SVOffice 2009 Features: Utilizing Planar Geometry in a 3D Model
November 23, 2009
Recent time and energy has been invested in improving the description of three-dimensional models in SVOffice 2009. Previously, SVOffice only allowed the description of three-dimensional objects built as a series of surface grids which were stacked upon each other. Regions in the old model paradigm cut through the surfaces similar to a cookie cutter effect to allow the creation of three dimensional region / layer combinations in a 3D model. While the surfaces paradigm of describing three-dimensional models is powerful, it was often difficult to create specific structures which were engineered to exact slopes and dimensions. These unique shapes include:
The Planes feature, which is now implemented in all of the SVOffice 2009 finite element products, allows the creation of a surface based upon a series of interconnected planes. Each plane is described by three points and a region which dictates the edges of a plane. Any number of planes can be spliced together to form a three-dimensional surface. This new feature greatly simplifies the creation of engineered structures. Three new examples have been created to illustrate the use of planes to simplify the creation of complex three-dimensional models:
Figure 1: Multiple layer deposition of earth
Multi-Layer Deposition of Earth
The first step in the geometry of this model is to create the non-level ground plane. This is easily done from field measurements at the extents of the model. Note that only three points are required, as a flat plane is precisely defined from three points.
The key feature in the geometry for this model is in the mine tailings pile. A truncated square pyramid is a good geometric shape as it is easy to understand and approximates real-world conditions. The shape is created using a square for the top and drawing in the sides based on field measurements. Note that any angle and grid point will do, as long as the points all join. After creation, the bottom of the pyramid can be “chopped off” to intersect the lower plane using a built-in function in SVOffice, to ensure a proper division between the tailings and the ground plane.
Figure 2: Earth dam with tailings pit
Earth Dam with Tailings Pit
The geometry for this model consists of a dam, a tailings pit, and banks surrounding the tailings pit. Three surfaces are defined. Surfaces 1 and 2 are constant and define the bottom and top of the model, respectively. Surface 2 is defined entirely by planes, i.e., the dam, the tailings pit, and the surrounding banks are all defined by plane surfaces. Note that along the sides of the tailings pit the quadrilateral regions are split into two triangles. This is required to properly model the slope of the surrounding banks. A minimum of two planes, at slightly different angles, is required to form the slope of the bank.
Figure 3: Earth dam in valley
Earth Dam in Valley
This earth dam model demonstrates a highly irregular shape, at an elbow in the valley. This makes the representation of the earth dam geometry much more complex as there are multiple pinch-out zones throughout the model. These pinch-out zones are handled with the planar surfaces feature in which each surface can be represented as a series of interlocking planes. The valley floor is represented as a surface and the top of the earth dam is represented as a separate surface. Additional regions are added where needed to create the exact intersections necessary for a proper mesh.
Two-dimensional models often fall short in their ability to adequately represent these types of numerical models. The interest in these models is to establish a reasonable flow regime through the earth structure. For example, the flow through the earth dam in a tailings reservoir may be needed to ensure that daylighting of the water table does not happen on the downstream slope. A similar type of objective may be realized with the three-dimensional earth dam in the valley. The three-dimensional earth dam in the valley may also require analysis of rapid drawdown in order to establish the design. In particular, the effect of rapid drawdown on the side slope interfaces where the earth dam meets the original side slopes of the valley may be of interest in this case.