Fractal Box Dimension Research Articles

Fractal and Multifractal Analysis of Microscopic Pore Structure of UHPC Matrix Modified with Nano Silica

Nano silica (NS) has been found to have a positive impact on enhancing the microporous structure of Ultra-High-Performance Concrete (UHPC). However, there is a lack of effective methods to accurately characterize the regulatory improvement mechanism of NS on the pore structure of UHPC. In this study, our objective is to investigate the influence of NS on various characteristic parameters of the pore structure in UHPC, including porosity, average pore size, box fractal dimension, and multifractal spectral parameters. To analyze these effects, we employ a combination of X- CT image processing techniques and fractal theory. Furthermore, we conducted regression analysis using linear functions to explore the correlation between these parameters and the 28d compressive strength of UHPC. The experimental results demonstrate that NS promotes the refinement of matrix pore size, leading to a denser microstructure of the matrix. Fractal analysis revealed that the pore structure of NS-modified UHPC exhibited favorable fractal characteristics. The fractal dimension and multiple fractal parameters provided complementary insights into the pore structure of NS-modified UHPC from different perspectives. The fractal dimension described the global information, indicating that NS improved matrix defects and reduced the complexity of the pore structure. On the other hand, the multiple fractal parameters supplemented local information, highlighting how the increase in micropores contributed to the heterogeneity of the pore structure. The results of the correlation analysis indicate that the developed mathematical model has a good fit with the 28d compressive strength of UHPC.

Development, Application and Utility of a Machine Learning Approach for Melanoma and Non-Melanoma Lesion Classification Using Counting Box Fractal Dimension.

The diagnosis and identification of melanoma are not always accurate, even for experienced dermatologists. Histopathology continues to be the gold standard, assessing specific parameters such as the Breslow index. However, it remains invasive and may lack effectiveness. Therefore, leveraging mathematical modeling and informatics has been a pursuit of diagnostic methods favoring early detection. Fractality, a mathematical parameter quantifying complexity and irregularity, has proven useful in melanoma diagnosis. Nonetheless, no studies have implemented this metric to feed artificial intelligence algorithms for the automatic classification of dermatological lesions, including melanoma. Hence, this study aimed to determine the combined utility of fractal dimension and unsupervised low-computational-requirements machine learning models in classifying melanoma and non-melanoma lesions. We analyzed 39,270 dermatological lesions obtained from the International Skin Imaging Collaboration. Box-counting fractal dimensions were calculated for these lesions. Fractal values were used to implement classification methods by unsupervised machine learning based on principal component analysis and iterated K-means (100 iterations). A clear separation was observed, using only fractal dimension values, between benign or malignant lesions (sensibility 72.4% and specificity 50.1%) and melanoma or non-melanoma lesions (sensibility 72.8% and specificity 50%) and subsequently, the classification quality based on the machine learning model was ≈80% for both benign and malignant or melanoma and non-melanoma lesions. However, the grouping of metastatic melanoma versus non-metastatic melanoma was less effective, probably due to the small sample size included in MM lesions. Nevertheless, we could suggest a decision algorithm based on fractal dimension for dermatological lesion discrimination. On the other hand, it was also determined that the fractal dimension is sufficient to generate unsupervised artificial intelligence models that allow for a more efficient classification of dermatological lesions.

A New Data Processing Approach for the SHPB Test Based on PSO-TWER

This study addresses the challenge of accurately determining the arrival time of stress wave signals in SHPB test data processing. To eliminate human error, we introduce the time-window energy ratio method and evaluate six filters for noise reduction using box fractal dimensions. A mathematical model is established to optimize the stress equilibrium and impact process, which is solved using particle swarm optimization, resulting in the PSO-TWER method. We explore the impact of inertia weight and calculation methods on optimization outcomes, defining a stress equilibrium evaluation index. The results indicate that time-window length significantly affects arrival-time outputs, and the dynamic inertia weight factor enhances optimization convergence. The method accurately determines arrival times and effectively screens test data, providing a robust approach for SHPB test data processing.

Kinematics, intensity, and spatial arrangement of extensional fractures in the Tuxtla-Malpaso fault system: Chiapas strike-slip fault province, southern Mexico

We describe the orientation, number, size, distribution, and fracture spatial arrangement in the central part of the kilometric Tuxtla-Malpaso fault system, one of the largest in the south of Mexico which cuts Cretaceous calcareous rocks. In this area, there are two sub-vertical extensional fracture sets (T1 and T2). The T1 fractures have ∼ N–S orientation and recorded 4.48 % of extension. The T2 fractures cut the T1 fractures, have NE-SW orientation, and accommodate an amount of extension of 3.87 %. These two fracture sets are parallel to two normal fault groups. The youngest normal faults (F2) have NE-SW strike and cut the N–S normal faults (F1). The F1 faults record a reactivation as strike-slip faults contemporaneous with F2.The T1 and T2 fractures have a fracture intensity between 9.08 and 9.39 (P10) on mesoscopic scale. In the case of the spacing, the value of this parameter (0.28–1) is related to fracture clustering. This behavior agrees with the values of fractal box dimension (0.72–0.81), correlation dimension (0.24–0.6), Lyapunov exponent (1.31–2.42), and coefficient of variation (0.94–1.85) on mesoscopic scale. The cumulative aperture vs. distance shows that T1 and T2 fractures have heterogeneous strain distribution. The fracture spatial arrangement is verified with the normalized correlation count analysis (NCC). The NCC graphs show a clustering behavior for T1 and T2 fractures, which are related to a regulary-spaced fractal clusters pattern. We suggest that this pattern is related to the mechanical stratigraphy and the strain location in the fault zones, while the fracture intensity depends on the degree of fracture clustering and rock type more than the amount of strain.Finally, the T1 fractures were associated with the right strike-slip kinematic for the NW-SE Tuxtla-Malpaso fault. This activity recorded a transtension behavior during the middle Miocene. The T2 fractures were formed during the reactivation (Pliocene) of the Tuxtla-Malpaso fault as the left strike-slip fault behind wrenching-transpression kinematics.

Research on the impact of pre‐existing geological fractures on hydraulic fracturing in high in situ stress environments

AbstractThe formation of complex fracture network is a difficult problem in the process of deep rock reservoir reconstruction, and the key to the generation of intricate fracture systems in deep reservoirs is to communicate more pre‐existing fractures through hydraulic fracturing, so as to enhance oil recovery. At present, there are few studies on the interactions of hydraulic fractures with pre‐existing fractures under high stress. Therefore, this research studied the influence of the number of pre‐existing fractures on the characteristics of hydraulic fractures by using advanced hydraulic fracturing instruments, and then analyzed the characteristics of hydraulic fractures under different pre‐existing fracture number based on three‐dimensional topography scanning technology and three‐dimensional square box fractal dimension calculation method. Based on the three‐dimensional finite element discrete element method, further research is carried out. The laboratory test findings indicated that the increase of pre‐existing fractures will make the pump pressure curve more stable during the test, and will significantly improve the roughness of hydraulic fractures. The numerical simulation indicated that as the quantity of pre‐existing fractures grows, the fracture area and width also increase, and in instances of a substantial quantity of pre‐existing fractures, the hydraulic fractures are prone to bifurcation, which contributes to the development of intricate fracture networks. With the increase of natural fracture angle, the fracture width decreased, but the fracture area increased. In this study, the influence of the number of pre‐existing fractures on hydraulic fracturing was studied through laboratory tests and numerical simulations, which provided theoretical reference for engineering practice.

RF fingerprint extraction and device recognition algorithm based on multi-scale fractal features and APWOA-LSSVM

RF fingerprints can be used for device identification and network access authentication. An RF fingerprint extraction and device identification algorithm based on multi-scale fractal features and APWOA-LSSVM is proposed. First, a Hilbert transform is performed on the original RF signal, and differential operations are performed on the I/Q signal. Then, the variational modal decomposition is performed on the differentially processed I/Q signals separately to obtain a number of band-limited Intrinsic Modal Function (IMF) components. The fractal box dimension of each IMF component is calculated separately as the first-dimensional RF fingerprint. The multi-fractal spectrum of the original RF signal is further computed by Multi-fractal Detrended Fluctuation Analysis (MFDFA) as the second-dimensional RF fingerprint. The RF fingerprint feature vector consists of a combination of the first- and second-dimensional RF fingerprints and is used to train the LSSVM model. Since the penalty factor and kernel parameter width directly affect the recognition accuracy and generalization ability of the LSSVM model, APWOA is used to optimize the hyperparameters of the LSSVM model. Finally, the LSSVM model is constructed using the optimal hyperparameters and the performance of the model is verified on a test dataset. The experimental results show that the proposed model achieves an average recognition accuracy of 99.13%\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\%$$\\end{document} for 16 Bluetooth devices. Multi-scale fractal features consisting of fractal box dimensions and multiple fractal dimensions are more beneficial in the recognition of wireless devices as compared to single features. In addition, the proposed model possesses superior recognition capabilities when compared to classical machine learning algorithms.

Dynamic damage and energy dissipation of fiber-reinforced cemented tailings backfill under confinement

ABSTRACT In this paper, the mechanical damage characteristics and energy dissipation patterns of fibre-reinforced cemented tailings backfill (FRCTB) under different strain rates are investigated based on the Hopkinson pressure bar apparatus equipped with confining pressure facilities, and this investigation is conducted by combining the theories of box fractal dimension and energy dissipation. The findings reveal notable observations: under lower confining pressures, the strain rate strengthening effect exhibits pronounced influences on both failure patterns and energy dissipation. However, as the confining pressure escalates, the strengthening effect gradually diminishes. The dissipation energy density displays an increasing trend with the rise in confining pressure, while the energy dissipation rate exhibits a quadratic decline as the strain rate increases. The stress-strain curves of FRCTB, under both unconfined and confined conditions, can be subdivided into four and five distinct segments, respectively. Under the lower confining pressure conditions, the fractal dimension exhibits linear growth with the increasing dissipation energy. As the confining pressure increases, this trend gradually transforms into a cubic function. Remarkably, a strong resemblance emerges between the fractal dimension, energy dissipation rate, strain rate, and confining pressure, reflecting the intricate interplay among these crucial mechanical parameters.

Analogue study on the classification and identification of landslide dynamics based on spectral features of slidequake signals

Landslides are powerful, destructive events that can generate slidequakes. Monitoring passive slidequake signals can facilitate hazard assessments, dynamic calculations, and early warning. However, there have been few direct observations of landslide dynamics. This hampers the classification and identification of landslide movements based on spectral features of slidequake signals. Here, physical analogue tests were conducted to simulate the landslide movements of three boundary conditions: open flat (OF), gully constrained curve (GC) and barrier blocking (BB). Different slope gradients, movement paths, blocking conditions and slide material structures were employed in 96 experiments to analyse the spectral features of slidequake signals and compensate for the lack of active observation data. Via spectrum identification, we analysed the vibration characteristics of the collected three-component high-frequency slidequake signals of analogue modelling landslides. Then, we modelled the landslide dynamics through feature extraction of the fractal box dimension of the slidequake signals. The OF and BB slidequake signals were identified with a prediction accuracy of 87.5%. Hence, the accurate classification and identification and capability for early warning of remote landslide dynamics based on passive slidequake signal monitoring is presented.

Recognition of rock materials after high-temperature deterioration based on SEM images via deep learning

Accurately identifying the high-temperature history experienced by rocks is essential for understanding their behaviour and predicting properties. However, current approaches are limited by the heterogeneity of rocks, test scale and costs. Here, we proposed an economical, efficient and accurate approach to identifying the rocks after high-temperature deterioration via deep learning. This deep learning-based method exhibited superior abilities in distinguishing the heat-treated rock. Using a scanning electron microscopy (SEM) image covering a size of 14.6 μm × 14.6 μm, the high-temperature deterioration history of rocks can be recognized with an accuracy of 80.2%. Features such as cracks, rock patterns, and cleavage steps in SEM images would further improve the recognition accuracy. For example, SEM images with higher fractal box dimensions show a higher recognization accuracy, especially for temperatures under 600 °C. Besides, using the deep Taylor decomposition algorithm, the high-temperature deterioration regions of the rocks in the microscale were successfully located, extracted, and characterized for the first time. This study highlights the vast potential of the deep learning-based approach in damage deterioration identification of rock after high temperature, which significantly extends the application of deep learning in underground projects.

Waveforms Eavesdropping Prevention Framework: The Case of Classification of EPG Waveforms of Aphid Utilizing Wavelet Kernel Extreme Learning Machine

ABSTRACT Since all information depends solely on the training data, machine learning algorithms typically do not employ external knowledge or other experiences during the learning process. Methods for machine learning have been rigorously tested against novel varieties of highly technical “black box” or “white box” adversarial attacks. By employing attacks, attackers can change systems to serve a harmful end goal. When authorized implementers and eavesdroppers are geographically close together, it is difficult to perform secure beamforming in waveform applications, for instance, leading to erroneous beam forms and, as a result, disastrous beam leakages. As a result, the first move in a prospective black-box offense will be based on the waveform features of a learning signal. By including a non-orthogonality concept into the physical layer signal waveform, the Waveforms Eavesdropping Prevention Framework (WEPF) proposed in this work aims to boost machine learning security to address these difficulties. The implementation scenario is based on a waveforms scenario used to categorize the Electrical Penetration Graph (EPG) for insects, a crucial tool for researching the feeding conduct of piercing-sucking insects and the transition mechanism between viruses and insects. An attribute vector with six dimensions, consisting of low-frequency wavelet energy (LFWE) in the second and third layers of the Wavelet Kernel Extreme Learning Machine, fractal box dimension (FBD), the Hurst exponent (HE), and spectral centroid (SC) in the first two layers of the HHT, was used to test the proposed framework. Two adversarial scenarios were explored. However, the suggested architecture secures all waveform signals, demonstrating the method’s effectiveness in lowering the risk of eavesdropping or tampering with the waveforms used in advanced machine-learning methods.

Spatial Analysis of Structure and Metal Mineralization Based on Fractal Theory and Fry Analysis: A Case Study in Nenjiang−Heihe Metallogenic Belt

Regional tectonics can provide excellent transport channels and precipitation sites for mineralized hydrothermal fluid. Studying the spatial relationship and distribution trends of regional tectonics and metal mineralization has theoretical and practical significance for revealing regional mineralization regularities and guiding mineral exploration. This study considers the Nenjiang-Heihe metallogenic belt, through the fractal box dimension method and Fry analysis, to explore the spatial distribution characteristics and patterns of tectonics. The results were as follows. (1) NE and NW directions are the main tectonic directions in the study area, with high-density areas concentrated in the central-eastern and central-western regions, demonstrating an overall ring-like distribution pattern. (2) Fractal dimensions of the linear structures of the NE and NW directions and the entire study area are 1.543, 1.493, and 1.622, respectively, with a strong coupling relationship between the lineament fractal high-value area and rhombic-grid spatial distribution of known deposits. (3) Gold mineralization shows the NEE and NWW directions as two main mineralization trends; the intersection area is the gold-potential area. The main trend direction of the Cu-Mo metallogenic trend belt is the NNW direction; the intersection area with the NEE direction gold metallogenic trend belt is the Au-Cu-Mo potential mineralization area.

Automatic Identification System for Rock Microseismic Signals Based on Signal Eigenvalues

The microseismic signals of rock fractures indicate that the rock mass in a particular area is changing slowly, and the microseismic signals of rock blasting indicate that the rock mass in a particular area is changing violently. It is of great significance to accurately distinguish rock fracture signals and rock microseismic signals for analyzing the changes in the rock mass in the area where the signal occurs. Considering the microseismic signals of the Dahongshan Iron Mine, the time domain, frequency domain, energy characteristic distribution, and fractal features of each signal were analyzed after noise reduction of the original signal. The results demonstrate that the signal duration and maximum amplitude of the signal could not accurately distinguish the two types of signals. However, the main frequency of the rock fracture signal after noise reduction is distributed above 500 HZ, and the main frequency of the rock blasting signal is mainly distributed below 500 HZ. After the denoised signal is decomposed by the ensemble empirical simulation decomposition, the energy of the IMF1 frequency band of the rock fracture signal occupies an absolute dominant position, and the sum of the energy of the IMF2–IMF4 frequency bands of the rock blasting signal occupies a dominant position. The fractal box dimension of the rock fracture signal is mainly below 1.1, and the fractal box dimension of the rock blasting signal is mainly above 1.25. According to the above research results, an automatic signal recognition system based on the BP neural network is established, and the recognition accuracy of the rock blasting and rock fracture signals reached 93% and 94% respectively, when this system was used.

Comparative investigation on the pyrolysis of crop, woody, and herbaceous biomass: Pyrolytic products, structural characteristics, and CO2 gasification

Pyrolysis and gasification are efficient clean energy conversion technologies used in energy research. Clean utilization of biomass energy can effectively alleviate severe energy challenges in the world. In this study, wheat straw, peach wood, and bamboo were pyrolyzed in a quartz tube furnace, and the pyrolysis gas production and physical and chemical properties of the char products were analyzed systematically. The CO2 gasification performance of the pyrolyzed char was investigated experimentally. The results indicated that the pyrolysis temperature had a significant effect on char properties. A high pyrolysis temperature accelerates the gas release rate and improves the final gas production. As the pyrolysis temperature increased, the quality of the char decreased, and the O/C and H/C molar ratios of the biomass char decreased gradually. The char calorific value was also affected by the temperature. The Fourier Transform Infrared Spectroscopy (FTIR) results demonstrated that the functional groups of the biomass decomposed. Scanning Electron Microscope (SEM) images indicated that as the pyrolysis temperature increased, pore development expanded, and various folds appeared on the surface. The fractal box dimensions first increased and then decreased. The specific surface area and micropore volume of the char first increased and then decreased; however, the temperature at which the peak value occurred was slightly different. In the gasification experiment, the peach wood char prepared by pyrolysis at 600 °C had a superior gasification effect. Biomass with a lower ash content, higher O/C ratio, and more developed pore structure exhibited superior gasification performance. The conclusions of this study have important reference value for large scale, clean, and efficient utilization of biomass resources.

Evolution Law of Micro-Pore Structure of Cement-Emulsified Asphalt Mortar Based on NMR

Cement emulsified asphalt mortar (CA) is widely used as the cushion of two types of ballastless track (CRTS I and CRTS II) in high-speed railways. Nowadays, the lack of durability of CA mortar has severely affected the quality of high-speed railways, failing to meet the requirements of sustainability. Since CA mortar is a kind of porous material, its performance can be significantly affected by its microstructures, which means that revealing the evolution law of its microstructures can provide the basis for improving its durability. Therefore, CA mortar species with different asphalt-cement ratio under different curing ages were prepared based on the requirements of CRTS II in this research and the pore structures were determined based on SEM and NMR methods. Then, a fractal model of CA mortar pore volume was proposed based on the concept of box fractal dimension, and the fractal dimension of pore volume was calculated. The relationship between fractal dimensions and mechanical property was analyzed based on Pearson correlation coefficient and regression analysis. The results suggested that the overall microstructure of CA mortar shows a loose porous space structure with cement hydration products being the continuous phase and asphalt being the dispersed phase. With the increase in A/C ratio, the hydration products produced by cement hydration decrease, and the total porosity and average porosity of CA mortar gradually increase due to the increase of asphalt hindering the hydration process of the cement. With the increase in curing age, the pore structure of CA mortar becomes more compact. However, the evolution law of CA mortar pore structure with age is not consistent under different A/C ratios due to the influence of asphalt. The pore structure of CA mortar was proved to have obvious fractal characteristics based on the concept of box fractal dimension and the experimental data of NMR. In addition, the correlation analysis proves that the fractal dimension of pore structure has an obvious positive correlation with the compressive and flexural strength, which suggests that the fractal dimension of pore volume can be a bridge for connecting the macro-property and micro-structures of CA mortar.

Numerical study of fractal analysis of crack propagation in concrete under different strain rates by meso‑scale particle element modeling

In order to explore the influence of concrete multiple cracks development on dynamic improvement mechanism under higher strain rates, a method to quantitatively describe the relationship between stress and multiple cracks development in the procesds of higher strain rates is proposed. By meso‑scale particle element modeling, SHPB stamping tests of concretes under different strain rates (30s−1≤ε˙≤140s−1) are simulated. The simulation results show that the stress-strain relationship and the law of dynamic strength improvement of concrete are consistent with the experimental results. The crack propagation in concrete under different strain rates is recorded and quantitatively described by the fractal box dimension. The crack propagation in concrete under different higher strain rates is divided into three stages, including micro crack initiation and stability stage, connectivity, extension and widening stage and fragmentation stage. This paper establishes and analyzes the relationships between stress, crack fractal dimension and strain rates under different strain rates. The research shows that at low strain rate the development of multiple cracks and failure of aggregates in concrete have a great impact on the dynamic improvement of concrete. As the strain rate increases, the inertia effect has a greater impact on the dynamic improvement of concrete.

Study on dynamic fracture properties of sandstone under the effect of high-temperature using large-scale sample

High temperatures are a crucial factor in the drilling of rock and the extraction of geothermal resources, to investigate the change rules of the dynamic fracture mechanism and physical parameters of sandstone under high temperature environment, this study conducted a series of physical parameter measurements on the sandstone treated in a range of temperatures (room temperature to 700 °C) using large single cleavage semicircle compression (LSCSC) sample. According to the experimental results, it can be observed that 400 °C is the threshold for the variation of the physical parameters of sandstone. The mass, P-wave velocity, S-wave velocity, elastic modulus and Poisson’ ratio have a significant downward trend with the temperature. The main mineral components of sandstone undergo thermochemical reactions and the variation of quartz is a fundamental cause for the deterioration of sandstone. The dynamic loading test was conducted using a drop hammer impact device and the fractured sample, the dynamic fracture test results indicate that the dynamic crack initiation time (CIT) of the samples is advanced with the temperature, but the crack speed and dynamic fracture toughness decreased with the temperature. Further discussions about SEM images and fractal box dimension of fracture surfaces can be found that with the temperature increases, the proportion of intergranular fractures of sandstone gradually increases, the effect of dynamic loads changes from destroying the grain structure of sandstone to orderly coalescing the micro-cracks in the sandstone.

A FINGERPRINT REMOVAL METHOD BASED ON FRACTAL–CRIMINISI TECHNOLOGY

Against the circumstance of redundant fingerprint information remaining in photographed images due to lens contamination, a fingerprint removal method is proposed by combining fractal technology and the Criminisi method. Fingerprints on an image are usually distributed in a dispersive pattern, and show statistical fractal characteristic. Therefore, based on the Criminisi method, the textural complexity of image pixel blocks expressed by box-counting fractal dimension is introduced into this method as a parameter of pixel block size and subitem of the data item with priority. On the one hand, this way of operation can select the size of the pixel blocks to be removed adaptive to the box fractal dimension; on the other hand, the box fractal dimension, as the subitem of the data item with priority, can avoid the effect of particular value and improve the reliability and stability of priority. The experimental results show that the proposed method can satisfactorily perform the fingerprint removal task and fill the information.

Pore Characteristics and Fractal Dimension Analysis of Tectonic Coal and Primary-Structure Coal: A Case Study of Sanjia Coal Mine in Northern Guizhou.

Understanding the pore heterogeneity of tectonic coal and primary-structure coal is of great significance for predicting and preventing tectonic coal. This study adopts the low-temperature nitrogen adsorption method, mercury injection experiment, and other methods, combined with fractal theory, to quantitatively analyze the pore distribution of coal samples inside and outside the outburst cavities of the Sanjia coal mine. The experiments have shown that the contents of aliphatic functional groups and hydrogen in tectonic coal are higher than those of aromatic structural functional groups. Raw coal has more straight chains than side chains, whereas aliphatic hydrocarbon mostly has short chains, and the branching degree is high. Soft and primary-structure coals have similar elemental content and tectonic effects endow the coal with better connectivity. The pores are filled with particles and flakes, and the surfaces of tectonic coal have more pores and fissures on them. According to the experimental curve, the pores are divided into five types. The pore size of primary-structure coal is mainly type II pores, and the pore size distribution of tectonic coal is relatively wide, with the majority being class I and class II pores. The specific surface area of tectonic coal is 60.7% more than that of primary-structure coal. The box fractal dimension of coal decreases with the increase in scanning electron microscopy (SEM) magnification. The minimum fractal dimension of tectonic coal is 2.49, which is 7.8% lower than the peak of 2.70. It can be seen from the fractal dimension that the fractal dimensions of pore types II, III, and IV are rougher.

Experimental Study of Multi-Angle Effects of Micron-Silica Fume on Micro-Pore Structure and Macroscopic Mechanical Properties of Rock-like Material Based on NMR and SEM

The experiment of rock-like material plays an important role in the simulation of engineering fractured rock mass. To further understand the influence of raw materials on rock-like materials, this paper carried out the indoor mechanical properties test and the micro-pore structure detection combining NMR and SEM. The effects of micron-silica fume (SF) on microporous structure parameters and macroscopic mechanical properties under different conditions of water–cement ratio (WCR) and sand–cement ratio (SCR) were discussed. The intrinsic relationship between parameters of different scales was analyzed. The experimental results showed that the porosity parameters of different radii gradually decreased with the increase in SF. The reduction rate of macroporous porosity was the greatest, and the decreasing rate of microporous porosity was the smallest. With the increase in SF, the microscopic characteristics of the internal surface changed from more pores, complex morphological distribution, rough surface to fewer pores, regular morphological distribution and flat and uniform surface. The box fractal dimension also showed a decreasing trend. Micro-pore structure makes a valuable contribution to the influence of SF on mechanical properties. The compressive strength and tensile strength increased with the increase in SF. The box fractal dimension and porosity of different radii were negatively correlated with mechanical strength. Different porosity parameters conformed to a good exponential relationship with mechanical properties. The research results can provide reference value and research space for subsequent rock-like material research.

A new multiple-factor clustering method considering both box fractal dimension and orientation of joints

The paper proposes a new multiple-factor clustering method (NMFCM) with consideration of both box fractal dimension (BFD) and orientation of joints. This method assumes that the BFDs of different clusters were uneven, and clustering was performed by redistributing the joints near the boundaries of clusters on a polar map to maximize an index for estimating the difference of the BFD (DBFD). Three main aspects were studied to develop the NMFCM. First, procedures of the NMFCM and reasonableness of assumptions were illustrated. Second, main factors affecting the NMFCM were investigated by numerical simulations with disk joint models. Finally, two different sections of a rock slope were studied to verify the practicability of the NMFCM. The results demonstrated that: (1) The NMFCM was practical and could effectively alleviate the problem of hard boundary during clustering; (2) The DBFD tended to increase after the improvement of clustering accuracy; (3) The improvement degree of the NMFCM clustering accuracy was mainly influenced by three parameters, namely, the number of clusters, number of redistributed joints, and total number of joints; and (4) The accuracy rate of clustering could be effectively improved by the NMFCM.