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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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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.