{"id":59110,"date":"2024-05-14T10:24:19","date_gmt":"2024-05-14T10:24:19","guid":{"rendered":"https:\/\/ingeoexpert.com\/en\/?p=59110"},"modified":"2025-12-24T07:59:08","modified_gmt":"2025-12-24T07:59:08","slug":"use-of-fem-software-in-solving-mechanical-problems-in-geotechnical-engineering","status":"publish","type":"post","link":"https:\/\/ingeoexpert.com\/en\/2024\/05\/14\/use-of-fem-software-in-solving-mechanical-problems-in-geotechnical-engineering\/","title":{"rendered":"Use of FEM software in solving mechanical problems in geotechnical engineering"},"content":{"rendered":"
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Here you can read a fragment of one of the “Finite element modelling in geotechnical engineering<\/a>” course units.<\/b><\/p>\n<\/blockquote>\n

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This section will show how to use a commercial software package (Plaxis 2D) to do mechanical analysis in geotechnical engineering. An example on the bearing capacity of shallow foundations will be used. The problem is 2D, plain strain for a strip footing and axisymmetric for a circular footing (Figure 3.1). Though this problem is simple, it can show the key features of mechanical analysis in geotechnical engineering, including element selection and setting up boundary and initial conditions. The basic principles to be discussed here also apply to other more complex problems.<\/p>\n

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Figure 1 Examples of shallow foundations: (a) circular footing and (b) strip footing.<\/figcaption><\/figure>\n

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3.1 Creating the geometry for analysis<\/h3>\n

The first step of a FEM analysis is to create the geometry. For a 2D problem, a 2D geometry is needed. In the case of circular footing, one must use half of the cross section and the left vertical side is the axis of symmetry. For the strip footing, one can use the entire cross-section. Note that half of the cross-section can also be used when the problem is symmetric about the vertical axis (e.g., the soil is composed of horizontal soil layers and there is no existing structure beside the footing).<\/p>\n

In the analysis, the force displacement relation of the footing is of concern. Therefore, we do not want the size of the geometry (or size of soil beneath the foundation) to have influence on this relation. The width of the geometry must be bigger than the width of the footing. As will be shown in the boundary conditions later, the height of the geometry should be so big that the soil does not move in either the horizontal or vertical directions at the bottom. The width of the geometry should be big enough so that there is no horizontal displacement at the right vertical side (Figure 3.2a) or both of the vertical sides (Figure 3.2b). The proper height and width of the geometry can be found by studying their effect on the force displacement relation. As the height (H1, H2, H3) and\/or width (B1, B2, B3) increases, the simulated bearing capacity (the maximum value of the force) will decrease (Figure 3.3). The reason is that smaller height and width will give more confinement to the soil and make the soil stronger. However, when the width and height and width is big enough, further change in then will have little effect on the bearing capacity. Such critical width and height should be used in the analysis. For the case shown in Figure 3.3, B2 and H2 are essentially big enough for the analysis. In Plaxis 2D, the contour option is used to set the size of the geometry (Figure 3.4).<\/p>\n

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Figure 2 (a) Half of the cross-section and (b) the full cross-section.<\/figcaption><\/figure>\n

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Figure 3 Effect of geometry size on the solution.<\/figcaption><\/figure>\n

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Figure 4 Project properties in Plaxis 2D (element type and contour are discussed here).<\/figcaption><\/figure>\n

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3.2 Selecting the element type<\/h3>\n

The element is crucial for the FEM analysis. First, one needs to decide whether the problem is 2D or 3D. In geotechnical engineering, the 2D analysis is more widely used, even for some 3D problems. This is because the 3D analysis is more computationally expensive and the geometry is harder to create. Indeed, the 2D analysis does offer reasonable solutions. For the 2D analysis, one should choose either plain strain or axisymmetric element according to the problem features (see the Type option in Figure 3.4). In each FEM software package, there are several options for the geometry and node numbers of elements. Generally, elements with more nodes give more accurate results. But the computational time will be longer if there are more nodes in the problem. In Plaxis 2D, the only element geometry available is triangle. One can select 6-noded or 15-noded elements (see the Type option in Figure 3.4).<\/p>\n

3.3 Selecting the element size<\/h3>\n

In FEM analysis, a problem is discretized into small meshes (Figure 3.5). The mesh size has significant influence on the solutions. Generally, smaller mesh size (smaller element) gives more accurate solutions, as the simulated deformation field is more accurate. When the problem shown in Figure 3.5 is simulated using 2 or 3 elements (very big mesh size), the soil will behave more like a rigid body, which indicates the solution will be far from being accurate. Therefore, the mesh size should be small enough. For the shallow foundation problem, one can find out the proper mesh size by investigating the effect of mesh size on the force and displacement relation of the footing. Finer mesh will make the soil more flexible and the simulated bearing capacity smaller (Figure 3.6). When the mesh size is small enough, further decrease in mesh size will not affect the solution.<\/p>\n

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Figure 5 Meshes of a problem in Plaxis 2D.<\/figcaption><\/figure>\n

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Figure 6 Effect of mesh size on the force displacement relation.<\/figcaption><\/figure>\n

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3.4 Setting up the boundary conditions<\/h3>\n

There are different types of boundary conditions for geotechnical problems. Here are some examples:<\/p>\n

Mechanical analysis (force displacement relation is of concern):<\/p>\n