CESAR-LCPC 2D v5 Tutorial 1 - itech soft 1 - CESAR-LCPC version 5 CESAR-LCPC proposes 3 levels for the surface meshing procedure, giving the possibility to generate a coarse or dense

CESAR-LCPC 2D v5

Tutorial 1: Stability of a circular footing

12-16 Rue de Vincennes 93100 Montreuil

France Tel : +33 1 48 70 47 41

Fax : +33 1 48 59 12 24 [email protected]

www.cesar-lcpc.com

© itech - 2011

Tutorial 1 - CESAR-LCPC version 5

1. PREVIEW

The maximum load that can be sustained by shallow foundation elements due to the bearing capacity is a function of the cohesion and friction angle of soils as well as the width B and shape of the foundation. In this tutorial, the foundation is a rigid circular footing (diameter B, 1 m) resting on an undrained homogeneous soil modelled using a Tresca criterion (undrained cohesion cu).

CESAR-LCPC helps the design of shallow foundation. With the Finite Element method we will search for the limit equilibrium of the system.

1.1. Tutorial objectives

- Learn how to design a mesh. - Get familiar with the incremental-iterative process for non-linear analysis. - Get the safety factor on forces. - Handle post-processing tools.

1.2. Problem Specifications

General assumptions

- Static analysis, - Non-linear behaviour of the soil. - Axisymmetrical problem. Only a part of the foundation is modelled and analysed.

Material properties

h (kN/m3)

Eu (MPa)

cu (kPa)

u (°)

K0

Soil mass 20 50 0,45 20 0 0,5

This 3D model is equivalent

to this axisymmetrical model

uniform pressure 0,51m

uniform pressure


1.3. Benchmark solution

According to “Undrained bearing capacity factors for conical footings on clay”, G. T. Houlsby and C. M. Martin, Geotechnique 53, No. 5, 513–520, 2003, the ultimate bearing capacity obtained for the considered footing problem is:

kPa 8.113c69.5p u

This result corresponds to a rigid circular footing with a perfectly sliding flat base. It was obtained using the numerical method of characteristics. The method assumes the soil to behave in a rigid-perfectly plastic manner following the Tresca criterion.

2. INPUTS FOR SAFETY FACTOR ANALYSIS

2.1. General settings

1. Run CLEO2D. .

2. Set the units in the menu Preferences > Units.

3. In the tree, select the leaf General/Length and set the unit m in the bottom left combo box.

4. In the tree, select the leaf Mechanic/Force and set the unit kN in the bottom left combo box.

5. In the tree, select the leaf Mechanic/Displacement and set the unit mm.

6. Click on Validate to close.

7. Set the grid

Use “Save as default” to set this system of units as your user environment.

2.2. 2D Meshing

Drawing of the geometry:

Limits of the model are linked to the size of the foundation. For a shallow foundation, it is recommended to set the frontiers at 6xB in width and 10xB in depth.

1. A new project starts in the stage Geometry.

2. Click on . The point definition dialog is displayed.

3. Enter ‘0, 0’ as X and Y, and press Apply.

4. Tick “Linked points” to generate the segments between the points.

5. Enter ‘0.5 , 0’, and press Apply button. Segment A is created.

6. Enter ‘6, 0’, and press Apply button. Segment B is created.

7. Enter ‘6, -10’, and press Apply button. Segment C is created.

8. Enter ‘0, -10’, and press Apply button. Segment D is created.

9. Enter ‘0, 0’, and press Apply button. Segment E is created.


Density definition:

Define dense divisions in the area of high strains, i.e. below the loaded foundation. Use a progressive density definition to generate a progressive evolution from small segments to large segments on the boundary edges.

1. Go to the stage on the project flow bar to start the definition of divisions along edges.

2. Select edge A. Click on Constant density to divide this segment in a fixed number. Enter the number of divisions, 5. Click on Validate.

3. Click on Variable density to divide the segment with a variation of lengths. Tick First division and Last division to define the method. Enter 0,1 m as First division and 1 m as Last division. Click on edge B. Click on Close.

The position of the click defines where the initial division is.

4. Select edge C. Click on Fixed length density. to divide this segment with a fixed length. Enter 1 m. in the dialog box. Click on Validate.

The software algorithm will adjust the length for the best fit with the input value of length.

5. Select edge D. Click on to impose a length for the divisions of this segment. Enter 1 m in the Fixed length density dialog box. Click on Validate.

6. Click on to divide the segment with a variation of lengths. Tick First division and Last division to define the method in the Variable density dialog box. Enter 0,1 m as First division and 1 m as Last division. Click on edge E. Click on Close.

Figure 1: Geometry

Figure 2: Example of mesh

Meshing:

1. Go to the stage Mesh.

2. Select the area corresponding to the soil mass.

3. Click on . Chose Quadratic as interpolation type. Chose Triangle as element shape. Click on Validate to generate the mesh.

A B

C E

D


CESAR-LCPC proposes 3 levels for the surface meshing procedure, giving the possibility to generate a coarse or dense mesh. The choice is made in Preferences>Program settings: linear interpolation = coarse, cubic interpolation = dense.

Groups definition:

This step is facultative but it eases the recognition of the group of elements if more than one has been generated.

1. Click on Groups edition.

2. Select the area corresponding to the soil mass. Enter Soil as a name. Click on Validate.

2.3. Calculation properties for safety factor analysis

Model definition:

1. Click on Model definition.

2. Enter Calculation 1 as name.

3. Click Open.

4. Chose Static as domain of application. Select MCNL as calculation module. Tick Axisymmetrical as model configuration. Click on Validate.

5. Select Initialisation of parameters as initialization type. Click on Validate.

See chapter “Initial stress field” in the document “Get Started with CESAR-LCPC v5”

Material properties:

1. Click on Properties.

2. Click on Properties assignment.

3. Chose Mohr-Coulomb without hardening as material model. Enter the properties of the soil mass.

(kg/m3)

E (MN/m²)

c (MN/m²)

(°)

(°)

Soil mass 2000 50 0,45 0,02 0 0

4. Select the group of elements for the soil mass. Click on Apply and Close.


Figure 3: Toolbox for properties assignment

Figure 4: Toolbox for initial geostatic stresses

input

Initial stress field:

The initial stress field is initialized as an existing geostatic stress field; vertical stress is linked to the horizontal stress by KO value.

1. Click on Initial conditions.

2. Select Geostatic stresses.

3. Click on Insert to define a new layer.

4. Enter the following values:

Height (m) Volumic weight (MN/m3)

KO_X

0 0,02 0,5

5. Validate.

Boundary conditions:

1. Click on Boundary condition sets.

2. Enter Standard supports as a name. Click Open.

3. Click on to define side and bottom supports. Supports are automatically affected to the limits of the mesh.


Load case:

1. Click on Loading sets.

2. Enter Pressure as a name. Click Open.

3. Select the segment A. Click Selection options. In this dialog box, click on Select none, then click on Segments on edges.

4. Click on Linearly distributed pressure.

- Tick Uniform pressure. - Enter the value of 0,120 MN/m². - Click on Validate.

Calculation parameters:

1. Click on Analysis settings.

2. In the General parameter tab, enter the following values:

- Iteration process: Max number of increments: 1 Max number of iterations per increment: 1000 Tolerance: 0,001

- Analysis type: Safety factor Tick “Non-convergence detection” Set “Minimum Value” to 0.1 Set “Maximum Value” to 10 Set precision to 0.1

- Solution method: 1- initial stresses - Algorithm type: Multi frontal

3. Close using Validate.

The option “Analysis with secondary storage” is required when the matrix size of the model will be larger than the random memory (RAM) of the computer.

Figure 5: toolbox for the setting of the calculation parameters


Solve:

Now that all data are input, the

1. Click on Calculations manager.

2. Select the model Calculation #1.

3. Select Create input files for the solver and calculate. Click on Validate.

The computation will take few minutes depending on the computer configuration.

If the model is not displayed in the list, it means that the model is not ready for calculation. Click on

Model definition. Select Calculation #1. Click on Info. The model status is displayed, all steps should be validated with a tick mark.

All the messages during the analysis will be shown in an Output Window. Especially, one needs to be very cautious about warning messages, because these messages indicate that the analysis results may not be correct. The result is saved as a binary file (*.RSV4) in the temporary folder (…/TMP/), defined during setup. The detailed analysis information is also saved in a text file (*.LIST).


2.4. Results

The result is the safety factor. It is displayed:

- In the Output Window - In the listing file.

The calculated safety factor is 0,9805.

Thus the limit pressure is 114 kPa, very close to the theoretical value of 113,8 kPa.

Display of the scalar plot of plastic strains

1. Click on Results visualization

2. Click on Display settings.

- Select Deformed as Mesh, - Tick on Contours, select Norm of plastic strain, - Select Scalar as Legend, - Click on Apply.

3. Click on Scalar settings.

- Tick on Contouring, - Click on Apply.

Figure 6: View of the field of plastic strains


3. OTHER TYPES OF CALCULATIONS FOR RESEARCH OF THE LIMIT PRESSURE

3.1. Calculation properties for load controlled analysis

This calculation is similar to the previous one, but the process of loading is not automatic but user-defined.

Model definition:

As the model is similar to the previous one, one makes a copy of Calculation 1, and modifies it where necessary.


2. Enter Calculation 2 as name in the Model definition dialog box.

3. In the Based on area, select Calculation 1.

4. Select Initial parameters as initialization type”. Click on Validate.


No changes.


No changes.


No changes.

Load Case

No changes.






3. Click on Validate.

It is not necessary to modify the factors applied to the Boundary conditions in the Boundary sets control tab as the displacement are set to zero. In the Loading sets control tab, the program automatically sets the factors to 1 (default value), divided by 12 (the number of increments). Therefore one gets 12 fractions of 120 kPa as loading program.


Solve:

1. Click on Analysis manager.

2. Select Calculation 2.


All the messages during the analysis will be shown in an Output Window. Especially, one needs to be very cautious about warning messages, because these messages indicate that the analysis results may not be completed, for example when the equilibrium cannot be achieved (non convergence). The result is saved as a binary file (*.RSV4) in the temporary folder (…/TMP/), defined during setup. The detailed analysis information is also saved in a text file (*.LIST).

3.2. Calculation properties for displacement controlled analysis

This calculation is similar to the previous one. Only Loads and boundary conditions are modified.

Model definition:

As the model is similar to the previous one, one makes a copy of Calculation 1, and modifies it where necessary.


2. Enter Calculation 3 as name in the Model definition dialog box.

3. In the Based on area, select Calculation 1.

4. Select Initial parameters as initialization type”. Click on Validate.


No changes.


No changes.


The imposed displacements are considered as a new set of boundary conditions. There are no changes for standard supports at the boundaries.

1. Click on Boundary condition sets.

2. Enter Imposed displacement as a name. Click Open.

3. Select the nodes of the segment A.

4. Click on General definition.

5. Tick v.

6. Enter the value of 40 mm.



Load Case

As we impose a displacement, the uniform pressure is useless. One will delete it.

Nevertheless, as CESAR needs at least one load case; one will create a fake one.


2. Enter No load as a name. Click Open.


4. Select the loading set Pressure. Click on Delete.

5. Click on Close.

The active set cannot be deleted.







There is no need to modify the factors applied to the Boundary conditions in the Loading sets control. In the Boundary conditions sets control tab, the program automatically sets the factors to 1 (default value), divided by 20. Therefore one gets 20 fractions of 40 mm as displacements steps.

Solve:

1. Click on Analysis manager.

2. Select Calculation 2.


All the messages during the analysis will be shown in an Output Window. Especially, one needs to be very cautious about warning messages, because these messages indicate that the analysis results may not be correct. The result is saved as a binary file (*.RSV4) in the temporary folder (…/TMP/), defined during setup. The detailed analysis information is also saved in a text file (*.LIST).


3.3. Alternative analyses

3.3.1 Linear elastic drained analysis

A linear elastic analysis can be carried out to assess the settlement under the footing in drained conditions. The increase of the modulus with depth is an important factor to take into consideration. Divide the model in several layers (2 m, 3 m and 5 m for instance) and assess the drained modulus at the centre of each layer using the Ohde-Janbu empirical formula:

N

refverrefEE

with the soil properties:

h (kN/m3)

E (MPa)

N

Soil mass 20 10 at ref = 100 kPa

0,7 0,33

3.3.2 Non-linear analysis with variable undrained cohesion

The increase of the undrained cohesion with depth is an important factor to take into consideration. Divide the upper part of the model in several thinner layers and assess the undrained cohesion at the centre of each layer using the following formulae:

0u

coscsin21c ini

horini

vertu

with the soil properties:

h (kN/m3)

Eu (MPa)

N cu (kPa)

u (°)

K0

Soil mass 20 50 at ref = 100 kPa

0,7 0,45 22 35 0,5

Note 1: The plasticity concentrating in the first meter of soil, the layers with varying cohesion must be thin enough to obtain the desired effect on the solution.

Note 2: Use the Ohde-Janbu formula to assess the undrained stiffness of each of the model layers.


4. RESULTS

Load control analysis

The convergence is not achieved for the 12th step. This indicates that the soil is ruptured. The limit pressure value is between 110 kPa and 120 kPa.

Displacement control analysis

The stress-displacement curve obtained by finite element analysis is compared with the benchmark solution. The results for various load application assumptions at the centre of the footing are presented in the figure below.

Figure 7: Stress-displacement curve at the centre point of the footing

Non-linear analysis with variable undrained cohesion:

Results are presented below for a model where the upper 2 meters of soil, are divided in 3 equal sub-layers (each 667 mm thick). Figure 8 shows the obtained stress displacement results. Note that a discontinuity of the curve is observed at the intersection with the analytical bearing capacity corresponding to the cohesion of the first sub-layer.

Figure 8: Stress-displacement curve at the centre point of the footing

0

20

40

60

80

100

120

140

0 5 10 15 20 25 30 35 40

displacements (mm)

Vert

ical

str

ess

(kPa

)

Load controlledDisplacement controlledBenchmark solution

loss of convergence

0

20

40

60

80

100

120

140

0 10 20 30 40 50 60 70 80 90 100

displacements (mm)

vert

ical

str

ess

(kPa

)

FEM solution displacement controlled

analytical solution for Cu = 19.0 kPa



Edited by :

12-16 rue de Vincennes

F-93100 MONTREUIL

Tél. : +33 1 48 70 47 41

Fax : +33 1 48 59 12 24

[email protected]

www.cesar-lcpc.com

© itech - 2011

Documents

CESAR-LCPC 2D v5 Tutorial 1 - itech soft 1 - CESAR-LCPC version 5 CESAR-LCPC proposes 3 levels for the surface meshing procedure, giving the possibility to generate a coarse or dense