Tutorial 2: Model of a Six-Slab System
This example considers a model of a six slab system with skewed joints. In addition to complex geometry, this tutorial illustrates the specification of dowels and transverse ties, aggregate interlock, nonlinear thermal gradients, and a variety of axle loads. In addition to these tutorials, solved examples can be found under the topics of mesh refinement; linear aggregate interlock and nonlinear aggregate interlock; and dowel looseness and dowel-slab support. This example is identical to the solved project "test_2_3_skew" that is installed with EverFE2.23 with the exception of dowel, tie and aggregate interlock properties.
Model Creation and Geometry. Start model creation from scratch by opening EverFE and using the New-Metric option under the File menu, which will cause EverFE to display a single slab resting on a single base layer. Now, in the Geometry panel, select a 3 rows, 2 columns layout. Set Column 1 Length and Column 2 Length to 4600 mm, and set the Column 1 Width and Column 2 Width to 3600 mm. The third row of slabs will be a shoulder, which will have a width of 1800 mm. The slab thickness should be fixed at 250 mm. Finally, set the First Skew Angle to 15, the Second Skew Angle to -12, and the Third Skew Angle to 15. A single base layer of 150 mm thick will be considered in the analysis. Save the model as "Example 2" with the Save As option from the File menu. The basic geometry of the model has now been defined, and the EverFE main window should appear as shown below in Figure 1. Note that by default, transverse joints are doweled and all longitudinal joints are tied.
Figure 1: Geometry Panel During Model Construction
Material Properties. At this point, we are ready to define material properties. Click on the Material tab. In this example, we will not change the slab material properties or the dowel and tie properties from the default values; however, set the base layer elastic modulus E to 1000 MPa. The Slab/Base Interface should be unbonded (i.e. the Bonded Base checkbox must not be checked). Set the Initial Stiffness of the interface to 0.1 MPa/mm and the Slip Displacement to 0.1 mm. The dense liquid subgrade k should be left at the default value of 0.03 MPa/mm. The material properties are now defined, and the EverFE main window should appear as shown below in Figure 2.
Figure 2: Material Panel During Model Construction
Axle and Thermal Loads. The next step is defining the loads. Click on the Loading tab to bring up the Loading panel, and start by creating a Dual Wheel Tandem axle with a total load of 120 kN (the default value). The axle will appear in blue centered at (x,y) = (0,0); re-position the load to (x,y) = (3100, -2950), which will locate the lower right wheel pair near the upper left slab corner. Leave all other axle geometric properties at the default values. Now, create a second axle load by clicking the Dual Wheel Axle button. The default load for this axle is 80 kN, but change it to 120 kN. Locate the axle at (x,y) = (5100, 650) by manually entering these coordinates in the appropriate entry boxes. The remaining axle parameters should remain at their default values. The last axle load must be created using the Multi-Wheel Axle button, which by default has three wheels and a load of 120 kN. Change the number of wheels to six, and position this axle at (x,y) = (2400,2400). Finally, create a bilinear thermal gradient by specifying three temperature changes of -6, -4, and 5 degrees. All loads have now been defined, and the Loading panel should appear as shown below in Figure 3.
Figure 3: Loading Panel During Model Construction
Dowels and Transverse Ties. Enter the dowel and transverse tie modeling parameters panel by clicking on the Dowel tab. In this model, the top two slabs are travel lanes, and the bottom row is a shoulder. First, make sure that the Looseness checkbox is de-selected, since we will model dowel-slab interaction with dowel-slab support and restraint moduli. To set the dowel parameters for the transverse joint in the first row, select First Row Dowels from the list at the upper left of the input panel. Select the Even spacing option, and specify a value of 300 mm for Edge 1 and a total of 11 dowels, which gives a dowel spacing of 300 mm. In this model, we want to simulate high load transfer efficiency with no dowel-slab bond, i.e. nearly ideal performance. To do this, change the dowel-slab support modulus from the default value of 1000 MPa/mm to 100,000 MPa/mm, and keep the dowel-slab restraint modulus fixed at 0. The dowel Diameter will be set to 32 mm. Now, select Second Row Dowels from the list on the upper left of the input panel, and use the same geometric and material parameters used for the First Row Dowels. The shoulder (bottom row of slabs) is not doweled, which is treated by setting the number of dowels in the third row to 0.
Both longitudinal joints will be tied with 13 mm diameter, 1000 mm long ties spaced at 600 mm on center. At the bottom of the dowel input panel, change the tie Spacing for both joint from the default value of 1000 to 600. In addition, change both the Tie-slab support and restraint moduli from their default values to 100,000 MPa/mm to simulate good tie load transfer and a high degree of bond typical of deformed ties. All dowel and tie parameters are completely defined, and EverFE should appear as shown below in Figure 4.
Figure 4: Dowel Panel During Model Construction
Aggregate Interlock. No aggregate interlock will be considered for this model. Click on the Interlock tab, select Linear Model, and set the Joint Stiffness to 0 MPa/mm. The Joint Opening should be set to 1.0 mm. The aggregate interlock panel will appear as shown below in Figure 5.
Figure 5: Aggregate Interlock Panel During Model Construction
Meshing. Now, click on the Meshing tab and enter the meshing panel. Here, we will use the default meshing parameters with the exception of the Number of Elements along Y in Row 3, which will be set to 8. The meshing panel will appear as shown below in Figure 6. Note that mesh refinement is an important issue, and a similar example to this tutorial can be found here.
Figure 6: Meshing Panel During Model Construction
Solve. Now, we are ready to generate a solution. Click on the Solve menu and select Run the Shown Analysis, which will execute the finite-element solver. There is no need to save the project before running, since it is automatically saved when the analysis is run. While the model is running, a small frame with a white background will appear that displays details of the progress of the finite-element solution. This particular project requires about 12 minutes to run on a Dell Optiplex with a 2.80 GHz Pentium IV.
View Displaced Shape. Note that the title of the EverFE window now displays Current Project: Example_2 (A Solution Exists). The Visualize menu is now active, and the model results can be displayed. Start by selecting Displacements from the Visualize menu. This will bring up a dialog box; simply click OK, and a few seconds later (after the solution has been loaded) the EverFE displacement visualization sub-panel will appear. Click on the Show all Slabs and the Show the Base checkboxes at the top left of the panel, and then click the View Displacements button. This will bring up a window with a white background and a picture of the displaced shape of the slab and base layer as shown below in Figure 7. Note how the slabs have separated from their base at the edges and corners under the action of the negative thermal gradient. The view can be rotated and zoomed. Zooming in and rotating the view about the z axis gives the view shown in Figure 8, which illustrates the high degree of load transfer at the transverse joint in the upper two rows of slabs due to the dowels; in contrast, there is substantial differential displacement at the transverse joint in the tied shoulder. Do not close the visualization window, as this will also end your EverFE session. However, you can minimize the window to reduce screen clutter.
Figure 7: Displaced Shape
Figure 8: View Showing Differential Joint Displacements
View Stresses. The x-y plane at the top of the slab is the default plane for stress viewing, and the Max Principal stress is also selected by default. The scaling parameter is set to Local, and the Color Map is selected. Selecting all of the slabs by clicking on each individually in the plan view, clicking on the View Stresses button, and zooming in with the right mouse button will give visualization window shown below in Figure 9. The view shown in Figure 9 is a plan view looking down the z-axis; however, the view can be scaled and rotated in three dimensions. The maximum principal stress in this plane is 1.05 MPa, which occurs the the top center of the upper right slab, which is significantly longer than the other slabs and therefore more affected by the negative thermal gradient.
Figure 9: Stresses in x-y Plane at Top of Slabs
View Results for Points. Detailed information on all stress and displacement components can be retrieved at any point in the slabs or base layer. Select the Results for Points option from the Visualize menu. Set Z to -250 mm in the entry box on the lower right of the panel, which moves the red dot to the top of the slab. Now, click and drag on the red dot in the plan view to move it around the model; note how coordinates of the dot and the stress and displacement components are continually updated. Drag the red dot to the position (x, y) = (6910, -280) shown below in Figure 10 ; the maximum principal stress should read about 0.572 MPa.
Figure 10: Results for Points
Results for Dowels. It is interesting to view the internal forces in the dowels. Select Results for Dowels from the Visualization menu. This will automatically highlight the uppermost dowel in the model in red, and show a peak shear in this dowel of 5,174 N. Clicking on the dowel below it shows that it has a peak shear of 4,750 N. Checking each dowel in the model shows that the maximum shear of 20,266 N occurs in the bottom-most dowel highlighted in Figure 11. With the Fs checkbox selected, click the View Now button to bring up the shear diagram for this dowel shown in Figure 12. Note the locally high shear that is constant across the joint. This value decays very quickly due to the high dowel-slab support modulus used in this simulation; use of a softer dowel-slab support modulus will result in a lower peak dowel shear and a more gradual decrease in shear along the embedded portions of the dowel.
Figure 11: Selecting the Critical Dowel
Figure 12: Shear Diagram for the Critical Dowel