CE640/CE646 - Example on Plaxis software (version 8) for
Analysis of an isolated circular footing on sand
(a) Rigid Method of Analysis
A circular footing with a radius of 1.0 m is placed on a sand layer of 6.0 m in thickness as shown
below. Under the sand layer there is a stiff rock layer that extends to a large depth. The purpose of
the exercise is to find the displacement and stresses in the soil caused by the load applied to the
footing. The analysis is carried out for both rigid and flexible footings. The rock layer is not included
in the FEM model. The model is extended to a total radius of 8 m in the horizontal direction.
The settlement of the footing is simulated by uniform displacement at the top of the sand layer.
General Settings
(1) Start Plaxis. Create/Open project dialog box will appear. Choose New project and click OK.
The General settings window appears, consisting of two tab sheets Project and Dimensions.
These settings include the description of the problem, the type of analysis, the basic type of
elements, the basic units and the size of the draw area.
(a)
(b)
(c)
(d)
Enter Title (Example 1) and Comments (Settlement of footing).
Select Model (Axisymmetry) and Elements (15-Node). Click Next or Dimensions.
Select Dimensions (or keep the default units).
In the Geometry dimensions box, enter the size of the required draw area. Plaxis will add
a small margin so that the geometry will fit well within the draw area. Enter 0, 8, 0, 6 in
the Left, Right, Bottom and Top edit boxes respectively. Click OK.
Geometry
(2) Select Geometry line option (already pre-selected)
(a) Position the cursor (appearing as a pen) at the origin of the axes. Click the left mouse
button once.
(b) Move along the x-axis to position (8.0, 0.0). Click the left mouse button.
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(c) Move upward to position (8.0, 6.0) and click again.
(d) Move to the left to position (0.0, 6.0) and click again.
(e) Finally, move back to the origin (0.0, 0.0) and click the left mouse button again. Plaxis
will detect a cluster (area that is fully enclosed by geometry lines) and will give it a light
colour.
(f) Click the right mouse button to stop drawing.
The proposed geometry does not include plates, hinges, geogrids, interfaces, anchors or
tunnels. Therefore, skip these buttons.
Boundary Conditions
(3) (a) Click the Standard fixities button on the toolbar (or Standard fixities option from the
Loads menu) to set the standard boundary conditions. Plaxis will generate full fixity at
the base of the geometry and roller conditions at the vertical sides (ux=0).
(b) Select the Prescribed displacements button from the toolbar or select the option from
the Loads menu).
(c) Move the cursor to point (0.0, 6.0) and click the left mouse button.
(d) Move along the upper geometry line to point (1.0, 6.0) and click the left mouse button
again.
(e) Click the right button to stop drawing. A prescribed downward displacement of 1 unit
(1.0 m) in a vertical direction and a fixed horizontal displacement are created at the top
of the geometry and pointing in the direction of movement. The prescribed
displacement is activated when defining the calculation stages. Initially it is not active.
Material data
In Plaxis, soil properties are collected in material data sets and the various data sets are stored in a
material database. From a database, a data set can be assigned to one or more clusters. Different
types of structures have different parameters and therefore different types of data sets.
(4) (a) Select the Material Sets button on the toolbar.
(b) Click the New button at the lower side of the Material Sets window. A new dialog box will
appear with three tab sheets: General, Parameters and Interfaces.
(c) In the Material Set box of the General tab sheet, write "Sand" in the Identification box.
(d) Select Mohr-Coulomb from the Material model combo box and Drained from the
Material type combo box (default parameters).
(e) Enter the proper values in the General properties box and the Permeability box according
to the material properties.
(f) Click the Next button or the Parameters tab to input the model parameters.
(g) Since the geometry does not have Interfaces the third tab sheet can be skipped. Click OK
button to confirm the input values.
(h) Drag the data set "Sand" from the Material Sets window to the soil cluster in the draw
area and drop it. Correct assignment will change the colour of the cluster. Click OK to
close the database.
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Mesh Generation
Plaxis allows for a fully automatic mesh generation procedure.
(5) Click the Generate mesh button in the toolbar (or select the Generate option from the Mesh
menu). Click the Update button to return to the geometry input mode.
The Global coarseness setting can be changed from the Mesh menu.
Initial conditions
Before starting the calculations, the initial conditions must be generated. The initial conditions
comprise the initial groundwater conditions, the initial geometry configuration and the initial
effective stress state. Since the sand layer in the current analysis is dry, there is no need to enter
ground water conditions. The analysis requires the generation of effective stresses by means of the
K0 procedure.
(6) (a) Click the Initial conditions button on the toolbar (or select the Initial conditions from the
Initial menu). Click OK to accept the default value.
(b) Since water pressure is not involved, click the right hand side of the switch (Initial
stresses and geometry configuration). A phreatic level is automatically placed at the
bottom of the geometry.
(c) Click the Generate initial stresses button (or select the Initial stresses option from the
Generate menu). Accept default values of K0 and click OK.
(d) The generated effective stresses are presented in the Output window. Click the Update
button to return to the Input program geometry configuration mode.
Calculation
(7) (a) Click the Calculate button. Save the work.
(b) Calculation program can be used to select calculation phases.
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(c) Write an appropriate name in the Phase ID box.
(d) In the General tab sheet, select Plastic from the Calculation type combo box.
(e) Click the Parameters button (or click the Parameters tab).
(f) Keep the default value for maximum number of Additional steps (250) and select the
Standard setting from the Iterative procedure box.
(g) From the Loading input box, select Staged construction.
(h) Click the Define button. The Staged Construction window appears, showing the currently
active geometry configuration.
(i) Select the prescribed displacement by double-clicking the top line.
(j) Enter -0.1 in both input fields, signifying a downward displacement of 0.1 m. Click OK.
(k) Click the Update button to return to the Parameters tab sheet.
(l) Select nodes or stress points for a later generation of load-displacement curves or stress
and strain diagrams. Click the Select points for curves button on the toolbar. Select the
points. Click Update button to return to the Calculations window.
(m) Click the Calculate button.
View Output Results
(8) (a) Click the last calculation phase in the Calculations window. Click the Output button in the
toolbar. Deformed mesh can be observed with an indication of the maximum
displacement.
(b) Select Total displacements from the Deformations menu.
(b) Flexible Method of Analysis
The analysis is now modified so that the footing is modelled as a flexible footing. The geometry is
therefore, essentially the same as before except that additional elements are used to model the
footing. The calculation itself is based on the application of load rather than prescribed
displacements. Initially, save the previous work under a different name which is modified as outlined
below.
Modifying the geometry
(1) (a) Click the Go to Input button (LHS of the toolbar).
(b) Select the previous file from the Create/Open project window.
(c) Select Save as option of the File menu and save under a different name.
(d) Select the geometry line on which the prescribed displacement was applied and press the
<Del> key on the keyboard. Select Prescribed displacement from the Select items to delete
window and click the Delete button.
(e) Click the Plate button in the toolbar. Move to position (0.0, 6.0) and click the left mouse
button.
(f) Move to position (1.0, 6.0) and click the left mouse button, followed by the right mouse
button to finish the drawing. A plate is created which simulates the flexible footing.
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Modifying the geometry
(2) (a) Click the Distributed load - load system A button in the toolbar.
(b) Click point (0.0, 6.0) and then on point (1.0, 6.0).
(c) Click the right mouse button to finish the input of distributed loads. Accept the default
input value of the distributed load (1.0 kN/m2 perpendicular to the boundary). It can be
later changed to the real value when the load is activated.
Modifying the geometry
(3) (a) Click the Material sets button.
(b) Select Plates from the Set type combo box in the Material Sets window.
(c) Click the New button. A new window appears where the properties of the footing can be
entered.
(d) Write "Footing" in the Identification box and select the Elastic material type.
(e) Enter the properties as listed in Table below. Click the OK button. The new data set now
appears in the tree view of the Material Sets window.
(f) Drag the set "Footing" to the draw area and drop it on the footing. Click the OK button.
Generating the mesh
(4) (a) Click the Mesh Generation button to generate the finite element mesh.
(b) Click the Update button.
Initial Conditions
(5) (a) Click the Initial conditions button.
(b) Since the current project does not involve pore pressures, proceed to the Geometry
configuration mode by clicking the 'switch' in the toolbar.
(c) Click the Generate initial stresses button, after which the K0 procedure dialog box
appears.
(d) Keep Mweight equal to 1.0 and accept the default value of K0. Click OK button to
generate stresses. Click Update button.
(e) Click the Calculate button and confirm the saving of the current project.
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Calculations
(6) (a) In the General tab sheet, select for the Calculation type: Plastic.
(b) Enter an appropriate name for the phase identification and accept 0 - initial phase as the
phase to start from.
(c) In the Parameters tab sheet, select the Staged Construction option and click the Define
button.
(d) The plot of the active geometry will appear. Click the load to activate it. A Select items
dialog box will appear. Activate the both the plate and the load by checking the check
boxes to the load.
(e) While the load is selected click the Change button at the bottom of the dialog box. The
distributed load - load system A dialog box will appear to set the loads. Enter a Y-value of
-350 kN/m2 for both geometry points. [total footing force = 350 kN/m 2 x  x (1.0 m)2 
1100 kN]. Close the dialog box. Click Update.
(f) Check the nodes and stress points for load-displacement curves.
(g) Check if the calculation phase is marked for calculation by a blue arrow. If this is not the
case, double-click the calculation phase.
(h) Click the Calculate button to start the calculation.
Viewing the Results
(7) (a) Click the Output button. Select the plots that are of interest.
(b) Double-click the footing. A new window opens in which either the displacements or the
bending moments of the footing may be plotted.
Generating a load-displacement curve
(8) (a) Click the Go to curves program button on the toolbar.
(b) Select New chart from the Create / Open project dialog box.
(c) Select the file name of the latest footing project and click the Open button. A curve
generation window appears.
(d) For the X-axis select the Displacement radio button, from the Point combo box select A
(0.00 / 6.00) and from the type combo box Uy.
(e) For the Y-axis select the Multiplier radio button and from the Type combo box select
Mstage. Click the OK button.
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Practice Problem
A circular footing of diameter 3 m and 0.49 m in thickness placed on a 12 m thick cohesionless soil
deposit is to carry an axial load of 1200 kN. Evaluate the settlement of the footing, if the footing was
analysed as a (a) rigid footing (b) flexible footing. Also evaluate the maximum bending moment and
shear force developed in the flexible footing. Use the material properties of sand used in the
classroom demonstration problem for the cohesionless soil and EA = 500,000 kN/m and EI=10,000
kNm2/m for the footing.
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