The durability of cement-based materials is related to water transport and storage in their pore network under different humidity conditions. To understand the mechanism and characteristics of water adsorption and desorption processes from the microscopic scale, this study introduces different points of view for the pore space model generation and numerical simulation of water transport by considering the “ink-bottle” effect. On the basis of the pore structure parameters (i.e., pore size distribution and porosity) of cement paste and mortar with water-binder ratios of 0.3, 0.4 and 0.5 obtained via mercury intrusion porosimetry, randomly formed 3D pore space models are generated using two-phase transformation on Gaussian random fields and verified via image analysis method of mathematical morphology. Considering the Kelvin-Laplace equation and the influence of “ink-bottle” pores, two numerical calculation scenarios based on mathematical morphology are proposed and applied to the generated model to simulate the adsorption-desorption process. The simulated adsorption and desorption curves are close to those of the experiment, verifying the effectiveness of the developed model and methods. The obtained results characterize water transport in cement-based materials during the variation of relative humidity and further explain the hysteresis effect due to “ink-bottle” pores from the microscopic scale.

Durability is one of the most prominent problems of cement-based materials. The transport of water in the pore network directly influences the mechanical (shrinkage, creep) and chemical (penetration of aggressive agents) degradation of cement-based materials [

Given the same temperature and humidity conditions, hysteresis frequently occurs between adsorption and desorption curves. This phenomenon is closely related to “ink-bottle” pores in the microscopic pore network of cement-based materials [

In general, pores are formed naturally in porous media. Quantitatively describing their geometric and spatial characteristics is extremely difficult due to their complicated morphology and disordered distribution. That is, a pore network model which is constructed on the basis of the definition of specific shapes and relevant parameters differs significantly from real pore space, and thus, is not sufficiently convincing for predicting the migration of fluid [

To date, few kinds of research have been conducted to generate models of cement-based materials with stochastic pore space morphology and then study water transport by considering the ink-bottle effect. In the current study, the issue of water transport in an isothermal adsorption-desorption process is investigated using “experimental + numerical” methods. In the experimental part, cement pastes and mortars with different water-binder ratios were prepared. The isothermal adsorption-desorption experiment and mercury intrusion porosimetry (MIP) test were performed to identify the variation in water content and obtain the porosity and pore size distribution of cement-based materials. In the numerical part, 3D pore space models that satisfy the porosity and the pore size distribution of cement-based materials were constructed using biphasic transformation on Gaussian random fields. This method does not rely on an initial setting of pore form, and it can present the heterogeneity and randomness of pore space morphology. On the basis of the generated model, numerical prediction scenarios that use the image processing method of mathematical morphology were proposed and applied to obtain the isothermal adsorption-desorption curve. After comparison with the experimental data, the hysteresis phenomenon caused by ink-bottle pores was verified and water transport characteristics and transport mechanism during the adsorption-desorption cycle were revealed from the microscopic scale, providing theoretical support for the further analysis of the durability of cement-based materials.

The samples of cement paste and mortar are shown in ^{3}. The mix proportions of cement paste (P-0.3, P-0.4, P-0.5) and mortar (M-0.3, M-0.4, M-0.5) are provided in

Specific surface area /(m^{2}/kg) |
Density/ (g/cm^{3}) |
Standard consistency |
Compressive strength/MPa | Flexural strength/ |
Setting |
|||
---|---|---|---|---|---|---|---|---|

3 d | 28 d | 3 d | 28 d | Initial setting | Final setting | |||

358 | 3.12 | 25.6 | 16.3 | 38.8 | 5.7 | 11.8 | 115 | 176 |

Material | SiO_{2} |
Al_{2}O_{3} |
Fe_{2}O_{3} |
CaO | MgO | SO_{3} |
Na_{2}Oeq |
f-CaO | Loss | Cl^{−1} |
---|---|---|---|---|---|---|---|---|---|---|

Cement | 21.14 | 4.69 | 3.15 | 64.02 | 2.57 | 2.09 | 0.56 | 0.92 | 1.36 | 0.030 |

GGBS | 36.10 | 16.32 | — | 35.58 | 11.32 | — | — | — | 4.09 | — |

Sample | Water-binder ratio | Mix proportion/(kg/m^{3}) |
|||
---|---|---|---|---|---|

Water | Cement | GGBS | Fine aggregate | ||

P-0.3 | 0.30 | 484 | 484 | 1129 | — |

P-0.4 | 0.40 | 581 | 444 | 1011 | — |

P-0.5 | 0.50 | 612 | 367 | 857 | — |

M-0.3 | 0.30 | 267 | 267 | 623 | 1120 |

M-0.4 | 0.40 | 350 | 263 | 612 | 1120 |

M-0.5 | 0.50 | 385 | 231 | 539 | 1120 |

The samples were divided into two groups: the adsorption group and the desorption group. The desorption group was taken from the saturated samples, while the adsorption group was dried to a constant weight before the experiment. A drying temperature of above 100°C is capable of decomposing C-S-H gel; hence, the selected temperature should not be too high [

The isothermal adsorption-desorption curves that reflect the variation of water content with RH are shown in

The dried cement paste and mortar samples were subjected to MIP test by using an Autopore IV 9500 fully automatic mercury intrusion instrument (

The general idea of model construction can be summarized as follows: by setting a threshold, a continuous Gaussian random field will be transformed into a two-phase field to represent the pores and the matrix of the porous medium.

As illustrated in _{1} and _{2} is to select a threshold _{1} and _{2} are obtained where the value of field is within [D, +∞) and (−∞, D). This operation can be expressed as:

According to the study of Adler et al. [_{1} and _{2} can be expressed using _{P}_{1} and _{P}_{2} after the two-phase transformation, as presented in _{1} and _{2}, and they can be estimated using the Gaussian cumulative density function and its tail function in accordance with the chosen threshold _{1} is given in

Suppose that phase _{1} represents the pores and phase _{2} stands for the matrix, then the two-phase field is capable of representing porous media. The function _{1}, and can also be interpreted as the porosity of material.

Notably, the fluctuation of a Gaussian random field is determined by correlation length (_{C}

If _{C}_{1} shown in _{C}_{2} in _{1}, F_{2} and F_{3}) with gradually decreasing _{2} may be covered by the pores in F_{1}, and some of pores in F_{3} may be covered by the pores in F_{1} and F_{1}. Hence,

The cement paste models (P-0.3, P-0.4, P-0.5) were built in a cube with a side length of 1 μm and a mesh division of 400 × 400 × 400, leading to a cell size of 0.0025 μm. Therefore, the model can cover the pore size ranges of 0.003–0.09 μm and 0.003–0.2 μm. The cement paste models are the results of the superposition of eight independent fields. The mortar models (M-0.3, M-0.4, M-0.5) were generated in cube of 0.3 μm with a grid division of 300 × 300 × 300. The cell size is 0.001 μm, and the investigated pore size range is 0.003–0.05 μm. The pore size range of mortar is relatively smaller compared with that of cement paste; thus, the model is created by superimposing six independent fields with different

Sample | Cube size/ (μm) | Mesh | Cell size/ (μm) | Total porosity of model (including isolated pores)/% | |
---|---|---|---|---|---|

P-0.3 | 1.0 | 400^{3} |
0.0025 | 0.005, 0.006, 0.008, 0.01, 0.02, 0.03, 0.05, 0.07 | 24.11 |

P-0.4 | 1.0 | 400^{3} |
0.0025 | 0.006, 0.008, 0.01, 0.03, 0.05, 0.08, 0.11, 0.15 | 27.25 |

P-0.5 | 1.0 | 400^{3} |
0.0025 | 0.007, 0.01, 0.03, 0.06, 0.09, 0.11, 0.14, 0.17 | 36.45 |

M-0.3 | 0.3 | 300^{3} |
0.001 | 0.004, 0.007, 0.01, 0.015, 0.02, 0.03 | 15.46 |

M-0.4 | 0.3 | 300^{3} |
0.001 | 0.006, 0.009, 0.012, 0.017, 0.025, 0.035 | 21.15 |

M-0.5 | 0.3 | 300^{3} |
0.001 | 0.007, 0.01, 0.015, 0.02, 0.03, 0.04 | 24.73 |

Model validation is accomplished by verifying pore size distribution and open porosity by using the image analysis method of mathematical morphology. Mathematical morphology is a theory and technique for analyzing and processing geometric structures; it is commonly used in binary images [

Geodesic reconstruction is used to extract components that are connected to the boundary of an image. In the current work, it is numerically implemented and applied to extract open pores in a pore space model. As illustrated in

In summary, the model generation and validation are finished following the five steps: 1. investigate the pore space characteristics of the material (open porosity and open pore size distribution obtained from the MIP test) and preset

Condition: Standard atmospheric pressure and 20°C.

^{3}).

For example,

In accordance with the experimental result, a hysteresis phenomenon occurs between the isothermal adsorption and desorption processes. This phenomenon is attributed to the fact that the sequence of pore drainage depends not only on size but also on arrangement. Large pores that are connected outward through small pores will not drain at the corresponding RH because the path is blocked by small pores. “Large pores” are called “ink-bottle” pores, and this phenomenon is known as the “ink-bottle” effect. The drainage of ink-bottle pores occurs when RH decreases to the value that corresponds to the smallest size in the water migration path. The “ink bottle” effect should be considered in numerical simulation.

A schematic diagram of the desorption process with decreasing RH is shown in

The scenario of the numerical simulation of desorption is designed on the basic of the image analysis operation of mathematical morphology. In the 1st step, the characteristic diameter

A schematic diagram of adsorption characteristics with increasing RH is shown in

The idea of the numerical simulation of adsorption is illustrated in

In the simulation work, as illustrated in

In addition, the model was generated on the basis of the pore size distribution obtained from MIP test. The pore size ranges are 0.003–0.09 μm for P-0.3, 0.003–0.2 μm for P-0.4/P-0.5, and 0.003–0.05 μm for M-0.3/M-0.4/M-0.5. No pores smaller than 0.003 μm are found inside. According to the Kelvin-Laplace equation, this size is the characteristic diameter that corresponds to 49% RH. Therefore, the starting point of the simulated adsorption curve and the end point of the desorption curve are chosen to be the experimental values at 49% RH. The investigation is focused on 49%–100% RH interval. The experimental curve shows that a certain adsorption effect still exists in the 0%–49% RH interval. This phenomenon may be attributed to two reasons. 1. The sample may have a part with tiny pores that measure less than 0.003 μm. Limited by the performance of Autopore IV 9500, the smaller the pores, the more difficult they are to detect. The part with tiny pores might not have been traced in the MIP test, and therefore, was omitted from the model creation. However, they will complete water saturation during the growth of 0%–49% RH. 2. Water saturation is a gradual accumulation process. It is not that the corresponding pores are filled instantly when a certain RH value is reached, but water is progressively adsorbed as humidity increases, and the filling is completed in the corresponding pores when the RH value is reached. Consequently, a certain adsorption effect still exists in 0%–49% RH. From this perspective, it also explains why the major part of the simulation curve lies below the experiment curve. In general, the simulation results are close to the experimental ones, verifying the effectiveness of the adsorption-desorption theory and the numerical simulation scenarios.

The subsequent research can be further improved from the following two aspects: 1. A study on the microstructure of cement-based materials with the use of instruments and means with greater measuring range and accuracy can determine the existence and proportion of tiny pores, and thus, improve the 3D pore structure model of material; 2. With regard to the numerical simulation, the grid division will affect the simulation results to a certain extent. The denser the grid division and the smaller the cell size, the larger the pore size range that the model can contain, on the one hand, and the more accurate the adsorption-desorption simulation will be, on the other hand. As shown in

To investigate water transport during the isothermal adsorption and desorption of cement-based materials, the following research has been conducted:

Cement paste and mortar samples with water-binder ratios of 0.3, 0.4 and 0.5 were prepared. Isothermal adsorption and desorption experiments were performed by considering 20%, 40%, 60%, 80% and 100% RH. Significant hysteresis occurs between the two curves due to the “ink-bottle” effect. Pore structure parameters, such as pore size distribution and porosity, were obtained by conducting MIP test. The open porosities of P-0.3, P-0.4 and P-0.5 are 19.39%, 23.74% and 32.34%, respectively. Pore diameter mostly ranges from 0.003 to 0.09 μm in P-0.3, from 0.003 to 0.2 μm in P-0.4 and P-0.5. The open porosities of M-0.3, M-0.4 and M-0.5 are 10.91%, 17.77% and 19.86%, respectively. Pore size distribution is between 0.003 and 0.05 μm.

Based on the pore structure parameters, the 3D pore structure models of cement paste and mortar were constructed using two-phase transformation on the continuous Gaussian random field and the superposition of multiple fields. The generated models were numerically investigated and validated using the operations of morphological opening and geodesic reconstruction from the mathematical morphology image analysis method.

Water transport during the adsorption and desorption of cement-based materials is not only influenced by pore size but also by the spatial location. Considering the Kelvin-Laplace equation and the influence of “ink-bottle” pores, two numerical calculation scenarios based on mathematical morphology were proposed and applied to the generated model to simulate the adsorption-desorption process. The investigation was focused on 49%–100% RH interval. The simulated adsorption and desorption curves are close to those of the experiment, verifying the effectiveness of the presented model and methods. The results show that a certain adsorption effect still exists in the low RH range. This effect is due to the existence of tiny pores that are outside the measuring range of MIP, on the one hand, and the gradual accumulation process of adsorption, on the other hand. The simulation also reflects that the saturation degree of adsorption is about 75%–85% at 100% RH, indicating the presence of 15%–25% ink-bottle pores, which must be filled subsequently following gas dissolution and diffusion. In general, the simulated adsorption and desorption curves are close to those of the experiment, verifying the effectiveness of the presented model and methods. The obtained results characterize water transport in cement-based materials during variations in RH and further explain the hysteresis effect due to “ink-bottle” pores from the microscopic scale.

The authors wish to express their appreciation to the reviewers for their helpful suggestions. The authors also are deeply thankful for the support and contribution from journal editors.

This work was supported in part by “

The authors declare that they have no conflicts of interest to report regarding the present study.

_{2}transfer in basalt and sandstone using 3D pore space model generation and mathematical morphology