Page 153 - Numerical Analysis and Modelling in Geomechanics

134 C.L.RAMSHAW AND A.R.SELBY

Figure 5.2 Example ground vibrations from an impact hammer.

The three components of velocity can be combined into a single vector trace
by taking the values of radial, transverse and vertical velocities at each instant
in time, and combining them to give the true peak particle velocity, ppv. The
vector direction is ignored.

(5.2)

The practice of taking the peaks of each signal regardless of time, and applying
equation (5.2) gives a spurious value which is typically 20% in excess of the true
value (Hiller and Hope, 1998). Conversely, the practice of using vertical peak
velocity alone underestimates the true value by 20% or more. Indeed there is no
obvious pattern to show which component is the largest of the three; vertical
vibration may be largest close to a pile with large toe depth, while radial
vibration may be largest at greater distance from the pile.
The peak particle velocity attenuates with distance away from the source, as
energy density around the expanding wave front is reduced, i.e. geometric
damping. However, the rate of attenuation is not well defined because the
observed signal contains components of primary P-wave, vertical shear, SV, and
surface or Rayleigh, R, waves, which attenuate differentially. The soils
contribute a small degree of material damping. The non-uniformity of attenuation
has been observed and discussed by Attewell et al. (1991) and Hiller (2000).
For practical purposes, a simplified estimate for ppv has been developed from
Attewell and Farmer (1973), through BS5228 part 4 (1992), and culminating in
Eurocode 3 Ch 5 (1996), as

(5.3)