凸块体的一种几何建构方法

An analytic method for geometrical construction of convex polyhedron block

块体的描述和建构是工程岩体稳定分析过程中不可或缺的重要环节。方程表示是描述和建构工程开挖面上所有可能出现的块体几何模型的有效途径。现有块体建构方法没有采用凸块体方程表示这种途径,其结果虽然可以建构任意复杂的块体,但由于缺少配套的参数化描述方法,所建构的块体难以得到精确的几何描述。为此,提出凸块体的一种几何建构方法。首先,建立了以边界平面的单位外法向量和原点距为输入变量的凸多面体的一种方程表示形式;其次,给出了凸多面体方程的基于单纯形方法的一种求解算法,以及输入变量的辨识方法;最后,引入控制变量,建立了凸块体的几何建构方法。通过算例,演示了工程开挖面上所有可能出现的类型、任意形状和大小的凸块体的参数化描述能力和几何建构能力。

Description and construction of blocks play a significant role in the analysis of rock mass stability. The equation representation is an effective approach to describe all possible blocks geometry. However, this approach has not been applied to block construction in the literature. Although it is possible to construct arbitrarily complex block geometry, it is hard to obtain a precise geometrical information of blocks, due to the lack of appropriate parametric description method. Therefore, we proposed a geometric construction method for convex polyhedron block. First, an equation representation for convex polyhedron was established by defining two input variables of boundary planes of polyhedron. Then, a simplified algorithm was developed to solve the convex polyhedron equation and a procedure was further presented to identify these two input variables. Finally, an analytic method was proposed for geometrical construction of convex block by introducing four control variables. A numerical example was conducted to verify the effectiveness for parametric representation and geometrical construction of block geometry in engineering rock mass.