Mesh size 1

[Jhno]

Hi,
I would like cue on a issue I have with my FE model. I do model (or try ot) the ultime bearing capacity of a footing resting on a purely frictionnal soils (I do take account the weight of the soil). I use quad element to mesh to soil. The stress-strain rel. is a Drucker-Prager. I did use result from 3-axials tests I did in the lab to calibrate the model.
I wish to compute the displacement - contact pressure of the footing during the loading of the foundation.
I do impose displacement at foundation's nodes (so if I have 3 node for a footing I do impose 3 vertical displacement, if I have 11 nodes I do impose 11 displacements).

The foundation dimension (B) is 0.5 m right now.
When I use large mesh (0.5x0.5m), I get very large displacement on the soil before I obtain numerical instability. As I reduce the dimension of the mesh, I get less displacement of the soil before numerical instability (I do reduce the increment of displacement when I decrease the mesh dimension).

The curves of displacement - pressure does looks good with small mesh (I get a plastic plateau like I would expect from a elastic-perfectly-plastic) whilst with the large mesh I do obtain a plastic region but it nevers gets to a plateau, it still looks like a unfnished curve. Also, the value with the large mesh are 3-4x larger than those with the smaller mesh (even considering the edge effect of the pressure distribution under the foundation).

Any1 got a clue here? Thanks!

 

[corus]

Your large mesh is too coarse to give any meaningful results. You appear to begin with a mesh size that has the same size as the objest you're studying. Any comparisons with a refined mesh will be a waste of time.

 

[IDS]

Your large mesh is too coarse to give any meaningful results. You appear to begin with a mesh size that has the same size as the objest you're studying. Any comparisons with a refined mesh will be a waste of time.

I don't totally agree with that. The object being studied is the soil foundation, not the concrete footing, so for some applications, with soil pressures below the footing bearing capacity, elements of the order of 0.5 m square would be fine.

However, if the analysis is modelling non-linear behaviour of the soil under applied deformations it is a different matter. In that case your model needs to be able to replicate the plastic strains of the soil around the footing, and also model the behaviour at the soil-concrete interface, which a single plate element is obviously incapable of doing.

I had a look at this using some simple models using Strand7 software (see graphical output below). I modelled a footing 0.5 m wide, with soil 2.5 m deep below and the edge of the model 7.5 m from the centre line. The different models were:

Footing 0: 0.5x0.5 4 node elements. Deformations applied to 2 nodes at the soil surface. Drucker-Prager properties, phi = 30 degrees, C = 0.1 kPa
Footing 1: As above but 8 node elements.
Footing 2: 0.125x0.125 4 Node elements.
Footing 3a: As 2, but 8 Node elements.
Footing 3b: As 3a, but deformations applied to a beam element connected to the soil surface with friction elements (friction factor = 0.5)
Footing 3c: As 3a, but elements at the footing location given concrete properties (depth = 0.25 m), connected to the soil beneath with friction elements.
Footing 3c2: As 3c, but analysis modelled non-linear materials only (i.e. non-linear geometry effects ignored).
Footing 3c3: As 3c, but Mohr-Coulomb soil properties.

Summarising the results:
Refining the mesh substantially reduces the peak bearing capacity, and the stiffness.
Replacing 4 node elements with 8 node elements has almost as much effect as reducing the element size by a factor of 4.
Modelling the footing-soil interface has a significant effect, increasing the bearing capacity and stiffness, especially where the interface is below the soil surface.
Even the minimum bearing capacity found (Footing 3a) is much higher than given by standard bearing capacity formulae! Further refinement of the mesh can be expected to produce further reductions in stiffness and maximum load.
The results with the finest mesh ignoring geometric non-linearity are even worse than those from the coarsest mesh!
Replacing the Drucker-Prager properties with Mohr-Coulomb substantially reduced the stiffness at the second load increment, and the analysis failed to complete the third increment.

So in summary:
Make sure your material model is appropriate.
Continue refining the mesh until there is no significant difference in results.
Include geometric non-linearity.
Review your results against experiment and other published work.

I found the links below interesting (both indicate that modelling non-linear footing behaviour is not a simple exercise):

http://www.iaeme.com/MasterAdmin/Up...UNDRAINED SHEAR BEHAVIOUR OF CLAYEY SOILS.pdf

http://www-civ.eng.cam.ac.uk/geotech_new/people/bolton/mdb_pub/208.pdf

Doug Jenkins
Interactive Design Services

http://newtonexcelbach.wordpress.com/

 

[Jhno]

Thanks for the answer. I do find similar trends in my numerical model, wasn't sure if this was normal or not. The articles you propose are very interesting reading. Experimental results will proove usefull for my validation. Thanks again!