Dynamic Analysis of Machine Foundation


 Neil Elwin Harris
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1 Dynamic Analysis of Machine Foundation 351 Dynamic Analysis of Machine Foundation In this tutorial, RS2 is used to simulate a foundation experiencing cyclic machine loading. This tutorial covers the basics of setting up a model for dynamic analysis in RS2, and interpreting the dynamic analysis results. Topics Covered Project Settings Dynamic Boundary Conditions Dynamic Loading Time Line Queries Dynamic Results Interpretation Geometry The geometry is provided below. Ensure that the joint boundary provided between point (66, 70) and (74, 70) has a Joint End Condition of "Both ends open". In addition to the external boundary and joint boundary displayed above, a material boundary will be provided in order to define two areas with different mesh densities.
2 Dynamic Analysis of Machine Foundation 352 Model Project Settings Open the Project Settings dialog from the toolbar or the Analysis menu. Under the General page, define the units as being Metric, stress as kpa. For this tutorial the Time Units need to be specified as "Seconds". In the Project Settings dialog, select the Dynamic page. Check the Dynamic Analysis checkbox in order to enable the dynamic analysis to be conducted on specific stages. On this tab the general dynamic parameters are defined such as Rayleigh Damping. For this analysis the model will be damped at 5% critical damping for the frequencies 2 and 5 Hz. Check the Frequency1 radio button and enter 2 and 5 Hz for the frequencies and 0.05 for both Damping ratios.
3 Dynamic Analysis of Machine Foundation 353 Instead of using the auto time stepping option, each stage will be made to always have 70 time steps regardless of the duration of the dynamic stage. Keep the integration method parameters at their default values. In addition to an initial static stage, four dynamic stages will be added in order to see the state of the model at intermediate time stages and in its final state. The total duration of the dynamic simulation will be 1.5 s. Three intermediate stages will be provided at 0.7, 0.73, and 0.75, seconds. In the Project Settings dialog, select the Stages page. The first stage in the analysis is by default always a static analysis stage. Insert four new stages and check the Dynamic checkbox for each of the new stages. In the time column the simulation time at which each stage will end is inserted. Add the corresponding times and name the stages.
4 Dynamic Analysis of Machine Foundation 354 TIP: If a static stage is placed between two dynamic stages, the latter dynamic stage will still proceed from the time the previous time stage ended to the latter stage's end time. Close the Project Settings dialog by pressing the OK button. Boundaries Select the Geometry workflow tab. Select the Add External option in the Boundaries menu and enter the coordinates shown in the figure at the beginning of this tutorial. Select the Add Joint option and add a single joint boundary between the coordinates (66,70) and (74,70). Make sure the joint end condition is Both Ends Open. Select the Add Material Boundary option, and add a material boundary joining the following points: (50, 70), (50, 35), (90, 35) and (90, 70). Within this new bounded area, the mesh density will be increased. Mesh Now generate the finite element mesh. Before we do this, let s define the parameters (type of mesh, number of elements, type of element) used in the meshing process. 1. Select the Mesh workflow tab. Select the Mesh Setup option in the toolbar or Mesh menu. 2. In the Mesh Setup dialog, change the Mesh Type to Graded, the Element Type to 6 Noded Triangles and the Default Number of Nodes on External to Select the Advanced button to reveal the Advanced Meshing options. Check the Use Advanced Mesh Regions checkbox. Set the Gradation Factor to 0.3.
5 Dynamic Analysis of Machine Foundation Click the Add... button and select the region bounded by the material boundaries. Click the Add... button once more and select the region above the joint boundary (you may have to zoom in to select this region). 5. Two hatched regions are added to the model indicating the Advanced Mesh Regions. In the table in the Mesh Setup dialog, change the Element Length of the regions to have a value of Close the Mesh Setup dialog by selecting the OK button. The model of the soil and foundation with the two hashed regions of advanced meshing is shown below. 2 1
6 Dynamic Analysis of Machine Foundation 356 Mesh the model by selecting the Discretize and Mesh option from the toolbar or the Mesh menu. Notice the uniform mesh within the material boundaries, and graded mesh outside. Mesh and default boundary conditions Boundary Conditions All the external boundaries will be unrestrained. 1. Select the Loads & Restraints workflow tab. Select the Free option in the Displacements menu. 2. Use the mouse to select all the line segments that define the external boundary. 3. Rightclick and select Done Selection. Free boundary condition applied to the entire external boundary
7 Dynamic Analysis of Machine Foundation 357 Material Properties Now we will define the material properties of the soil and the machine foundation. Select the Materials and Staging workflow tab. Select Define Materials from the toolbar or the Properties menu. Type Soil for the name. Make sure the Initial Element Loading is set to None. Enter 19 kn/m 3 for the Unit Weight. Select the Stiffness tab and enter kpa for the Young s Modulus and 0.4 for the Poisson ratio. The strength properties should remain at their default values. A second material will be defined for the concrete foundation. Select Material 2 to begin editing it. Type Concrete for the name. Make sure the Initial Element Loading is set to None. Enter 24 kn/m 3 for the Unit Weight. Select the Stiffness tab and enter kpa for the Young s Modulus and 0.25 for the Poisson ratio. The strength properties are to remain at their default values. Press the OK button to save the properties and close the dialog.
8 Dynamic Analysis of Machine Foundation 358 Select Assign Properties in the Properties menu to bring up the Assign dialog. Select the Concrete material and click on the portion of the mesh above the joint boundary that represents the concrete pad foundation (zoom in if necessary). Select Define Joints in the Properties menu to open the Define Joint Properties dialog. For this analysis the joint will be defined to be very stiff so that it does not contribute to the response. In the Additional section at the end of this tutorial, the joint will be allowed to slip and deform and a comparison can be made between a rigid and elastic interface. 1. Rename Joint 1 to Interface. 2. Set the Normal Stiffness and the Shear Stiffness to both have a value of kpa/m. 3. Check the Initial Joint Deformation checkbox to ensure no field stresses are applied on the joint. 4. Press the OK button and save the model using the Save option in the File menu.
9 Dynamic Analysis of Machine Foundation 359 Dynamic Loads Define the Machine Loading that will be applied on the foundation. Select the Dynamic workflow tab. Select Define Dynamic Load from the toolbar or the Dynamic menu. The Define Dynamic Loads dialog will appear allowing dynamic loads to be defined in the X and/or Y directions. Name the load Machine Load. Make sure the Type field is set to Distributed Force. Check the X checkbox and press the Define button in order to define a force time history. This will open the Function Defining Dialog.
10 Dynamic Analysis of Machine Foundation The value of the force at each time step may now be inputted in the table provided on the left side of the dialog and the resulting force history is plotted on the right side. The force that will be applied along the top of the foundation is a harmonic force with a frequency of 5 Hz and an amplitude of 10 kn/m, resulting in a total maximum force of 80 kn over the surface of the 8 meter wide concrete foundation. Click the Import button in the Distributed Force vs Time dialog and select the import file "Tutorial 35 machine_load.txt". This will import the desired harmonic load. Click OK to save the force function and to close the Force vs. time dialog and click OK once more to close the Dynamic Loads dialog. The machine load has been defined, now it must be added to the model. 1. Select Add Dynamic Load from the Dynamic menu. This will open the Add Dynamic Load dialog. 2. Select Machine Load (Distributed Force) from the Load Function dropdown box and click the OK button. 3. Zoom in to the foundation and select the top line edge.
11 Dynamic Analysis of Machine Foundation Rightclick and select Done Selection The distributed machine load has now been added to the top surface of the concrete foundation. NOTE: dynamic loads are only visible when a dynamic stage is being viewed and the Dynamic tab is selected. Dynamic Boundaries RS2 provides a number of dynamic boundary conditions and elements that are utilized only in dynamic analysis. For this model absorbing boundaries will be applied on the lateral and bottom external boundaries of the model in order to absorb incoming shear and pressure waves travelling in the soil. 1. Select Set Dynamic Boundary Conditions from the Dynamic menu or from the Dynamic toolbar. 2. Make sure that the BC Type is set to Absorb. 3. Use the mouse to select the three line segments that comprise the lateral and bottom boundaries of the model. Note that absorbing boundaries may only be applied to line segments. 4. Rightclick and select Done Selection. Close the dialog.
12 Dynamic Analysis of Machine Foundation The dynamic boundaries are now correctly applied. These boundaries are only visible when a dynamic stage is being viewed and the Dynamic tab is selected (in this case stages 2 to 5). Time Query Line A number of time steps will occur between the defined stages and RS2 will not output data for all the nodes for these time steps. The modeler does allow the user to specify points in the mesh, Time Queries, where the dynamic data will be recorded for all dynamic time steps occurring in the simulation. In addition to this, a Time Query Line may be added by the user to obtain graphs that provide visual representation of the motion of points on a line over time. Select Add Time Query Line from the Dynamic toolbar or from the Dynamic menu in Time Query section. The Specify Query Locations dialog will appear asking how many evenly spaced points should be placed on the query line. Specify 7 query points. Select OK. Clicking anywhere will place a vertex that the query line will contain, or the exact coordinates may be typed in. Add a time query line with the following endpoints: (72, 0), and (72,70).
13 Dynamic Analysis of Machine Foundation Compute Run the model using the Compute option in the Analysis menu. The analysis should take a number of minutes to run depending on the specifications of the computer the analysis is being performed on. Once the model has finished computing (Compute dialog closes), select the Interpret option in the Analysis menu to view the results. Interpret After you select the Interpret option, the Interpret program starts and reads the results of the analysis. The model is producing only values of zero for this stage because there is no external force, field stress or gravity applied at stage 1. Note that the end time of the dynamic stages are displayed in parenthesis next to the stage name in the tabs along the bottom of the screen. Cycling through the tabs allows one to get an idea of the stresses that are changing over time during the dynamic loading event. TIP: you can also change the viewing stage by selecting the Page Up / Page Down keys, or by placing the mouse cursor over the stage tabs and rotating the mouse wheel. To obtain a contour that provides an understanding of how the waves propagate from the foundation proceed with the following steps. 1. Switch to the second stage labeled Intermediate Use the combobox in the toolbar to select the Horizontal Displacement dataset from the Solid Displacement data option. 3. Select Display Options in the View menu. Choose the Boundaries tab.
14 Dynamic Analysis of Machine Foundation Deselect the Material boundary option in order to prevent it from being displayed. 5. Select Done to save and exit the dialog. 6. Select Contour Options in the View menu. In the Contour Range section select the AutoRange (all stages) option so that all the stages are using the same data range allowing them to be compared. 7. Select Done to save and exit the dialog. From the contour map that should be displayed, the shear wave that descends from the foundation down towards the bottom boundary is easily observed. The travelling wave is apparent from the alternating blue (cold) and green (warm) zones which represent negative and positive horizontal displacement respectively. This motion is the expected soil behavior from a foundation with lateral machine loading acting on it. Toggling through the Intermediate stages one can observe the progression of the shear wave as it travels down and the formation of a new negative displacement zone at the surface as the foundation translates left. In RS2 there are other ways to visualize this shear wave propagation. Using the Time Query Line that was added in the modeler a visual comparison of the horizontal displacement of each of the query points can be made. The generated graph allows one to observe the amplitude reduction of the wave and the time spent traveling between the query points, which can be used as an indication of shear velocity of the soil. 1. RightClick on the Time Query Line and select Graph Time Query Line Data. The Graph Time Query Data Dialog will be open.
15 Dynamic Analysis of Machine Foundation Select all the dynamic stages, stages two through five. In the Vertical Axis option ensure that X displacement is selected. Select the Plot button. The time query line data is now plotted on a graph. 3. Under the Chart menu, deselect Show Point Markers and select the Show Peak Values option. From the generated graph it is apparent that the amplitude greatly reduces from the motion at the surface to that at the bottom boundary. Comparing the time the peak values occur it is apparent that the wave takes about 0.12 s to travel from one query point to the next. The top and bottom boundaries are exceptions since they are near the surface boundary and bottom absorbing boundary.
16 Dynamic Analysis of Machine Foundation Another graph that would be useful is that of the deformation of the soil column in the center. To obtain that shape in a graph a vertical material query line will be added at the center of the model. 1. Select Add Material Query in the Query menu. 2. Enter the starting vertex of (70, 0) and another at (70, 70) and rightclick and select Done. 3. The Specify Query Locations will open and in the first entry specify 100 locations. Turn off the Show queried values checkbox. 4. Press OK. Ensure that the Horizontal Displacement dataset is selected from the Solid Displacement data option. You should see the following screen in the Interpret program. To obtain the plot of the vertical soil profile the following steps need to be executed. 1. Rightclick on the material query polyline (not the Time Query line) and select Graph Data.
17 Dynamic Analysis of Machine Foundation Select only the intermediate dynamic stages to plot on the graph and click the Plot button. 3. The graph is generated. Select Swap Horizontal and Vertical Axes from Axes submenu in the Chart menu. Swapping the axes will ensure that the horizontal displacement is on the horizontal axis. From this curve a clear decaying sinusoidal curve centered about 0 displacement is apparent. This wave is the shear wave that causes horizontal movement but travels vertically in the soil model. From the three stages displayed here the creation of a new peak in the shear wave is evident close to the soil surface. This peak begins to propagate vertically immediately. Additional The interface between the foundation and soil system can be made not rigid in order to add some realism to the system. To do this the properties of the joint that was created in the tutorial will be altered. 1. Select Define Joint Properties from the Properties menu. 2. Change the shear stiffness to be kpa/m and the normal stiffness to kpa/m. Ensure the slip criterion remains on the None option. Allowing slip in the system would allow the foundation and soil to become unattached and may cause the model to produce erroneous results.
18 Dynamic Analysis of Machine Foundation Computing this new model and obtaining the plot from the same time query line as in the previous section, one will observe that the displacements have increased. Where the peak displacement of the surface for the rigid joint model was mm, the model with the elastic joint has a surface displacement of mm. The peaks still occur at the same times indicating that the shear wave velocity is unchanged in the soil, as would be expected since the soil's properties were unaltered. This concludes the tutorial, you may now exit the RS2 Interpret and Model programs.
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