This is yet another paper which cited my work, in this case the ZWAVE paper. Once again I’m not sure why they picked this one; it’s probably because I explored a soil model based on that of Randolph and Simons (1986), which they also cited and discussed. I came back to models like this in Closed Form Solution of the Wave Equation for Piles.
This paper, however, explores a topic that has bothered me (and hopefully a few others in the industry) concerning the wave equation for piles: what are the effects due to the fact that impact pile driving is a semi-continuous process which produces damage/change in the soils around it as the blows are consecutively applied and the pile advances in the soil? Most all wave equation analyses from Smith onwards use a single blow analysis to analyse the pile-soil response to impact.
The limitations of that have been recognised for a long time. The best known of those effects are pile set-up, which are due to the elevation of pore water pressures during impact. That elevation can be affected by a number of factors, including the nature of the soil and the blow rate of the hammer (a poorly researched phenomenon.) Another recognition of this fact is residual stress analysis (RSA,) which goes back to the days of WEAP87.
In this paper the authors proposed a 1D model which includes cyclic degradation in the shaft model and the progressive effect of toe advancement on the non-linear spring model. Additionally the toe model adds a soil toe mass. I considered doing this in Closed Form Solution of the Wave Equation for Piles (I was unaware of Deeks and Randolph (1995) at the time) but my objective was different: to use the mass as a form of Rayleigh damping (which seldom seems to work out the way it’s supposed to.) I ultimately took a pass on this.
As one would expect the authors got good results and proposed future studies to make adjustments to the method. One pleasant surprise was their use of a Vulcan #1 Hammer for the model validation; that used to be common in deep foundations papers but isn’t so much these days.
As far as the model they propose, I think it has promise. Sometimes I feel like I’m back in Beijing and my Chinese counterpart Zhu Li Cai is telling me “I hope you are right” when we tell him our hammers last a long time, some made during Qing Dynasty still in operation. (They actually do.) I hope these researchers are right. 1D models have the advantage of simplicity and computational efficiency. But I think that, in the long run, we will transition to 2D/3D models as I used in Improved Methods for Forward and Inverse Solution of the Wave Equation for Piles. Such a model would shift the rheological decision making to the continuum model, but that in turn would require a more sophisticated model than I used in my study.
I am grateful that these researchers have tackled a problem which has been for too long overlooked in pile dynamics.
vulcanhammer.info 