3D Fractal Dimension Research Articles

The Control of Isolated Kerogen on Pore Structure and Heterogeneity in Marine-Continental Transitional Shale: A Case Study on the Taiyuan Formation, Northern Ordos Basin

Accurately determining the pore structure and heterogeneity characteristics of marine-continental transitional shale in the Taiyuan Formation is crucial for evaluating the shale gas resources in the northern Ordos Basin. However, the studies on pore characteristics and heterogeneity of marine-continental transitional shales and isolated kerogen are limited. This study collected Taiyuan Formation shale in the northern Ordos Basin, and corresponding kerogen isolated from shale and used N2 and CO2 adsorption experiment and Frenkel–Halsey–Hill and Volume-Specific Surface Area model to investigate the pore structure and heterogeneity of both. The results show that the isolated kerogen is dominated by micropores, and the micropore’s specific surface area and volume are 4.7 and 3.5 times the corresponding shale, respectively. In addition, the microporous heterogeneity of the isolated kerogen is stronger than that of shale, while the mesoporous heterogeneity is exactly the opposite. Meanwhile, the micropores fractal dimension Dm is positively correlated with organic matter (OM) content, while mesopores fractal dimension D1 and D2 are negatively linearly correlated with TOC content and have no significant relationship with clay mineral and quartz content (but show a significant positive correlation with illite and illite/smectite mixed layer). Isolated kerogen plays an important role in the pore (especially micropores) heterogeneity of shale, while other minerals (such as clay minerals) have a controlling effect on the mesopores heterogeneity of shale. Compared with marine shale, the marine-continental transitional shale of the Taiyuan Formation has a lower fractal dimension and better connectivity, which is conducive to shale gas seepage and migration. The final result can provide a significant basis for the reserve evaluation and the optimization of desert areas in the marine-continental transitional shale gas in the northern Ordos Basin.

Investigation of the Impact of Moisture in Various States on the Adsorption of CH4, N2, and CO2 by Coal.

To investigate the impact of moisture in various states on the adsorption of CH4, N2, and CO2 by coal, this study conducted isothermal adsorption experiments on dry coal for moisture and on coal with varying moisture content for CH4, N2, and CO2. The results revealed that coal moisture adsorption progresses through four stages: monolayer adsorption, multilayer adsorption, cluster formation, and condensation into free moisture filling pores. The presence of moisture in coal varies across these stages, with its impact on CH4, N2, and CO2 adsorption decreasing as moisture content increases. As the moisture content rises, the adsorption constants (a and b values) progressively decline and eventually level off. Based on differences in coal moisture states, delineated by a relative humidity of 0.50 (corresponding to a moisture content of 2.39% in experimental samples), adsorption potential theory identified low moisture content stages where the monolayer and multilayer adsorption potentials for moisture (E1 = 4.99 kJ/mol, E2 = 39.71 kJ/mol) exceeded those for CH4, N2, and CO2, suggesting competitive adsorption effects. In the high-water content stage, the mesoporous structural fractal dimension D2 of the coal samples was found to be 2.77, nearly reaching 3, as determined through liquid nitrogen adsorption experiments and fractal dimension theory. This suggests that the intricate pore structure leads to water condensation, free water formation, and pore blockage, making it the primary factor influencing the adsorption of CH4, N2, and CO2 in coals, which is inherently linked to the characteristics of coal.

Fractal Analysis of Particle Size and Morphology in Single-Particle Breakage Based on 3D Images

The accurate modeling of single-particle breakage based on three-dimensional (3D) images is crucial for understanding the particle-level mechanics of granular materials. This study aims to propose a systematic framework incorporating single-particle breakage experiments and numerical simulations based on a novel 3D particle reconstruction technique for fractal analysis of particle size and morphology in single-particle breakage. First, the vision foundation model is used to generate accurate particles from 3D images. The numerical approach is validated by simulating the single-particle breakage test with multiple Fujian sand particles. Then, the breakage processes of reconstructed sand particles under axial compression are numerically modeled. The relationship between 3D fractal dimensions and particle size, particle crushing strength, and morphology is meticulously investigated. Furthermore, the implications of these relationships on the particle breakage processes are thoroughly discussed, shedding light on the underlying mechanisms that govern particle breakage. The framework offers an effective way to investigate the breakage behavior of single sand particles, which will enhance understanding of the mechanism of the whole particle breakage process.

Fractal dimension and lacunarity measures of glioma subcomponents are discriminative of the grade of gliomas and IDH status.

Since the overall glioma mass and its subcomponents-enhancing region (malignant part of the tumor), non-enhancing (less aggressive tumor cells), necrotic core (dead cells), and edema (water deposition)-are complex and irregular structures, non-Euclidean geometric measures such as fractal dimension (FD or "fractality") and lacunarity are needed to quantify their structural complexity. Fractality measures the extent of structural irregularity, while lacunarity measures the spatial distribution or gaps. The complex geometric patterns of the glioma subcomponents may be closely associated with the grade and molecular landscape. Therefore, we measured FD and lacunarity in the glioma subcomponents and developed machine learning models to discriminate between tumor grades and isocitrate dehydrogenase (IDH) gene status. 3D fractal dimension (FD3D) and lacunarity (Lac3D) were measured for the enhancing, non-enhancing plus necrotic core, and edema-subcomponents using preoperative structural-MRI obtained from the The Cancer Genome Atlas (TCGA) and University of California San Francisco Preoperative Diffuse Glioma MRI (UCSF-PDGM) glioma cohorts. The FD3D and Lac3D measures of the tumor-subcomponents were then compared across glioma grades (HGGs: high-grade gliomas vs. LGGs: low-grade gliomas) and IDH status (mutant vs. wild type). Using these measures, machine learning platforms discriminative of glioma grade and IDH status were developed. Kaplan-Meier survival analysis was used to assess the prognostic significance of FD3D and Lac3D measurements. HGG exhibited significantly higher fractality and lower lacunarity in the enhancing subcomponent, along with lower fractality in the non-enhancing subcomponent compared to LGG. This suggests that a highly irregular and complex geometry in the enhancing-subcomponent is a characteristic feature of HGGs. A comparison of FD3D and Lac3D between IDH-wild type and IDH-mutant gliomas revealed that mutant gliomas had ~2.5-fold lower FD3D in the enhancing-subcomponent and higher FD3D with lower Lac3D in the non-enhancing subcomponent, indicating a less complex and smooth enhancing subcomponent, and a more continuous non-enhancing subcomponent as features of IDH-mutant gliomas. Supervised ML models using FD3D from both the enhancing and non-enhancing subcomponents together demonstrated high-sensitivity in discriminating glioma grades (~97.9%) and IDH status (~94.4%). A combined fractal estimation of the enhancing and non-enhancing subcomponents using MR images could serve as a non-invasive, precise, and quantitative measure for discriminating glioma grade and IDH status. The combination of 2-hydroxyglutarate-magnetic resonance spectroscopy (2HG-MRS) with FD3D and Lac3D quantification may be established as a robust imaging signature for glioma subtyping.

Influence of in-situ lunar temperature on the pore structure and solid phases of alkali-activated lunar regolith simulant

The construction of extraterrestrial bases has become an indispensable step in the active exploration of deep space. In this study, alkali-activated lunar regolith simulant (AALRS) activated by sodium hydroxide (SH) and sodium silicate (SS) were prepared and then cured at various lunar temperatures. The compressive strength was tested, and the pore structure characteristics were characterized using mercury intrusion porosimetry (MIP), followed by further in-depth quantitative analysis through fractal theory. The solid phases were characterized using thermogravimetry analysis (TGA) and scanning electron microscopy (SEM). It is found that all the fractal curves are divided into three regions, and the fractal dimensions in all regions are between 2 and 3, suggesting the pores of AALRS paste always have self-similar physical significance. The fractal dimension D1 of the small pore is the largest, followed by fractal dimension D3 of the great pore and fractal dimension D2 of the middle pore. The increase in modulus and temperature leads to an increase in the pore surface area, fractal dimension, amount of N-A-S-H gel and compressive strength and a decrease in total pore volume and characteristic pore diameter, which is mainly attributed to the nucleation effect of soluble Si. The turning pore diameter at the micrometer scale and excessive porosity of AALRS paste, which is distinctly different from that of common cementitious materials, demonstrates looser pore structure of AALRS paste. Based on these results, the influence mechanism of in-situ lunar temperature on the performance of AALRS paste is profoundly discussed and elucidated, which provides a deep understanding of designing and tailoring the various properties of AALRS material.

Comprehensive Characterization and Metamorphic Control Analysis of Full Apertures in Different Coal Ranks within Deep Coal Seams

The pore fracture structure of deep coal reservoirs is crucial for evaluating the potential of deep coalbed methane resources, conducting exploration and development, and controlling coal mine gas disasters. Mercury intrusion porosimetry, the liquid nitrogen method, and the low-temperature carbon dioxide adsorption method were used to study the full pore size structure and pore fractal characteristics of different coal grades in deep coal and comprehensively characterize the pore structure of kilometer-level coal mining. The sponge, Frenkel–Halsey–Hill (FHH), and density function models were applied to comprehensively analyze the pore complexity of coal, and the influence of metamorphic degree on pore size structure was evaluated. The distribution relationship of pore volume in different stages of coal samples was macropore→mesopore→micropore, and macropores had the best connectivity. Micropores and mesopores had the largest specific surface area, and the development of micropores and microcracks controlled the deep gas adsorption performance. The micropore volume and specific surface area both revealed a nonlinear decreasing trend with the increase in volatile matter, and coal metamorphism promoted the development of micropores. The pore volume and specific surface area of mesopores and macropores decreased first and then increased in a “U” shape with increasing volatile matter. In contrast, the fractal dimension D1 revealed an inverted U shape with increasing volatile matter, followed by a decrease. The D2 value decreased nonlinearly with increasing volatile matter, whereas the D3 value increased nonlinearly with increasing volatile matter. The degree of metamorphism increased, and the microporous structure became more regular.

3D characteristic indicator analysis and comprehensive evaluation of manufactured sand particles used in high-performance concrete

Two-dimensional particle morphology indices face challenges in accurately depicting the characteristics of three-dimensional (3D) manufactured sand (MS), which does not effectively guide the selection of MS for high-performance concrete (HPC). This study aimed to obtain a quantified comprehensive evaluation of actual MS particle groups with specific gradations by thoroughly analysing 3D geometric characteristics. Two representative MS samples were selected for exploration, and river sand (RS) was used as the control. A random selection of sand particles was screened on six sieve levels ranging from 0.15 mm to 4.75 mm. Using X-ray computed tomography and associated image processing technologies, 3D models of these particles were generated, and MATLAB was used to extract their 3D morphology information. Subsequently, the change rules and validity of current 3D particle morphology indicators were examined, focusing on shape, angularity, and texture. Moreover, a comprehensive morphology index, Cm, was proposed by considering the effects of gradation and particle shape classification. The results showed that shape indices more accurately reflected particle characteristics, notably, a higher proportion of spheroid particles, a lower aspect ratio, and greater sphericity correlated with improved particle shape; contrary to traditional beliefs, the angularity index suggested that greater roundness did not necessarily equate to more rounded particles owing to the influence of the proportion of spheroid and cubic particles; meanwhile, texture indices showed minimal difference in the mean values of the 3D fractal dimension for the three types of sand. The proposed index Cm effectively differentiated the particle morphology states of the three sands, with higher Cm values indicating superior particle morphology. The smaller the difference between the Cm values of MS and RS, the better substitute of MS for RS.

Micro-morphology and fractal characteristics of pore structure of aeolian sand concrete under long-term semi-immersion with chloride solution

To investigate the influence of chloride exposure on hydraulic concrete, we investigated the microstructural changes and pore evolution of aeolian sand concrete (ASC) during prolonged semi-immersion in chloride solution. Our analysis included examining the mass loss rate, relative dynamic elastic modulus, and maximum depth of chloride erosion. Utilizing scanning electron microscopy (SEM), X-ray diffraction (XRD), and nuclear magnetic resonance (NMR), we assessed the microscopic morphology and pore structure evolution. Additionally, we employed fractal theory to evaluate pore structure heterogeneity in ASC before and after exposure to chloride erosion. After 450 days of chloride erosion, ASC displayed minimal changes in mass loss rate and relative dynamic elastic modulus, with a maximum erosion depth of 9.8 mm. Chlorides adhered to the immersed end at the concrete's base and migrated from the surface to the exposed top end during erosion. The erosion depth at the top end ranged from 23.9 % to 25.9 % of that at the bottom end. Within ASC, hydration products reacted with chlorides, resulting in the formation of Friedel's salt, a characteristic corrosion crystal. Following erosion, the total porosity of ASC increased, accompanied by shifts in pore size distribution. The internal structure of ASC underwent distinctive evolution, transitioning from small to large pores. ASC consistently exhibited fractal properties both before and after erosion. The fractal dimension D1 demonstrated an inverse relationship with pores of radius (r) less than 0.01 μm, while D2 was directly proportional to pores with r ≤ 0.01 μm and 0.01 <r ≤ 0.1 μm, and inversely proportional to pores with 1 <r ≤ 10 μm and r > 10 μm. This study significantly contributes to the theoretical understanding of ASC's endurance mechanisms in chloride environments.

A quantitative study of the microstructure of Indian Gondwana shale: a fractal and algebraic topology approach

This paper covers a novel micro-level application of image processing in understanding the topological and petrophysical properties of Indian Gondwana shale using X-ray computed microtomography images. The complexity and randomness in the pore system are explained through the concept of fractal dimension (FD). In this paper, a quantitative analysis of 2D and 3D fractal dimensions of pores, grains and interfaces was performed for Indian Gondwana shale, using the box-counting method. A pore network is formed by the connection of many subpore clusters, each with a different volume. Hence, an image segmentation algorithm was applied to label different subclusters, and subsequently an analysis of FD was carried out on such subclusters of pores and grains. We implemented a novel application of Betti numbers (B0, B1 and B2) and Euler characteristics on our sample and calculated the possible flow channels of the sample. The FD of grains was found to be greater than the FD of the pore–grain interfaces, while the FD of pores was found to have the smallest value. Consequently, we also observed how the FD of both pores and grains was majorly controlled by the largest subcluster, and during fluid intrusion we observed a significant decrease in the FD of pores. Finally, the pore network with a larger B0 and larger difference of B1 was proved to be best for the storage of hydrocarbons and for fluid movement along more flow channels.

Digital reconstruction of three‐dimensional contours and its application to microstructural evaluation of postblast rock fissure surfaces

AbstractFracture surface contour study is one of the important requirements for characterization and evaluation of the microstructure of rocks. Based on the improved cube covering method and the 3D contour digital reconstruction model, this study proposes a quantitative microstructure characterization method combining the roughness evaluation index and the 3D fractal dimension to study the change rule of the fracture surface morphology after blasting. This method was applied and validated in the study of the fracture microstructure of the rock after blasting. The results show that the fracture morphology characteristics of the 3D contour digital reconstruction model have good correlation with the changes of the blasting action. The undulation rate of the three‐dimensional surface profile of the rock is more prone to dramatic rise and dramatic fall morphology. In terms of tilting trend, the tilting direction also shows gradual disorder, with the tilting angle increasing correspondingly. All the roughness evaluation indexes of the rock fissure surface after blasting show a linear and gradually increasing trend as the distance to the bursting center increases; the difference between the two‐dimensional roughness evaluation indexes and the three‐dimensional ones of the same micro‐area rock samples also becomes increasingly larger, among which the three‐dimensional fissure roughness coefficient JRC and the surface roughness ratio Rs display better correlation. Compared with the linear fitting formula of the power function relationship, the three‐dimensional fractal dimension of the postblast fissure surface is fitted with the values of JRC and Rs, which renders higher correlation coefficients, and the degree of linear fitting of JRC to the three‐dimensional fractal dimension is higher. The fractal characteristics of the blast‐affected region form a unity with the three‐dimensional roughness evaluation of the fissure surface.

Pore heterogeneity analysis and control mechanisms in Cambrian shale of the Shuijingtuo Formation, Yichang area, China

This study focuses on understanding the fractal characteristics and controlling factors of micropore structures within organic-rich shale of the Cambrian Shuijingtuo Formation in the Yichang area of Hubei Province. Mineralogy, petrology, and organogeochemical characteristics were confirmed through comprehensive testing methods, including whole-rock X-ray diffraction and organic geochemical analyses. Additional experiments included low-temperature carbon dioxide adsorption, low-temperature nitrogen adsorption, and high-pressure mercury injection. Fractal dimensions of micropores, mesopores, and macropores were calculated using the V-S, FHH, and MENGER sponge models, respectively. Results indicate that the Cambrian Shuijingtuo Formation represents a typical deposit from an alkaline water body, resulting in high-calcareous shale. Fractal dimensions were as follows: micropores (D1) ranged from 2.1138 to 2.3475 (average 2.2342), mesopores (D2) ranged from 2.5327 to 2.7162 (average 2.6171), and macropores (D3) ranged from 2.7361 to 2.9316 (average 2.82905). Correlations were observed between total organic carbon (TOC) content and Ro with D1 and D2 (positive) and D3 (negative). Shale pore volume and specific surface area exhibited positive correlations with D1 and D2 but negative correlations with D3. High bio-deposited silica positively influenced micropore and mesopore development, while clay mineral compaction and dehydration transformations favored macropore development. Carbonate minerals primarily contributed to regular macropores, with complex correlations involving fractal dimensions D1, D2, and D3. The research results provide theoretical support for analyzing pore fractal characteristics of shallow old Marine shale reservoirs and the prediction and development plan of high-quality reservoirs of the Shuijingtuo Formation in the Yichang area.

Fractal Characteristics and Microstructure of Coal with Impact of Starch-Polymerized Aluminum Sulfate Fracturing Fluids

The degree of irregularity and complexity of the pore structure are comprehensively reflected in the fractal dimension. The porosity of coal was determined by its fractal dimension, where a larger dimension indicates a lower porosity. Fractal theory and the Frenkel–Halsey–Hill (FHH) model were applied to explore the variation rules of concentration on functional groups and pore structure in this study. Combined with infrared spectroscopy (FTIR) and low-temperature nitrogen adsorption, a starch-polymerized aluminum sulfate composite fracturing fluid was prepared, which plays an important role in methane adsorption and permeability of coal samples. The test results showed that, compared with the original coal, the pore volume and specific surface area of each group of coal samples were reduced, the average pore diameter was initially enlarged and then declined, and fractal dimension D1 dropped by 5.4% to 15.4%, while fractal dimension D2 gained 1.2% to 7.9%. Moreover, the nitrogen adsorption of each group of coal samples was obviously lower than the original coal, and the concentration of starch-polymerized aluminum sulfate solution existed at a critical optimal concentration for the modification of the coal samples, and the nitrogen adsorption reached a minimum value of 0.6814 cm3/g at a concentration of 10%. The novel composite solution prepared by the combination of starch and flocculant in this paper enhanced the permeability of the coal seam, which is of great significance in improving the efficiency of coalbed methane mining.

Microscopic pore structure characteristics and controlling factors of marine shale: a case study of Lower Cambrian shales in the Southeastern Guizhou, Upper Yangtze Platform, South China

A systematic study of the pore structure characteristics of Lower Cambrian shales in the southeastern Upper Yangtze Platform, was conducted using organic geochemistry, mineralogy, nitrogen adsorption, physical property analysis, and scanning electron microscopy. The results indicate that: 1) The Total organic carbon (TOC) content shows a strong correlation with quartz and clay minerals. Shales with low TOC content and rich in clay minerals primarily exhibit slit-shaped and narrow slit-like inter-clay particle pores with pore size distribution is dominated by mesopores and macropores. Shales with high TOC content predominantly feature narrow slit-like and ink bottle-shaped pores with pore size distribution dominated by micropores and mesopores. 2) Shale pore structures vary significantly under different gas content and preservation conditions. Shales under favorable preservation conditions exhibit a relatively “high porosity, low permeability, and high gas content” pattern, with well-developed organic pores and a strong pore-permeability correlation. In contrast, shales under unfavorable preservation conditions appear dense, with excessively developed fractures increasing both average pore size and local permeability. The pore-permeability correlation is weak, presenting a relatively “low porosity, high permeability, and low gas content” pattern. 3) TOC content plays a crucial role in controlling pore structure, showing overall positive correlations with pore volume, specific surface area, and porosity, and negative correlations with pore size. High TOC content enhances shale plasticity, resulting in lower pore diameters. Factors such as compaction and unfavorable preservation conditions lead to the shrinkage, collapse, and closure of some narrow pore throats, negatively impacting pore volume, specific surface area, brittleness, and fractal dimension, exhibiting a negative correlation with TOC content. 4) The pore structure of Lower Cambrian shales is complex, with fractal dimensions D1 and D2 exhibiting negative correlations with average pore size and positive correlations with TOC, specific surface area, and total pore volume. A high D1 value indicates well-preserved nanoscale pore surface structures with low complexity, suggesting minimal alteration by external fluids and better shale gas preservation. D1 serves as an indicator for shale gas content and preservation conditions. D2 shows better correlations with various pore structure parameters, making it suitable for characterizing pore structures.

Experimental investigation on pore characteristics of vitrain and durain in low rank coal based on fractal theory

The macro petrographic compositions and its pore characteristics of coal reservoir play critical role in the accumulation and development of coalbed methane (CBM). In this paper, the pore characteristics of vitrain and durain were analyzed through the experiment and fractal theory. The results indicated that the micropores and microfractures develop in vitrain, and that transitional pores develop in durain. The pore volume and specific surface area (SSA) of vitrain are larger than those of durain, with the micropore SSA of vitrain being 35% higher than that of durain. The threshold pressure and tortuosity of vitrain are greater than that of durain, but the mean pore size of vitrain is smaller than that of durain. The fractal dimension D1 of vitrain is greater than that of durain, while the fractal dimension D2 is opposite, indicating that the pore surface of vitrain is coarser, and the pore structure of durain is more complex. The fractal dimension Dk of vitrain is larger than that of durain, the mean fractal dimension Ds of vitrain is smaller than that of durain, which shows that the diffusivity of vitrain is weak but the seepage capacity is strong due to the developed fractures. The difference in material composition and pore characteristics between vitrain and durain provides a new understanding for the development of CBM in low rank coal.

Characterization of seismicity and precursor monitoring in northern Baja California using RESNOM data

Northern Baja California, Mexico, is part of the boundary between the Pacific and North American plates, and the relative motion between these plates causes seismicity that has attained a recorded magnitude M7.3. This seismicity represents a hazard for towns and cities located in this area and, in order to be able to contribute to the hazard estimation, we propose to establish monitoring of possible precursors to major earthquakes.We will use data from the RESNOM seismological network, operated by CICESE, to monitor the area between longitudes −117.4° and −114.5°, and latitudes 30.5° and 33.2°.Since the study area presents a complex array of seismogenic regions, we define three regions for monthly precursor monitoring, based on long-term epicentral spatial distributions, together with geological and tectonic considerations. We propose monthly monitoring because it is a good tradeoff between useful temporal definition and having enough events for evaluation of statistical measures.We are monitoring monthly two types of measures, those that can be directly evaluated from data for each month (number of events/day, released seismic moment/day, and average magnitude and depth), and measures requiring more processing and larger amounts of data (direct clustering, clustering from apparent velocities, Poisson entropy, and fractal dimensions D0, D1, and D2).We estimate that coverage is adequate from 2005 to date (June 2023), and monitoring of data over this period suggests that, for two of the regions, it may be possible to identify precursory activity before earthquakes with magnitudes M≥7.0 and, possibly M≥6.0. The third region, however, needs improved network seismographic coverage for monitoring to be effective. There are not enough recorded strong and major earthquakes to be able to estimate reliability for precursory signals yet.Monitoring will continue indefinitely and may evolve to consider more or different measures and/or regions. We hope that this monitoring may help in identifying regions of interest for detailed observation and, eventually, to help in the estimation of seismic hazard in northern Baja California.

Digital Fracture Surface Morphology and Statistical Characteristics of Granite Brazilian Tests after Non-Steady-State Thermal Disturbance

With the widespread advent of digital technologies, traditional perspectives in rock mechanics research are poised for further expansion. This paper presents a Brazilian test conducted on granite after non-steady-state thermal disturbance at 25 °C, 200 °C, 400 °C, and 600 °C, with detailed documentation of the damage process and failure response using an acoustic emission (AE) apparatus and a digital image correlation (DIC) system. Subsequently, utilizing point cloud data captured by a three-dimensional (3D) laser scanning system, a digital reconstruction of the failed specimen’s fracture surface was accomplished. The 3D fractal characteristics and roughness response of the digitized fracture surface were studied using the box-counting method and least squares approach. Furthermore, texture information of the digitized fracture surface was calculated using the Gray Level Co-occurrence Matrix (GLCM), and statistical characteristics describing the elevation distribution were analyzed. The results elucidate the influence of thermal disturbance temperature on the mechanical parameters of the specimen, acoustic emission behavior, surface strain field evolution, and digital fracture morphology characteristics. The findings indicate a non-linear degradation effect of temperature on the specimen’s tensile strength, with a reduction reaching 80.95% at 600 °C, where acoustic emission activity also peaked. The rising thermal disturbance temperature inhibited the crack initiation load at the specimen’s center but expanded the high-strain concentration areas and the growth rate of horizontal displacement. Additionally, varying degrees of linear or non-linear relationships were discovered between thermal disturbance temperature and the 3D fractal dimension of the fracture surface, average roughness (Ra), peak roughness (Rz), and root mean square roughness (Rq), confirming the potential of Rsm in predicting the 3D fractal dimension of Brazilian test fracture surfaces. The study of the GLCM of the digitized 3D fracture surface demonstrated a high dependency of its four second-order statistical measures on thermal disturbance temperature. Finally, the statistical parameters of the fracture surface’s elevation values showed a significant non-linear relationship with thermal disturbance temperature, with a critical temperature point likely existing between 400 and 600 °C that could precipitate a sudden change in the fracture surface’s elevation characteristics.

Influences of Different Acid Solutions on Pore Structures and Fractal Features of Coal

The effect of different acids on the pore structure and fractal characteristics of micropores and mesopores was determined with the help of low-temperature liquid nitrogen adsorption, X-ray diffraction, and the Frenkel–Halsey–Hill (FHH) model by using Yuwu coal as a sample and placing it in acidic environments, such as HF, HCl, HNO3, and CH3COOH. The results show that the acidization effects of HF and CH3COOH are separately dominated by the micropore and mesopore formation effects, while HCl and HNO3 mainly play their roles in expanding mesopores. After acidization, the surface fractal dimensions D1 and D1′ of micropores and mesopores in coal are always negatively correlated with the total specific surface area SBET, specific surface area Smic of micropores, and specific surface area Smes of mesopores. After being acidized by HF, D2 is negatively correlated with the total volume Vtot and the corresponding micropore volume Vmic, while acidization with HCl and HNO3 leads to the opposite result. After being acidized by CH3COOH, D2 has a negative correlation with Vtot and a positive correlation with Vmic. The structural fractal dimensions D2′ of mesopores in samples acidized by HF and CH3COOH are positively correlated with both the volume Vtot and mesopore volume Vmes, while it is the opposite for samples acidized by HNO3. D2′ of coal samples acidized by HCl is negatively correlated with Vtot while positively correlated with Vmes.

3D Fractal Dimension Analysis: Prognostic Value of Right Ventricular Trabecular Complexity in Participants with Arrhythmogenic Cardiomyopathy.

Arrhythmogenic cardiomyopathy (ACM) is characterized by progressive myocardial fibro-fatty infiltration accompanied by trabecular disarray. Traditionally, two-dimensional (2D) instead of 3D fractal dimension (FD) analysis has been used to evaluate trabecular disarray. However, the prognostic value of trabecular disorder assessed by 3D FD measurement remains unclear. To investigate the prognostic value of right ventricular trabecular complexity in ACM patients using 3D FD analysis based on cardiac MR cine images. Retrospective. 85 ACM patients (mean age: 45 ± 17 years, 52 male). 3.0T/cine imaging, T2-short tau inversion recovery (T2-STIR), and late gadolinium enhancement (LGE). Using cine images, RV (right ventricular) volumetric and functional parameters were obtained. RV trabecular complexity was measured with 3D fractal analysis by box-counting method to calculate 3D-FD. Cox and logistic regression models were established to evaluate the prognostic value of 3D-FD for major adverse cardiac events (MACE). Cox regression and logistic regression to explore the prognostic value of 3D-FD. C-index, time-dependent receiver operating characteristic (ROC) curves and area under the ROC curve (AUC) to evaluate the incremental value of 3D-FD. Intraclass correlation coefficient for interobserver variability. P < 0.05 indicated statistical significance. 26 MACE were recorded during the 60 month follow-up (interquartile range: 48-67 months). RV 3D-FD significantly differed between ACM patients with MACE (2.67, interquartile range: 2.51 ~ 2.81) and without (2.52, interquartile range: 2.40 ~ 2.67) and was a significant independent risk factor for MACE (hazard ratio, 1.02; 95% confidence interval: 1.01, 1.04). In addition, prognostic model fitness was significantly improved after adding 3D-FD to RV global longitudinal strain, LV involvement, and 5-year risk score separately. The myocardial trabecular complexity assessed through 3D FD analysis was found associated with MACE and provided incremental prognostic value beyond conventional ACM risk factors. 4 TECHNICAL EFFICACY: Stage 1.

Multifractal temporal analysis of seismicity of the Trans-Alboran shear zone

This study provides a temporal analysis of the seismicity occurring before three significant energetic earthquakes recorded in the Al Hoceima, Morocco, area: earthquakes in 1994 (Mw 6.0), 2004 (Mw 6.4), and 2016 (Mw 6.3). The analysis is based on the multifractal seismicity characteristics in the Trans-Alboran shear zone. For the computation of the multifractal spectrum f(α)-α, two measurements were considered, the temporal distribution of earthquakes and the temporal distribution of energy released by the earthquakes. In addition, the quantities D1 (entropy), D+∞ (dimension of the large measurements), R (α0-αmax) and L (αmin-α0), from the multifractal spectrum, were also defined. The obtained results prove that maximum values in the fractal dimensions D1 and D+∞ appear just before the occurrence of the largest earthquakes in the multifractal spectrum computed from the earthquake-released energy. This particular trend, which is connected to the maximum values, is also noticeable before the occurrence of seismicity, which is less energetic for earthquakes with magnitudes above Mw 4.5, and may be evidence that the dynamic and geometrical properties of seismicity are associated.

Effect of disturbed coal pore structure on gas adsorption characteristics: mercury intrusion porosimetry

Studying pore structures of disturbed coal and their influences on adsorption characteristics is conducive to in-depth understanding of occurrence and migration of gas in reservoirs in areas prone to coal and gas outbursts. A mercury porosimeter and a high-pressure gas adsorption instrument were separately used to investigate pore structures and measure adsorption characteristics of disturbed coal and undisturbed coal in Ningtiaota Coal Mine and Xigu Coal Mine (Shaanxi Province, China). In addition, pore structures and gas adsorption characteristics of coal samples were studied. The Menger’s sponge model was adopted to calculate fractal dimensions of coal samples, to estimate influences of pore structures and fractal features on the gas adsorption characteristics of disturbed and undisturbed coal. Results show that the pore volume of undisturbed coal is mainly contributed by micropores and transitional pores, while that of disturbed coal arises mainly from macropores and mesopores. Micropores and transitional pores account for large proportions of the specific surface area of pores in both disturbed and undisturbed coal. The adsorption isotherms of disturbed and undisturbed coal conform to the Langmuir equation and tectonism increases the limiting adsorption quantity of coal. The fractal dimensions D1 of the four types of coal samples in the experiments are in the range of 2.7617–2.9961, while the fractal dimensions D1 and D2 of disturbed coal are both larger than those of undisturbed coal, indicating that disturbed coal is more likely to collapse under high pressure. The total pore volume, total specific surface area of pores, and fractal dimensions are positively correlated with the adsorption constant a, while they have U-shaped correlations with the adsorption constant b of coal samples. The adsorption constant a of disturbed coal is always greater than that of undisturbed coal, while no obvious trend is observed between the adsorption constant b and tectonism. The research results can provide theoretical basis for further study of gas occurrence in disturbed coal seams.