Gate)
4. Results of analysis
Three analyses were conducted whose results are summarised in Table 3. Computed contours of final vertical displacement due to the load on the first footing, Figure 12, may be compared with typical observations of the physical models (Figure 6b). The predicted footing settlement lies in the middle of the experimental range (based on results in Table 1 for Tests DF2, SP1, SP2 and FX2). Figure 12 also shows the footing dragging down the surrounding soil surface, whereas in the physical model it tended to punch more cleanly into the soil.
Figure 18: Computed contours of vertical displacement caused by first loading
Vertical displacements arising from loading on the second footing in the absence of a vertical wall are illustrated in Figure 13a. It can be seen (by comparison with Figure 10a) that the observed displacement pattern has been fairly well captured, although the induced tilt of the second footing is in the opposite sense to that observed and zone of soil displaying settlement is more extensive. Corresponding results for the case of a floating wall and a vertically restrained wall are shown in Figs 13b and 13c respectively (for comparison with Figs 10b and 10c) and similar comments apply. In all cases, the computed footing settlements (Table 3) are substantially lower than the observed values (Table 1). For the first footing, ongoing creep beneath the footing contributed significantly to the observed settlement, as already mentioned, and this partly accounts for the difference. Possible reasons for the discrepancy in the case of the second footing are discussed below.
Figure 19: Computed contours of vertical displacement caused by second loading (a) without a wall (b)
with a floating wall and (c) with a vertically restrained wall
Table 5: Summary of numerical modelling results
Loading on Footing 1
Loading on Footing 2
FOOTING 1 FOOTING 2 FOOTING 1
Analysis
Settlement Settlement Tilt Settlement Tilt
(mm) (mm) (º) (mm) (º)
Plain double footing
18.3
7.0 - 0.69 2.4 - 0.34
Double footing with a floating wall 6.1 - 0.54 1.9 - 0.10
Double footing with a vertically
restrained wall 5.8 - 0.41 0.3 - 0.02
Tilt: (+) = clockwise rotation
(-) = counter clockwise rotation 5. Discussion
This work has demonstrated that a floating wall may be largely ineffective in reducing footing interaction, while a significant benefit may be obtained with a vertically restrained wall. This is clear in Tables 1 and 3 where the central settlement and tilt of the first footing due to loading of the second footing are given. The improvement
mechanism with the vertically restrained wall is revealed in Figure 14 showing the computed final distribution of shear stress on each side of the wall. On the left of the wall (second footing side) a net downward force is transferred into the wall rather than into the soil on the right (first footing side), so shielding the latter from an increase of vertical stress. Further research is needed to check whether vertically restrained walls would be as effective in a variety of prototype situations.
Figure 20: Distributions of shear stress on a vertically restrained wall
The comparisons made in the previous section provide some encouragement for similar analysis to be applied to predict prototype behaviour, assuming that a plane strain idealisation is appropriate. However, it is a concern that the direction of tilt of the second footing was always wrongly predicted and that its settlement was under-predicted. Figure 15 shows the predicted displacements due to loading of the first footing and, by comparison with Figure 6a, it can be seen that horizontal displacements beneath the second footing were over-predicted by the analysis. In the analysis, the first footing also moved horizontally in the direction of the second footing and most of the available soil strength was mobilised to resist a bearing capacity failure. In the physical models horizontal movement of the footing was prevented by the loading system and the some resistance would have been mobilised on the container walls to supplement the soil strength. Thus, horizontal movements did not propagate beneath the second footing to the same extent. In the analysis, it is believed that the horizontal movements increased the stiffness of the soil to subsequent vertical loading and that this effect diminished with distance from the model centreline. This would explain both the under-predicted settlement and incorrectly predicted tilt direction of the second footing.
Other factors may also have been involved. For example, in the analysis fully drained deformations were assumed, whereas in the physical models partially drained deformations must have occurred as each load increment was applied. It is also possible that the soil shear strength itself could have been under-predicted.
Figure 21: Computed displacement vectors after first loading
It is a limitation of the analysis that the effect of installing the walls was not included, although in the physical models this effect was not large. In the case of a diaphragm wall, the installation could perhaps be modelled following Ng et al. (1995).
An interesting feature of the experimental results, also captured by the analysis, is the asymmetry of deformation that developed, even in the absence of a wall between the footings. Observed and computed final settlement contours with the datum taken at the start of the first footing loading are compared in Figure 16. This asymmetry would not be predicted by routine methods of calculation.
(a)
(b)
Figure 22: Final settlement contours (a) measured and (b) computed
6. Conclusion
The problem of settlement interaction of relatively stiff shallow foundations on clay has been studied with a combination of physical and numerical modelling. It is concluded that the installation of a vertically restrained, and perhaps partially penetrating, wall in compressible ground between two closely spaced strip foundations can significantly reduce interaction. However, an unrestrained or floating wall with a depth of the same order as the foundation width is unlikely to be effective. Further analysis is needed to explore the potential of vertically restrained walls to reduce interaction in prototype situations.
The use of the BRICK constitutive model in the finite element analysis proved generally successful in predicting settlement interaction behaviour patterns, including the asymmetry that can develop when identical foundations are constructed at different times. An incorrect prediction of the sense of tilting of one of the foundations can probably be attributed to additional restraints that existed in the physical models.