BEARING CAPACITY OF STRIP FOOTING

BEARING CAPACITY OF STRIP FOOTING

This document describes an example that has been used to verify the bearing capacity ofstrip footing in PLAXIS.

F

1 m ½ B

cref

c

ν = 0.495

G = 100 · c

φ = 0 ◦

No tension cut-off

Figure 1 Problem geometry

Used version:

• PLAXIS 2D - Version 2011

• PLAXIS 3D - Version 2012

Input: Calculations are carried out for a rough and a smooth footing. The geometry ofthe 2D models is shown in Figure 2. Because of symmetry, only half of the geometry ismodelled using 15-node elements. Note that for the smooth case, the x-direction of theprescribed displacement is set to free whereas in the rough case the x-direction of theprescribed displacement is set to fixed.

1 m

2 m

3 m

Figure 2 Model geometry (PLAXIS 2D)

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The geometry of the 3D model is shown in Figure 3. The strip footing is defined as asurface prescribed displacement. A soil cluster and a surface are defined underneathand at the right of the strip footing respectively to enable local control of the mesh. A lineprescribed displacement fixed in the x and y directions is defined between (0; 0; 2) and(0; 1; 2).

1 m

1 m0.5 m

2.5 m

0.4 m

1.6 m

Figure 3 Model geometry (PLAXIS 3D)

Materials: The material properties are shown in Figure 1. The Mohr-Coulomb model isused to model the behavior of the soil in order to be consistent with the conventionalfoundation design (Potts & Zdravkovic (2001)). The cohesion at the soil surface, cref , istaken 1 kN/m2. In the Advanced settings, the cohesion gradient, cinc , is set equal to 2kN/m2/m, using a reference level, yref = 0 m (= top of layer). The stiffness at the top isgiven by Eref = 299 kN/m2 and the increase of stiffness with depth is defined by Einc =598 kN/m2/m.

Meshing: In the 2D model the Medium option is selected for the Global coarseness.The point at the left and at the right of the prescribed displacement are refined with aLocal element size factor of 0.5 and 0.05 respectively. The resulting finite element meshis shown in Figure 4.

In the 3D model the Coarse option is selected for the Global coarseness. The soil clusterbelow the footing and the surface prescribed displacement representing the footing arerefined with a Local element size factor of 0.25. The surface at the right of the footing isrefined with a Local element size factor of 0.1. The resulting finite element mesh isshown in Figure 5.

Calculations: In the Initial phase zero initial stresses are generated by using the K0procedure with Σ -Mweight equal to zero. The prescribed displacement is activated in aseparate phase. A vertical displacement of -0.1 is applied. In the case of the smoothfooting the horizontal prescribed displacement is set to Free. In the case of the rigidfooting the horizontal prescribed displacement is fixed. The calculation type is Plasticanalysis and a Tolerated error of 0.001 is defined. The Reset displacements to zerooption is selected and the Additional steps parameter is set to 500.

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Figure 4 The finite element mesh(PLAXIS 2D)

Figure 5 The finite element mesh (PLAXIS 3D)

Output: In PLAXIS 2D model the calculated maximum average vertical stress under thesmooth footing is 7.831 kN/m2, giving a bearing capacity of 15.662 kN/m. For the roughfooting this is 9.174 kN/m2, giving a bearing capacity of 18.358 kN/m. The computedload-displacement curves are shown in Figure 7.

In PLAXIS 3D model the calculated maximum average vertical stress under the smoothfooting is 8.095 kN/m2, giving a bearing capacity of 16.19 kN/m. For the rough footingthis is 9.820 kN/m2, giving a bearing capacity of 19.640 kN/m. The load-displacementcurves are shown in Figure 8.

Verification: The analytical solution derived by Davis & Booker (1973) for the meanultimate vertical stress beneath the footing, pmax , is:

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Figure 6 Deformed mesh (PLAXIS 2D - Smooth case)

0.00 0.02 0.04 0.06 0.08 0.10uz [m]

0

2

4

6

8

10

Fz

[ kN

/m]

Smooth case

Rough case

Figure 7 Comparison of results for smooth and rough footing (PLAXIS 2D)

pmax =FB

= β

[(2 + π)cref +

B × cinc

4

]where B is the footing width and β is a factor that depends on the footing roughness andthe rate of increase of clay strength with depth. The appropriate values of β in this caseare 1.27 for the smooth footing and 1.48 for the rough footing. The analytical solutiontherefore gives average vertical stresses at collapse of 7.8 kN/m2 for the smooth footingand 9.1 kN/m2 for the rough footing. The errors in the PLAXIS 2D solution are 0.40% and0.81% respectively. The errors in the PLAXIS 3D solution are 3.64% and 7.91%respectively.

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0.00 0.02 0.04 0.06 0.08 0.10

uz [m]

0

2

4

6

8

10

Fz

[ kN

/m]

Smooth case

Rough case

Figure 8 Comparison of results for smooth and rough footing (PLAXIS 3D)

REFERENCES

[1] Davis, E.H., Booker, J.R. (1973). The effect of increasing strength with depth on thebearing capacity of clays. Geotechnique, 23(4), 551–563.

[2] Potts, D.M., Zdravkovic, L. (2001). Finite element analysis in geotechnicalengineering application. Thomas Telford, London.

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