Fractal analysis on the spatial distribution of acoustic emission in the failure process of rock specimens

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.

FRACTAL ANALYSIS APPLIED TO SPATIAL STRUCTURE OF CHINA'S VEGETATION

Based on the fractal theory, the spatial structure of China’s vegetation has been analyzed quantitatively in this paper. Some conclusions are drawn as the following. 1) The relationships between size and frequency of patch area and patch shape index exist objectively for China’s vegetation. 2) The relationships between perimeter and area exist objectively for China’s vegetation. 3) The fractal dimension of evergreen needleleaf forests on mountains in subtropical and tropical zones is the largest, while the smallest for deciduous broadleaf and evergreen needleleaf mixed forests in temperate zone, reflecting the most complex spatial structure for evergreen needleleaf forests on mountains in subtropical and tropical zones and the simplest for deciduous broadleaf and evergreen needleleaf mixed forests in temperate zone. 4) The fractal dimensions of China’s vegetation types tend to decrease from the subtropics to both sides. 5) The stability of spatial structure of deciduous broadleaf and evergreen needleleaf mixed forests in temperate zone is the largest, while the smallest for double-cropping rice, or double-cropping rice and temperate-like grain, and tropical evergreen economic tree plantations and orchards, reflecting the steadiest for deciduous broadleaf and evergreen needleleaf mixed forests in temperate zone and the most unstable for double-cropping rice, or double-cropping rice and temperate-like grain, and tropical evergreen economic tree plantations and orchards in spatial structure. 6) The stability of spatial structure of China’s vegetation tends to decrease from the temperate zone to both sides. It is significantly pertinent to understand the formation, evolution, dynamics and complexity rule of ecosystem of vegetation.

Fractal Analysis on the Spatial Structure of Land Use Patterns in a Non-Point Source Polluted Area in Southern China

Based on the TM remote sensing interpretation of land use data of a non-point source polluted area in southern China in 2015, supported by ArcGIS and the fractal theory, this paper established the perimeter-area fractal equation of the spatial structure of land use types, quantitatively calculated the fractal dimension and stability index of various land use types in this non-point source polluted area in 2015, and analyzed the spatial structure characteristics of land use types. The results showed that the fractal dimension values of the different land use types in the research area ranged 1.141–1.657, and the whole fractal dimension of the research area was 1.206. To be specific, the fractal dimension values of unused land, grass land and rural residential land were high, and the fractal dimension values of dry land, paddy filed and waters were low, and the fractal dimension values of urban land, industrial traffic construction land and forest land were moderate. The area of the land use types whose stability index values were 0.2–0.4 accounted for 89.5% of total area, suggesting that the stability of the spatial structure of land use types of Beibei District in 2015 was not high generally. The rural residential land and urban land of the research area should be planned and managed more properly from now on.

等差关系的个性阐释与序列技术的空间化解读——-勋伯格《钢琴组曲》(Op.25)新识

勋伯格的《钢琴组曲》(Op. 25)在序列原型设计上,以音高关系的“等差”为控制,特别突出差数为1和6的音程;在十二音方阵中,则以“等差”关系为本源,用分形将一维音高关系拓展至二维空间中;在作品创作中,更是以“等差”关系为其控制与转圜的枢纽,作大量的音级换序,展现出此类技法之个性化处理及观念化表达的各种可能。勋伯格的这部序列音乐作品不仅突破了传统音高逻辑方式,其中第二首又以织体形态体现加沃特舞曲的舞姿意象;不单从内容形式方面强化音乐的自洽性与逻辑性,更以有意味的谱式形态复沓昔日的哥特式审美,在展现表现主义的观念风格的同时,将美术与建筑中的空间观念纳入其序列音乐创作中。

基于分形理论的城市空间结构及其影响因素研究——以贵阳市为例

以贵阳市为研究区,以2010、2020年各土地利用类型数据为基础,采用分形理论探究贵阳市土地利用的变化速度和幅度,并分析贵阳市土地空间结构变化的驱动因素。结果表明:(1)贵阳市主要以耕地和林地为主,研究期间耕地、林地、草地等农业用地面积下降,建设用地和水体面积增加显著。(2)研究期间贵阳市各地类分形维数相差较大,整体边界维数呈上升趋势,形态维数下降,说明城市空间结构不规则性增加,城市土地利用复杂化,紧凑性降低。(3)贵阳市土地利用类型的变化是自然、人为因素共同导致的,尤其是经济与政策的影响。

近47年吐鲁番盆地人工绿洲精明增长的时空过程分析

以1976、1990、2000、2010、2023年5期Landsat遥感影像进行解译,借助数理统计模型、分形维数、紧凑度指数等方法,结合精明增长理论,构建了绿洲精明增长指标体系,测度并分析了近47年吐鲁番盆地人工绿洲的扩张及分布情况以及绿洲精明增长水平的时空表现。结果表明:(1)吐鲁番盆地绿洲规模空间扩张态势明显,呈现出明显的阶段性特征,绿洲面积由1976年的1259.33 km^(2)扩张至2023年的1810.27 km^(2);其扩展强度在经历缓慢下降—慢速增长—快速增长后转变为精明增长背景下的中低速增长。(2)吐鲁番盆地绿洲空间扩张方向具有分异性,扩张方向以西北、东北最为显著,空间重心迁移轨迹为西南—东北—西南,最大迁移距离为55.60 km。(3)在研究时间段内绿洲紧凑度维持在较高水平,土地利用率较高,但近10年呈现下降趋势;空间扩张模式呈现蔓延式—跳跃式—填充式的演变特征。(4)吐鲁番盆地的绿洲精明增长水平较低,精明得分由1976年的0.474下降至1990年的0.383,随后回升,2023年达到最大值0.517;从精明增长水平的空间差异看,以大河沿—塔尔朗流域下游、托克逊—白杨河流域下游为高水平的双核心趋势明显,呈现由中心向四周波动递减的态势。研究结果可为未来绿洲区的合理发展,防止绿洲无序蔓延扩张,保障干旱区绿洲土地资源的合理配置提供参考依据。

基于谷歌地球引擎和分形理论的黄河三角洲土地利用空间结构研究

基于谷歌地球引擎(Google earth engine,GEE),以Landsat-5(TM)、Landsat-7(ETM)和Landsat-8(OLI)数据为遥感数据源,采用随机森林分类方法对黄河三角洲生态功能保护区1985—2020年的土地利用类型进行了划分,在此基础上利用分形理论方法计算了土地利用分形维数和稳定性指数,并分两个阶段对研究区土地利用空间结构的复杂度和稳定性进行了定量分析。结果表明:①1985—2020年,研究区的耕地面积逐渐减少;草地面积相对较稳定;水体面积逐渐扩大,2015—2020年增长率最高;裸地面积的变化较为波动,先增加后又逐渐下降;建筑物面积呈指数增长。②研究区土地利用空间结构的分形维数总体上呈降低趋势,表明土地利用复杂度降低。③研究区土地利用空间结构的稳定性指数总体上呈升高趋势,表明土地利用空间结构趋向稳定。总体上,黄河三角洲生态功能保护区随着环境保护政策的实施,土地利用空间结构逐渐得到改善,水、草等自然资源逐渐丰富。

高速铁路网络协同发展对城市群空间重构的分形研究

高速铁路的建设发展,带动了城市群的协同发展与空间格局转变。为探索高速铁路网络协同发展对城市群空间结构的影响,基于分形理论,运用盒子维数和长度-半径维数描述高速铁路网络的覆盖均匀度与复杂程度,将豪斯多夫维数与齐夫定律相结合分析城市群规模序列结构,通过关联维数和集聚维数分析城市群空间结构相关性和集聚性。以高速铁路网络发展较为完善的5个城市群为例,比较分析高速铁路开通前后其空间结构的演变。结果表明,高速铁路网络覆盖均匀度不高,部分地区通达性良好,高速铁路建成后,辽中南等城市群的可达性明显得到改善,城市之间联络更加紧密,高速铁路的经济效应促进了城市群协同发展;关中平原等城市群呈现出集聚分布的趋势,因此应加强以高速铁路为基础、城际铁路为辅的快速交通系统建设。

基于分形理论的青岛城市空间形态演化特征研究

随着滨海城市发展对集约化需求的增加,如何高效布局城市所处空间成为城市发展的关键。文章运用分形理论对青岛这一兼具“带形”与“环形”形态双重时空属性的滨海城市进行研究,并揭示其演变特征。结果显示:(1)青岛城市外部形态演变呈“轴带均衡集聚→环状多组团均衡分布”的演变趋势。(2)工业用地呈现均衡扩展趋势,商业与居住用地呈波动扩展的趋势。在此基础上提出相关建议,以期为青岛未来城市发展中明确空间发展方向与重点建设区域、提升用地资源的填充效率提供参考。

张家口市蔚县军事堡寨村落的保护与更新研究——以白后堡村为例

自古以来,张家口地区就是北方少数民族和中原地区的必争之地,特殊的历史背景孕育了数量众多的军事堡寨村落。现今,随着生活环境的改变,村堡的防御属性正在不断降低,原有的空间肌理与历史记忆也在不断丧失。如何保留这一份历史成为张家口村落保护的重点问题之一。文章通过分形理论的方法,以白后堡村为例,研究张家口地区蔚县军事堡寨村落的空间肌理与历史记忆。运用计盒维数法计算老村与新村的分维数值,分析其差异并指导村落的延续与再生,为张家口军事堡寨村落的保护与更新提供新的思路。

Spatial Structure of Central Places in Jilin Central Urban Agglomeration, Jilin Province, China

Using the radius of gyration from fractal theory, this paper describes the calculation of fractal dimensions for the four tiers of central places in the Jilin Central Urban Agglomeration(JCUA), Jilin Province, China and the structural characteristics of each tier: 1) the 1st tier central place, Changchun Proper(not including Shuangyang District), provides the most service functions and has the most stable primate position; 2) the 2nd tier central places, Jilin Proper, Siping Proper, Liaoyuan Proper and Songyuan Proper have unclear statuses and do not provide certain functions; 3) the 3rd tier central places comprise 23 county-level cities, counties and urban districts(including Shuangyang District of Changchun), exhibiting a dense spatial structure that agrees with theory; 4) the 4th tier contains the largest number of central places(248 designated towns), but they are loosely distributed. In this study, a spatial image of the JCUA was created, based on vectorized data of the urban settlement distribution, which was then modified and abstracted to create a hexagonal network covering the JCUA. Compared to the traditional central place model, the modified spatial image conforms to the K = 3 principle. In reality, however, the growth of some 3rd tier central places should be increased with the cities being upgraded to the 2nd tier so as to overcome that tier′s functional deficiency. The loose distribution in the 4th tier should also be changed. This apparent anomaly can be explained by the fact that the classic hexagon model used to describe the way market areas layout does not exist in the real world. However, this should not be viewed as an obstacle to using central place theory. If its assumptions are properly applied, it can still assist research into the spatial structure of regions.

Fractal characterization of sediment particle-size distribution in the water-level fluctuation zone of the Three Gorges Reservoir, China

The combined effect of periodic water impoundment and seasonal natural flood events has created a 30 m high water-level fluctuation zone(WLFZ) around the Three Gorges Reservoir(TGR), China, forming a unique eco-landscape. Siltation, eutrophication, enrichment of heavy metals, and methane emissions in the WLFZ have been widely associated with sediment and soil particles generated from the upstream catchment or upland slopes. However, little attention has been paid to the complexity of sediment particle-size distributions in the WLFZ. In the present study, core samples(from a 345 cm thick sediment core from the base of the WLFZ), slope transect surface samples(across/up a WLFZ slope), and along-river/longitudinal surface samples(from the reservoir reaches) were collected. Laser granulometry and a volume-based fractal model were used to reveal the characteristics of sediment particle-size distributions. Results indicate that the alternation of coarse and fine particles in the sedimentary core profile is represented as a fluctuation of low and high values of fractal dimension(D), ranging from 2.59 to 2.77. On the WLFZ slope transect, surface sediment particles coarsen with increasing elevation, sand content increases from 3.3% to 78.5%, and D decreases from 2.76 to 2.53. Longitudinally, surface sediments demonstrate a downstream-fining trend, and D increases gradually downstream. D is significantly positively correlated with the fine particle content. We conclude that D is a useful measure for evaluating sediment particle-size distribution.

Urban Spatial Expansion Characteristics in China’s Rapid Urbanization Region—A Case Study of SXC Region

Urban spatial expansion characteristics are the responses of urbanization acts on the geographical space. Analyzing the characteristics can reveal the process of urban expansion and mechanism which is one of useful methods to find out the sustainable land use strategy balancing development and protection. In this paper, two main methods have been deployed in analyzing the spatial expansion characteristics of rapid urbanization region. One is the expansion index method and the other is fractal dimension method. And the results show that town-level urban sprawl has increased in a non-linear way since 1985, and even the increments of the urban expansion intensity are fluctuated. Morphology transformation from scatter to concentration is common phenomenon in the process of urbanization in the towns. From the morphology point of view, downtowns are more homogenous than towns with less variation. The concentration is the leading development trend in downtowns. And the more distance from the downtown is, the more spatial pattern morphology will be observed. These characteristics indicate that macro-scale policies of economic development and land use management have great impacts on the formation and characteristics of spatial patterns of urban dynamic patterns.

A FRACTAL STUDY ON URBAN SYSTEM IN NORTHEAST CHINA

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Spatial Density Distributions and Correlations in a Quasi-one-Dimensional Polydisperse Granular Gas

由蒙特卡罗模拟，空间密度分布和伪的关联上的粒子尺寸分发的分散的效果一个维的 polydisperse 有分数维的尺寸分发的小粒的气体在一样的无弹力被调查。粒子尺寸分发的散度能被分数维的尺寸 d f , 和光滑的粒子被抑制沿着长度 L 的一个圆移动，碰撞在有弹性地与由粘性的对方和 thermalized 一起加热洗澡。当开车 Brownian 过程的典型松驰时间 τ 比吝啬的碰撞长时，预定 τ 系统能到达的 c , 一非平衡稳定的状态。腐烂指数地与向稳定的 asymptotic 的时间珍视的系统的平均精力，和精力松驰预定 τ 到稳定的状态的 B 与增加 d f 。处于稳定的状态，空间密度分发作为 d f 增加，它能是系统的统计的熵描绘的份量上。而且，密度和速度的空间关联功能被发现是一种幂定律形式因为关联的粒子的小分离距离，和两个随 d f 。另外，密度 clusterization 从关联被解释。

吉兰泰盐湖盆地土壤颗粒分形特征与空间变异分析

[目的]阐明盐湖盆地流域土壤颗粒分形特征和空间变异特征,揭示区域土壤环境演变和影响因子的响应规律,为旱区盐湖流域沙害治理提供数据和理论支持。[方法]以吉兰泰盐湖盆地流域为研究区,布设50个土壤采样点,采集表层、50 cm、100 cm土层150个土壤样本,基于土壤粒径分布和土壤基本理化指标pH值、总溶解性固体TDS、总氮TN、含水率θ的测试数据,采用多因素相关分析的方法,分析了土壤分形维数与各粒级含量和土壤基本理化因子的相关性;应用地统计学方法对土壤剖面分形维数空间变异特征及分布规律开展了研究。[结果]研究区0—100 cm土壤质地以砂土、壤砂土为主,不同土层深度土壤质地类型基本一致,土壤颗粒分形维数D值为1.672~2.785。土壤分形维数与黏粒和粉粒呈极显著正相关,与粗砂、中砂、细砂呈显著负相关,0.1 mm粒径是D值随土壤粒径变化的分界值。D值与含水率、总氮在3土层均呈现显著正相关,而与pH值和TDS相关性不显著。土壤分形维数具有强烈的空间自相关性,各层土壤D值均呈现出由南向北逐渐增大的条块状镶嵌分布特征,流域北部的巴音乌拉山和乌兰布和沙漠地区是D值的高值区,西南部边缘的图格力高勒沟台地和东南部边缘的贺兰山地区是全流域D值的最低区域,土壤表层在吉兰泰盐湖附近有带状分布的高值区。[结论]受气候和人类活动的影响,吉兰泰盐湖盆地土壤质地发生变化,表层土壤颗粒风蚀严重,较深层土壤具有粗粒化现象,未来应加强土壤侵蚀和退化状况观测研究。

土壤养分的空间变异性研究进展

土壤养分具有变异性,其变异性特征能够反映区域生态功能和景观格局的动态变化,是土壤的重要属性之一。本文从土壤养分空间变异的研究意义出发,通过对相关文献的阅读分析,简述了国内外关于土壤养分空间变异研究的发展历程和研究现状,分析了土壤养分空间变异的来源,简述了地统计学、地理信息系统(Geographic Information System, GIS)、遥感以及人工神经网络等研究方法在土壤养分空间变异研究的应用现状,并对目前研究所存在的问题进行了剖析,在此基础上对未来的研究方向进行了展望。

花岗岩岩爆试验声发射源时空分布特征研究

运用具有定位功能的多通道声发射系统采集花岗岩岩爆试验声发射源数据,基于分形理论定量描述花岗岩试件岩爆试验各阶段声发射源时空分布特征。结果表明:声发射源定位与试验结果较好对应;各阶段声发射源空间分维值在2~3,并呈现复杂的非线性变化趋势;在初始加载阶段,内部大量初始裂纹闭合,空间分维值较大;之后试件趋于稳定,声发射源数量少,分维值降低;快速卸载后应力增加,微裂纹稳定扩展,声发射源空间分布离散,分维值上升至峰值;竖向应力逐渐接近峰值,宏观裂纹形成,声发射源集中分布特征越明显,分维快速下降。该研究可加深对岩爆破坏过程的认识,也可为岩爆预测提供指标参考。

胶东和鲁西金矿床空间分布分形差异及对金来源的启示

胶东和鲁西地体发育大量的中生代金矿床,其金元素的来源一直是学术界争论的焦点,可能的来源方式为:交代岩石圈地幔、前寒武纪变质基底和中生代二长花岗岩。为了进一步厘定金的来源,文章从金的富集阶段模式和金矿床是金元素超常富集地质体的思想出发,运用金矿床的空间分布数据和空间分析的分形地质统计方法,进行了研究。研究结果发现,胶东金矿床(N=823)具有一阶段的空间分形分布模式,其分形维数α=0.726,具有单一来源或单一成因的特征;结合前人研究和克拉通破坏和西太平洋俯冲的地质背景,推断胶东金元素极有可能是单一的交代岩石圈地幔来源;而胶东地体西侧鲁西地体中发育的金矿床(N=139)则具有二阶段的空间分形分布模式,其分形维数分别为α_(1)=1.630和α_(2)=0.850,具有2种金元素来源或2种成因类型的特征,可能分别对应着早前寒武纪变质岩及韧性剪切带有关金矿床和晚中生代岩浆活动有关金矿床空间分布的分形维数,后者的值与胶东地体的分形维数相近,结合前人研究,推测鲁西部分金矿床来源于交代岩石圈地幔的贡献,另一部分则可能来自于花岗质岩浆。

分级加载浸水泥质粉砂岩声发射分形特征试验研究

为探究不同浸水时间对泥质粉砂岩加载破坏过程的影响,以天然状态、浸水1,3,7 d状态下滇中引水工程大理Ⅱ标段板凳山隧洞的泥质粉砂岩为样品,进行单轴分级加载试验,监测岩样从加载至破坏的全过程声发射(AE)活动。试验表明:(1)随着浸泡天数的增加,AE累计振铃计数逐渐衰减,在分级加载时,天然岩样的累计振铃计数曲线有明显上升台阶,浸水岩样的累计振铃计数曲线的跃升主要集中在破坏阶段。(2)天然岩样较浸水岩样的脆性更强,破坏时AE活动频度较高,表现为AE定位点在主破裂面附近泵集,破坏面附近定位点的能级较浸水岩样高1~2个能级。(3)随着加载应力增加,浸水岩样的含水率越高,岩样的破裂损伤阶段较天然岩样有所提前,AE定位点主要集中在破坏阶段,定位点数量的激增更加明显,这与振铃计数的变化规律相吻合。(4)不同含水率岩样在相对破坏应力80%之前,关联维数均呈现上升的趋势,在相对应力的80%附近关联维数上升至最大值,应力继续增大,岩样破坏,关联维数跌落至最小值,不同含水率岩样的关联维数最小值均介于0.020~0.035之间。以上岩样的破坏特点可为隧洞涌水情况下岩体稳定性监测提供参考依据。