土颗粒形态的二维数学表达及其适用性  

Two-dimensional Mathematical Expression and Its Applicability of Soil Particle Morphology

作　　者：李强[1] 乔志甜 沈伟 李萍[1] 李同录[1] Li Qiang;Qiao Zhitian;Shen Wei;Li Ping;Li Tonglu(Department of Geological Engineering,Chang’an University,Xi’an 710054,China)

机构地区：[1]长安大学地质工程与测绘学院

出　　处：《甘肃科学学报》2020年第1期52-59,共8页Journal of Gansu Sciences

基　　金：国家自然科学基金(41772278);陕西省科技统筹创新工程计划(2017ZDCXL-SF-03-01-01)

摘　　要：颗粒大小和形态是建立土体微观力学模型的基本单元。土颗粒的形态可用不同的函数进行描绘,但这些函数对黄土颗粒的适用性并不清楚。研究分别用Fourier函数、Lagrange函数、Hermite函数和Spline函数对实际黄土颗粒进行描绘。结果表明Fourier函数适合描绘轮廓圆滑的土颗粒,但该函数需要的采样点远多于其他3种函数,且拟合的形态曲线不通过采样点;相对于Fourier和Spline函数,Lagrange函数更适合描绘棱角分明的颗粒。当在较少的采样点下使用Lagrange函数时,采样点的位置需能控制颗粒的轮廓;Hermite函数对具有棱角形态的土颗粒和圆滑的土颗粒均适用,但一个采样点要同时给出坐标位置和切线的参数;Spline函数适合描绘圆滑颗粒,其对采样点的选取要求最低。Particle size and morphology are the basic units for building up micromechanical model of soil mass.The morphology of soil particles could be described by different functions which applicability of these functions to loess particles is not clear.The actual loess particles were depicted by the Fourier function,the Lagrange function,the Hermite function and the Spline function respectively.The results show that the Fourier function is suitable for depicting soil particles with sleek contour which requires far more sampling points than the other three functions,and the fitted curve of morphology does not pass through the sampling points.Compared with the Fourier function and the Spline function,the Lagrange function is more appropriate to depict angular particles.When the Lagrange function is used at fewer sampling points,the positions of the sampling points need to control the profile of the particles.The Hermite function is applicable to both sleek-contoured and angular soil particles,but the coordinate position and parameters of tangent line should be provided for one sampling point at the same time.The Spline function fits for depicting sleek particles with the lowest requirements for selection of sampling points.

关 键 词：土力学 微观力学模型 颗粒形态 插值函数 

分 类 号：P642[天文地球—工程地质学]