砂土颗粒三维形态的定量表征方法

A quantitative characterization method of 3D morphology of sand particles

颗粒形态是影响砂土力学特性的重要因素,特别是影响砂土在低应力状态下的抗剪强度、剪胀效应和临界状态行为,以及高应力状态下的颗粒破碎行为。因此,准确地重构砂粒的三维形态,并量化计算其形态表征参数是研究砂粒形态效应的前提工作。借助于高精度的CT扫描技术和图像处理技术,获得近海石英砂和风化花岗岩残积砂这两类砂土颗粒的三维形态信息。采用球谐函数序列实现两种砂颗粒三维形态的准确重构,并通过球谐函数分析计算砂土颗粒的体积来验证该方法的有效性。基于球谐重构的三维砂粒表面,提出了实用性的方法来计算砂粒的表面积、表面曲率和三维尺寸等,进而计算砂粒的三维球度、圆度和伸长率等形态表征参数。结果表明,当球谐函数阶达到15时,其重构的砂粒基本形状和表面纹理均与真实砂粒非常接近;近海石英砂在水流搬运和磨蚀的作用下颗粒形态较为规则和圆滑,球度和圆度较大,而风化花岗岩残积砂则在物理风化和剥蚀作用下颗粒形态较为复杂和粗糙,球度和圆度较小;而这两种地质作用对砂土颗粒的伸长率则没有明显的影响。

Particle morphology is an important factor affecting mechanical properties of granular sands （especially the shear strength, dilation and critical state behaviours under low stress conditions）, as well as particle crushing behaviours under high stress conditions. Therefore, in order to study the morphological effects of sand particles, it is the prerequisite to accurately reconstruct and quantitatively characterize the three-dimensional （3D） morphological features of sand particles. In this study, the 3D morphological information of Leighton Buzzard sand and decomposed granite sand particles was obtained by means of high-precision CT scanning and a series of image processing techniques. The spherical harmonic （SH） function sequence was then used to reconstruct the accurate 3D particle morphology. Furthermore, the particle volume calculated by SH analysis was used to validate the efficiency of SH reconstruction of the 3D particle morphology. Based on the SH-reconstructed particle surface, we proposed practical methods to calculate the surface area, the surface curvature distribution and the 3D dimensions of the sand particles, and further calculate the 3D sphericity, roundness and elongation of the sand particles. The results show that the SH-reconstructed particle surface agrees well with the real sand particle including the general shape and surface texture when the order of the SH function reaches 15. In addition, the particle morphology of Leighton Buzzard sand is more regular and smooth due to geological action of water transportation and abrasion, while the particle morphology of granite residual sand is more complex and rough due to physical weathering and denudation. However, both two geologic actions have no significant effect on the 3D dimension ratio of the sand particles.