The split-Hopkinson pressure bar(SHPB)and digital image correlation(DIC)techniques are combined to analyze the dynamic compressive failure process of coal samples,and the box fractal dimension is used to quantitativel...The split-Hopkinson pressure bar(SHPB)and digital image correlation(DIC)techniques are combined to analyze the dynamic compressive failure process of coal samples,and the box fractal dimension is used to quantitatively analyze the dynamic changes in the coal sample cracks under impact load conditions with different loading rates.The experimental results show that the fractal dimension can quantitatively describe the evolution process of coal fractures under dynamic load.During the dynamic compression process,the evolution of the coal sample cracks presents distinct stages.In the crack propagation stage,the fractal dimension increases rapidly with the progress of loading,and in the crack widening stage,the fractal dimension increases slowly with the progress of loading.The initiation of the crack propagation phase of the coal samples gradually occurs more quickly with increasing loading rate;the initial cracks appear earlier.At the same loading time point,when the loading rate is greater,the fractal dimension of the cracks observed in the coal sample is greater.展开更多
A fractal pore structure model of combustible cartridge cases was established by virtue of the fractal geometry. Pore structure information, such as backbone fractal dimension and pore fractal dimension, of four kinds...A fractal pore structure model of combustible cartridge cases was established by virtue of the fractal geometry. Pore structure information, such as backbone fractal dimension and pore fractal dimension, of four kinds of combustible cartridge case were obtained by mercury intrusion porosimetry (MIP) . The formation mechanism of fractal pore structure of combustible cartridge was studied. The results show that the backbone fractal dimension consists of the component and influenced by the component number and size of components; the pore percolation fractal dimension reflects the pore structures of components; and the fractal dimension of pore structure is positively relative to the tensile strength of combustible cartridge case.展开更多
Deep geothermal extraction processes expose rock masses to frequent and significant temperature fluctuations. Developing a comprehensive understanding of the shear fracture mechanisms and crack propagation behaviors i...Deep geothermal extraction processes expose rock masses to frequent and significant temperature fluctuations. Developing a comprehensive understanding of the shear fracture mechanisms and crack propagation behaviors in rocks under the influence of cyclic heating is imperative for optimizing geothermal energy extraction. This study encompasses several critical aspects under cyclic heating conditions, including the assessment of stress distribution states, the characterization of two-dimensional fracture paths, the quantitative analysis of three-dimensional damage characteristics on fracture surfaces, and the determination of the fractal dimension of debris generated after the failure of granite. The test results demonstrate that cyclic heating has a pronounced adverse effect on the physical and mechanical properties of granite. Consequently, stress tends to develop and propagate in a direction perpendicular to the two-dimensional fracture path. This leads to an increase in the extent of tensile damage on the fracture surface and accelerates the overall rock failure process. This increases the number of small-sized debris, raises the fractal dimension, and enhances the rock’s rupture degree. In practical enhanced geothermal energy extraction, the real-time monitoring of fracture propagation within the reservoir rock mass is achieved through the analysis of rock debris generated during the staged fracturing process.展开更多
In Xikuangshan antimony ore-field, the western fracture zone is a composite of major fault, F75, and its secondary faults, such as F71, F72 and F3 etc.. On plane, the fracture zone scatters from southwest to northeast...In Xikuangshan antimony ore-field, the western fracture zone is a composite of major fault, F75, and its secondary faults, such as F71, F72 and F3 etc.. On plane, the fracture zone scatters from southwest to northeast, and concentrates from upper to deeper level on profile. All ore-bodies exist in the carbonate of footwall of the major fault or that of the footwall of its secondary faults. From 480 m and 320 m to 120 m level, the fractal dimensional number of the fault system decreases from 1.482 2 and 1.448 6 to 1.339 2, which indicates the form of fracture zone becoming more simple at deeper level. And in five sub-ranges, the III and IV sub-ranges are the known area, and the I, II and V sub-ranges are unknown. The fractal studies of the western fracture zone in these sub-ranges show that the fractal dimensional numbers of the I and II, being 1.201 5 and 1.278 0, respectively, are smaller than that of the III and IV, being 1.475 9 and 1.576 9, respectively; and that of the V, being 1.571 2, keeps with that of the III, IV sub-ranges. So mineralization is not well in I and II sub-ranges, and V sub-range is the best to benefit mineralization.展开更多
this paper, a more stable and accurate recursing equation and computing procedure are proposed to calculate scattering width of the multilayered cylinder. This procedure is applied to compute the distribution of the s...this paper, a more stable and accurate recursing equation and computing procedure are proposed to calculate scattering width of the multilayered cylinder. This procedure is applied to compute the distribution of the scattering width and to analyze the characteristic of scattering from fractal multilayered cylinder. The connection between the characteristic of scattering and fractal dimension is discussed, and some important results are obtained.展开更多
The geological structure of coal seams in China is remarkably varied and complex,with coalbed methane reservoirs marked by significant heterogeneity and low permeability,creating substantial technical challenges for e...The geological structure of coal seams in China is remarkably varied and complex,with coalbed methane reservoirs marked by significant heterogeneity and low permeability,creating substantial technical challenges for efficient extraction.This study systematically investigates the impact of liquid nitrogen immersion(LNI)on the coal’s pore structure and its mechanism of enhancing permeability with a combination of quantitative nuclear magnetic resonance(NMR)analysis,nitrogen adsorption experiments,and fractal dimension calculations.The results demonstrate that LNI can damage the coal’s pore structure and promote fracture expansion through thermal stress induction and moisture phase transformation,thereby enhancing the permeability of coal seams.The T_(2)peak area in the NMR experiments on coal samples subjected to LNI treatment shows a significant increase,the Brunauer-Emmett-Teller(BET)specific surface area decreases to 6.02 m^(2)/g,and the Barrett-Joyner-Halenda(BJH)total pore volume increases to 14.99 mm^(3)/g.Furthermore,changes in fractal dimensions(D_(1)rising from 2.804 to 2.837,and D_(2)falling from 2.757 to 2.594)indicate a notable enhancement in the complexity of the pore structure.With increasing LNI cycles,the adsorption capacity of the coal samples diminishes,suggesting a significant optimization of the pore structure.This optimization is particularly evident in the reconstruction of the micropore structure,which in turn greatly enhances the complexity and connectivity of the sample’s pore network.In summary,the study concludes that LNI technology can effectively improve the permeability of coal seams and the extraction efficiency of coalbed methane by optimizing the micropore structure and enhancing pore connectivity,which offers a potential method for enhancing the permeability of gas-bearing coal seams and facilitating the development and utilization of coalbed methane.展开更多
根据分形几何理论的基本概念,就无序分形多孔介质孔隙率φ和渗透率K与多孔介质结构分数维数Df的关系进行了推导,利用Sierpinski固相分形体(Solid mass fractal)与孔相分形体(Pore mass fractal)概念对分形多孔介质微结构特征、孔隙累积...根据分形几何理论的基本概念,就无序分形多孔介质孔隙率φ和渗透率K与多孔介质结构分数维数Df的关系进行了推导,利用Sierpinski固相分形体(Solid mass fractal)与孔相分形体(Pore mass fractal)概念对分形多孔介质微结构特征、孔隙累积数量-尺寸分布和孔隙率φ等参数及其物理关系给予了详细论述,定量地分析和讨论了基于不同模型的渗透率-分形维数关系与它们的差异。展开更多
The relationship among the surface fissure ratio, moisture content, seepage coefficient and deformation modulus of field unsaturated expansive soil in Nanning, Guangxi Province, China, was obtained by a direct or indi...The relationship among the surface fissure ratio, moisture content, seepage coefficient and deformation modulus of field unsaturated expansive soil in Nanning, Guangxi Province, China, was obtained by a direct or indirect method. Digital images of expansive soil of the surface fissure with different moisture contents were analyzed with the binarization statistic method. In addition, the fissure fractal dimension was computed with a self-compiled program. Combined with in situ seepage and loading plate tests, the relationship among the surface fissure ratio, moisture content, seepage coefficient and deformation modulus was initially established. The surface fissure ratio and moisture content show a linear relation, ＂y=-0.019 1x＋1.028 5＂ for rufous expansive soil and ＂y=-0.07 1x＋2.610 5＂ for grey expansive soil. Soil initial seepage coefficient and surface fissure ratio show a power function relation, ＂y=1× 10^-9exp（15.472x）＂ for rufous expansive soil and ＂y=5× 10^-7exp（4.209 6x）＂ for grey expansive soil. Grey expansive soil deformation modulus and surface fissure ratio show a power fimction relation of ＂y=3.935 7exp（0.993 6x）＂. Based on the binarization and fractal dimension methods, the results show that the surface fissure statistics can depict the fissure distribution in the view of two dimensions. And the evolvement behaviors of permeability and the deformation modulus can indirectly describe the developing state of the fissure. The analysis reflects that the engineering behaviors of unsaturated expansive soil are objectively influenced by fissure.展开更多
原始精细的路面谱是研究车辆与路面耦合的重要基础,对车辆的通过性和噪声、振动及不平顺性NVH(noise,vibration and harshness)分析有重要的应用价值。为了构建与原始路面相同或相近的路面谱,利用非接触式激光路面不平度仪测量沥青路面...原始精细的路面谱是研究车辆与路面耦合的重要基础,对车辆的通过性和噪声、振动及不平顺性NVH(noise,vibration and harshness)分析有重要的应用价值。为了构建与原始路面相同或相近的路面谱,利用非接触式激光路面不平度仪测量沥青路面、水泥路面、比利时路面和砂石路面的三维路面不平度;基于分形理论,采用迭代函数法重构这四种路面谱;结合路面不平度的统计特性评价指标和分形维数对四种路面的原始谱和重构谱进行评价。研究结果表明:重构前、后路面谱的平均值、标准差、峰度系数以及分形维数变化范围在±5%以内,除水泥路面的偏态系数变化范围均在±9%以内,重构路面谱与原始谱具有一致性;重构路面谱保持了原始路面的结构特性,并具有路面的细微结构。展开更多
Surface textures had long been recognized as primary factors to provide the skid resistance on pavements; however, no measurement of skid resistance on pervious concrete pavement with various surface texture parameter...Surface textures had long been recognized as primary factors to provide the skid resistance on pavements; however, no measurement of skid resistance on pervious concrete pavement with various surface texture parameters had been made. Fractal geometry was introduced in the present work to accurately simulate transect contour curves of pervious concrete specimens through fractal interpolation. It is proved that its fractal dimension (D) can be adopted to measure the skid resistance on pervious concrete pavement, overcoming the shortcomings of both macrotexture depth (DT ) and British portable pendulum number (NBP). Combined with Fujikawa-Koike tire/road contact model, the optimization method of all surface textures was recommended for designing and constructing excellently skid-resistant and noise-absorptive pervious concrete pavement. In addition, evaluating of the abrasion process and attenuation of the surface textures on concrete pavement slabs was also the focus of this work based on accelerated abrasion test. Results show that the surface textures on pervious concrete pavement slabs is extremely durable, compared to those on conventional grooved or exposed aggregate concrete pavement slabs.展开更多
基金Projects(51822403,51827901)supported by the National Natural Science Foundation of ChinaProject(2019ZT08G315)supported by the Department of Science and Technology of Guangdong Province,China。
文摘The split-Hopkinson pressure bar(SHPB)and digital image correlation(DIC)techniques are combined to analyze the dynamic compressive failure process of coal samples,and the box fractal dimension is used to quantitatively analyze the dynamic changes in the coal sample cracks under impact load conditions with different loading rates.The experimental results show that the fractal dimension can quantitatively describe the evolution process of coal fractures under dynamic load.During the dynamic compression process,the evolution of the coal sample cracks presents distinct stages.In the crack propagation stage,the fractal dimension increases rapidly with the progress of loading,and in the crack widening stage,the fractal dimension increases slowly with the progress of loading.The initiation of the crack propagation phase of the coal samples gradually occurs more quickly with increasing loading rate;the initial cracks appear earlier.At the same loading time point,when the loading rate is greater,the fractal dimension of the cracks observed in the coal sample is greater.
基金Sponsored by Young Fund Programs of Explosives&Propellants ( HYZ08010202-4)
文摘A fractal pore structure model of combustible cartridge cases was established by virtue of the fractal geometry. Pore structure information, such as backbone fractal dimension and pore fractal dimension, of four kinds of combustible cartridge case were obtained by mercury intrusion porosimetry (MIP) . The formation mechanism of fractal pore structure of combustible cartridge was studied. The results show that the backbone fractal dimension consists of the component and influenced by the component number and size of components; the pore percolation fractal dimension reflects the pore structures of components; and the fractal dimension of pore structure is positively relative to the tensile strength of combustible cartridge case.
基金Project(52409132) supported by the National Natural Science Foundation of ChinaProject(ZR2024QE018) supported by the Natural Science Foundation of Shandong Province,China+2 种基金Project(BK20240431) supported by Basic Research Program of Jiangsu,ChinaProject(SNKJ2023A07-R14) supported by the Major Key Technical Research Projects of Shandong Energy Group,ChinaProject(2024M751813) supported by China Postdoctoral Science Foundation。
文摘Deep geothermal extraction processes expose rock masses to frequent and significant temperature fluctuations. Developing a comprehensive understanding of the shear fracture mechanisms and crack propagation behaviors in rocks under the influence of cyclic heating is imperative for optimizing geothermal energy extraction. This study encompasses several critical aspects under cyclic heating conditions, including the assessment of stress distribution states, the characterization of two-dimensional fracture paths, the quantitative analysis of three-dimensional damage characteristics on fracture surfaces, and the determination of the fractal dimension of debris generated after the failure of granite. The test results demonstrate that cyclic heating has a pronounced adverse effect on the physical and mechanical properties of granite. Consequently, stress tends to develop and propagate in a direction perpendicular to the two-dimensional fracture path. This leads to an increase in the extent of tensile damage on the fracture surface and accelerates the overall rock failure process. This increases the number of small-sized debris, raises the fractal dimension, and enhances the rock’s rupture degree. In practical enhanced geothermal energy extraction, the real-time monitoring of fracture propagation within the reservoir rock mass is achieved through the analysis of rock debris generated during the staged fracturing process.
文摘In Xikuangshan antimony ore-field, the western fracture zone is a composite of major fault, F75, and its secondary faults, such as F71, F72 and F3 etc.. On plane, the fracture zone scatters from southwest to northeast, and concentrates from upper to deeper level on profile. All ore-bodies exist in the carbonate of footwall of the major fault or that of the footwall of its secondary faults. From 480 m and 320 m to 120 m level, the fractal dimensional number of the fault system decreases from 1.482 2 and 1.448 6 to 1.339 2, which indicates the form of fracture zone becoming more simple at deeper level. And in five sub-ranges, the III and IV sub-ranges are the known area, and the I, II and V sub-ranges are unknown. The fractal studies of the western fracture zone in these sub-ranges show that the fractal dimensional numbers of the I and II, being 1.201 5 and 1.278 0, respectively, are smaller than that of the III and IV, being 1.475 9 and 1.576 9, respectively; and that of the V, being 1.571 2, keeps with that of the III, IV sub-ranges. So mineralization is not well in I and II sub-ranges, and V sub-range is the best to benefit mineralization.
文摘this paper, a more stable and accurate recursing equation and computing procedure are proposed to calculate scattering width of the multilayered cylinder. This procedure is applied to compute the distribution of the scattering width and to analyze the characteristic of scattering from fractal multilayered cylinder. The connection between the characteristic of scattering and fractal dimension is discussed, and some important results are obtained.
基金Projects(52204226,52104204,52474276)supported by the National Natural Science Foundation of ChinaProject(tsqnz20221140)supported by the Taishan Scholars Project of China+1 种基金Projects(ZR2022QE243,ZR2024ME097)supported by the Natural Science Foundation of Shandong Province of ChinaProject(252300421010)supported by the Excellent Youth Foundation of Henan Scientific Committee,China。
文摘The geological structure of coal seams in China is remarkably varied and complex,with coalbed methane reservoirs marked by significant heterogeneity and low permeability,creating substantial technical challenges for efficient extraction.This study systematically investigates the impact of liquid nitrogen immersion(LNI)on the coal’s pore structure and its mechanism of enhancing permeability with a combination of quantitative nuclear magnetic resonance(NMR)analysis,nitrogen adsorption experiments,and fractal dimension calculations.The results demonstrate that LNI can damage the coal’s pore structure and promote fracture expansion through thermal stress induction and moisture phase transformation,thereby enhancing the permeability of coal seams.The T_(2)peak area in the NMR experiments on coal samples subjected to LNI treatment shows a significant increase,the Brunauer-Emmett-Teller(BET)specific surface area decreases to 6.02 m^(2)/g,and the Barrett-Joyner-Halenda(BJH)total pore volume increases to 14.99 mm^(3)/g.Furthermore,changes in fractal dimensions(D_(1)rising from 2.804 to 2.837,and D_(2)falling from 2.757 to 2.594)indicate a notable enhancement in the complexity of the pore structure.With increasing LNI cycles,the adsorption capacity of the coal samples diminishes,suggesting a significant optimization of the pore structure.This optimization is particularly evident in the reconstruction of the micropore structure,which in turn greatly enhances the complexity and connectivity of the sample’s pore network.In summary,the study concludes that LNI technology can effectively improve the permeability of coal seams and the extraction efficiency of coalbed methane by optimizing the micropore structure and enhancing pore connectivity,which offers a potential method for enhancing the permeability of gas-bearing coal seams and facilitating the development and utilization of coalbed methane.
文摘根据分形几何理论的基本概念,就无序分形多孔介质孔隙率φ和渗透率K与多孔介质结构分数维数Df的关系进行了推导,利用Sierpinski固相分形体(Solid mass fractal)与孔相分形体(Pore mass fractal)概念对分形多孔介质微结构特征、孔隙累积数量-尺寸分布和孔隙率φ等参数及其物理关系给予了详细论述,定量地分析和讨论了基于不同模型的渗透率-分形维数关系与它们的差异。
基金Projects(41102229,51109208)supported by the National Natural Science Foundation of ChinaProject(2011CDB407)supported by Natural Science Foundation of Hubei Province,ChinaProject supported by Qing Lan Project of Jiangsu Province,China
文摘The relationship among the surface fissure ratio, moisture content, seepage coefficient and deformation modulus of field unsaturated expansive soil in Nanning, Guangxi Province, China, was obtained by a direct or indirect method. Digital images of expansive soil of the surface fissure with different moisture contents were analyzed with the binarization statistic method. In addition, the fissure fractal dimension was computed with a self-compiled program. Combined with in situ seepage and loading plate tests, the relationship among the surface fissure ratio, moisture content, seepage coefficient and deformation modulus was initially established. The surface fissure ratio and moisture content show a linear relation, ＂y=-0.019 1x＋1.028 5＂ for rufous expansive soil and ＂y=-0.07 1x＋2.610 5＂ for grey expansive soil. Soil initial seepage coefficient and surface fissure ratio show a power function relation, ＂y=1× 10^-9exp（15.472x）＂ for rufous expansive soil and ＂y=5× 10^-7exp（4.209 6x）＂ for grey expansive soil. Grey expansive soil deformation modulus and surface fissure ratio show a power fimction relation of ＂y=3.935 7exp（0.993 6x）＂. Based on the binarization and fractal dimension methods, the results show that the surface fissure statistics can depict the fissure distribution in the view of two dimensions. And the evolvement behaviors of permeability and the deformation modulus can indirectly describe the developing state of the fissure. The analysis reflects that the engineering behaviors of unsaturated expansive soil are objectively influenced by fissure.
文摘原始精细的路面谱是研究车辆与路面耦合的重要基础,对车辆的通过性和噪声、振动及不平顺性NVH(noise,vibration and harshness)分析有重要的应用价值。为了构建与原始路面相同或相近的路面谱,利用非接触式激光路面不平度仪测量沥青路面、水泥路面、比利时路面和砂石路面的三维路面不平度;基于分形理论,采用迭代函数法重构这四种路面谱;结合路面不平度的统计特性评价指标和分形维数对四种路面的原始谱和重构谱进行评价。研究结果表明:重构前、后路面谱的平均值、标准差、峰度系数以及分形维数变化范围在±5%以内,除水泥路面的偏态系数变化范围均在±9%以内,重构路面谱与原始谱具有一致性;重构路面谱保持了原始路面的结构特性,并具有路面的细微结构。
基金Project(kfj080205) supported by Key Laboratory of Road Structure and Material of Ministry of Transport of Changsha, China
文摘Surface textures had long been recognized as primary factors to provide the skid resistance on pavements; however, no measurement of skid resistance on pervious concrete pavement with various surface texture parameters had been made. Fractal geometry was introduced in the present work to accurately simulate transect contour curves of pervious concrete specimens through fractal interpolation. It is proved that its fractal dimension (D) can be adopted to measure the skid resistance on pervious concrete pavement, overcoming the shortcomings of both macrotexture depth (DT ) and British portable pendulum number (NBP). Combined with Fujikawa-Koike tire/road contact model, the optimization method of all surface textures was recommended for designing and constructing excellently skid-resistant and noise-absorptive pervious concrete pavement. In addition, evaluating of the abrasion process and attenuation of the surface textures on concrete pavement slabs was also the focus of this work based on accelerated abrasion test. Results show that the surface textures on pervious concrete pavement slabs is extremely durable, compared to those on conventional grooved or exposed aggregate concrete pavement slabs.
