Scatterplot fundamental of rail traffic vibrations on no. of data
The assessment of railway-induced GBV is closely tied to established threshold limits, which determine the extent to which vibrations may cause annoyance or discomfort in residential environments. Figure 13 presents a scatterplot of the recorded vibration data in comparison with the permissible limits outlined by the DOE guidelines. For residential areas, the DOE specifies maximum allowable vibration levels of 0.8-1.6 mm/s during the daytime and 0.4 mm/s at night, thresholds that are consistent with ISO and BS 6472 standards. These benchmarks provide a basis for evaluating whether railway operations exceed acceptable levels of vibration exposure.
The scatterplot in Fig. 13 consolidates all data collected from the study sites, regardless of train type, speed, or distance from the receiver. Analysis of the results shows that the majority of recorded vibration events exceeded the DOE guideline limits for human annoyance, raising concerns about the implications of long-term railway operations for nearby residents. This observation is reinforced by international standards, which also highlight 0.8 mm/s as a critical threshold beyond which vibrations are likely to cause annoyance. Comparable exceedances were reported by Yuan et al., further validating the significance of these findings.
While broadly aligned with European standards such as those adopted in the Netherlands (0.8 mm/s) and Germany (0.4-1.6 mm/s), the DOE thresholds are stricter than those applied by the United States FTA. The FTA sets the nighttime residential limit at 0.254 mm/s, with more lenient values for commercial and industrial zones. Such variations reflect regional considerations, including differences in geotechnical conditions, population density, and cultural expectations regarding environmental comfort.
The comparative analysis of train types highlights significant differences in vibration behaviour. High-speed trains exhibited the widest range of PPV values, with a considerable number of measurements surpassing residential thresholds. This outcome indicates that the higher operating speeds of high-speed trains generate vibrations strong enough to intrude upon residential comfort, leading to a heightened potential for human annoyance. In contrast, LRT systems generally produced lower PPV values, with most measurements remaining below the 0.8 mm/s limit, suggesting that LRT operations are comparatively less disruptive to nearby communities. Commuter trains displayed a more variable pattern, with several readings exceeding the residential threshold. This highlights the potential for commuter services, particularly in densely populated urban corridors, to generate ground vibrations capable of affecting household comfort and daily activities.
These findings support previous research on railway-induced GBV, which consistently demonstrates that vibration intensity is not only influenced by proximity to the track but also strongly dependent on train type and operational characteristics.
The scatterplot analysis illustrates that a substantial proportion of vibration levels recorded at the study sites exceeded the DOE thresholds for residential comfort. High-speed trains, due to their greater velocities, were the primary contributors to exceedances, while LRT services showed minimal disturbance potential. Commuter trains produced intermediate outcomes, with several cases surpassing the recommended limits. Collectively, these results emphasise the importance of incorporating train type and operating conditions into GBV management strategies. Establishing context specific thresholds, supported by robust monitoring and predictive modelling, remains essential for protecting residential well-being in areas adjacent to railway corridors.
Train speed is one of the most influential operational parameters affecting the generation and propagation of GBVs. As velocity increases, the dynamic interaction between wheels and rails intensifies, leading to higher excitation frequencies and greater energy transmission into the surrounding soil. Understanding this relationship is essential for assessing compliance with regulatory thresholds, mitigating annoyance in residential areas, and ensuring the long-term safety of infrastructure. Figure 14 presents a scatterplot of the PPV versus train speed.
The scatterplot reveals a consistent positive correlation between train speed and PPV, with vibration levels rising steadily as velocity increases. High-speed trains exhibit the steepest gradient, frequently exceeding the 0.8 mm/s threshold recommended for residential areas. At lower operational speeds (< 60 km/h), PPV values remain moderate across all train types, but beyond this threshold, vibration levels escalate rapidly particularly for high-speed trains operating above 120 km/h. This behaviour is attributed to intensified dynamic loading effects, as higher velocities increase the frequency and magnitude of wheel-rail interactions, thereby transmitting greater vibrational energy into the ground.
Comparable amplification effects have been documented in high-speed rail systems worldwide, with studies confirming strong correlations between PPV and velocity increments. Connoly et al. further demonstrated that resonance effects can occur when the frequency of train-induced vibrations aligns with the Rayleigh wave velocity of the local soil profile, resulting in marked amplification at certain speed ranges.
Variability in vibration response is also influenced by train type and soil-track conditions. At moderate speeds (40-80 km/h), commuter and light rapid train services display wider dispersion of PPV values, reflecting differences in axle loads, track structures, and soil conditions. Lazi et al. highlighted that increases in commuter train speed are strongly associated with higher GBV levels. Beyond 120 km/h, vibration wavelengths shorten and tend to remain confined within near-surface soil layers. This results in greater amplification for high-speed trains while producing less pronounced increases for lighter train types, such as LRT systems.
These observations underscore the critical role of train speed in vibration propagation mechanisms. Track segments where trains accelerate, decelerate, or pass through areas with soil resonance potential are especially vulnerable to exceedances of annoyance thresholds. Such effects are most concerning near residential areas, railway stations, or gradient transitions, where prolonged exposure intensifies human perception of vibration. Zhang et al. similarly reported that higher speeds exacerbate dynamic wheel-rail interactions, axle loading, and excitation frequencies, thereby increasing the severity of vibration propagation.
The analysis confirms that train velocity is a dominant determinant of railway-induced GBVs, with exceedances of perceptibility and annoyance thresholds particularly associated with high-speed services. While lower speeds produce moderate vibration levels, velocities above 120 km/h significantly amplify PPV, posing challenges for nearby residential environments. These findings highlight the direct causal relationship between train speed and ground vibration severity, reinforcing the need for speed management strategies as a practical mitigation measure. Operational controls, combined with consideration of soil resonance characteristics, can provide an effective approach for minimising vibration impacts in sensitive zones along railway corridors.
GBVs generated by railway operations are strongly influenced by the proximity of receivers to the vibration source and, to a lesser extent, by train configuration. This section examines the effects of distance and coach length on vibration levels, providing insights into the attenuation mechanisms of vibration propagation and the potential implications for residential exposure. Figures 15 and 16 illustrate the relationships between PPV and distance, and PPV and coach length, respectively.
The scatterplot in Fig. 15 presents the relationship between PPV and source-receiver distance, covering a range of 4-13 m. A clear attenuation trend is evident, with PPV values decreasing progressively as distance increases. These findings underscore proximity as the dominant factor in determining vibration exposure and subsequent annoyance among residents near railway alignments.
The scatterplot in Fig. 15 presents the relationship between PPV and source-receiver distance, covering a range of 4-13 m. A clear attenuation trend is evident, with PPV values decreasing progressively as distance increases. High-speed trains consistently generated higher PPV values than commuter and light rapid train systems, particularly at short distances (< 7 m), where frequent exceedances above the perceptibility threshold of 0.8 mm/s were recorded. Commuter trains also exhibited moderate exceedances in the near field, while light rapid train systems largely maintained vibration levels below the threshold across all distances. These findings underscore proximity as the dominant factor in determining vibration exposure and subsequent annoyance among residents near railway alignments.
The relationship between distance and vibration attenuation aligns with findings by Xiao et al. and Connolly et al., who reported that vertical vibration levels diminish as distance from the track increases. This attenuation is primarily governed by two mechanisms: geometric spreading, whereby vibrational energy disperses over a larger area, and material damping, where soil media absorb and dissipate vibrational energy. Consequently, the further vibrations propagate, the more their intensity decreases, reflecting the combined effects of energy dispersion and soil absorption. These outcomes are consistent with established vibration propagation theory, as also supported by recent research.
Figure 16 illustrates the relationship between train coach length and PPV for different train types. The scatterplot demonstrates only a weak correlation, indicating that PPV values remain largely unaffected by increases in coach length. High-speed trains consistently exhibited higher PPV values regardless of train length, often exceeding the 0.8 mm/s threshold, while commuter and LRT services showed lower amplitudes with minimal variation across differing train lengths. These findings suggest that coach length is not a primary determinant of vibration intensity, with velocity, axle configuration, and bogie spacing exerting greater influence.
Nevertheless, the influence of coach length should not be entirely disregarded. Kumar et al. provided detailed insights into the dynamic behaviour of metro coaches, showing how speed, acceleration, and track curvature shape vibration characteristics. These factors are directly relevant to human annoyance, since both amplitude and exposure duration contribute to perceived severity. In high-speed rail operations, longer train sets combined with elevated speeds can amplify both the duration and magnitude of vibration exposure, thereby intensifying annoyance levels within nearby residential communities.
The analysis highlights two important aspects of vibration behaviour. First, distance from the source is the most critical factor in reducing vibration levels, with attenuation occurring through geometric spreading and soil damping. High-speed trains, however, generate significantly higher PPV values at close range, posing the greatest risk of annoyance for residents. Second, while coach length demonstrates only a marginal effect on vibration magnitude, its contribution to prolonged exposure becomes relevant in high-speed rail contexts where longer train formations operate at elevated velocities. Collectively, these findings reinforce the need for mitigation strategies that prioritise track-side distance buffers and consider train configuration in managing GBV impacts in sensitive residential environments.
Ballast and embankment configurations are fundamental elements of railway track systems, serving to distribute loads, provide structural stability, and reduce the transmission of vibration. Their role in mitigating GBV, however, remains the subject of ongoing research, particularly under the demanding conditions of high-speed rail operations. Figure 17a and b present scatterplots showing the relationship between PPV and both ballast depth and embankment height, providing insights into their influence on vibration levels.
The scatterplot in Fig. 17a demonstrates that variations in ballast thickness (0.0-1.2 m) exert only a marginal influence on PPV levels. High-speed trains consistently generated PPV values exceeding the 0.8 mm/s threshold regardless of ballast depth, indicating that train dynamics in which particularly velocity and axle load, are the dominant factors governing vibration behaviour rather than ballast configuration. In contrast, commuter and LRT trains recorded substantially lower PPV values, with measurements remaining within perceptibility thresholds across all ballast depths. Khan and Dasaka observed that PPV is greatest in ballast layers directly beneath wheel loads, with high-speed trains predominantly influencing ballast while low-speed trains affect the subgrade. Vibrations attenuate rapidly with depth but more gradually along the ground surface. Similarly, Kolos and Konon reported that ballast vibration amplitudes increase almost linearly with train speed up to 190 km/h, reaching 420-450 µm under high-speed operations before stabilising. These findings suggest that while standard ballast depths provide sufficient mitigation for commuter and LRT systems, they are ineffective under the dynamic loads of high-speed rail operations.
Figure 17b illustrates the relationship between embankment height and PPV levels. A weak negative correlation is evident, with slightly reduced vibration levels at greater embankment heights. Although the attenuation effect is modest, it appears consistent, as higher embankments increase soil mass beneath the track and create greater geometric separation between the vibration source and surrounding receivers. Suyal and Maheshwari highlighted that ground vibrations at speeds approaching the Rayleigh wave velocity of soft soils may amplify, compromising both embankment stability and the safety of nearby structures. Consequently, embankment design, in combination with soil stiffness, is a critical factor in the long-term control of railway-induced vibrations.
The analysis demonstrates that ballast depth has minimal influence on PPV levels, particularly under high-speed operations where train dynamics dominate vibration responses. While commuter and LRT trains are effectively mitigated by standard ballast configurations, high-speed systems demand more advanced engineering interventions, such as reinforced embankments, isolation layers, or foundation treatments. Embankment height contributes only modestly to vibration attenuation by increasing soil mass and source-receiver separation, yet its effect alone remains insufficient for controlling high-speed vibration impacts. These findings underline the need for integrated geotechnical and structural solutions to effectively manage GBVs, particularly in sensitive residential environments adjacent to high-speed rail corridors.
To further substantiate these observations, regression analyses were conducted to quantify the extent to explain variations in PPV. The regression coefficients (R) reflect the degree of correlation between the measured PPV and the variable parameters for each train type. The correlation values was found PPV, speed and distance have a stronger relationship with PPV. The scatterplot analyses in Sections "Scatterplot fundamental of rail traffic vibrations on no. of data"-"Scatterplot fundamental of rail traffic vibrations on height of ballast and embankment" highlighted clear trends, demonstrating that train speed and receiver distance are the most influential parameters governing PPV, while coach length and embankment or ballast height exert comparatively minimal effects. Table 3 summarises the regression equations for PPV as a function of train operating parameters for each type of train.
For the high-speed train, the regression yielded a moderate correlation (R = 0.6816). Although speed and distance are confirmed as dominant predictors of vibration levels, the lower R suggests that high-speed operations are governed by more complex dynamics. According to Kapper and Che Mamat, higher R values approaching 1 reflect stronger explanatory power, suggesting that additional factors beyond speed and distance may be necessary to fully capture vibration behaviour in high-speed systems. Additional factors such as axle loads, aerodynamic influences, and resonance within the soil-track system likely contribute to variability beyond what a simple speed-distance model can capture. This finding indicates that while the correlation remains strong, high-speed rail requires multivariate approaches to adequately model PPV behaviour.
The light rapid train system exhibited the strongest correlation, with an R of 0.9015. The regression demonstrates that variations in speed and distance explain nearly all observed PPV values. This can be attributed to the lower speeds, lighter axle loads, and more consistent train-track interactions characteristic of operations. The strong correlation underscores that speed and distance alone are sufficient to predict PPV behaviour in this category with high reliability. Similar findings were reported by Yuan et al., who observed regression coefficients (R) for PPV equations consistently above 0.8 and frequently exceeding 0.9 under comparable operating conditions.
For commuter trains, the regression produced an R of 0.8629, indicating a strong relationship between PPV, speed, and distance. However, the slightly lower coefficient compared with light rapid train reflects the greater variability in commuter operations, which typically involve longer coaches, high passenger loads, and a wider range of operating speeds. These factors may contribute to fluctuations in PPV despite the clear dependence on speed and distance.
Taken together, the regression analysis confirms that train speed and distance are the most consistent predictors of PPV across all train types, though the degree of correlation varies. LRT systems demonstrate the most stable behaviour, followed by commuter services, while high-speed tarin introduces additional complexities that weaken direct correlations. These findings reinforce the significance of incorporating speed-distance relationships in GBV assessments, while also highlighting the need to integrate supplementary for railway modelling.
The geotechnical properties of soils beneath railway corridors exert a critical influence on the propagation and attenuation of GBVs. Soil layering, density, and stiffness govern how vibration energy is transmitted, amplified, or damped, ultimately affecting nearby residential structures. To investigate this relationship, JKR probe tests were conducted at three representative case study locations such as Klang, Ampang, and Serdang, each characterised by distinct soil profiles. Figures 18, 19 and 20 present the number of blows per penetration depth at two points within each site, offering a comparative insight into subsoil conditions and their implications for vibration behaviour.
Figure 18 illustrates the soil profile at Klang for commuter train, where dense soils such as gravel, dense sand, and stiff clay are found at depths of 8-10 m, reflected in high blow counts. These layers effectively attenuate vibrations, thereby reducing their transmission to nearby residential areas. In contrast, softer soils with low blow counts at depths of 6-8 m are less suitable, as they tend to amplify vibrations. When underlain by such soft deposits, PPV values can increase substantially, particularly at low frequencies where resonance effects with building structures may occur.
The presence of fill material above existing soft soil layers further contributes to amplification, necessitating reinforcement of upper strata to mitigate GBV. According to Lazi et al. , low-frequency subsurface vibrations are capable of travelling significant distances, meaning that residents within 30 m of railway lines in soft soil areas such as silt or soft clay, are more likely to perceive discomfort. These findings highlight the importance of anchoring railway infrastructure in deeper, denser soil layers to reduce vibration transmission.
The JKR probe results for Light Rapid Train at Ampang (Fig. 19) indicate the presence of soft, loose soils near the surface, with blow counts increasing progressively from depths of 2.0-3.0 m, marking a transition to denser, more compact materials. These upper soft soils, likely silts or clays, tend to amplify vibrations at low frequencies, which are common in railway operations. While deeper layers provide greater damping capacity, the shallow deposits remain prone to transmitting vibrations directly to surface structures.
This layered condition is particularly relevant for residential environments, where single-storey houses and older buildings may be more vulnerable to amplified vibrations. Although attenuation becomes more noticeable with transmission distance, nearby residents remain at risk of exposure due to the influence of soft surficial soils.
Figure 20 presents the soil profile at Serdang for high speed train, where soft clays and silts dominate the upper layers, as evidenced by low blow counts in shallow depths. A transition to denser material occurs at approximately 1.5 m, characterised by significantly higher blow counts, suggesting compact clay with sandy or gravelly inclusions. The soft surficial layers are particularly prone to amplifying vibrations and allowing horizontal propagation, thereby increasing exposure risks for nearby residences.
Although deeper compact soils provide some attenuation, the persistence of soft upper layers ensures that surface-level vibrations remain a concern. Comparative studies indicate that gravel and dry sand exhibit stronger vibration absorption, while soft clays and peat amplify vibration levels. Thus, residents in Serdang, especially those near railway tracks, are likely to experience perceptible GBVs despite partial damping from deeper layers.
The soil profile analyses for Klang, Ampang, and Serdang highlight the strong influence of subsurface conditions on vibration propagation. Dense soils at depth offer effective attenuation, while soft surficial soils amplify vibrations, increasing risks for nearby residential areas. These findings emphasise the need for soil reinforcement and strategic foundation design in railway construction within soft soil environments.
To complement the bivariate scatterplot analyses presented in Sections "Scatterplot fundamental of rail traffic vibrations on no. of data"-"Scatterplot fundamental of rail traffic vibrations in relation to type of soil based on JKR probe test", a Classification and Regression Tree (CART) model was employed to examine the combined influence of operational and infrastructural factors on GBV outcomes. This machine-learning approach enables the identification of interaction effects that are not readily observable through univariate analyses.
The CART model was developed using a dataset of 2685 observations, with vibration classes defined from field-recorded PPV. Model performance was assessed through both training and testing datasets, yielding coefficients of determination R = 97.94% for training and 97.75% for testing in Table 4. The marginal difference between these values indicates that the CART model generalises effectively, demonstrating robust predictive capacity without evidence of overfitting. As noted in prior methodological discussions, instances where test accuracy marginally exceeds training performance may reflect random variation in data partitioning rather than modelling deficiencies, and remain acceptable when differences are small.
The relative importance of predictors, illustrated in Fig. 21, reveals a clear hierarchy. Train speed was identified as the most influential variable (100%), followed by distance from the receiver (79.7%). This outcome is consistent with vibration propagation theory, whereby increasing speeds amplify dynamic forces while shorter source-to-receiver distances reduce attenuation. Among infrastructural parameters, embankment height exerted a moderate influence (42.6%), highlighting its role in modifying wave propagation through soil-structure interactions. In contrast, coach length (13.2%) and ballast height (11.0%) contributed only marginally, suggesting their effects are conditional and secondary relative to train dynamics. The parametric study support by finding from Javaid et al. the effectiveness of decision tree regression in identifying the relative influence of input variables on traffic-induced vibrations, demonstrating how speed and source distance dominate the prediction of peak particle velocity.
Overall, the CART regression model provided an advanced multivariate perspective that complements the empirical scatterplot analyses. By confirming the dominant role of operational variables while also recognising the conditional influence of infrastructural characteristics, the model underscores the value of machine-learning approaches in railway vibration studies.