# Influence of MgO on the Hydration and Shrinkage Behavior of Low Heat Portland Cement-Based Materials via Pore Structural and Fractal Analysis

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## Abstract

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## 1. Introduction

_{2}S) and a smaller proportion of alite (C

_{3}S) compared with conventional ordinary Portland cement (or ASTM Type I and CEM I) [1,2]. Due to the much slower hydration rate and higher content of C

_{2}S than C

_{3}S in LHP cement, the hydration heat generated by LHP cement is much lower than OPC [3,4,5,6]. For example, the accumulated hydration heat of LHP cement at 3, 28, and 360 days is about 15.6–25.0%, 14.9–18.0%, and 15.3% lower than that of OPC, respectively [3,5,6,7]. Similarly, given the same proportions, the peak adiabatic temperature of LHP cement concrete is about 5.5–6.2 °C lower than OPC concrete [3,5,6]. The conditions in mass concrete are nearly adiabatic and the peak temperature can easily achieve as high as 50–80 °C, and the large temperature difference between inside and outside of structures can easily lead to thermal stress development and cracking [8]. Therefore, LHP cement is a perfect cement to be used in mass concrete structures, which could obviously reduce the potential thermal-stress-induced cracking risk [1,4]. In recent years, LHP cement was utilized in dozens of huge dams in China to replace OPC, e.g., Baihetan dam, Wudongde dam, etc. [3,6,9]. However, the thermal stress of LHP cement-based materials cannot be considerably avoided since the hydration of LHP cement still releases a large amount of heat, even though its peak value is declined and postponed to some extent compared with OPC. Moreover, the LHP cement concrete would inevitably shrink due to the chemical reaction of cement and moisture loss in the drying environment, which also increase the cracking risk [6,10]. Therefore, how to reduce the shrinkage of LHP cement concrete remains a challenging issue for engineers.

## 2. Materials and Analytical Methods

#### 2.1. Materials

_{3}S, 47.0 wt.% C

_{2}S, 4.1 wt.% C

_{3}A, 12.8 wt.% C

_{4}AF, and 3.9 wt.% gypsum. LHP cement meets the technical requirements for type IV Portland cement (low heat cement) conforming to ASTM C150 [38] and LHP cement conforming to GB 200 [39]. The basic physical properties and chemical oxides of LHP cement and MgO are exhibited in Table 1.

^{3}. The fineness modulus of fine aggregate is 2.71.

#### 2.2. Mix Proportion Design

#### 2.3. Test Methods

#### 2.3.1. Hydration Heat Tests by TAM AIR

#### 2.3.2. Mechanical Properties

#### 2.3.3. Shrinkage Behavior

#### 2.3.4. Pore Structural Tests by Mercury Intrusion Porosimeter (MIP)

#### 2.3.5. Fractal Dimension Calculation

_{s}) reflects the roughness and irregularities of pore surfaces of porous material. D

_{s}can be obtained from Zhang’s model.

^{3}.

_{s}can be calculated, which is the slope of the straight line in Equation (1).

## 3. Results and Discussion

#### 3.1. Hydration Heat Results of LHP Cement Paste Added with MgO

_{2}(also termed as brucite) from cement paste solution that reduces the concentration of OH

^{−}ions, the time when the Ca(OH)

_{2}saturation ratio reaches the maximum is increased, and thus, the initiation of the second peak on the heat evolution curve of cement, i.e., the end of the induction period, is delayed; (2) the generated brucite with a tiny crystallite size could precipitate on the cement grain surfaces to form a thin layer which retards further hydration of the cements.

#### 3.2. Mechanical Property of LHP Concrete Added with MgO

#### 3.3. Autogenous Shrinkage

^{−6}and 20.1 × 10

^{−6}of autogenous shrinkage of LC4M50 and LC8M50 can be compensated at 5 days, respectively. After the first inflexion points, they begin to climb up to the second inflexion points at about 14 days, when M50 exhibits the maximal shrinkage-compensating effect. Thereafter, they start to shrink significantly and reach a constant value between 180 and 360 days. From the trend revealed above, it can be seen that although M50 can effectively compensate the shrinkage at early age, it exhibits much little or even no compensation action afterwards until the age of 360 days. This finding corresponds well with the autogenous shrinkage results of cement pastes [87] and mortars containing MgO with various reactivities [33].

^{−6}, while adding 8% M300 produces a 360-day expansion of 14.3 × 10

^{−6}. Overall, this enhanced compensation effect with MgO dosage is in good aggreement with the results obtained from cement pastes [25,87,94], mortars [34,89], and concretes [27,31,95].

#### 3.4. Drying Shrinkage

^{−6}) and 24.6% (40.6 × 10

^{−6}) of drying shrinkage of LC0 concrete could be reduced after the addition of 4% and 8% M50, respectively. Afterwards, no more drying shrinkage can be compensated by M50, both LC4M50 and LC8M50 present quite similar shrinking behavior to the LC0 until 360 days, when the drying shrinkage of LC4M50 and LC8M50 are 7.2% and 13.5% lower than that of LC0, respectively. In contrast, Figure 4b indicates that the shrinkage curve of LC8M300 steadily climb up until 180 days, indicating M300 exhibits a much longer duration of compensation effect than M50. Thereafter LC8M300 maintains a nearly constant shrinkage value until 360 days. Finally, about 16.0% and 25.5% of the 360-day drying shrinkage is reduced by adding 4% and 8% M300, respectively. Similar compensation effects of MgO have been observed on cement mortars reported by Cao et al. [33,34,91].

#### 3.5. MIP Results

#### 3.6. Fractal Dimension of Pore Surface (D_{s})

_{s}) of control LHP concrete (LC0) and concretes containing MgO with different reactivities and dosages at 7, 60, and 360 days are shown in Table 5. The correlation coefficients (R

^{2}) of the fitting line in Equation (1) was also listed in Table 5, which are so close to 1.0, demonstrating the obtained D

_{s}values are accurate and reliable.

_{s}values of all LHP concrete are between 2.709 and 2.987 and increase with hydration time. According to the fractal theory, D

_{s}is meaningful between 2.0 and 3.0 for a porous material, and the material with a D

_{s}value >3.0 or <2.0 is considered non fractal [51,97]. When the D

_{s}value is close to 3, it means the pore structure becomes rougher and more complex [80]. Therefore, the pore structures of LHP concrete and concretes containing MgO in this study have obvious fractal characteristics.

_{s}values of LHP concrete are increased due to MgO addition. This is a widely reported phenomenon when admixtures are used in concrete. Table 6 summarizes the D

_{s}values determined by Zhang’s model and Neimark’s model in this study and other studies in recent years. Table 6 clearly illustrates that the addition of admixtures such as silica fume (SF), fly ash, and granulated blast furnace slag (GBFS), etc., could noticeably increase the D

_{s}values, since these admixtures could make the pore structure of cement-based materials more complex [10,51,59,97].

#### 3.7. Pore Structural and Fractal Analysis of Shrinkage Behavior

#### 3.7.1. Correlation between Pore Structure and D_{s}

_{s.}The relationship between D

_{s}and the porosity can be seen in Figure 5a. Many researchers confirmed that the fine pores less than 50 nm dominantly affect the shrinkage behavior of concrete [36,61,99,100,101,102,103,104]. The V

_{2.5}

_{–50 nm}values estimated from Table 4 are shown in Table 7. The relationship between D

_{s}and V

_{2.5}

_{–50 nm}is displayed in Figure 5b.

_{s}is negatively correlated with the porosity of LHP concrete with a high R

^{2}value of 0.98. This trend is in good agreement with previous findings [51,52,53,55,59,98]. Additionally, Figure 5b indicates that D

_{s}exhibits a negatively linear correlation with V

_{2.5–50 nm}, and the R

^{2}between them is 0.964. The results indicate that the pore structure of LHP concrete can be studied by D

_{s}. As Jin et al. [59] stated, D

_{s}can perform more accurately and comprehensively than other pore structure parameters to characterize the overall situations of pore structures.

#### 3.7.2. Pore Structural and Fractal Study on Shrinkage Behavior

_{2.5–50 nm}) was plotted in Figure 6. The correlation between drying shrinkage and pore structure is shown in Figure 7.

^{2}values between them are not very high; some of them are even less than 0.1. This means the shrinkage behavior of these concretes are not closely related with their pore structures. However, this finding seems contradictory to the common consensus that the pores have a dominate role in determining the shrinkage of concrete. For instance, Li et al. [99] reported that the pores with a size range of 5–50 nm largely affect the shrinkage because the capillary stress is easy to develop within the pores in this size range. Wang et al. [5,10] revealed the shrinkage of concrete is linearly correlated with its porosity and V

_{2.5–50 nm}. This seemingly conflicting results may be explained by the following points: the shrinkage of concrete incorporated with MgO is not solely influenced by the pores, but also critically affected by the expansion of concrete which depends on the MgO dosage and reactivity. Specifically, the hydration products of MgO could fill into the large pore and increase the proportions of fine pores, as evidenced in Section 3.5. Moreover, such hydration products in solid phase (i.e., not in pores) could cause expansion in concrete and thus directly reducing or completely compensating the shrinkage of concrete, as revealed in Section 3.3 and Section 3.4. Therefore, no close and definite correlation between shrinkage behavior of expansive concretes and their pore structure parameters can be found in this study.

_{s}, which are helpful for the understanding of shrinkage behavior from the standpoint of fractal theory.

_{s}because the R

^{2}values between them are low. This can be expected because pore structure parameters of expansive concrete in this study are closely correlated with D

_{s}whereas they exhibit weak or no correlations with shrinkage behavior, as revealed above. As a result, D

_{s}which characterizes the overall pore structures exhibits a poor relationship with shrinkage strains of LHP concrete containing MgO.

## 4. Conclusions

_{s}of LHP concrete exhibits a close correlation with the main pore structure parameters. Both the pore structure parameters and D

_{s}exhibit weak (or no) correlations with shrinkage behavior value. This is because the shrinkage behavior of LHP concrete incorporated with MgO is not only influenced by the pores, but also critically affected by the expansion of concrete caused by MgO.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

- Mori, K.; Fukunaga, T.; Sugiyama, M.; Iwase, K.; Oishi, K.; Yamamuro, O. Hydration properties and compressive strength development of low heat cement. J. Phys. Chem. Solids
**2012**, 73, 1274–1277. [Google Scholar] [CrossRef] - Koumpouri, D.; Angelopoulos, G.N. Effect of boron waste and boric acid addition on the production of low energy belite cement. Cem. Concr. Compos.
**2016**, 68, 1–8. [Google Scholar] [CrossRef] - Wang, L.; Dong, Y.; Zhou, S.H.; Chen, E.; Tang, S.W. Energy saving benefit, mechanical performance, volume stabilities, hydration properties and products of low heat cement-based materials. Energ. Build.
**2018**, 170, 157–169. [Google Scholar] [CrossRef] - Maheswaran, S.; Kalaiselvam, S.; Saravana Karthikeyan, S.K.S.; Kokila, C.; Palani, G.S. β-Belite cements (β-dicalcium silicate) obtained from calcined lime sludge and silica fume. Cem. Concr. Compos.
**2016**, 66, 57–65. [Google Scholar] [CrossRef] - Wang, L.; Yang, H.Q.; Dong, Y.; Chen, E.; Tang, S.W. Environmental evaluation, hydration, pore structure, volume deformation and abrasion resistance of low heat Portland (LHP) cement-based materials. J. Clean. Prod.
**2018**, 203, 540–558. [Google Scholar] [CrossRef] - Wang, L.; Yang, H.Q.; Zhou, S.H.; Chen, E.; Tang, S.W. Mechanical properties, long-term hydration heat, shinkage behavior and crack resistance of dam concrete designed with low heat Portland (LHP) cement and fly ash. Constr. Build. Mater.
**2018**, 187, 1073–1091. [Google Scholar] [CrossRef] - Wang, L.; Yang, H.Q.; Zhou, S.H.; Chen, E.; Tang, S.W. Hydration, mechanical property and C-S-H structure of early-strength low-heat cement-based materials. Mater. Lett.
**2018**, 217, 151–154. [Google Scholar] [CrossRef] - Klemczak, B.; Batog, M.; Pilch, M.; Żmij, A. Analysis of cracking risk in early age mass concrete with different aggregate types. Procedia Eng.
**2017**, 193, 234–241. [Google Scholar] [CrossRef] - Xie, Z.; Zhu, Z.; Fu, Z.; Lv, X. Simulation of the temperature field for massive concrete structures using an interval finite element method. Eng. Comput.
**2020**, 37, 45. [Google Scholar] [CrossRef] - Wang, L.; Jin, M.M.; Wu, Y.H.; Zhou, Y.X.; Tang, S.W. Hydration, shrinkage, pore structure and fractal dimension of silica fume modified low heat Portland cement-based materials. Constr. Build. Mater.
**2021**, 272, 121952. [Google Scholar] [CrossRef] - Ha, J.H.; Jung, Y.S.; Cho, Y.G. Thermal crack control in mass concrete structure using an automated curing system. Automat. Constr.
**2014**, 45, 16–24. [Google Scholar] [CrossRef] - Wang, L.; Guo, F.X.; Lin, Y.Q.; Yang, H.M.; Tang, S.W. Comparison between the effects of phosphorous slag and fly ash on the C-S-H structure, long-term hydration heat and volume deformation of cement-based materials. Constr. Build. Mater.
**2020**, 250, 118807. [Google Scholar] [CrossRef] - Wang, L.; Guo, F.X.; Yang, H.M.; Wang, Y.; Tang, S.W. Comparison of fly ash, PVA fiber, MgO and shrinkage-reducing admixture on the frost resistance of face slab concrete via pore structural and fractal analysis. Fractals
**2021**, 29, 2140002. [Google Scholar] [CrossRef] - Zhang, P.; Wang, K.X.; Wang, J.; Guo, J.J.; Ling, Y.F. Macroscopic and microscopic analyses on mechanical performance of metakaolin/fly ash based geopolymer mortar. J. Clean. Prod.
**2021**, 294, 126193. [Google Scholar] [CrossRef] - Dong, Y.; Yang, H.; Rao, M. Effects of mineral admixture on the carbonic acid leaching resistance of cement-based materials. Ceram. Silik.
**2017**, 61, 276–284. [Google Scholar] [CrossRef] [Green Version] - Prasad, N.; Murali, G.; Abid, S.R.; Vatin, N.; Fediuk, R.; Amran, M. Effect of needle Type, number of layers on FPAFC composite against low-velocity projectile impact. Buildings
**2021**, 11, 668. [Google Scholar] [CrossRef] - Zhang, P.; Gao, Z.; Wang, J.; Wang, K. Numerical modeling of rebar-matrix bond behaviors of nano-SiO
_{2}and PVA fiber reinforced geopolymer composites. Ceram. Int.**2021**, 47, 11727–11737. [Google Scholar] [CrossRef] - Wang, L.; Zhou, S.H.; Shi, Y.; Tang, S.W.; Chen, E. Effect of silica fume and PVA fiber on the abrasion resistance and volume stability of concrete. Compos. Part B Eng.
**2017**, 130, 28–37. [Google Scholar] [CrossRef] - Ramkumar, V.; Murali, G.; Asrani, N.P.; Karthikeyan, K. Development of a novel low carbon cementitious two stage layered fibrous concrete with superior impact strength. J. Build. Eng.
**2019**, 25, 100841. [Google Scholar] [CrossRef] - Wang, X.; Wu, D.; Zhang, J.; Yu, R.; Hou, D.; Shui, Z. Design of sustainable ultra-high performance concrete: A review. Constr. Build. Mater.
**2021**, 307, 124643. [Google Scholar] [CrossRef] - Zhang, P.; Wang, K.X.; Wang, J.; Guo, J.J.; Hu, S.W.; Ling, Y.F. Mechanical properties and prediction of fracture parameters of geopolymer/alkali-activated mortar modified with PVA fiber and nano-SiO
_{2}. Ceram. Int.**2020**, 46, 20027–20037. [Google Scholar] [CrossRef] - Prasad, N.; Murali, G. Research on flexure and impact performance of functionally-graded two-stage fibrous concrete beams of different sizes. Constr. Build. Mater.
**2021**, 288, 123138. [Google Scholar] [CrossRef] - Yuan, B.; Li, Z.; Chen, Y.; Hong, N.; Zhao, Z.; Chen, W.; Zhao, J. Mechanical and microstructural properties of recycling granite residual soil reinforced with glass fiber and liquid-modified polyvinyl alcohol polymer. Chemosphere
**2021**, 268, 131652. [Google Scholar] [CrossRef] [PubMed] - Yang, Z.Y.; He, J.R.; Luo, G.Q. Crack prevention techniques for face concrete of Hongjiadu CFRD with height about 200 m. Water Power
**2008**, 7, 59–63. [Google Scholar] - Mo, L.W.; Fang, J.W.; Hou, W.H.; Ji, X.K. Synergetic effects of curing temperature and hydration reactivity of MgO expansive agents on their hydration and expansion behaviours in cement pastes. Constr. Build. Mater.
**2019**, 207, 206–217. [Google Scholar] [CrossRef] - Gao, P.W.; Wu, S.X.; Lin, P.H.; Wu, Z.R.; Tang, M.S. The characteristics of air void and frost resistance of RCC with fly ash and expansive agent. Constr. Build. Mater.
**2006**, 20, 586–590. [Google Scholar] [CrossRef] - Chen, X.; Yang, H.Q.; Li, W.W. Factors analysis on autogenous volume deformation of MgO concrete and early thermal cracking evaluation. Constr. Build. Mater.
**2016**, 118, 276–285. [Google Scholar] [CrossRef] - Kabir, H.; Hooton, R.D. Evaluating soundness of concrete containing shrinkage-compensating MgO admixtures. Constr. Build. Mater.
**2020**, 253, 119141. [Google Scholar] [CrossRef] - Chen, X.; Yang, H.Q.; Zhou, S.H.; Li, W.W. Sensitive evaluation on early cracking tendency of concrete with inclusion of light-burnt MgO. J. Wuhan Univ. Technol. Mater. Sci. Ed.
**2011**, 26, 1018–1022. [Google Scholar] [CrossRef] - Ruan, S.; Unluer, C. Comparison of the environmental impacts of reactive magnesia and calcined dolomite and their performance under different curing conditions. J Mater. Civ. Eng.
**2018**, 30, 04018279. [Google Scholar] [CrossRef] - Huang, K.J.; Shi, X.J.; Dan, Z.; Mirsayar, M.; Wang, A.G.; Mo, L.W. Use of MgO expansion agent to compensate concrete shrinkage in jointed reinforced concrete pavement under high-altitude environmental conditions. Constr. Build. Mater.
**2019**, 202, 528–536. [Google Scholar] [CrossRef] - DL/T 5296-2013. Technical Specification of Magnesium Oxide Expansive for Use in Hydraulic Concrete, China; China Electric Power Press: Beijing, China, 2014.
- Cao, F.Z.; Yan, P.Y. The influence of the hydration procedure of MgO expansive agent on the expansive behavior of shrinkage-compensating mortar. Constr. Build. Mater.
**2019**, 202, 162–168. [Google Scholar] [CrossRef] - Cao, F.Z.; Miao, M.; Yan, P.Y. Effects of reactivity of MgO expansive agent on its performance in cement-based materials and an improvement of the evaluating method of MEA reactivity. Constr. Build. Mater.
**2018**, 187, 257–266. [Google Scholar] [CrossRef] - Liu, P.; Chen, Z.Y.; Deng, M. Regulating the expansion characteristics of cementitious materials using blended MgO-type expansive agent. Materials
**2019**, 12, 976. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Wang, L.; Li, G.; Li, X.; Guo, F.; Tang, S.; Lu, X.; Hanif, A. Influence of reactivity and dosage of MgO expansive agent on shrinkage and crack resistance of face slab concrete. Cem. Conc. Compos.
**2022**, 126, 104333. [Google Scholar] [CrossRef] - CBMF 19-2017. Magnesium Oxide Expansive Agent for Concrete; China Building Materials Industry Press: Beijing, China, 2017.
- ASTMC150/C150M-2016. Standard Specification for Portland Cement; ASTM International: West Conshohocken, PA, USA, 2016.
- 200-2003, G.Standard Specification for Moderate Heat Silicate Cement, Low Heat Portland Cement, Slag Added-Low Heat Portland Cement, China; China Standard Press: Beijing, China, 2003.
- ASTM C1702-17. Standard Test Method for Measurement of Heat of Hydration of Hydraulic Cementitious Materials Using Isothermal Conduction Calorimetry; ASTM International: West Conshohocken, PA, USA, 2009.
- Niu, M.; Zhang, J.; Li, G. Mechanical properties of polyvinyl alcohol fiber-reinforced sulfoaluminate cement mortar containing high-volume of fly ash. J. Build. Eng.
**2021**, 35, 101988. [Google Scholar] [CrossRef] - Tang, S.W.; Li, Z.J.; Chen, E.; Shao, H.Y. Impedance measurement to characterize the pore structure in portland cement paste. Constr. Build. Mater.
**2014**, 51, 106–112. [Google Scholar] [CrossRef] - Niu, M.; Li, G.; Li, Q.; Zhang, G. Influence of naphthalene sulphonated and polycarboxylate acid-based superplasticizer on the mechanical properties and hydration behavior of ternary binder: A comparative study. Constr. Build. Mater.
**2021**, 312, 125374. [Google Scholar] [CrossRef] - Tang, S.W.; Li, Z.J.; Zhu, H.G.; Shao, H.Y.; Chen, E. Permeability interpretation for young cement paste based on impedance measurement. Constr. Build. Mater.
**2014**, 59, 120–128. [Google Scholar] [CrossRef] - DL/T 5150-2017. Test Code for Hydraulic Concrete, China; China Electric Power Press: Beijing, China, 2017.
- Deboodt, T.; Fu, T.; Ideker, J.H. Evaluation of FLWA and SRAs on autogenous deformation and long-term drying shrinkage of high performance concrete. Constr. Build. Mater.
**2016**, 119, 53–60. [Google Scholar] [CrossRef] - Wongkeo, W.; Thongsanitgarn, P.; Chaipanich, A. Compressive strength and drying shrinkage of fly ash-bottom ash-silica fume multi-blended cement mortars. Mater. Des.
**2012**, 36, 655–662. [Google Scholar] [CrossRef] - Lv, X.D.; Shen, W.G.; Dong, Y.; Zhang, J.F.; Xie, Z.Q. A comparative study on the practical utilization of iron tailings as a complete replacement of normal aggregates in dam concrete with different gradation. J. Clean. Prod.
**2019**, 211, 704–715. [Google Scholar] [CrossRef] - Hu, X.; Shi, C.J.; Shi, Z.G.; Tong, B.H.; Wang, D.H. Early age shrinkage and heat of hydration of cement-fly ash-slag ternary blends. Constr. Build. Mater.
**2017**, 153, 857–865. [Google Scholar] [CrossRef] - Wang, L.; He, T.S.; Zhou, Y.X.; Tang, S.W.; Tan, J.J.; Liua, Z.T.; Su, J.W. The influence of fiber type and length on the cracking resistance, durability and pore structure of face slab concrete. Constr. Build. Mater.
**2021**, 282, 122706. [Google Scholar] [CrossRef] - Zeng, Q.; Luo, M.Y.; Pang, X.Y.; Li, L.; Li, K.F. Surface fractal dimension: An indicator to characterize the microstructure of cement-based porous materials. Appl. Surf. Sci.
**2013**, 282, 302–307. [Google Scholar] [CrossRef] - Wang, L.; Jin, M.M.; Guo, F.X.; Wang, Y.; Tang, S.W. Pore structural and fractal analysis of the influence of fly ash and silica fume on the mechanical property and abrasion resistance of concrete. Fractals
**2021**, 29, 2140003. [Google Scholar] [CrossRef] - Wang, L.; Luo, R.Y.; Zhang, W.; Jin, M.M.; Tang, S.W. Effects of fineness and content of phosphorus slag on cement hydration, permeability, pore structure and fractal dimension of concrete. Fractals
**2021**, 29, 2140004. [Google Scholar] [CrossRef] - Wang, L.; Chen, E.; Ruan, S.; Tang, S. Editorial: New technologies for investigating microstructures and enhancing performance of cementitious materials. Front. Mater.
**2021**, 8, 669862. [Google Scholar] [CrossRef] - Wang, L.; Tang, S.W. Editorial: An introduction to fractals in construction materials. Fractals
**2021**, 29, 2102001. [Google Scholar] [CrossRef] - Neimark, A.V. A new approach to the determination of the surface fractal dimension of porous solids. Phys. A
**1992**, 191, 258–262. [Google Scholar] [CrossRef] - Tang, S.W.; Cai, R.J.; He, Z.; Cai, X.H.; Shao, H.Y.; Li, Z.J.; Yang, H.M.; Chen, E. Continuous microstructural correlation of slag/superplasticizer cement pastes by heat and impedance methods via fractal analysis. Fractals
**2017**, 25, 1740003. [Google Scholar] [CrossRef] [Green Version] - Tang, S.W.; Huang, J.S.; Duan, L.; Yu, P.; Chen, E. A review on fractal footprint of cement-based materials. Powder Technol.
**2020**, 370, 237–250. [Google Scholar] [CrossRef] - Jin, S.S.; Zhang, J.X.; Han, S. Fractal analysis of relation between strength and pore structure of hardened mortar. Constr. Build. Mater.
**2017**, 135, 1–7. [Google Scholar] [CrossRef] - Tang, S.W.; He, Z.; Cai, X.H.; Cai, R.J.; Zhou, W.; Li, Z.J.; Shao, H.Y.; Wu, T.; Chen, E. Volume and surface fractal dimensions of pore structure by NAD and LT-DSC in calcium sulfoaluminate cement pastes. Constr. Build. Mater.
**2017**, 143, 395–418. [Google Scholar] [CrossRef] - Wang, L.; Zeng, X.; Yang, H.; Lv, X. Investigation and application of fractal theory in cement-based materials: A review. Fractal Fract.
**2021**, 5, 247. [Google Scholar] [CrossRef] - Tang, S.W.; Chen, E.; Shao, H.Y.; Li, Z.J. A fractal approach to determine thermal conductivity in cement pastes. Constr. Build. Mater.
**2015**, 74, 73–82. [Google Scholar] [CrossRef] - Tang, S.W.; Yuan, J.H.; Cai, R.J.; Chen, E. In situ monitoring of hydration of magnesium oxysulfate cement paste: Effect of MgO/MgSO
_{4}ratio. Constr. Build. Mater.**2020**, 251, 119003–119013. [Google Scholar] [CrossRef] - Shi, Y.; Dong, Y.; Chen, X.; Li, X. Different chemical composition of aggregate impact on hydraulic concrete interfacial transition zone. Asian J. Chem.
**2014**, 26, 1267–1270. [Google Scholar] [CrossRef] - Tang, S.W.; Wang, L.; Cai, R.J.; Cai, X.H.; He, Z.; Chen, E. The evaluation of electrical impedance of three-dimensional fractal networks embedded in a cube. Fractals
**2017**, 25, 1740005. [Google Scholar] [CrossRef] - Tang, S.W.; Cai, X.H.; Zhou, W.; Shao, H.Y.; He, Z.; Li, Z.J.; Ji, W.M.; Chen, E. In-situ and continuous monitoring of pore evolution of calcium sulfoaluminate cement at early age by electrical impedance measurement. Constr. Build. Mater.
**2016**, 117, 8–19. [Google Scholar] [CrossRef] - Mandelbrot, B.B. The fractal geometry of nature. Am. J. Phys.
**1988**, 51, 468. [Google Scholar] [CrossRef] - Tang, S.W.; Wang, Y.; Geng, Z.C.; Xu, X.F.; Yu, W.Z. Structure, fractality, mechanics and durability of calcium silicate hydrates. Fractal Fract.
**2021**, 5, 47. [Google Scholar] [CrossRef] - Mandelbrot, B.B. The Fractal Geometry of Nature; W.H. Freeman and Company: San Francisco, CA, USA, 1983. [Google Scholar]
- Tang, S.W.; Chen, E.; Li, Z.J.; Shao, H.Y. Assessment of steady state diffusion of volatile organic compounds in unsaturated building materials based on fractal diffusion model. Build. Environ.
**2015**, 84, 221–227. [Google Scholar] [CrossRef] - Xiao, J.; Long, X.; Li, L.; Jiang, H.; Zhang, Y.; Qu, W. Study on the influence of three factors on mass loss and surface fractal dimension of concrete in sulfuric acid environments. Fractal Fract.
**2021**, 5, 146. [Google Scholar] [CrossRef] - Zarnaghi, V.N.; Fouroghi-Asl, A.; Nourani, V.; Ma, H. On the pore structures of lightweight self-compacting concrete containing silica fume. Constr. Build. Mater.
**2018**, 193, 557–564. [Google Scholar] [CrossRef] - Xiao, J.; Long, X.; Qu, W.; Li, L.; Jiang, H.; Zhong, Z. Influence of sulfuric acid corrosion on concrete stress-strain relationship under uniaxial compression. Measurement
**2021**, 185, 110318. [Google Scholar] [CrossRef] - Huang, J.; Li, W.; Huang, D.; Chen, E. Fractal analysis on pore structure and hydration of magnesium oxysulfate cements by first principle, thermodynamic and microstructure-based methods. Fractal Fract.
**2021**, 5, 164. [Google Scholar] [CrossRef] - Li, L.; Li, Z.L.; Cao, M.L.; Tang, Y.; Zhang, Z. Nanoindentation and porosity fractal dimension of calcium carbonate whisker reinforced cement paste after elevated temperatures (up to 900 °C). Fractals
**2021**, 29, 2140001. [Google Scholar] [CrossRef] - Xiao, J.; Qu, W.J.; Jiang, H.B.; Li, L.; Huang, J.; Chen, L. Fractal characterization and mechanical behavior of pile-soil interface subjected to sulfuric acid. Fractals
**2021**, 29, 2140010. [Google Scholar] [CrossRef] - Li, L.; Sun, H.; Zhang, Y.; Yu, B. Surface cracking and fractal characteristics of bending fractured polypropylene fiber-reinforced geopolymer mortar. Fractal Fract.
**2021**, 5, 142. [Google Scholar] [CrossRef] - Xiao, J.; Xu, Z.; Murong, Y.; Lei, B.; Chu, L.; Jiang, H.; Qu, W. Effect of chemical composition of fine aggregate on the frictional behavior of concrete–soil interface under sulfuric acid environment. Fractal Fract.
**2022**, 6, 22. [Google Scholar] [CrossRef] - Zhang, B.Q.; Liu, W.; Liu, X. Scale-dependent nature of the surface fractal dimension for bi- and multi-disperse porous solids by mercury porosimetry. Appl. Surf. Sci.
**2006**, 253, 1349–1355. [Google Scholar] [CrossRef] - Zhang, B.Q.; Li, S.F. Determination of the surface fractal dimension for porous media by mercury porosimetry. Ind. Eng. Chem. Res.
**1995**, 34, 1383–1386. [Google Scholar] [CrossRef] - Pfeifer, P.; Avnir, D. Chemistry in noninteger dimensions between two and three. I. Fractal theory of heterogeneous surfaces. J. Chem. Phys.
**1983**, 79, 3558–3565. [Google Scholar] [CrossRef] - Zheng, L.; Xuehua, C.; Mingshu, T. Hydration and setting time of MgO-type expansive cement. Cem. Concr. Res.
**1992**, 22, 1–5. [Google Scholar] [CrossRef] - Huang, L.M.; Yang, Z.H.; Wang, S.F. Influence of calcination temperature on the structure and hydration of MgO. Constr. Build. Mater.
**2020**, 262, 120776. [Google Scholar] [CrossRef] - Kuenzel, C.; Zhang, F.; Ferrandiz-Mas, V.; Cheeseman, C.R.; Gartner, E.M. The mechanism of hydration of MgO-hydromagnesite blends. Cem. Concr. Res.
**2018**, 103, 123–129. [Google Scholar] [CrossRef] - Mo, L.W.; Deng, M.; Tang, M.S. Effects of calcination condition on expansion property of MgO-type expansive agent used in cement-based materials. Cem. Concr. Res.
**2010**, 40, 437–446. [Google Scholar] [CrossRef] - Mo, L.W.; Fang, J.W.; Huang, B.; Wang, A.G.; Deng, M. Combined effects of biochar and MgO expansive additive on the autogenous shrinkage, internal relative humidity and compressive strength of cement pastes. Constr. Build. Mater.
**2019**, 229, 116877. [Google Scholar] [CrossRef] - Mo, L.W.; Liu, M.; Al-Tabbaa, A.; Deng, M. Deformation and mechanical properties of the expansive cements produced by inter-grinding cement clinker and MgOs with various reactivities. Constr. Build. Mater.
**2015**, 80, 1–8. [Google Scholar] [CrossRef] - Beshr, S.S.; Mohaimen, I.M.A.; Azline, M.N.N.; Azizi, S.N.; Nabilah, A.B.; Aznieta, A.A. Feasibility assessment on self-healing ability of cementitious composites with MgO. J. Build. Eng.
**2021**, 34, 101914. [Google Scholar] [CrossRef] - Gonçalves, T.; Silva, R.V.; de Brito, J.; Fernández, J.M.; Esquinas, A.R. Hydration of reactive MgO as partial cement replacement and its influence on the macroperformance of cementitious mortars. Adv. Mater. Sci. Eng.
**2019**, 2019, 9271507. [Google Scholar] [CrossRef] [Green Version] - Wang, L.; Jin, M.; Zhou, S.; Tang, S.W.; Lu, X. Investigation of microstructure of C-S-H and micro-mechanics of cement pastes under NH4NO3 dissolution by 29Si MAS NMR and microhardness. Measurement
**2021**, 185, 110019. [Google Scholar] [CrossRef] - Cao, F.Z.; Yan, P.Y. Effects of reactivity and dosage of magnesium oxide expansive agents on long-term volume variation of concrete. J. Chin. Ceram. Soc.
**2018**, 46, 1126–1132. [Google Scholar] - Cao, F.Z.; Miao, M.; Yan, P.Y. Hydration characteristics and expansive mechanism of MgO expansive agents. Constr. Build. Mater.
**2018**, 183, 234–242. [Google Scholar] [CrossRef] - Choi, S.W.; Jang, B.S.; Kim, J.H.; Lee, K.M. Durability characteristics of fly ash concrete containing lightly burnt MgO. Constr. Build. Mater.
**2014**, 58, 77–84. [Google Scholar] [CrossRef] - Mo, L.W.; Deng, M.; Wang, A. Effects of MgO-based expansive additive on compensating the shrinkage of cement paste under non-wet curing conditions. Cem. Concr. Compos.
**2012**, 34, 377–383. [Google Scholar] [CrossRef] - Huang, K.J.; Deng, M.; Mo, L.W.; Wang, Y.G. Early age stability of concrete pavement by using hybrid fiber together with MgO expansion agent in high altitude locality. Constr. Build. Mater.
**2013**, 48, 685–690. [Google Scholar] [CrossRef] - Mindess, S.; Young, J.F.; Darwin, D. Concrete; Prentice-Hall: Hoboken, NJ, USA, 2003. [Google Scholar]
- Zeng, Q.; Li, K.F.; Teddy, F.C.; Patrick, D.L. Surface fractal analysis of pore structure of high-volume fly-ash cement pastes. Appl. Surf. Sci.
**2010**, 257, 762–768. [Google Scholar] [CrossRef] - Liu, P.; Cui, S.G.; Li, Z.H.; Xu, X.F.; Guo, C. Influence of surrounding rock temperature on mechanical property and pore structure of concrete for shotcrete use in a hot-dry environment of high-temperature geothermal tunnel. Constr. Build. Mater.
**2019**, 207, 329–337. [Google Scholar] [CrossRef] - Li, Y.; Bao, J.; Guo, Y. The relationship between autogenous shrinkage and pore structure of cement paste with mineral admixtures. Constr. Build. Mater.
**2010**, 24, 1855–1860. [Google Scholar] [CrossRef] - Ma, Y.; Ye, G. The shrinkage of alkali activated fly ash. Cem. Concr. Res.
**2015**, 68, 75–82. [Google Scholar] [CrossRef] - Zhang, W.; Hama, Y.; Na, S.H. Drying shrinkage and microstructure characteristics of mortar incorporating ground granulated blast furnace slag and shrinkage reducing admixture. Constr. Build. Mater.
**2015**, 93, 267–277. [Google Scholar] [CrossRef] - He, W.; Liu, C.; Zhang, L. Effects of sodium chloride on the mechanical properties of slag composite matrix geopolymer. Adv. Cem. Res.
**2019**, 31, 389–398. [Google Scholar] [CrossRef] - He, W.; Hao, W.; Meng, X.; Zhang, P.; Sun, X.; Shen, Y. Influence of graphite powder on the mechanical and acoustic emission characteristics of concrete. Buildings
**2022**, 12, 18. [Google Scholar] [CrossRef] - Chen, C.; Zhang, R.; Zhou, L.; Wang, Y. Influence of waste tire particles on freeze-thaw resistance and impermeability performance of waste tires/sand-based autoclaved aerated concrete composites. Buildings
**2022**, 12, 33. [Google Scholar] [CrossRef]

**Figure 2.**Mechanical property of LHP concrete containing MgO: (

**a**) compressive strength and (

**b**) splitting tensile strength.

**Figure 3.**Autogenous shrinkage of LHP concrete containing two kinds of MgO at a dosage of (

**a**) 4% and (

**b**) 8%.

**Figure 4.**Drying shrinkage of LHP concrete containing two kinds of MgO at a dosage of (

**a**) 4% and (

**b**) 8%.

Parameter | LHP Cement | M50 | M300 |
---|---|---|---|

Oxides (wt.%) | |||

CaO | 61.9 | 2.4 | 2.6 |

SiO_{2} | 23.9 | 1.3 | 1.4 |

Fe_{2}O_{3} | 4.2 | 0.6 | 0.5 |

MgO | 2.9 | 91.2 | 91.0 |

SO_{3} | 2.3 | 0.1 | 0.1 |

Al_{2}O_{3} | 4.2 | 0.1 | 0.1 |

Loss on ignition | 0.5 | 3.7 | 3.1 |

Physical property | |||

Specific surface area (SSA) by Blaine (m^{2}/kg) | 318 | - | - |

SSA by BET (m^{2}/g) | 0.86 | 31.2 | 12.50 |

Median particle size (D50, μm) | 17.6 | 11.8 | 19.8 |

Specific gravity | 3.22 | 3.51 | 3.50 |

Designations | Water to Binder Ratio | MgO Content (wt.%) |
---|---|---|

LP0 | 0.28 | 0 |

LP4M50 | 0.28 | 4 |

LP8M50 | 0.28 | 8 |

LP4M300 | 0.28 | 4 |

LP8M300 | 0.28 | 8 |

Designations | W/B Ratio | MgO Dosage (wt.%) | Mix Proportions (kg/m^{3}) | Slump (mm) | |||||
---|---|---|---|---|---|---|---|---|---|

Water | Cement | MgO | Sand | Coarse Aggregate | Water Reducing Agent | ||||

LC0 | 0.4 | 0 | 125 | 313 | 0 | 626 | 1330 | 2.2 | 65 |

LC4M50 | 0.4 | 4 | 125 | 300 | 13 | 626 | 1330 | 2.8 | 55 |

LC8M50 | 0.4 | 8 | 125 | 288 | 25 | 626 | 1331 | 3.1 | 51 |

LC4M300 | 0.4 | 4 | 125 | 300 | 13 | 626 | 1330 | 2.5 | 62 |

LC8M300 | 0.4 | 8 | 125 | 288 | 25 | 626 | 1331 | 2.8 | 57 |

Designations | Hydration Age | The Most Probable | Porosity | Pore Size Distribution | ||
---|---|---|---|---|---|---|

(Days) | Pore Diameter (nm) | (%) | <10 nm (%) | 10–50 nm (%) | 50 nm–10 μm (%) | |

LC0 | 7 | 155 | 35.2 | 7.3 | 24.6 | 67.4 |

60 | 72.5 | 24.1 | 14.7 | 46.5 | 38.5 | |

360 | 32.6 | 15.6 | 22.2 | 59.3 | 17.6 | |

LC4M50 | 7 | 121.3 | 31 | 7.9 | 33.2 | 58.2 |

60 | 58.7 | 20.2 | 14.8 | 49.3 | 35.5 | |

360 | 28.2 | 13.2 | 22.5 | 61.2 | 15.3 | |

LC4M300 | 7 | 157.4 | 35.8 | 6.9 | 22.9 | 69.8 |

60 | 65.2 | 22.3 | 13.5 | 49.8 | 36.4 | |

360 | 21.5 | 11.6 | 22.6 | 64.1 | 12.9 | |

LC8M50 | 7 | 102.2 | 26.5 | 7.1 | 39.1 | 52.9 |

60 | 42.5 | 18.7 | 13.5 | 53.2 | 31.6 | |

360 | 25.7 | 11.5 | 21.8 | 63.3 | 13.6 | |

LC8M300 | 7 | 160 | 36.3 | 6.5 | 21.4 | 71.3 |

60 | 60.2 | 20.9 | 12.1 | 53.2 | 34.3 | |

360 | 18.3 | 8.9 | 22.0 | 67.3 | 10.3 |

Designations | Hydration Age (Days) | D_{s} | R^{2} |
---|---|---|---|

LC0 | 7 | 2.721 | 0.953 |

60 | 2.851 | 0.969 | |

360 | 2.934 | 0.936 | |

LC4M50 | 7 | 2.795 | 0.958 |

60 | 2.896 | 0.978 | |

360 | 2.952 | 0.962 | |

LC4M300 | 7 | 2.718 | 0.956 |

60 | 2.876 | 0.983 | |

360 | 2.967 | 0.978 | |

LC8M50 | 7 | 2.839 | 0.956 |

60 | 2.916 | 0.983 | |

360 | 2.969 | 0.979 | |

LC8M300 | 7 | 2.709 | 0.958 |

60 | 2.885 | 0.968 | |

360 | 2.987 | 0.976 |

**Table 6.**Fractal dimensions determined by various fractal models in this study and other literature.

Samples | Fractal Dimension Type | Fractal Dimension Value | Method | Fractal Model | Source |
---|---|---|---|---|---|

LHP concrete (W/B = 0.4) | D_{s} | 2.721–2.934 | MIP | Zhang’s model | In this study |

LHP concrete (W/B = 0.4, 4–8% MgO) | D_{s} | 2.709–2.987 | MIP | Zhang’s model | In this study |

OPC concrete (W/B = 0.4) | D_{s} | 2.822–2.942 | MIP | Zhang’s model | [10] |

LHP concrete (W/B = 0.4, 4–12% SF) | D_{s} | 2.756–2.981 | MIP | Zhang’s model | [10] |

Concrete (W/B = 0.5) | D_{s} | 2.928–2.965 | MIP | Zhang’s model | [59] |

Concrete (W/B = 0.5, 10–30% fly ash) | D_{s} | 2.949–2.996 | MIP | Zhang’s model | [59] |

Concrete (W/B = 0.5, 15–35% GGBS) | D_{s} | 2.906–2.987 | MIP | Zhang’s model | [59] |

Concrete (W/B = 0.5, 5–10% SF) | D_{s} | 2.989–3.000 | MIP | Zhang’s model | [59] |

Concrete | D_{s} | 2.834–2.984 | MIP | Zhang’s model | [98] |

Mortar (W/B = 0.3–0.5) | D_{s} | 2.23–2.35 | MIP | Zhang’s model | [51] |

Mortar (W/B = 0.3–0.5, 70% GGBS) | D_{s} | 2.77–2.89 | MIP | Zhang’s model | [51] |

Pastes | D_{s} | 2.487–2.695 | MIP | Zhang’s model | [97] |

Pastes added fly ash | D_{s} | 2.454–2.782 | MIP | Zhang’s model | [97] |

Pastes | D_{s} | 2.592–2.965 | MIP | Neimark’s model | [97] |

Pastes added fly ash | D_{s} | 2.620–2.997 | MIP | Neimark’s model | [97] |

Notation | Hydration Time (Days) | V_{2.5–50 nm} (%) |
---|---|---|

LC0 | 7 | 31.9 |

60 | 61.2 | |

360 | 81.5 | |

LC4M50 | 7 | 41.1 |

60 | 64.1 | |

360 | 83.7 | |

LC4M300 | 7 | 29.8 |

60 | 63.3 | |

360 | 86.7 | |

LC8M50 | 7 | 46.2 |

60 | 66.7 | |

360 | 85.1 | |

LC8M300 | 7 | 27.9 |

60 | 65.3 | |

360 | 89.3 |

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## Share and Cite

**MDPI and ACS Style**

Wang, L.; Lu, X.; Liu, L.; Xiao, J.; Zhang, G.; Guo, F.; Li, L.
Influence of MgO on the Hydration and Shrinkage Behavior of Low Heat Portland Cement-Based Materials via Pore Structural and Fractal Analysis. *Fractal Fract.* **2022**, *6*, 40.
https://doi.org/10.3390/fractalfract6010040

**AMA Style**

Wang L, Lu X, Liu L, Xiao J, Zhang G, Guo F, Li L.
Influence of MgO on the Hydration and Shrinkage Behavior of Low Heat Portland Cement-Based Materials via Pore Structural and Fractal Analysis. *Fractal and Fractional*. 2022; 6(1):40.
https://doi.org/10.3390/fractalfract6010040

**Chicago/Turabian Style**

Wang, Lei, Xiao Lu, Lisheng Liu, Jie Xiao, Ge Zhang, Fanxing Guo, and Li Li.
2022. "Influence of MgO on the Hydration and Shrinkage Behavior of Low Heat Portland Cement-Based Materials via Pore Structural and Fractal Analysis" *Fractal and Fractional* 6, no. 1: 40.
https://doi.org/10.3390/fractalfract6010040