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61 CHAPTER 6 Parametric Studies The parametric studies provide numerical simulation of the a greater proportion of the lateral resistance is carried by the behavior of the pile group subjected to lateral loading and upper part of the mass mix block. eliminate the cost of additional field tests. The basic approach The improvement ratio is defined as the lateral load in the for the parametric studies is to develop calibrated soil and pile improved soil over the lateral load in the virgin soil at a refer- parameters based on the results of the field testing. Then, ence cap lateral displacement of 1.5 in. Figure 6-3 provides a plot using these calibrated parameters, the depth, width, and the improvement ratio versus the depth of the mass mix zone strength of the improved ground can be systematically varied adjacent to the cap. An equation for the trend line computed to determine the effect on computed pile group response such using the least square method is also shown in Figure 6-3. The as load-deflection curves, maximum moment-load curves, slope of the trend line becomes flatter as the depth of the mass etc. This chapter describes parametric studies associated with mix depth increases, which suggests increasing the depth is the various soil improvement methods. becoming less effective in increasing the lateral resistance. Beyond a certain limit, increasing the depth of mass mix treat- ment provides only a relatively limited increase in lateral 6.1 Mass Mix Depth Effect (Beside capacity. These results suggest that the optimal soil improve- the Cap) on Lateral Resistance ment depth of mass mixing beside the pile cap would be about The first parametric study involved an investigation of the 10 pile diameters for a similar soil and pile profile. depth of the mass mix block produced by soil improvement on the pile group capacity. The mass mix block is assumed to be 6.2 Mass Mix Depth Effect (Below immediately adjacent to the pile cap but does not contact the the Cap) on Lateral Resistance piles themselves. As shown in Figure 6-1, the mass mix block length was held constant at 4 ft in the direction of loading with The second parametric study investigated the effect of the a width of 9 ft (cap width) perpendicular to the lateral load depth of a mass mix layer below the pile cap on the lateral direction while the depth was increased. The top of the mass pile group resistance. The mass mix block is assumed to have mix was assumed to be at the same depth as the cap top, which the same cross section as the cap (length of 9 ft in the direc- is at a depth of zero ft. Analyses were performed for mass mix tion of loading and a width of 9 ft perpendicular to loading), blocks with bottom depths of 2.5, 5.0, 7.5, 10.0, and 12.5 ft and has variable depths along the depth direction. The top (about 2.4D, 4.7D, 7.0D, 9.4D, and 11.8D, where D is the pile of the mass mix block is at the base of the pile cap (a depth of diameter). Other soil and pile parameters were kept the same 2.5 ft) and the bottom of the mass mix block is at depths of 5.0, as described in Section 5.4. 7.5, 10.0, and 12.5 ft (see Figure 6-4). Other soil and pile The load-displacement curves calculated by the FEM analy- parameters remain the same as described in Section 5.4. There sis for each soil mix depth are plotted in Figure 6-2. The per- is no linkage between base of the cap and the top of the mass cent increase in lateral resistance for improved soil relative to mix block. the virgin soil at a reference lateral displacement of 1.5 in. is The load-displacement curves computed with the FEM 14%, 27%, 33%, 36%, and 41% for the mass mix bottom depth model are presented in Figure 6-5. The depth of the mass mix of 2.5, 5.0, 7.5, 10.0, and 12.5 ft, respectively. It is readily appar- block below the cap has a significant effect on the lateral capac- ent that the lateral load increases as the depth of the block ity of the pile group. The increased lateral capacity at the refer- increases; however, the increase is not uniform, indicating that ence cap lateral displacement of 1.5 in. is 41%, 60%, 75%, and

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62 Figure 6-1. Mass mixing depth intervals adjacent to cap for parametric study. 450 400 350 300 Load (kips) 250 200 Depth to 2.5 ft Depth to 5.0 ft 150 Depth to 7.5 ft 100 Depth to 10.0 ft Depth to 12.5 ft 50 Virgin Soil 0 0.0 0.5 1.0 1.5 2.0 Displacement (in) Figure 6-2. Parametric study of mass mix depth adjacent to the cap on the computed load-displacement curve.

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63 2.0 1.8 Improvement Ratio 1.6 0.1289 y = 1.0204x 2 R = 0.9956 1.4 1.2 1.0 0.0 5.0 10.0 15.0 Depth (ft) Figure 6-3. Improvement ratio as a function of mass mix depth adjacent to cap. Figure 6-4. Mass mixing depth intervals below cap for parametric study.

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64 600 500 400 Load (kips) 300 Depth to 5.0 ft 200 Depth to 7.5 ft Depth to 10.0 ft 100 Depth to 12.5 ft Virgin Soil 0 0.0 0.5 1.0 1.5 2.0 Displacement (in) Figure 6-5. Results of parametric study of the effect of the mass mix depth below the cap on the computed load-displacement curve. 86% for the mass mix depths of 5.0, 7.5, 10.0, and 12.5 ft, tens somewhat as the depth of the mass mix zone increases, respectively. which suggests that the upper mass mix zone provides more Figure 6-6 provides a plot of the improvement ratio versus lateral resistance, as expected. the depth of the mass mix below the cap using a best-fit trend It should also be noted that the improvement ratio pro- line. These results suggest that mass mixing below the cap will duced by mass mixing below the cap is much higher than that dramatically increase the lateral capacity of the pile group rel- produced by mass mixing beside the cap for the same depth of ative to that in virgin clay. For mass mix zones with thick- treatment. This may be due to the larger cross section (9 × 9 ft nesses ranging from 2.5 ft to 10.0 ft (2.4D to 9.4D) underneath for mass mix below the cap in this section, 9 × 4 ft for mass the cap, the lateral resistance will increase by approximately beside the cap as in Section 6.1) as well as the constraint of 40% to 86% for similar soil and pile profiles. The increased piles by the mass mix. However, in practical design, since the resistance from the soil treatment is partially due to the external load (e.g., wind or earthquake load) direction is very increased passive area and partially due to constraint of piles by random, the soil improvement beside the cap should be pre- the mass mix (so that the mass mix and the piles can be consid- formed on all four sides of the cap. In contrast, the mass mix ered as an integrated block). The slope of the trend line flat- below the cap will resist external load in any direction. 2.0 1.8 Improvement Ratio 1.6 y = 0.8691x0.3021 R2 = 0.9986 1.4 1.2 1.0 0.0 5.0 10.0 15.0 Depth (ft) Figure 6-6. Improvement ratio as a function of mass mix depth below the cap.