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Statistical analysis of the vertical human walking forces and human structural interaction effects



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Peters, Angus 


The increased ambition of architects, advancements in structural materials, and the rapidly growing pressure on the civil engineering sector to reduce embodied carbon has resulted in more slender pedestrian structures. Such structures are susceptible to excessive vibrations due to human activities, for example, walking, which is the most frequent human activity. Due to the slender design, modern structures provide a greater likelihood to have low natural frequencies. Low natural frequencies can result in resonant walking paces matching a vertical mode of the structure. Therefore, the structures are prone to resonant and often excessive vibrations that may compromise the serviceability limit state. Current industry guidance is used ubiquitously to provide all information on the vibration serviceability assessment due to walking, with academic research outcomes often overlooked. Recent research concludes that industry load models incorporate inherent bias through the limited intra-subject variation and poor correlation with actual walking loads.

Current guidance pertaining to the vibration serviceability assessment does not disclose or encourage human structure interaction effects, even though a significant body of research demonstrates the benefits of its inclusion. Current estimations of structural responses do not align with the physical measurements of structures. The resultant acceleration estimations from the guidance are often overestimated compared to the actual structural response. Therefore, many structures may have been overdesigned due to the exclusion of human structural interaction effects and inaccurate load models within current guidance.

For the stated reasons, demand for further investigation into the correct representation of vertical walking forces and the human structure interaction is required. This thesis seeks to deepen understanding of both topics' appropriate and accurate representation through an experimental campaign and analysis, to reduce the error between predicted and monitored results.

An innovative method of extracting walking load parameters encompasses all information within the close frequency range of the walking frequency. A representative interpolation of the vertical walking is formed through the successive sampling of individual footsteps based on both the inter- and intra-subject variation. The proposed model is demonstrated to minimise the error between the resultant acceleration output of the structure compared to the acceleration of real walking loads, than any current guidance. Furthermore, it is statistically shown that walking parameters and characteristics depend on the participants' sex.

Current industry guidance and research load models are then investigated in their ability to model the acceleration response of structures compared to their real load counterparts. It is demonstrated that current research models in the low and high-frequency ranges outperform current industry load models, with respect to minimising the difference between the synthetic force and real force acceleration output. Several current industry guidance models oversimplify the vertical walking load, causing an overestimation of acceleration results compared to real walking forces. Such models are shown to overestimate the acceleration response by double that of real walking loads. One of the two models, that produced the smallest errors with respect to real walking, has been published for over 12 years. However, there needs to be more uptake within the engineering community for the models' use. A disconnect between industry and academia is noted, resulting in poor dissemination of knowledge and current best practices.

Current representations of the human structure interaction effects of the moving pedestrian, modelled through a single degree of freedom (SDOF) spring, mass, and damper (SMD), are compared to physical measurements of a flexible fibre-reinforced polymer bridge. These estimations of the human structure interaction are used to provide a numerical approximation of the vertical acceleration of the structure, by comparing the responses to the actual measurement of 56 volunteers. It is shown that all numerical simulations of SDOF SMD parameters from research, bar one paper, provide consistent responses with those monitored on the structure. Yet the specific parameters demonstrate a wide range of acceptable values. Many current parameter estimations are viewed monolithically through a single deterministic value; however, an entire spectrum of parameter values is evidenced. Finally, an inverse analysis of the measured accelerations is used to produce updated human structure interaction parameter estimates of the SDOF SMD human model. The resultant mean estimations of the parameters produce values both consistent and inconsistent with previously published results; however, the consequent acceleration response is within the physical range of the volunteer acceleration time histories. A limitation of the study and previous studies is highlighted. As the exact walking force is unknown, the parameters' estimations diverge depending on the input walking force.





Orr, John


Human induced Vibrations, SLS


Doctor of Philosophy (PhD)

Awarding Institution

University of Cambridge
EPSRC (2106111)