Human perception of vibrations according different assessment methods

2.1. RMS method

RMS method according to latest update of ISO standard [14] is called “basic evaluation method” and it is defined using weighted RMS acceleration which should be calculated according to following formula:

In the same standard, there are guidelines for frequency weighted functions $w_k$ (weighted function in $z$ direction) and $w_d$(weighted function in $x$ and $y$ direction) which are given in proper tables and illustrated in Fig. 1.

Fig. 1Basic lines corresponding to vibration perception threshold

Weighted functions $w_k$ and $w_d$ are known as principal frequency weightings and their values in one-third octave band are also given in ISO standard. That is why the procedure to evaluate human perception of vibrations in buildings is simple.

Values of frequency weightings in one third octave band determine lines characterizing the so-called vibration perception threshold. Fig. 1 summarizes the sensitivity threshold lines received in the $z$ direction (feet to head) and in the $xy$directions (back to chest, side by side). To create comfort lines form basic lines values defining these lines should be multiplied by the so-called correction factor “$n$”. Values of factor “$n$” are given in ISO standard [14] and they depend on destination of the room, time of occurrence of vibration, nature of vibrations and their repeatability.

2.2. VDV method

VDV method in ISO standard [14] is an additional method which could be useful in situations when crest factor of the recorded signal is higher than 9. Crest factor is the modulus of the ratio of the maximum peak value of the signal to its RMS value. In practice, it means the signal with occasional shocks and transient vibrations. But it should be noticed that in British standard [13] VDV method is the only one method of assessment and in Australian standard [15] VDV method should be considered when the crest factor is equal 6 and higher.

The value of this parameter is determined by the formula:

The determined value of the vibration dose (VDV) is compared with the values given in standards [13, 15]. In the appropriate table the three levels of sensitivity to vibration are described. Level one (low probability of complaints) is comparable with vibration perception threshold (Fig. 1). Highest level (adverse comments probable) could be compared with comfort limit. All three levels of vibration perception in residential rooms are listed in Table 1 [13].

Assessment of human perception of vibrations caused by tram, heavy truck and subway.

The building chosen for analysis is the four-storey building with basement located in Warsaw caused by dynamic excitation from tram, subway and heavy truck passages. Measurement points were located at the first, second and fourth storey in the middle of residential room which is located close to excitation sources. Measurement lasted from 16.15 to 17.59. During that time, there were 26 passages registered: 11 trams, 10 subway, 1 heavy truck and 4 passages during which two different sources of vibration occurred. For all registered episodes RMS and VDV analysis were made.

2.3. RMS analysis

In 9 from registered 26 episodes vibration perception threshold was exceeded, in 5 of them also the comfort line during night was exceeded (“$n$” factor equal 1.4) and in one episode both comfort lines during night and day (“$n$” factor equal 4) were exceeded. The registered signal and RMS analysis for this extreme episode is shown on Fig. 2.

All exceedances occurred in $z$ direction. Most of them are from tram passages, only one is from simultaneously passing tram and subway.

2.4. VDV analysis

In VDV analysis the most important is proper calculation of overall day (16 h) or night (8 h) exposure to vibration. That is why in [13] formula for so-called total value of VDV is given:

For every 26 vibration episodes VDV values were calculated and they are listed in Table 2.

Fig. 2RMS analysis for extreme episode of tram passages

As can be seen from above Table values of VDV in $z$ direction are much higher than in both horizontal directions. Grey marked episode is the same for which RMS analysis is shown on Fig. 2. As also could be seen from Table 2 the highest $VDV$ values are vibrations caused by tram passages and these episodes influence on total value of $VDV$. Subway passages give the smallest excitations which means that, despite of the fact that Warsaw Metro is shallow subway, vibro-insulation was made properly.

Because $VDV$ values in $z$ direction are dominant and significant, $VD{V}_{total}$ for day and night were calculated for that direction only. Some assumptions were made: during the day, the same intensity of transport passages was assumed as for representative measurement, for the night according to the subway and tram timetables intensity of passages was assumed to be 25 % of the representative. Appropriate values for day and night are as follows:

$VD{V}_{day}=$ 0.5807 – adverse comments possible;

$VD{V}_{night}=$ 0.3453 – adverse comments possible.

According VDV analysis comfort is not exceeded but residents may complain about vibrations.