gtl s08 ex 03 elasto plastic analysis of drained footing

Elasto-plastic analysis of drained footing

PLAXIS Standard Course 1

ELASTO-PLASTIC ANALYSIS OF DRAINED FOOTING

0 0.03 0.06 0.09 0.121

2

3

4

5

|U| [m]

Sum-MloadA

Computational Geotechnics


2 PLAXIS Standard Course



INTRODUCTION

In addition to the previous exercise, the elasto-plastic modelling of soil behaviour is now applied to the footing problem. This enables the calculation of a bearing capacity (failure load), and corresponding failure mechanism. Moreover, the exercise demonstrates the use of the load-displacement curves module.

AIMS:

• Calculating a bearing capacity (failure load). • Using the load-displacement curves module.

0

Failure load

Clay

6 7 8 14

4.25 4

0

Failure mechanism

Figure 1: Scheme of the exercise.



SCHEME OF OPERATIONS:

A) GEOMETRY INPUT

• Use previous input file • Save as new data file • Change material properties, (Mohr-Coulomb for clay) • Mesh generation

B) INITIAL CONDITION

• (Re) generation of pore pressures • (Re) generation of initial stresses

C) CALCULATIONS

• Define load displacement points • Re-define existing calculation phases • Construct footing • Apply vertical force

D) LOAD DISPLACEMENT CURVES

• Create load displacement curves.

New

New



GEOMETRY INPUT - USE PREVIOUS INPUT FILE

• Select the existing project of the first exercise (drained footing). • From the File menu select Save As and save the existing project under a new file name (exercise 2, for

example).

GEOMETRY INPUT - CHANGE MATERIAL PROPERTIES

• Change material properties by selecting the item Soils & Interfaces from the Materials menu or click on the

Material Sets button . Select the 'clay' from the Material Sets box and click on the Edit button. On the first tab sheet General change the Material model to "Mohr-Coulomb". Continue with the second tab sheet Parameters. On the selection of the Mohr-Coulomb model, input for additional (strength) parameters is requested. Enter the values according to the box as presented below. Enter a cohesion c = 5 kN/m² and an internal friction angle f = 20º. Close the database.

Figure 2: New material properties for clay.

GEOMETRY INPUT - MESH GENERATION

• Use the mesh from the previous example of the elastic drained footing, no need for a new mesh generation in this exercise. In order to compare results of different mesh coarsenesses you may generate a much coarser or a much finer mesh after running this exercise and compare results of the failure load in the curves program.

INITIAL CONDITIONS

• Proceed to the initial conditions.

As the mesh has been re-generated it is also necessary to re-generate Pore water pressures and Initial stresses.

• (Re) generation of pore pressures • Switch off cluster for strip footing • (Re) generation of initial stresses



CALCULATIONS - DEFINE LOAD DISPLACEMENT POINTS

A new option will be used. After the calculation it is possible to create load-displacement curves. These can be used to inspect the behaviour in a node during the calculation steps. In order to create load-displacement curves it is first necessary to indicate for which node(s) the displacements should be traced.

Note that in this exercise only the vertical load is applied, the horizontal load is not used in this analysis.

• Select the first phase. Check if the footing is reactivated. • Select the second phase and check if load A is active and set to -50 kN/m. This load is considered to be a

working load.

In order to calculate a failure load it is necessary to increase the existing load of -50 kN/m until failure. In this case we assume the failure load is lower than -500 kN/m.

• Select the third calculation phase and on the Parameters tab sheet select the option Total multipliers in the Loading input combo box. Click on the Define button.

• Enter for the third calculation phase a EMloadA of 10. In this way the working force is increased to a

maximum load of 10 x 50 = 500 kN/m

• Click on the Select points for curves button in the toolbar. This will result in a plot of the mesh, showing all generated nodes. Click on the node, located in the centre directly underneath the footing. For a

correct selection of this node it may be necessary to use the zoom option . After selection of the node it will be indicated as point A. Press the Update button to proceed to calculations.

• Click on the Calculate button to start the calculation.

During the calculation a small load-displacement curve is shown. At the end of the calculation a red cross appears in front of the second phase, indicating that failure has occurred.

Hint: In Plaxis total load multipliers may be used to increase a working load. The magnitude of the activated load is the input load multiplied by the total load multiplier. Hence in this exercise: EMloadA x input load of point load A = Active load A 10 x 50 kN/m = 500 kN/m

Hint: When using a Plastic calculation – Total multipliers, the calculation program will continue to apply the load until the indicated load is reached, or until failure is detected.



INSPECT OUTPUT

• Click on the output button to view the output results. • From the Displacements menu select Total increments. Display the incremental displacements as contours

or shadings. The plot clearly shows a failure mechanism (see Figure 3).

Figure 3: Shadings of displacement increments.



LOAD DISPLACEMENT CURVES

• Start the curves program by clicking on the Curves button. • Create a New curve and select the appropriate problem in the file requester. • The Curve Generator window as indicated below will appear.

Figure 4: Curve generation window.

• In the group box X-Axis Displacements of type |U| (absolute) should be selected for Point A. • On the Y-axis the Multiplier Sum-Mload A is selected. • After clicking the Ok button a curve is presented.

0 0.03 0.06 0.09 0.121

2

3

4

5

|U| [m]

Sum-MloadA

Figure 5: Load displacement curve.

The input value of point load A is 50 kN/m and the load multiplier ΣMloadA reaches approximately 4.5. Therefore the failure load is equal to 50 kN/m x 4.5 = 225 kN/m. You can inspect the load multiplier by moving the mouse cursor over the plotted line. A tooltip box will show up with the coordinates of the current location.



RESULTS DRAINED BEHAVIOUR

In addition to the mesh used in this exercise calculations were performed using a very coarse mesh with a local refinement at the bottom of the footing and a very fine mesh. Fine meshes will normally give more accurate results than coarse meshes. In stead of refining the whole mesh, it is generally better to refine the most important parts of the mesh, in order to reduce computing time. Here we see that the differences are small (when considering 15-noded elements), which means that we are close to the exact solution. The accuracy of the 15-noded element is superior to the 6-noded element, especially for the calculation of failure loads.

The results of fine/coarse and 6-noded/15-noded analyses are given below.

Table 1: Results for the maximum load reached on the drained sub-soil for different meshes. Mesh size Elements Nr. of elements Max. load

very coarse mesh with local refinements under footing

6-noded 79 281 kN/m

coarse mesh 6-noded 121 270 kN/m very fine mesh 6-noded 1090 229 kN/m very coarse mesh with local refinements under footing

15-noded 79 236 kN/m

coarse mesh 15-noded 121 248 kN/m very fine mesh

15-noded 1090 220 kN/m

The failure load calculated from FE for a fine mesh is

15-noded dB

loadMaximumB

Qconcrete

u *_ γ+= 116kN/m2

Analytical solution by Vesic 106 kN/m2 Analytical solution by German DIN

107 kN/m2

From the above results it is clear that fine FE meshes give more accurate results. On the other hand the performance of the 15-noded elements is superior over the performance of the lower order 6-noded elements. Needless to say that computation times are also influenced by the number and type of elements.

A solution is also given by Vesic 1:

1 Vesic, A.S., In: Foundation Engineering Handbook, Eds. Winterkorn & Fung. The factor N( is not exact and depends strongly on the assumed boundary conditions.

Hint: In plane strain calculations, but even more significant in axi-symmetric calculations, for failure loads, the use of 15-noded elements is recommended. 6-noded elements are known to overestimate the failure load, but are ok for deformations at serviceability states.



• 2c

f m/kN10693.3*2*8*21

83.14*5N*B'21

N*cBQ

≈+=+= γγ

• 93.320tan)14.6(2tan)1N(2N q =−=−= ϕγ

• 83.14Nc =

• 33w m/kN81018m/kN10' =−=−= γγ

L = '

Qf

B

I

II

III

Table 2: Bearing capacity factors n Nc Nq N

( Nq/Nc tan n

0.00 5.14 1.00 0.00 0.19 0.00 1.00 5.38 1.09 0.00 0.20 0.02 2.00 5.63 1.20 0.01 0.21 0.03 3.00 5.90 1.31 0.03 0.22 0.05 4.00 6.19 1.43 0.06 0.23 0.07 5.00 6.49 1.57 0.10 0.24 0.09

6.00 6.81 1.72 0.15 0.25 0.11 7.00 7.16 1.88 0.22 0.26 0.12 8.00 7.53 2.06 0.30 0.27 0.14 9.00 7.92 2.25 0.40 0.28 0.16 10.00 8.35 2.47 0.52 0.30 0.18

11.00 8.80 2.71 0.66 0.31 0.19 12.00 9.28 2.97 0.84 0.32 0.21 13.00 9.81 3.26 1.04 0.33 0.23 14.00 10.37 3.59 1.29 0.35 0.25 15.00 10.98 3.94 1.58 0.36 0.27

16.00 11.63 4.34 1.92 0.37 0.29 17.00 12.34 4.77 2.31 0.39 0.31 18.00 13.10 5.26 2.77 0.40 0.32 19.00 13.93 5.80 3.31 0.42 0.34 20.00 14.83 6.40 3.93 0.43 0.36

21.00 15.82 7.07 4.66 0.45 0.38 22.00 16.88 7.82 5.51 0.46 0.40 23.00 18.05 8.66 6.50 0.48 0.42 24.00 19.32 9.60 7.66 0.50 0.45 25.00 20.72 10.66 9.01 0.51 0.47

26.00 22.25 11.85 10.58 0.53 0.49



27.00 23.94 13.20 12.43 0.55 0.51 28.00 25.80 14.72 14.59 0.57 0.53 29.00 27.86 16.44 17.12 0.59 0.55 30.00 30.14 18.40 20.09 0.61 0.58

gtl s08 ex 03 elasto plastic analysis of drained footing

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