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Fractal Fract
Special Issues
Fractures and Fragments by Fractal Analysis
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Fractures and Fragments by Fractal Analysis

A special issue of Fractal and Fractional (ISSN 2504-3110). This special issue belongs to the section "Engineering".

Deadline for manuscript submissions: closed (22 May 2022) | Viewed by 9714

Special Issue Editors

Dr. Xiaohan Yang

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Guest Editor
School of Civil, Mining and Environmental Engineering, University of Wollongong, Wollongong, NSW 2522, Australia
Interests: rock mechanics; coal/rock burst; underground Mining
Special Issues, Collections and Topics in MDPI journals
Dr. Lihai Tan

E-Mail Website
Guest Editor
School of Resource Environment and Safety Engineering, University of South China, Hengyang 412001, China
Interests: fractal analysis; rock mechanics; discreet numerical modelling; damage mechanics
Special Issues, Collections and Topics in MDPI journals
Dr. Xin Cai

E-Mail Website
Guest Editor
School of Resources and Safety Engineering, Central South University, Changsha 410083, China
Interests: rock mechanics; rock dynamics; fracture; rock-water Interaction
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear colleagues,

The statistical and mathematical analysis of rock, coal and other rock-like brittle material has been a fundamental way to describe the fracture evolution and fragmentation characteristics during the engineering structure failure process. The theoretical model of fracture length, fracture distribution, fragment size etc. has been established based on fractal theory, which enable a better understanding of failure mechanism and energy dissipation of engineering instability in mining and tunneling engineering. The further application of fractal theory in fractures and fragments analysis will benefit the research of engineering instability (such as rock burst, coal burst and slope instability) and engineering practice.

This special issue would like to invite any submission related to fractures and fragments by fractal analysis in tunnelling, mining, resources and civil engineering. Particularly, the following topics are highly encouraged:

  • Fractal analysis of fracture pattern and fragmentation characteristics of brittle/dynamic failure
  • Analytical tools application for determination and observation of fractal such as DIC (digital image correlation), AE (acoustic emission) and CT (computed tomography)
  • Fundamental theory to explain the fractal behaviour of brittle materials from mathematical and physical aspects such as fractal of micro structure
  • Application of fractal analysis to predict the fracture evolution and fragments characteristics of engineering dynamic hazards

Dr. Xiaohan Yang
Dr. Lihai Tan
Dr. Xin Cai
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Fractal and Fractional is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2700 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • fracture
  • fragments
  • rock and coal
  • rock mechanics
  • engineering application

Published Papers (5 papers)

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Research

19 pages, 9291 KiB  
Article
Mechanical Properties and Chloride Penetration Resistance of Copper Slag Aggregate Concrete
by Lu Zhang, Hongyu Gong, Jianping Liu and Haizhou Li
Fractal Fract. 2022, 6(8), 427; https://0-doi-org.brum.beds.ac.uk/10.3390/fractalfract6080427 - 04 Aug 2022
Cited by 4 | Viewed by 1419
Abstract
The authors of this paper systematically studied the mechanical properties and durability of concrete prepared with copper slag instead of natural aggregates. An analysis index was used to assess compressive strength, and a statistical method was used to establish a mix proportion design [...] Read more.
The authors of this paper systematically studied the mechanical properties and durability of concrete prepared with copper slag instead of natural aggregates. An analysis index was used to assess compressive strength, and a statistical method was used to establish a mix proportion design theory of copper slag aggregate concrete. The analysis was used to quantify the effect of copper slag aggregate concrete on resistance to chloride ion migration. Combined with the morphological analysis of SEM images and fractal calculations, the tests were used to explain the improvement mechanism of copper slag as a fine aggregate on concrete’s mechanics and durability from the microscopic mechanism perspective. The results showed that replacing a natural sand fine aggregate with copper slag improved the compressive strength of concrete, and the optimum replacement rate was found to be 40%. The influence of the water–cement ratio on the strength of copper slag aggregate concrete was exceptionally conspicuous—the more significant the water–cement proportion was the lower the compressive strength of the concrete. The optimum dosage of the water-reducing agent was found to be 3.8 kg/m3. A rapid chloride ion migration test and potential corrosion analysis showed that copper slag aggregate concrete’s initial density and corrosion resistance were higher than those of natural aggregate concrete. Electrochemical impedance spectroscopy analysis results showed that the structural concrete comprising copper slag aggregate instead of natural sand had a better anticorrosion effect on embedded steel bars. SEM morphology and fractal dimension analyses showed that the incorporation of steel slag aggregate decreased the initial damage to the concrete internal section. Full article
(This article belongs to the Special Issue Fractures and Fragments by Fractal Analysis)
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17 pages, 7041 KiB  
Article
Discrimination of Microseismic Events in Coal Mine Using Multifractal Method and Moment Tensor Inversion
by Jiliang Kan, Linming Dou, Jiazhuo Li, Shikang Song, Kunyou Zhou, Jinrong Cao and Jinzheng Bai
Fractal Fract. 2022, 6(7), 361; https://0-doi-org.brum.beds.ac.uk/10.3390/fractalfract6070361 - 29 Jun 2022
Cited by 4 | Viewed by 1317
Abstract
Discrimination of various microseismic (MS) events induced by blasting and mining in coal mines is significant for the evaluation and forecasting of rock bursts. In this paper, multifractal and moment tensor inversion methods were used to investigate the waveform characteristics and focal mechanisms [...] Read more.
Discrimination of various microseismic (MS) events induced by blasting and mining in coal mines is significant for the evaluation and forecasting of rock bursts. In this paper, multifractal and moment tensor inversion methods were used to investigate the waveform characteristics and focal mechanisms of different MS events in a more quantitative way. The multifractal spectrum calculation results indicate that the three types of MS waveform have different distribution ranges in the multifractal parameters of ∆α and Δf(α). The results show that the blasting schemes also have a great influence on MS waveform characteristics. Consequently, the multifractal parameters of ∆α and Δf(α) can be used to discriminate different MS events. Further, the focal mechanisms of MS events were calculated by seismic moment tensor inversion. The results show that an explosion is not the dominant mechanism of deep-hole blasting MS events, and the CLVD and DC components account for an important proportion, indicating that some additional processes occur during blasting. Moreover, the coal-rock fracture MS events are characterized by compression implosion or compression/shear implosion mixed focal mechanisms, while the overburden movement MS events are tensile explosion or tensile/shear explosion mixed focal mechanisms. The focal mechanisms and nodal plane parameters have close relationships with the inducing factors and occurrence processes of MS events. Full article
(This article belongs to the Special Issue Fractures and Fragments by Fractal Analysis)
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18 pages, 7289 KiB  
Article
Effect of Heterogeneity on the Extension of Ubiquitiformal Cracks in Rock Materials
by Beibei Yang, Xiaoshan Cao, Tielin Han, Panfeng Li and Junping Shi
Fractal Fract. 2022, 6(6), 317; https://0-doi-org.brum.beds.ac.uk/10.3390/fractalfract6060317 - 05 Jun 2022
Cited by 3 | Viewed by 1303
Abstract
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 [...] Read more.
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. Full article
(This article belongs to the Special Issue Fractures and Fragments by Fractal Analysis)
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17 pages, 4686 KiB  
Article
Dynamic Response and Damage Regularity of Sandstone with Different Moisture States under Cyclic Loading
by Fujiao Chu, Dunwen Liu, Xiaojun Zhang, Hui Yu and Guangli Zhu
Fractal Fract. 2022, 6(4), 226; https://0-doi-org.brum.beds.ac.uk/10.3390/fractalfract6040226 - 18 Apr 2022
Cited by 3 | Viewed by 1809
Abstract
In the process of geotechnical engineering excavation, wet and water-filled rock masses are inevitable. To obtain the mechanical properties of these rocks, indoor tests are required, and most of the rock tests rock tests are dry or nearly dry. They cannot really reflect [...] Read more.
In the process of geotechnical engineering excavation, wet and water-filled rock masses are inevitable. To obtain the mechanical properties of these rocks, indoor tests are required, and most of the rock tests rock tests are dry or nearly dry. They cannot really reflect the true nature of the rock, let alone its nature under a dynamic load. The rock was repeatedly impacted during the blasting excavation process. To determine the mechanical response characteristics and damage evolution of rocks with different moisture states under cyclic dynamic loads, rock samples with three saturation levels were prepared. In the experiment, the Hopkinson pressure bar equipment was utilized to perform five cycles of impact with the same incident energy, and the dynamic response of rocks with different impact times was recorded. Nuclear magnetic resonance technology was employed to obtain the change law of the pores of rock specimens after impact, and the cumulative damage rules of rock were combined with the fractal theory. From the experiments, it can be observed that the stress-strain curves of all rock samples are similar, in that they all have stress addition and unloading stages. The peak stress is proportional to the impact time and moisture content, whereas the opposite is true for the peak strain. After the impact, the small and large pores closed and increased, respectively. The porosity and porosity change rate increased with an increase in the impact time. With an increase in moisture content, this trend is more obvious. It can be observed via magnetic resonance imaging that the internal fractures of the water-bearing rock are obvious after multiple impacts. In particular, the saturated rock specimens exhibited severe damage. Fractal analysis of the NMR figures revealed that after three impact times, the fractal dimension change in the water-bearing rock samples was not obvious. This phenomenon indicated that a macro gap appeared. The fractal dimensions of the dry rock samples continued to increase, and the internal damage was less obvious. Full article
(This article belongs to the Special Issue Fractures and Fragments by Fractal Analysis)
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19 pages, 4247 KiB  
Article
A Scaled Boundary Finite-Element Method with B-Differentiable Equations for 3D Frictional Contact Problems
by Binghan Xue, Xueming Du, Jing Wang and Xiang Yu
Fractal Fract. 2022, 6(3), 133; https://0-doi-org.brum.beds.ac.uk/10.3390/fractalfract6030133 - 27 Feb 2022
Cited by 15 | Viewed by 2313
Abstract
Contact problems are among the most difficult issues in mathematics and are of crucial practical importance in engineering applications. This paper presents a scaled boundary finite-element method with B-differentiable equations for 3D frictional contact problems with small deformation in elastostatics. Only the boundaries [...] Read more.
Contact problems are among the most difficult issues in mathematics and are of crucial practical importance in engineering applications. This paper presents a scaled boundary finite-element method with B-differentiable equations for 3D frictional contact problems with small deformation in elastostatics. Only the boundaries of the contact system are discretized into surface elements by the scaled boundary finite-element method. The dimension of the contact system is reduced by one. The frictional contact conditions are formulated as B-differentiable equations. The B-differentiable Newton method is used to solve the governing equation of 3D frictional contact problems. The convergence of the B-differentiable Newton method is proven by the theory of mathematical programming. The two-block contact problem and the multiblock contact problem verify the effectiveness of the proposed method for 3D frictional contact problems. The arch-dam transverse joint contact problem shows that the proposed method can solve practical engineering problems. Numerical examples show that the proposed method is a feasible and effective solution for frictional contact problems. Full article
(This article belongs to the Special Issue Fractures and Fragments by Fractal Analysis)
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