Modeling of vibratory pile driving

Vibratory installation of piles and casings can be extremely economical and therefore the contractors’ preferred method of pile driving. Compared to impact pile driving it also has the advantage of reduced noise pollution. Unfortunately, this installation method is still fraught with uncertainties. The foremost question is driveability and equally important is the question of bearing capacity of the installed pile. Both are difficult to answer prior to actually driving a pile. In other words, given a soil profile and pile type, the question of which vibratory hammer could drive the pile to a certain depth often cannot be answered with sufficient certainty. Once the pile has been installed, its bearing capacity cannot be calculated with sufficient accuracy based on the observed final rate of penetration. Many attempts have been made to calculate the pile capacity based on the driving resistance, however, to date it is still required that the pile is redriven with an impact hammer for acceptance as a bearing pile. As far as driveability is concerned, simple charts issued by hammer manufacturers based on pile size or weight seem to be as reliable as other more sophisticated methods of hammer selection. This paper summarizes current analytical methods and explains how wave equation analysis can be used in a manner comparable to the analysis of impact driven piles. Hammer and soil modeling details are discussed. A few examples demonstrate capabilities and limitations of the methods and, for the wave equation approach, sensitivity of results to important soil resistance parameters. mer may produce undesirable vibrations in nearby structures, a limitation that will not be discussed in this paper. The economic advantage of the vibratory hammer can only be realized if the contractor correctly predicts which size hammer will drive the pile to a required depth. Additional savings would be realized if it were assured that the pile had the required bearing capacity after installation. The simulation of the installation by vibratory hammers should therefore enable the analyst to predict the rate of penetration vs. depth (driveability analysis). In addition, a so-called bearing graph should be constructed, which would relate the pile bearing capacity to the rate of penetration at the end of the installation. Examples of these relationships will be demonstrated below. 3 BASIC COMPONENTS OF A VIBRATORY HAMMER The vibratory hammer, in its most common form, consists of pairs of eccentrically mounted masses which are contained in a frame whose appreciable mass may be called the oscillator. A bias mass isolates the oscillator from the hammer support – usually a crane line. The oscillator is separated from the bias mass by a very soft spring (Figure 1). The bias mass therefore adds a static force to oscillator and pile. The force in the crane line reduces this static force and, if it is greater than all weights, allows for pile extraction. Conveniently, the pile is attached to the oscillator by means of a hydraulic clamp. This connection may be considered rigid and, for modeling purposes, the clamp can be considered an integral part of the oscillator mass. When eccentrically supported masses (combined eccentric mass me) spin at a rotational frequency Τ = 2Β f (f in Hz), their centrifugal force is Fc = me Τ (1) This centrifugal force (actually it differs slightly from Eq. 1 because of the oscillator’s vertical motion) is transmitted through the eccenter mass bearings to the oscillator and thus to the pile. Only vertical components of the centrifugal force are transmitted to the pile because pairs of eccenters are spinning in opposite directions. Normally the hammer frequency is between 20 and 40 Hz and each peak compressive force generated by the vibratory hammer therefore occurs at intervals of 25 to 50 ms. For a resonant hammer, successive peak force values may occur at intervals of only 8 or 10 ms. The free-free frequency, fF, of a 20 m steel pile of wave speed c = 5120 m/s is ff = c/2L = 5120/40 = 128 Hz Comparing this free pile frequency with that of a low frequency hammer shows that resonance is unlikely in piles of normally encountered lengths. However, the mass of the vibratory hammer and the clamp, attached through the clamp to the pile, tends to reduce the lowest frequency of the overall system and, when piles get long and drivers heavy, makes resonance possible. According Poulos et al. (1980) the lowest resonance frequency of a system roughly reduces to 50% of the pile frequency if the mass on top of the pile equals the weight of the pile. If the hammer frequency is significantly lower than the hammer-pile frequency, then the particles of the pile have practically the same direction of motion at the same instance in time. Figure 2 demonstrates in a length-time diagram the different loading patterns of a vibratory hammer and an impact hammer. The relationship shown is approximately scaled Line Pull