Search Results (1,003)

To address the inefficiency of traditional concrete crack detection methods and the heavy reliance of supervised learning on extensive labeled data, in this study, an intelligent assessment method of concrete damage based on pseudo-label semi-supervised learning and fractal geometry theory is proposed to solve two core tasks: one is binary classification of pixel-level cracks, and the other is multi-category assessment of damage state based on crack morphology. Using three-channel RGB images as input, a dual-path collaborative training framework based on U-Net encoder–decoder architecture is constructed, and a binary segmentation mask of the same size is output to achieve the accurate segmentation of cracks at the pixel level. By constructing a dual-path collaborative training framework and employing a dynamic pseudo-label refinement mechanism, the model achieves an F1-score of 0.883 using only 50% labeled data—a mere 1.3% decrease compared to the fully supervised benchmark DeepCrack (F1 = 0.896)—while reducing manual annotation costs by over 60%. Furthermore, a quantitative correlation model between crack fractal characteristics and structural damage severity is established by combining a U-Net segmentation network with the differential box-counting algorithm. The experimental results demonstrate that under a cyclic loading of 147.6–221.4 kN, the fractal dimension monotonically increases from 1.073 (moderate damage) to 1.189 (failure), with 100% accuracy in damage state identification, closely aligning with the degradation trend of macroscopic mechanical properties. In complex crack scenarios, the model attains a recall rate (Re = 0.882), surpassing U-Net by 13.9%, with significantly enhanced edge reconstruction precision. Compared with the mainstream models, this method effectively alleviates the problem of data annotation dependence through a semi-supervised strategy while maintaining high accuracy. It provides an efficient structural health monitoring solution for engineering practice, which is of great value to promote the application of intelligent detection technology in infrastructure operation and maintenance. Full article

Marine–continental transitional shale is a promising unconventional gas reservoir, playing an increasingly important role in China’s energy portfolio. However, compared to marine shale, research on marine–continental transitional shale’s fractal characteristics of pore structure and complete pore size distribution remains limited. In this work, high-pressure mercury intrusion, N₂ adsorption, and CO₂ adsorption techniques, combined with fractal geometry modeling, were employed to characterize the pore structure of the Shanxi Formation marine–continental transitional shale. The shale exhibits generally high TOC content and abundant clay minerals, indicating strong hydrocarbon-generation potential. The pore size distribution is multi-modal: micropores and mesopores dominate, contributing the majority of the specific surface area and pore volume, whereas macropores display a single-peak distribution. Fractal analysis reveals that micropores have high fractal dimensions and structural regularity, mesopores exhibit dual-fractal characteristics, and macropores show large variations in fractal dimension. Characteristics of pore structure is primarily controlled by TOC content and mineral composition. These findings provide a quantitative basis for evaluating shale reservoir quality, understanding gas storage mechanisms, and optimizing strategies for sustainable of oil and gas development in marine–continental transitional shales. Full article

The Silurian marine shale in the Sichuan Basin is currently the main reservoir for shale gas reserves and production in China. This study investigates the reservoir evolution of the Silurian marine shale based on fractal dimension, quantifying the complexity and heterogeneity of the shale’s pore structure. Physical simulation experiments were conducted on field-collected shale samples, revealing the evolution of total organic carbon, mineral composition, porosity, and micro-fractures. The fractal dimension of shale pore was characterized using the Frenkel–Halsey–Hill and capillary bundle models. The relationships among shale components, porosity, and fractal dimensions were investigated through a correlation analysis and a principal component analysis. A comprehensive evolution model for porosity and micro-fractures was established. The evolution of mineral composition indicates a gradual increase in quartz content, accompanied by a decline in clay, feldspar, and carbonate minerals. The thermal evolution of organic matter is characterized by the formation of organic pores and shrinkage fractures on the surface of kerogen. Retained hydrocarbons undergo cracking in the late stages of thermal evolution, resulting in the formation of numerous nanometer-scale organic pores. The evolution of inorganic minerals is represented by compaction, dissolution, and the transformation of clay minerals. Throughout the simulation, porosity evolution exhibited distinct stages of rapid decline, notable increase, and relative stabilization. Both pore volume and specific surface area exhibit a trend of decreasing initially and then increasing during thermal evolution. However, pore volume slowly decreases after reaching its peak in the late overmature stage. Fractal dimensions derived from the Frenkel–Halsey–Hill model indicate that the surface roughness of pores (D1) in organic-rich shale is generally lower than the complexity of their internal structures (D2) across different maturity levels. Additionally, the average fractal dimension calculated based on the capillary bundle model is higher, suggesting that larger pores exhibit more complex structures. The correlation matrix indicates a co-evolution relationship between shale components and pore structure. Principal component analysis results show a close relationship between the porosity of inorganic pores, microfractures, and fractal dimension D2. The porosity of organic pores, the pore volume and specific surface area of the main pore size are closely related to fractal dimension D1. D1 serves as an indicator of pore development extent and characterizes the changes in components that are “consumed” or “generated” during the evolution process. Based on mineral composition, fractal dimensions, and pore structure evolution, a comprehensive model describing the evolution of pores and fractal dimensions in organic-rich shale was established. Full article

In order to design new materials at atomic-length scales, there is a need to connect the fractal nature of fracture surfaces at the atomic scale using quantum mechanics modeling with that of the experimental data of fracture surfaces at macroscopic-length scales. We use a semi-empirical quantum mechanics simulation of fracture in amorphous silica to calculate a parameter identified as a critical characteristic length, $a_0$, which has been experimentally derived from the fractal nature of fracture for many materials that fail in a brittle matter. To our knowledge, there are no known simulation models other than our related research that use the fractal parameter $a_0$ to describe the fractal fracture of the fracture surface using quantum mechanical simulations. We provide evidence that $a_0$ can be calculated at both the atomic and macroscopic scale, making it a fundamental property of the structure and one of the elements of fractal fracture. We use a continuous random network model and reaction coordinate method to simulate fracture. We propose that fracture in amorphous silica occurs due to bond reconfiguration resulting in increased strain volume at the crack tip. We hypothesize two specific configurations leading to fracture from a four-fold ring reconfiguration to three-fold ring or (newly observed) five-fold ring configurations resulting in a change in volume. Finally, we define a reconfiguration fracture energy at the atomic level, which is approximately the value of the experimental fracture surface energy. Full article

In comparison to shallow coal seams, deep coal seams exhibit characteristics of high temperature, pressure, and in-situ stress, leading to significant differences in reservoir properties that constrain the effective development of deep coalbed methane (CBM). This study takes the Carboniferous deep 8# coal seam in the Yulin area of Ordos basin as the research subject. Based on the test results from core drilling wells, a comprehensive analysis of the characteristics and variation patterns of coal reservoir properties and a comparative analysis of the exploration and development potential of deep CBM are conducted, aiming to provide guidance for the development of deep CBM in the Ordos basin. The research results indicate that the coal seams are primarily composed of primary structure coal, with semi-bright to bright being the dominant macroscopic coal types. The maximum vitrinite reflectance (R_o,max) ranges between 1.99% and 2.24%, the organic is type III, and the high Vitrinite content provides a substantial material basis for the generation of CBM. Longitudinally, influenced by sedimentary environment and plant types, the lower part of the coal seam exhibits higher Vitrinite content and fixed carbon (FC_ad). The pore morphology is mainly characterized by wedge-shaped/parallel plate-shaped pores and open ventilation pores, with good connectivity, which is favorable for the storage and output of CBM. Micropores (<2 nm) have the highest volume proportion, showing an increasing trend with burial depth, and due to interlayer sliding and capillary condensation, the pore size (<2 nm) distribution follows an N shape. The full-scale pore heterogeneity (fractal dimension) gradually increases with increasing buried depth. Macroscopic fractures are mostly found in bright coal bands, while microscopic fractures are more developed in Vitrinite, showing a positive correlation between fracture density and Vitrinite content. The porosity and permeability conditions of reservoirs are comparable to the Daning–Jixian block, mostly constituting oversaturated gas reservoirs with a critical depth of 2400–2600 m and a high proportion of free gas, exhibiting promising development prospects, and the middle and upper coal seams are favorable intervals. In terms of resource conditions, preservation conditions, and reservoir alterability, the development potential of CBM from the Carboniferous deep 8# coal seam is comparable to the Linxing block but inferior to the Daning–Jixian block and Baijiahai uplift. Full article

Three-dimensional geological modeling combined with the information value method offers a powerful approach for predicting mineralization in complex geological settings. This study applies these techniques to the Bainiuchang Ag polymetallic deposit in Southwest China. We constructed a detailed 3D geological model to identify key geological factors influencing mineralization, such as the F₃ fault, secondary faults, and the middle Cambrian Tianpeng Formation. Using the information value method, we evaluated the mineralization potential of each unit in the study area. Receiver operating characteristic (ROC) curves and fractal analysis were employed to determine an optimal threshold (information value > 2.6) for delineating high-potential exploration targets. Our results identified three priority targets (A1, A2, and A3), demonstrating the effectiveness of integrating 3D modeling with probabilistic mineral prospectivity mapping. This approach provides a robust framework for deep and peripheral exploration in structurally complex deposits, offering valuable insights for future mineral exploration efforts. Full article

The palm-vein recognition system has garnered attention as a biometric technology due to its resilience to external environmental factors, protection of personal privacy, and low risk of external exposure. However, with recent advancements in deep learning-based generative models for image synthesis, the quality and sophistication of fake images have improved, leading to an increased security threat from counterfeit images. In particular, palm-vein images acquired through near-infrared illumination exhibit low resolution and blurred characteristics, making it even more challenging to detect fake images. Furthermore, spoof detection specifically targeting palm-vein images has not been studied in detail. To address these challenges, this study proposes the Fourier-gated feature-fusion network (FGFNet) as a novel spoof detector for palm-vein recognition systems. The proposed network integrates masked fast Fourier transform, a map-based gated feature fusion block, and a fast Fourier convolution (FFC) attention block with global contrastive loss to effectively detect distortion patterns caused by generative models. These components enable the efficient extraction of critical information required to determine the authenticity of palm-vein images. In addition, fractal dimension estimation (FDE) was employed for two purposes in this study. In the spoof attack procedure, FDE was used to evaluate how closely the generated fake images approximate the structural complexity of real palm-vein images, confirming that the generative model produced highly realistic spoof samples. In the spoof detection procedure, the FDE results further demonstrated that the proposed FGFNet effectively distinguishes between real and fake images, validating its capability to capture subtle structural differences induced by generative manipulation. To evaluate the spoof detection performance of FGFNet, experiments were conducted using real palm-vein images from two publicly available palm-vein datasets—VERA Spoofing PalmVein (VERA dataset) and PLUSVein-contactless (PLUS dataset)—as well as fake palm-vein images generated based on these datasets using a cycle-consistent generative adversarial network. The results showed that, based on the average classification error rate, FGFNet achieved 0.3% and 0.3% on the VERA and PLUS datasets, respectively, demonstrating superior performance compared to existing state-of-the-art spoof detection methods. Full article

The investigation of the pore structure and fractal characteristics of coal-bearing shale is critical for unraveling reservoir heterogeneity, storage-seepage capacity, and gas occurrence mechanisms. In this study, 12 representative Upper Paleozoic coal-bearing shale samples from the Yangquan Block of the Qinshui Basin were systematically analyzed through field emission scanning electron microscopy (FE-SEM), high-pressure mercury intrusion, and gas adsorption experiments to characterize pore structures and calculate multi-scale fractal dimensions (D₁–D₅). Key findings reveal that reservoir pores are predominantly composed of macropores generated by brittle fracturing and interlayer pores within clay minerals, with residual organic pores exhibiting low proportions. Macropores dominate the total pore volume, while mesopores primarily contribute to the specific surface area. Fractal dimension D₁ shows a significant positive correlation with clay mineral content, highlighting the role of diagenetic modification in enhancing the complexity of interlayer pores. D₂ is strongly correlated with the quartz content, indicating that brittle fracturing serves as a key driver of macropore network complexity. Fractal dimensions D₃–D₅ further unveil the synergistic control of tectonic activity and dissolution on the spatial distribution of pore-fracture systems. Notably, during the overmature stage, the collapse of organic pores suppresses mesopore complexity, whereas inorganic diagenetic processes (e.g., quartz cementation and tectonic fracturing) significantly amplify the heterogeneity of macropores and fractures. These findings provide multi-scale fractal theoretical insights for evaluating coal-bearing shale gas reservoirs and offer actionable recommendations for optimizing the exploration and development of Upper Paleozoic coal-bearing shale gas resources in the Yangquan Block of the Qinshui Basin. Full article

To explore the influence of mine roof on the damage and failure of sandstone surrounding rock under different pressure rates, mechanical experiments with different strain rates were carried out on sandstone rock samples. The strength, deformation, failure, energy and damage characteristics of rock samples with different strain rates were also discussed. The research results show that with the increases in the strain rate, peak stress, and elastic modulus show a monotonically increasing trend, while the peak strain decreases in the reverse direction. At a low strain rate, the proportion of the mass fraction of complete rock blocks in the rock sample is relatively high, and the shape integrity is good, while rock samples with a high strain rate retain more small-sized fragmented rock blocks. This indicates that under high-rate loading, the bifurcation phenomenon of secondary cracks is obvious. The rock samples undergo a failure form dominated by small-sized fragments, with severe damage to the rock samples and significant fractal characteristics of the fragments. At the initial stage of loading, the primary fractures close, and the rock samples mainly dissipate energy in the forms of frictional slip and mineral fragmentation. In the middle stage of loading, the residual fractures are compacted, and the dissipative strain energy keeps increasing continuously. In the later stage of loading, secondary cracks accelerate their expansion, and elastic strain energy is released sharply, eventually leading to brittle failure of the rock sample. Under a low strain rate, secondary cracks slowly expand along the clay–quartz interface and cause intergranular failure of the rock sample. However, a high strain rate inhibits the stress relaxation of the clay, forces the energy to transfer to the quartz crystal, promotes the penetration of secondary cracks through the quartz crystal, and triggers transgranular failure. A constitutive model based on energy damage was further constructed, which can accurately characterize the nonlinear hardening characteristics and strength-deformation laws of rock samples with different strain rates. The evolution process of its energy damage can be divided into the unchanged stage, the slow growth stage, and the accelerated growth stage. The characteristics of this stage reveal the sudden change mechanism from the dissipation of elastic strain energy of rock samples to the unstable propagation of secondary cracks, clarify the cumulative influence of strain rate on damage, and provide a theoretical basis for the dynamic assessment of surrounding rock damage and disaster early warning when the mine roof comes under pressure. Full article

Stylolites are a common mineral dissolution feature in rocks that develop during compression and form distinct tooth structures. On a tectonic plate scale, mid-ocean ridges (MORs) and transform faults are a significant feature of the Earth’s surface that develop due to accretion of new material in an extensional regime. We present a comparison between the two features and argue that transform faults in MOR are similar to the sides of stylolite teeth, with both features representing kinematic faults (KFs). First, we present a numerical model of both stylolite and MOR growth and show that in both cases, KFs nucleate and grow spontaneously. In addition, we use a well-established technique (Family–Vicsek scaling) of describing fractal self-affine interfaces, which has been used for stylolites, to characterize the pattern of MOR systems in both simulations and natural examples. Our results show that stylolites and MOR have self-affine scaling characteristics with similar scaling regimes. They both show a larger roughness exponent at the small scale, a smaller exponent at the intermediate scale, followed by a flattening of the system at the largest scale. For stylolites, the physical forces behind the scaling are the surface energy at the small mineral scale, the elastic energy at the intermediate scale, followed by the system reaching the correlation length where growth stops. For MORs, the physical forces behind the scaling are not yet clear; however, the self-affine scaling shows that transform faults at MORs do not have a preferred spacing, but that the spacing is fractal. Our study offers a new perspective on the study of natural roughening phenomena on various scales, from minerals to tectonic plates, and a new view on the development of MORs. Full article

The microfractured tight reservoirs in Yongjin Oilfield have low permeability and a complex pore structure. The development of microfractures in reservoirs is crucial for their impact on productivity. To understand the impact of pore structure and microfracture development on permeability and productivity, research on the fractal dimension and classification evaluation of microfractured tight reservoirs is proposed. Micropore and microfracture parameter characteristics are determined via CT scanning and mercury intrusion experiments. Based on the fractal theory and box counting dimension methods, the fractal dimension of pores and fractures in microfractured tight reservoirs are calculated, which can be used as an evaluation index. Then, a comprehensive quantitative evaluation method (REI) is conducted on the microfractured tight reservoir of Yongjin Oilfield to determine the classification boundary of evaluation indicators and reservoir classification results. The research results show that the microfractured tight reservoirs in Yongjin Oilfield can be classified into three types based on their development effect from good to poor. The comprehensive evaluation index (REI) of type I reservoirs is greater than 0.7, and the fractal dimension of pores and fractures is less than 2.4. The comprehensive evaluation index (REI) of type II reservoirs ranges from 0.4 to 0.7, and the fractal dimension of pores and fractures ranges from 2.4 to 2.6. The comprehensive evaluation index (REI) of type III reservoirs is less than 0.4, and the fractal dimension of pores and fractures is greater than 2.6. The classification results are consistent with the dynamic data, and this achievement can provide a scientific basis for rapid reservoir evaluation and development strategy formulation. Full article

This study systematically investigates the effect of steel fiber content on the fractal evolution characteristics of bending cracks in alkali-activated slag concrete (AASC) beams. A four-point bending test on simply supported beams, combined with digital image correlation (DIC) technology, was employed to quantitatively analyze the fractal dimension of crack propagation paths in AASC beams with steel fiber contents ranging from 0% to 1.4%, using the box-counting method. The relationship between fracture energy and fractal dimension was examined, along with the fractal control mechanisms of mid-span deflection, crack width, and the fractal evolution of fracture toughness parameters. The results revealed that as the steel fiber content increased, the crack fractal dimension decreased from 1.287 to 1.155, while the critical fracture energy of AASC beams increased by approximately 75%. Both mid-span deflection and maximum crack width were positively correlated with the crack fractal dimension, whereas the fractal dimension showed a negative correlation with critical cracking stress and fracture toughness and a positive correlation with the energy release rate. When the steel fiber content exceeded 1.2%, the performance gains began to diminish due to fiber agglomeration effects. Overall, the findings suggest that an optimal steel fiber content range of 1.0% to 1.2% provides the best crack control and mechanical performance, offering a theoretical basis for the design of AASC structures. Full article

Existing theoretical models of wave-induced flow face challenges in coal applications due to the scarcity of experimental data in the seismic-frequency band. Additionally, traditional viscoelastic combination models exhibit inherent limitations in accurately capturing the attenuation characteristics of rocks. To overcome these constraints, we propose a novel binary classification physical fractal model, which provides a more robust framework for analyzing wave dispersion and attenuation in complex coal. The fractal cell was regarded as an element to re-establish the viscoelastic constitutive equation. In the new constitutive equation, three key fractional orders, $\alpha$, $\beta$, and $\gamma$, emerged. Among them, $\alpha$ mainly affects the attenuation at low frequencies; $\beta$ controls the attenuation in the middle-frequency band; and $\gamma$ dominates the attenuation in the tail-frequency band. After fitting with the measured attenuation data of partially saturated coal samples under variable confining pressures and variable temperature conditions, the results show that this model can effectively represent the attenuation characteristics of elastic wave propagation in coals with different coal structures. It provides a new theoretical model and analysis ideas for the study of elastic wave attenuation in tectonic coals and is of great significance for an in-depth understanding of the physical properties of coals and related geophysical prospecting. Full article

In the development of deep coalbed methane (CBM) resources, the adsorption behavior of supercritical methane is a key factor restricting reserve evaluation and development efficiency. This study integrates scanning electron microscopy (SEM), low-temperature CO₂ adsorption (LTCO₂A), mercury intrusion porosimetry (MIP), high-temperature and high-pressure CH₄ adsorption experiments (HTHP-CH₄A), and theoretical models to reveal the pore–fracture structure of deep coal seams and the adsorption characteristics of supercritical methane. Based on a predictive model for supercritical methane adsorption capacity, the adsorption capacity of deep methane was predicted. Results show that micro-pores are well-developed in deep coal rocks, but pore connectivity is generally poor, predominantly consisting of fine bottleneck pores and semi-closed pores, with a certain proportion of open pores. The fractal dimension (D_m) of micro-pore structures in deep coal samples ranges from 2.0447 to 2.2439, indicating high micro-pore surface roughness and a large specific surface area, which provide favorable sites for methane adsorption. Pores larger than 100 nm exhibit fractal values between 2.6459 and 2.8833, suggesting that the pore surfaces in deep coal seams approach a three-dimensional pore space with rough surfaces and complex pore structures. As temperature and pressure enter the supercritical region, the adsorption capacity shows an abnormal trend of “first increasing and then decreasing” with increasing pressure. The deep coal rock–supercritical methane adsorption system exhibits two scenarios in low-pressure and high-pressure regions, corresponding to self-adsorption driven by strong methane adsorption potential and external force adsorption or overpressure micro-pore adsorption, respectively. The supercritical adsorption prediction model considering temperature and methane adsorption phase density has extremely low deviation (1.11–1.25%) and high accuracy. The average dispersion between predicted and actual values ranges from 0.44 cm³/g to 0.48 cm³/g, with small error fluctuations and no significant deviation. This study provides theoretical support for the recoverability evaluation and efficient development of deep CBM resources. Full article

Fuel electro-hydraulic servo valves are core components in the fuel control system of aero-engines, and their performance directly affects thrust regulation and power output precision. Due to the combustibility of the working medium in fuel systems and the lack of effective circulation filtration, the retention of micron-sized particles within the valve gap can lead to valve spool jamming, which is a critical reliability issue. This study, based on fractal theory and the liquid–solid two-phase flow model, proposes a parametric model for non-ideal surface valve gaps and analyzes the dynamics of particles subjected to drag, lift, and buoyant forces on rough surfaces. By numerically analyzing flow field models with different roughness levels and comparing them with an ideal smooth gap model, the migration characteristics of particles were studied. To verify the accuracy of the model, an upscaled experimental setup was built based on similarity theory, and PIV experiments were conducted for validation. Experimental results show that the particle release position and valve surface roughness significantly affect particle migration time. The weight of the release position on particle migration time is 63%, while the impact of valve surface roughness is 37%. In models with different roughness levels, the particle migration time increases more rapidly for roughness values greater than Ra0.4, while for values less than Ra0.4, the increase in migration time is slower. Furthermore, the study reveals that particle migration trajectories are independent of flow velocity, with velocity only affecting particle migration time. This research provides theoretical support for enhancing the reliability of fuel electro-hydraulic servo valves and offers a new perspective for the design of highly reliable hydraulic components. Full article