Pedestrian-structure Interaction Research Articles

Long-term solutions of calibrated and generalised Macdonald’s model for pedestrian-induced lateral forces

The inverted pendulum pedestrian model (IPM) for walking on laterally-oscillating structures, originally proposed by Macdonald, has been recently calibrated based on data from pedestrians walking on a laterally-oscillating instrumented treadmill. It was then generalised to be suitable for the application in a predictive manner, i.e. in simulations of lateral structural response for any population of pedestrians. The generalised IPM captures the fundamental pedestrian-structure interaction mechanism and pedestrian-generated lateral forces onto a structure, including the self-excited forces which are critical from the point of view of structural stability. However, since the closed-form solutions of the generalised IPM are currently unavailable, its application requires numerical integration. To address this shortcoming, closed form solutions for the long-term average lateral self-excited forces are derived in this study based on the framework introduced by McRobie. A parametric study is conducted revealing complex interdependencies between pedestrian and bridge behaviour and their influence on the self-excited forces. The presented results are related to the measurements from full-scale bridges and laboratory investigations.

Análisis por condición de servicio causado por vibración vertical inducida por peatones en estructuras

Civil engineering structures such as grandstands, slabs, footbridges and staircases have reported unacceptable vertical vibration when they are affected by human activities. Even when most of these structures are designed according to current guidelines and design codes, there are still misunderstandings in the human-structure interaction effects that, in some cases, may increase the vibration response compromising the structural serviceability performance. As a result, the serviceability load conditions due to pedestrian activities control, in most cases, the design for these structures. Therefore, a systematic overview regarding vertical pedestrian-structure interaction is carried out to demonstrate the need for a realistic analysis to properly incorporate these effects toward more rational structural designs. The discussion establishes a body of knowledge regarding pedestrian loads and structural responses, yielding the potential for more rational approaches to improving the analysis and design of pedestrian structures.

Identification of Dynamic Parameters of Pedestrian Walking Model Based on a Coupled Pedestrian–Structure System

As human occupancy has an enormous effect on the dynamics of light, flexible, large-span, low-damping structures, which are sensitive to human-induced vibrations, it is essential to investigate the effects of pedestrian–structure interaction. The single-degree-of-freedom (SDOF) mass–spring–damping (MSD) model, the simplest dynamical model that considers how pedestrian mass, stiffness and damping impact the dynamic properties of structures, is widely used in civil engineering. With field testing methods and the SDOF MSD model, this study obtained pedestrian dynamics parameters from measured data of the properties of both empty structures and structures with pedestrian occupancy. The parameters identification procedure involved individuals at four walking frequencies. Body frequency is positively correlated to the walking frequency, while a negative correlation is observed between the body damping ratio and the walking frequency. The test results further show a negative correlation between the pedestrian’s frequency and his/her weight, but no significant correlation exists between one’s damping ratio and weight. The findings provide a reference for structural vibration serviceability assessments that would consider pedestrian–structure interaction effects.

Spatio-temporal assessment of gait kinematics in vertical pedestrian-structure interaction

Pedestrian structures regularly exhibit excessive vibrations when they are dynamically excited by human activities. Traditional modeling approaches neglect, due to the lack of suitable data, the temporal and spatial kinematic changes (such as the step length, step width, pace frequency and horizontal speed) when pedestrians are walking on a vibrating surface in the vertical direction such as slabs, footbridges, or stairs. Although several experimental studies have quantified the variability of human gait, most of these were conducted overground. These procedures do not fully account for the interaction between the pedestrian and an oscillating surface, compromising the comfort in service conditions for their occupants. In this paper, the spatio-temporal gait parameters were measured when six adults were instructed to walk on the beam and on the ground. The kinematic parameters were compared among the individual subjects to evaluate their variability associated with the vertical acceleration influence. Two gait modes were examined in this study, metronomic walk and self-selected pace. The results show that the walking locomotion parameters such as step length, step width, pace frequency, and pedestrian horizontal speed were found to have substantial differences on the ground as compared with the structural vibration under different walking modes. The findings here clearly demonstrate that gait and bridge kinematics interact, and continued research is warranted with larger numbers of participants under a wider range of structural conditions.

Theoretical Derivation and Parameters Analysis of a Human-Structure Interaction System with the Bipedal Walking Model

The excessive vertical vibration of structures induced by walking pedestrians has attracted considerable attention in the past decades. The bipedal walking models proposed previously, however, merely focus on the effects generated by legs and ignore the effects of the dynamics of body parts on pedestrian-structure interactions. The contribution of this paper is proposing a novel pedestrian-structure interaction system by introducing the concept of the continuum and a different variable stiffness strategy. The dynamic model of pedestrian-structure coupling system is established using the Lagrange method. The classical mode superposition method is utilized to calculate the response of the structure. The state-space method is employed to determine natural frequencies and damping ratio of the coupled system. Based on the proposed model, numerical simulations and parametric analysis are conducted. Numerical simulations have shown that the continuum enables the pedestrian-structure system to achieve the stable state more efficiently than the classic model does, which idealizes the body as a concentrated or lumped mass. The parametric study reveals that the presence of pedestrians is proved to significantly decrease the frequency of human-structure interaction system and improve its damping ratio. Moreover, the parameters of the bipedal model have a noticeable influence on the dynamic properties and response of the pedestrian-structure system. The bipedal walking model proposed in this paper depicts a pattern of pedestrian-structure interactions with different parameter settings and has a great potential for a wide range of practical applications.

Vertical Vibrations of Footbridges Due to Group Loading: Effect of Pedestrian–Structure Interaction

The vibration serviceability of footbridges has evolved from the adoption of a single pedestrian crossing in the resonance condition to load cases in which several pedestrians cross the structure simultaneously. However, in spite of this improvement, pedestrians continue to be considered as applied loads in codes of practice. Recent research has pointed out that modeling pedestrians as dynamic systems is a step further in the search for a more realistic design approach. This is explored in this paper, focusing on the case of vertical vibration. A two-span cable-stayed test structure was selected, and accelerations were measured from single and group crossings, both at the structure and at a pedestrian’s waist. Numerical simulations considering the pedestrians modeled as loads only and also as dynamic systems were implemented, and numerical and experimental time response vibration signatures were compared. Reductions of up to 25% and 20% in peak and RMS acceleration, respectively, were obtained when pedestrians were modeled as dynamic systems, in comparison with the less realistic model of pedestrians as loads only. Such reductions were shown to depend on the number of pedestrians involved in the group. The results, thus, highlight that pedestrian–structure interaction is an asset for the vibration serviceability design of footbridges.

Guidance for footbridge design: a new simplified method for the accurate evaluation of the structural response in serviceability conditions

This paper proposes a simplified hand-calculation methodology that permits a fast response assessment (both in vertical and lateral direction) under different pedestrian scenarios. This simplified method has the same accuracy than that of very sophisticated numerical nonlinear finite element models including pedestrian inter-variability, interaction among pedestrians in flows, and pedestrian-structure interaction. The method can capture the effects of pedestrian loads in and out of resonance. This methodology is based on a new, and experimentally contrasted, stochastic pedestrian load model derived by the authors implementing a multi-disciplinary state-of-the-art research, and on a large set of sophisticated finite element analyses.There is a significant gap in the literature available for bridge designers. Some current codes do not indicate how the performance for serviceability limit-states should be assessed, in particular for lateral direction. Others define methods that are not based on the latest research in this field and that require the use of dynamic structural analysis software. A very sophisticated load model, such as that described above, and recently proposed by the authors, may not be accessible for most of the design offices, due to time and software constraints. However, an accurate assessment of the serviceability limit state of vibrations during the design stages is paramount. This paper aims to provide designers with an additional simple tool for both preliminary and detailed design for the most typical structural configurations.First, the paper presents the methodology, followed by an evaluation of the impact of its simplifications on the response appraisal. Second, the paper evaluates the validity of the methodology by comparing responses predicted by the method to those experimentally measured at real footbridges. Finally, the paper includes a parametric analysis defining the maximum accelerations expected from pedestrian streams crossing multiple footbridges. This parametric analysis considers different variables such as section type, structural material, span length and traffic-flow characteristics, and shows the sensitivity of the serviceability response to traffic-flow characteristics and span length in particular.

Impact of stochastic representations of pedestrian actions on serviceability response

Over the past 15 years, there have been some research outcomes in other disciplines that could be used to produce new, more accurate and realistic numerical models to characterise pedestrian loads and to significantly improve predictions of response for multiple-pedestrian scenarios. However, the disconnection between fields has not facilitated this further research. Using this, the paper presents (a) a new sophisticated load model that includes a description of vertical and lateral loads, including pedestrian–structure interaction, (b) the numerical description of relationships to describe the key parameters of the proposed model and (c) the evaluation of the effects of pedestrian characteristics that are relevant for serviceability response of footbridges. The proposed new load model allows for the inherent variability of individual pedestrian actions (intra-subject variability), a probabilistic description of how pedestrian characteristics vary among subjects (inter-subject variability) and collective human behaviour (pedestrian–pedestrian interaction). Some of these characteristics are not currently considered in design approaches and can have a substantial impact on structural response assessments. Finally, recommendations are made for many of these characteristics to be introduced in analyses to evaluate the vibration serviceability limit state of footbridges in a more accurate and realistic manner.

Structured uncertainty for a pedestrian-structure interaction model

A yearning for visually appealing bridges that are longer and more slender is driving advances in construction materials and techniques, alongside the necessary improvements in design guidelines and standards. However, lighter and more slender structures are also more susceptible to vibration. Certain pedestrian structures do frequently exhibit excessive vibrations when they are dynamically excited by walking pedestrians. To improve pedestrian-structure design procedures, uncertainties in the human biodynamic subsystem should be systematically included, and should represent a suitable range of possible body characteristics. Variations in the representation of the human body are intended to capture differences in physical characteristics while that human is walking on a lively surface. Here these variations are described as parametric uncertainties, while the structure is assumed to be known and deterministic. A time-varying and coupled model of the pedestrian-structure system is adopted, and the corresponding perturbations are defined as a set of structured uncertainties describing imprecise biodynamic parameters that can adopt any value within their proposed intervals. This parametric model with structured uncertainty is then used to obtain the range of biodynamic parameters for a variety of pedestrians by comparing the predicted structural responses against the experimental data. Experimental results are used to determined a set of intervals of biodynamic parameters such as mass, damping, stiffness, and pace frequency for a walking pedestrian. The simulation results show that the developed human-structure model with associated parameter intervals is able to obtain realistic serviceability demands by predicting the range of structural responses for a wide range of pedestrians.

A Three-Dimensional Pedestrian–Structure Interaction Model for General Applications

A three-dimensional (3D) pedestrian–structure interaction (PSI) system based on the biomechanical bipedal model is presented for general applications. The pedestrian is modeled by a bipedal mobile system with one lump mass and two compliant legs, which comprise damping and spring elements. The continuous gaits of the pedestrian are maintained by a self-driven walking kinetic energy, which is a new driven mechanism for the mobile unit. This self-driven mechanism enables the pedestrian to operate at a varying total energy level, as an important component for further modeling of the crowd-structure dynamic interaction. Numerical studies show that the pedestrian walking on the structure leads to a reduction in the natural frequency, but an increase in the damping ratio of the structure. This model can also reproduce the reaction forces between the feet and structure, similar to those measured in the field. In addition, the proposed model can well describe the 3D pedestrian–structure dynamic interaction. It is recommended for use in further study of more complicated scenarios such as the dynamic interaction between a large scale kinetic crowd and slender footbridge.

A framework for quantification of human-structure interaction in vertical direction

In lightweight structures, there is increasing evidence of the existence of interaction between pedestrians and structures, now commonly termed pedestrian-structure interaction. The presence of a walker can alter the dynamic characteristics of the human-structure system compared with those inherent to the empty structure. Conversely, the response of the structure can influence human behaviour and hence alter the applied loading. In the past, most effort on determining the imparted footfall-induced vertical forces to the walking surface has been conducted using rigid, non-flexible surfaces such as treadmills. However, should the walking surface be vibrating, the characteristics of human walking could change to maximize comfort. Knowledge of pedestrian-structure interaction effects is currently limited, and it is often quoted as a reason for our inability to predict vibration response accurately. This work aims to quantify the magnitude of human-structure interaction through an experimental-numerical programme on a full-scale lively footbridge. An insole pressure measurement system was used to measure the human-imparted force on both rigid and lively surfaces. Test subjects, walking at different pacing frequencies, took part in the test programme to infer the existence of the two forms of human-structure interaction. Parametric statistical hypothesis testing provides evidence on the existence of human-structure interaction. In addition, a non-parametric test (Monte Carlo simulation) is employed to quantify the effects of numerical model error on the identified human-structure interaction forms. It is concluded that human-structure interaction is an important phenomenon that should be considered in the design and assessment of vibration-sensitive structures.

Modelling framework of pedestrian-footbridge interaction in vertical direction

This study presents a modelling framework of human-structure interaction in the vertical direction, which integrates the three following key issues: crowd dynamics, pedestrian-structure interaction (PSI) and inter-subject and intra-subject variability of pedestrian walking loads. The framework comprises two main models: a microscopic model of crowd dynamics and a coupled dynamic model of the PSI. The latter is composed of three sub-models: a SDOF system having the dynamic properties of the empty structure, a SDOF system for each pedestrian and a stochastic force model. Each pedestrian SDOF moves along the footbridge following the trajectory and at the velocity simulated by the crowd model and is accompanied by a stochastic walking force time-history that accounts for inter- and intra-subject variability. Performance of the suggested modelling framework is studied through simulations of the vibration responses of four virtual footbridges due to different traffic scenarios.

Vertical Crowd–Structure Interaction Model to Analyze the Change of the Modal Properties of a Footbridge

In this paper, a biomechanical crowd–structure interaction model is proposed and further implemented to adequately estimate the energy exchange between pedestrians and a footbridge. The proposed model focuses on the vibrations in the vertical direction, and it allows for taking into account the change of the modal properties of the structure due to the presence of the pedestrians, thus improving the numerical estimation of the response of the structure under pedestrian flows. The model involves two submodels, namely (1) a pedestrian–structure interaction submodel and (2) a crowd submodel. The first submodel follows from a modal projection of a system with two degrees of freedom, which simulates the behavior of each pedestrian, on the vibration modes of the structure. The parameters of this model have been estimated from the accelerations recorded on a real footbridge. For the second submodel, the crowd behavior is simulated via a multiagent method. The performance of the resulting overall model is assessed by correlating the experimental and numerical dynamic of a real footbridge under a group of pedestrians at different controlled step frequencies. In particular, the change in the first natural frequency induced by the pedestrian–footbridge interaction is discussed in detail. The proposed model leads to numerical results that exhibit good agreement with the recorded experimental values. Therefore, it becomes a valuable tool for estimating the change on the modal properties of a footbridge induced by the crowd–structure interaction phenomenon.

Experimentally fitted biodynamic models for pedestrian–structure interaction in walking situations

The interaction between moving humans and structures usually occurs in slender structures in which the level of vibration is potentially high. Furthermore, there is the addition of mass to the structural system due to the presence of people and an increase in damping due to the human body´s ability to absorb vibrational energy. In this paper, a test campaign is presented to obtain parameters for a single degree of freedom (SDOF) biodynamic model that represents the action of a walking pedestrian in the vertical direction. The parameters of this model are the mass (m), damping (c) and stiffness (k). The measurements were performed on a force platform, and the inputs were the spectral acceleration amplitudes of the first three harmonics at the waist level of the test subjects and the corresponding amplitudes of the first three harmonics of the vertical ground reaction force. This leads to a system of nonlinear equations that is solved using a gradient-based optimization algorithm. A set of individuals took part in the tests to ensure inter-subject variability, and, regression expressions and an artificial neural network (ANN) were used to relate the biodynamic parameters to the pacing rate and the body mass of the pedestrians. The results showed some scatter in damping and stiffness that could not be precisely correlated with the masses and pacing rates of the subjects. The use of the ANN resulted in significant improvements in the parameter expressions with a low uncertainty. Finally, the measured vertical accelerations on a prototype footbridge show the adequacy of the numerical model for the representation of the effects of walking pedestrians on a structure. The results are consistent for many crowd densities.

A direct pedestrian-structure interaction model to characterize the human induced vibrations on slender footbridges

Although the scientific community had knowledge of the human induced vibration problems in structures since the end of the 19th century, it was not until the occurrence of the vibration phenomenon happened in the Millennium Bridge (London, 2000) that the importance of the problem revealed and a higher level of attention devoted. Despite the large advances achieved in the determination of the human-structure interaction force, one of the main deficiencies of the existing models is the exclusion of the effect of changes in the footbridge dynamic properties due to the presence of pedestrians. In this paper, the formulation of a human-structure interaction model, addresses these limitations, is carried out and its reliability is verified from previously published experimental results.

Benchmark Footbridge for Vibration Serviceability Assessment under the Vertical Component of Pedestrian Load

Vibration serviceability criteria are governing the design and determining the cost of modern, slender footbridges. Efficient and reliable evaluation of dynamic performance of these structures usually requires a detailed insight into the structural behavior under human-induced dynamic loading. Design procedures are becoming ever more sophisticated and versatile, and for their successful use, a thorough verification on a range of structures is required. The verification is currently hampered by a lack of experimental data that are presented in the form directly usable in the verification process. This study presents a comprehensive experimental data set acquired on a box-girder footbridge that is lively in the vertical direction. The data are acquired under normal operating conditions and are presented using a range of descriptors suitable for easy extraction of desired information. This will allow researchers and designers to use this bridge as a benchmark structure for vibration serviceability checks under the vertical component of the pedestrian loading. In addition, capabilities of a sophisticated force model (developed for walking over rigid surfaces) to predict vibrations on this lively bridge are investigated. It was found that there are discrepancies between computed and measured responses. These differences most likely are a consequence of the pedestrian-structure interaction on this lively bridge. The interaction was then quantified in the form of pedestrian contribution to the overall damping of the human-structure system.

Synchronization among Pedestrians in Footbridges due to Crowd Density

AbstractCrowding is a critical condition for footbridges that are prone to vibration problems from pedestrian loads. Synchronization of pedestrian movements has been identified as the cause of the excessive lateral vibration in some footbridges. Two conditions have been named as the cause of synchronization: increase in crowd density and pedestrian-structure interaction. The former would be related to the onset of the phenomenon; the latter takes place after structural vibration reaches a certain level. This paper focuses on the former condition. A test program to investigate whether this condition occurs was carried out for a range of pedestrian densities, complementing data previously published on this subject. The head movement of pedestrians walking both in groups and in a flow was recorded by a video camera, and the examination of the video indicated no synchronization from densification. However, it was observed that the lateral sway of the pedestrians’ bodies increased with the increase of density....

Numerical analysis of a synchronization phenomenon: Pedestrian–structure interaction

The pedestrian–structure interaction is considered by developing a non-linear double pendulum model, representing the lateral walking of the pedestrian and the horizontal vibration mode of the structure. To understand the synchronization phenomenon, the two oscillators were considered in their phase spaces, and a ring-dynamics approach was applied. As synchronization occurs, pedestrian motion becomes in phase quadrature with a quarter-of-period in advance of the bridge motion: this ensures stability of walking conditions on a moving deck, but causes random cancellation of forces typical of an incoherent crowd. Correspondingly, the lateral force transmitted to the structure increases its value, approaching resonance conditions.

Lateral excitation of bridges by balancing pedestrians

On its opening day, the London Millennium Bridge (LMB) experienced unexpected large amplitude lateral vibrations due to crowd loading. This form of pedestrian–structure interaction has since been identified on several other bridges of various structural forms. The mechanism has generally been attributed to ‘pedestrian synchronous lateral excitation’ or ‘pedestrian lock-in’. However, some of the more recent site measurements have shown a lack of evidence of pedestrian synchronization, at least at the onset of the behaviour. This paper considers a simple model of human balance from the biomechanics field—the inverted pendulum model—for which the most effective means of lateral stabilization is by the control of the position, rather than the timing, of foot placement. The same balance strategy as for normal walking on a stationary surface is applied to walking on a laterally oscillating bridge. As a result, without altering their pacing frequency, averaged over a large number of cycles, the pedestrian effectively acts as a negative (or positive) damper to the bridge motion, which may be at a different frequency. This is in agreement with the empirical model developed by Arup from the measurements on the LMB, leading to divergent amplitude vibrations above a critical number of pedestrians.