Jana Koteich

Nathalie Mitton

PILOT Dataset: A Collection of Multi-Communication Technologies in Different Mobility Contexts

Keywords: Dataset generation, WiFi, BLE, LoRa, Acceleration, IoT, FiPy

L'omniprésence des appareils mobiles équipés de technologies de communication radio a rendu courante la collecte de données à grande échelle sur la mobilité humaine [SSGL15]. Par conséquent, avec le manque d'ensembles de données, la collecte et la publication de données s'avèrent lever de nouvelles questions scientifiques. Dans cet article, nous présentons l'ensemble de données PILOT et sa méthodologie de collecte de données préservant la confidentialité des technologies de communication sans fil. L'ensemble de données est une collection de quatre éléments d'information collectés conjointement dans différents contextes de mobilité. Il comprend trois technologies de communication sans fil : balises WiFi, balises BLE (Bluetooth Low Energy) et paquets LoRa (Long Range Radio), ainsi que des informations supplémentaires qui comprennent : Accélération, Roulis et Tangage, toutes collectées en même temps. Nous fournissons les clés pour reproduire cette collecte de données. Le jeu de données est collecté pendant environ 60 heures, avec une taille de 150 Mo en utilisant les dispositifs FiPy de Pycom et il est téléchargé sur GitHub. Nous pensons que la combinaison des différents types d'informations collectées dans différents scénarios de mobilité constitue une nouvelle génération d'un riche ensemble de données qui offre une nouvelle perspective pour analyser le réseau et obtenir de nouvelles informations.

Introduction

These days, the rapidly evolving information technology and the development of wireless and mobile networks have promoted a new wave of information and industrial tide [START_REF] Gu | A scalable and virtualized testbed for iot experiments[END_REF]. Several promising applications like tracking smartphones, traffic monitoring, crowd dynamics monitoring, and other scientific research are based on the gathering and analysis of measurement data. This increases the urge of creating new forms of datasets that provide a new perspective to analyze data and bring out new measurements. The collected datasets are mainly characterized by the Model and Parameters recorded. Each type of dataset can serve a new form of analysis, that is why there are always newly generated datasets with different characteristics.

To this end, we noticed a lack of a collective dataset that includes several traces from wireless communication technologies and sensors recorded at the same time in different mobility contexts. Such dataset provides a new generation of collecting data that could help in studying human mobility. So, in this paper, we introduce a new approach to a collected dataset that is characterized by mainly two novel approaches: 1) Collecting different types of data from sensors (Acceleration, Roll and Pitch) and wireless communication technologies (WiFi beacons, BLE beacons, LoRa packets). 2) The data is collected in different mobility scenarios and mainly classified into Static and Mobile scenarios. The overall collected data till now is approximately 60 hours in total from different mobility scenarios with a size of 150 MB collected using a Micropython enabled microcontroller called FiPy device. The dataset is released as a collection of text files and comma-separated values (CSV) files with mainly the timestamp, a unique identifier of the emitting device, RSSI (Received Signal Strength), and other information dedicated to each wireless technology. This dataset is privacy-preserving since it fully meets the GDPR specification, where the MAC addresses and the device names are masked and it is uploaded to GitHub.

In [FJG + 14], Friesen et. al. present a complete data collection system developed at the University of Manitoba that uses a variety of wireless networking technologies and devices to collect inferred traffic data. They used XBee, GSM and Bluetooth modules for designing and implementing a slave probes network with the objective to collect Bluetooth device information. In [VNRG10], Vu et. al. introduce a new framework that collects location information and ad hoc contacts of humans at the University of Illinois campus. The Bluetooth MAC address is used to infer contact information and Wi-Fi MAC addresses are used to infer physical location of the phone. In [START_REF] Girolami | A bluetooth low energy dataset for the analysis of social interactions with commercial devices[END_REF], a data collection campaign and a dataset of BLE beacons for detecting and analysing human social interactions is described, and it is collected in a High School. Although useful, these approaches are limited to contact tracing applications in a single environment (university campus or high school). To the best of our knowledge, the literature does not present any previous work that has generated a labeled dataset from multi-communication wireless technologies and sensors at the same time in different mobility contexts as we propose in this paper. PILOT dataset provides a group of collected packets from three different wireless communication technologies: WiFi, BLE and LoRa, and as additional useful information, the dataset includes the acceleration, roll, pitch and the battery voltage for collecting these data. These traces have been jointly collected all together in several mobility contexts using FiPy microcontrollers from pycom. The duration of each scanned data is between 10 min and 3 hours, and each recorded log file is labeled by its specific mobility scenario of scanning with a description of the conditions of scanning. The dataset is uploaded to github † as a collection of text files and CSV files.

PILOT Dataset

Experimental Design

The experimental setup described in this section is the basis of the collected data and the formation of the desired dataset. The aim is to scan the different wireless communication activities in the range of the scanning device. To do so, we used FiPy devices since they support the three wireless communication technologies: WiFi, Bluetooth, and LoRa. The FiPy is connected to a Pytrack or Pysense expansion board that includes Accelerometer and an SD card module. The development boards of the FiPy include an onboard WiFi and Bluetooth antenna, and for LoRa, an external antenna is connected. To ensure all needed information is gathered at the same time, the scanning process is distributed on four devices as shown in Figure 1. To get the actual time, the FiPy is connected to an access point, to be able to connect to the Network Time Protocol (NTP) server that will help to synchronize the real-time clock (RTC) and get the current timestamp. The collected data by each device is saved on an SD card.

Configuration and Received Data

The configuration of each wireless technology is as follows:

WiFi Node (𝑁 𝑊 ): The WiFi node is configured to start active scanning, as the device radio transmits a probe request and listens for a probe response from an AP or active devices such as phones or laptops. The FiPy device supports 802.11b/g/n so the radio scanning is in the 2.4-GHz to 2.4835-GHz spectrum. Upon detecting a probe request, scanners log several pieces of information related to that probe, as it indicates †. https://github.com/Janakoteich/PILOT-Dataset-Collection-of-Multi-communication-Technologies the following named tuples: (SSID, BSSID, sec, channel, RSSI). The saved log mainly includes 1) the timestamp related to the probe request detection, 2) the service set identifier (SSID) which is the name of the device, 3) the basic service set identifier (BSSID) which is the MAC address of the sender, 4) the sec that stands for security, 5) the channel number which is in the range of 1 to 11, and 6) the received signal strength (RSSI). The value of sec attribute defines the type of security where each value means the following: '0' is open, '1' is WEP, '2' is WPA-PSK, '3' is WPA2-PSK, and '4' is for WPA/WPA2-PSK.

Bluetooth Node (𝑁 𝐵 ): The BLE node is configured for passive scanning to receive the advertising packets (PDUs) that are retrieved every second. The following named tuple with the advertisement data is received during the scanning: (𝑀 𝐴𝐶, 𝑎𝑑𝑑𝑟_𝑡𝑦 𝑝𝑒, 𝑎𝑑𝑣_𝑡𝑦 𝑝𝑒, 𝑟 𝑠𝑠𝑖, 𝑑𝑎𝑡𝑎), where data contains the complete 31 bytes of the advertisement message. Then this data is parsed to get the following information: 𝑎𝑑𝑣_ 𝑓 𝑙𝑎𝑔, 𝑠𝑐𝑎𝑛_𝑡𝑥_𝑝𝑤𝑟, 𝑐𝑜𝑛𝑛_𝑡𝑥_𝑝𝑤𝑟, 𝑡𝑥_𝑟𝑎𝑛𝑔𝑒 and 𝑎𝑑𝑣_𝑡𝑥_𝑝𝑤𝑟. The log is first saved with a timestamp since the advertisement is received, with the MAC address of the sender and the RSSI. Other information is retrieved like the advertising flag, the 𝑛𝑎𝑚𝑒 of the device, scanning transmission power, connection transmission power, transmission range, and advertising transmission power.

LoRa Node (𝑁 𝐿 ): The LoRa Alliance has defined two frequency bands for the usage of LoRa technology in Europe. In our location, only EU868 is supported. The microcontroller will be listening to different frequencies and switch between them every second. In this way, we can receive some LoRa packets that are operating on the following frequencies: 863000000, 864000000, 865000000, 866000000, 867000000, 868000000, 869000000, 864862500, 865062500, 865402500, 865602500, 865985000, 866200000, 866400000, 866600000. These frequencies are defined randomly in the configuration of the FiPy. As we increase the number of frequencies to listen on, the delay will increase for switching between selected frequencies, and as a consequence, the chance of receiving packets will decrease.So, if by chance we received data while listening on a specific frequency, the data will be saved in the file with mainly the following information: The timestamp, the spreading factor, the data itself (which will be masked for privacy issues), the frequency, RSSI, the signal-to-noise ratio (SNR), and other information as shown in the log sample in Figure .   Acceleration Node (𝑁 𝑥 ): Is the node that collects the acceleration information, roll and pitch.

Data Collection Methodology

After scanning, each log is saved with a real timestamp in a text file on the SD card. The goal is to observe and record the variations of the wireless technologies in different mobility contexts, which are mainly categorized into two: Static and Mobile scenarios. For Static we defined the following cases: Home, Office, Restaurant, Bus_station, University and Meetings, and for Mobile we have the following scenarios: Pedestrian, Car, Bus, Metro, and Trains. We took into consideration the different conditions of each scenario, as we have rural areas (auto-route), urban areas like cities, and less crowded places like villages.

Dataset Description

One of the main characteristics of the dataset is that it is labeled. This is achieved by tracking the places and the time of scanning, then the data is retrieved from the four devices and saved in a file with a label based on the scanning conditions that were noted. In the first step we get four text files, then using python programming language, the MAC addresses, and SSIDs' are encrypted, then each text file is transferred to a CSV file. The data is classified and uploaded on GitHub. For each scenario, we have sub-folders named by the prefix of the name of this scenario, and each of them includes the scanned data. At the time this paper is written, 72 datasets are made available with different scanning time slots and intervals for 11 mobility contexts.

Dataset Insights

In this section, a comparison between static and mobile scenarios is presented. Figures 2 and3, represent the received beacons from each access point over time, with the corresponding RSSI. In Figure 2 which displays the WiFi data collected from an office (static scenario), it can be seen that the beacons are detected over the whole scanning time. Knowing that the scanner is fixed, would indicate that the access points detected by the scanner are also fixed. While in Figure 3 which is related to the data collected from a bus (mobile scenario) in an urban area, the beacons are appearing only for a very short duration. This is because we are losing connection with the access point because of the mobility of the bus. From these observations, we can see how each scenario has its unique pattern of received beacons. What is more interesting is that several datasets for the same scenario, show the same behavior of received beacons. Such results could be important for building new knowledge and bringing a new perspective to analyzing human mobility. In this work, we have provided a rich dataset called PILOT dataset that includes four jointly collected information from multi-communication wireless technologies and sensors. The traces are collected in different mobility scenarios mainly categorized as Static and Mobile. The dataset is a collection of WiFi beacons, BLE beacons, LoRa packets, acceleration, roll, and pitch information. The methodology to reproduce the dataset is illustrated and provided on GitHub. This dataset is reproducible and will be enriched with more data with time. In the meantime, we are still collecting data for an average of 4 hours per week. In future work, we will add new scenarios for collecting data, and we will add a new category for the collected dataset related to predefined mobility models that meet the expectation of more research work.

FIGURE 1 :

 1 FIGURE 1: Data Collection Setup

FIGURE 2 :

 2 FIGURE 2: WiFi beacons -Office monitoring FIGURE 3: WiFi beacons -Bus monitoring


Maxime Gonthier
email: maxime.gonthier@ens-lyon.fr

Loris Marchal

Samuel Thibault

Memory-Aware Scheduling of Tasks Sharing Data on Multiple GPUs

Why focus on memory-aware scheduling ? GPU 1 memory GPU 2 memory GPU 3 memory GPU 4 memory CPU memory of infinite size PCI Express bus Loading data Evicting data GPUs are quick but have a limited memory They share the same PCI bus with limited bandwidth

Example with 2D grid dependencies The scheduling is done by GPU k when it needs new tasks.

Find D opt ∈ dataNotInMem k such that the number of tasks depending on D opt and on other data already in memory is maximum (if there is a tie: choose with transfer time, priority of the associated tasks and most total unprocessed task)

plannedTasks k ← set of unprocessed tasks depending only on D opt and on other data already in memory

Our eviction policy: LUF (Least Used in the Future)

Try to evict a data not useful for any task already in the GPU's buffer.

Try to evict a data used by a minimal number of tasks in the set of task planned by the scheduler.

Maxime GONTHIER Memory-Aware Scheduling March 23, 2023 5 / 11

2D matrix multiplication with 2 Tesla V100 GPUs q q q q q q q q q q q q q q q A and B fits in cumulated memory B fits in cumulated memory Working set (MB) GFlop/s q q q q DARTS+LUF DMDAR DARTS EAGER Amount of data transfers on the 2D matrix multiplication with 2 Tesla V100 GPUs q q q q q q q q q q q q q q q A and B fits in cumulated memory B fits in cumulated memory Working set (MB)

Data transfers (MB)

q q q q q DARTS+LUF DMDAR DARTS EAGER Cholesky decomposition with 2 GPUs q q q q q q q q q q q q All data fit Cholesky decomposition with 8 GPUs q q q q q q q q q q q q q q q

All data fit LU with 8 GPUs q q q q q q q q q q All data fit Export it to other out-of-core applications. DARTS is not specific to GPUs! Sparse 2D matrix multiplication without memory limitation (32GB by GPU) with 4 Tesla V100 GPUs q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q GFlop/s max GFlop/s q q q q q q q q q q q q q q q q q q q q q q q q DARTS+LUF+OPTI hMETIS+R DMDAR DARTS+LUF hMETIS+R no part. time EAGER

No memory constraint DARTS produces a processing order that best distributes transfers over time

  GPUs → Reduce total execution time Ordering tasks inside each GPU → Reduce data transfers Having a generic scheduler → Efficient with any application or memory their completion time is minimal based on computation + communication times + Ready reordering heuristic on GPU k From the list L of tasks allocated on GPU k , it will search the task T ∈ L requiring the fewest data transfers Data-Aware Reactive Task Scheduling: DARTS

GFlop

P

G

G

G

  matrix multiplication, Cholesky decomposition, LU, GEMM and sparse matrix multiplication DARTS can achieves good performance when the memory is not constrained and always get very good performance when it is a scarce resource Areas for improvement Improve computational complexity. It's holding us back to get good performances on Gemms and large matrics of the outer product Manage multiple MPI nodes


Cécile Dagès
email: cecile.dages@supagro.inra.fr

Jean-Stéphane Bailly

Jeanne Dollinger

Marthe Lanoix

David Crevoisier

Marc Voltz

Impact of soil management in ditches on water related ecosystem services

Ditches, providers of regulating ecosystem services

Farm ditches are human-made linear elements that constitute the upstream parts of the permanent hydrographic networks in agricultural landscapes. Primarily implanted to collect surface and subsurface water for soil waterlogging and/or erosion control, farm ditches may also provide other services such as water purification, flood regulation, groundwater recharge, and biodiversity conservation [START_REF] Dollinger | Managing ditches for agroecological engineering of landscape. a review[END_REF].

By changing ditch characteristics, ditch maintenance operations (fig 1) influence the provision of ecosystem services. The project presented in this poster aimed to investigate the impact of ditch management on water related ecosystem services, notably water purification against pesticides.

We focus on infiltrating ditches because of their ambivalent position: they are known to buffer surface water pesticide contamination, but they may also contribute to groundwater contamination.

Simulating reach scale retention with an indicator approach

A large range of retention capacities

Ditch bed soils

Ditch bed soil's are formed from layered fine sediments deposited by surface flow structured by wetting/drying cycles and root activity [START_REF] Vaughan | Morphology and Characterization of Ditch Soils at an Atlantic Coastal Plain Farm[END_REF] . Their characteristics are different from neighbouring soils : porous structure, infiltration properties or organic matter content [START_REF] Margoum | Investigation of various physicochemical and environmental parameter influence on pesticide sorption to ditch bed substratum by means of experimental design[END_REF]Dagès et al., 2015). We follow a 3 steps approach:

1-Characterization of ditches variability by building classifications of ditch characteristics and by linking ditch types with maintenance operation.

2-Analysis of retention capacity at the reach scale with an indicator based approach to asses range of retention capacities and virtuous/bad types.

3-Analysis of the retention capacity at the network scale with a distributed physically based modelling approach to evaluate management strategies.

Each type is a result of a ditch maintenance operation and a natural evolution in relation with the climate. Transition matrix between types after maintenance were also built (see fig 3). The method and the results are detailled in [START_REF] Dollinger | Managing ditches for agroecological engineering of landscape. a review[END_REF].

Example of a ditch bed soil

A granular structure with high porosity and few very coarse fragments occurred in each horizon.

A physically based approach

Coupling of surface and subsurface water flow and reactive solute transport within the OpenFLUID coupling plateform framework [START_REF] Fabre | OpenFLUID : a software environment for modelling fluxes in landscapes[END_REF] :

Simulating network retention with a spatially distributed modeling approach

Analysing scenarii at the network scale is essentiel to evaluate management strategies.

Concluding remarks

This work shows that i) ditches may be classified from basic characteristics, but that types depend on the nature of the pollutant; ii) distribution of ditch types within catchment can be predicted with simple landscape covariables; iii) soil play a key role in water ditch purification for hydrophilic molecules such as glyphosate, with soil sorption counting for 77-99% of retention capacity. Soil sorption is also a major processes for hydrophobic (diuron) and super-hydrophobic molecules (chlorpyrifos), but other ditch materials, respectively ashes and living vegetation are significantly involved in (super)-hydrophobic molecules ditch retention. Management of ditches should be considered as a valuable tools to limit water contamination.

Next steps

Running contrasted scenarii at the network scale

  fig 1. Ditch maintenance, a combination and a succession in time of basic operations

  fig 2. Example of the hydrrophilic (e.g. glyphosate) typology.

  fig 4. Distribution of ditch retention

Fig 4- 6

 6 Fig 4-6 illustrate the sensitivity of ditches for the hydrophilic classification (fig2). Soil Kd and width are the most sensitive parameters. Effect of type is not clear for this classification, unlike for the other two classifications.


Y Copin

Supernova Factory

C Buton

E Gangler

G Smadja

E Pécontal

G Rigaudier

P Antilogus

S Bailey

R Pain

R Pereira

C Wu

G Aldering

C Aragon

S Bongard

M Childress

S Loken

P Nugent

S Perlmutter

K Runge

R C Thomas

B A Weaver

C Baltay

A Bauer

D Rabinowitz

R Scalzo

The Nearby Supernova Factory (SNfactory) is an international project to discover and study a large sample of type Ia supernovae in the redshift range 0.03 < z < 0.08. Follow-up spectro-photometric observations are performed using the dedicated Supernovae Integral-Field Spectrograph, mounted since 2004 on 2.2 m UH telescope. The goal is to acquire for each supernova and over its full life-time (more than 10 epochs) high spectro-photometric quality spectra over the extended optical range (320-1000 nm).

I will present the current status of the SNfactory project, from search efficiency to first scientific results, with an emphasis on the spectro-photometric calibration issues and achievements.

THE NEARBY SUPERNOVA FACTORY: TOWARD A HIGH-PRECISION SPECTRO-PHOTOMETRY 1 Introduction

Due to their high intrinsic luminosity and their standardizable aspect, type Ia supernovae (SNe Ia) are among the finest distance indicators for cosmology. High redshift observations played a major role in the discovery of the "dark energy" component of the universe (e.g. [START_REF] Leibundgut | [END_REF] and references therein).

As expressed by Linder (2006), nearby SNe Ia (typically z < 0.2) play two important roles for cosmological use of the supernova distance-redshift relation: as an anchor for the Hubble diagram, and as an indicator of possible systematics. For these purposes, the author states that a "local" sample should comprise few hundreds SNe with redshifts centered on z = 0.05.

The spectro-photometric follow-up of this local sample will allow various studies to be undertaken with improved precision, such as:

• To calibrate the luminosity-lightcurve width ("stretch") relation, as well as intrinsic colors for dust extinction correction;

• To compute high-accuracy multi-parameters (phase, color, etc.) K-corrections, needed for photometric observations of distant SNe;

• To discover and study new spectral indicators, to derive independent estimates of intrinsic luminosity;

• To probe any potential evolutionary effects through systematic comparison of high-z SN Ia spectra with local templates;

• To improve the understanding of SN explosion physics.

The Nearby Supernova Factory project

To address these well-defined scientific goals, the search and follow-up strategies should meet the following requirements:

• Large sample of type Ia SNe (screening and typing required) located in the low-redshift end of the "Smooth Hubble flow" (0.03 < z < 0.08), discovered through an unbiased search;

• Spectro-photometric follow-up observations from -15 to +45 days every 4 to 7 days, over the extended optical range (320-1000 nm) with a percent-level absolute flux calibration.

The Nearby Supernova Factory (SNfactory, [START_REF] Aldering | Overview of the Nearby Supernova Factory[END_REF]) is an international collaboration dedicated to implement these optimal strategies. The targets are detected in unbiased wide-field images from the Palomar-QUEST Survey, using the Yale 112 CCD, 9.4 sq • camera permanently mounted on the Palomar 1.2 m Oschin telescope [START_REF] Rabinowitz | The Palomar-QUEST large-area CCD camera[END_REF]. It covers ∼ 400 sq • /night, to a depth of ∼ 20.5. As of July 2007, this procedure found 186 type Ia, 81 type II and 15 type Ib/c (see Fig. 1).

The selected SNe are then spectro-photometrically followed using SNIFS (see below), a fully-integrated integral field spectrograph specifically designed for semi-autonomous observation of point sources on a diffuse background. A summary of the dataset acquired with SNIFS is given in Table 1. The breakdown by discoverer is precised in Fig. 1, and the distributions of SNfactory SNe Ia screening (for type identification) and follow-up over redshifts and initial phases are shown in Fig. 2. Spectroscopically confirmed SNe discovered by the SNfactory used to be announced through Astronomer's Telegrams (∼ 210 announcements), and are now available online1 under an "open access honor system".

The Supernova Integral Field Spectrograph

The Supernova Integral Field Spectrograph (SNIFS) is the dedicated integral field spectrograph (IFS) used by the SNfactory for the spectro-photometric follow up of nearby SNe. It is described in [START_REF] Lantz | SNIFS: a wideband integral field spectrograph with microlens arrays[END_REF] and The black histograms represent the distribution of all SNe Ia observed with SNIFS, the red histogram gives the distribution of SNe Ia observed at 6 or more epochs, and the blue gives the distribution for 10 or more observations. In the redshift histogram, the turquoise shaded region represents the target redshift range (0.03 < z < 0.08) in the smooth Hubble flow.

Copin et al. ( 2006), we summarize here the main characteristics:

• Micro-lens based spatial stage: 15 × 15 spaxels, covering a field of view (FoV) of 6 ′′ × 6 ′′ with a spatial sampling of 0. ′′ 42.

• Dual channel spectral stage: channel B (320-520 nm, 2.4 Å/px) and channel R (510-1000 nm, 2.9 Å/px).

• Additional guiding and multi-filter photometric channels (2 × 4. ′ 8 × 9. ′ 6) located around the IFS FoV, used for target acquisition, guiding and real-time atmospheric transmission chromatic monitoring (see below).

The spectrograph is permanently mounted on the south bent Cassegrain port, and is run semi-automatically from remote locations -mainly from France and Berkeley -about three half nights per week from August 2004 to May 2006, and three full nights per week since then. SNIFS is a relatively simple and high throughput IFS. The overall efficiency, from telescope to CCD included, reaches 18% in B, and 28% in R. Furthermore, operational overhead has been reduced to 20% through highly automated operations. This makes SNIFS a very efficient instrument on sky, which can observe more than 10 SNe per night.

Flux calibration scheme

The observational goal of the SNfactory is to acquire "percent-level" spectro-photometry of SNe over a decent part of their lifespan, no matter high airmass observations, moonlight, unstable atmospheric conditions and heavy clouds! This requires a very strict flux calibration scheme, which we describe now.

Photometric case

By definition, atmospheric extinction is stable during a photometric night. In this case, extinction can therefore be estimated from different spectro-photometric standard stars observed over a range of airmasses, and then used for the flux calibration of the science target.

Target accuracy requires various elements to be precisely controlled.

• It is advantageous to have an external estimate of the atmospheric stability, besides the fact that standard stars of the night form or not a flux coherent set. For that purpose, we use SkyProbe2 [START_REF] Cuillandre | CFHT's SkyProbe: a real-time sky-transparency monitor[END_REF], giving a real-time estimate of the atmospheric attenuation (see an example on right panel of Fig. 3).

• The atmospheric extinction is decomposed on its physical components: Rayleigh and aerosol scatterings, ozone absorption and telluric lines (see Buton et al., this volume). It is particularly important to treat telluric component separately, because of its different airmass dependency.

• The spectro-photometric standard star spectra should be known to high accuracy, and with a spectral resolution similar to the SNIFS ones (σ = 2.5 Å in B, 3.4 Å in R), so that spectral resolution matching has only a weak impact. We selected ∼ 40 well observed stars as our primary set of calibrators, with ∼ 4 ≤ V ≤∼ 15.

• The "3D point source extraction" of the standard star spectra from the IFS datacubes3 requires a precise knowledge of the spatial PSF, dominated by the atmospheric seeing. Its large scale behavior (e.g. presence of non-gaussian wings) is of particular importance for an accurate flux estimate, since the small size of SNIFS FoV (6 ′′ × 6 ′′ ) limits the usability of simpler aperture-based spectro-photometry.

Non-photometric case

Atmospheric extinction is not stable during a non-photometric night: T atm (z, λ) depends also on t, and cannot be simply estimated from standard stars. Since a generic atmospheric extinction curve cannot be derived for the night as a whole, one has to estimate an effective atmospheric extinction valid for the science observation under consideration. In SNIFS, this is done using the secondary sources acquired in the multi-filter photometric channel surrounding the IFS FoV during the science exposure. By comparing the poly-chromatic4 flux of these sources between the current exposure and a reference exposure obtained in photometric conditions, the chromatic differential atmospheric extinction can be determined. In conjunction with the reference atmospheric extinction, this provides the effective curve to be used for the flux calibration of this exposure.

Note that even if SNIFS has the potential to derive chromatic differential atmospheric extinction, it appears -as it is already well known -that clouds are gray with a high level of accuracy over the full optical spectral range (see Fig. 3, see also Ivezić et al. 2007).

Spectro-photometric accuracy

The flux calibration scheme has been tested on the Calspec5 fundamental primary standard GD 71 [START_REF] Bohlin | HST Calibration Workshop[END_REF], observed with SNIFS in various atmospheric conditions with an attenuation of up to 0.3 mag (see Fig. 4). This results in a spectro-photometric calibration accuracy better than 2%.

High spectro-photometric accuracy requires not only a detailed flux calibration scheme, but also a thorough understanding of the instrumental details. In particular, from the IFS data reduction point of view, one faces various percent-level effects, such as CCD non-linearities, dark current sub-e -residuals, low-level diffuse light background, inter-spectra cross-talks, humidity-related dichroic bandpass variations. These effects will impact precision mainly in the low-flux regime. Most of them are now under control in the SNfactory (diffuse light subtraction, optimal spectrum extraction, dichroic corrections), while some others (mainly CCD non-linearities) are still under scrutiny.

Conclusions

We presented the current status of the Nearby Supernova Factory project, an international effort aimed at discovering and obtaining detailed light-curves and spectro-photometric observations for a large sample of nearby SNe Ia. The SNfactory is now well under way, and will obtain ∼ 100"gold" SNe Ia by end of 2007. While the accurate flux calibration scheme is subtle and requires a full understanding of the instrument, we have demonstrated that it can be achieved with a constant precision of ∼ 2% in generic atmospheric conditions. It is important to acknowledge that such a precision is largely due to the proper use of the integral field spectrograph technology.

First scientific results on individual objects (the massive circumstellar envelope of SN 2005gj, [START_REF] Aldering | [END_REF]; carbon signatures in early spectra of SN 2006D, Thomas et al. 2007) have been published, and the whole sample is now under scrutiny.

Fig. 1 .

 1 Fig. 1. Left: Full sample of SNe Ia discovered by the SNfactory to date. The dashed box corresponds to the optimum sample of nearby (0.03 < z < 0.08) SNe in the Hubble flow that are found more than 6 days before maximum. Right:Total number of SNe Ia followed by SNIFS (blue curve), and a breakdown by discoverer. The green curve represents the cumulative number of targets discovered by others outside the SNfactory collaboration, and the red describes the number of SNfactory-discovered SNe Ia followed up.

Fig. 2 .

 2 Fig. 2. Distribution of SNIFS SN Ia screening and follow-up over redshifts (left panel ) and initial phases (right panel ).The black histograms represent the distribution of all SNe Ia observed with SNIFS, the red histogram gives the distribution of SNe Ia observed at 6 or more epochs, and the blue gives the distribution for 10 or more observations. In the redshift histogram, the turquoise shaded region represents the target redshift range (0.03 < z < 0.08) in the smooth Hubble flow.

Fig. 3 .Fig. 4 .

 34 Fig.3. Observation of secondary spectro-photometric standard star HR 1544 with SNIFS in highly extinguished conditions (night 2006/10/01). Left: B-and R-channel spectra (solid blue and red lines), compared to the reference flux (green dashed line,[START_REF] Hamuy | [END_REF]. Shaded areas indicate regions impacted by telluric lines. No matter the high atmospheric attenuation (more than 95%), the extinction is gray at the 0.2% level. Right: atmospheric attenuation as measured by SkyProbe[START_REF] Cuillandre | CFHT's SkyProbe: a real-time sky-transparency monitor[END_REF] during the night. Observations of HR 1544 and Feige 110 (used as reference for flux calibration) are indicated by green lines.

Fig. 5 .

 5 Fig. 5. Nearby supernova SN 2005el observed with SNIFS. Left: F λ spectral time series, from ∼ -7 to ∼ 50+ days days with respect to B-band maximum (shaded areas indicate regions affected by telluric corrections). Right: reconstructed broad band (BV RI) light curves (diamonds: photometric conditions, dots: non-photometric conditions -smaller is worse, open triangles: unknown photometricity, treated as non-photometric).

Table 1 .

 1 Nearby Supernova Factory data summary (as of July 2007).

						Spectral epochs Total SNe Ia Pre-max SNf discoveries
							1+			265	123			184
							6+			89	65			63
							10+			76	63			50
		30									60
		25						≥ 1 SNIFS epoch ≥ 6 SNIFS epoch ≥ 10 SNIFS epoch	50					≥ 1 SNIFS epoch ≥ 6 SNIFS epoch ≥ 10 SNIFS epoch
	Number of SNe Ia	10 15 20							Number of SNe Ia	20 30 40
		5								10
		0	0	0.02	0.04	0.06	0.08	0.1	0.12	0.14	-20 0	-10	0	10	20	30	40	50
						Redshift							Initial Phase

http://snfactory.lbl.gov/snf/open access/login.php

http://www.cfht.hawaii.edu/Instruments/Skyprobe/

An IFS naturally produces 3D datasets, with two spatial dimensions and one spectral dimension.

The multi-filter comprises

selected bands representative of the different atmospheric extinction contributions. 5 http://www.stsci.edu/hst/observatory/cdbs/calspec.html


MD, MSc Paul Mclellan

MD, PhD Julien Kirchgesner
email: julien.kirchgesner@gmx.com

Perianal fistulizing Crohn's disease and overall risk of cancer: no red flag

Inflammatory bowel disease (IBD) is not only associated with an increased risk of colorectal cancer, with the greatest risk in patients with extensive and chronically active disease, but also with an increased risk of skin cancer, haematological malignancies, and urinary tract cancer.

(1) Perianal fistulizing disease affects 20-30% of patients with Crohn's disease (CD), ( 2 The authors identified 824 patients with perianal fistulizing CD among 10 208 patients with CD.

Patients were followed from January 2015 to December 2020, accounting for 4222 personyears of follow-up in patients with perianal fistulizing CD. The authors observed that the incidence of any type of cancer was higher in patients with non perianal fistulizing CD compared to patients with perianal fistulizing CD (2365 [95% CI 2219-2519] and 1184 [95% CI 879-1561] cancers per 100 000 person years, respectively). Compared to the general population, the standardized incidence ratio of any type of cancer in patients with perianal fistulizing CD was more than 1.5-times higher, which is in line with findings observed in the overall population of patients with CD. Of note, the prevalence of anal and perianal cancer was higher in patients with perianal fistulizing CD (1.3%) compared to non perianal fistulizing CD(0.6%). Some limitations need to be acknowledged. Treatment exposure was only assessed at cohort entry, which could lead to treatment misclassification. Smoking status was not collected and residual confounding could not be excluded. The study was also underpowered to specifically assess risk of incident anal cancer in patients with perianal fistulizing CD. Nevertheless, this study is of great value compared to the available literature, notably by being the first study reporting the overall risk of cancer in patients with perianal fistulizing CD.

Overall, these reassuring data suggest no overall increased risk of cancer in patients with perianal fistulizing CD compared to patients with non perianal fistulizing CD. The risk of perianal cancer remains to be tackled in patients with perianal fistulizing CD. While waiting for the development of dedicated surveillance programs, long lasting anal fistulas especially in case of persistent pain should raise attention and discuss clinical examination with histological samples under general anesthesia.

  ) and has been associated with an increased risk of anal cancer. (3) Despite advances in the therapeutic management, the risk of poor disease course remains substantial. (4) Chronic perianal inflammation plays a key role in carcinogenesis and due to their location, cancers in this setting are rarely diagnosed at an early stage.(5) While immunosuppressive treatments contribute to the increased risk of cancer in patients with IBD, (6) patients with perianal fistulizing CD are more exposed to immunosuppressive treatments and for a longer period of time compared to the overall population of patients with IBD. (7) Finally, the overall risk of cancer in patients with perianal fistulizing CD remained to be elucidated. In the current issue of the United European Gastroenterology Journal, Podmore et al. assessed the risk of cancer in patients with perianal fistulizing CD based on German administrative healthcare databases including 4.8 millions of persons.


Androniki-Anna Doulgeroglou
email: androniki-anna.doulgeroglou@ec-nantes.fr

Panagiotis Kotronis

Giulio Sciarra

Catherine Bouillon

3D interaction diagrams for symmetrically reinforced concrete square sections with various reinforcement ratios

Keywords:

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

Introduction

Interaction diagrams are functions that define the acceptable combinations of generalized forces' components (e.g. moment, shear force and axial force) of a structural member. Of particular interest in Reinforced Concrete (RC) design they are often constructed using limit analysis. To characterize the combination of axial force and bending moment limit states, in the Eurocode [START_REF]Eurocode, Eurocode 2: Design of concrete structures: Part 1-1: General rules and rules for buildings[END_REF] a suitable set of admissible loadings, is identified for a given RC structure and a convex hull of them is constructed adopting the so-called lower bound approach. More specifically, steel is described by an elastic perfectly plastic constitutive law, symmetric in traction and compression, while concrete has zero tension resistance and follows a parabolic curve in compression. A rectangular distribution of the normal stress is assumed, multiplied by a correction factor. Eurocode [START_REF]Eurocode, Eurocode 2: Design of concrete structures: Part 1-1: General rules and rules for buildings[END_REF] provides also interaction diagrams for biaxial bending and axial loading and for shear force and torsion but not for axial force, shear force and bending moment.

In the framework of limit analysis the upper bound approach is also frequently used which provides an upper bound of a combination of the limit loadings, see e.g. [START_REF] Salenc ¸on | Calcul à la rupture et analyse limite[END_REF]. The definition of limit loading in this case is based on a global energetic criterion which compares the power dissipated along a plastic process to the power of external forces. It is typically used introducing kinematically admissible velocity fields exhibiting a jump through the body which is therefore separated into two blocks having a relative motion one with respect to the other. If a kinematic admissible mechanism can be found for which the work of the external loads exceeds the internal work, then the structure collapses and the load computed on the basis of the assumed mechanism is greater than or equal to the true failure load. The limit load is determined by searching for the least upper bound for loads inducing collapse. In literature, this method is used to study failure of beams and plates.

Koechlin [START_REF] Koechlin | Modèle de comportement membrane-flexion et critère de perforation pour l'analyse de structures minces en béton armé sous choc mou[END_REF] introduced a global failure criterion for RC beams considering coupled loading of axial force and bending moment. This criterion was extended to plates by accounting for combination of membrane forces and bending moments.

In a subsequent work, Koechlin [START_REF] Koechlin | Failure criterion for reinforced concrete beams and plates subjected to membrane force, bending and shear[END_REF] derived a failure criterion for beams submitted to a combination of axial force, shear force and bending moment.

It is possible to construct interaction diagrams by numerical methods or combining analytical and numerical methods. Elachachi [START_REF] Elachachi | Sur l'elaboration d'une methode simplifiee d'analyse des structures de genie civil par macro-elements adaptes aux constructions composites et endommageables[END_REF] used a multi-fiber beam finite element model to reproduce the bending moment -axial force interaction diagram for a reinforced concrete structure (for zero shear force) and constructed the moment -shear force diagram for zero axial force.

Vecchio and Collins [START_REF] Vecchio | Predicting the response of reinforced concrete beams subjected to shear using modified compression field theory[END_REF] combined analytical and numerical approaches. The analytical framework is based on the Modified Compression Field Theory (MCFT), formulated for in-plane stress conditions [START_REF] Vecchio | The modified compression-field theory for reinforced concrete elements subjected to shear[END_REF] that relates average stress to average strains in a cracked RC element, satisfying compatibility and equilibrium requirements. The authors present interaction diagrams for shear force and bending mo-ment for different axial loads and interaction diagrams for shear force and axial force.

Rahal [START_REF] Rahal | Shear strength of reinforced concrete: Part 1-membrane elements subjected to pure shear[END_REF] proposed a simplification of the MCFT assuming a parabolic stressstrain relationship for concrete in compression and provided a graphical method to compute the ultimate shear strength of members. In a subsequent work [START_REF] Rahal | Shear strength of reinforced concrete: Part ii-beams subjected to shear, bending moment, and axial load[END_REF], the author extended the method to beams under combined shear, bending and axial load.

Nguyen [START_REF] Nguyen | Development of an enhanced finite element model for reinforced concrete memebers subjected to combined shear-bending-torsion actions[END_REF] constructed interaction diagrams for the following loading combinations: bending moment and torsion, bending moment and shear force, coupled shear force -bending moment -torsion. The author developed a 3D multi-fiber beam element that takes into account warping. The cross-section is divided into three zones (named 1D, 2D and 3D) according to the direction of transversal reinforcement and the stress state.

Carpinteri et al. [START_REF] Carpinteri | Size-scale effects on interaction diagrams for reinforced concrete columns[END_REF] studied the influence of size scale effects on the moment -axial force interaction diagrams using a numerical step-by-step approach based on the integrated Cohesive/Overlapping Crack Model. Constitutive modeling of concrete is different in compression (Overlapping Crack Model with fictitious interpenetration) and tension (Cohesive Crack Model with fictitious crack). Stressdisplacement relationships are adopted for the post-peak behavior to avoid scale dependency.

In the following, we present 3D interactions diagrams for symmetrically reinforced concrete square sections constructed using 3D non-linear finite element calculations without adopting any kinematic assumptions and that take into con-sideration an accurate description of the constitutive modeling of the materials and stress redistributions . The contribution of this work relies on estimating the ultimate resistance of a RC section which is different than the Ultimate Limit State (ULS) found in the design codes. The interaction diagrams are expressed in terms of generalized forces (axial force, bending moment and shear force). Another advantage of the numerical simulations is that access is provided to any intermidiate state of the response during loading and thus they allow to identify two characteristic states: the first characteristic state corresponds to the elastic limit of the reinforcement bars (while concrete exhibits a non-linear behavior) and the second characteristic state to the peak values of the generalized forces generalized displacements curves. The purpose of the identification of these characteristic states is to use them in a future work for the development of a macro-element for reinforced concrete beam and columns, in the light of what has been already done for example for shallow foundations ( [START_REF] Nova | Settlements of shallow foundations on sand[END_REF], [START_REF] Grange | A macro-element to simulate 3d soilstructure interaction considering plasticity and uplift[END_REF], [START_REF] Cremer | Elaboration of a ssi macro-element with uplift of shallow foundation[END_REF]) and piles ( [START_REF] Li | Numerical study of the 3d failure envelope of a single pile in sand[END_REF], [START_REF] Li | A hypoplastic macroelement for single vertical piles in sand subject to three-dimensional loading conditions[END_REF], [START_REF] Li | A hypoplastic macroelement formulation for single batter piles in sand[END_REF]).

The article is structured as follows: section 2 presents the adopted 3D constitutive models for concrete and steel; in section 3 the 3D finite element model is validated with reference to the experimental results of a RC cantilever -type column submitted to complex loading [START_REF] Bousias | Load-path effects in column biaxial bending with axial force[END_REF]. After establishing the criteria for the two characteristic states, numerical interaction envelopes for a specific RC section are derived in section 4 and this procedure is repeated for the construction of numerical interaction envelopes for symmetrically reinforced concrete square sections with different reinforcement ratios in section 5. Analytical convex expressions of these surfaces are finally introduced in section 6 and a comparison with interaction diagrams form the Eurocode [START_REF]Eurocode, Eurocode 2: Design of concrete structures: Part 1-1: General rules and rules for buildings[END_REF] is proposed in section 6.6.

Constitutive models

Concrete

Concrete behavior is described by the 3D constitutive model developed by Faria et al. [START_REF] Faria | A strain-based plastic viscous-damage model for massive concrete structures[END_REF]. The model follows the damage mechanics framework and is coupled with plasticity to consider inelastic permanent strains in compression.

The 3D (effective) stress tensor is defined by:

σ (ε, ε p ) = D 0 : (ε -ε p ) (1)
where D 0 is the fourth-order isotropic linear elastic constitutive matrix, ε is the strain tensor and ε p is the plastic strain tensor. Stress contributions due to tension or compression are expressed by spliting the effective stress tensor into tensile σ + and compressive σcomponents:

σ + = ∑ i ⟨ σi ⟩p i ⊗ p i (2)
σ -= σ -σ + ( 3
)
where σi is the i th principal stress, p i is the unit vector corresponding to the i th principal direction, ⟨•⟩ are the Macaulay brackets and indices (+) and (-) correspond to positive and negative entities.

Even though it does not account for permanent strains during tension, the model is able to reproduce the differences in the behavior in tension and compression using two scalar damage variables which are assumed to correspond to independent processes. Two damage criteria are considered:

τ+ = σ + : D -1 0 : σ + (4) τ-= √ 3 3 KI 1 + 2J 2 (5)
where τ+ and τare the tensile and compressive equivalent stress respectively, The unilateral effect, also known as stiffness recovery, takes place as the load changes sign and results in tensile cracks' closure and gradual compressive stiffness recovery. This model takes into account the unilateral effect in a simplified way (no permanent strains during traction unloading and no progressive stiffness recovery).

I
The evolution laws for the damage variables in tension and in compression are given by:

d + = G + (r + ) = 1 - r + 0 r + e A + (1-r + /r + 0 ) (6)
d -= G -(r -) = 1 - r - 0 r -(1 -A -) -A -e B -(1-r -/r - 0 ) (7)
where r + and r -are the current damage thresholds, r + 0 and r - 0 are the elastic thresholds, A + controls the softening response in tension and A -and B -define the non-linear part of the response in compression.

The plastic strain tensor rate in compression is given by:

ε p = β EH( ḋ-) ⟨ σ : ε⟩ σ : σ D -1 0 : σ (8)
where β ≥ 0 is a material parameter which controls the rate intensity of plastic deformation and H is the Heaviside function. The consideration of plastic strains during compression and of the unilateral effect makes the constitutive law appropriate for cyclic loading.

Mesh objectivity (in tension but not in compression) is taken into account via an energy type approach [START_REF] Hillerborg | Analysis of crack formation and crack growth in concrete by means of fracture mechanics and finite elements[END_REF] that requires that the tension softening branch (parameter A + ) is calibrated according to the tensile fracture energy and a geometrical characteristic length:

A + = G f E l ch ( f + 0 ) 2 - 1 2 -1 ≥ 0 (9)
where G f is the tensile fracture energy, E is the Young's modulus, f + 0 is the tensile elastic limit, l ch is a geometrical characteristic length computed as 3 √ ∆V with ∆V the finite element volume in 3D simulations. Although this approach is not able to regularize the results in the local level, results in terms of forces and displacements are less sensitive to the finite element mesh discretization [START_REF] Bažant | Crack band theory for fracture of concrete[END_REF]. From the latter, it can be seen that the constitutive law reproduces satisfactorily the biaxial strength of concrete and this for all biaxial loading conditions.

Steel

The classical 3D Von Mises elastoplastic law is considered for the reinforcement bars. A linear kinematic hardening is adopted to capture the Bauschinger effect observed during cyclic loading.

Structural model validation: a reinforced concrete column under complex loading

In order to validate the 3D finite element model used in section 4 to construct the interaction diagrams, the reinforced concrete cantilever -type columns, studied experimentally by Bousias et al. [START_REF] Bousias | Load-path effects in column biaxial bending with axial force[END_REF] under various loading combinations, are simulated hereafter. During this campaign the researchers studied the behavior of twelve identical columns under cyclic uniaxial or biaxial flexure with constant or time varying axial load. The only test variable was the load path and the concrete compressive strength.The specimens were similar to those tested by Gutierrez et al. [START_REF] Gutierrez | Experimental studies of loading rate effects on reinforced concrete columns[END_REF]. The geometry of the specimens is represented in Fig. 3. 3D volumetric finite elements are used for the numerical simulations with the code Cast3M [START_REF]Cast3M, Description of the finite element code cast3m[END_REF]. All the components of the reinforced concrete column are discretized; concrete, longitudinal reinforcing steel bars and stirrups. Perfect bonding is assumed between concrete and steel. The finite element mesh of each component is constructed independently. Displacement compatibility of the different components is ensured by forcing every point of the steel mesh to follow a linear combination of the nodal displacements of the concrete mesh. This approach results into an additional structural stiffness, which in our case is proved to be negligible (see Appendix A). A mesh of 10560 3D finite elements is adopted and this choice is explained in further details in Appendix B. he Newton-Raphson algorithm is adopted at the global level for the resolution of the non-linear system of equations. The radial return algorithm and the backward-Euler scheme is used for the integration of the constitutive law.

Test Specimen f ′ c N/(A c f ′ c ) Load Path S6 25
During the experimental campaign, the columns were built in a heavily reinforced foundation base. The numerical model is considered therefore fixed at the bottom. The choice of 3D numerical models for concrete and steels allows considering complex indirect phenomena such as the confinement of concrete inside the stirrups, which leads to an increased concrete strength.

The S6 and S8 tests are simulated hereafter. Loading is applied on the top of the column in two steps; firstly, the axial compressive load is applied as a force of negative sign in the z direction and it is equally distributed to all the nodes of the section at the top. Secondly, the transversal load along x, y is applied as a displacement homogeneous for all the nodes of the section at the top. The loading program of S6 and S8 is presented in Table 1.

The parameters for the concrete constitutive law are listed in Table 2 and Table 3 and for steel in Table 4. Calibration of the non-linear concrete response in compression is achieved by selecting two points of the curve representing the uniaxial response in compression; point 1 (ε c1 ,σ c1 ) and point 2 (ε c2 ,σ c2 ). The selected points vary for every test simulated resulting to different resistances in compression according to the experimental values. The reference stress σ cp and strain ε cp are used for the determination of the material parameter β as shown in Eq. 10 [START_REF] Faria | Avaliac ¸ão do comportamento sísmico de barragens de betão através de um modelo de dano contínuo[END_REF]:

β = (Eε cp -σ cp ) f cu (Eε cp -f c0 )(σ cp + f cu ) (10)
As stated in section 2.1 β is a material parameter which controls the rate intensity of plastic deformation. As the ratio σ cp /ε cp increases, β decreases and the permanent plastic strains during unloading are less important. Conversely, as the ratio σ cp /ε cp decreases, β increases and the permanent plastic strains during unloading are more significant. When β tends to zero the model turns to a purely damage model in compression and the coupling to plasticity vanishes.

Fig. 4 and Fig. 5

Interaction diagrams for a symmetrically RC square section

For the construction of the interaction diagrams the validated numerical model of section 3 is adopted. The column is again considered fixed at the bottom and specific displacement loading combinations, described in section 4.2 are applied on its free top surface. Interaction diagrams are presented for different characteristic states, detailed hereafter.

Characteristic states

The interaction diagrams presented in this article are defined for the following two characteristic states:

• 1 st characteristic state: corresponds to the elastic domain of the reinforcement steel bars (identical in tension and compression) fixed to 460MPa.

• 2 nd characteristic state (termed hereafter 'failure'): corresponds to the peak values of the generalized forces-generalized displacement curves. More specifically, for the combined flexion to tension area, the failure criterion, is given in terms of maximum longitudinal steel strain equal to 7.5%, see also [START_REF]Eurocode, Eurocode 2: Design of concrete structures: Part 1-1: General rules and rules for buildings[END_REF]. For the combined flexion to compression region, failure is reached at the maximum axial force (absolute value). This choice is made because the imposition of a criterion in terms of concrete maximum compression stress leads to very conservative estimations, as the maximum axial force is reached after several material points have attained their ultimate resistance.

The driving idea behind the choice of those two characteristic states is that steel controls the behavior of the reinforced concrete composite section when tension is predominant, while in compression, concrete crushing is considered to limit the buckling risk.

Loading program

The displacement controlled loading program follows the swipe and radial tests commonly used in geotechnical engineering, see for example [START_REF] Faccioli | TRISEE: 3D site effects and soil-52 foundation interaction in earthquake and vibration risk evaluation[END_REF], [START_REF] Grange | A macro-element for a circular foundation to simulate 3d soil-structure interaction[END_REF]. The following loading conditions are applied:

• 1D loading: pure tension and pure compression in order to obtain the uniaxial section resistance (Fig. 6). • 2D loading: combined flexion with axial loading. The procedure is repeated in two ways; for the 2D swipe tests, an axial load is first applied followed by a flexure load (Fig. 7). The same procedure is repeated for different levels of axial loading. The axial load is applied similarly to the case of 1D loading, while the flexural load is applied as a linear distribution of axial displacments, see Fig. 7. For the radial displacemet controlled tests, the axial and flexural loads are applied simultaneously (Fig. 8) by keeping their ratio constant. The procedure is repeated for different ratios. The moment -axial force interaction diagram is obtained by both procedures and the results are compared to verify the influence of the loading path, which is found negligible.

Results

The data obtained by numerical simulations correspond to the points of the elastic domain of the reinforcing steel (Fig. 10) and to the discrete failure points (Fig. 11) respectively. By the application of uniaxial, 2D and 3D loading conditions the moment -axial force -shear force interaction diagrams are produced and correspond to the inner section of the column, at 0.3m from the fixed edge. This section is found to be the most charged, is sufficiently far from the fixed edge (its distance from the fixed edge is greater than the largest cross-sectional dimension, following the Saint-Venant's Principle) and its planeness is verified. Numerical simulations of this member under pure flexion have also shown that after this length (0.3m) the results in terms of moment -curvature are homogeneous for all the sections. It is found that as the reinforcement ratio increases, the failure domain expands, but the form remains similar.

Analytical expressions of the interaction diagrams

Background

Analytical expressions for the interaction diagrams are very useful for the practitioners to efficiently design reinforced concrete sections. For a robust numerical implementation, these functions should be convex. Suryasentana et al. [START_REF] Suryasentana | A systematic framework for formulating convex failure envelopes in multiple loading dimensions[END_REF] proposed a systematic framework employing a restricted set of sum of square convex polynomials for the construction of convex and sufficiently regular functions with the following characteristics: continuity, differentiability with a continuous gradient and Hessian, absence of singularities in the function and in its derivatives and the fact that they always have real values. Odd degree polynomials are excluded because of their lack of convexity.

The coefficients of the analytical expression of the failure envelope are computed through a convex optimization problem which minimizes the objective function:

F = n ∑ i=1 ( f ( Xi data ) -1) 2 (11)
subjected to constraint: Ȳ ⊤ ∇ 2 f ( X) Ȳ is sum of squares for all X, Ȳ ∈ domain of f , which guarantees that the Hessian ∇ 2 f ( X) of f is positive semi-definite. In Eq. 11 Xi data is a vector of a discrete failure loading combination points and n is the number of failure points.

In this work, this procedure is adopted for the identification of the coefficients of the analytical expression and the sum of squares convex optimization problem is solved using YALMIP, a toolbox developed by Lofberg [START_REF] Lofberg | Yalmip: A toolbox for modeling and optimization in matlab[END_REF] in Matlab together with the SeDuMi semi-definite solver [START_REF] Sturm | Using sedumi 1.02, a matlab toolbox for optimization over symmetric cones[END_REF].

Computation of the analytical expression at failure (2 nd characteristic state)

The procedure to compute the analytical expressions of the interaction diagram for the limit loading has as follows:

At first, the data of the numerical simulations (section 5) are enriched in order to be used afterwards as input for the resolution of the sum of squares convex optimization problem. In particular, every set of data of the numerical simulations (for sections M1, M2, M3, M4) are introduced in the following homogeneous polynomial expression of degree 6 (found to provide a good fit) in order to obtain with a non-linear least squares method the coefficients of the polynomial expression for each RC section tested:

f 6 = 6 ∑ i, j,k=0 |i+ j+k|=6 a I(i, j,k) Ni M j V k -1 (12)
This analytical expression, for which the coefficients are calculated, is not guaranteed to be convex. The next step is to use this analytical expression as a tool to obtain further data points, referred as 'interpolated points' from now on.

These interpolated points are used as input for the resolution of the sum of squares convex optimization problem [START_REF] Suryasentana | A systematic framework for formulating convex failure envelopes in multiple loading dimensions[END_REF]. More specifically, the interpolated points are standardized in a way that for uniaxial loading conditions their values are 1 (for the positive loading direction) and -1 (for the negative loading direction).

For every set of data (sections M1, M2, M3, M4) two distinct sum of squares convex failure envelopes of the standardized loading variables of degree 4 and 6 are then selected, for which the coefficients need to be identified (Eq. 13 -Eq. 12).

f 4 = 4 ∑ i, j,k=0 |i+ j+k|=4 a I(i, j,k) Ni M j V k -1 ( 13
)
The coeffcients of all monomials containing a single loading variable are 1 as long as the uniaxial loading conditions are applied.

Finally, the objective function is minimized, subjected to the condition of positive semi-definite Hessian. Thus, the coefficients of all monomials are obtained for every set of data (sections M1, M2, M3, M4). The coefficients of the monomials for all the tested sections are presented in Tables 5-8 for the expression of degree 4 and in Tables 9-12 for the expression of degree 6. It can be clearly seen that the polynomial of degree 6 gives a better approximation of the failure envelope. In particular the sum of squares convex problem is solved for the RC section M3 with an overall precision of 1.1 e-6 for the polynomial of degree 4 and a precision of 9.4 e-10 for the polynomial of degree 6. The correponding figures for the sections M1, M2 and M4 can be found in Appendix C where one can observe that the conclusions are similar. Fig. 16 presents the failure envelope of degree 6 in the 3D space of the RC section M3.

a

Computation of the analytical expression of the domain of elasticity (1st characteristic state)

The procedure to compute the analytical expression of the interaction diagram for the 1 st characteristic state is different than the one of section 6.2. In particular, the interaction diagram for the 1 st characteristic state (Fig. 10) presents similar form to the one for the 2 nd characteristic state (Fig. 11) but the centers of the two surfaces are offset to each other. Thus, the proposed analytical expression for the 1 st characteristic state is the same as Eq. 12 but the standardized variables N, M, V for the 1 st characteristic state is given by Eq. 14 for which the coefficients of all monomials are already calculated and presented in Tables 9-12 for the RC sections M1, M2, M3 and M4. Eurocode without applying the security coefficients is also provided.

f 6 = 6 ∑ i, j,k=0 |i+ j+k|=6 a I(i, j,k) N -N0 N * i M -M0 M * j V -V0 V * k -1 (14)
It can be observed that all surfaces obtained by finite element simulations and by the methodology described in Eurocode present similar forms. Furthermore, as expected, the surface obtained by Eurocode underestimates the points of failure.

More specifically, for the combined flexion to traction area the ultimate longitudinal strain of the steel bars is fixed to 7.5%, as stated before. This criterion allows for obtaining a less conservative interaction diagram, compared to the one provided by the methodology in Eurocode which (i) considers as an ultimate limit the point at which steel reaches its elastic limit in tension and (ii) ignores the tensile strength of concrete. The choice of such a less conservative criterion can be beneficial for applications in civil engineering as it can offer the option of a more economical design of reinforced concrete structures.

For the combined flexion to compression region, the numerically produced surface presents a good fit to the curve obtained by the method of Eurocode without application of security coefficients.

Conclusions

In this article a numerical methodology is presented on the construction of failure envelopes for given symmetrically RC square sections with various reinforcement ratios. Suitable constitutive models are first chosen for the description of the material behavior, both for concrete and steel. The choice of a 3D finite element modeling leads to more precise results as there are no kinematical assumptions as in classical beam finite element calculations. Finally, a methodogy is provided to derive analytical expressions of two characteristics states based on the numerical results.

Further investigating factors, such as steel strength, concrete compressive strength, consideration of non-perfect bonding between concrete and steel, ratio and posi- As stated in section 6.3, polynomial expressions of degree 6 ( f 6 ) give better approximations of the failure envelopes. For the RC section M1, the precision of the resolution of the sum of squares convex optimization problem is 5.9 e-7 for the polynomial of degree 4 ( f 4 ) and 5.1 e-9 for the polynomial of degree 6 ( f 6 ).

  1 and J 2 are the first invariant of the compressive stress tensor and the second invariant of the deviatoric compressive stress tensor respectively and K is a material parameter conceived to fit the ratio of 2D and 1D compressive strengths σ c,2D /σ c,1D in experimentally observed values (1.16-1.2). The model accounts for the increase of concrete strength when biaxial or triaxial compressive loading conditions are considered.

Fig. 1

 1 Fig. 1 depicts the constitutive model during a 1D tension-compression cyclic test, while Fig. 2 the comparison with the biaxial plane stress experiments of [22].

Fig. 1 .

 1 Fig. 1. Cyclic behavior during 1D cyclic test.

Fig. 2 .

 2 Fig. 2. Comparison of the numerical and experimental biaxial strength of concrete normalized by the uniaxial concrete compressive strength f c [22].

Fig. 3 .

 3 Fig. 3. RC columns: geometry, [23].

  and not the cyclic behavior, the level of accuracy, as far as the peak of the response is concerned, is judged satisfactory; the 3D finite element model correctly reproduces the global behavior of the column in terms of forces -displacements and this for all the loading combinations and tests.

(a)Fig. 4 .Fig. 5 .

 45 Fig. 4. Test S6: Numerical vs. experimental results.

Fig. 6 .

 6 Fig. 6. Uniaxial loading.

Fig. 7 .

 7 Fig. 7. 2D swipe test: I: axial loading, II: radial bending loading.

Fig. 8 .

 8 Fig. 8. 2D radial test: coupled bending -axial loading.

Fig. 9 .

 9 Fig. 9. 3D loading: I: axial loading, II: radial bending and shear loading by keeping constant the ratio u bending u transversal

  Fig. 10. 1 st characteristic state ('elastic domain'): Interaction diagram (discrete points) obtained by numerical simulations.

5 .

 5 Fig. 11. 2 nd characteristic state ('failure'): Interaction diagram (discrete points) obtained by numerical simulations.

Fig. 12 .

 12 Fig. 12. 2 nd characteristic state ('failure'): Interaction diagrams (discrete points) for sections with different reinforcement ratios obtained by numerical simulations.

Fig. 13 .

 13 Fig. 13. M3 section: Moment -axial force interaction diagrams obtained by polynomials f 4 , f 6 compared to data by numerical simulations and interpolated points.

Fig. 14 .

 14 Fig. 14. M3 section: Moment -shear force interaction diagrams obtained by polynomials f 4 , f 6 compared to data by numerical simulations and interpolated points.

Fig. 15 .

 15 Fig. 15. M3 section: Axial force -shear force interaction diagrams obtained by polynomials f 4 , f 6 compared to data by numerical simulations and interpolated points.

Fig. 16 .

 16 Fig. 16. Failure envelope in 3D standardized space for the RC section M3.

Fig. 17 .

 17 Fig. 17. M3 section: 1 st and 2 nd characteristic states in 3D standardized space.

Fig. 18 .

 18 Fig. 18. Moment -axial force interaction diagram for M3 RC section. Comparison to the one obtained by the method in Eurocode with and without the appplication of the security coefficients.

  Fig. A.19. Beam mesh.

  Fig. B.21. Coarse mesh.

Fig. B. 23 .

 23 Fig. B.23. Test S1: comparison of the responses of the coarse and fine meshes with the experimental results.

Fig. C. 24 .

 24 Fig. C.24. M1 section: Moment -axial force interaction diagrams obtained by polynomials f 4 , f 6 compared to data by numerical simulations and interpolated points.

Fig. C. 25 .

 25 Fig. C.25. M1 section: Moment -shear force interaction diagrams obtained by polynomials f 4 , f 6 compared to data by numerical simulations and interpolated points.

Fig. C. 26 .

 26 Fig. C.26. M1 section: Axial force -shear force interaction diagrams obtained by polynomials f 4 , f 6 compared to data by numerical simulations and interpolated points.

Fig. C. 27 .

 27 Fig. C.27. M2 section: Moment -axial force interaction diagrams obtained by polynomials f 4 , f 6 compared to data by numerical simulations and interpolated points.

Fig. C. 28 .

 28 Fig. C.28. M2 section: Moment -shear force interaction diagrams obtained by polynomials f 4 , f 6 compared to data by numerical simulations and interpolated points.

Fig. C. 29 .

 29 Fig. C.29. M2 section: Axial force -shear force interaction diagrams obtained by polynomials f 4 , f 6 compared to data by numerical simulations and interpolated points.

Fig. C. 30 .

 30 Fig. C.30. M4 section: Moment -axial force interaction diagrams obtained by polynomials f 4 , f 6 compared to data by numerical simulations and interpolated points.

Fig

  Fig. C.31. M4 section: Moment -shear force interaction diagrams obtained by polynomials f 4 , f 6 compared to data by numerical simulations and interpolated points.

Fig

  Fig. C.32. M4 section: Axial force -shear force interaction diagrams obtained by polynomials f 4 , f 6 compared to data by numerical simulations and interpolated points.

Fig. D. 34 .

 34 Fig. D.34. M2 section: 1 st and 2 nd characteristic states in 3D standardized space.

Fig. E. 37 .

 37 Fig. E.37. Moment -axial force interaction diagram for M2 RC section. Comparison to the one obtained by the method in Eurocode with and without the appplication of the security coefficients.

Fig. E. 38 .

 38 Fig. E.38. Moment -axial force interaction diagram for M4 RC section. Comparison to the one obtained by the method in Eurocode with and without the appplication of the security coefficients.

Table 1 .

 1 RC columns: test specimens, compressive strength, applied axial load and transversal load (schematically).

		.7	0.10
	S8	25.4	0.11

Table 2 .

 2 RC columns: parameters for concrete (constant for all the tests).

	Bousias et al.(1995). The obtained prediction accuracy can be certainly improved
	using a more advance 3D constitutive model istead of the classical 3D Von Mises
	constitutive model with linear kinematic hardening. The purpose of the work be-
	ing however the numerical computation of 3D interaction diagrams up to failure

present the numerical simulation results of the S6 and S8 tests. After concrete cracking and during alternate loads, the global response is mainly controlled by the reinforcement steel bars. The parameters for the steel constitutive law have been taken as reported in the experimental campaign of

Table 3 .

 3 RC columns: parameters for concrete (varying for each test).

	Parameter	Description	SI Unit Value
	E a	Young Modulus	GPa	180
	ν a	Poisson's ratio	-	0.3
	f y	Elastic stress limit	MPa	460
	H a	Kinematic hardening modulus	GPa	2.3

Table 4 .

 4 RC columns: parameters for steel.

Table 5 .

 5 M1 section: Coefficients of monomials for the failure envelope expression of degree 4.

	1	a 2	a 3	a 4	a 5
	1	0	5.7	0.01	1
	a 6	a 7	a 8	a 9	a 10
	0.01 -4.18 -0.01 -2.34 3.24
	a 11	a 12	a 13	a 14	a 15
	0.02 4.71 -0.01 -3.49	1
	a 1	a 2	a 3	a 4	a 5
	1	0	5.87	0	1
	a 6	a 7	a 8	a 9 a 10
	0.01 -5.26 -0.01 2.36 3.9
	a 11	a 12	a 13	a 14 a 15
	0.02 4.81 -0.02 -3.5	1

Table 6 .

 6 M2 section: Coefficients of monomials for the failure envelope expression of degree 4.

	a 1	a 2	a 3	a 4	a 5
	1	0	5.58 0.01	1
	a 6	a 7	a 8	a 9	a 10
	-0.01 -2.67 -0.03 -2.19 1.23
	a 11	a 12	a 13	a 14	a 15
	0.04 4.76 -0.01 -3.45	1

Table 7 .

 7 M3 section: Coefficients of monomials for the failure envelope expression of degree 4.

	a 1	a 2	a 3	a 4	a 5
	1	-0.01 5.88 0.02	1
	a 6	a 7	a 8	a 9	a 10
	0.01 -3.59 -0.06 -1.8 3.18
	a 11	a 12	a 13	a 14	a 15
	0.05 4.25 -0.03 -3.28	1

Table 8 .

 8 M4 section: Coefficients of monomials for the failure envelope expression of degree 4.

	a 1	a 2	a 3	a 4	a 5	a 6	a 7
	1	0	13.22 0.05 10.07 0.02	1
	a 8	a 9	a 10	a 11	a 12	a 13	a 14
	0.01	-9.44 -0.04 -10.43 -0.04 -3.39 6.79
	a 15	a 16	a 17	a 18	a 19	a 20	a 21
	-0.04 25.72 0.08 10.89 0.01 -17.33 -0.11
	a 22	a 23	a 24	a 25	a 26	a 27	a 28
	-15.40 4.56 0.07 12.65 -0.02	-5.5	1

Table 9 .

 9 M1 section: Coefficients of monomials for the failure envelope expression of degree 6.

	a 1	a 2	a 3	a 4	a 5	a 6	a 7
	1	0	14.03 0.03 12.26 0.02	1
	a 8	a 9	a 10	a 11	a 12	a 13	a 14
	0.01 -12.73	0	-17.97 -0.06 -3.34 8.29
	a 15	a 16	a 17	a 18	a 19	a 20	a 21
	-0.05 35.83 0.13 11.09	0	-22.46 -0.18
	a 22	a 23	a 24	a 25	a 26	a 27	a 28
	15.42 5.56	0.1	12.69 -0.02 -5.51	1

Table 10 .

 10 M2 section: Coefficients of monomials for the failure envelope expression of degree 6.

	a 1	a 2	a 3	a 4	a 5	a 6	a 7
	1	0.02 12.56 0.02 9.41 0.02	1
	a 8	a 9	a 10	a 11	a 12	a 13	a 14
	-0.02 -9.38 -0.01 -6.44 -0.06 -3.27 5.34
	a 15	a 16	a 17	a 18	a 19	a 20	a 21
	-0.03 10.68 0.09 11.17	0	-4.31 -0.11
	a 22	a 23	a 24	a 25	a 26	a 27	a 28
	-15.26 0.48 0.06 12.56 -0.01 -5.44	1

Table 11 .

 11 M3 section: Coefficients of monomials for the failure envelope expression of degree 6.In order to choose the analytical expression of the failure envelope for a given reinforced concrete section, in the following Figs. 13, 14, 15 we present 2D sections of the failure envelope in the moment -axial force, shear force -moment and shear force -axial force planes, together with the data obtained by the numerical simulations and the interpolated data for the RC section M3.

	6.3 Comparison of different analytical expressions at failure (2 nd characteristic
	state)

Table 12 .

 12 M4 section: Coefficients of monomials for the failure envelope expression of degree 6.

Table B .

 B [START_REF] Cremer | Elaboration of a ssi macro-element with uplift of shallow foundation[END_REF]. Test specimen S1, compressive strength, applied axial load and transversal load (schematically).

	Parameter	σ c1	σ c2
	Description Stress of point 1 Stress of point 2
	SI Unit	MPa	MPa
	S1	-25.4	-24.4

therefore conducted with the coarse mesh. Table B.15. RC columns: parameters for concrete (varying for each test).

Acknowledgments

The authors would like to gratefully acknowledge Dr Stephen Suryasentana for his contribution to the computation of the analytical expression of the failure envelope, by providing a code example of the application of the methodology described in [28]. The authors would also like to thank Pr Stathis Bousias from the University of Patras (Greece) for providing the experimental results of the reinforced concrete column. The first author would like to acknowledge the financial support of Groupe Essor for funding her Cifre PhD.

Each set of data points that correspond to the 1 st characteristic state (Fig. 10) are subsequenlty introduced in Eq. 14. The center ( N0 , M0 , V0 ) and the radii ( N * , M * , V * ) of the ellipsoid corresponding to the 1 st characteristic state are calculated by the resolution of a non-linear least squares optimization problem. The obtained values for the RC sections M1, M2, M3 and M4 are presented in Table 13. Fig. 17 presents both characteristic states of degree 6 in the 3D space for the RC section 6.5 Summary of the steps for the calculation of the analytical expressions of the two characteristic states

The general procedure for the derivation of the analytical expressions of the two characteristic states is briefly summarized in th following steps:

• enrichment of the data points of the 2 nd characteristic state from the numerical simulations

• standardization of the enriched data points of the 2 nd characteristic state tion of the longitudinal and transversal reinforcement, section geometry and shape should be examined in order to provide more complete research results. The 3D calculations being however extremely costly, as more than 1428000 core hours of computational time were necessary to obtain the presented interaction diagrams (the calculations took place using the supercomputer Liger of the Centrale Nantes SuperComputing Center. Liger is a BULL/Atos DLC720 cluster of 252 compute nodes and 14 visualization nodes with 24 cores per node and a total compute memory of 36608GB.), this can be the scope of future work.

Appendix A. About the additional stiffness

The chosen mesh discretization results to an additional stiffness. To verify the influence of this additional stiffness on the global response, two finite element models are built for a comparative study of a reinforced concrete beam under the first type of modeling (AS) on the global response of the beam can be ignored.

Appendix B. Comparison of different meshes

In order to optimize computational time, a comparison between the numerical results obtained with different mesh refinements with reference to the experimental data is shown hereafter (S1 test). The loading program of S1 is presented in Table B.14. The parameters for the concrete constitutive law are listed in Table 2 and Table B.15 and for steel in Table 4. Two meshes of 10560 (Fig