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![Three rock fracture network diagrams (Reprinted from Figure 11 of reference [28]. Journal of Petroleum Science and Engineering, 92, Alireza Jafari and Tayfun Babadagli, Estimation of equivalent fracture network permeability using fractal and statistical network properties, 110-123, Copyright (2012), with permission from Elsevier (Amsterdam, The Netherlands)).](publication/361546849/figure/fig5/AS:1182493927579671@1658939930525/Three-rock-fracture-network-diagrams-Reprinted-from-Figure-11-of-reference-28-Journal.png)
Three rock fracture network diagrams (Reprinted from Figure 11 of reference [28]. Journal of Petroleum Science and Engineering, 92, Alireza Jafari and Tayfun Babadagli, Estimation of equivalent fracture network permeability using fractal and statistical network properties, 110-123, Copyright (2012), with permission from Elsevier (Amsterdam, The Netherlands)).
Source publication
Fractal characteristics and the fractal dimension are widely used in the description and characterization of rock fracture networks. They are important tools for coal mining, oil and gas transportation, and other engineering problems. However, due to the complexity of rock fracture networks and the difficulty in directly applying the limit definiti...
Contexts in source publication
Context 1
... diagrams are used to compare and verify the effectiveness of the simple method of fractal calculation. First, for a, b, and c, from left to right, as shown in Figure 5, Figure 6 is obtained by inversing the three rock fracture network diagrams. Then, the boxcounting dimension of the inversed rock fracture network diagram is calculated using the FRACLAB toolbox in MATLAB (2018a), which uses the box-counting dimension calculation method discussed in Section 3.1. ...
Context 2
... to the new definition of fractal dimensions, an HT index of no less than 3 can be considered to be a fractal, meaning that the fractal dimensions of the three rock fracture networks can be calculated. According to the data in Table 1, the calculation results of the fractal dimensions of the rock fracture networks are as follows: Figure 5 (where N is the number, M is the average, Hi (i = 1,2,3,4,5) is the head of the ith breaking, and Ti (i = 1,2,3,4,5) is the tail of the ith breaking). The fractal dimensions of the rock fracture networks are 1.852, 1.668, and 1.498. ...
Citations
... There can be different types of objects measured to embody fractal urban morphology, from built-up areas to road network structures [16][17][18]. When the objects are architectures, there exists a spatial correlation between the distribution of architecture and urban morphology [19]. ...
Urban morphology has been empirically demonstrated to be self-organized and can be quantified by fractal dimension. However, the spatial variation rule of fractal features at the sub-zone scale has yet to be uncovered, as well as the relationship between fractal dimension values and road network or land-use patterns. In this study, the urban area is partitioned into 158 grid units, with subsequent calculations conducted to determine the fractal dimensions (using 2D box-counting and 3D voxel-counting methods), road network characteristics, and land-use patterns within each individual unit. The pattern of how architectures fill into the 2D or 3D embedding space at the grid level is revealed. Moreover, the spatial relationship between the road network, land-use, and their impacts on the local architectural layout is elucidated by employing MGWR, a model that incorporates the principles of fitting localized spatial regression. The results are as follows: (1) urban morphology follows fractal laws at a sub-zone scale, both in a 2D plane and 3D volume; (2) the filling degree of architecture is high in the urban center but low in the periphery areas; (3) the selected variables fit well with the regression models; (4) there is spatial heterogeneity regarding the influence of each factor. The research findings provide valuable insights into the theoretical relationship between urban morphology and the composite structure of road networks and land use. This facilitates identifying crucial areas and priority directions for urban renewal construction, as well as optimizing architectural design to improve efficiency and functionality.
... The expansion stress of the self-stress grouting material was tested using a self-developed test device, and the relationship between the expansion stress and the content of the expansion agent was analyzed. Wang Zhi et al. [37,38] studied the mechanical properties of grouting reinforcements in rock under static and cyclic impact loads and used a drop hammer impact test device to study a failure mechanism and damage evolution model of red sandstone samples with different grouting types. ...
With increases in mining depth and intensity, disasters such as stress concentration, slab failure, and coal body dynamic outbursts at the coal–rock interface have become more serious. Therefore, it is important to analyze the stress–strain behavior of coal–rock combinations to explore the deterioration process and failure characteristics of coal–rock combinations. In this study, we used field survey, theoretical analysis, and numerical simulation methods to explore the microstructure characteristics of the coal–rock interface and the influence of interlayer thickness on the composite body. The results show that with the increase in interlayer thickness, the compressive strength of the composite body gradually decreases. This reduction is mainly due to the interlayer dividing the coal sample, resulting in a decrease in the equivalent elastic modulus of the composite body, weakening of the overall integrity, and a decrease in carrying capacity. In addition, the failure mode and mechanical properties of the coal–rock combination are influenced by the interlayer position. Different “soft layer” positions can lead to changes in the overall carrying and failure modes of the coal–rock composite. The position of the interlayer also has a significant influence on the failure mode and fracture propagation of the composite body. This study provides an important theoretical reference for the control of coal–rock deformation and instability and regional rock mass modification in underground engineering.
... FRACLAB, a general signal and image processing toolbox based on fractal and multifractal methods in MATLAB, is employed to calculate the box-counting fractal dimensions of hydraulic fractures (Movassagh et al. 2021;Sui et al. 2022). Figure 24a shows that the complexities of the hydraulic fractures depicted by the two models under the different hydrostatic in-situ stress conditions are similar. ...
Hydraulic fracturing, which determines geothermal resource productivity, is one of the critical technical components in the construction of hot dry rock (HDR) reservoirs. Although the mechanical coupling between solid and fluid has been included in algorithms based on the discrete element method (DEM) generally employed to investigate hydraulic fracturing, crystalline rocks of reservoirs are mostly treated as homogeneous isotropic models without considering their petrographic texture. By combining a grain-based model (GBM) and a modified fluid–solid coupling algorithm, a novel hydro-GBM is constructed in this study to analyze the hydraulic fracturing response of polycrystalline rocks. Moreover, acoustic emission (AE) events during fracturing are extracted to describe the characteristics of hydraulic-fracturing-induced seismicity. Under in-situ conditions with high differential stress, the propagation direction of hydraulic fractures is mainly perpendicular to the direction of minimum in-situ stress, with little influence by material heterogeneity and fluid viscosity; under near-hydrostatic in-situ stress conditions, the microcracks along the mineral boundaries increase remarkably, and the fracture pattern tends to be complex, especially when a low-viscosity fluid is injected into the rock. From the Gutenberg-Richter type relationship between the AE event numbers and the moment magnitudes, it is found that large induced seismic events increase with in-situ stress and with fluid viscosity. In summary, the proposed hydro-GBM can well reproduce the propagation behavior of hydraulic fractures influenced by material heterogeneity, and the research results reveal the interactions between petrographic texture, in-situ stress, fluid viscosity, and hydraulic fracturing characteristics, which will provide a valuable reference for on-site reservoir stimulation.
... The compaction characteristics of graded crushed gangue are influenced by external factors, many scholars have investigated the compaction and deformation characteristics of bulk gangue particles [34,35]. However, previous work has been limited by the test conditions, and the compaction characteristics of graded gangue under high stress and considerations for intermittent graded gangue compaction stage division research remains to be clarified. ...
The compaction and re-crushing characteristics of crushed gangue are important factors which affect the quality and effectiveness of the filling of the quarry. To study the compaction and re-crushing characteristics of the gangue particles, continuous grading and intermittent grading of two different structures were designed to study the bulk gangue particle size distribution. By conducting a side-limited uniaxial compression test on the crushed gangue, the compaction deformation parameters and particle re-crushing parameters of the samples under different axial pressure and grading conditions were calculated, the interaction between compaction and re-crushing was determined, and a compaction-re-crushing model of the crushed gangue was established. The following conclusions were obtained, (1) the axial displacement increment and fractal dimension of the graded crushed gangue are closely related to the graded structure of the skeletal particles; (2) the compaction stage of the graded crushed gangue can be divided into a fast compaction stage, a slow compaction stage, and a stable compaction stage—the fast compaction stage is significantly elastic, the slow compaction stage is more plastic, and the stable stage behavior approaches that of the original rock body; (3) the degree of crushing of the graded crushed gangue increases with an increase in axial stress, and the re-crushing of the specimen mainly occurs in the slow compaction stage; (4) the compaction-crushing-fractal evolution of the graded crushed gangue in the lateral limit compression process is established as the line of questioning. The physical significance of the parameters in the equation is discussed in this paper. The study can provide theoretical support and engineering guidance for the precise filling of a quarry and the prevention of later collapse.
The transition from the “spatial turn” of the 1980s to the “topological turn” in the twenty-first century brought about a “topological revolution” in geography. Yet, while geographers employ a wide range of possible geometric analyses, they seldom use notions or methods of topology, with the exception of GIS. There is a wide range of intersections between topology and geography however, since there are several hitherto disregarded notions of topology, that are nevertheless useful in geography (fractal urban morphologies and the Four Colors Theorem are characteristic cases), but the topological turn can be traced in several more facets of geography, at the crossroads of geography with anthropology, sociology and ICTs.
As one of the most important geophysical methods for detecting the lunar underground structure of the Moon, the lunar penetrating radar (LPR) is applied to the Chang’e-4 (CE-4) mission to explore the Von Kármán crater on the far side of the Moon. With the Yutu-2 rover continues to move towards the Zhinyu crater at the west, radar will likely detect the fractures created by the impact that formed the Zhinyu Crater. Therefore, the establishment of a comprehensive lunar subsurface structure model with fracture, random media and fractal terrain is crucial for the LPR data processing and the understanding of the lunar geological impact process. In addition, the method that can image the radar data with fractures well has great significance to the interpretation of the LPR data. In this paper, we establish a comprehensive lunar subsurface structure model firstly, the considering factors including fractures, random media, fractal terrain, and the radar response are calculated through forward modeling. Secondly, according to the high resolution and the sensitive to inhomogeneities of LPR data, we design a set of processing flow including plane-wave destruction, velocity analysis based on the focusing analysis method and migration imaging based on the velocity continuation. Finally, the results including simulation data and Antarctic fracture data are used to verify the effectiveness of imaging method.
