Study on the Influence of Three Factors on Mass Loss and Surface Fractal Dimension of Concrete in Sulfuric Acid Environments

Effect of Heterogeneity on the Extension of Ubiquitiformal Cracks in Rock Materials

Fracture energy, as an important characteristic parameter of the fracture properties of materials, has been extensively studied by scholars. However, less research has been carried out on ubiquitiformal fracture energy and the main method used by scholars is the uniaxial tensile test. In this paper, based on previous research, the first Brazilian splitting test was used to study the ubiquitiformal crack extension of slate and granite, and the complexity and ubiquitiformal fracture energy of rock material were obtained. The heterogeneity of the material was then characterized by the Weibull statistical distribution, and the cohesive model is applied to the ABAQUS numerical software to simulate the effect of heterogeneity on the characteristics of ubiquitiformal cracks. The results demonstrate that the ubiquitiformal complexity of slate ranges from 1.54 to 1.60, and that of granite ranges from 1.58 to 1.62. The mean squared deviations of the slate and granite ubiquitiformal fracture energy are the smallest compared with the other fracture energies, which are 0.038 and 0.037, respectively. When the homogeneity of the heterogeneous model is less than 1.5, its heterogeneity has a greater influence on the Brazilian splitting strength, and the heterogeneity of the rock is obvious. However, when the homogeneity is greater than five, the effect on the Brazilian splitting strength is much less, and the Brazilian splitting strength tends to be the average strength. Therefore, it is particularly important to study the fracture problem of cracks from the nature of the material structure by combining the macroscopic and mesoscopic views through the ubiquitiform theory.

Map of a Bending Problem for Self-Similar Beams into the Fractal Continuum Using the Euler–Bernoulli Principle

The bending of self-similar beams applying the Euler–Bernoulli principle is studied in this paper. A generalization of the standard Euler–Bernoulli beam equation in the FdH3 continuum using local fractional differential operators is obtained. The mapping of a bending problem for a self-similar beam into the corresponding problem for a fractal continuum is defined. Displacements, rotations, bending moments and shear forces as functions of fractal parameters of the beam are estimated, allowing the mechanical response for self-similar beams to be established. An example of the structural behavior of a cantilever beam with a load at the free end is considered to study the influence of fractality on the mechanical properties of beams.

Editorial for Special Issue “Fractal and Fractional in Cement-Based Materials”

Cement-based materials, including cement paste, mortar, and concrete, are the most widely used construction materials in the world [...]

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

Currently, low heat Portland (LHP) cement is widely used in mass concrete structures. The magnesia expansion agent (MgO) can be adopted to reduce the shrinkage of conventional Portland cement-based materials, but very few studies can be found that investigate the influence of MgO on the properties of LHP cement-based materials. In this study, the influences of two types of MgO on the hydration, as well as the shrinkage behavior of LHP cement-based materials, were studied via pore structural and fractal analysis. The results indicate: (1) The addition of reactive MgO (with a reactivity of 50 s and shortened as M50 thereafter) not only extends the induction stage of LHP cement by about 1–2 h, but also slightly increases the hydration heat. In contrast, the addition of weak reactive MgO (with a reactivity of 300 s and shortened as M300 thereafter) could not prolong the induction stage of LHP cement. (2) The addition of 4 wt.%–8 wt.% MgO (by weight of binder) lowers the mechanical property of LHP concrete. Higher dosages of MgO and stronger reactivity lead to a larger reduction in mechanical properties at all of the hydration times studied. M300 favors the strength improvement of LHP concrete at later ages. (3) M50 effectively compensates the shrinkage of LHP concrete at a much earlier time than M300, whereas M300 compensates the long-term shrinkage more effectively than M50. Thus, M300 with an optimal dosage of 8 wt.% is suggested to be applied in mass LHP concrete structures. (4) The addition of M50 obviously refines the pore structures of LHP concrete at 7 days, whereas M300 starts to refine the pore structure at around 60 days. At 360 days, the concretes containing M300 exhibits much finer pore structures than those containing M50. (5) Fractal dimension is closely correlated with the pore structure of LHP concrete. Both pore structure and fractal dimension exhibit weak (or no) correlations with shrinkage of LHP concrete.

Investigation and Application of Fractal Theory in Cement-Based Materials: A Review

Cement-based materials, including cement and concrete, are the most widely used construction materials in the world. In recent years, the investigation and application of fractal theory in cement-based materials have attracted a large amount of attention worldwide. The microstructures of cement-based materials, such as the pore structures, the mesostructures, such as air voids, and the morphological features of powders, as well as the fracture surfaces and cracks, commonly present extremely complex and irregular characteristics that are difficult to describe in terms of geometry but that can be studied by fractal theory. This paper summarizes the latest progress in the investigation and application of fractal theory in cement-based materials. Firstly, this paper summarizes the principles and classification of the seven fractal dimensions commonly used in cement-based materials. These fractal dimensions have different physical meanings since they are obtained from various testing techniques and fractal models. Then, the testing techniques and fractal models for testing and calculating these fractal dimensions are introduced and analyzed individually, such as the mercury intrusion porosimeter (MIP), nitrogen adsorption/desorption (NAD), and Zhang’s model, Neimark’s model, etc. Finally, the applications of these fractal dimensions in investigating the macroproperties of cement-based materials are summarized and discussed. These properties mainly include the mechanical properties, volumetric stability, durability (e.g., permeability, frost and corrosion resistance), fracture mechanics, as well as the evaluation of the pozzolanic reactivity of the mineral materials and the dispersion state of the powders.