三维地层的三棱柱剖分与土方计算  

Research on incision of triangular prisms in 3D-stratum and calculation of excavated earth volume

作　　者：周翠英[1] 董立国[1] 

机构地区：[1]中山大学应用力学与工程系/地下工程与信息技术研究中心

出　　处：《岩土力学》2006年第2期204-208,共5页Rock and Soil Mechanics

基　　金：国家自然科学基金资助项目(No.59809008);广东省重大科技攻关十五专项(No.2001B30903);广东省科技计划项目(No.2004B10101002);广东省东深供水改造工程建设总指挥部委托项目资助(No.DSGZ-KJ-042;No.DSGZ-KJ-043)

摘　　要：三维地层剖分算法是实现地层三维可视化与土方计算的重要基础。采用三棱柱体建模方法构造三维地层,分析任意平面切割三棱柱的不同情形,得出了针对三棱柱地层的剖分算法;提出了以切割面为分界面,将单个三棱柱剖分成多个小三棱柱的三角投影分割法——将三棱柱顶面、底面及切割截面按一定规则进行合理三角化划分,使划分后三角形在水平面上的投影相重合;将该3层三角形组合成以切割面为分界面的2层小三棱柱,从而完成剖分。土方计算中首先给出开挖体的边界控制方程,根据该控制方程所限定的内边界得到开挖区域,结合上述剖分算法,对该区域内所有小三棱柱体积求和,得到开挖土方量。将以上算法应用到广东省某重大水利工程中,实现了基坑模拟开挖及其土方计算。The algorithm of three dimensional stratum （3D stratum） incision is the essential basis of the visualization of 3D-stratum and the calculation of excavated earth volume. For the moment, there is short of practical arithmetic in the cutting of stratum. Firstly, the 3D stratum is constructed by the method of modeling of triangular prisms, and then, by discussing all the cases of incised triangular prisms with an oblique plane, the incision algorithm for the stratum, which is composed by triangular prisms, are obtained. Thus, by taking the incision plane as an interface, a useful way to divide one triangle prism into several smaller ones is brought forward. The main principle is that, divide the top surface, bottom surface and the intersection of a triangle prism into several triangles according to a certain rule; and make the projections of these triangles in the horizontal plane coincided with each other; Constitute the three layered triangles into two layered small triangular prisms, which.take the incision plane as an interface; thereby, the incision is finished. Further more, the calculation method of excavated earth volume is put forward too; i.e., given the boundary controlled equation for the excavated body; according to the inside boundary （which is limited by the equation）, the excavated area can be easily obtained, By combining the excavated equation with the incision algorithm, incising triangular prisms with the planes that contain the excavated surfaces, aggregating all the triangle prisms that locate in the excavated volume, thus, the total volume of these triangular prisms will be equal to the excavated earth volume. Finally, by applying these two methods about triangular prism division and earth volume calculation to a certain major water supply project in Guangdong area, South China, the simulation of excavation for a foundation pit and its volume estimation is successfully realized.

关 键 词：三维地层 三棱柱剖分 算法 开挖 土方计算 

分 类 号：TU452[建筑科学—岩土工程] TB115[建筑科学—土工工程]