Eeklo Footbridge: Benchmark Dataset on Pedestrian-Induced Vibrations

Van Nimmen, Katrien; Van Hauwermeiren, Jeroen; Van den Broeck, Peter

doi:10.1061/(ASCE)BE.1943-5592.0001707

Open access

Case Studies

Apr 29, 2021

Eeklo Footbridge: Benchmark Dataset on Pedestrian-Induced Vibrations

Authors: Katrien Van Nimmen https://orcid.org/0000-0002-8188-1297 [email protected], Jeroen Van Hauwermeiren, and Peter Van den BroeckAuthor Affiliations

Publication: Journal of Bridge Engineering

Volume 26, Issue 7

https://doi.org/10.1061/(ASCE)BE.1943-5592.0001707

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Abstract

Vibration serviceability under crowd-induced loading has become a key design criterion for footbridges. Although increased research efforts are put into the characterization of crowd-induced loading, including related interaction phenomena, and first-generation design guides are available, a major challenge lies in the further development and validation of prediction models for crowd-induced vibrations. Full-scale benchmark datasets that simultaneously register structural and crowd motion make an invaluable contribution to meeting this need by providing detailed information on representative operational loading and response data. Currently available datasets either (1) involve a (too) small number of pedestrians or (2) do not involve the simultaneous registration of pedestrian and bridge motion, or else they involve a footbridge (3) where only a single mode or a very limited number of modes are sensitive to walking excitation, (4) for which no suitable digital twin is available, or (5) that is not open access. This paper therefore presents a new and publicly available full-scale dataset collected specifically for the further development and validation of models for crowd-induced loading. The dataset is collected for a real footbridge, with a number of modes that are sensitive to pedestrian-induced vibrations, and with a digital twin available. The pedestrian and bridge motions are registered simultaneously using wireless triaxial accelerometers and video cameras. In addition to two data blocks involving purely ambient excitation, four data blocks are collected for two pedestrian densities, 0.25 and 0.50 persons/m², representing a total of more than 1 h of data for each pedestrian density. Analysis of the structural response shows that the different data blocks can be considered representative for the involved load case. The identified distribution of step frequencies in the crowd indicates a significant contribution of (near-)resonant loading for a number of modes of the footbridge. Furthermore, the dataset displays clear signs of human–structure interaction, suggesting a significant increase in effective modal damping ratios due to the presence of the crowd.

Introduction

Environmental, economic, and aesthetic objectives stimulate the design of lightweight, slender, and, consequently, vibration-sensitive footbridges (Živanović et al. 2005; Ney and Poulissen 2014). As a result, the dynamic performance of these structures under medium to high crowd densities has started governing their design. Current design guidelines (AFGC 2006; Heinemeyer et al. 2009; BSI 2008) propose load models, upscaled from single-person force measurements performed on a rigid surface, to represent the effect of larger numbers of pedestrians, including small groups and crowds. This upscaling involves numerous (simplifying), often unvalidated, assumptions, such as the distribution of step frequencies in the crowd and pedestrian arrival times, and disregards human–structure interaction (HSI) and human–human interaction (HHI) phenomena. Recent contributions show that HSI phenomena (Bruno and Venuti 2009; Živanović et al. 2010; Agu and Kasperski 2011; Dong et al. 2011; Ingólfsson et al. 2012; Salyards and Hua 2015; Fujino and Siringoringo 2016; Caprani and Ahmadi 2016; Dang and Živanović 2016; Shahabpoor et al. 2016; Van Nimmen et al. 2017; Tubino 2018) and the distribution of step frequencies (Živanović 2012; Tubino and Piccardo 2016), which in turn is influenced by HHIs (Venuti et al. 2016; Ferrarotti and Tubino 2016; Bocian et al. 2018), are of high importance, and sometimes even decisive factors in vibration serviceability assessment. However, because full-scale validation is lacking, the further improvement of load models is prevented and there remains a reluctance to implement state-of-the-art developments in current design practice.

In-field observations are the only way to obtain detailed and accurate information on representative loading and response data and, hence, are essential for the further development and validation of models of crowd-induced loading. Although many interesting experimental studies involving the structural response to pedestrian excitation are reported in the literature, they are rarely suitable for comprehensive validation purposes, for one or more of the following reasons.

•

Only a small number of pedestrians is involved. Although studies reporting validation tests with a limited number of pedestrians are numerous, those of Fanning et al. (2010), Tubino et al. (2016), Dey et al. (2016), Van Nimmen et al. (2016), and Bocian et al. (2018) being only a few examples, the dynamic performance under high crowd densities—which are often imperative for the design—have virtually never been validated (Georgakis and Ingólfsson 2014). This is mainly related to the practical feasibility of organizing these large-scale experimental studies. Two well-known examples of large- and full-scale tests are those on the London Millennium Footbridge (Dallard et al. 2001) and the T-bridge (Nakamura and Kawasaki 2006), both mainly focusing on the analysis of (synchronous) lateral walking loads.

•

The duration of the tests is (relatively) short. If the test duration is short, it cannot be ensured that the tests are representative of the involved load case. This limitation often results from the fact that experimental studies are restricted in time, for example, because the footbridge has to be closed for normal use during the tests.

•

Insufficient information documenting the walking behavior of the pedestrians is gathered. As the structural response is highly sensitive to the distribution of step frequencies, and, particularly for small groups of pedestrians, also to small variations in the time-variant pacing rate, it is essential that this information can be determined from the measurements with a high level of accuracy. For example, the time-variant pacing rate can be derived from data collected by individually adopted motion tracking technologies (Van Nimmen et al. 2014b; Bocian et al. 2018). Furthermore, given that body motion data are collected synchronously, it enables the analysis of interactions within groups of walking pedestrians (Van Nimmen et al. 2014b; Bocian et al. 2018). This, in turn, enables analysis of the level of synchronization that constitutes a normative parameter in the vibration serviceability assessment. In most cases, however, only the total number of pedestrians is reported (Fanning et al. 2010; Caetano et al. 2010; Carroll et al. 2013), for example, in tests involving free or metronome-guided walking (Brownjohn and Middleton 2005; Tubino et al. 2016; Gheitasi et al. 2016; Dey et al. 2016; Van Nimmen et al. 2016), or an estimate is made of the mean pacing rate by analyzing video footage (Dallard et al. 2001; Živanović 2012; Gomez et al. 2017).

•

Limited information is gathered on the resulting structural response. The more structural modes are excited, the more information can be derived from the source of the vibrations (Maes et al. 2015). In many cases reported in the literature, the structural response is dominated by the contribution of one or two modes (Živanović 2012; Dey et al. 2016; Gomez et al. 2017). To gather broad and versatile information on crowd-induced loading, tests should be performed on a number of footbridges, for which, ideally, several modes are excited by the walking load. In the latter case, the structural response is to be registered at different locations, such that the modal contributions can be well identified.

•

A comprehensive experimental setup, where the walking behavior of each pedestrian is registered synchronously with the structural response, has only rarely been applied at full scale and, so far, only involving a small number of pedestrians. To examine if and how the walking behavior of the pedestrians is modified—consciously or unconsciously—in response to the vibration of the surface, requires synchronous registration of the motion of the pedestrians and the surface. A detailed analysis requires pedestrians to be individually equipped with one or more sensors registering their three-dimensional (3D) body motion. So far, these techniques have only be applied at full scale, involving a limited number of persons (<10) (Van Nimmen et al. 2014b; Bocian et al. 2018).

•

An accurate model representing the dynamic behavior of the structure, a so-called digital twin, is not available. To exploit the full potential of the collected dataset, the influence of modeling errors related to the structural behavior should be minimized. This requires a numerical model that accurately describes the dynamic behavior of the empty footbridge, as, for example, developed for the Pedro e Inês footbridge (Portugal, Caetano et al. 2010) and the Ligong footbridge (China, Qin et al. 2019). Owing to modeling errors and simplifications, this is a challenge, even when using detailed finite-element (FE) models that are calibrated based on experimentally identified modal parameters (Živanović et al. 2006; Nimmen et al. 2014a).

•

Not many datasets are publicly available. To the knowledge of the authors, only the datasets collected by Živanović (2012) and Gomez et al. (2017) are publicly available.

In this paper, a novel publicly available full-scale dataset is introduced, documenting a comprehensive experimental study involving pedestrian-induced vibrations on the Eeklo footbridge. The experimental study is unique and suitable for comprehensive validation purposes, as it involves a number of pedestrian densities, the synchronous and detailed registration of the pedestrians’ body motion and footbridge vibrations, a duration of the tests sufficiently long to be representative of the involved load cases, and a structure for which a reliable digital twin is available. In this way, this unique dataset contributes to addressing the need for the further development and the full-scale validation of models for crowd-induced loading. This dataset thereby addresses a lacuna in the civil engineering community. All procedures were approved by the social and societal ethics committee of KU Leuven and each participant gave written informed consent prior to participation.

The Eeklo footbridge was selected for two reasons. The first reason concerns its dynamic behavior. The Eeklo footbridge is characterized by a number of low-frequent modes that lie within the dominant spectrum of pedestrian excitation, of which many are sensitive to pedestrian excitation (Nimmen et al. 2014a). Furthermore, within the relevant range of temperature and vibration amplitudes, up to 5 m/s² and more, the steel footbridge behaves linearly (Van Nimmen et al. 2014b). Second, a highly accurate digital twin can be presented to simulate the dynamic behavior of the empty footbridge.

The experimental study considered ambient excitation and a number of tests with durations of about 10 up to 20 min, involving the pedestrian densities 0.25 and 0.50 persons/m², and amounting to a total of more than 1 h of test data for each pedestrian density. Structural vibrations were registered using wireless triaxial accelerometers along several locations on the bridge deck. The body motion of each pedestrian was registered using a wireless triaxial accelerometer, securely fixed to each participant close to the participant’s body center of mass. The position of each pedestrian along the bridge deck was captured by video cameras. The pedestrian densities 0.25 and 0.5 persons/m² were selected to ensure that, for this present case, HSI and HHI were relevant and identifiable from the gathered data, while, at the same time, keeping the experiment practically feasible.

For the tests involving a pedestrian density of 0.25 and 0.50 persons/m², respectively, 73 and 148 pedestrians walked at a self-selected speed along the bridge deck. At both ends of the bridge, room was provided for the pedestrians to turn around and continue walking in the other direction. It has to be acknowledged that these traffic conditions are artificial. As such, they cannot be considered representative for investigating realistic HHI phenomena. That being said, it may be argued that this dataset will allow the derivation of some general characteristics of crowd dynamics on footbridges, such as the strength of the boundary forces and the repulsive interaction forces between pedestrians, as used in the widely applied social force model for pedestrian dynamics (Helbing and Molnar 1995; Helbing et al. 2005). Conversely, the registered 3D body motion allows the time-variant pacing rate of each pedestrian to be identified (Bocian et al. 2018; Van Nimmen et al. 2018). Some impressions of this large-scale measurement campaign are given in Fig. 1.

Fig. 1. Impressions of the large-scale measurement campaign on the Eeklo footbridge.
(Images © Tine Desodt Photography, reprinted with permission.)

The objective of this paper is to present the novel benchmark dataset, share expertise regarding the dynamic behavior of the footbridge and the performed experiments, and interpret and analyze the gathered data. The paper describes the comprehensive experimental study and presents a discussion of the essential pedestrian (time-variant pacing rate and trajectory) and footbridge (operational modal parameters, structural response) parameters that can be obtained from the collected dataset.

The outline of this paper is as follows. First, the Eeklo footbridge, the experimental study, and data preprocessing are described. This is followed by a discussion of the results of the operational modal analysis (OMA), the distribution of identified step frequencies, the identified trajectories, and observations regarding the structural response to ambient and pedestrian excitation. Next, an overview is given of the potential use of the Eeklo Footbridge Benchmark Dataset. Finally, conclusions are summarized.

Eeklo Footbridge

The Eeklo footbridge has a total length of 96 m, with a main central span of 42 m and two side spans of 27 m each (Fig. 2). The cross section of the bridge consists of two main beams with a height of 1.2 m at a spacing of 3.4 m, supporting a steel deck of 8 mm thickness via three secondary beams. The bridge is simply supported with land abutments at the sides and two piers at the midspan. The abutments and piers are equipped with neoprene supports. The total mass of the footbridge equals 121 t, which is composed of 98 t for the steel bridge deck and 23 t for the concrete pillars. In the framework of a previous study (Van Nimmen et al. 2014b), a detailed FE model was developed, based on the as-built plans, and an operational modal analysis (OMA) was conducted, identifying a total of 14 modes with frequencies up to 12 Hz (Table 1). The FE model was subsequently calibrated using only the translational stiffness of the neoprene supports as calibration parameters (Van Nimmen et al. 2014b). Table 1 documents the excellent agreement that is found between the experimentally identified modal characteristics and the characteristics calculated by the calibrated FE model: the relative errors in the frequencies of all 14 modes are limited to

1.76 %

and the modal assurance criterion (MAC) values are all close to 1. For more information related to the footbridge and the model calibration, the reader is referred to Van Nimmen et al. (2014b). Some of the lower modes are presented in Fig. 3, which illustrates that combined lateral–torsional modes alternate with vertical bending modes. The digital twin of the Eeklo footbridge, which aims to describe the dynamic behavior of the footbridge accurately, is composed of the experimentally identified natural frequencies and modal damping ratios, and the corresponding mass-normalized mode shapes computed using the calibrated FE model.

To support the interpretation of the structural response in the results section, Table 1 furthermore lists the apparent modal mass in the vertical (m_j,v) and lateral (m_j,l) directions, calculated as

m_{j, e} = max (| Φ_{j, e} |)^{- 2}

with

Φ_{j, e}

the components in direction e (lateral l or vertical v) of the mass-normalized mode shape

Φ_{j}

. For a purely vertical mode, m_j,v corresponds to the proportion of the physical mass of the structure that is engaged in that mode (Brownjohn and Pavić 2007). For that same vertical bending mode, infinitesimal small modal displacements in the lateral direction result in an apparent lateral modal mass that is infinitely large. It is noted that this apparent modal mass is different from the modal mass of 1 kg that is conventionally related to mass-normalized mode shapes (Brownjohn and Pavić 2007). The smaller m_j,e, the more sensitive mode j is to dynamic excitation in direction e. In turn, large values of the apparent modal mass, which can easily be larger than the total mass of the bridge, indicate an insensitivity to dynamic excitation in direction e. The values for m_j,v and m_j,l listed in Table 1 clearly indicate that Modes 2, 5, 8, and 11 are purely vertical bending modes, associated with a low apparent vertical modal mass m_j,v. As these modes display hardly any motion in the lateral direction, the corresponding apparent lateral modal mass is particularly large, indicating that these modes are insensitive to dynamic excitation in the lateral direction.

Fig. 2. (a) Eeklo footbridge (image by authors); (b) cross section; and (c) side view.

Fig. 3. Top and side views of the first six modes of the original digital twin of the empty Eeklo footbridge: (a) Mode 1 with f₁ = 1.71 Hz; (b) Mode 2 with f₂ = 2.99 Hz; (c) Mode 3 with f₃ = 3.25 Hz; (d) Mode 4 with f₄ = 3.46 Hz; (e) Mode 5 with f₅ = 5.77 Hz; and (f) Mode 6 with f₆ = 5.82 Hz.

Table 1. Experimentally identified modal characteristics (mode number

\tilde{j}

, natural frequencies

{\tilde{f}}_{j}

, damping ratios

{\tilde{ξ}}_{j}

) of all modes with a natural frequency below 13 Hz and corresponding mode number j and natural frequencies f_j predicted by the calibrated FE model, calculated modal assurance criterion (MAC) and the relative frequency deviations ɛ_j [as identified in Van Nimmen et al. (2014b)], and corresponding apparent modal mass in the vertical m_j,v and lateral m_j,l directions, calculated with the calibrated FE model;

≫

indicates very large values

$\tilde{j}$	${\tilde{f}}_{j}$ (Hz)	${\tilde{ξ}}_{j}$ (%)	j	f_j (Hz)	ɛ_j (%)	MAC	m_j,v	m_j,l
1	1.71	1.94	2	1.71	0.26	0.99	202	57
2	2.99	0.19	3	3.02	0.90	1.00	22	$≫$
3	3.25	1.45	4	3.30	1.76	0.98	54	167
4	3.46	2.97	5	3.43	−0.67	0.98	501	82
5	5.77	0.23	6	5.75	−0.31	0.99	27	$≫$
6	5.82	0.16	7	5.80	−0.46	0.97	56	229
7	6.04	2.08	8	6.10	0.89	0.97	67	116
8	6.47	0.60	9	6.47	0.00	1.00	26	$≫$
9	6.98	3.38	10	6.94	−0.48	0.96	66	36
10	7.44	4.77	11	7.36	−1.09	0.97	162	37
11	9.64	0.87	15	9.80	1.67	1.00	15	$≫$
12	9.89	2.50	14	9.71	−1.76	0.96	177	106
13	10.48	1.43	16	10.65	1.62	0.97	57	75
14	12.01	3.49	17	12.16	1.30	0.93	324	102

Experimental Study

This section describes the full-scale experimental study involving OMA and pedestrian excitation. The following elements are successively discussed: the measurement equipment and setup; the data preprocessing; the events; and the participants.

Measurement Equipment and Setup

Structural Accelerations

Bridge deck accelerations were measured using wireless triaxial acceleration sensors [GeoSIG GMS sensors, range ±2g, least significant bit (LSB) 2.649095 × 10⁻⁷g, Fig. 5(a) (GeoSIG 2012)], with a sample rate of 200 Hz. A maximum of 14 sensors was used. The corresponding measurement grid is shown in Fig. 4 and given in Table 2, using the same coordinate system as for the calibrated FE model (Fig. 4). All sensors were used for the OMA. A total of 10 sensors was used for the events involving pedestrian excitation (Fig. 4).

Fig. 4. Top view of measurement grid, indicating global coordinate system (axes), pedestrian zones (A–V), and sensor location numbers for the Eeklo footbridge. Locations of the 21 cameras are indicated by numbers 1 to 21. The field of view of each camera is approximately one pedestrian zone left and right of the camera’s position. Open circle = sensor used during the setups involving pedestrian excitation; open square = additional sensor used during the setups involving ambient excitation.

Fig. 5. Sensor types used to register (a) structural accelerations and (b and c) 3D body motions: (a) GeoSIG GMS, reprinted with permission from GeoSIG (2012); (b) USB X16-1D accelerometer; and (c) human activity monitor (HAM).

Table 2. Sensor identification (ID), longitudinal (X) and lateral (Y) coordinates

GeoSIG ID	X (m)	Y (m)
194	47.66	−1.55
490	25.22	1.55
491	38.66	−1.55
492	−0.28	1.55
493	34.22	1.55
494	25.16	−1.55
824	−21.34	−1.55
825	20.66	−1.55
826	−8.74	−1.55
827	8.12	1.55
828	−47.66	−1.55
213	12.26	−1.55
214	−0.34	−1.55
215	−34.84	−1.55

3D Body Motion

Each participant was equipped with an inertial sensor: a USB X16-1D accelerometer [participants 1–145, range ±16g, LSB 4.8828 × 10⁻⁴g, Fig. 5(b) (Gulf Coast Data Concepts 2016b)] or a human activity monitor [HAM, range ±16g, LSB 4.8828 × 10⁻⁴g, participants 146–148, Fig. 5(c) (Gulf Coast Data Concepts 2016a)]. A single sensor was securely fixed to the lower back of each pedestrian using a belt (Fig. 6). The sampling rate of these devices was set to 100 Hz.

Fig. 6. Smartphone belt and two clips used to securely fix the inertial sensor to the participant.
(Image by authors.)

Video Footage

In total, 21 cameras [GoPro Hero Session, resolution 1080p (Go Pro 2016)] were used to capture the entire bridge deck at 30 frames/s. Each camera was mounted on an aluminum truss at a height of approximately 5 m, fixed to a transverse stiffener of the bridge deck (Fig. 7). By doing this, the bridge deck was divided into 22 pedestrian zones, each of which were further divided into two subzones (Fig. 4). The field of view of each camera was approximately one pedestrian zone left and right of the camera. Hence, each pedestrian was always recorded by at least two cameras for every possible position on the bridge deck. The exact location and orientation of each camera was determined through bundle adjustment using a set of two-dimensional (2D)–3D correspondences of a total of 331 marker points on the bridge deck and parapet. The world coordinates of these marker points were obtained using a total station (standard deviation measurement error, 1 mm) (Van Hauwermeiren et al. 2020).

Fig. 7. Camera setup: the camera is mounted on an aluminum truss, which is securely fixed to the transverse stiffener of the bridge.
(Image © Tine Desodt Photography, reprinted with permission.)

Data Preprocessing

The structural acceleration signals were preprocessed in MATLAB as follows: (1) remove offset (detrend); (2) decimate by a factor of 2, resulting in a sample frequency of 100 Hz and a filter cut-off frequency of 50 Hz; (3) apply high-pass filtering using a fifth-order Butterworth filter with a cut-off frequency of 0.25 Hz; and (4) select the relevant time window, depending on the event duration. For the decimation operation, the built-in MATLAB function decimate was used; this is a two-step operation of low-pass filtering followed by downsampling. In this way, the decimated signal was protected against aliasing errors.

The 3D body motion acceleration signals were preprocessed as follows: (1) resample at 100 Hz to remove the slightly irregular sampling rate of the devices (to this end, the signal is first upsampled to 1,000 Hz, then downsampled to 100 Hz); (2) synchronize the data with the structural acceleration data by removing the drift of the internal clock of the sensors and subsequently applying the proper time shift. This time shift was determined based on three synchronization events: one in the morning, one at noon, and one in the evening.

The synchronization events consisted of a random human-induced movement that was simultaneously applied to a group of USB accelerometers securely clipped to a beam (Fig. 8). First, these synchronization operations were performed for groups of 20 USB accelerometers [Fig. 8(a)]. Second, a master USB accelerometer was selected from each group and used to perform an additional synchronization operation with a GeoSIG sensor [Fig. 8(b)]. By maximizing the cross-correlation between the signals corresponding to these events, the time shift between the time vectors of the involved sensors could be identified. This time shift was then used to define a common timescale for all sensors, in this case the GeoSIG timescale (GMT+0). A typical registered acceleration during a synchronization event is shown in Fig. 9(a). Three synchronization events (morning, noon, evening) were used, allowing three time shifts to be derived for each USB accelerometer with respect to the GMT+0 time axis (via the structural accelerations measured using the GeoSIG sensors). The drift was defined as the ratio of the difference in time shift at the two events to the total duration between those events. The drift during the morning was calculated by considering the synchronization events in the morning and at noon. The drift during the afternoon was additionally obtained by considering the synchronization events at noon and in the evening. The drift over the entire day was determined by considering the synchronization events in the morning and the evening. The internal clocks of the USB accelerometers had a (linear) drift between 0 and 50 ppm (Gulf Coast Data Concepts 2016a, 2016b). Fig. 9(b) compares the drift during the morning and the afternoon for the master USB accelerometers and shows that the drift was indeed (nearly) identical during the morning and the afternoon. Considering the duration between the synchronization events during the morning (12,202 s) and afternoon (15,457 s), the theoretical maximum offset between the estimated time and the real time was 15,457 s/2 × 50 ppm = 0.39 s. It is, however, reasonable to assume that the actual offset between true and estimated time was smaller. The maximum difference in the observed drifts during the morning and afternoon and over the entire day were calculated for the master USB 81 with values of, respectively, 3.31, 7.05, and 5.41 ppm. Therefore, the practical maximum offset between true and estimated time could be approximated as

max (| 12, 202 s / 2 \times (5.41 - 3.31) ppm |

,

| 15, 457 s / 2 \times (5.41 - 7.05) ppm |) = 0.01 s

which corresponds to a single time sample. As the USB accelerometers were only used to analyze the walking behavior of the pedestrians (see also the results and discussion section), this difference was assumed to be negligible, given that the average step frequency of a pedestrian is ≈2 Hz (50 time samples).

Fig. 8. Equipment to perform the synchronization operations between the USB and the GeoSIG accelerometers: (a) large beam; and (b) small beam with several anchorages for the USB accelerometers placed on a GeoSIG sensor.
(Images by authors.)

Fig. 9. (a) Typical magnitude of the total acceleration during a synchronization operation between a GeoSIG sensor (black solid line) and USB accelerometer 1 (gray dashed line); and (b) drift of the internal clocks of the master inertial sensor units in the morning (white) and afternoon (black), and over the entire day (gray). Sensors 101, 121 and 141 were only used in the afternoon (see the right-hand side of the graph).

All 21 cameras were synchronized offline based on common events captured in adjacent cameras. The video footage was then used to obtain pedestrian trajectories through a sequence of pedestrian detection and tracking, as comprehensively described in Van Hauwermeiren et al. (2020). First, the pedestrians were detected in the consecutive frames using a color-segmenting approach. Second, each detection was allocated to the corresponding track. Third, the measurement noise was mitigated using a Kalman filter and smoother; this yielded a final uncertainty of 3 cm.

Events

An overview of the events considered during the measurement campaign is given in Table 3. The events are listed in chronological order with their name, the type of the activity, and the duration of the event. Two types of event were involved: (1) OMA of the empty bridge; and (2) pedestrian excitation, where 73 persons (≈0.25 persons/m²) or 148 persons (≈0.50 persons/m²) walked freely along the bridge.

Table 3. Overview of events

Test no.	Name	Duration (s)	Description
A	OMA_A	900	OMA
1	W073_free1	720	Free walking, 73 persons
2	W073_free2	660	Free walking, 73 persons
3	W073_free3	649	Free walking, 73 persons
4	W072_free4	1,860	Free walking, 72 persons
B	OMA_B	1,200	OMA
1	W148_free1	1,200	Free walking, 148 persons
2	W148_free2	1,200	Free walking, 148 persons
3	W148_free3	950	Free walking, 148 persons
4	W148_free4	300	Free walking, 148 persons

Participants

The heights and body masses of the participants are given in Table 4. For the tests involving a pedestrian density of 0.25 persons/m², the average height was 1.80 m and the average body mass 74.9 kg. For the tests involving a pedestrian density of 0.50 persons/m², the average height was 1.80 m and the average body mass 73.2 kg. Every pedestrian wore a brightly colored hat (red, blue, magenta, or orange) to facilitate the identification of the pedestrians’ trajectories (Van Hauwermeiren et al. 2020).

Table 4. Identification number (ID), height (H), and body mass (BM) of each participant

ID	H (m)	BM (kg)	ID	H (m)	BM (kg)	ID	H (m)	BM (kg)	ID	H (m)	BM (kg)
1	1.88	76	38	1.82	90	75	1.85	65	112	1.78	58
2	1.86	84	39	1.83	73	76	1.81	82	113	1.77	61
3	1.90	65	40	1.74	62	77	1.95	78	114	1.80	69
4	1.81	75	41	1.78	67.5	78	1.82	75	115	1.57	49
5	1.68	70	42	1.84	72	79	1.84	73	116	1.80	68
6	1.60	51	43	1.90	75	80	1.81	75	117	1.89	79
7	1.67	84	44	1.79	54	81	1.82	67	118	1.83	71
8	1.78	60	45	1.81	64	82	1.87	68	119	1.79	66
9	1.79	64	46	1.90	73	83	1.79	90	120	1.72	79
10	1.71	55	47	1.85	80	84	1.75	63	121	1.81	76
11	1.76	64	48	1.78	78.5	85	1.63	75	122	1.77	69
12	1.68	68	49	1.76	67	86	1.85	72	123	1.85	70
13	1.78	67	50	1.92	93	87	1.82	80	124	1.75	65
14	1.70	66	51	1.79	68	88	1.90	83	125	1.72	62
15	1.68	60	52	1.68	70	89	1.87	80	126	1.82	68
16	1.77	73	53	1.71	71	90	1.85	75	127	1.75	62
17	1.82	72	54	1.75	63	91	1.77	58	128	1.72	63
18	1.73	72	55	1.64	52	92	1.81	64	129	1.85	75
19	1.84	100	56	1.85	75	93	1.72	58	130	1.92	85
20	1.76	78	57	1.87	62	94	1.60	48	131	1.84	64
21	1.95	82	58	1.89	73	95	1.65	60	132	1.86	75.5
22	1.88	76	59	1.86	74	96	1.73	87	133	1.85	69
23	1.99	72	60	1.79	74	97	1.85	77	134	1.85	80
24	1.70	71	61	1.92	80	98	1.90	70	135	1.80	73
25	1.78	67	62	1.94	84	99	1.75	64	136	1.87	79
26	1.84	72	63	1.86	80	100	1.78	70	137	1.78	72
27	1.92	80	64	1.76	85	101	1.86	70	138	1.80	75
28	1.80	77	65	1.84	84	102	1.82	82.5	139	1.79	68
29	1.84	80	66	1.80	77	103	1.93	74	140	1.64	68
30	1.80	70	67	1.80	110	104	1.93	72	141	1.72	71
31	1.83	70	68	1.80	62	105	1.82	70	142	1.87	85
32	1.75	70	69	1.78	78	106	1.72	66	143	1.74	74
33	1.75	73	70	1.88	150	107	1.85	76	144	1.86	78
34	1.74	83	71	1.79	92	108	1.90	100	145	1.73	77
35	1.75	70	72	1.76	80	109	1.80	75	146	1.83	70
36	1.75	75	73	1.78	100	110	1.85	75	147	1.71	73
37	1.86	82	74	1.71	56	111	1.83	79	148	1.84	69

Results and Discussion

First, the results from the OMA are presented and discussed. Second, the registered 3D body motion is used to identify the distribution of step frequencies in the crowd. Third, the identified pedestrian trajectories are analyzed. In a last step, the structural response observed for the different events is analyzed.

OMA

On the day of the measurement campaign, two datasets were collected to perform the OMA analyses: one in the morning and one during lunch break (OMA_A and OMA_B in Table 3). Ambient vibration data were processed using the reference-based covariance-driven stochastic subspace identification (SSI-cov) algorithm (Reynders and De Roeck 2008; Peeters and De Roeck 1999) (MACEC v. 3.3). The two setups were processed independently. Table 5 compares the natural frequencies, modal damping ratios, and modal phase collinearities (MPCs) of the modes as identified based on the bridge deck outputs in the morning and at noon. The following observations can be made. (1) The average difference in natural frequency is less than 0.5%. This is within the uncertainty bound that is expected for the identified natural frequencies (Reynders et al. 2008). (2) The average difference in modal damping ratio is 30%. Also, this difference is within the uncertainty bound that is expected for the identified modal damping ratios (Reynders et al. 2008). (3) All MPCs are close to unity, indicating a high quality of the identified modes.

Table 5. Experimentally identified modal characteristics [mode number N, natural frequency f, modal damping ratio ξ, and modal phase collinearity (MPC)] of all modes with a natural frequency <7 Hz, as identified in the morning (OMA_A, morning) and at noon (OMA_B, noon), and corresponding relative deviation ɛ

j	f_j (Hz)			ξ_j (%)			MPC
j	Morning	Noon	ɛ (%)	Morning	Noon	ɛ (%)	Morning	Noon	ɛ (%)
1	1.70	1.69	−0.8	1.31	1.94	47	1.00	0.99	−0.4
2	2.97	2.97	0.0	0.16	0.25	56	1.00	1.00	0.0
3	3.21	3.21	0.0	1.15	1.49	29	0.97	0.84	−12.7
4	3.43	3.45	0.6	3.02	3.72	23	0.89	0.83	−7.0
5	5.67	5.68	0.3	0.19	0.22	19	0.98	0.96	−2.3
6	5.74	5.74	0.1	0.12	0.24	96	0.99	0.99	−0.5
7	5.95	6.07	2.1	1.52	2.14	41	0.88	0.90	2.3
8	6.42	6.42	0.1	0.40	0.28	−28	0.94	0.99	5.4

Table 6 compares the natural frequencies and modal damping ratios of the modes of the empty footbridge as identified from previous research (as discussed previously) with the modes identified from the vibration data collected on the day of the full-scale measurements. The following observations can be made. (1) An average decrease of 1% in natural frequency is observed with respect to the originally identified values. Although this difference is small, this can be mainly attributed to the additional mass (trusses, cables, etc., estimated at 800 kg) that was present on the bridge deck during the full-scale measurements. This was also confirmed by the analysis of the calibrated FE model, updated to account for the presence of these materials by means of the corresponding added (translational) masses. (2) The modal damping ratios, identified in the morning and at noon, fall within the uncertainty bound that is expected for the originally identified modal damping ratios. The digital twin of the Eeklo footbridge was updated to account for the added mass and the slight shift in natural frequencies. The natural frequencies and modal damping ratios of the digital twin are summarized in Table 7.

Table 6. Comparison between the experimentally identified modal characteristics (mode number N, natural frequency f, modal damping ratio ξ, and MPC) of all modes with a natural frequency <7 Hz, as identified in previous research (Van Nimmen et al. 2014b) (original) and at the day of the full-scale measurements (average of OMA_A and OMA_B: current), and corresponding relative deviation ɛ

j	f_j (Hz)			ξ_j (%)
j	Original	Current	ɛ (%)	Original	Current	ɛ (%)
1	1.71	1.69	−1.0	1.94	1.62	−16.3
2	2.99	2.97	−0.6	0.19	0.20	7.9
3	3.25	3.21	−1.3	1.45	1.32	−9.0
4	3.46	3.44	−0.5	2.97	3.37	13.4
5	5.77	5.68	−1.6	0.23	0.20	−11.9
6	5.82	5.74	−1.4	0.16	0.18	13.2
7	6.04	6.01	−0.5	2.08	1.83	−12.0
8	6.47	6.42	−0.8	0.60	0.34	−43.4

Table 7. Summary of the modal characteristics of the digital twin of the Eeklo footbridge: mode number j, natural frequency f_j, and modal damping ratio ξ_j

j	f_j (Hz)	ξ_j (%)
1	1.69	1.94
2	2.97	0.19
3	3.21	1.45
4	3.44	2.97
5	5.68	0.23
6	5.74	0.16
7	6.01	2.08
8	6.42	0.60
9	6.98	3.38
10	7.44	4.77
11	9.64	0.87
12	9.89	2.50
13	10.48	1.43
14	12.01	3.49

These results indicate that, apart from the small impact of the additional mass, the dynamic behavior of the Eeklo footbridge has not changed with respect to the original study presented in Van Nimmen et al. (2014b). Hence, the calibrated FE model discussed here, which accounts for the additional mass present on the bridge, can be considered as an excellent representation of the true dynamic behavior of the Eeklo footbridge in terms of natural frequencies and mode shapes. Concerning the modal damping ratios, a good estimate is obtained based on the OMA analysis. As the estimates in the original study (Van Nimmen et al. 2014b) were obtained using a much larger dataset (10 different setups, each collecting 20 min of ambient vibration data), the originally estimated modal damping ratios presented in Table 1 are considered most reliable. Based on the comparison with the current estimates (Table 6), an uncertainty bound of 15% is expected for the modal damping ratios.

Distribution of Step Frequencies

This subsection uses the registered 3D body motion to estimate the distribution of step frequencies in the crowd for the setups involving walking persons. Fig. 10 gives an example of the vertical acceleration levels registered on the lower back of Pedestrian 1. Based on the measurements of all USB sensors, the time-variant pacing rate for each pedestrian was determined, using the procedure detailed in Van Nimmen et al. (2018). The steps taken within 2 m of each end of the bridge deck, i.e., where the pedestrians slowed down to turn around, were excluded from the analysis. Fig. 11 is a histogram of the identified pacing rates for Pedestrian 1. This figure shows that the distribution of steps can be well fitted by a Gaussian distribution. A goodness of fit (chi-square test) of 89% was found. Similar observations were made for the other pedestrians in the crowd.

Fig. 10. Example of vertical acceleration signals registered by USB accelerometer on lower back of Pedestrian 1 for Event W073_free1: (a) full time history; and (b) enlargement over 5 s.

Fig. 11. Histogram with fitted Gaussian distribution of identified pacing rates for Pedestrian 1 for Event W073_free1.

Fig. 12 shows the Gaussian distribution of the identified pacing rates for the different individuals and the corresponding aggregated distribution, as identified for Tests W073_free1 (0.25 persons/m²) and W148_free1 (0.50 persons/m²). The individual distributions characterize the intraperson variability in step frequency. On average, individual standard deviations

σ_{f_{s}}

[Hz] of 0.023 and 0.032 Hz were found for a pedestrian density of 0.25 and 0.50 persons/m², respectively. For these particular tests (Tests W073_free1 and W148_free1), the aggregated distributions of step frequencies

N (μ_{f_{s}}, σ_{f_{s}})

[Hz] with mean value

μ_{f_{s}}

were characterized by

N (1.78, 0.14)

and

N (1.69, 0.18)

Hz for pedestrian densities of 0.25 and 0.50 persons/m², respectively.

Fig. 12. Gaussian distribution of the experimentally identified time-variant pacing rate for the different individuals (gray) and the corresponding aggregated distribution (black): (a) W073_free1; and (b) W148_free1.

Fig. 13 compares the Gaussian distribution of the experimentally identified pacing rates for the four events involving the same pedestrian density. In addition, this figure presents the corresponding aggregated histogram and distribution. These results show that the distributions of step frequencies derived for the different tests are highly similar and can be well fitted by a Gaussian distribution. For pedestrian densities of 0.25 and 0.50 persons/m², the distributions of step frequencies are characterized by

N (1.77, 0.13)

and

N (1.66, 0.19)

Hz, respectively. These results show that, as a result of the increase in pedestrian density from 0.25 to 0.50 persons/m², the mean walking speed slightly decreases (Weidmann 1993; Venuti and Bruno 2007) resulting, in turn, in a decrease of the mean step frequency from 1.77 to 1.66 Hz. Conversely, the standard deviation in step frequency increases, from 0.13 to 0.19 Hz. It is expected that this is due to the increasing impact of HHI: for a higher pedestrian density, the number of interactions between pedestrians increases, causing them to display more variations in their walking behavior, as also observed in Wei et al. (2017).

Fig. 13. (a and b) Gaussian distributions of the experimentally identified pacing rates for Events 1 to 4 (gray) and the corresponding aggregated distribution (black), involving pedestrian densities of (a) 0.25 persons/m²; (b) 0.50 persons/m²; and (c and d) the corresponding histograms.

It is noted that when no information is available on the 3D body motion of the pedestrians, the distribution of step frequencies is to be estimated using empirical relations, such as the speed–density relation introduced by Weidmann (1993) and the velocity–step frequency relation introduced by Bruno and Venuti (2008). Following these relations leads to mean values of 1.91 and 1.89 Hz for pedestrian densities of 0.25 and 0.50 persons/m², respectively. In terms of the interperson variability in step frequency, different values are found in the literature for the standard deviation. For example, a value of 0.16 Hz is found for unrestricted pedestrian traffic using Weidmann’s standard deviation in walking speed of 0.26 m/s (Weidmann 1993) and the velocity–step frequency relation (Bruno and Venuti 2008). Butz et al. (2008) specify a value of 0.10 Hz for pedestrian densities less than 1.0 persons/m², while the guidelines Sétra (Association Française de Génie Civil, Sétra/AFGC 2006) and Hivoss (Heinemeyer et al. 2009) list a value of 0.175 Hz for pedestrian densities less than 1.0 persons/m². When comparing these values with those identified from the 3D body motion, it is clear that there are significant discrepancies, in particular, in terms of the mean value of the step frequencies. This is partially attributed to the fact that the test setup at hand is artificial. Nevertheless, given the high sensitivity of the structural response to the distribution of step frequencies, this application illustrates the necessity of obtaining accurate information on the actual distribution of step frequencies to allow for further analysis of the crowd-induced vibrations.

Pedestrian Trajectories

Fujino et al. (1993) were the first to use video footage to retrieve the trajectories of a continuous flow of pedestrians crossing a footbridge, with up to 2,000 participants occupying the structure at a time. Their study investigated the lateral synchronization of the motion of pedestrians and the footbridge, where the body motion is captured using a single camera and a manual selection of the pedestrians’ positions. Of course, given the manual process, only a fraction of the pedestrians and a fraction of their corresponding trajectories was obtained and used in that analysis. The benchmark dataset presented in this paper aims for the complete registration of all relevant data (structural accelerations, body acceleration at the lower back and the trajectories) of all participants (up to 148) during the entire test duration (combined duration of all tests approximately 2.5 h). The state of the art in the field of computer vision and photogrammetry and the employed camera setup allow this objective to be met. A recent publication (Van Hauwermeiren et al. 2020) presents a methodology for collecting the trajectories of a high-density crowd, as well as application on a benchmark dataset. The related accuracy is of the order of a few centimeters; this allows the different lanes of the pedestrians to be clearly distinguished. A typical example of the results of the combined registered in-field pedestrian motion information (trajectory and step frequency) is shown in Fig. 14. This figure shows that, while the longitudinal position changes smoothly [Fig. 14(b)], the lateral position displays rather chaotic fluctuations across the width of the deck along the full length of the bridge [Fig. 14(c)]. This observation is attributed to the fact that pedestrians try to avoid collisions.

Fig. 14. Registered in-field motion information of Pedestrian 1 during the first 300 s of Test W073_free1: (a) trajectory; (b) longitudinal position; (c) lateral position; (d) velocity; and (e) identified step frequency.

The time-averaged spatial distribution of the pedestrians for Tests W073_free1 and W148_free1 are shown by means of heat maps in Figs. 15 and 16. These figures show that the spatial distribution is nonuniform for both densities. It is also observed that the spatial distribution varies (slightly) over the four considered consecutive time blocks, which span one-quarter of the entire test duration. The relative difference in spatial distribution of the four consecutive time blocks from the total test duration is calculated as the area-averaged absolute difference in spatial distribution from the average pedestrian density (0.25 or 0.50 persons/m²), which is normalized to the average pedestrian density. In the case of Test W073_free1, the relative differences of the spatial distribution are, respectively, 22%, 23% 21%, and 23%. In the case of Test W148_free1, relative differences of 14%, 13% 14%, and 12% are observed. The graphical representation and relative differences indicate that the spatial distribution is nonstationary. Moreover, during all tests, the formation of four lanes over the width of the bridge deck is observed. This is a natural phenomenon in pedestrian flows, which is also theoretically predicted by flow simulations using social force models (Helbing and Molnar 1995).

Fig. 15. Heat map of pedestrians during Test W073_free1 for (a) the full test duration; (b through e) four equal consecutive time blocks, each considering a quarter of the entire duration; and (f) the corresponding scale bar expressed in persons/m².

Fig. 16. Heat map of pedestrians during Test W148_free1 for (a) the full test duration; (b through e) four equal consecutive time blocks, each considering a quarter of the entire duration; and (f) the corresponding scale bar expressed in persons/m².

The average speed for every pedestrian is calculated, resulting in the following distributions for the pedestrian densities of 0.25 and 0.50 persons/m²:

N (1.28, 0.02)

and

N (1.10, 0.03)

m/s (Fig. 17). As for the determination of the distribution of step frequencies, the parts of the trajectories within 2 m of the ends of the bridge (the turning points) were excluded from the analysis. By way of comparison, Weidmann’s empirical speed–density relation (Weidmann 1993) returns lower and upper bounds of, respectively, 1.17 (1.07) and 1.68 (1.57) m/s for a density of 0.25 (0.50) persons/m². As is the case for the distribution of step frequencies, significant differences are observed between the identified and the empirically predicted mean values of the pedestrian velocity distribution. Moreover, even with the rather wide empirically predicted range of expected velocities, nearly 50% of the pedestrians walk more slowly than the lower limit in the case of 0.50 persons/m². These observations, again, indicate the importance of obtaining accurate information on the actual characteristics of pedestrian traffic, to allow for further analysis of crowd-induced vibrations.

Fig. 17. Average walking speed of pedestrians, with indication of the lower and upper bounds of the average velocity predicted by the Kladek formula (Weidmann 1993) (dashed line): (a) W073_free1 (0.25 persons/m²); and (b) W148_free1 (0.50 persons/m²).

The trajectories were used to investigate a possible correlation between the step frequency and the walking velocity with the walking slope. For every participant during Test W148_free1, the step frequency, walking velocity, and slope were collected at every footfall. The difference in step frequency and walking velocity with respect to the mean value was calculated and normalized to the mean value of that quantity. Then the correlation between the normalized difference of the step frequency and the walking slope was calculated, using all footfalls of all pedestrians. Also, the correlation coefficient of the normalized difference of the walking velocity and the walking slope was calculated. It was found that both the normalized difference of the step frequency and the walking velocity are weakly correlated with the walking slope, with an absolute value of the correlation coefficient less than 0.20.

Structural Response

The structural response was low-pass filtered, with a cut-off frequency of 10 Hz. Figs. 18, 19, and 20 present, respectively, the full time series and a 10-s close-up of the structural accelerations induced by ambient excitation (OMA_A), a pedestrian density of 0.25 pedestrians/m² (Test 4), and 0.50 pedestrians/m² (Test 1). The power spectral density (PSD),

{\tilde{G}}_{\ddot{u}}

, of the measured structural accelerations (

\tilde{\ddot{u}}

) was calculated considering consecutive time windows of length T = 25 s, with 50% overlap. Figs. 21, 23, and 24 present the PSD of the structural accelerations induced, respectively, by ambient excitation, a pedestrian density of 0.25 pedestrians/m², and 0.50 pedestrians/m². The following observations can be made.

•

Comparing the time series for ambient excitation (Fig. 18) with those involving pedestrian excitation (Figs. 19 and 20), the vibration levels appear to be of the same order of magnitude.

•

For ambient excitation, the PSD (Fig. 21) shows that the vertical structural accelerations are dominated by the contributions of the first (1.69 Hz) and second (2.97 Hz) modes of the footbridge. At the side spans, important contributions of Modes 5 (5.68 Hz) and 8 (6.42 Hz) are also observed: two weakly damped vertical bending modes that have an antinode at the center of the side span.

•

For pedestrian excitation, the focus is first on the convergence of the PSD of the structural response for an increasing number k_T of consecutive time windows of length T = 25 s (Fig. 22). The level of convergence is evaluated by means of the convergence error

Δ {\tilde{G}}_{\ddot{u}}

. This convergence error is defined as the 2-norm of the difference between the PSD calculated considering k_T consecutive time windows and considering the full time history of the test, and is then normalized to the latter. Fig. 22 shows that it takes 1,000 s (k_T = 40) to limit the convergence error to less than 10%.

•

For pedestrian excitation (Figs. 23 and 24), it is clear that the structural acceleration levels are dominated by the same modes that dominate the ambient vibration response: Modes 1 (1.69 Hz), 2 (2.97 Hz), 5 (5.68 Hz), and 8 (6.42 Hz).

•

For the different tests that consider the same type of excitation; thus, when comparing the PSDs in the same column of the same figure (Figs. 21, 23, and 24), the PSDs are highly similar, both quantitatively and qualitatively. This is also confirmed by Fig. 25, which shows that the individual PSDs involving the same load case are highly similar to the corresponding average PSD. These results indicate that the dataset collected for each pedestrian density, with a total length of more than 3,600 s (Table 3), can be considered representative of that involved load case.

•

Finally, Fig. 26 compares the average PSD due to ambient excitation (Fig. 21) with the PSDs considering pedestrian excitation (Fig. 25). Ambient excitation is, of course, also present when pedestrian excitation is considered. Based on Fig. 26, the following observations are made.

•

For the entire frequency range up to 10 Hz, with the exception of a small interval around 2.97 Hz (f₂), the PSD corresponding to pedestrian excitation is significantly larger than that corresponding to ambient excitation. This observation indicates that pedestrian excitation is by far the dominant source of vibrations for the tests involving walking persons.

•

The peak values of the PSD (evaluated at the midspan) close to the fundamental mode of the footbridge (f₁ = 1.69 Hz) are about 15 times and 20 times larger when the bridge is excited by, respectively, 73 and 148 pedestrians, with respect to the peak value due to ambient excitation. This observation indicates that the pedestrian excitation clearly prevails over the impact of ambient excitation. Furthermore, this observation is confirmed by the identified distributions of step frequencies shown in Fig. 13. This figure shows that a considerable proportion of the pedestrians are walking at (near) resonance with the fundamental mode.

•

The peak values of the PSD (evaluated at midspan) close to the second mode of the footbridge (2.97 Hz), are about 30 times and 20 times smaller when the bridge is excited by, respectively, 73 and 148 pedestrians, with respect to the peak value due to ambient excitation. Considering the second harmonic of the walking load, it is clear that, in this case, a considerable proportion of the pedestrians are also walking at (near) resonance with the second mode of the footbridge (Fig. 13). In addition, the second mode is highly sensitive to (near-)resonant excitation, much more even than the fundamental mode, because of its very low modal damping ratio (0.2%) and modal mass (Table 1). Therefore, it can be assumed that pedestrian excitation also dominates the structural response in this frequency range. The fact that the peak value of the PSD close to the second mode is considerably smaller than when only ambient excitation is considered, despite the significant contribution to the (near) resonant excitation by the pedestrians, can be assumed to be attributed to HSI. This is in agreement with recent studies (Dong et al. 2011; Salyards and Hua 2015; Shahabpoor et al. 2016; Van Nimmen et al. 2017; Tubino 2018) indicating that the effective damping ratio of the coupled crowd–structure system increases considerably for increasing crowd to structure mass ratios and for natural frequencies of the empty structure close to that of the human body of a pedestrian. This presumed increase in effective damping ratio is also in agreement with the observation that the peak in the PSD in Fig. 26 around the second mode (2.97 Hz) is considerably wider for the tests involving pedestrian excitation in comparison with the peak due to ambient excitation. Evidence of the increase in effective damping as a result of the presence of persons on the Eeklo footbridge, in particular for the second mode, has also been reported in Van Nimmen et al. (2014b).

•

At the side span, the contributions of Modes 5 (5.68 Hz) and 8 (6.42 Hz) are considerably greater for pedestrian excitation than for ambient excitation. Supported by the results presented in Fig. 13, it can be assumed that these contributions are due to (near-)resonant excitation with the third and fourth harmonic of the walking load.

•

The PSD induced by pedestrian excitation shows an additional peak around 1 Hz, in both the vertical and lateral components. Given the fact that this peak is located at half of the mean step frequency of the pedestrians (Fig. 13), it can be assumed that this is due to the contributions of the first subharmonic of the vertical component of the walking load and the fundamental harmonic of the lateral component of the walking load (exciting the fundamental lateral–torsional mode).

Fig. 18. Time series of the structural accelerations induced by ambient excitation, low-pass filtered with a cut-off frequency of 10 Hz, in the morning: (a and b) full time series of the vertical (black) and lateral (gray) components in the middle of (a) the center span; (b) the side span; and (c and d) 10-s enlargement.

Fig. 19. Time series of the structural accelerations induced by a pedestrian density of 0.25 pedestrians/m², low-pass filtered with a cut-off frequency of 10 Hz, for Test 4: (a and b) full time series of the vertical (black) and lateral (gray) components in the middle of (a) the center span; (b) the side span; and (c and d) 10-s enlargement.

Fig. 20. Time series of the structural accelerations induced by a pedestrian density of 0.50 pedestrians/m², low-pass filtered with a cut-off frequency of 10 Hz, for Test 1: (a and b) full time series of the vertical (black) and lateral (gray) components in the middle of (a) the center span; (b) the side span; and (c and d) 10-s enlargement.

Fig. 21. PSDs of the structural accelerations induced by ambient excitation, low-pass filtered with a cut-off frequency of 10 Hz: the vertical (black) and lateral (gray) components in (a and c) the middle of the center span and (b and d) the side span; (a and b) in the morning; and (c and d) during lunch break.

Fig. 22. (a and c) PSDs of the structural accelerations in the middle of the center span, calculated for an increasing number k_T of consecutive time windows of length T = 25 s, for (a) Test W072_free4 and (c) Test W148_free1; and (b and d) corresponding convergence error $Δ {\tilde{G}}_{\ddot{u}}$ for the vertical (black) and lateral (gray) components of the structural accelerations in the middle of the center span (solid) and the side span (dashed).

Fig. 23. PSDs of the structural accelerations induced by a pedestrian density of 0.25 pedestrians/m², low-pass filtered with a cut-off frequency of 10 Hz: vertical (black) and lateral (gray) components in (a, c, e, and g) the middle of the center span; and (b, d, f, and h) the side span, for (a and b) Test 1; (c and d) Test 2; (e and f) Test 3; and (g and h) Test 4.

Fig. 24. PSDs of the structural accelerations induced by a pedestrian density of 0.50 pedestrians/m², low-pass filtered with a cut-off frequency of 10 Hz: vertical (black) and lateral (gray) components in (a, c, e, and g) the middle of the center span; and (b, d, f, and h) the side span, for (a and b) Test 1; (c and d) Test 2; (e and f) Test 3; and (g and h) Test 4.

Fig. 25. PSDs for Test 1 through to Test 4 (dashed) and corresponding average PSDs (solid) of the structural accelerations, low-pass filtered with a cut-off frequency of 10 Hz: vertical (black) and lateral (gray) components in the middle of (a and c) the center span; and (b and d) the side span, induced by pedestrian densities of (a and b) 0.25 pedestrians/m²; and (c and d) 0.50 pedestrians/m².

Fig. 26. Average PSDs of structural accelerations due to ambient (dashed) and pedestrian (solid) excitation, low-pass filtered with a cut-off frequency of 10 Hz: vertical (black) and lateral (gray) components in the middle of (a and c) the center span; and (b and d) the side span, for pedestrian densities of (a and b) 0.25 pedestrians/m²; and (c and d) 0.50 pedestrians/m².

Potential Use of the Eeklo Benchmark Dataset

This final section gives a nonexhaustive overview of the potential use of the Eeklo Benchmark Dataset. As also stated in the introduction section, the further development and validation of pedestrian excitation models requires in-field observations, for they are the only way to obtain detailed and accurate information on representative operational loading data (Georgakis and Ingólfsson 2014; Živanović 2012). This is exactly the primary purpose of the collected dataset.

•

Further development of models for HSI on footbridges: In the literature, two types of HSI are distinguished: passive and active interaction phenomena (Van Nimmen et al. 2020). Passive HSI phenomena are produced because the human body is a mechanical system that interacts with the supporting mechanical system. As a result, the dynamic behavior of the coupled crowd–structure system can differ significantly from that of the empty structure, in particular for lightweight structures. Recent studies (Shahabpoor et al. 2017; Van Nimmen et al. 2017) show that these passive HSI effects, such as added damping, are, in many cases, a decisive factor when assessing vibration serviceability of footbridges. However, because full-scale validation is lacking, the further improvement of load models is prevented and there remains a reluctance to implement state-of-the-art developments in current design practice. The Eeklo Footbridge Benchmark Dataset offers detailed and synchronous measurements of the body motions of pedestrians and the structural response, together with a digital twin of the empty structure, leaving the parameters governing the mechanical interaction between the crowd and the structure as the remaining unknowns in the pedestrian-induced vibrations problem. The analysis of the structural response displays clear signs of passive HSI for a number of modes of the structure. These elements make the collected dataset ideally suited to calibrate and validate models for passive HSI. Possible approaches include inverse methods, where the input or unknown model parameters are estimated from the resulting vibration response and a dynamic model of the structure.

As the body motion of the pedestrian is registered synchronously with the structural response, the dataset can theoretically also be applied to investigate active interaction phenomena, whereby the walking behavior of the pedestrian (the internal driving term of the pedestrian) is modified in response to the vibration of the surface. These phenomena are known to occur for lateral bridge deck motions (Fujino and Siringoringo 2016). In the vertical direction, it is argued that they are only achieved for vibration amplitudes that exceed the acceptable limits for vibration comfort (Dang and Živanović 2016). Given that the sensitivity of the Eeklo footbridge to lateral vibrations is low and also that the maximum vertical acceleration levels observed during the experiments are limited (<0.5 m/s²), the dataset is probably less suited for investigations of active HSI phenomena.

•

Further development of models for HHI on footbridges: As, for each pedestrian, the position on the bridge deck and the pedestrian’s body motion (walking behavior) is known at each point in time, the dataset can be used to investigate interactions between pedestrians, at the level of individuals, groups, and crowds. Even though the travel purpose of the pedestrians is artificial (the participants were requested to cross the footbridge several times), the dataset can, for example, be used to (1) investigate (spatial) correlation or synchronization between pedestrians in terms of step frequency and phase (Bocian et al. 2018) or (2) quantify sociological and physical forces influencing the behavior of a crowd on footbridges (Helbing et al. 2000). In this way, the dataset can support the further development of microscopic and macroscopic models of pedestrian dynamics on footbridges (Ferrarotti and Tubino 2016; Bruno and Corbetta 2017).

In addition, the Eeklo Footbridge Benchmark Dataset aims to serve as a benchmark for future large-scale experiments involving pedestrian excitation, so as to maximize the leverage and outcomes of experimental investigations. In this way, this study can also contribute to and expedite the process of integrating state-of-the-art developments in the field of human-induced vibrations of footbridge in design guidelines and codes.

Conclusions

This paper presents a benchmark full-scale dataset of pedestrian-induced vibrations, collected on the Eeklo footbridge. This dataset is, to the authors’ knowledge, the largest publicly available dataset for a real footbridge, involving the synchronous registration of pedestrian and bridge motion. The Eeklo footbridge is a lightweight steel structure characterized by a number of low-frequency modes that lie within the dominant spectrum of pedestrian excitation. Because of their low modal mass and modal damping ratio, many of these modes are sensitive to pedestrian-induced vibrations. The structural vibrations are registered using wireless triaxial accelerometers. The 3D body motion of each pedestrian is registered using a wireless triaxial accelerometer, securely fixed close to the body center of mass, and the position along the bridge deck is captured using video cameras. In the experimental study a number of tests involving pedestrian densities of 0.25 and 0.50 persons/m² were considered, as well as two tests involving purely ambient excitation.

Analysis of the 3D body accelerations shows that the distributions of the step frequencies and walking speeds differ from those predicted by empirical relations; this is partly attributed to the artificial test setup. Also, the spatial distribution of the pedestrians on the bridge is observed to be slightly nonuniform and nonstationary. Given the high sensitivity of the structural response to the distribution of step frequencies, and in some cases also to the nonuniform spatial distribution of the pedestrians, this indicates the necessity of obtaining detailed and accurate information on pedestrian behavior in the case of verification and validation using full-scale testing.

In terms of the observed structural response, the analysis shows that the different tests involving the same load case can be considered representative for that involved load case. In addition, it is shown that pedestrian excitation dominates over ambient excitation when walking persons are involved. This observation is confirmed by the identified distribution of step frequencies in the crowd, indicating a significant share of (near-)resonant loading with a number of modes of the footbridge. Furthermore, the dataset displays clear signs of HSI, suggesting a significant increase in effective modal damping ratio, owing to the presence of the crowd, particularly, for modes with a natural frequency close to that of the human body.

The paper concludes by giving a nonexhaustive overview of potential uses of the Eeklo Footbridge Benchmark Dataset. The uniqueness of the dataset is that it offers data on the synchronous measurement of the body motion of pedestrians and structural response for large-scale experiments with pedestrian densities up to 0.5 persons/m² and a digital twin of the empty footbridge. This makes the dataset ideally suited for the further development and validation of models for crowd-induced loading on footbridges, including HSI and HHI phenomena. Finally, this work aims to serve as a benchmark for future large-scale experiments involving pedestrian excitation, thereby contributing to the process of integrating state-of-the-art developments in the field of human-induced vibrations of footbridges in design guidelines and codes.

Data Availability Statement

Some or all data, models, or code that support the findings of this study are available from the corresponding author on reasonable request. The Eeklo Footbridge Benchmark Dataset is freely available on request to the corresponding author and at https://iiw.kuleuven.be/onderzoek/structural-mechanics/tools-downloads.

Acknowledgments

The first author is a postdoctoral fellow of Research Foundation Flanders (FWO). The second author is a doctoral fellow of FWO. Financial support from FWO is gratefully acknowledged.

References

AFGC (Association Française de Génie Civil). 2006. Sétra: Evaluation du comportement vibratoire des passerelles piétonnes sous l’action des piétons (Assessment of vibrational behaviour of footbridges under pedestrian loading). Sétra/AFGC.

Abstract

Introduction

Eeklo Footbridge

Experimental Study

Measurement Equipment and Setup

Structural Accelerations

3D Body Motion

Video Footage

Data Preprocessing

Events

Participants

Results and Discussion

OMA

Distribution of Step Frequencies

Pedestrian Trajectories

Structural Response

Potential Use of the Eeklo Benchmark Dataset

Conclusions

Data Availability Statement

Acknowledgments

References

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