Abstract: 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.

Key words: 3D-stratum, incision of triangular prisms, algorithm, excavation, earth volume calculation