Research on Human Exposure to Transport-Induced Vibration in Buildings

Abstract

The analysis of human perception of vibrations in buildings is a critical aspect of structural engineering, particularly as urbanization intensifies and the proximity of vibration sources to buildings increases. This paper addresses the frequent errors in the assessment and diagnosis of the impact of vibrations on building occupants. Despite stringent standards and detailed methodologies, misinterpretations and incorrect implementations of these guidelines are common, leading to flawed diagnostic studies. These errors often stem from the misuse of measurement equipment, inappropriate selection of measurement points, and a general lack of comprehensive education on vibration analysis. National guidelines, although largely based on ISO standards, vary significantly, contributing to inconsistent practices across Europe. The dominant sources of urban vibrations include vehicle traffic, particularly heavy trucks and rail vehicles, which significantly impact both building structures and human comfort. This paper reviews the methodologies for measuring and interpreting vibrations, emphasizing the importance of correct sensor placement and data analysis. It highlights the necessity of integrating vibrational comfort into building design, considering both external and internal vibration sources. The study also explores the effectiveness of different evaluation methods, such as the RMS and VDV methods, and the impact of various weighting functions on the analysis results. The findings underscore the need for improved education and standardization in the field to ensure accurate assessments and enhance the vibrational comfort of building occupants.

1. Introduction

The immediate vicinity necessitates considering the impact of vibrations on people in building design. Unfortunately, this often leads to errors in the assessment and diagnosis of these influences. Despite precise requirements in various standards and relatively detailed provisions relating to the measurement and interpretation methodology [1], there are frequent diagnostic studies where conclusions and recommendations are formulated based on incorrectly conducted measurements and poorly developed diagnostic results (examples can be found in [2]). Such diagnostic studies and their results are sometimes disseminated in publications and even used in forecasting dynamic impacts on buildings. Errors in carrying out reliable measurements occur for various reasons. Although there are many standards and recommendations, misunderstanding their provisions is common.

In Europe, almost every country has its own national guidelines regarding vibration comfort. The vast majority of these guidelines are based on ISO standards. However, this does not eliminate the issue of incorrect execution or analysis of vibration measurements. These errors mainly stem from the use of expensive measuring equipment with appropriate sensitivity and from the incompetence of those performing the measurements. This incompetence is often not their fault but rather a result of an education system that treats vibrations in a very limited and theoretical way. All this makes the analysis of vibrations seem like secret knowledge available only to a few. The increasing urban density and new investments near vibration sources require a quick analysis of the impact of vibrations on buildings or the people inside them. The dominant source of vibrations in urban infrastructure is often vehicle traffic. Considering the mechanism of vibration generation, the weight of vehicles and the ability of the wheels and suspension to reduce vibrations, as well as the quality of tracks, vibrations induced by rail vehicles, including trams, are the most noticeable to people and have the greatest impact on buildings [3]. Therefore, research and implementation of new solutions in vehicle–track–ground coupling dynamics and railway-induced ground vibration are very important. Problems arise from the choice of measuring equipment, the correct selection of the point for receiving vibrations, and the correct analysis of the recorded signal [4,5]. Another issue is the designers’ awareness of the need to consider vibrational comfort. While many designers and researchers of building comfort focus on aspects such as thermal comfort, air quality, and acoustic insulation, few notice the problem of vibration. Vibrations are often an overlooked aspect of building design despite their significant impact on occupants’ well-being. Vibrations may not only be the source of disturbing material noise but can also be harmful in themselves [6,7]. These vibrations can originate from a variety of sources, both external and internal [8].

External vibrations are often transmitted through the ground and can come from numerous sources. Traffic is one of the most common sources of external vibrations. Heavy vehicles, such as trucks and buses, generate significant ground-borne vibrations that can travel through the soil and into building foundations. Railway lines, including subways and trams, are also substantial sources of ground vibrations. These vibrations can be particularly intense near railway crossings or along frequently used routes. Construction activities are another significant source of external vibrations. Pile driving, demolition, and the use of heavy machinery can create powerful vibrations that propagate through the ground and into nearby structures. Even after construction has ended, residual vibrations can persist due to ongoing use of the infrastructure, such as roads and bridges. Internal sources of vibrations are typically generated by machinery and equipment operating within the building. HVAC (heating, ventilation, and air conditioning) systems are a common source. Poorly insulated or improperly maintained HVAC systems can produce continuous vibrations that permeate through the building structure. Elevators, especially in high-rise buildings, can also generate significant vibrations. The movement of the elevator cars, coupled with mechanical operations, can create vibrations that are transmitted through the building’s framework. Another internal source of vibrations includes industrial equipment in buildings designed for manufacturing or laboratory use. Machines such as compressors, pumps, and motors can generate vibrations that affect both the structural integrity of the building and the comfort of its occupants.

Vibrations propagating through the ground into the building may not only be harmful to the building structure or cause its accelerated wear [9,10], but also affect the comfort of the residents [11,12]. Persistent vibrations can lead to material fatigue, resulting in cracks and structural weaknesses over time. This can compromise the integrity of the building, leading to costly repairs and maintenance. Additionally, vibrations can affect sensitive equipment and machinery, leading to operational inefficiencies or failures. The effects of vibrations on occupants are multifaceted and can range from mild annoyance to severe health issues. They can be annoying for residents and building users, causing disturbances that affect daily activities [13]. For instance, vibrations can disrupt sleep, making it difficult for residents to get restful sleep, leading to sleep disorders. Chronic sleep disruption can, in turn, lead to a range of health issues, including fatigue, decreased cognitive function, and mood disorders. Vibrations in the low-frequency range from 5 to 25 Hz are especially undesirable because the resonance frequencies of human internal organs fall within this range [14]. When the frequency of the vibrations matches the natural frequency of an organ, it can cause resonance, amplifying the effects of the vibrations on the body. This can lead to various physiological responses, such as increased heart rate, nausea, and a feeling of disorientation.

The human vestibular system, responsible for balance, is particularly sensitive to low-frequency vibrations. Exposure to such vibrations can lead to motion sickness-like symptoms, including dizziness and vertigo. Furthermore, prolonged exposure to low-frequency vibrations can affect the musculoskeletal system, leading to increased muscle tension and joint pain. In more severe cases, vibrations can lead to headaches and neurotic conditions [15,16]. Constant exposure to vibrations, especially in sensitive frequency ranges, can cause stress and anxiety, contributing to neurotic symptoms. Long-term exposure to such environmental stressors can have significant mental health implications, including heightened irritability, depression, and anxiety disorders [17]. Human perception of vibrations in buildings, despite numerous studies and standard records, is still not fully understood, mainly due to the subjective nature of vibration perception by various people. This is evidenced by the changes introduced over the last dozen years in the standard provisions of individual countries and in international ISO standards [18,19].

The issue of the impact of vibrations generated by means of transport has been the subject of many studies. The vast majority of them concern rail and metro transport in the context of the impact of vibrations on buildings and people as whole-body vibration (WBV). An example of a large research project is CargoVibes. The aim of this project completed in 2014 was to develop and assess measures to ensure acceptable levels of vibration for residents living in the vicinity of freight railway lines in order to facilitate the extension of freight traffic on railways [20]. In this project, the human response to the existing evaluation criteria was measured and new mitigation measures were designed. An important outcome of the project was the establishment of a guideline on the evaluation of adverse effects of vibration, which include exposure–response relationships for annoyance and some general conclusions on the influence on sleep [21]. The CargoVibes project focused on vibrations generated by freight trains. This article presents selected research results on the impact of passenger rail transport, including trams, in dense urban development.

The main purpose of this article is to demonstrate the correct measurement and interpretation methodology of the impact of vibrations on people who passively perceive these stimuli in buildings. The article also presents a historical outline of vibrational comfort to illustrate how this topic has evolved. Additionally, new trends that have recently emerged in this field are highlighted, and it is proposed to consider vibration comfort as a critical factor in building design and evaluation. Frequent errors in the assessment of vibrations’ impact on building occupants often arise from misunderstandings of existing standards and guidelines. The paper highlights the need for more uniform guidelines to ensure accurate and reliable results across different regions.

Transport-induced vibration has been identified as the dominant source of vibration in urban areas. These vibrations significantly impact both the structural integrity of buildings and the comfort of their occupants.

The main novelties presented in the paper are as follows:

• This research underscores the necessity of accurate measurement methodologies, including the appropriate selection of measurement points and the use of suitable equipment. Proper sensor placement and data collection are critical for obtaining reliable vibration data. Incorrect methodologies can lead to significant errors in assessing the impact of vibrations.
• Different evaluation methods, such as the Root Mean Square (RMS) and Vibration Dose Value (VDV) methods, are compared in the paper. Each method has its advantages and applications. The VDV, for example, is more sensitive to peak values and may be more effective in certain contexts, providing a more nuanced understanding of vibration impacts.
• This study examines the role of different weighting functions in vibration analysis. It finds significant differences in results depending on the weighting function used. Combined functions like Wm tend to provide substantially lower values compared to others. This finding highlights the importance of choosing the correct weighting function for accurate analysis.

By addressing these key areas, the paper aims to enhance the accuracy and reliability of vibration assessments and promote better standards and practices in structural engineering and urban planning.

2. The Measurement Methodology and Evaluation of Human Exposure to Vibration in Buildings

The assessment of the impact of vibrations on people in buildings is a crucial element in designing and managing vibrational comfort and is an important criterion when analysing vehicle–track–ground coupling dynamics and designing solutions to minimise railway-induced ground vibration. The methodology includes various stages, from selecting measurement points, through signal registration, to data analysis and result interpretation.

2.1. Measurement Point Selection

Locating the measurement points is a critical stage that affects the accuracy of the results. Standards such as [18,22,23] define different approaches to selecting measurement points depending on the vibration perception. Also, [18] recommends placing measurement points at locations where vibrations enter the human body. For external vibrations like ground-transmitted vibrations, the measurement point should be in the central part of the floor, within one-third of the length/width acc. [22]. For internal vibrations, the measurement points should be located according to the modal analysis of the structure. According to [23], the measurement point should be placed in the center of the floor in the room closest to the vibration source.

Therefore, if whole-body vibrations are analyzed, the more appropriate recommendations are those included in [18]. In the case of building occupants who perceive vibrations passively (no influence on the source of vibrations), then the appropriate ones are the recommendations included in [22,23]. These approaches differ in the method of locating the measurement point, which is shown in Figure 1.

The other problem in addition to the location of the measurement point is the equipment. Accelerometers are mostly used, but the problem is how to connect the sensor to the floor. Ref. [19] provides a description of a measurement disk that should be used during measurements of human perception of vibrations in buildings. The key specifications of this disk are outlined below:

• The measurement disk should have a significant mass to ensure stability and accurate transmission of vibrations. It is recommended that the disk should weigh at least 30 kg. This mass is substantial enough to mimic the weight of an average human being, thereby providing a realistic measure of how vibrations would affect a person in the same position.
• The diameter of the disk should be around 30 cm. This size ensures that the disk covers a sufficient area to interact with the vibration field effectively, capturing an accurate representation of the vibrations experienced in the building structure.
• The disk should be made of a material that does not significantly alter the characteristics of the transmitted vibrations. Typically, metals or composite materials that are dense and have minimal internal damping are used. The choice of material ensures that the disk does not absorb or dampen the vibrations excessively, which would otherwise lead to inaccurate readings.
• The disk is typically flat and circular to ensure uniform contact with the surface on which it is placed. This design minimizes the influence of the disk’s shape on the vibration measurements and ensures that the disk’s weight is evenly distributed.

An example measurement disk is shown in Figure 2.

2.2. Signal Recording and Analysis

In the context of assessing the impact of vibrations on people in buildings, signal recording and analysis are critical components of the methodology. This process involves capturing vibration data acquisition, processing it correctly, and interpreting it effectively to evaluate how these vibrations affect building occupants.

The selection of appropriate measurement equipment is fundamental to obtaining accurate vibration data. Key components include the following:

• Accelerometers: These devices measure the acceleration of vibrations and are essential for capturing the dynamic responses of the building structure. The accelerometers should be capable of measuring in the frequency range from 1 to 120 Hz and in three orthogonal directions (x, y, and z).
• Data Acquisition Systems: These systems record the data collected by the accelerometers. They must have high resolution and proper sampling rates to ensure the accuracy of the captured data. According to the Nyquist criterion, the sampling frequency should be at least twice the highest frequency of interest. For a cutoff frequency of 120 Hz, a minimum sampling frequency of 240 Hz is required, though 300 Hz is recommended for practical applications.

A separate problem is the determination of the duration of the vibrations. This aspect is crucial because the duration directly influences the accuracy and reliability of the vibration analysis especially in context of human perception of vibration. In this kind of analysis, the root-mean-squared value is taken into account, unlike during the analysis of vibrational influence on building structure in which the maximum value is used.

Various standards provide guidelines on how to measure and define this duration to ensure that the data collected are both representative and statistically valid. Standard [23] assumes that the duration of vibrations is determined by the interval during which the value of vibration acceleration amplitudes does not fall below 0.2 of the maximum amplitude in the recorded signal (Figure 3). This method focuses on the significant part of the vibration signal where the most relevant data are found. By disregarding periods of very low amplitude, the analysis can concentrate on the more impactful parts of the vibration signal. The ISO standard [18], which is primarily used to measure general nature vibrations, requires a recording time of at least 30 min. This extended duration helps in capturing a wide range of vibration patterns and ensures that the data collected is comprehensive. According to the [22] standard, the recorded signal should be sufficient to ensure rational statistical accuracy. Although this definition is broad and somewhat imprecise, it underscores the importance of collecting data that can support meaningful statistical analysis. The standard particularly emphasizes the use of the RMS (root mean square) method. In the German standard [24], the analysis is performed in cycles lasting 30 s. The data from these cycles are then averaged to provide a comprehensive overview of the vibrations. This method is particularly effective in capturing short-term fluctuations and trends.

The main problem in signal analysis is the choice of evaluation method. The most well-known method, which is called the basic method (acc. [18]), is the root-mean-squared method (RMS). The RMS method, already introduced in the first edition of the ISO standard, has its physical interpretation, which is the vibration energy. The effective value, a_RMS, of the vibration acceleration, a (t), is given by the following formula:

$$a_{RMS}=\sqrt{{\displaystyle \frac{1}{T}}{\int }_0^T{a}^2\left(t\right)dt}$$

(1)

where T is the duration time [s].

In the case of non-periodic vibrations, in measurement practice, the root mean square value of vibration accelerations in 1/3 octave bands is used to assess the impact of vibrations on people in buildings. The vibration acceleration signal is filtered in 1/3 octave bands and the root mean square value of vibration accelerations is determined for each center frequency. This approach allows for the presentation of the root mean square value in the frequency domain. This provides information not only about the exceedance of vibration perception threshold values, but also about the frequency band in which this exceedance occurred. In the assessment of the impact of vibrations on people staying in buildings, carried out in accordance with the RMS method, the following assessment factors are taken into account: the purpose of the room, the time of day when the vibrations occur, the nature and repeatability as well as the direction of the vibrations and the position of the human body receiving the vibrations in the room. The values of the n coefficient (vibration perception threshold multiplier [23]) relating to the purpose of the room, time of day and the nature of vibrations are shown in Figure 4.

In the revised Polish standard [23], a new index has been introduced to express the assessment result of the impact of vibrations on people in buildings. This index, called the Human Perception of Vibration Index (HPVI), in relation to vibrations transmitted to humans in the “z” direction, can be calculated using the following formula:

$$\mathrm{H}\mathrm{P}\mathrm{V}\mathrm{I}=max\left({\displaystyle \frac{a_{RMS}}{a_{zRMS}}}\right)$$

(2)

where a_RMS is the root mean square value of vibration accelerations obtained from the analysis and a_zRMS is the root mean square value of vibration accelerations equal to the vibration perceptibility threshold for humans in the “z” direction in the same frequency band in which a_RMS was determined.

The second common method of evaluation is the vibration dose value VDV [23]. This method is primarily used for general and local vibrations that actively affect humans. Its sensitivity to the occurrence of peak values in the recorded signal arises from the formula used to calculate it, where vibration acceleration is raised to the fourth power, as shown below:

$$\mathrm{V}\mathrm{D}\mathrm{V}={\left[{\int }_0^T{a}_w^4\left(t\right)dt\right]}^{{\displaystyle \frac{1}{4}}}$$

(3)

The transformation of the signal using Equation (3) results in the vibration dose value (VDV) being expressed in units of m/s^1.75. The procedure for determining the VDV is similar in essence to the procedure used in the RMS method.

Table 1. The values of VDV for assessing the probability of complaints from people in buildings.

Purpose of the Room	Daytime	Low Probability of Adverse Comments	High Probability of Adverse Comments
Hospitals, operating theatres, precision laboratories	Day and night	0.1	0.2
Residential	Day	0.2	0.4
	Night	0.13	0.26
Office	Day and night	0.4	0.8
Workshop	Day and night	0.8	1.6

presents threshold values for the probability of complaint occurrence according to the appendix of the Polish standard [23].

3. Weighting Function Problem

The first problem with signal analysis appears at the very beginning, where after applying an appropriate correction filter (values available in the standards [18] or [22]), the weight values corresponding to the directions of vibrations should be entered. According to the standard [19], weight values assigned to the directions of vibration reception by humans should be used. The standard [18] makes it possible to use the so-called combined weighting function. In different standards, there are also differences in weight values relating to the same directions. This is evident when comparing information from the two standards that first introduced the VDV method, i.e., British [19] and ISO [18]. In the provisions of both standards, there are differences in weight values in the vertical direction, and in the horizontal directions, these differences are negligible. The problem appears when comparing the combined function W_m acc. [19] with functions in the z-direction (W_k [18] or W_b [22]), which in most cases decides the results of evaluation of human perception of vibration in buildings. In Figure 5, the values of the weight functions in the “z” directions with the values of such a function in the combined direction W_m are shown. It can be seen that while the values of the weight functions in the direction “z” do not differ significantly from each other, the value of the combined weighting function W_m is significantly different from them.

This problem was examined on an example building located in Krakow at Mogilska St. Measurements were made on typical masonry building built before World War II (see Figure 6).

The building is subjected to the following two sources of transport excitation:

• Car and heavy truck passages on the road located 1 m from the building;
• Tram passages on the track located 10 m from the building.

In this case, the VDV evaluation method was analyzed. VDVs for vibration episodes using three different weighting functions were determined (

Table 2. The VDVs according to different weighting functions.

No.	Excitation Source	VDVtn (Wb acc. BS [18])	VDVtn (Wk acc. ISO [16])	VDVtn (Wm acc. ISO [17])
1	Tram 105 N (2 wag.)	0.0788	0.0707	0.0346
2	Tram 105 N (2 wag.)	0.1143	0.1083	0.0584
3	Tourist bus	0.2172	0.2705	0.1567
4	Tram EU8N (further track)	0.0454	0.0427	0.0217
5	Tram 105 N (3 wag.)	0.0697	0.0644	0.0321
6	Tram 105 N (2 wag.)	0.0747	0.0684	0.0375
7	Tram EU8N (further track)	0.0416	0.0382	0.0202
8	Tram GT8S	0.0458	0.0425	0.0219
9	Tram EU8N (further track)	0.3187	0.3183	0.1726
10	Heavy truck	0.0756	0.0731	0.0392
11	Tram 105 N (3 wag.)	0.1227	0.1186	0.0609
12	Heavy truck	0.1015	0.1008	0.0574
13	Tram E1-C3	0.0581	0.0541	0.0276
14	Tram 105 N (3 wag.)	0.0886	0.0804	0.0404
15	Tram 105 N (3 wag.)	0.0735	0.0682	0.0390
16	Tram GT6	0.0588	0.0551	0.0299
17	Tram 105 N (3 wag.)	0.0768	0.0708	0.0348
18	Heavy truck	0.2049	0.2017	0.1050
19	Heavy truck	0.3375	0.3446	0.1745
20	Tram 105 N (3 wag.)	0.0638	0.0599	0.0316
21	Heavy truck	0.2349	0.2327	0.1251
22	Heavy truck	0.2966	0.2955	0.1575
23	Heavy truck	0.0867	0.0857	0.0469
24	Tram EU8N (further track)	0.0392	0.0370	0.0199
25	Tram GT8S (closer track) and Tram 105 N 3 wag. (further track)	0.0914	0.0867	0.0474

).

The results listed in Table 2 refer to single event values. To evaluate the day/night exposure, VDV_day or VDV_night should be calculated using the following equation:

$${\mathrm{V}\mathrm{D}\mathrm{V}}_{\mathrm{d}\mathrm{a}\mathrm{y}/\mathrm{n}\mathrm{i}\mathrm{g}\mathrm{h}\mathrm{t}}=({{\displaystyle {\sum }_{k=1}^{k=N}}{\mathrm{V}\mathrm{D}\mathrm{V}}^4)}^{0.25}$$

(4)

where k is a single event and N is the number of events during the day/night.

Daily and night exposure to vibrations were calculated as follows:

• Using W_b acc. [18]:

VDV_b, 40′ = 0.444;

VDV_b, day = 0.983–adverse comments probable;

VDV_b, night = 0.695 (half intensity of tram and cars passages)–adverse comments probable.

• Using W_k acc. [16]:

VDV_k, 40′ = 0.454;

VDV_k, day = 1.005–adverse comments probable;

VDV_k, night = 0.711 (half intensity of tram and cars passages)–adverse comments probable.

• Using combined W_m acc. [17]:

VDV_m, 40′ = 0.243;

VDV_m, day = 0.538–adverse comments possible;

VDV_m, night = 0.381 (half intensity of tram and cars passages)–adverse comments possible.

The comparison of daily and night exposure to vibrations according to different documents is presented in

Table 3. Daily and night exposure to vibrations.

Exposure to Vibrations	Wb acc. BS [18]	Wk acc. ISO [16]	Wm acc. ISO [17]
VDV, 40′	0.444	0.454	0.243
VDV, day	0.983	1.005	0.538
VDV, night	0.695	0.711	0.381

.

Conclusions from the measurements are as follows:

Assessment of human exposure to vibrations in buildings made using VDV analysis should take into account the signal analysis weighting function W_b. It is possible to take the weighting function W_k into consideration because the differences between W_b and W_k are small and in the range of 5 and 25 Hz values of both of these functions, they are the same. Using W_m, smaller values are obtained than using W_b or W_k. Heavy trucks and buses generates higher VDVs than tram passages. In this case, it could be caused because by the differences in distances, i.e., tram to building (10 m) and road to building (1 m).

4. Measurement Point Location Problems

The ideal structural center of the floor is often impossible to find. Is the proper location of the sensor so important? This case was examined on a testing building located on a campus of Cracow University of Technology. It is a reinforced concrete building with an irregular structure (see Figure 7).

The measurements were taken for a period of 24 h. Two measurement points were taken into consideration because of difficulties to locate the center point of the floor. The locations of measurement points with accelerometers used to estimate the human vibration perceptivity ratio are presented in Figure 8.

There was passive excitation from traffic on the adjacent street.

In this case, the RMS method values expressed as HPVI ratios and VDVs were used for analysis. The results of monitoring are shown in Figure 9 and Figure 10.

The results obtained from two evaluation methods differ from each other. The VDV seems to underestimate the impact of vibrations on people in buildings. However, it should be noted that single events were compared, whereas the VDV should be considered in the context of daily/nightly exposure.

The differences between measurement results obtained from different points are significant, but the results of the whole analysis are similar. The location of measurement points has a greater influence on the analysis results. It is recommended to place the measurement point in the structural center of the floor.

5. The Choice of Evaluation Method

Requirements in national and international standards differ from each other. In the literature on the subject, one can find several attempts to link the value of the crest factor with the selection of evaluation method, as shown below:

$$CF={\displaystyle \frac{{\left|a_w\right|}_{PEAK}}{a_{wRMS}}}$$

(5)

where ${\left|a_w\right|}_{PEAK}$ is the maximum peak value in the recorded signal and a_wRMS is the RMS value calculated based on the weighted waveform.

In the Polish standard [23], the scope of applicability was dictated precisely by the value of the crest factor. According to the standard, the analyzed vibration waveforms must have a crest factor value less than 9 to use the RMS method. Standard [23] does not specify what happens if the crest factor has higher values. A very interesting reference to the crest factor was introduced in the Australian standard [25]. It provides ranges within which, depending on the crest factor, different evaluation methods should be used, as shown below:

• If CF < 6, the RMS method should be used;
• If CF ≥ 6 and CF ≤ 9, both RMS and VDV methods should be used, with the final evaluation result determined by the more unfavorable outcome;
• If CF > 9, the VDV method should be used.

This approach is not found in any other standards or recommendations. Generally, in a given country, the use of one evaluation method is recommended, for example, in Poland, it is the RMS method [23], and in the United Kingdom, it is the VDV method [22].

Measurements on the real structure were made to examine if the evaluations using the RMS and VDV method differ from each other. The analyzed building is located in Warsaw on 15 Targowa Street. It is a seven-story residential building constructed using traditional masonry technology (Figure 11). The building was erected before World War II. It is situated 5 m from the edge of the roadway and approximately 25 m from the tram line (distance measured from the rail head) and is directly above a metro tunnel.

The measurement point in the “Z” direction was located in the middle of the ceiling span in a room on the fifth floor on the side facing the roadway.

The same events analyzed using the RMS method were also subjected to analysis using the VDV method. The duration of the events, which varied from 14 to 24 s, was taken into account. The results of the VDV method analysis, along with a summary of the HPVI indicators, are shown in

Table 4. VDVs for individual events and the maximum HPVI values for these events.

No.	Vehicle Passage	Duration Time [s]	VDV [m/s1.75]	HPVI [–]
1	Tram	14	0.39	4.23
2	Tram	14	0.18	1.88
3	Bus	14	0.23	2.21
4	Tram	14	0.14	1.26
5	Tram	14	0.22	2.84
6	Tram	14	0.60	7.84
7	Heavy truck	14	0.32	4.62
8	Tram	14	0.40	5.39
9	Tram	16	0.24	2.74
10	Tram	14	0.41	7.09
11	Tram	16	0.52	6.04
12	Tram	14	0.13	1.13
13	Tram	16	0.16	1.35
14	Tram	16	0.30	3.98
15	Tram	14	0.35	3.05
16	Tram	14	0.21	2.57
17	Tram	14	0.28	3.83
18	Tram	14	0.23	2.93
19	Metro	18	0.11	0.55
20	Metro	18	0.10	0.37
21	Metro	24	0.15	1.44
22	Metro	18	0.10	0.38
23	Metro	18	0.10	0.49
24	Metro	18	0.10	0.43
25	Metro	18	0.09	0.41
26	Metro	18	0.10	0.40
27	Metro	18	0.16	0.98
28	Metro	18	0.12	0.59

.

The colors presented in Table 4 indicate the exceedance of the respective threshold lines, i.e., if VDV < 0.2, there are no complaints (white color), if 0.2 < VDV < 0.4, there is a low probability of complaints (yellow color), and if VDV > 0.4, there is a possible occurrence of complaints (red color). For the HPVI, yellow-marked values mean that the perception threshold of vibration was exceeded, while a red color means that even the comfort level was exceeded.

Threshold exceedances in the case of the VDV method analysis occurred for 14 events, with 4 of these exceedances corresponding to potential complaints regarding comfort. The assessment of the impact of different transportation sources on the VDV analysis results indicates that only tram passages caused exceedances of the threshold values for the probability of complaints. At the building on 15 Targowa Street, 19 events were recorded where the threshold for human perceptibility of vibrations, according to HPVI values, was exceeded, accounting for 68% of all recorded events. The ceiling of the room where the measurements were conducted proved to be more sensitive to vibrations generated by surface transport vehicles, mainly trams (see Table 4). In 100% of the recorded tram passages, the threshold for the perceptibility of vibrations was exceeded, and in six events, the requirements for ensuring the necessary comfort for people in this room during the day were violated (35%). Only one event generated by metro train passages in the tunnel caused an exceedance of the threshold for the perceptibility of vibrations by people.

In this case, it seems that the HPVI is more sensitive than VDVs, but it should be noticed that in Table 4, single events were compared to each other while the VDV is better to calculate the day/night exposure, although the standards are not consistent in this regard.

6. Discussion

Table 5. Comparison of various problems in the analyzed buildings.

Building	Investigated Problem	Conclusion	Recommendation
A	Weighting function	Assessment of human exposure to vibrations in buildings made using VDV analysis should take into signal analysis weighting function Wb.	It is possible to take weighting function Wk into consideration because the differences between Wb and Wk are small and in the range of 5 and 25 Hz values of both of these functions, they are the same.
B	Measurement point location	The differences between measurement results obtained from different points are significant, but the results of the whole analysis are similar. Location of measurement point has the greatest influence on analysis results.	It is recommended to place the measurement point in the structural center of the floor.
C	The choice of evaluation method	HPVI is more sensitive than VDV, but it should be noticed that in this case, single events were compared to each other while the VDV is better to calculate the day/night exposure, although the standards are not consistent in this regard	RMS method is preferable for general assessments, whereas the VDV is better for scenarios with significant peak vibrations.

presents the problems analyzed in the work, along with the most important conclusions and recommendations of the authors based on the conducted research and analyses. It should be emphasized that the authors had a large database of measurement results from various transport excitations. The next section presents discussions of the obtained results and conclusions with research conducted by other authors.

While comprehensive studies on the impact of transportation vibrations on people in buildings who passively receive these vibrations are limited, articles focusing on individual vehicle types still provide valuable comparisons. For example, in the article [26], the effect of heavy goods vehicles (HGVs) is examined, demonstrating that different vehicle types have varying impacts, especially railway vehicles (trams, metro). This is similar to discussions on metro trains, buses, and trucks. The study presented in [27] investigates how tram speeds affect residents’ perception of vibrations in nearby residential buildings, revealing that tram speed does not directly correlate with vibrational comfort. Our analyses similarly show that the travel time of trams does not straightforwardly relate to VDVs or HPVI values, indicating a complex relationship between tram speed and vibrational comfort in buildings close to tram lines. This underscores the need to consider multiple factors beyond just speed to minimize vibration impacts on residents.

A particularly interesting study by [28] explores the influence of tram traffic-induced vibrations on buildings damaged by the Zagreb 2020 earthquake. It examines various factors, including tram type, velocity, and proximity to buildings, and how these contribute to the propagation of existing cracks or new damage in earthquake-affected structures. Both our analysis and this document highlight the significant role of vehicle type in influencing vibration levels. Different vehicles (buses, metro trains, trams) have varying impacts on HPVI and VDVs, with specific tram models contributing differently to vibration levels and potential building damage.

Resident complaints about metro train passages often prompt studies, as seen in the article by [29], which focuses on diagnosing noise and vibrations from metro trains and designing buildings near metro lines to mitigate these issues.

In [30], a comprehensive study on traffic-induced vibrations in Istanbul, one of the world’s most populous and traffic-congested cities, the authors examine the effects on residential buildings and occupants. This study includes surveys of occupant perceptions, ground vibration measurements, and numerical modeling of buildings’ responses to these vibrations. Similar to our findings, Erkal’s study emphasizes the significant role of vehicle type, particularly trains, in influencing vibration levels and resident perceptions. This aligns with our results on the varying impacts of different vehicle types on HPVI and VDV measurements.

7. Conclusions

The conducted research and analyses of the obtained results in relation to the estimators of vibration perception in buildings show clear differences in the assessment of the impact of vibrations generated by vehicle traffic, especially for the dominant railway-induced ground vibration.

The main findings presented in the paper are as follows:

• Frequent errors in the assessment and diagnosis of vibrations’ impact on building occupants are a significant concern. These mistakes often arise from misunderstandings of existing standards and guidelines, incorrect measurement practices, and inadequate data interpretation. Such errors lead to flawed diagnostic studies and unreliable conclusions, which can affect building design and occupant comfort.
• National guidelines across Europe show considerable variability, despite many being based on ISO standards. This inconsistency poses a challenge to standardizing vibration assessment practices. The paper highlights the need for more uniform guidelines to ensure accurate and reliable results across different regions.
• Vehicle traffic, particularly heavy trucks and rail vehicles, is identified as the dominant source of vibrations in urban areas. These vibrations significantly impact both the structural integrity of buildings and the comfort of their occupants. Understanding these sources is crucial for developing effective mitigation strategies.

The study emphasizes the importance of proper measurement point selection, highlighting differences in guidelines between various standards. Accurate placement of measurement points is crucial for reliable data. The use of appropriate equipment, particularly accelerometers with the correct sensitivity and frequency range, is essential for capturing accurate vibration data. The study suggests using a measurement disk to ensure stability and accurate transmission of vibrations. However, due to the empirical approach related to vibration measurements, it is necessary to constantly expand the measurement database with new vibration sources and other locations. The authors of the study had no knowledge about the technical condition of the vehicles generating vibrations, and this may also affect the obtained results.

The root mean square (RMS) method and vibration dose value (VDV) method are both analyzed. The study finds that while the RMS provides a measure of vibration energy, the VDV is more sensitive to peak values, making it suitable for assessing potential discomfort. The study reveals that tram passages generally cause higher VDVs compared to other vehicles, indicating a greater potential for discomfort. However, the sensitivity of the HPVI (Human Perception of Vibration Index) suggests it may be more effective in certain contexts.

Different types of vehicles have varying impacts on vibration levels. Heavy goods vehicles (HGVs) and trams, in particular, are significant sources of vibrations that can affect human comfort and building integrity. The study highlights the need for tailored approaches depending on the vehicle type, as each has unique vibrational characteristics.

The study underscores the necessity of incorporating vibrational comfort into building design and planning. It recommends considering vehicle type, operational dynamics, and urban infrastructure to mitigate the adverse effects of vibrations. Designers and engineers should follow the guidelines for measurement and evaluation to ensure accurate assessments and effective mitigation strategies. It should be emphasized that it is necessary to design appropriate vibration-isolating solutions at the source of vibrations, such as vibration-isolating mats [31], elastic rail supports or underground barriers [32] in the case of rail transport (metro, railway and trams). The technical condition of rail and road roads may also affect the level of vibrations; therefore, maintaining the proper technical condition of rail and road roads is the responsibility of the manager.

The study highlights the crucial role of weighting functions in the accurate evaluation of human exposure to vibrations. Different weighting functions can significantly impact the analysis results. Weighting functions such as W_b, W_k, and W_m offer different sensitivities to vibration frequencies. The study finds that while W_b and W_k functions provide similar results in the frequency range of 5 to 25 Hz, the combined W_m function yields substantially lower values. The choice of weighting function directly influences the calculated VDVs. Using the W_m function results in approximately half the VDVs compared to W_b and W_k functions.

Measurement points should be located according to the relevant standards, which may vary. For external vibrations, measurement points should typically be in the central part of the floor within one-third of the length/width, while for internal vibrations, modal analysis of the structure should guide placement. It is recommended to place the measurement point in the structural center of the floor whenever possible to minimize discrepancies and ensure consistency in data collection.

The study compares the RMS (root mean square) and VDV (vibration dose value) methods, noting that each has specific applications and advantages. The RMS is beneficial for assessing continuous vibration exposure by providing a measure of vibration energy, while the VDV is more sensitive to peak values, making it suitable for evaluating potential discomfort and complaints. The selection of the evaluation method should be based on the nature of the vibration exposure and the specific requirements of the study. For instance, the RMS is preferable for general assessments, whereas the VDV is better for scenarios with significant peak vibrations. The study also highlights the need to consider the crest factor when choosing the evaluation method, as different standards provide specific guidelines based on this value.