4.1. Verification of numerical and experimental results
Finite element Pre- and post-processing software GiD + OpenSees V2.6.0 was used as an interface for OpenSees analyses. Effect of the soil-column grid in liquefiable sand was numerically simulated and analyzed in terms of footing settlement time-history and excess pore water pressures ratio for unimproved soil and improved soil with 16m*13m DSM grid (one structure exist in a grid) and 32m*13m DSM grid (two structures exist in a grid), on line 1 according to the Fig. 5
Fig. 6 present comparisons between experimental and numerical results. The numerical results are from the GID+OpenSees analyses using the as-built soil properties and the input motion of Tohoku earthquake with peak ground acceleration of 157g were recorded at the base of the container during the experiment. Fig. 6 compares the recorded and computed time history of the footing settlement during 200s. The computed settlement for unimproved soil is approximately 68 mm as against 83.5 mm observed in the experiment, for improved soil with 16m*13m DSM grid is 21 mm as against 17 mm in the experiment, and for 32m*13m DSM grid is 45 mm against 37 mm in the experiment. The improved soil settlement was 69% smaller than the settlement for unimproved soil. Soil improvement with DSM grid has reduced the rate of settlement as well as the maximum amount of settlement. The analytical results corresponded well with the experimental results. From the results, we realized that soil improvement in form of DSM grid was carried out to mitigate damages of liquefaction, the footing settlement was controlled, and the effect of the soil improvement was apparent.
Figure 7 through 9 compares experimental and analytical results for the time history of excess pore water pressure ratio (ru) in unimproved and improved soil with 13m*16m and 32m*13m DSM grid. The measurement points of ru are situated on ground level 2, 7, and 12m from the ground surface on line 1 according to Fig. 5.
For excess pore water pressure ratio (ru, where ru=∆u/σ'; ∆u = excess pore pressure and σ'= initial effective confining pressure) value of 0.9 or greater, liquefaction is expected. From the results, the amount of ru at GL 12m from the ground surface in experimental and analytical results for unimproved soil was 1 and 0.96, for soil improvement with 32m*13m grid was 0.95 and 0.88, and for 16m*13m grid was 0.95 and 0.83 so liquefaction occurs in all cases. Comparison of unimproved soil case and the improved cases showed that ru decreased after soil improvement with DSM grid. Experimental results also showed the rise of excess pore water pressure in the liquefiable soil without soil improvement was slightly greater than the liquefiable soil with DSM grid, and excess pore water pressure rose until liquefaction occurred in deep areas, while in shallow areas the results showed a smaller rise of excess pore water pressure (Tsukuni et al 2013). Analytical results showed the same. According to the results, the analytical excess pore pressure ratio was roughly equivalent in the centrifuge measurements at all locations.
Fig. 10 presents contour maps of maximum excess pore water pressure ratio in the experimental and analytical results. With the comparison of experimental and analytical results, we realized that using 32m*13m and 16m*13m grid squares showed a similar pattern rise of excess pore water pressure generation in shallow areas. By decreasing the grid area, it tends to a small rise, and this tendency was more pronounced in the case of a smaller 16m*13m grid.The cause of difference between experimental and analytical results can be explained as a limitation in dividing nodes in GID+OpenSees and maximum shear strain near the wall which leads to a pattern of a greater rise in excess pore water pressure.
Fig. 11 and 12 compare experimental and analytical results for horizontal response acceleration at ground level 2m with the input motion for unimproved soil and improved soil with a 16m*13m DSM grid. Hence, the acceleration response of the soil surface becomes one of the identifying factors in evaluating the performance of the soil improvement techniques. The analytical acceleration generally compares well with the experimental ones. In the case of unimproved soil, the results appear to capture the reductions in ground shaking at shallow depths in Urayasu sand due to liquefaction because of pore water generation in the underlying layers.
Parametric analyses in this study were performed to investigate the effect of parameters of soil-cement columns characteristics included dynamic analysis results for excess pore water pressure ratio (ru) and the settlement over liquefiable soil improved by DSM grid walls.
Effect of DSM grid wall space
Three different DSM grid wall spaces with the same condition of the centrifuge test for improved soil with DSM grid were analyzed to investigate the relation between grid wall space and the settlement. We modeled 32m*13m, 16m*13m, and 10m*13m grids. The spacing between the center of the DSM walls was 32m, 16, and 10m. According to Fig. 13, the results present the maximum settlement and excess pore water pressure ratio tend to decrease with smaller grid wall space because of more stiffness and shear stress on enclosed soil, through decreasing the distance between DSM walls, the extent of ru also decreased. In the case of 32m*13m, and 16m*13m grids liquefaction occurred but in the smallest grid size (10m*13m) no liquefaction occurred by decreasing the shear strains of the soil so it prevented liquefaction. The cases of 32m*13m and 16m*13m grid have the same rate of excess pore water pressure generation at depths of 2, 7, and 12m from the ground surface.
Effect of the diameter of DSM wall
Fig. 14 presents the effect of different diameters of 16m*13m DSM walls on the settlement and excess pore water pressure ratio over liquefiable soil. The dynamic analysis was conducted for improved soil using the DSM walls with diameters of 0.9, 0.8, and 0.7m. Accordingly, changes of ru were evaluated at depths of 2, 7, and 12 m on line 1 in Fig. 5. The results indicate that at the depth of 12 m from the ground surface, the improved soil experienced partial liquefaction, and with an increase of the DSM wall diameter, the risk of liquefaction decreases. However, this decrease is not significant. In the case of using DSM walls with the smallest diameter, the radius of influence decreased. This means that by decreasing the diameter of soil-cement columns, a lower area around the liquefiable soil will not safe from the risk of liquefaction and the settlement tends to increase, but it can't prevent liquefaction so the changes in the diameter of grid walls had little effect on mitigation liquefaction. Generally, the effectiveness of grid walls is not improved by increasing the diameter of grid walls.
Effect of the relative density of the liquefiable soil layer
Fig. 15 presents the effect of different relative densities of the liquefiable layer. The model in the experimental test consists of two liquefiable soil layers with NSPT= 5 and 10, Dr =50 and 70% which aren't acceptable so we considered these relative densities with the properties of Nevada sand, we analyzed again and compared the results. The two other models had similar loading histories, but different relative densities for the liquefiable layers. In the numerical models, relative density was considered 40 and 60% for the liquefiable layers according to the parameters of Nevada sand. Comparing these results, increasing relative density of the liquefiable layers to 40 and 60% showed down the rate of excess pore water pressure generation at all depths and positive effects on the settlement of liquefiable soil layer. This effect was greater for the higher relative density as expected, the influence of soil relative density on its resistance to pore pressure generation depends on the state of stress and ground motion intensity.
Effect of stiffness ratio (Gr)
The analytical analysis was performed with different ratios of stiffness for the effectiveness of soil-cement columns on liquefaction remediation. For this purpose, numerical models were carried out with stiffness ratios Gr= 20.8, 25, and 38.75. Gr shear-modulus ratio (Gsoil-cement /Gsoil); Gsoil-cement is shear modulus of the soil-cement column; and Gsoil is shear modulus of soil. The analysis results were evaluated based on the effect of soil-cement columns under varying stiffness ratios on the distribution of the settlement and excess pore water pressure ratio in the liquefiable soil layers and shown at various depths of 2, 7, and 12 m within liquefiable soil layers extending from a depth of 1 m to 12 m in Fig. 16. It was seen that soil-cement columns attracted a great portion of the shear stresses compared to the surrounding soil as they are stiffer than the liquefiable soil layer. The settlement and damages due to liquefaction decreased with increasing the stiffness of soil-cement columns and affected the occurrence of liquefaction.