基于隨機數結構面分維數估算的改進投影覆蓋法

陳世江; 朱萬成; 王創業; 郭國瀟; 楊志東

doi:10.13374/j.issn2095-9389.2018.09.004

基于隨機數結構面分維數估算的改進投影覆蓋法

doi: 10.13374/j.issn2095-9389.2018.09.004

1) 內蒙古科技大學礦業研究院, 包頭 014010
2) 東北大學資源與土木工程學院, 沈陽 110819

基金項目:

內蒙古自治區自然科學基金資助項目(2015MS0548)

內蒙古科技大學優秀青年基金資助項目(2016YQL04)

國家自然科學基金資助項目(51564038,51464036)

詳細信息

中圖分類號: TG142.71
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出版歷程
- 收稿日期: 2017-09-08

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

1) Institute of Mining Research, Inner Mongolia University of Science and Technology, Baotou 014010, China
2) School of Resources and Civil Engineering, Northeastern University, Shenyang 110819, China

摘要

摘要: 巖石結構面的定量化描述對于理解結構面的力學性質至關重要,投影覆蓋分形描述法是結構面定量化表征的主要方法之一.然而,投影覆蓋法計算結構面分形維數時存在三角形單元劃分的缺陷.從概率分析角度考慮,將隨機數應用于三角形單元的劃分中,提出了基于隨機數估算結構面分維數的投影覆蓋法.應用改進投影覆蓋法計算了紅砂巖結構面的分維數,獲得了120個分維值,并將其作為一個分維數樣本;然后分析了此樣本的分布特征,并將樣本均值作為結構面分維數的精準值.實例分析證明,采用改進投影覆蓋法所獲分維數樣本是來自正太分布總體;投影覆蓋法計算的分維數幾乎是改進投影覆蓋法所獲結果的極限值;基于隨機數進行三角形單元劃分更符合實際結構面形貌特征,從而計算的分維數更精準.
- 巖石結構面 /
- 分形維數 /
- 投影覆蓋法 /
- 隨機分析
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.
- rock discontinuities /
- fractal dimensions /
- projective covering method /
- stochastic analysis

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參考文獻(8)

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