(c)
Figure 6: Comparison of FEM simulations of (a) settlement curve (b) lateral displacement (c) excess pore water pressure for the ideal FEM model vs. case(4a) + case(4b) (surcharge and PVD + vacuum and PVDs) scenario
DiscussionAs it can be seen from all the simulations, the superposition law is not valid in proposed cases. The algebraic summation of cases based on different situations vs. FEM models is either decreasing or increasing. The interaction between PVDs, surcharge and the vacuum or the coupling effect can be easily seen on plotted curves. The predicted surface settlement curves from FEM (verified and ideal) models are compared with various scenarios. Figure 3(a) shows that in the absence of PVDs in only the surcharge model (case 1(a)) the results of the SUM case for settlement are underestimated after the 60th day. In contrast, by the inclusion of PVDs, the results as shown in figure 4(a) are overestimated after the 60th day. This is the time when the coupling effect starts. From the figure 4(a) the decreasing effect of coupling can be seen when the applied vacuum pressure is not constant and the ultimate settlement is lesser than the summation of the described cases. For the ideal constant 60 kpa vacuum case as shown in figure 5a the resultant SUM case curve is underestimated similar to figure 3(a). In the case with the inclusion of PVDs (6a) the results were overestimated only 7 percent after the 75th day. Figure 6(a) and 4(a) show that for discretizing complex models like combined surcharge and vacuum the inclusion of PVDs with surcharge gives better predictions for both cases with constant and variable applied vacuum pressure but for variable vacuum the results would be underestimated by 40 percent in the final settlement curve. By applying constant vacuum pressure the coupling effect has been minimized in settlement curves. Models with the inclusion of PVDs might be considered in the case of constant vacuum pressure for preliminary prediction or empirical equations for surface settlement (case 4(a) + case 4(b)). For variable vacuum pressure none of the models could predict the settlement. The predicted lateral displacement curves from FEM (verified and ideal) models are compared with various scenarios. Figure 3(b) and 4(b) show that for the field variable applied vacuum the resultant curve for lateral displacement in the SUM case is overestimated while as shown in figure 5b and 6b the resultant curve for lateral displacement in the SUM case is underestimated for the ideal case. For the variable applied vacuum in the field the predicted lateral displacement from the SUM case is twice as compared to the FEM model at ground surface. It can be seen that for this case the coupling effect reduced the lateral displacement at the ground surface from 8cm to 4cm and reduced the lateral displacement by about 30 percent in the very soft clay layer under the surface. For cases with variable vacuum pressure considering the lateral displacement from the case surcharge without PVDs (case 1(a)) might be considered for empirical equation except for ground surface where 50 percent of the SUM cases (case 1(a) + case 1(b) or case 2(a) + case 2(b)) in both cases of surcharge with and without PVDs might be considered for preliminary prediction or empirical equations related to lateral displacement. In contrast, for the ideal constant 60 kpa case, the SUM case is underestimated below the surface but agrees well on the ground surface. For constant vacuum pressure, the coupling effect would increase the lateral displacements for weak clay layers under the surface but don’t affect the ground surface that might be attributed to over-consolidation of the surface layer. Both models of the SUM cases with the inclusion of PVDs and in absence of PVDs might (case 3(a) + case 3(b) or case 4(a) + case 4(b)) might be considered in the case of constant vacuum pressure for preliminary prediction or empirical equations related to lateral displacement. One of the main obstacles in any FEM modeling simulations or comprising empirical or analytical solutions for combined vacuum and surcharge preloading is excess pore pressure. In the previous sections some aspects of this matter have been explained. Figure 3(c) shows that for the field variable applied vacuum the resultant curve for excess pore pressure in the SUM case is overestimated while as shown in figure 4(c) the resultant curve for excess pore pressure till the day 95 is underestimated while for the rest till 160th day it is overestimated. Since the applied vacuum pressure was reduced to -20 kpa on the 120th day none of the cases could predict the values of excess pore pressure. Figure 3(c) and 4(c) show the complicated mechanism of coupling in the dissipation of excess pore pressure. For the ideal case as shown in figure 5(c) and 6(c), the SUM curve in some areas overestimates and in some areas underestimates the FEM excess pore pressure because of the coupling effect. The cases assuming PVDs inclusion along with surcharge (case 2(a) and case 4(a)) agree best with both the ideal and verified FEM curves and they can be used properly for an acceptable estimation of excess pore pressure in systems with constant and variable vacuum pressure. This agreement by the FEM model is exactly the mechanism that was described in the first part of this literature. Although the vacuum effect is the same as surcharge loading in accelerating the process of consolidation, its acting mechanism is completely different and negative excess pore pressure attributed to vacuum preloading is only a term for describing the magnitude of applied suction through PVDs. Figure 3(a) shows a draw-back in the settlement curve on the 75th day in the case 1(b). This is the time when because of technical problems the applied vacuum pressure has dropped in real-world projects and an unloading condition occurred. In the absence of the surcharge preloading the acquired settlement reduced from 60 cm to 40 cm. As (Chai, Carter et al. 2006) reported this might be attributed to k0(no strain condition) where the vacuum pressure is no more larger thank0 condition to maintain the vertical deformation. If even the potential inward forces of the vacuum preloading are neglected, as it can be seen without any surcharge preloading the occurrence of undesirable heave is expected after removal or reduction in the vacuum preloading. This case clearly illuminates the necessity of applying the combined system of the surcharge and vacuum preloading to maintain the efficiency of the whole treatment process. At least 30 percent of preliminary designed preload is recommended for the surcharge preloading. The false idea might exist that the vacuum preloading necessarily induces surficial inward displacement. In fact as stated by (Chai, Ong et al. 2013) outward, inward or inward near the ground and outward at greater depth might occur.it can be seen that for all the cases in the verified and ideal cases, outward displacement is dominant except for the case that with PVDs and constant vacuum without surcharge preloading (case 3(b)) that inward displacement near the ground and outward displacement at greater depth dominates. As (Liu, Liang et al. 2019) reported The ground settlement of the clayey soils during vacuum removal is mainly attributed to fact that the Young’s modulus in the vertical direction is higher than that in the horizontal direction because of the soil anisotropy, and Lateral displacement is dominant for the ground deformation during vacuum removal. As it can be seen in fig 3(b), because of the variable applied vacuum pressure the lateral displacement on ground surface is outward similar to the surcharge preloading. If the magnitude and duration of the vacuum pressure don’t be high enough to counter-effect the soil anisotropy and k0 state, inward lateral displacement effect on ground surface should not be expected. This case clearly shows the necessity of constant application of a minimum quantity vacuum pressure that should be maintained the whole time, even if a stepped vacuum pressure is determined in the design procedure.ConclusionThe following conclusions are based on data, analyses, and interpretation presented in this paper:
  1. Superposition law is not valid in the combined vacuum and surcharge preloading and other phenomena exists which are the interaction between PVDs and vacuum and surcharge or the coupling. The mentioned hydro-mechanical coupling effect can be decreasing or increasing, based on the characteristics of any project.
  2. uvs is the coefficient of consolidation for a combined surcharge and vacuum preloading that considers the effect of coupling in analytical solution and should be accounted for in analytical equations and also in tests which are under combined surcharge and vacuum preloading.
  3. By applying constant vacuum pressure during the predicted time the coupling effect has been minimized in settlement curves.
  4. For discretizing of complex models like combined surcharge and vacuum for settlement prediction, the SUM models that include PVDs with surcharge gives better predictions for both cases with constant and variable applied vacuum pressure although for variable vacuum the results would be underestimated by 40 percent in the final settlement curve.
  5. For cases that include variable vacuum pressure, the lateral displacement prediction can be drawn from the case surcharge without PVDs for empirical equations except for ground surface where 50 percent of SUM in both cases of surcharge with and without PVDs might be considered.
  6. The lateral displacement prediction can be drawn from both models with and without PVDs in the case of constant vacuum pressure for empirical equations.
  7. The cases assuming PVDs inclusion along with surcharge agree best with both the ideal and verified FEM curves and they can be used properly for estimation of excess pore pressure in systems with constant and variable vacuum pressure.
  8. Although the effect of vacuum preloading is somehow the same as surcharge preloading in acceleration of the consolidation process, they shouldn’t be mistaken with each other as they have two different mechanisms.
  9. There is a difference in the magnitude and the rate of settlement, lateral displacement, and pore pressure resulting from a vacuum load or an equivalent fill load in combined systems, and as a result of coupling, and different acting mechanisms their effect cannot be used interchangeably.
  10. To keep the efficiency of combined vacuum and surcharge preloading the minimum 30 percentage of designed preload is recommended for the surcharge preloading.
  11. If the magnitude and duration of the vacuum pressure don’t be high enough to counter-effect the soil anisotropy andk0 state, the desired inward lateral displacement on ground surface from vacuum preloading should not be expected. Constant application of a minimum vacuum pressure should be maintained the whole time even if a stepped vacuum pressure is determined in the design procedure.
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