The technical note by Chow et al. contains valuable case history data on the increases in pile capacities of driven piles in sand with time after driving up to 2000 days. The authors have summarised the behaviour in terms of percentage increase in pile or shaft capacity per log cycle of time. These useful data on field behaviour can be also interpreted in terms of an expression for estimating time-related increase in penetration resistance.
Mesri et al. (1990) proposed the following expression for estimatingpost-densification penetration resistance, qc, at any time t after densification:
where (qc)R is the cone resistance measured at reference time tR shortly after densification, Cα/Cc is a fundamental soil constant with values in the range 0·02 ± 0·01 for all granular soils (Mesri et al. 1990, 1994),and parameter CD reflects a potential for stiffness increase that results from the ground-modification effort. Mesri et al. (1990) back-calculated values of CD in the range 3–20 for ground modification projects in granular soils, using methods that included blasting vibrocompaction and dynamic compaction.
For the pile and shaft capacities of driven piles in sand equation (1) may be rewritten as
where Q is the pile or shaft capacity measured at time t after driving, and QR corresponds to tR = 1 day after driving for the data summarised by the authors in Figs 4 and 5. These data have been replotted in Figs 8 and 9 together with equation (2) for Cα/Cc = 0·02 and CD = 4, 7, and 12. In fact Mesri et al. (1990) recommend that, in the absence of site-specific subsur-face information, Cα/Cc = 0·02 and CD = 7 together with equation (1) should be used for estimating time-dependent increase in penetration resistance in clean sands. Most of the data points reported by the authors are within the range defined by values of CD equal to 4 and 12. Long & Kerrigan (personal communication) have assembled a data set on pile capacity in sand up to 700 days after driving. It is interesting to note that, using Cα/Cc= 0 ·02, values of CD equal to 3·6, 7·0 and 11 correspond to the lower bound, average, and upper bound defined by Long & Kerrigan. However, cone penetration data after vibrocompaction analysed by Mesri et al. (1990) as well as some of the pile capacity data plotted by Long & Kerrigan suggest that CD may decrease with time.
For explaining time-related increases in the pile or shaft capacities of driven piles in sand, the parameter CD may be interpreted to reflect a potential for sand stiffness increase as well as the changes in the stress regime surrounding the pile that result from pile installation.
Authors' reply
The authors thank Mesri and Smadi for their interesting discussion showing that rates of increase in pile capacity can be seen to follow similar trends to post-densification CPT resistance, increasing logarithmically with thelogarithm of time.
Following the measurement of an 85% increase in pile shaft capacity at Dunkirk, the authors' investigation showed that this magnitude of gain in capacity could not be explained by an increase in sand stiffness around the pile shaft, and that most of the gain is attributable to an increase in radial effective stress due to sand creep. Mesri and Smadi conclude that, in their expression for post-densification increases, the parameter CD must reflect both the potential for increases in sand stiffness and the changes in the effective stress regime. While it is well known that cone penetration resistance is strongly affected by both sand stiffness and the horizontal effective stress around the cone tip (Gibson, 1950; Carter et al., 1986; Houlsby & Hitchman, 1988), it is improbable that the processes affecting the shaft of a single pile can be directly compared to those occurring generally in a large deposit of densified sand.
One point to note is that the expression proposed by Mesri and Smadi predicts a logarithmic rise in pile capacity. As long-term pile capacity measurements were sparse, the authors opted for a linear relationship with log time, which is supported in the short term (e.g. t = 10 days) by pile test data, but predicts only modest rises in pile capacity in the long term. The resulting differences in predictions beome significant after around five years, as illustrated in Fig. 10.
It is gratifying to see that further reports of pile capacity increases in sand are now emerging. Two additional case histories are given by Chow et al. (1998), and we look forward to the publication of the data collected by Long & Kerrigan. It is important that practising engineers are reminded of this phenomenon and the implications it has for both design and pile load testing.
