基于复数傅里叶分析的岩土颗粒细观特征识别与随机重构方法

Mesostructural characteristic and random reconstruction of soil-rock particles based on plural Fourier analysis

岩土细观特征的识别与分析是岩土力学研究的重要内容。基于傅里叶变换原理,将任意岩土颗粒的二维轮廓变换为傅里叶描述符与相位进行分析,建立了基于复数傅里叶分析的细观特征表征与重构方法。通过两组不同颗粒的傅里叶细观特征统计,研究了不同阶傅里叶描述符与细观特征参量的对应关系。结果表明:-12~0及16~20阶对应的傅里叶描述符决定颗粒的形状;-23^-11及1~15阶对应的傅里叶描述符与颗粒粗糙度密切联系;傅里叶描述符曲线峰值与颗粒的粒径显著线性相关;高阶傅里叶系数与阶数近似呈对数线性关系,低阶系数则由不同颗粒形状决定。采用建立的傅里叶描述符对应关系进行颗粒相似重构研究,发现重构颗粒的外轮廓及傅里叶统计参量与实际颗粒十分接近,且反映颗粒的粗糙度、纹理等细部特征,其成果可用于大量岩土颗粒与力学特性的相关性研究。

The identification and analysis of geotechnical mesocharacteristic play a crucial role in the study of rock and soil mechanics. Based on the principles of Fourier transform, a two-dimensional outline of rock and soil particles can be transformed into Fourier descriptors and phases, and then a mesocharacterization method is established based on plural Fourier analysis. The corresponding relationships between different orders Fourier descriptors and mesocharacteristic parameter are investigated through counting Fourier mesocharacteristics of two groups of different particles. It is shown that the Fourier descriptors corresponding to-12-0 and 16-20 orders determine the shape of particles, and the Fourier descriptors corresponding to-23--11 and 1-15 orders are closely connected with the roughness of particles. There exists a significant linear correlation between the peak value of Fourier descriptor curve and the particle size of rock and soil particles. High-order Fourier coefficient and its order are approximately in a logarithmic linear relation, however, low-order coefficient is determined by different particle shapes. By using the established Fourier descriptor corresponding relationship, particle similarity remodeling is studied. It is shown that the outlines and Fourier statistical parameters of remodeled particles are very close to the actual particles, and the remodeled particles can reflect the mesocharacteristics of particles such as roughness and texture. The method can be used for the study of correlation between a large number of rock and soil particles and their mechanical properties.