中文摘要：

在二维情形,从细观角度,将土石混合体视作石料与土的两相结构,其中,石料为凸多边形,剩余空间为土体。为此,提出凸多边形随机摆放区域的数值模拟方法。该方法首先随机生成一个菱形并将该菱形随机变形得到一个具有参数方程的凸多边形;然后,在给定的区域中,按照一定的分布函数随机投放不同大小的凸多边形直至满足一定的终止条件;在此过程中,若新生成的凸多边形与其他凸多边形的距离不为0,可对其进行下降,以此模拟土石混合体的真实物理状态。使用该方法,在边长为30 cm的正方形区域内,取颗粒径1-8 cm,模拟了含量为72.01%（面积比）的土石混合体。最后,将所模拟的土石混合体进行有限元网格划分以及力学加载试算,从试算结果的应力云图可以观察到土与石的界面是土石混合体内应力集中的地方,与实际情况相符。

英文摘要：

In mesoscopic level, the soil-rock mixture is treated as a two-phase composite of rock and soil in two dimensional case. Convex polygons are used to represent the rocks and empty space the soil contents. The convex polygons are randomly scattered in simulated region in the numerical simulation. A rhombus was randomly generated and was randomly transformed into a convex polygon according to the parametric expression of rhombus. The convex polygons of different sizes are randomly assigned into the area of simulation in accordance with a certain distribution functions until the terminating conditions are satisfied. If the distances between a newly generated convex polygon and other polygons the generated previously are not zero; the new generated convex polygon is then adjusted accordingly to simulate the real physical condition of the soil-rock mixture. As such, a soil-rock mixture with the rock content of 72.01% in terms of area ratio is generated within the square of 30 cm in length~ and the particle diameter is in the range of 1 - 8 cm. Finite element mesh of the soil-rock mixture is generated and a numerical analysis is carried out to simulate a mechanical loading test. The stress concentrations on the interfaces between soil contents and rock particles are observed from the simulated results stress nephograms, which agreed with those in real situations.