Limitations of the Danish driving formula for short piles

Abstract

Dynamic formulae are based on elementary laws of Physics, such as those that govern the conservation of energy or the shock between bodies. However, driving a pile is a more complex phenomenon. The pile is not a free body, but an elongated element inserted into the ground, with which it interacts under a hammer blow. An alternative to these formulae is the solution of the Wave Equation, introduced by Smith (1960). Dynamic formulae basically require the hammer and pile data and provide the set (permanent penetration of the pile per blow). On the other hand, a Wave Equation solution requires, in addition to these data, those related to the driving accessories and the soils (in terms of rigidity, resistance and viscosity), and outputs not only the set, but also the dynamic stresses (stresses along the pile under driving). In their use to estimate pile capacity, the dynamic formulae are fed simply by the measured set, while the Wave Equation solution requires more extensive measurements of the pile response to driving, in what is called the High Strain Dynamic Test (HSDT). The use of either of the two dynamic methods, however, pose a few questions, such as (e.g., Alonso, 1988): (i) the energy of the hammer blow is not always sufficient to bring about the maximum resistance of the soil; (ii) the resistance presented by the soil depends on the time between driving and the measurement of the set or the HSDT, with soil resistance usually increasing with time, hence this phenomenon being known as “set-up” (very rarely, resistance decreases over time, in this case, called “relaxation”); (iii) the energy losses in the accessories and the viscous response of soil are not properly incorporated in most dynamic formulae. The first two aspects are inherent to any dynamic method, leading to different load capacities obtained (i) with different driving energies and (ii) with set measurements or HSDTs made at different times after driving. As a consequence of aspect (i), it is common practice to refer to load capacity obtained in HSDTs – performed with a given driving equipment – as mobilized load capacity, implying that a higher capacity could be obtained with a higher energy. Despite the above issues, dynamic formulae are very useful in the control of a piling, especially if combined with HSDTs and static load tests (SLTs) − ideally executed right at the beginning of the construction −. The dynamic formulae serve to ensure homogeneity in load capacity, leading to different lengths of piles driven in heterogeneous soils. Abstract Dynamic formulae are a widely used expedient for the control of driven piles to ensure load capacity. These formulae have considerable limitations when used in the prediction of the load capacity on their own, but are very useful in the control of a piling when combined with other tests. This technical note presents an evaluation of the Danish Formula for 54 precast concrete piles, comparing its results with High Strain Dynamic Tests (HSDTs), Static Load Tests (SLTs) and predictions by a semi-empirical static method (Aoki & Velloso, 1975). The data used in the comparison come from three works in the city of Rio de Janeiro, Brazil. All piles were driven with free-fall hammers and in one particular work the piles were relatively short. The predictions of the Danish Formula were evaluated in relation to the pile length/diameter ratio. It was concluded that for short piles with lengths less than 30 times the diameter this formula indicates bearing capacities higher than the actual ones. A correction for a safe use of the Danish Formula for short piles is suggested.