基于分形理论构建随机粗糙节理模型的方法研究

doi:10.13722/j.cnki.jrme.2020.0487

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摘要粗糙节理三维形貌特征是影响岩体沿节理面剪切力学性质的关键因素。采用3D扫描方法重构巴西劈裂试验得到的砂岩张节理表面形貌模型。根据粗糙节理表面统计自相似性质，引入地形学领域广泛应用的随机分形数字高程模型生成方法，通过调节不同的随机参数d，采用“菱形–正方形”算法迭代生成一系列不同形貌特征的分形粗糙表面数字高程模型，并将其与天然砂岩张节理进行形貌特征比较。采用三维盒维数法计算天然砂岩张节理以及随机构建的分形高程模型的分形维数，并基于选定的剪切方向统计2种模型的视倾角统计分布规律。分别以分形维数以及视倾角统计分布标准差为表征粗糙模型三维形貌特征的参数，确定了该天然张节理的形貌特征参数对应的粗糙度水平符合随机参数d = 2～3 mm范围的分形高程模型的粗糙度水平，验证了基于分形理论构建随机数字高程模型的方法在模拟构建粗糙节理表面模型方面的可行性。

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	宋宇
	刘保国
	任大瑞
	于明圆
	黄芮

关键词 ：岩石力学, 节理模型, 分形理论, 数字高程模型, 三维盒维数法, 三维张节理形貌, 视倾角

Abstract：The three-dimensional morphology is the key factor affecting the shear mechanical properties of rock joints. 3D scanning is performed to reconstruct the surface morphology model of the sandstone tension joint obtained by the Brazilian splitting test. The stochastic methodology of generating fractal digital elevation models，which is widely used in topography，is introduced to construct surface models with different rough morphological features based on the statistical self-similarity of rough joint surfaces. By adjusting the random parameter d，a series of fractal rough joints with different morphological features are generated using the “diamond-square” algorithm，and compared with the natural sandstone tension joint obtained by the Brazilian splitting test. 3D box-counting method is used to calculate the fractal dimensions of both kinds of joint surfaces，and the statistical distribution of apparent dip angles along a specific shear direction is analyzed. Considering the fractal dimension and the standard deviation of the statistical distribution of apparent dip angles as characterization parameters of 3D joint roughness，it is confirmed that the morphological feature of the natural sandstone tension joint conform to that of the artificial surface with the random parameter d ranging from 2 mm to 3 mm，verifying the feasibility of the stochastic method of constructing digital elevation model based on fractal theory for modelling rough joints with different morphologies.

Key words： rock mechanics')" href="#">

rock mechanics joint model fractal theory digital elevation model 3D box-counting method 3D tension joint morphology ')" href="#">apparent dip angle

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引用本文:

宋宇，刘保国，任大瑞，于明圆，黄芮. 基于分形理论构建随机粗糙节理模型的方法研究[J]. 岩石力学与工程学报, 2021, 40(1): 101-112.
SONG Yu，LIU Baoguo，REN Darui，YU Mingyuan，HUANG Rui . Study on stochastic method for modeling rough joints based on fractal theory. , 2021, 40(1): 101-112.

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http://rockmech.whrsm.ac.cn/CN/10.13722/j.cnki.jrme.2020.0487 或 http://rockmech.whrsm.ac.cn/CN/Y2021/V40/I1/101

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