砂土颗粒形状的傅里叶描述符自动生成  

Automatic Fourier-descriptor-based Generation of Paticle Shape of Sandy Soil

作　　者：方浩 张巍[1] 肖瑞[1] 施斌[1] 刘岩 赵春发[2] FANG Hao;ZHANG Wei;XIAO Rui;SHI Bin;LIU Yan;ZHAO Chunfa(School of Earth Sciences and Engineering,Nanjing University,Nanjing 210023,China;Traction Power State Key Laboratory,Southwest Jiaotong University,Chengdu 610031,China)

机构地区：[1]南京大学地球科学与工程学院,南京210023 [2]西南交通大学牵引动力国家重点实验室,成都610031

出　　处：《高校地质学报》2018年第4期604-612,共9页Geological Journal of China Universities

基　　金：国家自然科学基金重点项目(41230636);国家自然科学基金项目(40902076);江苏省自然科学基金项目(BK20160366);苏州市科技计划项目(SYG201611)联合资助

摘　　要：颗粒形状是影响砂土密实度、力学与渗流等特性的主要因素之一。傅里叶描述法是一种有效表征颗粒形状的数学方法。基于傅里叶系数与颗粒平均半径定义傅里叶描述符D_n。采用傅里叶描述符D_2,D_3,D_8以及D_3与D_8对数线性组合的简化算法可自动生成复杂的砂土颗粒形状。颗粒形状由傅里叶描述符D_n与相位角δ_n序列共同控制。分析了傅里叶描述符D_2、D_3、D_8与颗粒几何参数间的相关性,结果表明,长宽比a与D_2正相关,圆形度C与D_2,D_8负相关,磨圆度R与D_8强负相关,球形度S与D_2,D_3之间均呈现显著负相关,规则度R_e与D_8呈负相关性,且在D_8=0时与D_3之间呈强负相关性。以显微CT扫描南京粉砂断层序列二值图像中典型颗粒为样本,基于Pearson相关性准则,计算了重构颗粒与实际颗粒轮廓相似性,相关系数大于0.94,表明算法具有较高的表征精度。算法可用于二维数值模拟中实际砂土颗粒的批量自动生成。Particle shape is one of the main factors affecting the compactness,mechanical and seepage properties of sandy soils.Fourier description is one of the mathematical methods effectively characterizing the grain shape.Based on the Fourier coefficient and grain mean radius,we define the Fourier descriptor Dn.Employ Fourier descriptor D2,D3,D8 and,the logarithmic linear combination of D3 and D8,we develop a simplified algorithm to automatically generate complicated soil grain shapes.The grain shape is controlled by both Fourier descriptor Dn and phase angleδn series.The correlation between Fourier descriptors D2,D3,D8 and the grain geometrical parameters.The results show that the length-width ratio a is positively correlated to D2,circularity C is negatively correlated to D2 and D8,roundness R is strongly negatively correlated to D8,sphericity S is strongly negatively correlated to both D2 and D3 and,regulation Re is negatively correlated to D8 and,negatively correlated to D3 when D8 equals to 0.Using the typical grains in the binary images of Nanjing silty sand,obtained by micro-CT scanning,as samples,the shape similarity is calculated based on Pearson correlation criterion.The correlation coefficient is higher than 0.94,suggesting that the algorithm possess the relatively high characterization accuracy.The algorithm can be used to automatically generate massive practical sand grains in the two-dimensional numerical simulation.

关 键 词：砂土 颗粒形状 傅里叶描述符 相位角 相似性分析 

分 类 号：TU43[建筑科学—岩土工程]