Fractal Dimension and Lacunarity Analysis in the Dentulous and Edentulous Mandibular Posterior Region Using Cone-beam Computed Tomography: A Cross-sectional Retrospective Study.

AIMS: This cross-sectional retrospective study was conducted to assess the differences in the microarchitecture of the trabecular bone of the posterior mandibular region at dentulous and edentulous sites with the help of fractal dimension (FD) and lacunarity using cone-beam computed tomography (CBCT). MATERIALS AND METHODS: Ninety CBCT scans were analyzed for the purpose of the present study. Inclusion criteria included subjects with unilaterally missing mandibular molars or premolars and an with intact contralateral opposing tooth. The coronal view of the dentulous and edentulous sites was used, and the region of interest (ROI) was selected 2.6 mm below the apex of the tooth present. These images were then transferred to ImageJ Software, and fractal analysis was done using the box-counting method of the FracLac plug-in. A paired samples t-test was performed to compare the means of FD and lacunarity, and a Kendall correlation was performed to check correlations. A p-value less than 0.05 was considered to indicate statistical significance. RESULTS: Statistical analysis revealed that the mean FD of the edentulous side was significantly greater than that of the dentulous side (p-value = 0.011). Additionally, the mean lacunarity of the edentulous side was marginally significantly greater than that of the dentulous side (p-value = 0.089). A significant negative correlation was detected between the FD and lacunarity of the edentulous region (p-value = 0.017), and a marginally significant negative correlation was detected between edentulous lacunarity and dentulous lacunarity (p-value = 0.081). CONCLUSION: The differences in occlusal forces exerted in dentulous and edentulous regions can lead to a change in the trabecular pattern of the bone in these regions. This change in the microarchitecture of bones can be detected by FD and lacunarity, which can further help us assess changes pre- and post-implant. CLINICAL SIGNIFICANCE: The advanced technology, the assessment of microarchitecture of the bone has been made easy, using FD and lacunarity, as done in the present study. This analysis can further aid us in both pre- and post-implant analysis to prevent failure of the implant. How to cite this article: Bhoraskar M, Denny C, Srikant N, et al. Fractal Dimension and Lacunarity Analysis in the Dentulous and Edentulous Mandibular Posterior Region Using Cone-beam Computed Tomography: A Cross-sectional Retrospective Study. J Contemp Dent Pract 2024;25(6):581-587.

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.

Research on the microscopic pore-throat structure and reservoir quality of tight sandstone using fractal dimensions.

The pore-throat structure is a crucial parameter for evaluating reservoir characteristics and assessing the potential of oil and gas resources. Understanding the relationship between reservoir pore-throat variations and oil-bearing properties is essential. Through a combination of techniques, including thin-section casting, scanning electron microscopy (SEM), micro-computed tomography (micro-CT), and high-pressure mercury injection (HPMI), we examined the tight sandstone reservoirs from the Chang 4 + 5 members of the Yanchang Formation in the study area. This analysis elucidates the relationship between the pore-throat structure and fractal characteristics of the samples and their oil-bearing properties. The results show that : (1) The tight sandstone reservoirs in the study area mainly develop three types of pores: dissolution pores, residual intergranular pores, and microfractures. Residual intergranular pores are primarily controlled by early compaction processes, while dissolution processes easily form secondary pores, increasing the porosity of the reservoir. Microfractures can significantly enhance both the permeability of the reservoir. (2) Using the characteristic parameters of HPMI, the reservoir is classified into four categories, labeled as type I to type IV. As the categories progress from type I to type IV, pore-throat size decreases, porosity and permeability decrease, and reservoir properties deteriorate. The overall fractal dimension of pores decreases, while the fractal dimensions of individual pore types increase. Pore connectivity becomes more complex, and heterogeneity strengthens. (3) Reservoir porosity shows a strong positive correlation with permeability. As reservoir properties improve, the number of macropores increases, leading to a higher Reservoir Quality Index (RQI) and better oil-bearing characteristics.

Complexity and phase transitions in citation networks: insights from artificial intelligence research.

In this study, we analyze the changes over time in the complexity and structure of words used in article titles and the connections between articles in citation networks, focusing on the topic of artificial intelligence (AI) up to 2020. By measuring unpredictability in word usage and changes in the connections between articles, we gain insights into shifts in research focus and diversity of themes. Our investigation reveals correspondence between fluctuations in word complexity and changes in the structure of citation networks, highlighting links between thematic evolution and network dynamics. This approach not only enhances our understanding of scientific progress but also may help in anticipating emerging fields and fostering innovation, providing a quantitative lens for studying scientific domains beyond AI.

The relationship between radiomorphometric indices and fractal dimension analysis: a cone-beam computed tomography study.

The purpose of this study is to evaluate the relationship between radiomorphometric indices and fractal dimension (FD) analysis in jawbone radiographic density using Cone-Beam Computed Tomography (CBCT). The study included 87 CBCT datasets from dental patients aged 50-79. Four radiomorphometric indices (Computed Tomography Cortical Index (CTCI), Computed Tomography Mental Index (CTMI), Computed Tomography Index-Superior (CTI-S), and Computed Tomography Index-Inferior (CTI-I)) along with age, gender, remaining teeth, and mandibular bone height were evaluated. FD was assessed in trabecular bone near the mental foramen (ROI 1) and on the mandibular cortical bone (ROI 2). Relationships between indices and variables were analyzed using Pearson chi-square, Fisher's exact, one-way ANOVA, Kruskal-Wallis, and Spearman's rho tests. ANOVA showed significant differences in mandibular bone height (p = .004) and FD at ROI 2 (p = .000) across three mandibular cortex types (C1, C2, C3). Spearman's rho indicated significant correlations between FD at ROI 2 and CTMI, CTI-S, CTI-I (p = .000), and between mandibular bone height and CTMI (p = .010). The correlations of FD at ROI 2 ranged from strongest to weakest with CTCI, CTMI, CTI-S, and CTI-I. High-risk osteoporosis radiomorphometric indices are associated with FD analysis of cortical bone.

Investigating fractal fractional PDEs, electric circuits, and integral inclusions via (ψ,ϕ)-rational type contractions.

The fixed point theory has been generalized mainly in two directions. One is the extension of the spaces, and the other is relaxing and generalizing the contractions. This paper aims to establish novel fixed point results of rational type generalized ( ψ , ϕ ) -contractions in the context of extended b-metric spaces. This will allow us to analyze generalized rational type contraction in a more relaxed and diversified framework in the light of the characteristics of ( ψ , ϕ ) . Some existing rational-type contractions have been recalled in this direction, and others are defined. New fixed point results have been established by utilizing the properties of ψ and ϕ and applying the iteration technique. Moreover, the established results are employed to investigate the stability of fractal and fractional differential equations and electric circuits. For the reliability of the established results, examples and applications to the system of integral inclusions and system of integral equations are presented.

Exploring cortical morphology biomarkers of amnesic mild cognitive impairment using novel fractal dimension-based structural MRI analysis.

Amnestic mild cognitive impairment (aMCI) is considered as an intermediate stage of Alzheimer's disease, but no MRI biomarkers currently distinguish aMCI from healthy individuals effectively. Fractal dimension, a quantitative parameter, provides superior morphological information compared to conventional cortical thickness methods. Few studies have used cortical fractal dimension values to differentiate aMCI from healthy controls. In this study, we aim to build an automated discriminator for accurately distinguishing aMCI using fractal dimension measures of the cerebral cortex. Thirty aMCI patients and 30 health controls underwent structural MRI of the brain. First, the atrophy of participants' cortical sub-regions of Desikan-Killiany cortical atlas was assessed using fractal dimension and cortical thickness. The fractal dimension is more sensitive than cortical thickness in reducing dimensional effects and may accurately reflect morphological changes of the cortex in aMCI. The aMCI group had significantly lower fractal dimension values in the bilateral temporal lobes, right limbic lobe and right parietal lobe, whereas they showed significantly lower cortical thickness values only in the bilateral temporal lobes. Fractal dimension analysis was able to depict most of the significantly different focal regions detected by cortical thickness, but additionally with more regions. Second, applying the measured fractal dimensions (and cortical thickness) of both cerebral hemispheres, an unsupervised discriminator was built for the aMCI and healthy controls. The proposed fractal dimension-based method achieves 80.54% accuracy in discriminating aMCI from healthy controls. The fractal dimension appears to be a promising biomarker for cortical morphology changes that can discriminate patients with aMCI from healthy controls.

Evaluation of fractal analysis and radiomorphometric measurements of mandibular bone structure in bruxism and non-bruxism paediatric patients.

OBJECTIVES: The goal of this examination was to compare the impact of probable sleep/awake bruxism on the mandibular trabecular bone structure by fractal analysis (FA) with digital panoramic radiograph (DPR) and radiomorphometric measurements in paediatric patients with bruxism. METHODS: The examination included 130 participants with 63 patients with probable sleep/awake bruxism and 67 control groups. Bilateral regions of interest (ROI) in three regions were examined as ROI1: mandibular ramus, ROI2: mandibular angulus, ROI3: anterior to the molar teeth. Radiomorphometric measurements were taken of the mandibular cortical width (MCW), panoramic mandibular index (PMI), and mandibular cortical index (MCI). p < 0.05 was approved for statistical significance. RESULTS: The ROI-1, ROI-2, and ROI-3 values were defined to be statistically significantly high in the bruxism group (p < 0.05). No significant difference was found between the groups in the other values (p > 0.05). There was no difference in the age and gender for any of the parameters (p > 0.05). CONCLUSION: In children and adolescents, the mandibular trabecular bone can be affected by bruxism. FA can be used as an auxiliary method for finding the mandibular trabecular differences of patients with bruxism in paediatric dentistry just as it can for adults.

Stress sensitivity analysis of vuggy porous media based on two-scale fractal theory.

Interparticle pore space and vugs are two different scales of pore space in vuggy porous media. Vuggy porous media widely exists in carbonate reservoirs, and the permeability of this porous media plays an important role in many engineering fields. It has been shown that the change of effective stress has important effects on the permeability of vuggy porous media. In this work, a fractal permeability model for vuggy porous media is developed based on the fractal theory and elastic mechanics. Besides, a Monte Carlo simulation is also implemented to obtain feasible values of permeability. The proposed model can predict the elastic deformation of the fractal vuggy porous media under loading stress, which plays a crucial role in the variations of permeability. The predicted permeability data based on the present fractal model are compared with experimental data, which verifies the validity of the present fractal permeability model for vuggy porous media. The parameter sensitivity analysis indicates that the permeability of stress-sensitivity vuggy porous media is related to the capillary fractal dimension, capillary fractal tortuosity dimension, Young's modulus, and Poisson's ratio.

A study on the impact of ultrasonic-stimulated clean fracturing fluid on the pore structure of medium to high rank coal.

The pore structure of coal plays a key role in the effectiveness of gas extraction. Conventional hydraulic fracturing techniques have limited success in modifying the pore structure using clean fracturing fluid (CFF), and the stimulating effects of ultrasonic can enhance the effectiveness of CFF in modifying coal pore structures. To research the effects of ultrasonic stimulation on the pore structure of medium to high-rank coal when using CFF, this study employed mercury intrusion porosimetry (MIP) and low-temperature nitrogen adsorption (LT-N2A) methods to analyze the changes in pore structures after cooperative modification. The results indicate that the pore volume and surface area of medium to high rank coal exhibit an increase and followed by a decrease with increasing Ro,max values, while the average pore diameter and permeability demonstrate a decrease and followed by an increase with Ro,max. Although there are some variations in the results of MIP and LT-N2A analysis for different pore size ranges, the overall findings suggest that ultrasonic stimulation in conjunction with CFF effectively alters the coal pore structure. The most significant improvement was observed in coking coal, where pore volume increased by 22%, pore area decreased by 11% and tortuosity decreased by 47%. The improvement of lean coal is the smallest, the pore volume increases by about 7%, and the surface area decreases by about 14%. It is found that the modification of coal pore volume is mainly concentrated in transition pores and macropores. These research outcomes provide valuable insights into the application of ultrasonic technology in coalbed gas extraction.

Nonlinear analysis of neuronal firing modulated by sinusoidal stimulation at axons in rat hippocampus.

Introduction: Electrical stimulation of the brain has shown promising prospects in treating various brain diseases. Although biphasic pulse stimulation remains the predominant clinical approach, there has been increasing interest in exploring alternative stimulation waveforms, such as sinusoidal stimulation, to improve the effectiveness of brain stimulation and to expand its application to a wider range of brain disorders. Despite this growing attention, the effects of sinusoidal stimulation on neurons, especially on their nonlinear firing characteristics, remains unclear. Methods: To address the question, 50 Hz sinusoidal stimulation was applied on Schaffer collaterals of the rat hippocampal CA1 region in vivo. Single unit activity of both pyramidal cells and interneurons in the downstream CA1 region was recorded and analyzed. Two fractal indexes, namely the Fano factor and Hurst exponent, were used to evaluate changes in the long-range correlations, a manifestation of nonlinear dynamics, in spike sequences of neuronal firing. Results: The results demonstrate that sinusoidal electrical stimulation increased the firing rates of both pyramidal cells and interneurons, as well as altered their firing to stimulation-related patterns. Importantly, the sinusoidal stimulation increased, rather than decreased the scaling exponents of both Fano factor and Hurst exponent, indicating an increase in the long-range correlations of both pyramidal cells and interneurons. Discussion: The results firstly reported that periodic sinusoidal stimulation without long-range correlations can increase the long-range correlations of neurons in the downstream post-synaptic area. These results provide new nonlinear mechanisms of brain sinusoidal stimulation and facilitate the development of new stimulation modes.

Robust unsupervised texture segmentation for motion analysis in ultrasound images.

PURPOSE: Ultrasound imaging has emerged as a promising cost-effective and portable non-irradiant modality for the diagnosis and follow-up of diseases. Motion analysis can be performed by segmenting anatomical structures of interest before tracking them over time. However, doing so in a robust way is challenging as ultrasound images often display a low contrast and blurry boundaries. METHODS: In this paper, a robust descriptor inspired from the fractal dimension is presented to locally characterize the gray-level variations of an image. This descriptor is an adaptive grid pattern whose scale locally varies as the gray-level variations of the image. Robust features are then located based on the gray-level variations, which are more likely to be consistently tracked over time despite the presence of noise. RESULTS: The method was validated on three datasets: segmentation of the left ventricle on simulated echocardiography (Dice coefficient, DC), accuracy of diaphragm motion tracking for healthy subjects (mean sum of distances, MSD) and for a scoliosis patient (root mean square error, RMSE). Results show that the method segments the left ventricle accurately ( DC = 0.84 ) and robustly tracks the diaphragm motion for healthy subjects ( MSD = 1.10 mm) and for the scoliosis patient ( RMSE = 1.22 mm). CONCLUSIONS: This method has the potential to segment structures of interest according to their texture in an unsupervised fashion, as well as to help analyze the deformation of tissues. Possible applications are not limited to US image. The same principle could also be applied to other medical imaging modalities such as MRI or CT scans.

Bioinspired Functional Composites for Enhanced Thermally Conductivity via Fractal-Growth CuNP Fillers.

Thermal conduction for electronic devices has attracted extensive attention in light of the development of 5G communication. Thermally conductive materials with high thermal conductivity and extensive mechanical flexibility are extremely desirable in practical applications. However, the construction of efficient interconnected conductive pathways and continuous conductive networks is inadequate for either processing or actual usage in existing technologies. In this work, spherical copper nanoparticles (S-CuNPs) and urchin-inspired fractal-growth CuNPs (U-CuNPs), thermally conductive metal fillers induced by ionic liquids, were fabricated successfully through the electrochemical deposition method. Compared to S-CuNPs, the U-CuNPs shows larger specific surface contact area, thus making it easier to build a continuous conductive pathway network in the corresponding U-CuNPs/liquid silicone rubber (LSR) thermally conductive composites. The optimal loading of CuNP fillers was determined by evaluating the rheological performance of the prepolymer and the mechanical properties and thermal conductivity performances of the composites. When the filler loading is 150 phr, the U-CuNPs/LSR produces optimal mechanical properties (e.g., tensile strength and modulus), thermal conductivity (above 1000% improvement compared to pure LSR), and heating/cooling efficiency. The enhanced thermal conductivity of U-CuNPs/LSR was also confirmed through the finite element analysis (FEA) overall temperature distribution, indicating that U-CuNPs with larger specific surface contact areas exhibit more advantages in forming a continuous network in composites than S-CuNPs, making U-CuNPs/LSR a promising and competitive alternative to traditional flexible thermally interface materials.

Quantification of immiscible displacement in a rough-walled fracture through direct visualization.

Subsurface substance migration in the fractured rock aquifer is mainly controlled by fractures, and immiscible fluid-fluid displacement in fractures is important to many geophysical processes and engineering activities. Using a fracture-visualization system, we present the qualitative and quantitative assessment of fracture geometry associated with fluid movement and distribution in the rough fracture. Based on fracture geometry and statistical analysis, we first conducted a quantitative study of fracture surface roughness and aperture distribution. Then, fractal dimensions of displacement front and residual oil distribution were determined by image processing procedures. Influenced by wettability and micro-scale roughness, at the end of the displacement, residual oil saturation of molded sample is lower (6.45%-25.74%), and displacement pattern is more uniform, indicating that displacement effect is better. Due to smaller differences in residual oil saturation (9.08%) under different injection directions, the impact of wettability on the displacement process is greater than that of anisotropic roughness. Additionally, the fractal dimension of the displacement front increased under low injection rates initially but decreased when the rate was increased later. Overall, visualized temporal monitoring of experimental images enabled us to provide a preliminary assessment of the impact of anisotropic roughness and the material constituting the fracture wall on invading fluid saturation and the fractal dimension of the displacement front under various injection rates.

Validation of Linear and Nonlinear Gait Variability Measures Derived From a Smartphone System Compared to a Gold-Standard Footswitch System During Overground Walking.

Smartphones, with embedded accelerometers, may be a viable method to monitor gait variability in the free-living environment. However, measurements estimated using smartphones must first be compared to known quantities to ensure validity. This study assessed the validity and reliability of smartphone-derived gait measures compared to a gold-standard footswitch system during overground walking. Seventeen adults completed three 8-minute overground walking trials during 3 separate visits. The stride time series was calculated as the time difference between consecutive right heel contact events within the footswitch and smartphone-accelerometry signals. Linear (average stride time, stride time standard deviation, and stride time coefficient of variation) and nonlinear (fractal scaling index, approximate entropy, and sample entropy) measures were calculated for each stride time series. Bland-Altman plots with 95% limits of agreement assessed agreement between systems. Intraclass correlation coefficients assessed reliability across visits. Bland-Altman plots revealed acceptable limits of agreement for all measures. Intraclass correlation coefficients revealed good-to-excellent reliability for both systems, except for fractal scaling index, which was moderate. The smartphone system is a valid method and performs similarly to gold-standard research equipment. These findings suggest the development and implementation of an inexpensive, easy-to-use, and ubiquitous telehealth instrument that may replace traditional laboratory equipment for use in the free-living environment.

Exponential Pixelating Integral transform with dual fractal features for enhanced chest X-ray abnormality detection.

The heightened prevalence of respiratory disorders, particularly exacerbated by a significant upswing in fatalities due to the novel coronavirus, underscores the critical need for early detection and timely intervention. This imperative is paramount, possessing the potential to profoundly impact and safeguard numerous lives. Medically, chest radiography stands out as an essential and economically viable medical imaging approach for diagnosing and assessing the severity of diverse Respiratory Disorders. However, their detection in Chest X-Rays is a cumbersome task even for well-trained radiologists owing to low contrast issues, overlapping of the tissue structures, subjective variability, and the presence of noise. To address these issues, a novel analytical model termed Exponential Pixelating Integral is introduced for the automatic detection of infections in Chest X-Rays in this work. Initially, the presented Exponential Pixelating Integral enhances the pixel intensities to overcome the low-contrast issues that are then polar-transformed followed by their representation using the locally invariant Mandelbrot and Julia fractal geometries for effective distinction of structural features. The collated features labeled Exponential Pixelating Integral with dually characterized fractal features are then classified by the non-parametric multivariate adaptive regression splines to establish an ensemble model between each pair of classes for effective diagnosis of diverse diseases. Rigorous analysis of the proposed classification framework on large medical benchmarked datasets showcases its superiority over its peers by registering a higher classification accuracy and F1 scores ranging from 98.46 to 99.45 % and 96.53-98.10 % respectively, making it a precise and interpretable automated system for diagnosing respiratory disorders.

Effects of thinning on structural complexity of Larix olgensis plantation.

In this paper, we collected the individual tree point cloud data in the plots of Larix olgensis plantations with different thinning intensities in Mengjiagang Forest Farm, applied the fractal analysis theory to extract box dimensions (Db) on MATLAB platform, and characterized the structural complexity of L. olgensis. We assessed the effect of different thinning intensities and tree attributes on the structural complexity of L. olgensis. The results showed significant differences in L. olgensis Db between control (CK: 1.68±0.07), low and medium intensity thinning (T1, T2, T3: 1.74±0.07), and high intensity thinning (T4: 1.81±0.06), which indicated that the thinning intensity increased tree structural complexity. For trunk attribute, the diameter at breast height and tree height was significantly positively correlated with Db, while the height-to-diameter ratio was significantly negatively correlated with Db. For canopy attribute, crown volume, surface area, projected area, and crown diameter was significantly positively correlated with Db. Hegyi competition index was significantly negatively correlated with Db in the control and low-moderate-intensity thinning treatments, but not significantly correlated with Db in the high-intensity thinning treatment. It indicated that thinning influenced L. olgensis structural complexity, with trunk attribute and canopy attribute as the main drivers of L. olgensis structural complexity.

Experimental study on dynamic mechanical properties of multidirectional constrained water-bearing coal samples under dynamic-static coupling loading.

The objective of this study is to investigate the dynamic mechanical properties of coal and rock under deep water conditions. The research employs an enhanced Split Hopkinson Pressure Bar (SHPB) testing system. Five sets of dynamic impact experiments were conducted on coal samples under varying loading conditions to analyse the changes in dynamic strength, energy dissipation, fractal dimension and other characteristics of coal samples under different water content states were analyzed. The experimental results demonstrate that: (1) Under specific strain rate conditions, the dynamic strength of saturated coal samples is lower than that of natural coal samples. As the strain rate gradually increases, the bonding force generated by free water and the Stefan effect jointly act, and the peak strength of saturated coal samples under high strain rate loading conditions is higher than that of natural coal samples. (2) Under certain strain rate conditions, the absorption energy of saturated coal samples is approximately 10% to30% lower than that of natural coal samples, and deformation hysteresis phenomenon occurs in natural coal samples, thereby improving the dynamic strength of natural coal samples relative to saturated coal samples; (3) The fractal dimension of saturated coal samples with a specific strain rate under three-dimensional dynamic static combination loading is higher than that of natural coal samples, and the percentage of small particle coal samples with debris is higher than that of natural coal samples; Finally, based on the HJC model, some coal samples were selected to simulate the coal rock failure characteristics during the triaxial loading process using ANSYS/LS-DYNA, and their stress-strain curves and failure morphology diagrams were obtained. The discrepancy between the numerical simulation and the experimental results was less than 10%, thereby further elucidating and corroborating the coal failure process and dynamic mechanical characteristics.

Experimental study on mechanical properties and breakage of high temperature carbon fiber-bar reinforced concrete under impact load.

To investigate the effects of high temperature and carbon fiber-bar reinforcement on the dynamic mechanical properties of concrete materials, a muffle furnace was used to treat two kinds of specimens, plain and carbon fiber-bar reinforced concrete, at high temperatures of 25, 200, 400 and 600 °C. Impact compression tests were carried out on two specimens after high-temperature exposure using a Hopkinson pressure bar (SHPB) test setup combined with a high-speed camera device to observe the crack extension process of the specimens. The effects of high temperature and carbon fiber-bar reinforcement on the peak stress, energy dissipation density, crack propagation and fractal dimension of the concrete were analyzed. The results showed that the corresponding peak strengths of the plain concrete specimens at 25, 200, 400, and 600 °C were 88.37, 93.21, 68.85, and 54.90 MPa, respectively, and the peak strengths after the high-temperature exposure first increased slightly and then decreased rapidly. The mean peak strengths corresponding to the carbon fiber-bar reinforced concrete specimens after high-temperature action at 25, 200, 400, and 600 °C are 1.13, 1.13, 1.21, and 1.19 times that of plain concrete, respectively, and the mean crushing energy consumption densities are 1.27, 1.31, 1.73, and 1.59 times that of plain concrete, respectively. The addition of carbon fiber-bar reinforcement significantly enhanced the impact resistance and energy dissipation of the concrete structure, and the higher the temperature was, the more significant the increase. An increase in temperature increases the number of crack extensions and width, and the high tensile strength of the carbon fiber-bar reinforcement and the synergistic effect with the concrete material reduce the degree of crack extension in the specimen. The fractal dimension of the concrete ranged from 1.92 to 2.68, that of the carbon fiber-bar reinforced concrete specimens ranged from 1.61 to 2.42, and the mean values of the corresponding fractal dimensions of the plain concrete specimens after high-temperature effects at 25, 200, 400, and 600 °C were 1.19, 1.21, 1.10, and 1.11 times those of the fiber-reinforced concrete specimens, respectively. The incorporation of carbon fiber-bar reinforcement reduces the degree of rupture and fragmentation of concrete under impact loading and improves the safety and stability of concrete structures.