channels (pore "neck") on the pore size distribution in the pore structure was verified by MIP
simulation, and it was verified that the experiment of MIP had underestimated the large pore size. It
could be seen that the water-cement ratio and the hydration degree had a significant influence on the
specific surface area. The smaller the water-cement ratio, the larger the specific surface area. And as
the degree of hydration increases, the tortuosity increases gradually. What’s more, the smaller the
water-cement ratio is, the greater the increase ratio of the degree of hydration will be. At the same
degree of hydration, the tortuosity decreases as the water-cement ratio increases.
5. CHLORIDE ION DIFFUSION COEFFICIENT UNDER UNSATURATED STATE
5.1 Construction of unsaturated microstructure
The established microstructure model of unsaturated hardened cement slurry needed to be
pretreated, that was, to distinguish the large pores and small pores in the microstructure model, which
was due to the large pores were partially saturated in the unsaturated state, and the small pores were
completely filled. Based on the MIP simulation and the 3DIEM, the directed scanning method (DSM)
(Chen W et al. 2010) was added to construct unsaturated microstructure and statistical aperture
distribution. The results of the same microstructure internal moisture distribution obtained by the three
methods were showed in Figure 8:
1.3 LX
DX
1.2 QS
Percent(%)
1.1
1.0
0.9
0.8
0 20 40 60 80 100
Layer
15th International Congress on the Chemistry of Cement
Prague, Czech Republic, September 16–20, 2019
Figure 8. Internal moisture distribution obtained by the three methods
It could be found that the first layer of unsaturated microstructure established by DSM had more
moisture content, and the overall variability was greater than that obtained by MIP simulation and
3DIEM, which was caused by the different definitions of the algorithm in the statistical aperture
distribution.
5.2 Chloride ion diffusion coefficient under unsaturated state
The transport mechanism of chloride ion in unsaturated cement-based materials mainly includes
convection and diffusion. For the hydration model of unsaturated cement-based materials
microstructure in this study, it was proposed to use RWM (Bentz DP et al. 1999) and LTM (Xie D
2015) to study the chloride ion diffusion performance in the unsaturated material.
The effects of calculation methods, particle shape, and saturation on the change of chloride ion
diffusion coefficient were calculated respectively. As shown in Figure 9-11. On the one hand, the
model constructed by LTM contained the transport grid in the C-S-H gel, on the other hand, there were
more water-filled pores in the microstructure, and the "ink-bottle" pores and isolate pores made the
chloride ion transportation seriously blocked. Those two reasons lead to the difference of statistical
results between the two methods. The hydration of cement-based materials based on non-spherical
particles was more than the spherical basis model. Under the same hydration degree, the diffusion
rate of voxel in the irregular-based model was faster, and the probability of state transition after
collision between voxels is higher, thus the internal pore structure became more complicated. It can be
concluded that, as the saturation increases, the chloride ion diffusion coefficient increases gradually.
At a hydration degree of 20%, when the saturation increases from 20% to 90%, the chloride ion
diffusion coefficient increases from about 6.42×10-15 m2/s to 2.71×10-12 m2/s (take the three simulation
methods to obtain the average of the results).
Microscale chloride ionic diffusivity
30
W53H20-DS-LD
25 W53H20-MIP-LD
W53H20-VEM-LD
20 W53H20-DS-SA
(10-12 m2/s)
W53H20-MIP-SA
W53H20-VEM-SA
15
10
5
0
20 40 60 80 100
Water saturation (%)
Figure 9. Chloride ion diffusion coefficient obtained by LTM and SARWM
15th International Congress on the Chemistry of Cement
Prague, Czech Republic, September 16–20, 2019
Microscale chloride ionic diffusivity
15
S-W35H20-DS
12 S-W35H20-MIP
S-W35H20-VEM
I-W35H20-DS
(10-12 m2/s)
9 I-W35H20-MIP
I-W35H20-VEM
0
20 40 60 80 100
Water saturation (%)
Figure 10. Chloride ion diffusion coefficients of cement-based materials composed of spherical
and non-spherical cement particles
15
Microscale chloride ionic diffusivity
12 W35H20-DS
W35H20-MIP
W35H20-VEM
9
(10-12 m2/s)
W35H35-DS
W35H35-MIP
W35H35-VEM
6
0
20 40 60 80 100
Water saturation (%)
Figure 11. Relationship between chloride ion diffusion coefficient and saturation
6. CONCLUSIONS
1) Based on the cellular automaton, the central growth method was used to reconstruct the cement
particles with irregular shape, and the microstructure in hydration based on irregular particles was
constructed.
2) A physical model for characterizing several parameters of the pore structure was established, and
quantitative estimates of their values were calculated. As hydration progresses, the volume of
continuous pores began to decrease, and that of the dead-end pores and isolated pores began to
increase; the smaller the water-cement ratio, the larger the specific surface area. As the degree of
hydration increases, the tortuosity increases gradually. At the same degree of hydration, the tortuosity
decreases as the water-cement ratio increases. Model estimates for large pore volume were
consistently higher than those determined by MIP experiments.
3) The unsaturated microstructure model was constructed based on three different methods. The
influence of calculation method, shape of particles and saturation on the chloride ion diffusion
coefficient was analyzed. Since the model established by LTM contained C-S-H transport grid and
LTM had a lower sensitivity to the "ink-bottle" pore, the results from LTM and SARWM were quite
different. The shape of the particles affected the hydration process and thus the microstructure pores.
And the greater the saturation, the greater the chloride ion diffusion coefficient.
15th International Congress on the Chemistry of Cement
Prague, Czech Republic, September 16–20, 2019
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