Gate)
3. Test Results
The model test programme and key results are summarised in Table 1. Three pairs of tests were carried out: tests without a wall between the footings (double footing tests, Tests DF1 and DF2), tests with a floating wall between the footings (sheet pile wall tests, Tests SP1 and SP2) and tests with a vertically restrained wall between the footings (fixed wall tests, Tests FX1 and FX2). The settlements given in the table were both recorded by the LVDTs at the footing centres and determined by using PIV to analyse the movements of the markers on the ends of the footings. The latter movements were also used to determine the footing tilts. The settlements obtained from PIV were up to 3 mm smaller than those recorded at the footing centres due to bending, and perhaps tilting, of the footings in the plane at right angles to the transparent panel, indicating that plane strain conditions were not perfectly achieved. However, bending of the footings in the plane of the panel appeared negligible. As the LVDT data were continuously recorded, for either footing it was possible to plot the settlement under each load increment applied to the footing against the logarithm of time and identify the point at which the relationship became linear. As when interpreting data from one-dimensional consolidation tests, it was assumed that, thereafter, settlement was due to creep and that primary consolidation was complete, Figure 4.
Table 3: Summary of physical model test results Loading on
Footing 1
Loading on Footing 2
FOOTING 1 FOOTING 2 FOOTING 1
Test
Settlement (mm)
Settlement
(mm) Tilt (º)
Settlement
(mm) Tilt (º) LVDT Marker LVDT Marker LVDT Marker Plain double footing
DF1 29.3 - 12.5 - - 4.1 - - DF2 17.4 16.2 11.7 8.6 0.45 4.4 3.8 -0.57 Double footing with a floating wall
SP1 23.2 21.6 13.5 10.6 0.40 2.8 2.4 -0.28 SP2 19.7 18.4 13.6 11.6 0.48 4.1 3.5 -0.31 Double footing with a vertically restrained wall
FX1 12.1 10.4 9.6 6.9 0.50 1.2 0.8 -0.03 FX2 16.8 15.2 12.1 9.2 0.61 1.7 1.5 -0.06
Marker results unavailable for Test DF1 Tilt: (+) = clockwise rotation
(-) = counter clockwise rotation
Figure 10: Settlements during first loading plotted against time
Figure 5 shows the settlements of the first footing to be loaded plotted against time, using LVDT data. Although the timing of the load increments varied, it can be seen that the final settlements in Tests DF2, SP1, SP2 and FX2 fall in a reasonably narrow range, approximately 17-23 mm. However, there are two outlying results. In Test DF1 a significantly greater settlement (29.3 mm) was caused by an unloading and reloading cycle part way through the loading sequence; the additional settlement observed during this cycle, which occurred at a time of around 6000 minutes, was about 7 mm. In Test FX1 a significantly smaller settlement (12.1 mm) was attributed to friction between the footing and container walls. In this test only, the normal clearance between the footings and the container walls was reduced in an attempt to stop clay being squeezed around the end of the footing and into the gap.
Figure 11: Examples of consolidation time estimation
The final images for PIV analysis were selected at the times shown in Figure 5. The earliest available image after the completion of consolidation under the final load increment was selected, but nevertheless some creep under the final load had occurred.
Typical displacement vectors and derived contours of vertical displacement beneath the first footing are shown in Figure 6 using the PIV data from the clay surface. For clarity, only vectors from alternate patches in each row are shown. Footing settlements inferred from the contours of settlement in the clay were invariably lower, by 1-2 mm, than those determined using the markers on the footings themselves. It is believed that the movements of the clay close to the footing and next to the transparent panel were not representative of those occurring in the interior of the model due to the clay being squeezed into the gap between the end of the footing and the panel, as mentioned above.
Consequently, the contours close to the underside of the footing should be regarded as unreliable.
(a)
(b)
Figure 12: Typical displacements caused by first loading (a) vectors and (b) contours of vertical
displacement
The effect of installing a wall between the footings is illustrated in Figure 7. As the wall was inserted, a wedge of soil was pushed up beneath the second footing and slight
additional settlement occurred beneath the first footing. After wall installation, virtually no movement of the second footing took place but settlement continued under the first footing due first to consolidation and then to creep. Figure 8 shows an example of vertical displacements variation at the footing centres with time during and after wall installation.
Figure 13: Typical displacements caused by wall installation
Figure 14: Example of footing settlements following wall installation
The settlement-time plots due to loading on the second footing are given in Figure 9.
The datum for these plots was taken as the start of the loading on the second footing.
The final settlements of the second footing (Figure 9b) show good repeatability except for tests FX1 and FX2 where it is only fair. It is thought that the smaller settlement in Test FX1 was again caused by friction between the footing and the container walls.
Only small settlements were recorded beneath the first footing (Figure 9a) and there is some variance in the results. In the case of Tests SP1 and SP2, it is possible that this was linked to variations in the effect of wall installation, which caused more settlement
beneath the first footing in Test SP1 than in Test SP2 (Effendi, 2007). Friction at the container walls probably accounts for the reduced settlement in Test FX1 compared with Test FX2.
Figure 15: Settlements during second loading plotted against time for (a) first footing and (b) second
footing
An obvious feature of these results is the reduction of settlement under the second footing compared to that observed previously under the first footing (Figure 5). Figure 9a suggests that the floating wall had little effect in mitigating the interaction but that the vertically restrained wall had a significant beneficial effect. This is again evident in the contours of vertical displacement in Figure 10. It should be emphasised that some of the displacement under first footing was the result of creep due to the original loading stage and, where applicable, wall installation.
(a)
(b)
(c)
Figure 16: Vertical displacements caused by second loading (a) without a wall (b) with a floating wall and (c) with a vertically restrained wall
4. Finite Element Analysis