Influence of Low-Frequency Vertical Vibration on Walking Locomotion

Vibration serviceability assessment of footbridges under pedestrian-induced dynamic actions has become a routine requirement in the contemporary structural engineering practice (Sétra 2006; ISO 2007; BSI 2008). This development is a result of increasing probability of pedestrians exciting resonance in modern, slender, lightweight, and low-frequency structures. In addition, these structures are usually lightly damped, resulting in high sensitivity of the vibration response to the variations in the excitation frequency. Stochastic modeling of pedestrian loading has emerged to address a need to genuinely represent both the intersubject variability in walking locomotion parameters (i.e., variability within a human population using a particular structure) and the intrasubject variability (i.e., step-by-step variations of a parameter within an individual) (Živanović et al. 2007; Ingólfsson and Georgakis 2011; Racic and Brownjohn 2011; Carroll et al. 2012; Bocian et al. 2014; Caprani 2014). In parallel, research into experimental quantification of both types of variability is being advanced to facilitate the calibration and verification of the stochastic models.

An experimental study that involved measuring both types of variability for seven walking locomotion parameters of potential interest in bridge engineering applications has recently been performed. The monitored parameters were the amplitude of the first forcing harmonic normalized by the pedestrian weight (so-called dynamic loading factor, ${\mathrm{DLF}}_1$), pacing rate $f_p$, step length $d$, step width $w$, angle of attack ${\theta }_0$, end-of-step angle ${\theta }_e$, and trunk angle ${\theta }_{tr}$ (Dang and Živanović 2015; Živanović et al. 2016). The parameters were derived from trajectories of 21 reflective markers attached to test subjects’ (TSs’) anatomical landmarks and measured using a motion-capture system Vicon (Oxford Metrics, Oxford, U.K.). While the exact anatomical positions of these markers, also utilized in the current study, have been reported in the previous paper (Dang and Živanović 2015), their graphical representation is shown in Fig. 1 for a quick reference.

The marker trajectories were used in conjunction with the data on mass and position of the center of mass of individual body segments (SCoMs) (de Leva 1996) to infer the kinematics of the body center of mass (BCoM). At the same time, the generated ground reaction force (GRF) was calculated by summing the inertial forces for the individual body segments (Racic et al. 2009). While the Vicon system records the marker trajectories with high accuracy (with the error up to 1 mm), the measurement error in the first forcing harmonic (for the chosen marker arrangement) was found to be less than 20% in the majority (90%) of trials (Dang 2014; Dang and Živanović 2015). This error mostly originates from modeling assumptions (that the body segments are rigid and undamped, and that mass distribution throughout the body is the same for all individuals as are geometric locations of the center of mass of individual body segments) and measurement errors due to soft tissue artifact.

The study concluded that, when walking at a range of normal (comfortable) speeds, the recorded ranges of monitored parameters were similar to those available in wider literature. The coefficient of variation (COV) on a step-by-step basis was also reported: it was less than 5% for all parameters except ${\mathrm{DLF}}_1$ ($\mathrm{COV}=1.5–8.3\%$) and step width ($\mathrm{COV}=13.4–39.2\%$).

Most studies available in the public domain, including Dang and Živanović (2015), investigated walking over a stationary surface. Because the number of lively structures is increasing, a need to understand walking locomotion on vibrating surfaces has become critical (Racic et al. 2009). Bipedal models of humans are increasingly utilized in numerical studies because they not only directly resemble the geometry of the human legs and sufficiently accurately represent the force generated on the rigid surface, but also have a potential to be used to model pedestrian interaction with vibrating structures (Bocian et al. 2013; Qin et al. 2013; Dang 2014). In an attempt to conceptually model the effects of the vertical vibration on pedestrian locomotion, Bocian et al. (2013) used a simple bipedal model (inverted pendulum with rigid legs) to represent a human walking over a vibrating bridge deck. They concluded that the simulated ground reaction force not only consists of the harmonic components at the pacing frequency and its integer multiples (as in the case of walking on stationary surfaces), but also of a component at the vibration frequency (so-called self-excited force). The existence of the self-excited force component was also found in comparative numerical and experimental studies into pedestrian-structure interaction with laterally oscillating decks (Macdonald 2009; Ingólfsson and Georgakis 2011). Bocian et al. concluded that the ground reaction force is most influenced by the vibration when a pedestrian walks at a pacing rate that is in the vicinity of the vibration frequency and that the effect can be modeled as equivalent damping and mass added to (or subtracted from) the damping and mass of the unoccupied bridge structure. They argued that the most likely net effect of a pedestrian crowd would be a reduction in the structural vibration response compared with the response that would occur if the interaction effects had been ignored. However, an experimental verification of these findings on decks vibrating in the vertical direction has not been provided yet beyond rare observations on full-scale structures that pedestrians, similar to standing people, seem to add damping to the system (Willford 2002; Brownjohn et al. 2004; Živanović et al. 2009; de Sebastián et al. 2011). The U.K. design guideline (BSI 2008) acknowledges that understanding of pedestrian-structure interaction in the vertical direction is still evolving, to draw attention of structural designers to the fact that the existing design procedures, at the time being, cannot provide all the answers.

Lack of experimental data in relation to the interaction with vertically vibrating supporting surfaces motivated the authors to perform an experimental study of walking locomotion on a lively laboratory bridge and compare the results with benchmark data acquired on a stationary surface. Three TSs took part in the experimental program. In this paper, the lively structure is introduced first, followed by a description of the experimental procedure. Then the TSs’ subjective perceptions of walking speed and vertical vibration are presented. The walking locomotion parameters recorded on the lively surface are then compared with the benchmark data. Finally, findings about effects of vertical vibration on the human walking locomotion are summarized.

The bridge, hereafter referred to as the Warwick Bridge (WB), is a simply supported structure situated in the Structures Laboratory at the University of Warwick [Fig. 2(a)]. The bridge was built in 2012 to investigate pedestrian interaction with lively, low-frequency structures. Its composite (steel-concrete) cross section consists of 150-mm-thick reinforced concrete deck connected to two steel I-beams (UC $203\times 203\times 52$) by means of welded shear studs. The deck is 2 m wide and 19.9 m long, and the bridge has a total mass of approximately 16,500 kg. More detailed information on the design and construction of the bridge is available elsewhere (Lasheen et al. 2014).

The span of the bridge can be altered by relocating either one or both supports. Two span lengths were utilized in this study: 16.2 m (WB1) and 17.4 m (WB2). A grid of test points on the bridge deck, some of which were utilized in the experimental work presented in this paper, is shown in Fig. 2(b).

The natural frequency of the fundamental vertical bending vibration mode is 2.44 Hz for WB1 and 2.18 Hz for WB2. The damping ratio is very low in both cases, and it ranges between 0.30 and 0.52%, depending on the vibration amplitude, while modal mass (including a treadmill placed at the midspan) is 7,700 kg for WB1 and 8,200 kg for WB2 (Dang and Živanović 2015). The low damping and low natural frequency make the bridge very lively, with accelerations as high as $3\mathrm{m}/{\mathrm{s}}^2$ being recorded due to a single person crossing the bridge fast with the intention to excite the resonance. When walking at a pacing rate away from the resonance, third vertical bending mode (at 18.18 Hz for WB1 and at 17.00 Hz for WB2) occasionally makes a significant contribution to the structural response due to its exceptionally low damping ratio of 0.3% (Lasheen et al. 2014). Both the third and the fundamental vibration modes have the maximum modal amplitude at the midspan.

Basic characteristics of the three healthy male TSs who participated in the experimental program are shown in Table 1. Depending on the TS and the configuration of the bridge, the ratio between mass of a test subject and the modal mass of the bridge was between 0.0076 and 0.0094. The test protocol was introduced to TSs prior to the experiments. The TSs were then asked to complete and sign a consent form and a physical readiness questionnaire. The experimental program was approved by the Biomedical and Scientific Research Ethics Committee at the University of Warwick.

In this section, data processing is explained first, followed by a data analysis with respect to:

Three TSs participated in an experimental program designed to measure characteristics of seven walking locomotion parameters on a lively footbridge deck and evaluate these characteristics against the benchmark data acquired on a stationary surface. The deck was pre-excited by an electrodynamic shaker to a steady-state acceleration level of 0, 0.5, 0.85, and $1.2\mathrm{m}/{\mathrm{s}}^2$. It was found that increasing vibration level leads to a marginal increase in the pacing rate, the attack angle, and the trunk angle, and a slight decrease in the step length compared with the benchmark data. The largest increase was approximately 8% only. These marginal differences are only circumstantial and should be further researched. The experiments also revealed that an increase in the vibration level could cause a noticeable increase in the step-by-step variation in all four walking locomotion parameters considered so far. This information could be utilized in the development of high-fidelity models of pedestrians (e.g., bipedal models that aim to represent mass, stiffness, and damping properties of the pedestrian body) with the aim of realistically representing the kinematic and geometry constraints of the human-structure interface.

The average and COV values of the step width seem to be influenced by testing on different testing days rather than by the vibration level imposed. The average value of the end-of-step angle is also vibration independent, i.e., the pedestrian’s geometry of the trailing leg at the toe-off event remains the same regardless of the presence or absence of vibration. The step-by-step variability, however, increased with an increase in vibration levels.

As for the walking-generated force, the results of the previous numerical studies by Bocian et al. (2013), arguing that there are two components contributing to the GRF on the vibrating structure, ${\mathrm{DLF}}_1$ and SEF, have been experimentally confirmed. It has also been found that SEF increases with an increase in the vibration amplitude. When the pacing rate was close to the vibration frequency, ${\mathrm{DLF}}_1$ and SEF combined to produce the TFF. In most of the trials they combined in such a way to reduce the force that would otherwise be induced on a stationary surface. This result confirms rare experimental observations from the previous studies (Willford 2002; Brownjohn et al. 2004; Živanović et al. 2009; de Sebastián et al. 2011) that pedestrians have a damperlike effect on the structures vibrating in the vertical direction. Twelve trials were studied in more detail, and it was concluded that the drop in the force was equivalent to adding damping (between 2.5 and $5\mathrm{kNs}/\mathrm{m}$) and mass (from $-100$ to 700 kg) to the system. These values are very similar to those predicted by the inverted pendulum model for pedestrians (Bocian et al. 2013). It should be kept in mind that all these results are observed for low-frequency vibrations at the frequency of approximately 2 Hz and with the average vibration amplitude in the range between 4 and 10 mm. The force reduction effect was also observed in experiments with people performing other types of activities, such as bouncing (Yao et al. 2004) and jumping (Yao et al. 2006).

Finally, a rarely available insight into human response to vibration in the walking posture has been obtained. The vibration perception and complaint thresholds were found to be approximately constant for walking frequency up to 1.75 Hz. For walking at pacing rates above 1.75 Hz, the two threshold levels increased with an increase in the walking speed. The perception threshold ranged from 0.3 to $1.3\mathrm{m}/{\mathrm{s}}^2$, while the complaint threshold was between 0.8 and $1.9\mathrm{m}/{\mathrm{s}}^2$. This result represents a rare attempt of observing subjective response to vibration at a range of pacing rates since the pioneering work on vibration perception in the walking posture by Leonard (1966) and Smith (1969). The response factor for walking posture was found to be approximately 2, which is similar to that adopted in the vibration serviceability guidelines for vibration exposure in residential buildings in standing or sitting postures. However, the vibration level that is perceived by a pedestrian is one to two orders of magnitude larger than that for a standing person, with greater difference seen at faster pacing rates.

This paper provides a unique insight into the human locomotion on and interaction with vibrating surfaces. It is hoped that the study will motivate further development of numerical models and that it will inspire additional experimental work that will look into the interaction under a wider range of vibration amplitudes and frequencies and with the participation of a larger number of test subjects.

Electronic format of the data collected in this research can be downloaded freely from the University of Warwick webpages http://wrap.warwick.ac.uk/79038/.

This research work was supported by the U.K. Engineering and Physical Sciences Research Council (Grant Number EP/I03839X/1: Pedestrian Interaction with Lively Low-Frequency Structures). The first author was also supported by the Warwick Postgraduate Research Scholarship. The authors would like to thank Birmingham Science City and Advantage West Midlands for the access to the Gait Laboratory.