Chaix

Sanjeev Bista

Isaac Debache

Basile Chaix

Physical activity and sedentary behavior related to transport activity assessed from multiple body-worn accelerometers: the RECORD MultiSensor Study

Keywords: Active transport, Accelerometers, Sedentary Behaviours, Moderate to Vigorous physical Activity (MVPA), GPS, Physical Activity

Physical activity and sedentary behaviour related to transport activity assessed with multiple body-worn accelerometers: the RECORD MultiSensor Study

Introduction

Surveillance article concluded that the level of physical activity is low throughout the world, where only about 69% of adults meet the recommended physical activity level (1). European commission in 2014 reported that 48% of the European adults were engaged in sports, 41% do other shorts of physical activity whereas 30% were totally inactive [START_REF] Wolf | Impact of underreporting on mileage and travel time estimates: Results from global positioning system-enhanced household travel survey[END_REF]. WHO in 2010 recommended that adults (18-64 years old) need to do 75 minutes of vigorous-intensity aerobic physical activity once a week (3), howevere, only 56% of the adult French population were found following the recommendation (3). A report from the united kingdom reported that lack of physical activity is ranked as 4th leading cause of mortality (4). Apart from physical activity itself, studies have highlighted that prolonged sedentary behaviour is associated with the risk of diabetes, obesity, and some cancers among adults (5)(6)[START_REF] Healy | Objectively Measured Sedentary Time, Physical Activity, and Metabolic Risk: The Australian Diabetes, Obesity and Lifestyle Study (AusDiab)[END_REF].

A pitfall of previous surveillance studies is that they have often aggregated the information on physical behaviors into daily or weekly averages of physical activity [START_REF] Wanigatunga | Physical activity fragmentation as a potential phenotype of accelerated aging[END_REF]. However, such analyses ignore the continuous sequence of physical behaviors performed by individuals over the day in their different activities. Instead, studies should investigate physical activity and sedentary behavior, by aggregating the physical activity information over relevant subperiods during the day, such as places visited or trips, in order to better identify the most important physical activity contexts [START_REF] Almanza | A study of community design, greenness, and physical activity in children using satellite, GPS and accelerometer data[END_REF][START_REF] Rodríguez | Out and about: Association of the built environment with physical activity behaviors of adolescent females[END_REF]. Investigating the relationship at both the trip stage and trip level is useful to distinguish what a mode (e.g., public transport) yields in itself in terms of physical activity and sedentary time from what it yields when distances of access to the mode and potential transfer episodes between trip stages are accounted for.

Active transport (referring to all trip stages based on human-powered transport), as a component of physical activity, has positive health effects [START_REF] Wanner | Active Transport, Physical Activity, and Body Weight in Adults[END_REF]. Adults have been shown to be active when they are travelling back and forth to work, and particularly in trips made with public transport [START_REF] Chaix | Active transportation and public transportation use to achieve physical activity recommendations? A combined GPS, accelerometer, and mobility survey study[END_REF]. However, measuring physical activity in trips is particularly challenging.

For example, a study used Global Positioning System (GPS) receivers, movement sensors, and heart rate monitoring for measuring the physical activity in a limited number of trips, only home-work trips, and therefore had a limited generalizability [START_REF] Costa | Quantifying the physical activity energy expenditure of commuters using a combination of global positioning system and combined heart rate and movement sensors[END_REF]. Many studies that used GPS receiver, accelerometers, and advanced algorithm to predict transport mode [START_REF] Wang | Accelerometer Based Transportation Mode Recognition on Mobile Phones[END_REF][START_REF] Zhang | A new post correction algorithm (PoCoA) for improved transportation mode recognition[END_REF] have not verified the predicted transport mode with participants, which likely results in prediction error in their data. On the opposite, studies should develop reliable methods for validating the transport modes that were used by the participants with the participants themselves, to make the findings more trustworthy [START_REF] Chaix | Active transportation and public transportation use to achieve physical activity recommendations? A combined GPS, accelerometer, and mobility survey study[END_REF][START_REF] Chaix | Mobile Sensing in Environmental Health and Neighborhood Research[END_REF].

Most studies of physical activity in particular places or during trips have provided crude differences in cumulated times of moderate to vigorous physical activity or sedentary time [START_REF] Chaix | A GPS-Based Methodology to Analyze Environment-Health Associations at the Trip Level: Case-Crossover Analyses of Built Environments and Walking[END_REF][START_REF] Chaix | Combining sensor tracking with a GPS-based mobility survey to better measure physical activity in trips: Public transport generates walking[END_REF]. To provide a more accurate picture, studies establishing profiles of physical behaviors in terms of duration, partition [START_REF] Wanigatunga | Physical activity fragmentation as a potential phenotype of accelerated aging[END_REF][START_REF] Chastin | Methods for objective measure, quantification and analysis of sedentary behaviour and inactivity[END_REF], and transitions between categories of behaviors are needed. Partitions, as opposed to the cumulative time of a behavior, relate to the number and lengths of continuous periods over which the behavior is detected. The rationale for focusing on transitions is that it is currently emphasized that prolonged sedentary bouts are particularly detrimental for health and that for a given amount of time spent in sedentary postures, it is better to incorporate activity breaks into these sedentary episodes [START_REF] Dempsey | Associations of context-specific sitting time with markers of cardiometabolic risk in Australian adults[END_REF].

Overall, the objective of our study was to analyze the relationships between transport modes used and the duration and partition profile of physical behaviors, at both the trip stage and trip levels, using linear mixed models. Relatedly, a secondary aim of our paper was to compare an hip-worn accelerometer with two combined thigh-and trunk-worn accelerometers in their ability to assess physical behaviors and body postures such as sitting or standing in trips.

Methods

Population

The data used come from the RECORD MultiSensor Study [START_REF] El Aarbaoui | Short-term association between personal exposure to noise and heart rate variability: The RECORD MultiSensor Study[END_REF], of the Record Cohort [START_REF] Chaix | Cohort profile: residential and non-residential environments, individual activity spaces and cardiovascular risk factors and diseases--the RECORD Cohort Study[END_REF]. Among the 286 final participants to the RECORD Multisensor Study, 157 were included in the substudy where they had to carry a BT-Q1000XT GPS receiver, a wGT3X+ waist-worn accelerometer, and two combined accelerometers at the trunk and thigh (VitaMove, Temec Instruments, The Netherlands) over a period of 7 days. The other 131 participants were included in another cardiovascular substudy and are not considered here. Participants in the two substudies were not statistically different in terms of age, sex, education level, employment status, and area of residence, as reported in Web Appendix 1. Regarding our 157 participants, for 2 participants, the trunk and thigh accelerometers did not function properly; these participants were excluded from the analysis, leaving 155 participants for the analyses. Out of 8085 stages of trips made by these 155 participants, 393 (4.9%) were not included due to a failure of the VitaMove devices or because these devices were not worn. Therefore, 7692 trip stages from 4683 trips were included in our analysis.

Classification of trip stages and trips

Trip stages are portions of trips with a unique mode. Within a trip, two trip stages are necessarily separated by an episode of transfer between the two assigned to a punctual location, which also count as a trip stage.

The data extracted from the BT-Q1000XT GPS receiver were pre-processed after the 7-day data collection in order to identify the visited places as well as the start and end times of each trip stage, defined as a segment of a trip using a unique transport mode. Such processing algorithms are integrated in the TripBuilder web mapping application [START_REF] Oliveira | Global Positioning System-Assisted Prompted Recall Household Travel Survey to Support Development of Advanced Travel Model in Jerusalem, Israel[END_REF][START_REF] Wolf | Eighty Weeks of Global Positioning System Traces: Approaches to Enriching Trip Information[END_REF], and are briefly described in Web Appendix 2. Using this application, the trip data were then consolidated during a phone mobility survey with the participants, producing in the end a detailed timetable covering the 7-day observation period (see Web Appendix 2 for details). This timetable consisted of a time-stamped list of the visited places and trip stages between them.

Each trip comprises one or several trip stages. In trips with several stages, the whole trip also includes the transfer time between several trip stages. Our crude classification of trip stages was as follows: entirely walked, biking/rollers/skateboard (other active modes); public transport; privately owned vehicles; and other non-local trips involving long-distance trains and planes. Our detailed classification of modes further distinguished driving own personal vehicle from travelling through a private vehicle as a passenger (including taxi); and subdivided public transport into (i) bus/coach, (ii) metro, (iii) suburban train including RER (trains travelling within Paris and suburban cities), standard suburban trains, and TER (trains for joining Paris to suburbs or nearby regions), and (iv) trams.

At the trip level, trips were classified into the same categories. Trips that comprised two or more non-walking modes were assigned to a separate multi-mode trip category.

Additionnally, each trip or trip stage was coded as on a weekday vs. weekend day and performed in Spring or Summer vs. Automn or Winter.

Processing of accelerometer data

The VitaScore software was used to process the VitaMove trunk and thigh accelerometer data, and classify each second into 5 groups: sitting, lying, standing, light physical activity (LPA, including slow walking), and moderate-to-vigorous physical activity (MVPA). The VitaMove monitors and the VitaScore software have already been validated and used in several studies [START_REF] Postma | Validity of the detection of wheelchair propulsion as measured with an Activity Monitor in patients with spinal cord injury[END_REF][START_REF] Bussmann | Measuring daily behavior using ambulatory accelerometry: The activity monitor[END_REF][START_REF] Nooijen | Validation of an activity monitor for children who are partly or completely wheelchair-dependent[END_REF]. The device on the trunk is a 3-axis accelerometer, with axes perpendicular to, longitudinal to, and transversal to the trunk, while the device on the thigh has only 1 axis, sagittal to the right upper leg. Information on the orientation of these axes compared to the gravitational axis are used to infer posture. For example, when both the trunk longitudinal axis and the leg sagittal axis are +1g and the other axes are zero, then the posture is assumed to be sitting. ActiLife 6.11.9 was used to process the waist-worn accelerometer data. The standard inclinometer data indicated the number of seconds of sitting, lying, and standing for each of the 5-second epochs. For comparing the VitaMove posure data to the Actigraph inclinometer [START_REF] Sasaki | Validation and comparison of ActiGraph activity monitors[END_REF] data, the VitaMove standing, LPA, and MVPA were considered as standing. The Actigraph algorithm assumes that the person is standing when counts are above 100 per minute [START_REF] Hänggi | Validation of the GT3X ActiGraph in children and comparison with the GT1M ActiGraph[END_REF]. When counts are less than 100, the accelerometer senses the acceleration due to gravity, which is a down vector from which the orientation of the device is determined. Based on the orientation of the 3 axes compared to gravity, two angles are calculated, which allow the device to distinguish between lying and sitting. Carr and Mahar concluded that in an average, standing, sitting, and lying were coded accurately for 88.0%, 82.9% and 96.3% of the time respectively by the Actigraph inclinometer function that we use [START_REF] Carr | Accuracy of Intensity and Inclinometer Output of Three Activity Monitors for Identification of Sedentary Behavior and Light-Intensity Activity[END_REF].

For each trip or each trip stage, we calculated the cumulated duration in each physical behavior.

We also calculated a version of these variables standardized per units of 10 minutes of trip or trip stage.

For a simplified partition analysis based on the VitaMove data, physical behaviours were categorized those into 3 broad groups: SB (combining lying and sitting), NSB (including standing and LPA), and MVPA. Identifying uninterrupted segments of SB, NSB, and MVPA within each trip / trip stage, we determined the median length of such segments separately for SB, NSB, and MVPA within each trip and trip stage. This indicator was standardized per 1 minute of trip or trip stage. We also calculated the number of transitions between SB and NSB, NSB and MVPA, and SB and MVPA within each trip and each trip stage. The latter partition indicator was standardized per units of 10 minutes of trip / trip stage.

Sociodemographic characteristics

Gender was coded in two categories. Age was coded as a continuous variable (age square was tested but not retained as useless). Education was subdivided in 4 categories: no formal education or primary or lower secondary education; higher secondary or lower tertiary education; intermediate tertiary education; upper tertiary education. Employment status was coded as having a stable job; having a fixed-term or precarious contract; or being unemployed.

Finally, we took into account the area of residence: Paris; close suburb; far suburb.

Statistical Analysis

Unstandardized and standardized durations of physical behaviors and partition indicators were tabulated by transport modes at the trip and trip stage levels. Relationships between transport modes and unstandardized and standardized durations of physical behaviors were estimated separately at the trip level and trip stage level (one observation per trip and trip stage) using multilevel linear models [START_REF] Goldstein | Multilevel time series models with applications to repeated measures data[END_REF] with a random effect at the individual level to account for trips nested within participants. Web Appendix Figure 1 in Web Appendix 3 (for sitting duration)

shows that there was some residual autocorrelation between trip stages that were 1 hour apart or less. The AR(1) autoregressive correlation structure was applied to a continuous time variable (in hours) for modeling this time autocorrelation of errors within participants in the multilevel model [START_REF] Kincaid | Guidelines for selecting the covariance structure in mixed model analysis[END_REF][START_REF] Pinheiro | Mixed-effects models in S and S-PLUS[END_REF]. The Akaike Information Criterion indicated that a model with an individual-level random intercept, sociodemographic covariates, and the transport mode variable was markedly improved when AR(1) was added to the model (models' AIC were improved by >400 for sitting duration and by >1300 for MVPA duration).

All models were adjusted for sociodemographic characteristics. Sociodemographic groups differ in their usual trips with a given transport modes, as they live in and travel to different places. Even for a given trip with a particular mode from point A to point B, although they would all have to walk the same distance, climb the same stairs, etc., they could differ for example in their propensity to stand or sit during public transport trips. If our sample of participants and trips were representative of the Ile-de-France region, the relationship between transport modes and physical activity not adjusted for sociodemographic characteristics would meaningfully represent the average physical activity condition per transport mode in the region.

However, because our sample is distorted towards well educated participants, it is needed to control for sociodemographic characteristics. However, it is important to emphasize that this statistical adjustment yields an abstract estimate artificially assuming a similar sociodemographic structure across transport modes (and thus for example ignoring the fact that a large share of itineraries with a particular mode are located in relatively disadvantaged neighborhoods or in relatively advantaged neighborhoods) Weekday/weekend day and season of the trip were associated with durations of certain physical behaviors, but not with durations standardized by 10 minutes of travel time. Therefore, they were only introduced in models for unstandardized outcomes.

We also estimated multilevel models with interaction terms between transport mode and weekdays/weekend days and/or between transport mode and season. The destinations and transport modes of trips may vary between the week and the week-end and between seasons, and this may affect both the distribution of physical activity and sedentary behaviors within each mode and the hierarchy between modes in terms of physical activity and sedentary behaviors.

Since the ranking of transport modes was similar in the models with only one or with the two interaction terms, we used the models with a single interaction term for plotting the predicted durations of physical behaviors by weekday/weekend day and season. Models with two interaction terms are reported in Web Appendix 4.

In order to compare the associations between transport modes and the duration of physical behaviors as estimated from waist-worn accelerometrers (Actigraph) and trunk-and thighworn accelerometers (VitaMove), we re-estimated the regression models among 4008 trips and 6901 trip stages (154 participants) with information for both sensors.

All statistical analyses were conducted using R software (version 3.4.4) and R Studio (version 1.1.463) [START_REF] Core | A language and environment for statistical computing[END_REF].

Results

Sample description

The 155 participants had an average age of 50 years (range: 34-82 years). Among them, 63% were males. Thirty-five percent of them were from Paris, 20% lived in the close suburb, and 45% in the far suburb. Twenty-five percent of participants had no formal education or had a primary education or lower secondary education; 21% had a higher secondary education or lower tertiary education; 19% had an intermediate tertiary education; and 35% of participants had an upper tertiary education. Among participants, 78% had a stable job, 19% had a fixed term or precarious contract, and 3% (4 participants) were unemployed.

Descriptive information on trips

The median follow up time of participants in our study was 7 days (mean 6.1 days, interdecile range: 5-7 days, standard deviation: 1.0 days). Participants had a median number of trips per day of 5 (mean: 5.1, interdecile range: 3-7, standard deviation: 2.1), corresponding to a median number of trip stages per day of 8 (mean: 8.5, interdecile range: 4-13, standard deviation: 3.7).

Participants were travelling (as opposed to being at a place) for a median of 1 hour 45 minutes per day (mean: 1 hour 52 minutes, interdecile range: 56 minutes -3 hours 2 minutes, standard deviation: 52 minutes). Following Web Appendix 5, the most frequently used mode of transport was walking, corresponding to 53.8% of trip stages 39.6% of trips, followed by private motorized vehicles, corresponding to 23.1% (19.9% as a driver and 3.2% as a passenger) of trip stages and 39.6% (31.8% as a driver and 4.5% as a passenger) of trips.

Association between transport mode and physical activity

Associations between sociodemographic characteristics and sitting time or MVPA (standardized outcomes) are shown in Web Appendix 6.

In models for both unstandardized and standardized outcomes (Tables 1 and2), not only trips or trip stages by walking or with other active modes but also (although to a lesser extent) those with public transport were associated with a lower sitting time than when using a personal motorized vehicle (after adjustment for sociodemographic characteristics). In the models with standardized outcomes (Table 2), the coefficient showing that there was less sitting time in public transport was stronger in the model at the trip level than at the trip stage level (as opposed to public transport trip stages, public transport trips also include the walking episodes). This is not the case in the models with unstandardized outcomes (Table 1) that are difficult to interpret due to the fact that trips and trip stages with different modes have different durations.

Regarding MVPA, when durations of trips and trip stages were accounted for (standardized outcome, Table 2, third and fourth columns), trips and trip stages by walking, other active modes, and as expected to a lesser extent with public transport were all associated with more minutes of MVPA than those with a personal motorized vehicle (after adjustment for sociodemographic characteristics). The coefficient showing more minutes of MVPA associated with public transport was stronger in the model at the trip level (Table 2, column 4) than in the model at the trip stage level (column 3), as public transport trips also typically include walked trip stages. Figure 1 reports average durations of sitting and MVPA in a trip by transport modes (predicted from separate models with an interaction of transport modes with either the weekend / weekday variable or the season variable and adjusted for sociodemographic characteristics, with the unstandardized outcome). MVPA duration in a trip was higher during weekends than on weekdays in trips with all modes, although the difference was particularly sharp only for multimodes trips (this finding is based, however, on 9 and 52 multi-mode trips on the weekend and on weekdays, respectively, and is attributable to the fact that these weekend trips had an average duration of 188 minutes vs. 81 minutes for the weekday trips). Regarding the interaction with seasons, spring or summer was associated with a longer duration of MVPA per trip for all transport modes (except perhaps multi-mode trips), with a non-overlapping confidence intervals only for trips with other active modes.

Partition profile: transition rates

As shown in Table 3, transport modes differ in the number of transitions among SB, NSB, and MVPA. For example, both at the trip stage and trip level, using public transport was related to a lower number of transitions between SB and NSB (or the other way round) than driving or being the passenger of a private motorized vehicle, but it was related to a larger number of transitions between NSB and MVPA. Walking or relying on other active modes had the largest Table 4 shows that the contrast in sitting duration between using a personal motorized vehicle and the other modes (public transport, walking, and other active modes) was substantially underestimated by the waist-worn accelerometer compared to the the thigh-and trunk-worn accelerometers, in both duration-unstandardized and standardized models (trip stage model).

The corresponding models at the trip level are reported in Web Appendix 8.

Discussion

Strengths and limitations compared to previous literature

Regarding strength of our approach, this paper is one of the few published studies to explore the association of transport mode with physical activity at the trip level using objective sensorbased measures measured outcomes [START_REF] Chaix | Active transportation and public transportation use to achieve physical activity recommendations? A combined GPS, accelerometer, and mobility survey study[END_REF][START_REF] Chaix | Combining sensor tracking with a GPS-based mobility survey to better measure physical activity in trips: Public transport generates walking[END_REF]. And it is the first to conduct such a detailed analysis with two complementary body-worn accelerometers that permit a more accurate assessment of body posture, including sitting. Two accelero-sensors placed on the trunk and thigh that provide information on the orientation of the body compared to the gravitation field are useful to infer body posture.

Another strength of this paper is that it performed this analysis comparatively at the trip stage level and trip level. Investigating the relationship between transport mode and physical behaviors is of interest both at the trip stage level, for a description of each transport mode, and at the trip level, to investigate how the different non-walking modes generate walking and physical activity. Previous studies did not reach this level of precision, for example those which modeled the relationship between transport mode and physical activity at the individual level rather than trip stage and trip levels [START_REF] Rissel | Physical activity associated with public transport use-a review and modelling of potential benefits[END_REF]. A study that analyzed trip-level information used selfreported rather than accelerometer-derived physical activity, which makes the findings less trustworthy [START_REF] Morabia | Potential health impact of switching from car to public transportation when commuting to work[END_REF]. Another study investigated the association between transport mode and physical activity using a linear mixed model [START_REF] Chaix | Active transportation and public transportation use to achieve physical activity recommendations? A combined GPS, accelerometer, and mobility survey study[END_REF]; however, trip level data but not trip stage level data were considered and temporal autocorrelation was not taken into account, which is important when analyzing repeated observations [START_REF] Goldstein | Multilevel time series models with applications to repeated measures data[END_REF]. To overcome these limitations, we collected trip data at the trip stage level, and timestamps were available for all transitions between modes within trips over 7 days, and had been pre-identified with algorithms and then verified on the phone with participants.

Regarding limitations, first, the recruitment of participants was not at random (convenience sample). Beyond non-randonmess, findings from a small sample of 155 participants cannot be generalized to the complex transport habits of a population of more than 24 million inhabitants (Paris and close and far suburbs). For instance, if the odds of participating in the study were lower for those public transport users living in municipalities far from recruitment area, then longer public transport trip stages would be underrepresented in the study. Since a larger segment of a public transport trip is related to walking when the trip is short than when the trip is long, such a hypothetical recruitment bias would influence the comparison of physical activity between private motorized vehicle trips and public transport trips. Second, there is certainly measurement error in the start and end times of trips due to the GPS data, processing algorithms, and mobility survey; and there is also measurement error in the inclinometry function of the accelerometers. These errors resulted in non-zero sitting time during entirely walked trip stages. the estimated time of physical behaviors assigned to transport modes was based on the accelerometer wear time. If specific trips in terms of physical behaviors were more frequently excluded due to nonwear of the accelerometer, then it would bias our comparisons.

Interpretation of findings

Trips and trip stages by walking or other active modes, but also (although to a lesser extent) with public transport, were associated with longer walking durations and shorter sitting durations than trips based on a personal motorized vehicle, and these findings hold whether sitting or MVPA time were standardized or not by trip or trip stage durations. This finding supports previous studies quantifying the physical activity gains of biking [START_REF] Litman | Transportation and Public Health[END_REF][START_REF] Sahlqvist | Is active travel associated with greater physical activity? The contribution of commuting and non-commuting active travel to total physical activity in adults[END_REF] and walking [START_REF] Chaix | Active transportation and public transportation use to achieve physical activity recommendations? A combined GPS, accelerometer, and mobility survey study[END_REF]. Regarding public transport, our findings are in accordance with previous research; for example, it has been found that public transport users had 24.3 minutes of physical activity per day while travelling, which is a substantial portion of recommended physical activity levels in guidelines [START_REF] Besser | Walking to public transit: Steps to help meet physical activity recommendations[END_REF]. The health benefits gained from the physical activity associated with the use of public transport have been investigated in previous literature [START_REF] Rissel | Physical activity associated with public transport use-a review and modelling of potential benefits[END_REF].

In our study, in models with standardized outcomes, the coefficient showing that there was less sitting time in public transport and the coefficient showing more minutes of MVPA with public transport were stronger in the models at the trip level than at the trip stage level. This is because, in addition to the potential active movements within public transport vehicles, trips also typically include walked trip stages to and from public transport stations [START_REF] Chaix | Active transportation and public transportation use to achieve physical activity recommendations? A combined GPS, accelerometer, and mobility survey study[END_REF]. Thus our study comparing analyses at the trip level and trip stage level was useful to distinguish between these two sources of physical activity. Walked distances to and from public transport stations and standing in public transport vehicles may thus help people achieve physical activity recommendations, especially people who do not have time for other kinds of physical activity [START_REF] Rissel | Physical activity associated with public transport use-a review and modelling of potential benefits[END_REF][START_REF] Besser | Walking to public transit: Steps to help meet physical activity recommendations[END_REF]. However, it is critical to keep in mind that it may not be possible for everyone to increase their level of physical activity by transport mode, due to various types of health, environmental, or time constraints. It should also be emphasized that the physical activity gains from choosing public transport instead of a private motorized vehicle as a transport mode is likely to differ from one city to the other, because of variations in the configuration of transport systems and travel habits of people.

Conclusion

In conclusion, our study is the first to assess the relationship between various transport modes and physical behaviors based on GPS, mobility survey, and waist, thigh, and trunk accelerometer data, with a comparative analysis at the trip stage and trip levels. This pioneering approach allowed us to accurately measure differences in physical behaviors between transport modes.

Even if future research will have to rely on larger and more representative study samples to yield more generalizable findings, our study shows that promoting walking and biking but also public transport in daily routines may have a significant impact at the population level in terms of increasing the share of people reaching the physical activity recommandation. Our study thus add evidence to recent calls [START_REF] Nieuwenhuijsen | Urban and transport planning pathways to carbon neutral, liveable and healthy cities; A review of the current evidence[END_REF] to promote these transport modes at the expense of car driving through urban and transport policies (including ensuring the local access to services, greening cities, developing networs of walking paths and biking lanes as well as public transport). a The multilevel linear models included a random effect at the individual level. The crude and the detailed transport mode variables were introduced in separate models. The models took account of temporal autocorrelation and were adjusted for sociodemographic characteristics and day of week and season. b Long-distance train and plane. a The multilevel linear models included a random effect at the individual level. The crude and the detailed transport mode variables were introduced in separate models. The models took account of temporal autocorrelation and were adjusted for sociodemographic characteristics. b Long-distance train and plane. a The multilevel linear models included a random effect at the individual level. The crude and the detailed transport mode variables were introduced in separate models. The models took account of temporal autocorrelation and were adjusted for sociodemographic characteristics and day of week and season. b Long-distance train and plane. proxy for acceleration were used to determine if the window's mode was motorized and whether or not it was likely to contain a mode transition:

-If the average point speed was above 16 m/s the window was classified as motorized.

-The window was determined to contain a mode transition if its motorized flag was different than that of the previous window and if the standard deviation of speeds was greater than 2.25 m/s. Once a given window was determined to contain a mode transition, the location of the transition was assigned by examining the GPS points within the window and locating the last point with characteristics either below or above the non-motorized mode speed threshold (16 m/s). Once the mode transition points were assigned, the trips were split and the resulting list was run through mode selection.

Like the method proposed by Stopher et al. (6), the mode selection process used GPS point speeds. More specifically, pre-computed values for average, maximum and standard deviation of mode speeds were used. The first step in the process was to compute average and standard deviation values of the trip segments' point speeds. Using these values, estimates of the mode segments' 95 th percentile speeds were computed by adding / substracting 1.96 times the point speed standard deviation to the segment's average speed (assuming a normal distribution of point speeds). The logic selected the travel mode for a trip segment that most closely matched its average and standard deviation of point speeds, while having its 95 th percentile speed lower than or equal to the mode's maximum speed. If a segment could not be assigned a travel mode, then it was given a null travel mode.

Mobility survey

Based on the TripBuilder Web application, a GPS-based mobility survey was conducted through a telephone interview as soon as possible after the data collection (median time of 10 days, interquartile range: 7, 15). Only the research assistants had access to the application, while participants had access to detailed screen copies of their trips sent by email or postal mail. Using these computer and paper supports, the research assistants walked the participant through the different days, reviewing and complementing information trip by trip. The research assistants confirmed the detected visits to places and trips between these places; they removed visits to places and trips that were incorrect; they could generate visits to places or trips to places undetected by the GPS receiver and/or algorithm (with itineraries then imputed as the shortest street network path and edited if needed). The research assistants manually edited each trip itinerary, if needed, to remove residual artefacts in the GPS track that would bias the assessment of the travel distance. Finally, research assistants confirmed or collected and modified the type of activity practiced at each visited place and the travel mode used in each trip segment.

A SAS program generated a detailed timetable over 7 days indicating the succession of places visited and trips subdivided in trip stages. Within a trip, two trip stages are necessarily separated by an episode of transfer between the two assigned to a punctual location. These transfer episodes coded with a spatial point in the mobility survey typically last from 0 minute to several minutes and correspond to no walking at all, walking few meters outdoor, or walking indoor, e.g., within a train or metro station (but these punctual transfer episodes cannot imply movement with any other mode). A transfer between two trip stages by bus would be coded as a walking trip stage if there was a detectable walking track between them, but would be coded as a punctual location if the two buses were few meters apart outdoor.

Start/end times are available for each visited place, trip, trip stage, and episode of transfer between trip stages. Due to costs, the mobility survey was only performed on days (i) where there was GPS data and (ii) where the additional sensors (VitaMove system) employed in this study were worn by the participants. On those days, the mobility survey was systematically performed for the whole day, even if GPS data were partly missing. In the latter case, missing portions of itineraries were complemented during the mobility survey, so that the day had full distance information. On the opposite, if the two conditions above were not satisfied, the whole day was excluded.

From

  February 2007 to March 2008, 7290 participants were recruited without a priori sampling (convenience sample) during preventive health cheakups conducted in four sites of the Centre d'Investigations Préventives et Cliniques (IPC) funded by the National Insurance System for Employees and Salaried Workers. People had to be 30 to 79 year old, had to live in 10 districts (out of 20) of Paris and 111 other municipalities of the Ile-de-France region, and had to be free of cognitive and linguistic disabilities to be eligible for the study. In 2011-2015, these participants as well as new participants from the IPC medical center were invited to take part in the second wave of the RECORD Study, in which 6460 participants were included. The RECORD MultiSensor Study sample was recruited among these participants. From September 2013 to June 2015, 919 participants from the second wave of RECORD were invited to participate in the RECORD MultiSensor Study (21) whenever sensor devices were available (i.e., brought back by previous participants). Of them, 319 accepted to participate and signed an informed consent form. Twenty-seven participants withdrew from the study and the data collection failed for 6 participants, resulting in a final acceptation and completion rate of 31.1% (N = 286). The study has been approved by the French Data Protection Authority (Decision No. DR-2013-568 on 2/12/2013).

  number of transitions from NSB to MVPA. Compared to other two types of transitions, those between SB and MVPA were particularly rare. Statistics on the length of uninterrupted episodes of physical behaviors (SB, NSB, and MVPA within trips and trip stages are reported in Web Appendix 7. Comparison of waist-worn to and thigh-and trunk-worn accelerometers Considering time periods with both waist-worn and thigh-and trunk-worn accelerometers, the standing duration per individual per eight hours of device wear time had a median of 290.4 minutes (interdecile range: 123.6, 434.1) when assessed with the thigh-and trunk-worn accelerometers, as compared to 271.6 minutes (interdecile range: 138.3, 388.5) when assessed with the single waist-worn accelerometer. The corresponding figures for sitting time were 183.8 minutes (interdecile range: 42.1, 352.2) and 208.6 minutes (interdecile range: 92.9, 330.0).

Figure 1 :

 1 Figure 1: Predicted duration of physical activity according to transport mode, by season or weekend/weekdays: unstandardized models at the trip level a

Table 1 . Association between transport mode used and physical behaviors (trip stage level n =7692, trip level n = 4683, N = 155 participants) a , unstandardized outcome Sitting duration in minutes MVPA duration in minutes Transport mode

 1 Confidence interval, MVPA: Moderate to vigorous physical activity, NA: Not applicable at the trip stage level.

		Trip stage level	Trip level	Trip stage level	Trip level
		β (95%CI)	β (95%CI)	β (95%CI)	β (95%CI)
	Detailed classification
	Private motorized (driver)	Ref	Ref	Ref	Ref
	Private motorized
	(passenger)	-2.19 (-3.70, -0.68)	-1.18 (-4.13, 1.77)	-1.26 (-2.07, -0.45)	1.49 (0.09, 2.89)
	Bus/coach	-10.71 (-11.82, -9.60)	-6.08 (-9.61, -2.55)	1.25 (0.72, 1.79)	7.97 (6.24, 9.70)
	Metro	-10.58 (-11.54, -9.62)	-3.95 (-6.57, -1.33)	0.90 (0.42, 1.37)	10.89 (9.61, 12.16)
	Tram	-10.63 (-12.66, -8.60)	-9.89 (-16.92, -2.86)	-0.13 (-1.06, 0.81)	8.57 (5.18, 11.96)
	Suburban train	-6.01 (-7.22, -4.80)	-2.39 (-6.56, 1.78)	-0.24 (-0.84, 0.35)	17.09 (15.11, 19.06)
	Biking and other active	-13.69 (-15.19, -12.19) -13.36 (-16.58, -10.14)	5.53 (4.75, 6.30)	6.82 (5.33, 8.31)
	Entirely walking	-14.07 (-14.78, -13.36) -15.30 (-16.87, -13.73)	2.00 (1.63, 2.37)	4.38 (3.64, 5.12)
	Multi-mode	NA	12.36 (9.85, 14.87)	NA	15.29 (14.06, 16.51)
	Other b	3.17 (0.51, 5.83)	1.37 (-3.95, 6.69)	2.60 (0.99, 4.21)	3.21 (0.80, 5.62)
	Crude classification
	Private motorized	Ref	Ref	Ref	Ref
	Public transport	-9.28 (-10.07, -8.49)	-1.07 (-2.95, 0.81)	0.98 (0.58, 1.38)	11.58 (10.68, 12.48)
	Other active mode	-13.38 (-14.88, -11.88) -13.20 (-16.40, -10.00)	5.77 (5.01, 6.53)	6.65 (5.16, 8.14)
	Entirely walking	-13.64 (-14.30, -12.98) -15.24 (-16.72, -13.76)	2.24 (1.90, 2.58)	4.17 (3.46, 4.88)
	Multi-mode	NA	24.65 (20.04, 29.26)	NA	20.98 (18.66, 23.30)
	Other b	3.52 (0.88, 6.16)	1.34 (-3.99, 6.67)	2.83 (1.22, 4.44)	3.02 (0.60, 5.44)
	CI:

Table 2 . Association between transport mode used and physical behaviors (trip stage level n = 7692, trip level n = 4683, N = 155 participants) a , standardized outcome Sitting time per 10 minutes of trip (minutes) MVPA time per 10 minutes of trip (minutes)

 2 Confidence interval, MVPA: Moderate to vigorous physical activity, NA: Not applicable at the trip stage level.

	Transport mode	Trip stage level	Trip level	Trip stage level	Trip level
		β (95%CI)	β (95%CI)	β (95%CI)	β (95%CI)
	Detailed classification
	Private motorized (driver)	Ref	Ref	Ref	Ref
	Private motorized
	(passenger)	-0.57 (-1.01, -0.13)	-1.15 (-1.58, -0.72)	0.27 (-0.14, 0.68)	0.47 (0.09, 0.84)
	Bus/coach	-2.78 (-3.19, -2.37)	-3.57 (-4.11, -3.03)	0.53 (0.14, 0.91)	1.91 (1.45, 2.37)
	Metro	-2.87 (-3.19, -2.55)	-3.43 (-3.83, -3.03)	1.52 (1.22, 1.81)	2.92 (2.58, 3.25)
	Tram	-3.35 (-4.15, -2.55)	-3.52 (-4.57, -2.47)	0.20 (-0.55, 0.94)	2.92 (2.00, 3.84)
	Suburban train	-1.66 (-2.05, -1.27)	-3.81 (-4.42, -3.20)	0.54 (0.18, 0.89)	3.16 (2.64, 3.69)
	Biking and other active	-5.57 (-6.03, -5.11)	-5.66 (-6.13, -5.19)	3.96 (3.53, 4.38)	4.02 (3.65, 4.38)
	Entirely walking	-5.36 (-5.58, -5.14)	-5.39 (-5.62, -5.16)	4.77 (4.57, 4.97)	4.82 (4.63, 5.01)
	Multi-mode	NA	-2.88 (-3.26, -2.50)	NA	1.67 (1.35, 2.00)
	Other b	-1.98 (-2.65, -1.31)	-1.82 (-2.57, -1.07)	1.18 (0.58, 1.78)	1.16 (0.60, 1.72)
	Crude classification
	Private motorized	Ref	Ref	Ref	Ref
	Public transport	-2.45 (-2.70, -2.20)	-3.09 (-3.37, -2.81)	0.94 (0.71, 1.17)	2.37 (2.14, 2.60)
	Other active mode	-5.48 (-5.94, -5.02)	-5.46 (-5.93, -4.99)	3.91 (3.49, 4.33)	3.93 (3.57, 4.29)
	Entirely walking	-5.25 (-5.45, -5.05)	-5.16 (-5.38, -4.94)	4.71 (4.53, 4.89)	4.74 (4.56, 4.92)
	Multi-mode	NA	-2.88 (-3.59, -2.17)	NA	1.22 (0.57, 1.87)
	Other b	-1.88 (-2.54, -1.22)	-1.63 (-2.38, -0.88)	1.12 (0.52, 1.72)	1.13 (0.57, 1.69)
	CI:

Table 3 . Number of transitions between physical behaviors (SB, NSB, and MVPA) standardized by 10 minutes of trip, by transport mode, at the trip stage and trip levels: median (10 th and 90 th percentiles)

 3 Sedentary behaviour, NSB: Non-sedentary behaviour, MVPA: Moderate to vigorous physical activity, NA: Not applicable at the trip stage level.

	Trip stage level

a Long distance train and plane.

Table 4 . Association between transport mode and sitting duration, comparing a waist-worn accelerometer with two thigh-and trunk-worn accelerometers (analyzed at the trip stage level, n = 6901, N = 154 participants) a

 4

	Transport mode	Sitting duration, waist-	Sitting duration, thigh-	Sitting duration per	Sitting duration per
		worn accelerometer	and trunk-worn	10 minutes of trip	10 minutes of trip
		(minutes)	accelerometers	stage, waist-worn	stage, thigh-and
		β (95%CI)	(minutes)	accelerometer	trunk-worn
			β (95%CI)	(minutes)	accelerometers
				β (95%CI)	(minutes)
					β (95%CI)
	Detailed classification
	Private motorized (driver)	Ref	Ref	Ref	Ref
	Private motorized (passenger) 2.59 (1.26, 3.92)	-1.46 (-2.84, -0.08)	0.92 (0.44, 1.40)	-0.41 (-0.88, 0.06)
	Bus/coach	-5.86 (-6.87, -4.85)	-10.32 (-11.33, -9.31)	-0.46 (-0.89, -0.03)	-3.12 (-3.54, -2.70)
	Metro	-7.29 (-8.15, -6.43)	-10.02 (-10.89, -9.15)	-1.40 (-1.73, -1.07)	-3.14 (-3.47, -2.81)
	Tram	-5.87 (-7.72, -4.02)	-10.18 (-11.99, -8.37)	-0.27 (-1.08, 0.54)	-3.58 (-4.37, -2.79)
	Suburban train	-3.75 (-4.83, -2.67)	-6.22 (-7.32, -5.12)	-0.46 (-0.87, -0.05)	-2.09 (-2.49, -1.69)
	Biking and other active	-5.98 (-7.27, -4.69)	-13.74 (-15.07, -12.41) -1.09 (-1.58, -0.60)	-6.00 (-6.48, -5.52)
	Entirely walking	-10.96 (-11.58, -10.34) -13.71 (-14.36, -13.06) -4.03 (-4.26, -3.80)	-5.67 (-5.90, -5.44)
	Other b	6.00 (2.97, 9.03)	15.65 (12.29, 19.01)	-2.96 (-3.96, -1.96)	1.29 (0.30, 2.28)
	Crude classification
	Private motorized	Ref	Ref	Ref	Ref
	Public transport	-6.57 (-7.27, -5.87)	-9.09 (-9.81, -8.37)	-1.08 (-1.35, -0.81)	-2.82 (-3.08, -2.56)
	Other active mode	-6.42 (-7.70, -5.14)	-13.56 (-14.88, -12.24) -1.24 (-1.72, -0.76)	-5.94 (-6.41, -5.47)
	Entirely walking	-11.38 (-11.96, -10.80) -13.43 (-14.03, -12.83) -4.19 (-4.41, -3.97)	-5.59 (-5.80, -5.38)
	Other b	5.63 (2.59, 8.67)	15.86 (12.52, 19.20)	-3.10 (-4.10, -2.10)	1.36 (0.38, 2.34)
	CI: Confidence interval.

Table 3 . Associations between the transport mode used (crude classification) and physical behaviors, and their interaction with season and day of week at the trip level (n = 4683 trips, N = 155 participants) a

 3 CI: confidence interval, MVPA: moderate to vigorous physical activity. a The multilevel linear models included a random effect at the individual level, taking account of temporal autocorrelation. It was also adjusted for sociodemographic characteristics. b Long-distance train and plane. The multilevel linear models included a random effect at the individual level, taking account of temporal autocorrelation. It was also adjusted for sociodemographic characteristics.

	Bus/coach	-9.84 (-20.28, 0.60)	4.92 (0.15, 9.68)	-2.92 (-4.37, -1.47)	1.65 (0.33, 2.97)
	Metro	-4.32 (-10.53, 1.89)	11.03 (8.09, 13.97)	-3.49 (-4.40, -2.58)	2.82 (2.00, 3.63)
	Tram	-7.99 (-29.81, 13.83)	7.46 (-2.68, 17.60)	-2.92 (-6.00, 0.16)	1.37 (-1.50, 4.25)
	Suburban train	-6.02 (-19.99, 7.95)	20.65 (14.02, 27.28)	-5.03 (-7.05, -3.01)	3.13 (1.27, 4.99)
	Biking and other active	-20.54 (-27.50, -13.58)	6.19 (3.05, 9.33)	-5.64 (-6.61, -4.67)	2.82 (2.00, 3.64)
	Entirely walking	-17.13 (-20.14, -14.12)	5.59 (4.19, 6.98)	-5.80 (-6.23, -5.37)	4.94 (4.57, 5.30)
	Multi-mode	38.14 (31.55, 44.73)	29.09 (25.82, 32.37)	-2.00 (-3.00, -1.00)	1.76 (0.83, 2.70)
	Other b	0.36 (-7.38, 8.10)	3.88 (0.48, 7.27)	-1.27 (-2.31, -0.23)	0.66 (-0.19, 1.51)
	Spring/Summer vs.
	Autumn/Winter	-1.85 (-4.75, 1.05)	0.87 (-0.40, 2.14)	-0.40 (-0.93, 0.13)	0.19 (-0.07, 0.45)
	× Private motorized
	(passenger)	-0.47 (-6.31, 5.37)	-1.00 (-3.79, 1.78)	0.45 (-0.41, 1.31)	-0.04 (-0.79, 0.71)
	× Bus/coach	-4.76 (-12.21, 2.69)	-1.83 (-5.41, 1.75)	-1.45 (-2.58, -0.32)	0.07 (-0.89, 1.02)
	× Metro	-0.57 (-5.67, 4.53)	1.08 (-1.38, 3.55)	0.06 (-0.73, 0.85)	0.11 (-0.53, 0.75)
	× Tram	-3.71 (-18.78, 11.36)	5.41 (-1.78, 12.60)	-2.57 (-4.80, -0.34)	1.44 (-0.53, 3.40)
	× Suburban train	-4.46 (-13.62, 4.70)	-4.05 (-8.36, 0.25)	-0.68 (-2.01, 0.65)	0.28 (-0.91, 1.46)
	× Biking and other active	7.86 (1.25, 14.47)	3.77 (0.75, 6.79)	0.18 (-0.78, 1.14)	0.97 (0.23, 1.71)
	× Entirely walking	2.76 (-0.29, 5.81)	0.02 (-1.41, 1.45)	0.47 (0.01, 0.93)	-0.19 (-0.54, 0.16)
	× Multi-mode	-13.36 (-18.42, -8.30)	-1.34 (-3.78, 1.10)	-0.38 (-1.15, 0.39)	-0.04 (-0.70, 0.62)
	× Other b	-19.43 (-33.66, -5.20)	3.75 (-2.88, 10.38)	-5.25 (-7.27, -3.23)	3.45 (1.66, 5.24)
	Weekdays vs. weekend day	-0.73 (-3.08, 1.62)	-0.12 (-1.16, 0.91)	0.06 (-0.25, 0.37)	-0.16 (-0.44, 0.12)
	× Private motorized
	(passenger)	-3.47 (-9.18, 2.24)	-1.00 (-3.69, 1.70)	0.28 (-0.54, 1.10)	0.07 (-0.68, 0.82)
	× Bus/coach	5.48 (-5.39, 16.35)	3.93 (-1.09, 8.95)	-0.23 (-1.75, 1.29)	0.32 (-1.09, 1.73)
	× Metro	0.89 (-5.00, 6.78)	-1.07 (-3.85, 1.71)	0.02 (-0.83, 0.87)	0.07 (-0.72, 0.85)
	× Tram	0.49 (-24.24, 25.22)	-2.16 (-13.64, 9.32)	0.84 (-2.65, 4.33)	0.90 (-2.35, 4.14)
	× Suburban train	7.42 (-6.41, 21.25)	-1.14 (-7.76, 5.49)	1.90 (-0.12, 3.92)	-0.19 (-2.06, 1.68)
	× Biking and other active	2.84 (-3.76, 9.44)	-2.27 (-5.34, 0.79)	-0.19 (-1.12, 0.74)	0.77 (-0.06, 1.60)
	× Entirely walking	0.60 (-2.43, 3.63)	-1.62 (-3.02, -0.23)	0.23 (-0.19, 0.65)	-0.04 (-0.41, 0.34)
	× Multi-mode	-20.70 (-26.91, -14.49)	-15.47 (-18.56, -12.38)	-0.74 (-1.69, 0.21)	-0.07 (-0.96, 0.82)
	× Other b	7.80 (-1.92, 17.52)	-1.91 (-6.01, 2.18)	0.48 (-0.74, 1.70)	0.30 (-0.82, 1.41)

a b Long-distance train and plane.

Physical activity and sedentary behavior related to transport activity assessed from multiple body-worn accelerometers: the RECORD MultiSensor Study

Acknowlegments

The RECORD MultiSensor Study was supported by the Ministry of Ecology (DGITM); Cerema (Centre for the Study of and Expertise on Risks, the Environment, Mobility, and Planning); INPES (National Institute for Prevention and Health Education); STIF (Ile-de-France Transportation Authority); and DRIEA (Regional and Interdepartmental Direction of Equipment and Planning) of Ile-de-France. The funding institutions had no role in the design of the study and collection, analysis, and interpretation of data and in writing the manuscript.

Conflict of interest

None were declared. Appendix 2: the GPS-based mobility survey

Appendix 1: Comparison of sociodemographic characteristics of participants included in the two substudies of the RECORD MultiSensor Study

Processing algorithms

Throughout the study period, participants were asked to maintain a travel diary recording the places they visited and the modes of transport taken. This diary was just used as a supporting piece of evidence during the mobility survey.

The GPS data (one point every 5 seconds) were uploaded in the TripBuilder Web mapping application where GPS data were processed with algorithms (1,2). These algorithms (i) The algorithms for the identification of trips and mode-specific trip stages are explained in details in the article by Simas Oliveira and colleagues (4). Briefly, the overall trips are identified using stops (no moving points) of at least 120 seconds. The application first removes any point with speed < 1 (km/h) and then look for gaps in the point sequence that are longer than or equal to 120 seconds, which are identified as stops.

The algorithm developed to split the trips based on transport mode transitions is based on the one proposed by Tsui (5). A moving window was used to detect if a mode transition existed in a short sequence of points within a trip (which equated to approximately 44 seconds). The window's average point speed and standard deviation of speed values as a there is some correlation between these observations. The AR(1) autocorrelation structure was intended to take it into account. The multilevel linear models included a random effect at the individual level. The crude and the detailed transport mode variables were introduced in separate models. The models were adjusted for sociodemographic characteristcs and day of week and season, and took account of temporal autocorrelation. b Long-distance train and plane.


Engineer Diana Khairallah
email: diana.khairallah@ifsttar.fr

Olivier Chupin
email: olivier.chupin@ifsttar.fr

Juliette Blanc
email: juliette.blanc@ifsttar.fr

Pierre Hornych
email: pierre.hornych@ifsttar.fr

Jean Michel Piau

Diego Ramirez Cardona

Alain Ducreau
email: alain.ducreau@reseau.sncf.fr

Frédéric Savin

Frederic Savin
email: frederic.savin@ferro.setec.fr

Monitoring and modeling of railway structures of the high-speed line BPL with asphalt concrete underlayment

Keywords: Ballasted railways, asphalt concrete, monitoring, railways modeling

établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

INTRODUCTION

In France, a significant feedback in the field of ballasted high-speed tracks with granular sublayers allowed to improve the track's design rules [START_REF] Lambert | 40 lat doświadczenia w budowie linii dużych prędkości[END_REF]. The phenomena of settlement and wear of the ballast, under dynamic loads, however remain an important problem on high-speed tracks and lead to high frequencies and maintenance costs. Several studies have shown that these settlements are linked to the high accelerations produced in the ballast by high-speed trains' circulation [START_REF] Martin | Analyse numérique de la réponse dynamique de structures ferroviaires[END_REF]. To alleviate the problem, it has been proposed to insert an asphalt concrete layer under the ballast.

The use of asphalt sublayers under the ballast has been identified as a possible solution for improving track structures. By interposing a semi-rigid layer of asphalt concrete (GB) between the ballast and the UGM layer, the behavior of the overall structure is greatly improved. This applies to both highspeed passenger and freight lines. The use of asphalt concrete (GB) in railway construction has emerged in different countries. Indeed, over the last decade 322 km of sub-ballast layers have been built for new projects in the Midwestern United States, mainly for heavy freight traffic [START_REF] Rose | Asphalt Railway Trackbeds: Recent Designs, Applications and Performances[END_REF].

In 2005, SNCF built a 3 km long test section in the East HSL (LGV Est), linking Paris to Strasbourg, with a GB sublayer. The data retrieved from this first instrumented test indicated satisfactory performance of the experimental railway section [START_REF] Cuccaroni | L'expérience grave-bitume de la LGV Est Européenne [Asphalt concrete experience on the East European high-speed line[END_REF][START_REF] Cardona | Use of a bituminous mixture layer in high-speed line trackbeds[END_REF]. The presence of the asphalt sublayer has proven to reduce the aggressiveness of the loading applied by passing trains, leading to an increase of the structure durability. The high-speed line Bretagne -Pays de la Loire (between Rennes and Le Mans, in the West of France) is the first large-scale application in France of the new asphalt sub-layer technique, with varied subgrade conditions, and using a high-performance asphalt concrete (GB4). 105 km of track were built with an asphalt sublayer under the ballast on its east route while the remaining 77 km have a classical granular sub-layer (UGM) on its west route. An asphalt concrete of class 4 (GB4), according to French standard NF EN 13-108-1, has been used for this project. The unbound granular material (UGM) has a particle size 0/31.5 mm, and is of type A, according to French specifications. The innovative track structure, described in Table 1, includes the upper part of the earthworks (PST), which is treated with lime and hydraulic binders. The PST is surmounted by a 15 cm thick Unbound Granular layer (UGM), and a 12 cm thick asphalt layer. The standard structure comprises a 20 cm thick granular sublayer in addition to a cementtreated subgrade layer.

In order to compare the responses of these different structures, two sections, with granular sublayer and with bituminous sub-layer were instrumented. The aim of this instrumentation is to monitor and compare the mechanical response of these two types of structures used on BPL HSL, by measuring accelerations, sub-ballast structure displacements, horizontal and vertical deformations and temperatures in different layers, and also water contents at the top of the subgrade.

Data acquisition and analysis started at the end of 2016, when trains were first put into circulation (for a test phase). The line was opened to commercial traffic in July 2017 with trains travelling at a speed of 320 km/h. This paper focuses on the measurements and results of the sections with asphalt concrete sublayers.

INSTRUMENTATION OF HSL BPL Sensors

The choice of sensors was made by IFSTTAR, drawing on its experience in the field of pavement monitoring. Section 4, with a bituminous sub-layer, is instrumented with 6 vertical strain gages, 10 horizontal strain gages in the asphalt layer, 8 accelerometers, 4 moisture content probes, 3 temperature sensors, 2 anchored displacement sensors and a weather station. Accelerometers, used to monitor the track's dynamic behavior, are positioned at several levels: under the sleepers and at the top of the asphalt concrete layer. The anchored sensors measure the structure's total vertical displacement under the ballast (GB + granular layer + subgrade for section with bituminous sublayer). Temperature probes are placed at the base and at the top and bottom of the GB layer, to monitor temperature variations. Moisture content probes quantify water content variations. Vertical strain gages monitor deformation levels of the unbound granular material (UGM). As a result, effects of seasonal moisture content variations can be inferred from the measured deformations. A plan showing the positions of accelerometers and anchored displacement sensors on section 4 (asphalt sublayer) is presented in Figure 1.

Figure 1 Section 4: instrumentation layout for accelerometers and displacement sensors Data acquisition system

Based on its performance and experience feedback, the data acquisition systems installed on each instrumented section are based on the Pegase platform developed by IFSTTAR [START_REF] Cam | p Improving wireless sensor behavior by means of generic strategies[END_REF]. Generic Experts Platform for Embedded Wireless Applications (PEGASE) is a concept derived from intelligent and wireless instrumentation. This system has been designed to support instrumentation needs such as wireless communication, dating, signal processing. As an example, on section 4 (with bituminous under layer), there are 5 Pegase data acquisition boards: two 0-10V input boards for the 16 accelerometers, a strain-gauge bridge board for the 6 vertical gauges and two temperature sensors, one RS232 input board for the 4 moisture probes, and a strain-gauge bridge board for two anchored displacement sensors. For all sections, the systems are fully autonomous in electricity. The power supply is provided by solar panels and batteries, for continuous year-round operation without interruption. Each system supports its connected sensors. Collected data on each section is transferred continuously via 4G network (within a few hours maximum) to a remote server. Each system is autonomous in energy and data transmissions. Results are stored in a relational database, enabling fast-multi-criteria searches. For each data acquisition board, one can visualize, in real time, slow and fast measurements associated with each sensor of the resource.

At each section's level, two types of measurements are performed: "slow" measurements and "fast" measurements. Slow measurements concern temperature probes, water content probes, weather data and anchored displacement sensors. These measurements are recorded continuously every 5 minutes. Fast measurements include accelerometers, vertical and horizontal extensometers and anchored displacement sensors. Fast measurements are recorded under the passage of trains. They are triggered when the measured acceleration at the top of the first sublayer exceeds a certain threshold level. This level is set at a very low value, in order to record all train passages. The signal acquisition frequency is 2000 Hz [START_REF] Khairallah | Monitoring of railway structure with bituminous underlayment[END_REF]. The measurements made on the BPL HSL can be divided in two phases. The first phase, entitled ''speed up phase", corresponds to a 3 months test phase of the track, between November 2016 and January 2017, before the start of commercial traffic. During this phase, the same train, with known characteristics (10 cars, 13 bogies), circulated on the track at increasing speeds, ranging from 160 to 352 km/h. The second acquisition phase corresponds to the commercial traffic phase, where the average train speed is 320 km/h, and where different high-speed trains, with different bogie loads and characteristics pass on the track. The results presented in this paper concern only the speed up phase. Comparisons between results obtained on the two structures, with granular and asphalt concrete sublayers, are detailed in [START_REF] Khairallah | Monitoring of railway structures of the high-speed line BPL with bituminous and granular sublayers[END_REF].

DATA PROCESSING

A train journey on the BPL railway track generates more than 50 data files that need to be treated and plotted. In view of the large amount of data recorded, it was essential to develop procedures for automating data processing. Scilab, a free numerically oriented programming language was therefore used to automate signal processing. Several routines were programmed, to determine the date and the exact time of each train's passage, to calculate the train velocities, to filter the recorded sensor signals using a low pass filter and finally to plot them.

After selection and filtering, a method called "superposition of carrier bogies" is used to process the measurements. Based on the recordings made, for a given sensor, for a train passage at a known speed, the procedure consists in separating the signals corresponding to each carrier bogie (excluding the motor bogies), and plotting them from the same time origin. It is thus possible, for each sensor, to calculate the mean curve and the curves corresponding to +/-one standard deviation. From theses mean curves, maximum accelerations and displacements, corresponding to a train passage, can be calculated and used for comparing the response of different structures. This processing method has been automated using Scilab, for the two instrumented sections.

To illustrate this processing method, Figure 2 presents an example of typical vertical displacement (or deflection) signals and vertical acceleration signals recorded on section 2, with a granular sub-layer, for a train speed of 320 km/h. Figure 2a shows the deflection signals, corresponding to the 7 carrier bogies, and the calculated average signal. Figure 2b shows similarly the 7 acceleration signals, and the calculated average signal. On these figures, positive values correspond to upwards accelerations and displacements. For the analysis of the results, it is also important to highlight that the speed up phase was carried out between November 2016 and January 2017. Temperature variations during this period were limited. The average temperature in the asphalt concrete layer was 7 °C +/-1 (with a minimum temperature of 2°C, and a maximum temperature of 10°C). Therefore, it is possible to compare all the signals recorded during this period, neglecting the influence of temperature variations on the stiffness of the asphalt layer.

MODELLING OF THE MECHANICAL RESPONSE OF THE SECTION WITH ASPHALT CONCRETE SUBLAYER USING THE VISCORAIL SOFTWARE Main principles of ViscoRail

ViscoRail (9-10) is a semi-analytical calculation code dedicated to the determination of the dynamic response of railway structures under moving loads (at constant magnitude and speed). This numerical program is well adapted to the simulation of railways incorporating either granular or asphalt layers as encountered on HSL BPL. The method implemented in this tool (9-10) extends the quasi-stationary approach used for road pavements and adopted in ViscoRoute© 2.0 (11) to the case of railways for which the load transfer to the infrastructure is performed through sleepers discontinuously distributed along its surface. As shortly explained further, this method is based on a specific decomposition of the pressure distribution under the discrete supports which makes it possible to consider the assumptions related to the quasi-stationary approach. ViscoRoute© 2.0 is a numerical program that solves the equations of motion for semi-infinite layered media subjected to constant moving loads. The problem of quasi-stationary motion is solved in the reference frame (𝑋 = 𝑥 -𝑉𝑡) moving simultaneously with the loads. In this calculation code, the structural layers are assumed homogeneous and their constitutive behavior can be set as isotropic linear elastic (Hooke's law) or as viscoelastic according to the Huet-Sayegh thermosensitive model [START_REF] Huet | Étude par une méthode d'impédance du comportement viscoélastique des matériaux hydrocarbonés[END_REF][START_REF] Sayegh | Variation des modules de quelques bitumes purs et bétons bitumineux[END_REF]. The latter is particularly well suited for asphalt materials. This model is represented by a purely elastic spring in the first branch connected in parallel to two parabolic dampers in series with an elastic spring in the second branch. Either sliding or fully bonded interfaces between the layers can be considered [START_REF] Chupin | Influence of sliding interfaces on the response of a layered viscoelastic medium under a moving load[END_REF]. ViscoRail extends the original ViscoRoute© 2.0 software in the sense that it also integrates the track system composed of the rail and the sleepers. The solving method in ViscoRail is based on a sub-structuring procedure that consists in splitting the initial model (railway track and structure) into two subsystems and in solving the global response iteratively (fixed-point iteration). The first subsystem that corresponds to the rails secured on the periodically positioned sleepers is modelled by Euler-Bernoulli beams and vertical springs. The second subsystem (or sub-structure) representing the multilayer track structure is modelled as a stacking of semi-infinite layers. The connection between these two subsystems is made through the vertical stress distribution p(x, t) under the sleepers (at the interface between the subsystems), which is straightly correlated to the load transfer across the track system. In the solving process, 𝑝(𝑥, 𝑡) is first initialized arbitrarily prior to running the iterative process that matches this pressure distribution with that resulting from the dynamic response of the global coupled system after convergence. The mechanical response of the railway structure to a moving train loading is that obtained once 𝑝(𝑥, 𝑡) has converged. Note that at each iteration, the dynamic response of the sub-structure to 𝑝(𝑥, 𝑡) is computed using ViscoRoute© 2.0 after an ad hoc decomposition of this pressure distribution into "loading waves" has been performed to conform to the quasi-stationary assumption. The solution is then obtained by recombination of the individual contribution due to each loading wave. The reader is referred to [START_REF] Chupin | Calculation of the dynamic response of a viscoelastic railway structure based on a quasi-stationary approach[END_REF] for more detail on this technique. Output results from ViscoRail allow us to plot the spatial and temporal evolutions of the various mechanical fields in the structure (displacements, accelerations, strain and stress fields, etc.), for any horizontal plane located at a given z-coordinate. Some advantages of ViscoRail are that the computation time is small because of the semi-analytical approach and viscoelasticity of asphalt concrete layers can be considered. Moreover, this is a tool of simple use that facilitates the pre-and post-treatment phases, as compared to finite element computations or example.

Inverse calibration of the model parameters

The modelling of HSL BPL structures by means of ViscoRail requires defining the model input parameters which are not all measured on site (e.g. the Young modulus of UGM or soil...). Layers modulus values used for the design of track structure (𝐸 𝑏𝑎𝑙𝑙𝑎𝑠𝑡 = 200 𝑀𝑃𝑎, 𝐸 𝑈𝐺𝑀 = 3x𝐸 𝑠𝑜𝑖𝑙 = 240 𝑀𝑃𝑎, 𝐸 𝐶𝐹 = 240 𝑀𝑃𝑎, 𝐸 𝑠𝑜𝑖𝑙 = 80 𝑀𝑃𝑎) weren't qualified to reproduce the track's mechanical response. True sensors data were nowhere near computed results with ViscoRail. Thus, the model input parameters are obtained from back calculation by minimizing the gap between the simulated response and that recorded by the instrumentation. To accomplish this, the measurements stemming from the granular section (deflections, strains and accelerations at different locations) for train velocities V = 160 and 320 km/h are selected. The model parameters to be determined are the Young moduli of the different layers and the stiffness of the rail pads. The values of these parameters are bracketed within ranges of variation that we define as acceptable for the problem under consideration:

-Modulus of the ballast Eballast between 150 and 600 MPa -Modulus of the granular sublayer EUGM between 200 and 1000 MPa -Modulus of the cement-treated capping layer ECF between 400 and 5000 MPa -Modulus of the subgrade Esoil between 80 and 200 MPa.

-Stiffness of the rail pads k between 50 and 150 MN/m. Then, series of ViscoRail calculations are performed for different combinations of parameters values picked out in the ranges defined previously, until a good match between the simulation results and the measurements is reached. The following set of parameters leading to satisfactory results for the two velocities V = 160 km/h and V = 320 km/h is obtained: { 𝐸 𝑏𝑎𝑙𝑙𝑎𝑠𝑡 = 250 𝑀𝑃𝑎 𝐸 𝑈𝐺𝑀 = 860 𝑀𝑃𝑎 𝐸 𝐶𝐹 = 2750 𝑀𝑃𝑎 𝐸 𝑠𝑜𝑖𝑙 = 160 𝑀𝑃𝑎 𝑘 = 100 𝑀𝑁/𝑚 } Later on, these track components are tested for adequate results outcome when it comes to other train speeds. In a second step, it is considered that the stiffness of the granular materials and of the subgrade is very similar on all the sections of the HSL BPL. Therefore, the elastic moduli determined previously on the granular section are assumed also valid for the asphalt section for which a layer of asphalt material (GB4) is simply added under the ballast. The behavior of the asphalt layer is modelled using the Huet-Sayegh viscoelastic model whose parameters are determined from complex modulus tests performed in the laboratory. The parameter values are given in Table 2 and are kept the same in all the simulations.

Comparison of ViscoRail calculation results with real measurements

After determining the model parameters, calculations with ViscoRail are performed for the section with an asphalt sub-layer and compared with the sensor measurements. Data processing routines filter the measurements using a low-pass filter adjusted according to the train velocity. The applied filter eliminates the dynamic effects observed at high frequencies linked to unsprung masses dynamics. We thus obtain data signals comparable to theoretical signals computed with ViscoRail, assuming the applied load as constant intensity load. The cut-off frequency fc is thus calculated as a function of the 3 meter "wheel" wavelength and the train speed. As it happens, the "wheel" frequency is the frequency at which one point of the wheel (and therefore possibly the defect point) comes into contact with the rail, 𝑓𝑐 = 𝑉2𝜋𝑅. The frequency obtained is increased by 10% to avoid any significant signal loss. Furthermore, ViscoRail computations are performed for four different traffic speeds: V = 160, 240, 320 and 350 km/h, and for a typical high-speed train carrier bogie composed of two axles spaced 3m apart and loaded at 160 kN each (80kN per wheel).

10

The longitudinal profiles can be calculated using ViscoRail for four different load instants, corresponding to the following positions 𝑥𝐹n of the bogie's two axles, occupying identical relative positions with respect to the track as seen in The behavior of the two sections was modeled using the ViscoRail software, developed for the prediction of the dynamic behavior of railway structures, and based on a multilayer model, considering elastic and viscoelastic behavior. A calibration procedure has been developed to determine the model parameters from sensor measurements at two speeds, 160 km/h and 320 km/h. After calibration, good predictions of the response of the two structures have been obtained. Vertical acceleration, deflection and vertical deformation have all been well reproduced, for the granular and bituminous sections, and for a wide range of speeds. The differences in maximum accelerations between the granular and bituminous sections were also confirmed by the calculations.

All these results are very encouraging, and confirm that the model of ViscoRail predicts correctly the response of ballasted track structures, with and without bituminous sub-layers. ViscoRail therefore appears as an efficient tool for fast calculations of the response of railway structures, for design applications, or parametric studies. In particular, it can be used to calculate mechanical parameters like acceleration levels in the ballast layer, which could be used as a criterion to evaluate the stability of the ballast (i.e. the risk of settlements), and the maximum tensile strains in the asphalt layer, which can be used to evaluate its fatigue life.

Figure 2

 2 Figure 2 Typical vertical displacement and vertical acceleration signals recorded under the seven carrier bogies, and calculated average signals, for a train speed of 320 km/hFor the analysis of the results, it is also important to highlight that the speed up phase was carried out between November 2016 and January 2017. Temperature variations during this period were limited. The average temperature in the asphalt concrete layer was 7 °C +/-1 (with a minimum temperature of 2°C, and a maximum temperature of 10°C). Therefore, it is possible to compare all the signals recorded during this period, neglecting the influence of temperature variations on the stiffness of the asphalt layer.MODELLING OF THE MECHANICAL RESPONSE OF THE SECTION WITH ASPHALT CONCRETE SUBLAYER USING THE VISCORAIL SOFTWARE Main principles of ViscoRailViscoRail (9-10) is a semi-analytical calculation code dedicated to the determination of the dynamic response of railway structures under moving loads (at constant magnitude and speed). This numerical program is well adapted to the simulation of railways incorporating either granular or asphalt layers as encountered on HSL BPL. The method implemented in this tool (9-10) extends the quasi-stationary approach used for road pavements and adopted in ViscoRoute© 2.0 (11) to the case of railways for which the load transfer to the infrastructure is performed through sleepers discontinuously distributed along its surface. As shortly explained further, this method is based on a specific decomposition of the pressure distribution under the discrete supports which makes it possible to consider the assumptions related to the quasi-stationary approach. ViscoRoute© 2.0 is a numerical program that solves the equations of motion for semi-infinite layered media subjected to constant moving loads. The problem of quasi-stationary motion is solved in the reference frame (𝑋 = 𝑥 -𝑉𝑡) moving simultaneously with the loads. In this calculation code, the structural layers are assumed homogeneous and their constitutive behavior can be set as isotropic linear elastic (Hooke's law) or as viscoelastic according to the Huet-Sayegh thermosensitive model[START_REF] Huet | Étude par une méthode d'impédance du comportement viscoélastique des matériaux hydrocarbonés[END_REF][START_REF] Sayegh | Variation des modules de quelques bitumes purs et bétons bitumineux[END_REF]. The latter is particularly well suited for asphalt materials. This model is represented by a purely elastic spring in the first branch

Figure 3 :

 3 wheels above the center of the sleeper: 𝑥𝐹1 = {0; 3} m , above the left edge of the sleepers: 𝑥𝐹2 = {0.15; 3.15} m, above midpoint between the sleepers: 𝑥𝐹3 = {0.3; 3.3} m and above the right edge of the sleeper: 𝑥𝐹4 = {0.45; 3.45} m. In the carried calculations and for every train speed, two different wheel positions are considered: position 𝑥𝐹1 and position 𝑥𝐹3.

Figure 3

 3 Figure 3 Consecutive load positions (xFn) considered in the calculationsComparison in terms of deflection

Figure 5

 5 compares the average signals of accelerometers A2, A4 and A6 located between the rails (graphs (a) and (c)), and of accelerometers A1, A3 and A5 located under the axis of the rail (graphs (b) and (d)) with the modelling results. The graphs show that ViscoRail predicts correctly the accelerometer signals both in shape and in amplitude for the two speeds. The predictions seem somewhat better for the accelerometers located under the rails (graphs (b) and (d)).

Figure 5

 5 Figure 5 Comparison between predicted and measured longitudinal acceleration profiles at the top of the GB layer (a) between the rails at V = 160 km/h, (b) under the rail axis at V = 160 km/h, (c) between the rails at V = 320 km/h, (d) under the rail axis at V = 320 km/hTo illustrate the effect of the train speed on the vertical acceleration in the track structure, Figure6presents a comparison between the maximum measured and calculated values of the upward and downward

Figure 6

 6 Figure 6 Comparison of measured and predicted maximum accelerations at the top of the GB layer under the rail axis, on the asphalt section, for two load positions, xF1 = {0; 3} and xF3 = {0.3; 3.3} CONCLUSIONS Two sections of the BPL high-speed line, with granular sub-layer and asphalt sub-layer have been largely instrumented, to study their mechanical response, under high-speed train loading. The measurements, made for speed levels varying between 160 and 352 km/h have shown that the introduction of a bituminous sub-layer under the ballast reduces significantly (approximately by a ratio of two) the vertical accelerations under the ballast.The behavior of the two sections was modeled using the ViscoRail software, developed for the prediction of the dynamic behavior of railway structures, and based on a multilayer model, considering elastic and viscoelastic behavior. A calibration procedure has been developed to determine the model parameters from sensor measurements at two speeds, 160 km/h and 320 km/h. After calibration, good predictions of the response of the two structures have been obtained. Vertical acceleration, deflection and vertical deformation have all been well reproduced, for the granular and bituminous sections, and for a wide range of speeds. The differences in maximum accelerations between the granular and bituminous sections were also confirmed by the calculations.All these results are very encouraging, and confirm that the model of ViscoRail predicts correctly the response of ballasted track structures, with and without bituminous sub-layers. ViscoRail therefore appears as an efficient tool for fast calculations of the response of railway structures, for design applications, or parametric studies. In particular, it can be used to calculate mechanical parameters like acceleration levels in the ballast layer, which could be used as a criterion to evaluate the stability of the ballast (i.e. the

TABLE 1 . Structure of the sections with and without asphalt concrete

 1

	Conventional track	Innovative track with GB sublayer
	30 cm of ballast	30 cm of ballast
	20 cm of UGM layer	12 cm of GB4 layer
	35 cm of earthwork treated layer (EV2 =	15 cm of UGM layer
	80 MPa)
	Earthwork treated layer (EV2 = 80 MPa) Earthwork treated layer (EV2 = 80 MPa)

TABLE 2 . Huet-Sayegh model parameters for the bituminous layer

 2 The complete characteristics of the track section with asphalt sublayer determined by this calibration process are given in Table3.

	E∞	E0	k	h	δ	τ0 (s)	A1 (°C -1 )	A2 (°C -2 )
	(MPa)	(MPa)
	32655	11	0.193	0.592	2.244	18.973	-0.397	0.00195

TABLE 3 . Geometric and mechanical characteristics of the asphalt track structure model

 3

		𝝆	𝑬 (MPa)	𝝂	𝒆 (m)
		(kg.m -3 )
	Ballast	1800	250	0.4	0.3
	GB sublayer	1800	Huet-Sayegh	0.4 0.12
			model
	UGM layer	1800	860	0.4 0.15
	Capping layer	1800	2750	0.4 0.35
	Subgrade	1800	160	0.4	6
	Bedrock	1800	100.10³	0.4	∞