| 题名 | 基于分形理论的滑坡时间分布研究—以三峡库区重庆段为例 |
| 作者 | 樊晓一 |
| 学位类别 | 博士 |
| 答辩日期 | 2007 |
| 授予单位 | 中国科学院水利部成都山地灾害与环境研究所 |
| 授予地点 | 成都 |
| 导师 | 乔建平 |
| 关键词 | 滑坡 时间分布 分维数 滑坡预测 |
| 学位专业 | 自然地理学 |
| 中文摘要 | 三峡库区重庆段是我国滑坡灾害的多发区和重灾区，平均每年发生滑坡灾害上百处，给该区域的社会经济建设和人民的生命财产造成了严重的损失。随着三峡工程的竣工和库区高水位的运行，需要对该区域滑坡灾害的发生演变的趋势进行分析，研究未来一定时间范围的发生规律，为库区的减灾防灾提供理论依据。本论文以分形理论为理论基础，1980～2000年的滑坡统计资料为数据基础，探讨三峡库区重庆段滑坡时间分布的分维数变化规律。通过分形理论研究该区域滑坡过去一定时间范围内滑坡发生的时间分布特征，为未来滑坡发育的规律、特征和滑坡预测研究提供理论依据。本文的研究内容如下：1. 将滑坡时间分布的分形规律划分为数学分形和物理分形进行研究。在许多研究滑坡分布的分形特征中，未能考虑无标度区的范围，并将滑坡分布作为数学点来描述而未考虑滑坡规模对分形结果的影响。这种研究结果主要反映了数量众多的规模较小滑坡的特点，掩盖了规模较大的滑坡分布特征。运用物理分形的方法，将滑坡划分为不同规模等级，避免了规模小、数量多的滑坡对较大规模滑坡的影响。并分析了各滑坡规模等级的分维数D，无标度区的范围和自然周期。2. 自相似性是分形理论的主要特征。论文利用了相似性系数和显著性检验方法研究了三峡库区重庆段滑坡时间年际分布和月分布的整体与部分以及部分之间的相似性特征和相似的显著性水平。年际分布的相似性系数最大值和最小值分别为0.993、0.768；月分布的相似性系数最大值和最小值分别为0.988、0.653。进行相似程度的显著性检验，检验结果仅有1～10×104m3与> 1000×104m3在月分布上没有显著相似性。利用层次结构研究了分形整体与内部精细结构部分关联关系。在研究4个规模等级内部次一级规模的滑坡数量与分维数的关系，得到了滑坡时间分布层次结构的一致性特征。3. 滑坡的分维数与滑坡的时间分布特征具有较大的相关性。利用Logistic分布对滑坡月分布进行拟合，研究了位置参数与滑坡月分布数量，尺度参数与滑坡分布的月份数量的相关关系。得到了位置参数a与r的线性关系，尺度参数与分维数的变化趋势图。利用滑坡年际分维数和滑坡数量的关系，建立了滑坡未来可能发生极大值的指数预测模型。根据模型预测了各规模等级在1998年和未来可能发生滑坡数量的极大值。结果显示1998年的预测值与实际值吻合较好。4. 运用R/S方法对滑坡数量年际分布进行时间记录分析，得到滑坡发生的年际统计规律及其发展趋势。建立了Hurst经验关系：R/S ＝c•τΗ。对不同规模等级的滑坡年际分布分别进行R/S分析，所有规模大于等于1×104m3滑坡的H值为0.73，各规模等级的H值都大于0.5。运用分数布朗运动理论分析，建立了变化时间相关函数与H值的函数关系。得到了各规模等级未来5、10、20年滑坡频度的最大涨落，根据H值都大于0.5，表明未来滑坡数量增减趋势与过去滑坡发生数量的增减趋势一致。 |
| 英文摘要 | There is the frequent and serious disaster area of landslide in Chongqing, Three Gorges Reservoir. Every year, more than 100 landslides happened and caused serious loss of social economy construction and people’s lives and property. With the completeness of the Three Gorges Engineering and the high water level function of reservoir, we need analyze the trend of landslide occurrence and evolution, study the occurrence law in certain time extension and offer the theory foundation for landslide prevention and reduction in the reservoir area. This paper studied the law of dimension of landslide time distribution in the study area, base fractal theory on theory and base landslide data from 1980 to 2000 on data. It offer the theory base for the occurrence law, characteristic, forecast of future landslide study, by the fractal studied the time distribution characteristic of landslides in past certain time. The study content of this paper as fallow:1. The fractal law of landslide time distribution was divided into mathematics fractal and physics fractal. In many study on the fractal of the landslides distribution, they could not think the scale spectrum. At the same time, they described the landslides distribution as the dot on the mathematics and could not study the sizes of landslides influence upon the fractal .The study result mainly reflected the characteristic of the numerous landslides with smaller size and covers the larger size. The landslides were divided into different sizes according to physics fractal which avoided the influence of the small size and numerous landslides to the large size. The study analyzed the dimensions, scales and natural cycles.2. The self-similarity is the main characteristic of fractal. By the comparability coefficient and significance test, this paper studied the comparability and significance level of yearly distribution of landslide time and between the total and part of month distribution. The maximum and minimum of comparability coefficient of yearly distribution were 0.993 and 0.768. The maximum and minimum of comparability coefficient of month distribution were 0.988 and 0.653. There was not significant comparability only between 1～10×104m3 and more than 1000×104m3 in month distribution. The relationships between the total and inside structure were studied by the hierarchy structure. The study results obtained the consistency of hierarchy structure of landslide time distribution when it studied the relationship of landslide number and dimension of the inside structures of the 4 sizes.3. There were more relativity between landslide dimension and the characteristic of landslide time distribution. When it imitated the month distribution by Logistic distribution, the paper studied the relation of situation parameter and landslide number of month distribution, of scale parameter and month number of landslide yearly distribution. The result showed the linearity relation between situation parameter (a) and r, and the variety figure between scale parameter and dimension. According to the relation of yearly dimensions and landslide number, the exponent forecast models of the maximum of likely occurrence were obtained. Using the model, it forecasted the maximums of each size in 1998 and future. The result showed the better consistency of the forecast and actual values. 4. The yearly statistic laws and development were obtained by which the R/S method analyzed the time record of yearly distribution of landslide number. The Hurst models(R/S ＝c•τΗ) were obtained. The values of H of landslides with size more than 1×104m3 were 0.73 and the H of each size was more than 0.5. On the base of the analysis of the Numeric Brown Movement, it obtained the function relation of the H and the relation function of variety time. It forecast the maximum fluctuation of landslide frequency of each size in 5, 10 and 20 years. According to the H values more than 0.5, it showed the consistency between the future trend of increase and decrease of landslide number and the past trend of increase and decrease of landslide number. |
| 语种 | 中文 |
| 学科主题 | 灾害学 |
| 公开日期 | 2010-10-21 |
| 分类号 | P64;S76 |
| 内容类型 | 学位论文 |
| 源URL | [http://ir.imde.ac.cn/handle/131551/2267]  |
| 专题 | 成都山地灾害与环境研究所_成都山地所知识仓储（2009年以前） |
| 推荐引用方式 GB/T 7714 | 樊晓一. 基于分形理论的滑坡时间分布研究—以三峡库区重庆段为例[D]. 成都. 中国科学院水利部成都山地灾害与环境研究所. 2007. |
| 个性服务 |
| 查看访问统计 |
| 相关权益政策 |
| 暂无数据 |
| 收藏/分享 |
除非特别说明，本系统中所有内容都受版权保护，并保留所有权利。
修改评论