Settlement Analysis of a Strip Footing Linear Static Analysis (Benchmark Example) analys: linear static. constr: suppor. elemen: ct12e pstrai. load: edge elemen force. materi: elasti isotro porosi. option: direct units. post: binary ndiana. pre: dianai. result: cauchy displa green princi strain stress total vonmis.
Outline 1 Description 2 Finite Element Model 2.1 Units 2.2 Geometry Definition 2.3 Properties 2.4 Boundary Conditions 2.5 Loads 2.6 Meshing 3 Structural Linear Static Analysis 3.1 Analysis Commands 3.2 Results 3.3 Comparison with Analytical Solution Settlement Analysis of a Strip Footing (Benchmark Example) https://dianafea.com 2/26
1 Description The main objective of this tutorial is to perform a settlement analysis (long-term) of a strip footing using Linear Elasticity. This is a benchmark example that will be compared with an analytical solution for settlement of an infinitely long rigid footing on smooth finite homogeneous isotropic ground, according to Giroud (1972) 1. The geometry of the model consists on a rigid concrete strip footing on an elastic soil layer of 5 m height. Due to symmetry, half of the geometry is simulated. Plane strain finite elements are used in this model. The work flow used in this tutorial is the following: Define geometry Define material properties Define boundary conditions and loads Generate the mesh Setup a linear elastic analysis Perform the analysis Interpret the results and compare with an analytical solution. Figure 1: Geometry of the example 1 Giroud JP (1972) Settlement of rectangular foundation on soil layer, Journal of the Soil Mechanics and Goundations Division, ASCE. Settlement Analysis of a Strip Footing (Benchmark Example) https://dianafea.com 3/26
The material models used are linear elastic isotropic with the properties described in Table 1. Soil Table 1: Material properties Young s modulus E Poisson s ratio ν 1.0E+4 0.33 kn/m 2 Mass density (dry) ρ 1.63165 T/m 3 Porosity (dry) φ 0.25 Concrete Young s modulus E Poisson s ratio ν 3.5E+7 0.15 kn/m 2 Mass density ρ 2.44748 T/m 3 Settlement Analysis of a Strip Footing (Benchmark Example) https://dianafea.com 4/26
2 Finite Element Model For the modeling session we start a new project. We will use quadratic tetra/triangle plane strain elements. Main menu File New [Fig. 2] Figure 2: New project Dialog Settlement Analysis of a Strip Footing (Benchmark Example) https://dianafea.com 5/26
2.1 Units For units we choose kilonewton for force and meter for length. Model Window Reference system Units [Fig. 3] Property Panel [Fig. 4] Figure 3: Geometry browser Figure 4: Property Panel - Units Settlement Analysis of a Strip Footing (Benchmark Example) https://dianafea.com 6/26
2.2 Geometry Definition We create two sheets, one for the soil and the other for the footing. Main Menu Geometry Create Add polygon sheet [Fig. 5] [Fig. 6] <Repeat this action 2 times> Figure 5: Geometry - Add sheet Soil Figure 6: Geometry - Add sheet Footing Settlement Analysis of a Strip Footing (Benchmark Example) https://dianafea.com 7/26
We fit the geometry in the workspace and hide the working plane. Main Menu Viewer Fit all Main Menu Viewer Show working plane <Hide> Figure 7: Geometry of the soil and footing Settlement Analysis of a Strip Footing (Benchmark Example) https://dianafea.com 8/26
We create a circle line where we want to have a finer mesh. Main Menu Geometry Create Add circle line [Fig. 8] Figure 8: Geometry - Add circle line Figure 9: Geometry - Circle line Settlement Analysis of a Strip Footing (Benchmark Example) https://dianafea.com 9/26
We imprint the circle line in the soil shape and the geometry definition is complete. Main Menu Geometry Modify Projection of shapes [Fig. 10] Figure 10: Imprint circle line Figure 11: Geometry of the model Settlement Analysis of a Strip Footing (Benchmark Example) https://dianafea.com 10/26
2.3 Properties We define the properties of the soil and footing using the parameters listed in Table 1. As we use 2D plain strain elements we do not need to define the geometry properties. We will use the default integration scheme, so no data group is required. We start by assigning the properties to the soil. Main Menu Geometry Analysis Property assignments [Fig. 12] Shape assignment Add new material [Fig. 13] [Fig. 14] Figure 12: Assign soil properties Figure 13: Soil - Add new material Figure 14: Soil - Material properties Settlement Analysis of a Strip Footing (Benchmark Example) https://dianafea.com 11/26
And we assign the properties to the concrete footing. Main Menu Geometry Analysis Property assignments [Fig. 15] Shape assignment Add new material [Fig. 16] [Fig. 17] Figure 15: Assign footing properties Figure 16: Concrete - Add new material Figure 17: Concrete - Material properties Settlement Analysis of a Strip Footing (Benchmark Example) https://dianafea.com 12/26
2.4 Boundary Conditions For the boundary conditions we defined two support sets: i) Gound support that includes fixing the translations in the X-direction of the side edges and fixing the translations in the X- and Y-directions in the bottom edge of the soil; i) Foundation support where we fix the translations in the X-direction in the symmetry edge of the footing. We start by defining the supports that belong to the support set Ground support. Main Menu Geometry Analysis Attach support [Fig. 18] [Fig. 19] Figure 18: Add edge supports to the soil Figure 19: View of the model - Supports in edges of the soil Settlement Analysis of a Strip Footing (Benchmark Example) https://dianafea.com 13/26
Main Menu Geometry Analysis Attach support [Fig. 20] [Fig. 21] Figure 20: Add bottom supports to the soil Figure 21: View of the model - Supports in the soil Settlement Analysis of a Strip Footing (Benchmark Example) https://dianafea.com 14/26
We know define the support set Foundation support. Main Menu Geometry Analysis Attach support [Fig. 22] [Fig. 23] Figure 22: Add edge support to footing Figure 23: View of the model - Supports of the model Settlement Analysis of a Strip Footing (Benchmark Example) https://dianafea.com 15/26
2.5 Loads We define the pressure load acting on the footing (see Figure 1). Main Menu Geometry Analysis Attach load [Fig. 24] [Fig. 25] Figure 24: Add pressure load Figure 25: View of the model - Pressure load Settlement Analysis of a Strip Footing (Benchmark Example) https://dianafea.com 16/26
2.6 Meshing We define the mesh properties. We will use edge divisions as depicted in Figure 27. Main Menu Geometry Analysis Set mesh properties [Fig. 26] <Repeat this action for all the edges as presented in Figure 27> Figure 26: Set mesh properties Figure 27: Mesh properties - edge divisions Settlement Analysis of a Strip Footing (Benchmark Example) https://dianafea.com 17/26
And we generate the mesh. Main Menu Geometry Analysis Generate mesh [Fig. 28] Figure 28: Finite element mesh Settlement Analysis of a Strip Footing (Benchmark Example) https://dianafea.com 18/26
3 Structural Linear Static Analysis 3.1 Analysis Commands We set-up the commands for a linear static analysis. Main Menu Analysis New Analysis [Fig. 29] <Rename Analysis 1 to Linear Analysis browser Linear Add command Structural linear static [Fig. 30] [Fig. 31] Figure 29: Analysis window Figure 30: Add command Figure 31: Analysis tree Settlement Analysis of a Strip Footing (Benchmark Example) https://dianafea.com 19/26
In the output properties we select the results of displacements, strains and stresses. We change the output file basename to Linear. Finally we run the analysis. Analysis browser Linear Structural linear static Output linear static analysis Edit properties [Fig. 32] Properties - OUTPUT Properties Output Device Properties [Fig. 33] Properties - OUTPUT User selection Results selection [Fig. 34] Analysis browser Linear Run analysis Figure 32: Output properties Figure 33: Output file Figure 34: Results selection Settlement Analysis of a Strip Footing (Benchmark Example) https://dianafea.com 20/26
3.2 Results We show the contour plot of the vertical displacements [Fig. 37]. We can increase the number of levels of the contour plot in the properties panel [Fig. 36]. Results browser Output linear static analysis Nodal results Displacements DtY [Fig. 35] [Fig. 37] Properties panel Result Contour plot settings Number of contour levels [Fig. 36] <We consider 15 levels> Figure 35: Results browser Figure 36: Set contour plot properties Settlement Analysis of a Strip Footing (Benchmark Example) https://dianafea.com 21/26
Figure 37: Displacements DtY Settlement Analysis of a Strip Footing (Benchmark Example) https://dianafea.com 22/26
We select the nodes at the interface between the soil and the footing. We tabulate the vertical displacements for these nodes. We observe that the displacements in this area are approximately 7.77 mm. Main menu Viewer Node selection [Fig. 39] <Drag the mouse around the nodes at the connection between Soil and Footing> Results browser Output linear static analysis Nodal results Displacements DtY Show table [Fig. 38] [Fig. 40] Figure 38: Results browser Figure 39: Select Figure 40: Table Settlement Analysis of a Strip Footing (Benchmark Example) https://dianafea.com 23/26
3.3 Comparison with Analytical Solution The settlement of an infinitely long rigid footing on smooth finite homogeneous isotropic ground is determined analytical through the expression from Giroud (1972) 2 : δ = Settlement δ = P B E p H = P = Normal pressure = 40 kn/m 2 F E p H (1) Analytical solution δ = 40 2.99 = 7.92 mm 10000 E = Young modulus = 10 kn/m 2 p H = parameter dependent on H 0.5B F = pressure on footing = 0.99 (for ν = 0.33) Diana solution = 7.77 mm The error in the FE solution is 2% 2 Giroud JP (1972) Settlement of rectangular foundation on soil layer, Journal of the Soil Mechanics and Goundations Division, ASCE. Settlement Analysis of a Strip Footing (Benchmark Example) https://dianafea.com 24/26
We also show the principal minimum stresses for the soil. Mesh browser Shapes Footing Hide Results browser Output linear static analysis Element results Cauchy Total Stresses S2 [Fig. 41] [Fig. 42] Figure 41: Results browser Figure 42: Stresses S2 Settlement Analysis of a Strip Footing (Benchmark Example) https://dianafea.com 25/26
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