Physical Modelling of the Upheaval Resistance of Buried Offshore ...

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Uplift factor, fd Uplift factor, fd Uplift factor, fd 2 1.8 1.6 1.4 1.2 1 0.8 0.6 0.4 0.2 C5 (dense sand) L5 (D = 32 mm) L6 (D = 48 mm) C3 (D = 250 mm) C5 (D = 250 mm) L8 (D = 48 mm) L13 (D = 48 mm) L12 (D = 48 mm) L13 (dense gravel) L8 (dense sand) 0 1 1.5 2 2.5 3 Embedment Cover ratio, ratio, H/D H/D 3.5 4 Figure 6. Uplift factors for 1g tests in dense sand and gravel. 3.2.2 Dense sand and gravel Load-displacement plots are shown for the laboratory tests in dense and loose sand and dense gravel in Figure 5. Tests were conducted with a pipe of diameter, D = 48 mm and an initial embedment ratio, H/D ≈ 3. There is a clear difference compared to the loose sand tests, with a peak uplift resistance, which drops quickly by half to a residual pull-out force. This residual force then reduces as the pipe moves towards the surface. The pattern is reflected in the uplift factors (Figure 6). A peak uplift factor (fd ≥ 1) on initial movement then reduces to values similar to the loose sample after a small pipe displacement. For the sand, the distance required to reach the residual value of fd is 5 mm, for gravel, it is 15 mm (see Figure 5). Further experiments are needed to examine this behaviour for a wider range of H/D and soil types. 3.2.3 Sand and gravel berms Uplift factors are shown against reducing embedment ratio for the tests with and without gravel or sand berms on loose, saturated sand in Figure 7. There is a clear increase in uplift resistance with either a gravel or sand berm, but this is more marked with the gravel berm. Indeed, the increase in uplift resistance due to the gravel berm compared to pure loose sand increases with the displacement of the pipe. This may be due to the rising soil surface due to the dilation of the angular gravel berm during pipe displacement, which ensures that the pipe burial is greater than calculated assuming H = Hi - δ. Uplift factor, fd 2 1.8 1.6 1.4 1.2 1 0.8 0.6 0.4 0.2 Vertical slip model C4 (sand) C7 (sand) C8 (gravel berm) C9 (sand berm) 0 1 1.5 2 2.5 3 3.5 4 4.5 3.3 Mobilisation of peak uplift load: initial loaddisplacement response 3.3.1 Loose sand The initial load-displacement data for the tests on dry loose sand are shown in Figure 8. Uplift load (Wu) is normalised by the peak uplift load (Wumax) for each model test to allow comparison of mobilisation distances. For the laboratory tests (when D = 32 mm or 48 mm), 90 % of peak uplift load was mobilised when pipe displacement, δ ≈ 0.5 mm and the peak capacity was reached by about 1 mm. However, the prototype displacement for 90% mobilisation in the centrifuge model tests was 3 or 4 mm. If the displacement is further normalised by embedment depth, H, the graph shown in Figure 9 is produced. There is good agreement between results for different pipe sizes in loose sand and it appears that 90% of the maximum uplift load is mobilised when δ/H ≈ 0.4 %. This agrees well with δ/H = 0.5 % recommended by Matyas and Davies (1983) in their laboratory tests and δ/H = 1 % recommended by Trautman et al. (1985). 3.3.2 Dense sand and gravel Normalised initial load-displacement behaviour from the laboratory tests in dense sand and gravel is also shown on Figure 9. Peak uplift load is mobilised within significantly smaller displacements than for loose sand. Further centrifuge tests are required to ascertain how this scales with pipe size or embedment depth. Embedment Cover ratio, ratio, H/D H/D Figure 7. Uplift factors for loose, sat. sand with/without berms. Figure 9. Normalised load-displacement data. Load, Wu/Wumax. Load, Wu/Wumax. 0.6 L5 (D = 32mm) 0.4 Centrifuge tests L6 (D = 48 mm) 0.2 0 C1 (D=48 mm) C2 (D=240 mm) -0.2 0 1 2 3 4 5 1 0.8 0.6 0.4 0.2 -0.4 0 1.2 1 0.8 1g tests Displacement, mm Figure 8. Load-displacement behaviour of pipes in loose sand L8 (dense sand) L13 (dense gravel) L6 (loose sand) C1 (loose sand) C3 (loose sand) C4 (loose sand) C7 (loose sand) C8 (gravel berm) C9 (sand berm) 0 0.002 0.004 0.006 0.008 0.01 0.012 0.014 Displacement/Embedment depth.
3.3.3 Rockfill berms Normalised load-displacement graphs for the loose sand with and without berms is also shown in Figure 9. There is some suggestion of a slightly softer normalised response for the gravel and sand berms compared to tests without berms. This is likely to be because the stiffness of the soil around the pipe for the same cover (whether consisting of only sand, or sand plus rockfill) will not be affected by the berm material, but the uplift capacity will be increased. 3.4 Soil displacement mechanisms 3.4.1 Loose sand Figure 10 shows a digital photograph of the front face of the soil model after a pipe displacement of δ/D ≈ 1.3 through loose sand in the laboratory. The initial embedment ratio, H/D = 3 and the embedment ratio when the photograph was taken was H/D ≈ 1.7. There appears to be negligible surface soil movement and only the two markers above the pipe appear to have moved (about 1/10 th of the pipe displacement) from their initial grid position. In all tests, a gap formed between the soil and pipe with sides of angle ≈ 30 o and this remained at a constant size after initial formation. To sustain the constant gap size with the upward moving pipe there was flow of soil around the pipe as sketched in Figure 10. During centrifuge test 2 (C2) there appeared to be some upwards movement of the soil surface as well as gapping beneath the pipe, but again there is negligible movement of soil markers to the sides of the pipe. 3.4.2 Dense sand sample Observed dense sand movements showed gapping behind the pipe of a similar size to the loose samples but there was a larger region of soil deforming above the pipe together with more surface movement (Fig.11). The top layer of marker pellets in Figure 11 (which were initially in a horizontal line) show that the soil moves upwards in a region about 2D wide near the surface. In addition, soil flowed around the pipe to maintain the gap at a constant size. Figure 10. Laboratory test in loose sand. Soil Gap Initial pipe position Gap Figure 11. Laboratory test in dense sand. 3.4.3 Berms Soil displacements as the pipe approaches the soil surface (Figure 12) reveal that there is more distortion of the top soil surface and the gravel/sand interface with a gravel berm than for the equivalent sand only tests (Figure 10). This suggests that the berm may be dilating during initial pipe displacement and this may contribute towards the higher uplift resistance. Details of this mechanism need to be confirmed by further study. 4 DISCUSSION Marker displacements Gap Initial pipe position Uplift load and mobilisation distance to peak are dependent on the soil properties, the pipe geometry and the soil deformation mechanism. The digital photography of the markers in the soil during pipe uplift tests has allowed determination of soil deformation mechanisms after failure. However, because full load is mobilised within a model displacement of less than 1 mm, the mechanism of initial load pick-up is harder to measure visually due to the small soil displacements. Post-peak deformation mechanisms suggest that soil flow around the pipe is a large component of the soil deformation because of a constant volume gap behind the pipe. This is very different from the mechanism proposed by Majer (1955). For dense sand, the increasing soil volume due to dilation causes soil displacements somewhat similar to the vertical slip plane model (Majer, 1955) which extend towards the soil surface. The peak uplift load, however, is mobilised while the gap is being formed (when there are only small displacements). This appears to be a process which requires a mobilisation distance which scales with embedment depth (H) (see Figure 9) as confirmed by Bransby et al. (2001). This suggests that for the soil conditions and embedment ratios tested, the peak uplift force is not generated by the formation of a discrete slip plane because the mobilisation distance of a slip plane would depend on soil particle size
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