Precedentes históricos

Pile driving formulae relate the ultimate bearing capacity of driven piles to the final set (i.e. penetration per blow). Various driving formulae have been proposed, such as the Hiley Formula or Dutch Formula, which are based on the principle of conservation of energy.

The inherent assumptions made in some formulae pay little regard to the actual forces, which develop during driving, or the nature of the ground and its behaviour.

Chellis (1961) observed that some of these formulae were based on the assumptions that the stress wave due to pile driving travels very fast down the pile and the associated strains in the pile are considerably less than those in the soil. As a result, the action of the blow is to create an impulse in the pile, which then proceeds to travel into the ground as a rigid body. Where these conditions are fulfilled, pile driving formulae give good predictions.

As noted by Chellis, if the set becomes small such that the second condition is not met, then the formulae may become unreliable.

In Hong Kong, Hiley Formula has been widely used for the design of driven piles.

The formula is as follow :

Rp = ηh αhWh dh

s + 0.5(cp + cq + cc) [6.1]

where Rp = driving resistance αh = efficiency of hammer

ηh = efficiency of hammer blow (allowing for energy loss on impact) = Wh + e² (Wp + Wr)

Wh + Wp+ Wr e = coefficient of restitution Wp = weight of pile

Wr = weight of pile helmet Wh = weight of hammer dh = height of fall of hammer s = permanent set of pile

cp = temporary compression of pile

cq = temporary compression of ground at pile toe

cc = temporary compression of pile cushion

The driving hammer should be large enough to overcome the inertia of the pile. In Hong Kong, the allowable maximum final set limit for driven piles in soils is often designed to be not less than 25 mm per 10 blows, unless rock is reached. A heavy hammer or a higher stroke may be used, but this would increase the risk of damaging the piles (Hannigan et al, 1998). Alternatively, a lower final set value (e.g. 10 mm per 10 blows) can be adopted, provided that adequate driving energy has been delivered to the piles. This can be done by measuring the driving stress by Pile Driving Analyzer (PDA), which can also be used to confirm the integrity of the piles under hard driving condition.

Hiley Formula suffers from the following fundamental deficiencies : (a) During pile driving, the energy delivered by a hammer

blow propagates along the pile. Only the compressive waves that reach the pile toe are responsible for advancing the pile.

(b) The rate at which the soil is sheared is not accounted for during pile driving. The high-strain rates in cohesive soils during pile penetration can cause the viscous resistance of the soil to be considerably greater than the static capacity of the pile. Poskitt (1991) shows that without considering soil damping, the driving resistance can be overestimated by several times.

(c) It only considers the hammer ram and the pile as concentrated masses in the transfer of energy. In fact, the driving system includes many other elements such as the anvil, helmet, and hammer cushion. Their presence also influences the magnitude and duration of peak force being delivered to the pile.

Despite these shortcomings, Hiley Formula continues to be widely accepted in Hong Kong. While an adequate depth is usually achieved in fairly uniform soil profiles (Davies &

Chan, 1981) using the Hiley Formula, this is not the case for piles driven through thick layers of soft marine clays to the underlying decomposed rocks, and there are a number of cases in Hong Kong of large building settlement and tilting occurring as a direct result of inadequate penetration of the piles into the bearing stratum (Lumb, 1972; Lumb, 1979). Yiu & Lam (1990) noted from five piles load-tested to failure that the comparison of the measured pile capacity with that predicted by Hiley Formula was variable and inconsistent. Extreme caution should be exercised in placing total reliance on the use of pile driving formulae without due regard to the ground conditions. Problems may also occur where a pile is driven to a set on a corestone, overlying medium dense saprolites, or where depth of soil is thin so the pile is driven to set on rock at shallow depth.

Some of the shortcomings of driving formulae can be overcome by a more sophisticated wave equation analysis. It is recommended that driving of selected piles should be measured using a Pile Driving Analyzer together with wave equation analysis, such as

CASE method and CAse Pile Wave Analysis Program (CAPWAP) (see Section 9.4.3.2 &

9.4.3.3). These can be used to supplement the information on the pile driving system, such as the rated energy of the hammer and dynamic response of soil.

HKCA (2004) proposed to measure directly the energy transfer of a hammer blow by PDA. Such an approach has the advantage that the actual energy impacted on the pile is measured. Variations on the temporary compression of the cushion, the efficiency of hammer and the coefficient of restitution are no longer relevant. This is sometimes termed as energy approach formula and is written as :

Rp = ΕΜX

s + 0.5 (cp + cq) [6.2]

where EMX = the maximum energy transferred

The EMX can be determined based on measurements taken in a number of PDA tests during trial piling and the measurements processed statistically to find an average value.

PDA tests should also be carried out on a selected number of working piles at final set. This can confirm the validity of the EMX value used in the formula. This formula is also suitable for driving piles by hydraulic hammers. Fung et al (2005) compared the load-carrying capacity predicted by the energy approach formula with that determined by static loading tests. They concluded that the energy approach formula tends to overestimate the load-carrying capacity.

Paikowsky & Chernauskas (1992) discussed an approach similar to Equation [6.2].

This approach considers only the energy losses of the pile-soil system. As energy losses due to the dynamic action are not included, the energy approach formula may be regarded as the maximum possible resistance. In order to account for all dynamic related energy losses, they suggested using a correction factor of 0.8, to reduce the capacity obtained by Equation [6.2].

This correction factor should be used unless site-specific measurements are taken to verify other values.

Based on the comparison of results of static loading tests and dynamic loading tests with CAPWAP analysis, Fung et al (2004) concluded that CAPWAP analysis was a reasonably accurate tool in predicting load-carrying capacity of driven piles. They proposed using CAPWAP analysis to calibrate the e and ηh values in Hiley Formula. The selected combination in Hiley Formula should give a pile capacity not greater than 85% of the pile capacity determined by CAPWAP analysis. They also recommended that the efficiency of the hammer blow, ηh, should not be greater than 0.98. This approach is adopted in piling projects managed by Architectural Services Department (ArchSD, 2003). The procedures can be considered as fitting parameters to match the load-carrying capacity predicted by CAPWAP analysis. The piling study undertaken by Fung et al (2004) principally involved driving grade 55C H-pile sections of 305 x 305 x 180 kg/m in size. The reliability of extending this approach to other heavier pile sections needs to be further established (HKCA, 2004).

According to dynamic stress-wave theory, it is not rational to take into account the full weight of a pile in Hiley Formula where the pile length exceeds about 30 m. For very long piles, Cornfield (1961) proposed a modification of Hiley Formula that involves

assuming a constant effective pile length instead of the full pile length. For such piles, it would be more rational, in principle, to undertake a wave equation analysis as described in Section 6.4.3 below.

The final set of a pile, particularly where the pile driving formula has been calibrated against satisfactory static loading test results and corresponding borehole information, will be useful as a site control measure. Experience suggests that driving to a target set pre-determined by a pile driving formula can help to ensure no 'slack' in the pile-soil system compared to the case of driving the pile to a pre-determined length only. Li (2005) observed that piles driven to a set smaller than that pre-determined by pile driving formulae were more likely to have met the residual settlement criterion (BD, 2004a) in subsequent pile loading tests.