6.3 Numerical Simulation of Stone Column Installation Process
6.3.3 Parametric study – Stone columns in sands and silts
The first set of simulations involved clean sand with no wick drains. Due to the uncertainties involved in cavity expansion phenomena, pore pressure changes due to
were used: (a) Dr=40%, (b) Dr=48%, and (c) Dr=59%. Three different area replacement ratios (Ar=5.6, 10.0, and 22.5%) were assumed for each initial density, where Ar=100(Ac/Ae)%, Ac is area of the stone-column, Ae is the tributary area (=πDe2/4), and De=equivalent diameter of the tributary area=1.053 times the center-to-center spacing between stone columns installed in a triangular pattern. The hydraulic conductivities were assumed to be 5x10-6m/s. Coefficient of Attenuation, α was assumed as 0.13. Table 6.2 summarizes the probe characteristics used for the simulation. Table 6.3 summarizes simulation parameters. The post-improvement densification results are shown in Fig.6.9a.
The area replacement ratio has a significant influence on the degree of improvement, as observed from Fig.6.9a. This influence diminishes as the initial density increases.
Table 6.2 Vibratory Probe Parameters
Length Frequency Power Rating η0 β
m Hz kW %
3 50 120 50 4
Table 6.3 Simulation Parameters Column Spacing
Column Dia.
Ar=5.6% 10.0% 22.5%
k
m m m/s
0.9 3.6 2.7 1.8 5*10-6
Note: Initial effective confining pressure at the depth considered is 100 kPa.
For qualitative comparison purposes, the data in Fig.6.9a may be converted to equivalent SPT blow counts (N1)60,c-s using Tokimatsu and Seed (1984) relationship (Appendix E) for clean sands, as shown in Fig.6.9b. This can be compared with the field- case history data compiled by Baez (1995) shown in Fig.6.10. The regression curves for post-improvement SPT blow counts obtained by Baez were based on an analysis of
extensive case histories, where vibro-stone columns were used to improve sandy soil sites with less than 15% silts. Although direct comparisons are not possible, due to lack of site-specific data, the trends found in Fig.6.9b agree well with the trend in Fig.6.10.
0 20 40 60 80 100
0 20 40 60 80 100
Pre-Dr (%) Post-Dr (%)
Ar=5.6%
Ar=10.0%
Ar=22.5%
(a)
0 10 20 30 40
0 5 10 15 20
Pre-(N1)60, c-s (blows/ft) Post-(N1)60, c-s (blows/ft)
Ar=5.6%
Ar=10.0%
Ar=22.5%
(b)
Fig.9 Vibro-Stone Column Simulation Results
0 10 20 30 40
0 5 10 15 20
Pre-(N1)60, c-s (blows/ft)
Post-(N1)60, c-s (blows/ft)
Ar=5%
Ar=10%
Ar=20%
Fig. 6.10 Regression Design Curves (Baez 1995)
6.3.3.1 Effect of hydraulic conductivity
According to the finding from laboratory experiments, the behavior silty soils are not much different from sands, except for their low hydraulic conductivity values. During the densification process, these hydraulic conductivity values are the ones that make stone columns less effective in silty soils compared to those in sands (Shenthan 2001) for a
Fig.6.11a shows average pore pressure changes within a sandy soil layer at depth of 12m during vibro stone column installation. Initial effective confining pressure is about 100 kPa; area replacement ratio is about 20%; and the probe diameter is 0.4m. Other relevant parameters are the same as for the above simulations.
The same simulation was done for a silty soil with k = 5x10-7 m/s, which is 10 times lower than that of the sand used in this simulation. Pore pressure changes are shown in Fig.6.11b.
0.0 0.2 0.4 0.6 0.8 1.0
0.0 0.5 1.0 1.5 2.0
r (m)
ru
20 s 40 s 70 s 100 s (a)
0.0 0.2 0.4 0.6 0.8 1.0
0.0 0.5 1.0 1.5 2.0
r (m)
ru
20 s 40 s 70 s 100 s (b)
k = 5E-7 m/s Pre-(Dr)eq = 40%
k = 5E-6 m/s Pre-(Dr)eq = 40%
Fig.6.11 Pore Pressure Changes within the Soil during Stone Column Installation To reach a depth of about 12m, a probe may take about 400s. In the above simulations, it was assumed that the pore pressure changes take place only after the probe tip reaches the specified depth. Vibratory energy assumed to be imparted into the soil at that depth when the elevation of the eccentric mass inside the probe is within ±0.5m from that of the specified depth.
Since the probe radius is about 0.2m, during the first 20s, the soil at 0.2m radial distance essentially remains liquefied. The extent of liquefaction varies depending on the soil type, and it’s state. Dissipation takes place through the outer columns, and radially outwards through the outer soil medium. However, as gravel is poured in, pore pressure start to dissipate through the center column as well. As more and more dissipation takes
place, it is possible to impart more and more energy into the soil, which is difficult, if not impossible, in low permeable silty soils.
During reinsertion of the probe, stones are being pushed laterally, increasing the diameter of the column. This increment further enhances pore pressure dissipation, which is noticeable in Fig.6.11a. The number of reinsertions depends on the probe diameter and the required stone column diameter. 0.9m column needs reinserting a probe of 0.4m diameter five times (0.4x√5 ≅ 0.9). At an average penetrating speed of 3 cm/s, it will take about 3 minutes per lift of 1m to build such a column.
It can be noticed from Fig.6.11 that a certain region between the center column and the outer columns remains liquefied all the time during stone column installation process.
This region gets smaller with time in high permeable sandy soils (Fig.6.11a), while only pushed outwards in low permeable silty soils (Fig.6.11b). This observation justifies the usage of wick drains, when installed, that expedites the pore pressure dissipation of the above liquefied region in silty soils.
Fig.6.12 shows the effect of hydraulic conductivity on post – improvement relative densities. It is evident from this figure that the effectiveness of stone columns in densifying soils depends greatly on the ability to dissipate the excess pore pressures generated during installation process in a higher pace. This figure also indicates that even for a high area replacement ratio of about 22.5 %, the degree of improvement is insufficient in soils with hydraulic conductivities below about 5x10-6 m/s. Spacing smaller than two times the diameters of the stone column might be needed if one prefers to achieve a reasonable densification in silts with stone columns alone. However, this attempt might be economically infeasible. Alternatively, one could introduce additional
drainage using much cheaper wick drains. The latter aspect is discussed in the following chapter.
40 50 60 70 80 90 100
1E-8 1E-7 1E-6 1E-5 1E-4
k (m/s)
Po s t ( Dr)eq(% )
SC Alone
Pre - (Dr)eq = 40%
Ar = 22.5%
Increasing Fines Content
Fig.6.12 Effect of Hydraulic Conductivity of Soil on the Post – Improvement Density