基于Monte Carlo法的黄土二维微观结构模型构建

A Method for Generating Two-dimensional Microstructure Model of Loess Based on Monte Carlo Method

从微观尺度研究土的力学行为是揭示其力学机理的一种有效途径,为此首先建立其微观结构模型。目前常通过光学显微镜或者扫描电镜图像获取黄土的微观结构,但将其直接用于二维建模时,存在颗粒悬浮和叠置的问题。基于黄土的颗粒累积分布曲线和实际颗粒形态,提出了一种随机生成其二维微观结构模型的方法。首先将颗粒累积分布曲线按粒径范围分为若干区间,从各区间上随机抽取粒径值,形成满足其粒径分布的粒径数据库;再根据黄土颗粒的微观图像建立颗粒的形态数据库。从这2个数据库中随机抽取颗粒粒径和形态,生成具有随机大小、形态的颗粒库。采用Monte Carlo法将这些颗粒在模型顶端随机投放,建立黄土的二维微观结构模型。该模型为黄土微观力学行为的分析提供了原型。

Simulating the mechanical behavior of loess in micro-scale is an effective way to reveal the mechanical mechanism of loess.Micro-mechanical model of loess is essential.At present,the microstructure of loess is often obtained by optical microscope or scanning electron microscope image,which,however,will lead to particle suspension and overlapping when directly used in two-dimensional modeling.In this paper,a method of randomly generating two-dimensional microstructure model of loess is proposed based on the cumulative distribution curve and the actual particle morphology of loess.Firstly,the cumulative particle distribution curve is divided into several intervals according to the particle size range,and the particle size is randomly extracted from each interval to form a particle size database which satisfies the size distribution.In subsequence,a database of particle morphology is established based on the microscopic images of loess particles.The size and morphology of particles are randomly extracted from the two databases to generate a particle bank with random sizes and morphology.Last but not the least,Monte Carlo method is used to randomly place these particles at the top of the model,hence a two-dimensional microstructure model of loess is established.The model established in this paper accords with the microstructure characteristics of loess and provides an initial model for the simulation and analysis of microscopic mechanical behavior of loess.