The spatial distribution of acoustic emission （AE） events in the failure process of several rock specimens was acquired using an advanced AE acquiring and analyzing system. The box counting method （BCM） was employ...The spatial distribution of acoustic emission （AE） events in the failure process of several rock specimens was acquired using an advanced AE acquiring and analyzing system. The box counting method （BCM） was employed to calculate the fractal dimension （FD） of AE spatial distribution. There is a similar correlation between the fractal dimension and the load strength for different rock specimens. The fractal dimension presents a decreasing trend with the increase of load strength. For the same kind of specimens, their FD values will decrease to the level below a relatively same value when they reach failure. This value can be regarded as the critical value, which implies that the specimen will reach failure soon. The results reflect that it is possible to correlate the damage of rock with a macroscopic parameter, the FD value of AE signals. Furthermore, the FD value can be also used to forecast the final failure of rock. This conclusion allows identifying or predicting the damage in rock with a great advantage over the classic theory and is very crucial for forecasting rockburst or other dynamic disasters in mines.展开更多
By Monte Carlo simulations, the effect of the dispersion of particle size distribution on the spatial density distributions and correlations of a quasi one-dimensional polydisperse granular gas with fractal size distr...By Monte Carlo simulations, the effect of the dispersion of particle size distribution on the spatial density distributions and correlations of a quasi one-dimensional polydisperse granular gas with fractal size distribution is investigated in the same inelasticity. The dispersive degree of the particle size distribution can be measured by a fractal dimension dr, and the smooth particles are constrained to move along a circle of length L, colliding inelastically with each other and thermalized by a viscosity heat bath. When the typical relaxation time τ of the driving Brownian process is longer than the mean collision time To, the system can reach a nonequilibrium steady state. The average energy of the system decays exponentially with time towards a stable asymptotic value, and the energy relaxation time τB to the steady state becomes shorter with increasing values of df. In the steady state, the spatial density distribution becomes more clusterized as df increases, which can be quantitatively characterized by statistical entropy of the system. Furthermore, the spatial correlation functions of density and velocities are found to be a power-law form for small separation distance of particles, and both of the correlations become stronger with the increase of df. Also, tile density clusterization is explained from the correlations.展开更多
This study examined the spatial distribution of the continent coastline in northern China using remote sensing and GIS techniques, and calculated the fractal dimension of the coastline by box-counting method, with a t...This study examined the spatial distribution of the continent coastline in northern China using remote sensing and GIS techniques, and calculated the fractal dimension of the coastline by box-counting method, with a time span from 2000 to 2012. Moreover, we ana- lyzed the characteristics of spatial-temporal changes in the coastline＇s length and fractal di- mension, the relationship between the length change and fractal dimension change, and the driving forces of coastline changes in northern China. During the research period, the coast- line of the study area increased by 637.95 km, at a rate of 53.16 km per year. On the regional level, the most significant change in coastline length was observed in Tianjin and Hebei. Temporally, the northern China coastline grew faster after 2008. The most dramatic growth was found between 2010 and 2011, with an increasing rate of 2.49% per year. The fractal dimension of the coastline in northern China was increasing during the research period, and the most dramatic increase occurred in Bohai Rim. There is a strong-positive linear relation- ship between the historical coastline length and fractal dimension （the correlation coefficient was 0.9962）. Through statistical analysis of a large number of local coastline changes, it can be found that the increase （or decrease） of local coastline length will, in most cases, lead to the increase （or decrease） of the whole coastline fractal dimension. Civil-coastal engineering construction was the most important factor driving the coastline change in northern China. Port construction, fisheries facilities and salt factories were the top three construction activi- ties. Compared to human activities, the influence of natural processes such as estuarine deposit and erosion were relatively small.展开更多
The relationship between fractal point pattern modeling and statistical methods of pa- rameter estimation in point-process modeling is reviewed. Statistical estimation of the cluster fractal dimension by using Ripley...The relationship between fractal point pattern modeling and statistical methods of pa- rameter estimation in point-process modeling is reviewed. Statistical estimation of the cluster fractal dimension by using Ripley＇s K-function has advantages in comparison with the more commonly used methods of box-counting and cluster fractal dimension estimation because it corrects for edge effects, not only for rectangular study areas but also for study areas with curved boundaries determined by re- gional geology. Application of box-counting to estimate the fractal dimension of point patterns has the disadvantage that, in general, it is subject to relatively strong ＂roll-off＂ effects for smaller boxes. Point patterns used for example in this paper are mainly for gold deposits in the Abitibi volcanic belt on the Canadian Shield. Additionally, it is proposed that, worldwide, the local point patterns of podiform Cr, volcanogenic massive sulphide and porphyry copper deposits, which are spatially distributed within irregularly shaped favorable tracts, satisfy the fractal clustering model with similar fractal dimensions. The problem of deposit size （metal tonnage） is also considered. Several examples are provided of cases in which the Pareto distribution provides good results for the largest deposits in metal size-frequency distribution modeling.展开更多
基金supported by the Special Subject of the National High-Tech Research and Development Program of China (No.2007AA06Z107)Supporting Project of New Century Excellence Talents in Chinese Universities (No.NCET-07-0163)+1 种基金Opening Research Foundation of CAS Key Laboratory of Rock and Soil Mechanics (No.Z110607)Youth Foundation of Henan Polytechnic University (No.Q2008-51)
文摘The spatial distribution of acoustic emission （AE） events in the failure process of several rock specimens was acquired using an advanced AE acquiring and analyzing system. The box counting method （BCM） was employed to calculate the fractal dimension （FD） of AE spatial distribution. There is a similar correlation between the fractal dimension and the load strength for different rock specimens. The fractal dimension presents a decreasing trend with the increase of load strength. For the same kind of specimens, their FD values will decrease to the level below a relatively same value when they reach failure. This value can be regarded as the critical value, which implies that the specimen will reach failure soon. The results reflect that it is possible to correlate the damage of rock with a macroscopic parameter, the FD value of AE signals. Furthermore, the FD value can be also used to forecast the final failure of rock. This conclusion allows identifying or predicting the damage in rock with a great advantage over the classic theory and is very crucial for forecasting rockburst or other dynamic disasters in mines.
基金supported by National Natural Science Foundation of China under Grant Nos.10675048 and 1068006the Natural Science Foundation of Xianning College under Grant No.KZ0916
文摘By Monte Carlo simulations, the effect of the dispersion of particle size distribution on the spatial density distributions and correlations of a quasi one-dimensional polydisperse granular gas with fractal size distribution is investigated in the same inelasticity. The dispersive degree of the particle size distribution can be measured by a fractal dimension dr, and the smooth particles are constrained to move along a circle of length L, colliding inelastically with each other and thermalized by a viscosity heat bath. When the typical relaxation time τ of the driving Brownian process is longer than the mean collision time To, the system can reach a nonequilibrium steady state. The average energy of the system decays exponentially with time towards a stable asymptotic value, and the energy relaxation time τB to the steady state becomes shorter with increasing values of df. In the steady state, the spatial density distribution becomes more clusterized as df increases, which can be quantitatively characterized by statistical entropy of the system. Furthermore, the spatial correlation functions of density and velocities are found to be a power-law form for small separation distance of particles, and both of the correlations become stronger with the increase of df. Also, tile density clusterization is explained from the correlations.
文摘This study examined the spatial distribution of the continent coastline in northern China using remote sensing and GIS techniques, and calculated the fractal dimension of the coastline by box-counting method, with a time span from 2000 to 2012. Moreover, we ana- lyzed the characteristics of spatial-temporal changes in the coastline＇s length and fractal di- mension, the relationship between the length change and fractal dimension change, and the driving forces of coastline changes in northern China. During the research period, the coast- line of the study area increased by 637.95 km, at a rate of 53.16 km per year. On the regional level, the most significant change in coastline length was observed in Tianjin and Hebei. Temporally, the northern China coastline grew faster after 2008. The most dramatic growth was found between 2010 and 2011, with an increasing rate of 2.49% per year. The fractal dimension of the coastline in northern China was increasing during the research period, and the most dramatic increase occurred in Bohai Rim. There is a strong-positive linear relation- ship between the historical coastline length and fractal dimension （the correlation coefficient was 0.9962）. Through statistical analysis of a large number of local coastline changes, it can be found that the increase （or decrease） of local coastline length will, in most cases, lead to the increase （or decrease） of the whole coastline fractal dimension. Civil-coastal engineering construction was the most important factor driving the coastline change in northern China. Port construction, fisheries facilities and salt factories were the top three construction activi- ties. Compared to human activities, the influence of natural processes such as estuarine deposit and erosion were relatively small.
基金supported by Geological Survey of Canada and China University of Geosciences (Wuhan)
文摘The relationship between fractal point pattern modeling and statistical methods of pa- rameter estimation in point-process modeling is reviewed. Statistical estimation of the cluster fractal dimension by using Ripley＇s K-function has advantages in comparison with the more commonly used methods of box-counting and cluster fractal dimension estimation because it corrects for edge effects, not only for rectangular study areas but also for study areas with curved boundaries determined by re- gional geology. Application of box-counting to estimate the fractal dimension of point patterns has the disadvantage that, in general, it is subject to relatively strong ＂roll-off＂ effects for smaller boxes. Point patterns used for example in this paper are mainly for gold deposits in the Abitibi volcanic belt on the Canadian Shield. Additionally, it is proposed that, worldwide, the local point patterns of podiform Cr, volcanogenic massive sulphide and porphyry copper deposits, which are spatially distributed within irregularly shaped favorable tracts, satisfy the fractal clustering model with similar fractal dimensions. The problem of deposit size （metal tonnage） is also considered. Several examples are provided of cases in which the Pareto distribution provides good results for the largest deposits in metal size-frequency distribution modeling.
