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Three bipedal models (IPM, RFM and SMM) were quantitatively reviewed in this chapter. In the analysis of each model, ranges of input parameters and parametric scan were provided. To assess the applicability of the models for modelling pedestrian-structure dynamic interaction (PSDI), each model is evaluated against three criteria defined in Section 2.3.5 and the results are summarised in Table 3.1. Three criteria are repeated as follows:

• Criterion 1: the model should be able to replicate the walking

phases and trajectory of BCoM (i.e. mp) which are in accordance

with the literature.

• Criterion 2: the model should be able to generate the realistic

range of kinematic parameters, e.g. pacing rate and walking speed.

• Criterion 3: the model should produce a genuine form of GRF

on rigid surface in terms of both the shape of the time domain waveform and the amplitude of the frequency spectrum.

As the simplest model reviewed, IPM cannot accurately reproduce all phases of walking gait or the trajectory of the BCoM. However, it does provide a good approximation of human walking gait in the single stance phase, which

Table 3.1: Evaluation of bipedal models against criteria for PSDI study.

Models Criterion 1 Criterion 2 Criterion 3

IPM RFM

SMM - -

represents 80 % of a gait cycle (Chapter 2). As a result, it can be considered that the IPM satisfies, at least partially, Criterion 1. The parametric scan shows that a wide range of walking parameters seen in experimental data can be reproduced. IPM can be used to represent different walking gaits of human population and can be said to satisfy Criterion 2. Finally, the model produces a realistic range of DLF1, which is sufficient for modelling human walking of low-frequency structures (i.e. natural frequency below 2.5 Hz). Thus, the IPM satisfies Criterion 3.

The introduction of the rocker foot feature in the RFM leads to reduced, i.e. more realistic, excursion of BCoM when compared to the IPM. Moreover, the rocker feature contributes to more genuine representation of the CoP pro- gression. As a result, the RFM is deemed satisfactory for Criterion 1. The parametric scan suggests that the RFM can produce a wide range of walking parameters and therefore it is considered to meet Criteria 2 and 3. Overall, the RFM possesses a number of improvements when compared to the IPM. However, as only a minor upgrade from the IPM, the RFM still has limita- tions that are inherited from the IPM (e.g. neglects the double support phase and provides unrealistic DLFs for second and higher harmonics). Thus, it is unlikely that utilising the RFM can provide significant improvements in PSDI modelling when compared with the application of the IPM.

Among the three models reviewed, the SMM is capable of best replicating the trajectory of BCoM. Therefore, the SMM satisfies Criterion 1. The para- metric scan shows that the SMM has difficulties in covering range of human walking speed and, therefore, only partly satisfies Criterion 2. In addition, the spring-like legs contribute to the qualitatively accurate replication of the typical M-shaped GRF pattern. DLFs of the higher harmonics are in realis- tic ranges, which is a significant improvement when compared to simulations using the IPM and the RFM. Unfortunately, the parametric scan only found limited number of stable solutions that have realistic DLF1 in the low range of pacing rate (1.4–1.7 Hz). This feature prevents the SMM from fully meeting Criterion 3. In summary, the SMM does not fully satisfy Criteria 2 and 3. These limitations, along with the complexity in selecting initial conditions to result in stable solutions, indicate that the SMM is not the best choice for further investigation of PSDI.

To conclude, the analysis in this chapter shows that the IPM, despite its limitations, has potential to be used in the study of PSDI. The IPM is, therefore, chosen for modelling PSDI in this thesis. After completing an ex- perimental programme to determine characterisation of walking on the rigid surface (Chapter 4) and the lively surface (Chapter 5), the IPM will be utilised for modelling human locomotion on vibrating surfaces in Chapter 6.

Chapter 4

Experimental characterisation

of walking on rigid surface

4.1

Introduction

To establish a model of pedestrian-structure dynamic interaction (PSDI), it is necessary to gain experimental insight into structural and human behaviour when structure vibrates perceptibly. Therefore, the next step in the study is to develop an understanding of the PSDI phenomenon through controlled experiments. The ultimate aim of the experimental work is to verify/correct assumptions made in numerical modelling, and to increase the reliability of the model and resulting vibration estimates.

To understand PSDI, it is also crucial to continuously monitor pedestrian behaviour while walking over perceptibly vibrating surfaces and observe any potential changes in human walking. In addition, it is important to compare the observed parameters to those recorded when walking on rigid surface. As a result, the experimental programme started with measurements on the rigid surface, and the results are reported in this chapter. These results will be

used as a benchmark in the analysis of experimental data acquired on a lively structure that will be reported in Chapter 5.

To quantify PSDI, knowledge about the pedestrian-induced dynamic force and pedestrian kinematics are required. In the context of this thesis, the first aim is to accurately quantify force in both time and frequency domains to allow structural engineers to use the information in vibration prediction. The second aim of monitoring the kinematic data is to improve understanding of variations in key walking parameters during PSDI (such as pacing rate, step length, step width etc.).

To study variations of the dynamic force and walking parameters dur- ing PSDI, it is necessary to monitor pedestrians over multiple steps. Since walking is an activity in which the pedestrian’s position in space changes with time, capturing consecutive steps is not a straightforward task. Section 4.2 of this chapter provides a short background information of ground reaction force (GRF) measurement. Among a number of methods to monitor the dy- namic loads, a motion capture system for indirect measurement of the force was at the author’s disposal, and is described in the same section. The pre- cision of this method has not been fully documented in literature. For this reason, Section 4.3 quantifies the accuracy of the method with respect to force measurement and propagation of the measurement error into the structural vibration estimate. In Section 4.4, the kinematic and kinetic data of pedes- trians are investigated. To the best knowledge of the author, this is the most comprehensive study investigating kinematic and kinetic data (while walking) relevant for civil engineering applications. Section 4.5 at the end of the chapter provides summary of main findings.

All experiments in this thesis were approved by the Biomedical and Sci- entific Research Ethics Committee at the University of Warwick. Before com- mencing experiments, test subjects (TSs) signed a consent form, acknowledg- ing their awareness of the test protocol and associated risks. In addition, each TS was asked to answer questions about their health status. Only TSs in good health condition were allowed to take part in the experiments. Both the consent and the questionnaire forms can be found in Appendix B.