Fractal Dimension Characteristics Research Articles

Effects of different sand fixation plantations on soil properties in the Hunshandake Sandy Land, Eastern Inner Mongolia, China

Planting forests is an effective way to improve desertification. In order to elucidate the impacts of different vegetation types on soil development and restoration of degraded lands, we compared the properties of soils at different depths in three plantation forests in the Hunsandak Sandy Land in the Chinese agro-pastoral ecotone (Ulmus pumila, Pinus sylvestris var. mongolica, and Populus simonii). The results show that all three plantation forests were able to significantly improve the soil properties, and they resulted in soil nutrient enrichment in the surface layer. As the soil depth increased, the soil became progressively poorer in nutrients, the fine particle content decreased, and the bulk density and water content increased. The orders of the fractal dimension characterization and soil improvement effects of the different tree species were as follows: U. pumila > P. sylvestris var. mongolica > P. simonii. Compared with the bare sand, the soil bulk density under the U. pumila plantation was 19% lower; the soil water content was 74% higher; the soil organic matter, total N, P, and K were 336%, 207%, 106%, and 31% higher; the available N, P, and K were 41%, 125%, and 21% higher; and the clay and silt contents were 498% and 387% higher, respectively. The ranges of the soil fractal dimension were 1.67–2.08 for the bare sandy land and 2.14–2.32 for the planted forests. The soil fractal dimension was strongly correlated with the soil physicochemical properties, especially with the soil nutrients and fine particle content, which exhibited highly significant correlations (p < 0.01), and the correlation coefficients were all greater than 0.8. Therefore, we believe that U. pumila is a suitable sand-fixing plant species in this area. In addition, the soil fractal dimension can be used as an important reference index for characterizing soil properties in sandy areas.

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

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

Pore Size Distribution and Fractal Characteristics of Deep Coal in the Daning-Jixian Block on the Eastern Margin of the Ordos Basin.

Important breakthroughs have recently been achieved in deep coalbed methane (CBM) exploration and development in regions such as the eastern margin of the Ordos Basin, China. Investigating the development characteristics of various-scale pores in deep coalbeds is of great significance for resource assessment and selection of favorable zones for CBM exploration. Herein, six deep coal samples were selected from the Shanxi and Taiyuan Formations in the Daning-Jixian block on the eastern margin of the Ordos Basin. Low-pressure CO2/N2 adsorption (LP-CO2/N2GA) and high-pressure mercury intrusion (HPMI) methods were employed to analyze pore volume, specific surface area, and pore size distribution, thereby evaluating the full-scale pore characteristics. Furthermore, the fractal dimension characteristics of deep coal rock pores were elucidated, revealing the influence of pore structure, burial depth, and coal composition. The results indicate that micropores in deep coal rocks have the highest volume and specific surface area proportions, while mesopores have the smallest volume proportion, and macropores make the least contribution to the total specific surface area. The V-S, Frenkel-Halsey-Hill, and Sierpinski models were suitable for calculating the fractal dimensions of micropores, mesopores, and macropores with LP-CO2GA, LP-N2GA, and HPMI experimental data, respectively. Other than the relatively smaller mesopore fractal dimension of samples 20-8 and 20-10, the micropore, mesopore, and macropore fractal dimensions successively increased in the other four samples. The comprehensive fractal dimension, which exhibited a decreasing trend with increasing pore volume and specific surface area, was negatively correlated with burial depth, mineral and moisture contents, and ash and volatile component yields, while it was positively correlated with vitrinite and fixed carbon contents.

The stability and morphology of laminar premixed hydrogen/air flames under various gravity conditions

In the present work, direct numerical simulations (DNS) were employed to understand the stability and morphology of laminar lean premixed hydrogen/air flames under various gravity conditions. The combined effect of Darrieus–Landau (DL) instability, thermal-diffusive (TD) instability and Rayleigh–Taylor (RT) instability was studied quantitatively for both the initial linear regime and the long-term nonlinear regime, with a particular focus on the effect of RT instability. In the linear regime, it was found that the RT instability has a negligible effect on the linear growth rate of flames with an equivalence ratio of 0.4, but the effect is significant when the equivalence ratio decreases to 0.3. The performance of various models for the dispersion relation was discussed, including a theoretical model considering the effects of all instabilities, which captures well the trend of the simulated results in the cases with unity Lewis numbers. The hydrogen/air flames with an equivalence ratio of 0.3 was investigated comprehensively in the nonlinear regime. For the cases with unity Lewis numbers, the RT-unstable flame exhibits a similar single-cusp structure as the RT-neutral flame, but with a deeper cusp and larger consumption speed as a result of the destabilizing effect of RT instability. The RT-stable flame gradually returns to a planar flame shape owing to the stabilizing effect of RT instability. For the cases with non-unity Lewis numbers, the effect of domain size on the flame evolution was investigated, showing a domain width of 200δT is enough to obtain a domain-independent result, where δT is the laminar flame thickness. It was found that the cases initialized with multimode perturbations reach the quasi-steady state faster, while the flame statistics are consistent with those of the cases initialized with single mode perturbations. The effect of RT instability was explored by comparing the results from various gravity conditions. The flame consumption speed is the largest in RT-unstable flames, and the smallest in RT-stable flames. The variation in flame consumption speed is due to the difference in the flame surface area, while the local reactivity and flame structure are not influenced by the RT instability. Further fractal analysis reveals that although the RT instability causes significant differences in flame surface area, the characteristic fractal dimension remains constant for flames under different gravity conditions.Novelty and significanceIn the present work, direct numerical simulations were employed to understand the stability and morphology of RT-unstable, RT-neutral and RT-stable laminar lean premixed hydrogen/air flames. For the first time, the effect of DL, TD and RT instabilities was quantitatively examined for both the linear regime and the nonlinear regime. A theoretical model considering various instabilities was compared with the simulated dispersion relations in the linear regime. In the non-linear regime, the flame surface area and corresponding flame consumption speed are influenced by the RT instability, while the flame stretch factor remains unaffected. A fractal analysis was conducted in laminar premixed hydrogen/air flames under the influence of various instabilities. Remarkably, it was discovered that the characteristic fractal dimension remains constant for the cases with and without the RT instability.

Estimation of the Multifractal Spectrum Characteristics of Fractal Dimension of Network Traffic and Computer Attacks in IoT

Estimation of the Multifractal Spectrum Characteristics of Fractal Dimension of Network Traffic and Computer Attacks in IoT

Investigations on the turbulentnon-turbulent interface in supersonic compressible plate turbulent boundary layer

The turbulent boundary layer (TBL) is a widely existing flow phenomenon in nature and engineering applications. Its strong mixing effect can achieve more sufficient material mixing, heat transport, etc. The understanding of the entrainment process and mechanism of irrotational fluids entering the turbulent region can be promoted by studying the geometric and dynamic characteristics of turbulent ${/}$ non-turbulent interfaces (TNTI). In compressible flow, it is unclear whether the properties of TNTI will change and whether the entrainment will show different features due to the influence of compressibility. Based on the direct numerical simulation results of supersonic compressible plate TBLs with Mach number of 2.9, the geometric and dynamic characteristics of TNTI are investigated in this paper. The interface is identified by the enstrophy method, and the height, thickness, fractal dimension, enstrophy transportation and entrainment characteristics of the interface are investigated. It is found that for the enstrophy transportation in a TBL, the contribution of compressibility-related terms accounts for approximately 13.4 % of the total enstrophy transportation, which tends to transfer the enstrophy of turbulence near the interface to both directions vertical to the interface. This promotes the expansion of the turbulent region towards the non-turbulent region, and the mean height, thickness and entrainment velocity are increased by approximately 3.7 %, 7.0 % and 8.5 %, respectively, while the fractal dimension is basically unaffected. Different from the incompressible flow, the contribution of the compressibility-related terms to the entrainment velocity is independent of the local curvature, and the intense entrainment process is more likely to occur on a highly curved concave surface.

STUDY ON QUANTIFICATION OF ROCK FRACTURE NETWORK TO PROMOTE SHALE GAS DEVELOPMENT

Shale gas is produced by fracturing the reservoir to increase production. Quantifying the complex structure of the rock fracture network has a very important role in shale gas development. In order to quantify the complex structure of rock fracture network, in this paper, combined with the hierarchical structure of fractal figure, long tail distribution and fractal self-similarity, the current calculation method of fractal dimension is improved, and the basic fractal dimension calculation method is proposed based on the principle. By removing the limit calculation method which causes the deviation of numerical results, a reasonable and convenient calculation model for engineering application is proposed. A set of two-dimensional fracture pictures are used to test the model. In the 10 pictures, the more complex the figure is, the larger the new fractal dimension value is, which is in line with the characteristics of fractal dimension describing the complexity of graphics. Furthermore, lattice Boltzmann method (LBM) is used to simulate the velocity field, and the permeability of the fracture network is calculated according to Darcy’s law. The permeability and fractal dimension of the fracture network are compared and analyzed. The conclusion that the permeability is positively related to the fractal dimension of the fracture network is obtained, which provides theoretical support for the further study of shale mining problems such as hydraulic fracturing.

Pore Structure and Fractal Characteristics of Coal Measure Shale in the Wuxiang Block in the Qinshui Basin

To study the fractal characteristics of the pore structure and the main controlling factors of coal measure shale in the Wuxiang block in Qinshui Basin, gas adsorption (CO2 and N2), mercury intrusion porosimetry (MIP), total organic carbon (TOC) content, and X-ray diffraction (XRD) experiments were carried out. The fractal dimensions of the micropores, mesopores, and macropores were computed by combining the V-S, FHH, and MENGER models. The results show that the fractal dimension increases with the increase in pore size; so, the macropore structure is the most complex. The effects of the TOC content, mineral fractions, and pore structure on the fractal dimensions were analyzed. The results showed that the TOC content certainly correlated with the mesopore fractal dimension, and the R2 is 0.9926. The pore volume and specific surface area show an obvious positive correlation with the macroporous fractal dimension, and their R2 values are 0.6953 and 0.6482, indicating that the macroporous pore structure of coal shale in the study area is more complex. There is a significant positive correlation between kaolinite and the macropore fractal dimension, and the R2 is 0.7295. Therefore, the organic carbon and kaolinite contents and the pore structure parameters are the most important factors affecting the fractal dimension characteristics.

A new mesoscopic calculation model of chloride ion erosion in recycled coarse aggregate concrete (RAC): Characteristic fractal dimension of pore structure and service life prediction

This research investigates the influence of water-cement ratio and recycled aggregate content on the chlorine erosion resistance of RAC by conducting a combination of experimental and theoretical analysis. In addition, a mathematical equation is developed to represent the chloride ion transport mechanism in RAC, taking into account fluid mechanics, energy conservation, and pore structure evolution characteristics. Furthermore, mathematical analysis and modeling are used to forecast the life of the chloride ion erosion process. The results show that both the recycled coarse aggregate replacement rate and the water-cement ratio adversely affect the chloride erosion resistance of RAC. The chloride diffusion coefficient model based on pore structure characteristic parameters exhibits high prediction accuracy. This model helps increase the use of recycled aggregates and fosters the growth of the circular economy in the construction industry sector by offering a theoretical foundation for evaluating and maintaining the durability of RAC.

Analyzing the Energy and Damage Constitutive of Cemented Backfill with Different Water Content under Dynamic Load.

The dynamic characteristics of the filling body are the key parameters for designing the filling ratio and evaluating the stability of an underground stope. The different environment (water-bearing state) of the filling body in the underground stope exerts a complex impact on the mechanical behavior of the filling body. Therefore, six groups of cemented filling body specimens with different states were formed and subjected to dynamic uniaxial impact tests. The effects of water content on the mechanical properties, fractal dimension, and deformation damage characteristics of the cemented backfill under dynamic load were analyzed in depth, and a dynamic damage constitutive model that considers water damage and the compaction stage was established. The results indicate the following: (1) Due to the change of the specimen from the dry state to the water saturation state, the dynamic compressive strength of the cemented filling body decreases from 5.03 Mpa to 1.79 Mpa; however, the ductility of the specimen generally increases, and the filling body specimens with different water contents mainly exhibit tensile failure. (2) There is a significant nonlinear relationship between the water content and the fractal dimension Db of the cemented backfill specimen, and the growth rate of the fractal dimension Db tends to slow down with the increase in the water content. (3) From the energy evolution perspective, the water content of the specimen exerts a significant effect on the elastic deformation and failure stage of the stress-strain curve, and the slope of the dissipated energy-strain curve decreases with the increase in water content. (4) Based on the Weibull distribution and damage theory, a statistical damage constitutive model of cemented backfill was established, and it was compared with the experimental curve to verify the rationality of the model. Therefore, the relationship between stress and damage and the strain curves is discussed, and it is inferred that the damage evolution curve of cemented backfill is a typical S-shaped curve that exhibits a stable development-rapid increase-tending to be gentle. This study can provide a theoretical reference for further understanding the dynamic behavior and stability of backfill under different water conditions.

Stress interference and interaction between two fractures during their propagation: insights from SCDA test and XFEM simulation

Understanding and predicting the propagation and disturbance of multiple fractures is the key to the successful implementation of hydraulic fracturing. In this study, the two-hole fracturing tests are carried out on granite samples by using soundless cracking demolition agent (SCDA). Combined with the extended finite element method (XFEM) simulation and the induced stress analysis, the interaction and stress interference during the propagation of two fractures are systematically investigated. The relative position of two holes determines whether attraction or repulsion effect occurs between adjacent fractures, the pattern of which can be classified into three modes: the fracture collinear, staggered propagation and parallel propagation. The fractures in collinear pattern are prone to coalescence, the staggered fractures are easy to attract each other and the parallel fractures tend to propagate independently, which ultimately lead to the formation of single, spiral and multiple main fractures, respectively. The stress near the fracture tip controls the possibility and direction of fracture propagation. The superposition of tensile stress is prone to promote fracture propagation, and the stress interference tends to make fractures deflection and mutual exclusion. The fracturing results are quantitatively evaluated by using fractal dimension and fracture surface characteristics. It is found that increasing perforation spacing makes the degree of internal rupture of the sample increase first and then decrease, and the fracturing scheme is optimal when the perforations are arranged perpendicular to the direction of maximum horizontal principal stress.

Fractal Dimension and Nuclear Magnetic Resonance Characteristics of Surfactants for Coal Gas Desorption

In this paper, the fractal dimension of coal surfaces was calculated using the fractal theory, and the influence of different surfactants on the fractal dimension of coal surface was studied. Six kinds of sustainable and traditional surfactants used in coal gas desorption processes were compared and analyzed. We used mineral gas fertilizer coal from Huainan Liuzhuang, China, as the research object and studied sodium dodecyl benzene sulfonate (SDBS), cohol diethanolamide (CDEA), nonylphenol polyoxyethylene ether (NP-10), tea saponin, sucrose ester and rhamnolipid surfactants used to modify coal. The methane adsorption capacity of coal before and after surfactant modification was measured by low field nuclear magnetic resonance methane adsorption, and Langmuir volume and Langmuir pressure were obtained according to the Langmuir fitting equation. The results showed that from the perspective of fractal dimensions, the best surfactant in the context of sustainability (in order) is rhamnolipid, CDEA, tea saponin, sucrose ester. According to the two important parameters VL and PL in the Langmuir equation, the coal sample modified by sucrose ester had the strongest gas adsorption capacity. According to the numerical analysis of the surface fractal dimension DS of the coal modified by surfactants, the soluble organic matter in the raw coal samples dissolved, and the micropore morphology evolved to become mesoporous or macroporous, which is more favorable for desorption. The coal samples modified by rhamnolipid and SDBS had the strongest gas desorption ability.

Analysis of China’s Coastline Changes during 1990–2020

As the boundary between the sea and the land, information on the location and type of coastline constantly changes with environmental changes in coastal zones. Monitoring of coastline changes in long time series becomes important for the monitoring and assessment of the coastal zone environment. In this study, Landsat series images from five time periods (1990, 2000, 2010, 2015, and 2020) were selected for monitoring and analyzing the changes in coastline length, sea–land pattern, the index of coastline diversity, and fractal dimension characteristics. Our conclusions are as follows: (1) The lengths of the entire coastline and the artificial coastline of mainland China increased from 30,041.22 km and 10,022.49 km in 1990 to 32,977.34 km and 17,660.84 km in 2020, with annual change rates of 97.87 km/year and 254.61 km/year, respectively. From 1990 to 2020, the rate of natural coastline decreased from 66.68% to 42.29%, and the artificial coastline increased from 33.32% to 57.71%. (2) The length of natural coastline decreased from 20,018.73 km to 15,316.5 km; among the types of natural coastline, the length of sandy coastline and bedrock coastline decreased the most, at 2062.95 km and 1815.8 km, respectively. (3) The coastal zone of mainland China had a significant increase in land area, with a net increase of about 10,902.55 km2. (4) The index of coastline diversity continued to decrease, and the coastline structure tended to be simple. The fractal dimension of the mainland coastline was consistent with the trend of the length of the coastline, which basically shows an increasing trend. Therefore, the length of the mainland coastline and artificial coastline displayed an upward trend between 1990 and 2020, which also led to simpler coastline diversity and more complex coastline shapes. Since the first year of the SDGs (2015), the growth rate of the artificial coastline has decreased by 158.32 km/year compared with that between 2010 and 2015. In recent years, China has enacted a number of laws, regulations, and action plans to protect its coastline, and it has proposed that by 2020, the proportion of natural coastline will be no less than 35%. The rapid development of China’s coastal areas drives the construction of coastal zone cities but also creates a variety of challenges for the ecological environment of the coastal zone, and the management and sustainable use of the mainland coastline resources should be further strengthened.

Pore structure and pore size change for tight sandstone treated with supercritical CO2 fluid

The effects of ScCO2 on pore structure should be investigated in order to properly apply supercritical carbon dioxide (ScCO2) fracturing on tight sandstone. ScCO2 treatment was applied to three sets of tight sandstone samples. The pore structure was characterized using a combination of high-pressure mercury intrusion porosimetry and nuclear magnetic resonance. Furthermore, the pore size distribution’s multi-fractal dimensions were estimated. After SCCO2 treatment, the number of transitional pores decreased significantly, while the number of mesopores and macropores increased. At all scales, the fractal dimension characteristics indicate that pore structure gets more complicated and heterogeneous. Furthermore, due to their larger contact area, large pores have a higher fractal dimension than small pores. The accumulative pore volume of the calcite-rich group increases and a decreasing trend occurs for the calcite-rare group. The content of calcite sharply decreased while clay, feldspar, and plagioclase content have a slight drop after ScCO2 treatment, which affects the alternation of pore structure. Thus, the accumulative porosity volume and pore connectivity do not always increase after ScCO2 exposure because re-precipitation and fine migration can potentially clog pores and channels.

Методический подход к изучению седиментационной устойчивости тонкодисперсных отходов переработки минерального сырья по спутниковым данным загрязнения природных водоемов

The paper presents the results of the study of sedimentation stability of suspended finely-dispersed mineral particles based on satellite observations of their aggregation and sedimentation. The authors studied satellite data on self-purification of subarctic lakes polluted by apatite-nepheline, iron, and copper-nickel ore processing wastes. The multispectral images of lakes taken by Sentinel-2 spacecraft have allowed determining the average size of suspended finely-dispersed mineral processing wastes and the density of particle size distribution. To account for aggregation, the authors have designed a computer model of the dynamics of suspended particles and have set parameters of the forces of electrostatic and dispersion interactions of mineral particles from the Kola deposits. It is shown that the balance of repulsive electrostatic and dispersion attractive forces appears in the generation of aggregates of finely-dispersed mineral particles with characteristic fractal dimension, using Nepheline, Hematite, Quartz, and Pyrite as examples. The authors have developed an algorithm for matching the computer simulation results of the dynamics of suspended particles with the results of satellite images processing of lakes. The developed methodological approach makes it possible to determine the sedimentation stability of lakes’ pollution by finedispersed mineral processing wastes without surface observations. The research results allow calculating the sedimentation velocity of mineral particles and their aggregates of a given size. The good correspondence between the calculated parameters of particles aggregation and sedimentation and satellite observations data can be used to monitor the pollution of water bodies when adapting mineral processing technologies to modern production ecologization requirements, as well as to assess the waterenvironmental potential of the territory for rational management of natural resources.

Preliminary Study on the Phenomenon and Mechanism of Granite Core Discing in Laboratory Drilling Test

It is generally believed that core discing is a rock failure phenomenon under high in-situ stress, and high stress is closely related to the characteristics of core discing. The core drilling tests of intact granite were conducted on the laboratory servo-controlled drilling test platform. It was observed that the granite core showed discing phenomenon at a high drilling rate (&gt; 15 mm/min) under no confining pressure (0 MPA). The fluctuation of the drilling parameter was consistent with the core discing section along the core. The failure mode of the core discs was determined by morphology and surface fractal dimension characteristics. Numerical simulation models considering the interaction between the drill bit and the rock were established using ANSYS software. Based on core drilling tests, failure morphology analysis of the core discs, and numerical simulation, the mechanism of granite core discing under low confining pressure is as follows: Tensile failure is caused by the stress concentration of the bit at the core root. The drilling rate is the critical factor affecting core discing.

The Dynamic Compressive Properties and Energy Dissipation Law of Sandstone Subjected to Freeze–Thaw Damage

To investigate the dynamic compressive properties and the law of energy dissipation of freeze–thaw-damaged sandstone, static and dynamic compressive experiments were conducted. The influences of the number of freeze–thaw cycles and strain rate on strength characteristics, energy dissipation rate and the fractal dimension characteristics of sandstone were evaluated. Based on the peak energy dissipation rate, a freeze–thaw damage variable was established. The results show that peak strength increases exponentially with strain rate, and there exists a strain rate threshold. When strain rate is below this threshold, the increasing rate of the DIF slows down with the increase in the number of freeze–thaw cycles; when strain rate is higher than this threshold, the increasing rate of the DIF increases with the increase in the number of freeze–thaw cycles. In addition, the fractal dimension increases with the number of freeze–thaw cycles as well as the strain rate. Based on the freeze–thaw damage variable established, the damage degree of sandstone under freeze–thaw cycling can be characterized.

Nano-mechanical properties of Cr-Zr-Nb-N medium entropy alloy films produced by reactive sputtering

Protective thin films have gained extensive applications in various industries, especially in machining. The present work investigates the structure-mechanical properties relations of Cr-Zr-Nb-N medium entropy films deposited by sputtering. First, chemical analysis (by means of EDS, GI-XRD and Raman spectroscopy), morphology (by SEM) and topology (by means of AFM) of the coatings are studied. By applying graphical methods, average and root mean square roughness, skewness, kurtosis, fractal dimension and texture characteristics are extracted from 2D-AFM images. In addition, hardness, toughness and friction coefficient of the films are reported by employing nano-indentation and nano-scratch tests. Finally, optimum sputtering conditions (substrate temperature = 500 ̊C, nitrogen flow rate = 15 sccm and − 10 V ≤substrate bias voltage≤ − 70 V) and fractal parameters necessary to obtain wear-resistant films are presented. The thin film deposited under the optimum condition demonstrates high hardness (21.3 GPa), toughness (H/E = 0.096 and H3/E2 = 0.195 GPa) and minimum wear characteristics (CoF < 0.2, wear width = 479 nm and wear depth = 56 nm).

Experimental study on rockburst fragment characteristic of granite under different loading rates in true triaxial condition

In order to study the effect of loading rate on rockburst, an indoor test of single-face fast unloading-three directions and five-face stress-vertical continuous loading is conducted under different loading rates using a new true-triaxial rockburst test system. The entire process of rockburst inoculation-occurrence-development is completely and accurately reproduced. The fragmentation degree, fractal dimension, and Weibull distribution characteristics of rockburst fragments under different loading rates are compared and analyzed. The results indicate that the rockburst ejection failure process can be summarized as four stages: grain ejection, rock spalling into plates, rock shearing into fragments, and rock fragment ejection. Rockburst fragments are mostly coarse-grained, medium-grained, and fine-grained. The macroscopic block characteristics of rockburst fragments reflect the fragmentation degree of rock, and the fragmentation degree of rockburst fragments increases with the loading rate. The fractal dimension shows the same trend with different loading rates, that is, the fractal dimension grows as the loading rate increases. As the loading rate increases, the crack expansion rate accelerates, which aggravates the damage to the rock specimen by decreasing its compressive strength and causing greater fragmentation when the specimen is failed. The loading rate has a significant effect on the energy consumption of rockburst fragments.

Fractal Dimension Characteristics of the Soil Cracking Process When Saline-Alkali Soil Is Mixed with Hippophae Roots

Fractal analysis is an effective tool to describe real world phenomena. Water evaporation from the soil surface under extreme climatic conditions, such as drought, causes salt to accumulate in the soil, resulting in soil salinization, which aggravates soil shrinkage, deformation, and cracking. Hippophae is an alkali tolerant plant that is widely grown in Northwest China. Laboratory drying shrinkage tests of Saline-Alkali soil samples with 0%, 0.5%, 1%, and 2% concentrations of hippophae roots were carried out to study the effect of hippophae roots on the evaporation and cracking of Saline-Alkali soil and to determine variation characteristics of the soil samples’ fractal dimensions. A series of changes in the cracking parameters of Saline-Alkali soil were obtained during the cracking period. Based on fractal theory and the powerful image processing function of ImageJ software, the relationships between samples’ cracking process parameters were evaluated qualitatively and quantitatively. The experimental results show that the residual water contents of Saline-Alkali soil samples with 0%, 0.5%, 1%, and 2% concentrations of hippophae roots were 2.887%, 4.086%, 5.366%, and 6.696%, respectively. The residual water content of Saline-Alkali soil samples with 0.5% and 1% concentrations of hippophae roots increased by 41.53% and 85.87%, respectively; the residual water content of the sample with a 2% concentration of hippophae roots was 131.94% higher than that of the sample without hippophae roots. The final crack ratios of Saline-Alkali soil samples with 0%, 0.5%, 1%, and 2% concentrations of hippophae roots were 21.34%, 20.3%, 18.93%, and 17.18%, respectively. The final crack ratios of Saline-Alkali soil samples with 0.5%, 1%, and 2% concentrations of hippophae roots reduced by 4.87%, 11.29%, and 19.49%, respectively, compared with that of the sample without hippophae roots. Fractal dimensions at the end of cracking were 1.6217, 1.5656, 1.5282, and 1.4568, respectively. Fractal dimensions increased with an increase in the crack ratio and with a decrease in water content. The relationship between water content and fractal dimension can be expressed using a quadratic function. Results indicate that hippophae roots can effectively inhibit the cracking of Saline-Alkali soil and improve its water holding capacity.