Several national and international standards provide guidance on metrics which can be used to quantify the human exposure to vibration. Guidance typically takes the form of single figure exposure metrics which are functions of frequency dependent weightings. The standard BS 6472-1:2008 recommends two frequency
weighting curves, Wb for the vibration acceleration in the vertical direction and Wd for the horizontal direction. This weighting curve, as well as others presented
in this section, intend to reflect the sensitivity of the human body to vibration as a function of frequency (see Section 2.2.3). TheWbweighting curve shows maximum
sensitivity to vertical vibration in the frequency range 4 to 12.5 Hz and the Wd
weighting curve shows maximum sensitivity to horizontal vibration in the range 1 to 2 Hz.
Other frequency weighting curves include the Wk weighting curve for vertical vi-
bration acceleration as recommended by BS ISO 2631-1:1997, which also recom- mends the use of the Wd weighting curve for horizontal vibration. The Wb and
the Wk weighting curves, which are utilised extensively throughout the thesis, are
presented in Figure 2.4. The two weighting curves differ slightly, though the dif- ference is less than the inter-subject variability recorded in the laboratory studies from which the weighting curves were developed (see Section 2.2.3). A further weighting curve, Wm, which applies for vibration acceleration in any direction,
is recommended in ISO 2631-1:2003. The Wm weighting curve is derived from
a combination of the Wk and Wd curves. The German national standard, DIN
4150-2 (1999), which is used as the basis for guidance in many parts of continental Europe, recommends the use of the Kb weighting curve for vibration velocity, as
opposed to acceleration. The Kb weighting curve is similar to the Wb weighting
curve when transformed and applied to acceleration (Woodcock, 2013).
The vibration metric that is perhaps most commonly used throughout the United Kingdom to quantify human exposure to vibration is the vibration dose value (VDV) as recommended by BS 6472-1:2008. VDV is defined using either the Wb
weighting curve for vertical vibration or the Wd weighting curve for horizontal
vibration and can be derived over a 16 hour daytime period (07:00 to 23:00) and an 8 hour night-time period (23:00 to 07:00). VDV is a fourth power integration of vibration acceleration and is defined as follows:
VDV = 4
s
Z T
0
10−1 100 101 102 10−2 10−1 100 101 Frequency (Hz) Modulus W b W k
Figure 2.4: Wb andWk frequency weighting curves for vertical vibration
acceleration
where a(t) is vibration acceleration varying with time t and total duration T. Due to the fourth power integration, VDV has unconventional units of m s−1.75. The fourth power relationship, which accounts more accurately for the greater perceptual effect of high magnitude peaks in a vibration signal, is based in part upon the laboratory studies of Griffin and Whitham (1980a,b) and Howarth and Griffin (1988a) as described in Section 2.2.4.
Another commonly utilised vibration metric, particularly in the United States, is the frequency weighted root mean square (rms) acceleration as recommended by BS ISO 2631-1:1997. The recommended weightings areWkfor vertical acceleration
and Wd for horizontal acceleration. The rms acceleration is analogous to rms
pressure that is widely used in the measurement of noise signals and is defined as follows: rms= s 1 T Z T 0 a(t)2dt (2.5)
The recommendation of BS ISO 2631-1:1997 is that the rms acceleration should only be used to quantify signals with a relatively low crest factor. The crest
factor of an acceleration signal is the ratio of the peak acceleration to the rms
acceleration. A higher crest factor indicates the signal may be dominated by peaks. For signals with a crest factor greater than 9, BS ISO 2631-1:1997 recommends the use of VDV or the maximum transient vibration value (MTVV), defined as the maximum value of the slow weighted running rmsover the evaluation period. The Norwegian standard NS 817 (2005) recommends the use of a statistical 95 percentile weighted velocity (vw,95) derived from 1 second averages of the velocity signals. This metric is calculated as follows:
vw,95= ¯vw,max+ 1.8σv (2.6)
where ¯vw,max is the mean value of the maximum weighted velocity for all train
passbys and and σv is the standard deviation of the maximum 1 second average
weighted velocity for all passbys.
The German national standard DIN 4150-2 (1999), used as the basis for guidance in much of continental Europe, suggests an evaluation procedure based on two vibration exposure descriptors. The first step of the procedure is to evaluate the metric KBF max which is a 0.125 s running exponential rms Kb weighted velocity
value of the evaluation period. This metric is then compared to context sensitive thresholds, taking into account time of day, the vibration source and location of the building, and if the thresholds are exceeded, a second metric,KBF T ris calculated:
KBF T r = s 1 Tr X j Te,jKBF T M,j2 (2.7)
where Tr is the evaluation period (16 hours for daytime, 8 hours for night-time), Te,j is the exposure period of the jth event and KB2F T M,j is the average of the
maximum 0.125 s running exponential rms velocity for each 30 second period of an event.
There are several other national standard which provide guidance for the evalua- tion of vibration exposure. A summary of these standards and their key features is provided by the Railway-Induced Vibration Abatement Solutions Collaborative Project (RIVAS, 2011). Many of the guidelines, including the Netherlands stan- dard SBR Richtlijn - Deel B (2006), the United States FTA guidelines (2006), the Swedish standard SS 460 48 61 (1992), the Spanish standard Real Decreto 1367/2007, the Italian standard UNI 9614:1990, the Japanese Vibration Regula- tion Law and the Austrian standard ¨OENORM S 9012:2010 recommend the use of some variation of the maximum running average rms velocity or acceleration. In a guidance document produced for the CargoVibes project, Woodcock et al. (2014b) state that there is insufficient evidence to recommend any one vibration exposure metric over another. They suggest that guidance should be provided, where possible, in terms of three metrics that can be easily related to other metrics found in national and international standards. These three metrics are Vdir,max
which is the maximum Wk weighted fast exponentially filtered rms velocity over
the entire assessment period, and the Wk weighted rms acceleration and VDV
which are defined above. They also recommend retaining raw acceleration time histories of measurements for future analysis.