基于傅里叶逆变换的土石混合体模型生成研究

针对土石混合体结构模型内部块石形态过于简单且无法对模型本身参数进行敏感性分析的现状,提出了一种新的土石混合体结构模型生成方法。首先,采用回归分析法建立傅里叶描述因子和块石形状参数之间的函数关系式,并通过傅里叶逆变换法生成具有特定形状的块石轮廓。接着,基于各粒径块石组面积相等的原则,推导出了指定面积级配曲线下各粒径组块石的个数,并利用拟采样法得到各块石对应的面积。再次,根据包围盒相交判定原理等,提出了块石相交判定算法,实现了块石的随机投放。最后,改变土石混合体模型结构参数,如含石量、粒径级配曲线和块石空间方向角等,生成具有特定块石形状的土石混合体随机结构模型并进行可行性验证。验证表明:该法可以重构出具有特定形状特征的块石轮廓,能生成满足计算精度要求的土石混合体随机结构模型,这为后续进行含石量、粒径级配曲线和块石形状等参数对土石混合体材料性能影响规律研究奠定了基础。

Inverse Fourier transform-based study on generating model of soil-rock mixture

Aiming at the status quo of that the rock-block configuration inside of the model of soil-rock mixture is too simple to make the sensitivity analysis on the parameters of the model itself,a new method for generating the structural model of soil-rock mixture is put forward herein. Firstly,the functional relationship between Fourier descriptors and the shape parameters of rock-block is established with the method of regression analysis,and then the outline of the rock-block with specific shape is generated through inverse discrete Fourier transform. Secondly,the numbers of the blocks of all the particle size groups with specific shapes under the specified area gradation curve are derived in accordance with the principle of that the areas of all the particle size groups of block are equal to each other,while the corresponding areas of all the rock blocks are obtained with the inverse transform sampling method. Once more,an overlapping detection algorithm for rock-block is put forward according to the principle of the overlapping detection of bounding box,and then the random rock-block riprapping is realized. Finally,the stochastic structural model of soil-rock mixture with specific shape of rock-block is generated through changing the structural parameters of the soil-rock mixture model,i. e. rock content,particle size gradation curve,spatial direction angle,etc. ,and then its feasibility is verified as well. The verification shows that this method can reconstruct the outline of rock-block with the specific shape feature and then generate the stochastic structural model that meets the requirement for the relevant calculation accuracy,which provides a basis for the following-up study made on the parameters of rock content,particle size gradation curve,shape of rock-block,etc.