Reliability-based design - Risk and Reliability in Geotechnical Engineering - page 374

quadrants: one was a control area, with no treatment of the marine clay, and the remain-
ing three quadrants were installed with vertical drains at different spacing through about
7-m-thick marine clay. The offshore geotechnical investigations, the test fill, and the instru-
mentation program were described in substantial detail by Foott et al. (1987) and Koutsoftas
et al. (1987), and further studied deterministically in Choa et al. (1990).
Low (2003b) presented a deterministic numerical method written in the VBA program-
ming environment of Microsoft Excel spreadsheet for consolidation analysis involving verti-
cal drains. The program uses Barron's solution for equal vertical strain of consolidation due
to radial drainage and Carillo's equation for combined radial and vertical drainage. The
program accounts—in an approximate manner—for stage loading, load reduction due to fill
submergence, delayed vertical drain installation, changes in length of vertical drainage path
with time, and variation of soil stress history with depth. A practical algorithm for predic-
tion of the rate of settlement was adopted because, even in the relatively simple approach
adopted, 15 or more values of individual input parameters were required. The uncertain-
ties associated with some of these parameters will limit the accuracy of prediction even if
sophisticated models are used. The computational algorithm in the program is not fully
rigorous, because idealizations and approximations have been made. Nevertheless, limited
comparisons made by the author suggest that the degree of accuracy achieved is adequate
for the purpose in hand. Its relative simplicity also gave rise to some insights on parametric
relationships and sensitivities. The results of deterministic analysis using the program com-
pared well with the instrumented settlement records of the soft clay beneath the Chek Lap
Kok test fills.
Figure 9.18 shows the results of a deterministic analysis using the program, for one of
the four test fills of the Chek Lap Kok land reclamation project where the prefabricated
vertical band drains were installed at a spacing of 1.5 m. There was staged loading due to
the increase in fill thickness with time as shown. The clay was overconsolidated since the
initial effective vertical stress profile was less than the profile of maximum past pressures
(preconsolidation pressures). The discrepancies between the computed curve and the mea-
sured range are partly attributable to the underestimation of the final consolidation settle-
ment by the program. The final consolidation settlements are functions of compression ratio
C R , recompression ratio C RR , stress history, and applied loadings, but are not affected by
the values of the rate parameters c v and c h , which are the coefficients of consolidation for
vertical and horizontal flow, respectively, nor by the idealizations and approximations in the
modeling of excess pore pressure dissipation in the program. The program-computed results
will be even closer to the observed settlement curves if different values of c h and compression
ratios are used, but such speculations belong to the realm of back analysis and hindsight and
will not be pursued here. Instead, the Low and Tang (2007) efficient spreadsheet FORM
procedure will be illustrated for the case in hand to highlight some subtleties and insights
of RBD involving serviceability limit states. The material in Sections 9.10.1 through 9.10.5
is based on Low (2008c).
9.10.1 lSS and performance functions g(x) pertaining to
magnitude and rate of soft clay settlement
As in Low (2008c), the following three aspects are studied:
i. The magnitude of the ultimate consolidation settlement s cf ;
ii. The degree of consolidation U at time = 1 year;
iii. The consolidation settlement remaining ( s r ) at time = 1 year, where s r = s cf - s 1 yr .