砂岩颗粒孔隙分布分形特征与强度相关性研究

doi:10.13722/j.cnki.jrme.2019.1555

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摘要岩石的组成成分与内部结构对强度特性起到决定性作用，基于砂岩细观尺度下物质与结构研究，采用分形维数理论与数值计算相结合的方法构建颗粒孔隙分布特征与力学强度的相关关系，实现对岩石强度特性的快速评价与估测。结果表明：(1) 颗粒孔隙呈偏态分布，即试件内部存在大量小尺寸颗粒孔隙，大尺寸颗粒孔隙较少，当颗粒几何比越接近1，表明颗粒圆度较高，否则多为针形或柱状颗粒密集分布；(2) 采用直方图双峰法确定的合理阈值可以增加孔隙定量表征试验的可操作性，有益于对尽可能多被筛选中的颗粒孔隙面积、数量、尺寸等9项指标的提取；(3) 表征单元格尺寸确定后，分形维数不随之相对变化。颗粒孔隙分布具备分形特征，可用维数来表征颗粒孔隙分布的复杂程度，即分布越复杂，维数值越大；(4) 分形维数与岩石强度具有显著的负相关关系，相关度为0.834，即随着分形维数的增大，试件的强度逐渐降低。

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	丁自伟1
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	李小菲1
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	唐青豹1
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	贾金兑1
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关键词 ：岩石力学, 结构表征, 分形维数, 抗压强度, 表征单元格

Abstract：The composition and internal structure of rocks play a decisive role in the strength characteristics. Based on the study of material and structure of sandstone at the mesoscopic scale，the correlation between the distribution characteristics of particle pores and the mechanical strength is constructed by using the method of combining fractal dimension theory and numerical calculation，so as to realize the rapid evaluation and estimation of rock strength characteristics. The results show that the pore distribution of particles is skewed. That is，there are a large number of small-sized particle pores inside the specimen while a less number of the large-sized particle pores. When the particle geometric ratio is closer to 1，the roundness of particles is higher. Otherwise，it is mostly densely distributed by needle or columnar particles. The reasonable threshold determined by histogram bimodal method can increase the operability of pore quantitative characterization experiment，which is beneficial to the extraction of 9 indexes such as particle pore area，number and size，etc. The fractal dimension does not change relatively after the representation cell size is determined. The particle pore distribution has fractal characteristics and hence，the dimension can be used to describe the complexity of particle pore distribution. In other words，the more complex the distribution is，the larger the dimension value is. It is also revealed that the fractal dimension has a significant negative correlation with the rock strength and the correlation degree is 0.834，indicating that the strength of the specimen decreases gradually as the fractal dimension increases.

Key words： rock mechanics structure characterization fractal dimension compressive strength representation cell

引用本文:

丁自伟1，2，李小菲1，2，唐青豹1，2，贾金兑1，2. 砂岩颗粒孔隙分布分形特征与强度相关性研究[J]. 岩石力学与工程学报, 2020, 39(9): 1787-1796.
DING Ziwei1，2，LI Xiaofei1，2，TANG Qingbao1，2，JIA Jindui1，2. Study on correlation between fractal characteristics of pore distribution and strength of sandstone particles#br#. , 2020, 39(9): 1787-1796.

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http://rockmech.whrsm.ac.cn/CN/10.13722/j.cnki.jrme.2019.1555 或 http://rockmech.whrsm.ac.cn/CN/Y2020/V39/I9/1787

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