As an example of calculations of factor of safety against liquefaction, results are presented of cone penetration soundings performed small trial area (12 m by 12 m) at Hong Kong Chek Lap Kok Airport in a sand fill before and after seven days after vibratory densification. The sand fill consisted partly of calcareous material (fragments of shells and clams), and contained about 15 % of fines and occasional layers of silt and silty sand. It was placed by bottom dumping, where the water depth exceeded 4 m, and by spraying, where the water depth was shallower. The final thickness of the sand fill prior to compaction was about 10 m. The groundwater level was located about 1 m below the fill surface. The sand fill was specified to contain less than 10 % of fines. The compaction study of the case is reported by Massarsch and Fellenius (2002).
Figure 2.34 present the results of four CPTU soundings through the as-placed fill before compaction, illustrating that the fill consists mainly of loose sand to a depth of about 4 m below which the sand contain frequent layers of silty sand and an occasional lens of silty clay and even clay. The homogeneity of the fill is demonstrated in the profiling chart shown in Fig. 2.35. The figures include all CPT records (readings were taken every 20 mm) from one CPT sounding. The data points in Zones 4a and 4b indicating silt, sandy silt, and silty sand are all from below 4 m depth. The silty clay and clay lens
( ) 200
1 45
10 50 135
34 1
2 − + +
− +
= N
N CRR N
indicated in the figure at about 6 m depth is 60 mm thick and the profiling chart shows it to be made up of three closely located values, one value indicating clay and two values indicating silty clay.
The site was densified using the Müller Resonance Compaction (MRC) method (Massarsch and Westerberg 1995). By changing the vibration frequency, the system makes use of the vibration amplification, which occurs when the soil deposit is excited at the resonance frequency. Different vibration frequencies are used during the particular phases of the compaction process in order to achieve optimal probe penetration and soil densification, as well as facilitate of probe extraction and to avoid undoing the compaction (“uncompacting” the soil).
Fig. 2.34 Results of four CPTU initial (before compaction) soundings at Chek Lap Kok Airport. The heavy lines in the cone stress, sleeve friction, and friction ratio diagrams are the geometric averages for each depth of the four soundings.
The results of three cone soundings performed seven days after the vibratory compaction are shown in Fig. 2.36. The diagrams show that the compaction has resulted in increased values of cone stress and sleeve friction, more directly demonstrated in Fig. 2.37, where only the average curves are shown.. The friction ratio is approximately the same, however. The average curves are produced by means of a geometric average running over a distance of 500 mm, that is 25 values. The purpose of the averaging is to reduce the influence of thin layers of soft material that could cause a smaller than actual cone stress and, therefore, indicate a larger than actual susceptibility to liquefaction.
Figure 2.38 shows the data points in an Eslami-Fellenius profiling chart, implying a coarser soil than that shown by the sounding before the compaction (Fig. 2.34). Of course, the soil composition is the same (but for minor variation below about 9 m depth, where the seven-day sounding encountered clay lenses not found in the "before" sounding). The densification has changed the sand from a normally consolidated sand to an overconsolidated sand. As a result, the points plot higher up in the chart implying a coarser soil than found in the "before" sounding.
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Sand PROFILE
Fine sand to Silty Sand
Silty Clay and Clay
Fig. 2.35 The CPT data from one of the initial cone soundings plotted in an Eslami-Fellenius CPT profiling chart (Eslami and Fellenius 2000). The three separate dots near the boundary between Zones 2 and 3 are from the clay layer at Depth 6.1 m. (Data from Massarsch and Fellenius 2002).
For purpose of demonstrating the seismic analysis described above, the susceptibility for liquefaction at the site is assumed to be affected by an earthquake of magnitude of 7.5 and a seismic acceleration of 30 % of gravity. This assumption determines the site-specific Cyclic Resistance Ratio, CRR, according to Eqs. 2.13 through 2.15. The cone stress measurements determine the Cyclic Stress Ratio, CSR, from the
"before" and "after" soundings, and the factor of safety against liquefaction is the CSR divided by the CRR as defined in Eq. 2.20. Figure 2.39 shows the calculated factors of safety for "before" and "after"
compaction and demonstrates that the compaction was highly efficient above about 6 m depth and plain efficient in the finer soils below (fine sand and silt are not as suitable for compaction as sand; Massarsch 1991).
0 5 10 15
0 20 40 60 80 100
Sleeve Friction (KPa) Cone Stress, qE (MPa)
1 = Very Soft Clays, Sensitive and/or Collapsible Soils 2 = Clay and/or Silt 3 = Clayey Silt and/or Silty Clay 4a = Sandy Silt and/or Silt
4b = Fine Sand and/or Silty Sand
5 = Sand to Sandy Gravel
5
4b 4a 3 1 2
Fig. 2.36 Results of three CPTU soundings at Chek Lap Kok Airport seven days after the vibratory compaction. The heavy lines in the cone stress, sleeve friction, and friction ratio diagrams are the geometric averages for each depth of the four soundings.
Fig. 2.37 Geometric average values of cone stress, sleeve friction, and friction ratios and measured pore pressures from CPTU soundings at Chek Lap Kok Airport before and seven days after the vibratory compaction.
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0.0 0.3 0.5 0.8 1.0 Friction Ratio (%)
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Friction Ratio (%)
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7 Days 7 Days
Before
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Sleeve Friction (KPa) Cone Stress, qE (MPa)
4b 4a
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B
1 = Very Soft Clays, Sensitive and/or Collapsible Soils 2 = Clay and/or Silt 3 = Clayey Silt and/or Silty Clay
4a = Sandy Silt and/or Silt 4b = Fine Sand and/or Silty Sand
5 = Sand to Sandy Gravel
CLAY LENSES BELOW 9 m DEPTH
Fig. 2.38 The CPT data from one of the 7-day after cone soundings plotted in an Eslami-Fellenius profiling chart (Eslami and Fellenius 2000).
Fs versus depth
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Factor of Safety, Fs (--)
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7 Days after compaction
Fig. 2.39 Factor of safety against liquefaction before and after vibratory compaction.