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基于随机数结构面分维数估算的改进投影覆盖法

陈世江, 朱万成, 王创业, 郭国潇, 杨志东

陈世江, 朱万成, 王创业, 郭国潇, 杨志东. 基于随机数结构面分维数估算的改进投影覆盖法[J]. 工程科学学报, 2018, 40(9): 1043-1049. DOI: 10.13374/j.issn2095-9389.2018.09.004
引用本文: 陈世江, 朱万成, 王创业, 郭国潇, 杨志东. 基于随机数结构面分维数估算的改进投影覆盖法[J]. 工程科学学报, 2018, 40(9): 1043-1049. DOI: 10.13374/j.issn2095-9389.2018.09.004
CHEN Shi-jiang, ZHU Wan-cheng, WANG Chuang-ye, GUO Guo-xiao, YANG Zhi-dong. Improved projective covering method for fractal dimensions of rock discontinuities based on stochastic analysis[J]. Chinese Journal of Engineering, 2018, 40(9): 1043-1049. DOI: 10.13374/j.issn2095-9389.2018.09.004
Citation: CHEN Shi-jiang, ZHU Wan-cheng, WANG Chuang-ye, GUO Guo-xiao, YANG Zhi-dong. Improved projective covering method for fractal dimensions of rock discontinuities based on stochastic analysis[J]. Chinese Journal of Engineering, 2018, 40(9): 1043-1049. DOI: 10.13374/j.issn2095-9389.2018.09.004

基于随机数结构面分维数估算的改进投影覆盖法

基金项目: 

内蒙古自治区自然科学基金资助项目(2015MS0548)

内蒙古科技大学优秀青年基金资助项目(2016YQL04)

国家自然科学基金资助项目(51564038,51464036)

详细信息
  • 分类号: TG142.71

Improved projective covering method for fractal dimensions of rock discontinuities based on stochastic analysis

  • 摘要: 岩石结构面的定量化描述对于理解结构面的力学性质至关重要,投影覆盖分形描述法是结构面定量化表征的主要方法之一.然而,投影覆盖法计算结构面分形维数时存在三角形单元划分的缺陷.从概率分析角度考虑,将随机数应用于三角形单元的划分中,提出了基于随机数估算结构面分维数的投影覆盖法.应用改进投影覆盖法计算了红砂岩结构面的分维数,获得了120个分维值,并将其作为一个分维数样本;然后分析了此样本的分布特征,并将样本均值作为结构面分维数的精准值.实例分析证明,采用改进投影覆盖法所获分维数样本是来自正太分布总体;投影覆盖法计算的分维数几乎是改进投影覆盖法所获结果的极限值;基于随机数进行三角形单元划分更符合实际结构面形貌特征,从而计算的分维数更精准.
    Abstract: The strength, deformability, and flow properties of rock discontinuities are strongly affected by the surface characteristics. Therefore, a quantitative description of the topography of the discontinuities is very important. The projective covering method (PCM) is useful in calculating the fractal dimensions to measure the irregularity and roughness of fracture surfaces. However, there is a defect in the division of a grid cell into two triangles, which is, for every grid cell, only one dividing scheme is used to calculate the fractal dimensions with the projective covering method, despite the availability of two schemes. Moreover, it has been confirmed that when a small grid cell is divided by a different triangulation division scheme, differing fractal dimensions are calculated. To obtain a grid cell division method whose result is consistent with the surface morphology of the studied fracture surface, which comprises thousands of grid cells, improved projective covering method (IPCM) was propose based on stochastic analysis. In this method, a random number was generated by the random function and its parity was judged. If the number was odd, the small grid cell was divided using one scheme. Otherwise, it was divided by the other scheme. With this method, the fractal dimensions of the discontinuity of a redsandstone was calculated and 120 fractal dimensions were obtained, which formed a sample space. Secondly, the distribution characteristics of the sample space was determined, and the average of the sample was regarded as the accurate fractal dimensions of the redsandstone discontinuity. The analysis shows that the sample of fractal dimensions follows a normal distribution, the calculated results by the projective covering method are the maximum or minimum values of the fractal dimensions estimation, and because the result of the dividing scheme using stochastic analysis method is more consistent with the surface morphology, the fractal dimensions obtained by improved projective covering method are more accurate.
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  • 期刊类型引用(3)

    1. 齐豫,邓华锋,李冠野,熊雨,李涛. 考虑层次结构的岩体结构面三维粗糙度表征方法. 长江科学院院报. 2022(01): 134-138+154 . 百度学术
    2. 李叶. 改进的投影覆盖方法对辽河河道粗糙床面分维量化研究. 水利规划与设计. 2020(01): 78-82 . 百度学术
    3. 陈世江,杨志东,王超,刘溪鸽. 基于改进投影覆盖法结构面粗糙度尺寸效应分析. 工程地质学报. 2019(06): 1244-1252 . 百度学术

    其他类型引用(4)

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出版历程
  • 收稿日期:  2017-09-07
  • 刊出日期:  2018-09-24

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