Lucas Deniel

Mathilde Gay

Diego Perez-Galacho

Charles Baudot

Laurent Bramerie

Oskars Ozolins

Frédéric Boeuf

Laurent Vivien

Christophe Peucheret

Delphine Marris-Morini

D Pérez-Galacho

Generation of O-band PAM-4 signal using a silicon modulator driven by two binary sequences

Keywords: PAM-4, silicon photonics, modulator, Mach Zehnder modulator, O-band

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

INTRODUCTION

On-off keying (OOK) modulation format may no longer keep up with the increasing spectral efficiency requirements for 400Gb/s intensity modulation / direct detection (IM-DD) intra-datacenter short-reach transmissions. Therefore, 4-level pulse amplitude modulation (PAM-4) format is considered as an interesting choice for this standard [START_REF]GbE Task Force[END_REF]. Among the different modulator technologies, silicon photonics present the benefit of allowing small footprints, high flexibility, low energy consumption, compatibility with the complementary metal oxide semiconductor (CMOS) fabrication process, and possibility of integration with electronics.

For these reasons many silicon modulator structures based on free-carrier plasma dispersion effect have been studied and compared over the past few years [START_REF] Shi | Silicon photonic modulators for PAM transmissions[END_REF]. Modulators are key elements to reduce the power consumption of a transmission link, but with PAM-4 modulation, the electrical driving scheme contains itself power hungry devices such as digital to analog converters (DACs), which are used to convert 2-level non-return-to-zero (NRZ) sequences into 4-level ones. Several dual-embedded structures based on ring modulators (RM), Mach Zehnder modulators (MZM) or segmented electrodes modulators have been investigated to optically generate a 4-level signal relieving the need for an electrical DAC [START_REF] Moazeni | A 40-Gb/s PAM-4 transmitter based on a ring-resonator optical DAC in 45-nm SOI CMOS[END_REF][START_REF] Samani | A silicon photonic PAM-4 modulator based on dual-parallel Mach-Zehnder interferometers[END_REF][START_REF] Dubray | 30Gbit/s PAM-4 transmission by modulating a dual silicon ring resonator modulator[END_REF]. They rely on the principle that it is possible to drive each of the two structure parts directly with a different NRZ electrical signal and combining these signals in the optical domain to obtain 4 distinct intensity levels. Most of the demonstrations were performed in the C-band. Among all of these structures, L. Zheng et al. showed that it is possible to use a dual-drive MZM to obtain PAM-4 levels out of two binary electrical signals of different peak-to-peak voltages, by applying each signal on a different arm of the MZM [START_REF] Zheng | Silicon PAM-4 optical modulator driven by two binary electrical signals with different peak-to-peak voltages[END_REF]. Interestingly, this simple and generic dual-drive MZM is one of the most flexible as it not only allows to generate intensity modulation formats but also phase modulation formats, simply by driving it in a proper way [START_REF] Perez-Galacho | QPSK modulation in the O-band using a single dual-drive Mach-Zehnder silicon modulator[END_REF]. However, it is not straightforward to find out the peak-to-peak voltage values to apply on each arm of the modulator in order to reach 4 equally spaced levels while benefiting from the full dynamic range. We thus developed and used a model for this purpose. After introducing the MZM design and characterization (static and dynamic), we focus on PAM-4 generation. We compare the model we developed for PAM-4 generation, based on realistic the phase shifter performances, i.e. effective index and absorption coefficient variations in the phase shifters with respect to the applied voltages, to a simple ideal and lossless MZM model. Then, we demonstrate 20Gb/s PAM-4 generation using the silicon MZM. This work is the first report of PAM-4 generation in the O-band based on a simple dual-drive silicon MZM. A schematic top view of the MZM structure can be seen in Fig. 1(a). A 3 dB 1×2 multimode interference (MMI) coupler splits the light from an input waveguide into two arms of same lengths containing phase shifters, and another 3 dB 1×2 MMI coupler combines the light from both arms into the output waveguide. Grating couplers are used for fiber-to-chip transitions. The cross-section of a phase shifter is shown on Fig. 1(b). The phase shifter is 1mm long, the waveguide height is 300 nm and its width is 400 nm while the rib part thickness is 50 nm. As the modulator is designed to operate in the depletion regime, a PN junction is realized, the P region is doped with a 5×10 17 cm -3 targeted Bore concentration and the N region is doped with a 4.5×10 17 cm -3 targeted Phosphorus concentration. It can be seen that the junction between P and N regions is shifted by 25nm apart from the waveguide center towards the N-doped region, improving the overlap between the P-doped area and the optical TE fundamental mode-profile, which leads to a more efficient phase shifter. Higher P ++ and N ++ doping concentrations of 10 19 cm -3 are used close to the electrical contacts to reduce the access resistance of the phase shifters, increasing the modulator bandwidth. The coplanar-waveguide (CPW) electrodes are ended with pads which allow them to be accessed with GSGSG probes. On each arm, metallic strips close to a passive part of the waveguides are used as resistors (heaters) to thermally tune the operating point of the MZM under the application of a DC voltage. The MZM was fabricated at ST-Microelectronics on a 300 mm SOI technological platform [START_REF] Baudot | Daphne silicon photonics technological platform for research and development on WDM applications[END_REF].

MODULATOR DESIGN AND CHARACTERIZATION.

Static characterization and loss modeling

To measure the phase shifter efficiency, ring resonators have been fabricated on the same photonic circuits. Indeed, by tracking the resonant wavelength shifts with the applied voltage, it is possible to deduce the effective index variation of the optical mode. An 80-µm radius ring resonator is used to this end. The PN junction is embedded in the ring, covering 87% of its perimeter. By measuring the resonance wavelength shift of the resonator for different applied DC voltage on the phase shifter, it is possible to calculate the corresponding change in effective refractive index of the optical mode and thus the efficiency (V×L product) of the phase shifter as a function of the applied reverse voltage. A 3.3×10 -4 change in effective index is measured between 0 V and 7 V (Fig. 2), corresponding to an efficiency of 1.13 V×cm around 0.5 V and 1.41 V×cm around 7V. Free carrier concentration variations are responsible for effective index variations but also absorption coefficient variations. A numerical model is used to evaluate the optical mode propagation losses. The free carrier concentrations within the phase shifter are given by a 1D electrical stimulation as a function of the applied reverse voltage. Absorption coefficients are then calculated from these carrier concentrations using Soref equations. Finally, a mode solver allows to estimate the resulting effective attenuation factor of the waveguide. From Fig. 3, we can see that these losses are estimated to be 1.8 dB×mm -1 at 0V and 1.14 dB×mm -1 at 7 V.

Figure 3. Optical losses in the phase shifter as a function of the DC applied reverse voltage, according to a simulation based on free carrier concentration variations.

Bandwidth characterization

An electro-optical bandwidth measurement is performed using Agilent 86030A 50GHz Lightwave Component Analyzer. For this measurement, the PN junction is biased under -4 V, and a 50 Ω termination is loaded at the end the RF line to avoid reflections. The normalized spectrum (Fig. 4) shows a 17 GHz bandwidth.

PAM-4 MODEL

When two binary electrical signals with different amplitudes are applied on both arms of the MZM, 4 levels of transmissions can be reached, as described in [START_REF] Zheng | Silicon PAM-4 optical modulator driven by two binary electrical signals with different peak-to-peak voltages[END_REF]. To obtain the lowest bit error rate, the levels should be equally spaced, and the extinction ratio must be maximized to work with the best signal-to-noise ratio. This section will introduce and compare two different models for finding out which peak-to-peak voltages to apply on each arm in order to respect the two aforementioned conditions. The first model is based on a simplified ideal MZM, while the second one is more realistic and takes account of the phase shifters behavior described in section 2.2. Finally, these models are compared to each-other.

Simplified model of an ideal dual-drive MZM

In the ideal case of a linear variation of the effective index with the voltage, and loss-less phase shifters, the transfer function of a MZM can be expressed as:

1 1 cos 2 OUT H IN I V I V         = + +           (1)
Where IOUT is the output optical intensity, IIN is the input optical intensity, V is the difference between the voltages applied on the two phase shifters, V is the voltage required on one phase shifter to obtain a  phase difference between the electric fields at the end of each arm, and H is the static phase difference set by tuning the DC voltage applied on heaters. The voltage differences between the two phase shifters in order to get specific transmission levels can then be found by reversing the above equation and solving it for each desired transmission levels. In the case of 4 equally spaced levels with a maximum transmission of 1 and a minimum of 0, the peak-to-peak voltages to apply on the first arm (VPP1) and on the second arm (VPP2) of a quadrature-biased MZM can be expressed in a simple way:

1 2 1 1 arcsin 2 3 PP V V       = -         (2) 1 PP PP V V V  =- (3)
According to Fig 2, the mean V L is 1.36 V. Considering a static phase imbalance of H=/2, assuming the phase shifters lengths are 1mm and that they are both biased at -4 V, the optimized peak-to-peak voltages given by this ideal MZM model are VPP1 = 8.3 V and VPP2 = 5.34 V.

Realistic model of the silicon dual-drive MZM

It was shown in section 2 that for the silicon MZM, the effective index variation in the phase shifters are not linear with the applied voltage, and their loss depends on the applied voltage. Therefore, the output electric field must be written as: with En being the electric field at the output of phase shifter n, such that:

( ) ( ) ( ) IN 2 exp ( ) exp j ( ) 2 n eff eff n eff eff n E E V L n n V L      = - +  +      ( 5
)
Where EIN is the electric field at the input of the MZM, L the length of the phase shifter, Vn the voltage applied on the phase shifter n,  the laser wavelength, eff the effective attenuation factor of the phase shifters, eff the effective attenuation variation introduced by the application of the voltage Vn on the phase shifter n, neff the effective index of the phase shifters, neff the effective index variation introduced by the application of the voltage Vn on the phase shifter n.

Equation 4 and 5 can be used to determine numerically the optimized peak-to-peak voltages to apply on each phase shifter in order to reach 4 equally-spaced levels while benefiting from the full dynamic range of the transfer function.

The static characteristics reported in section 2.2 are used (effective index variation and absorption coefficient as a function of the applied voltage). From the calculation the following optimized peak-to-peak voltages are obtained: VPP1 = 8 V and VPP1 = 4.72 V.

Model comparison

Fig. 5 shows the obtained transmission levels on the silicon MZM model, by applying peak-to-peak voltages given by (a) the ideal MZM model, and (b) the silicon MZM model. The black curves represent the push-pull transmission of the MZM (opposite voltages are applied on the arms), and the red lines represent the reached PAM-4 levels for given peakto-peak voltages VPP1 and VPP2. As it can be seen from this figure, neglecting the losses and non-linearities of the phase shifters gives rise to inequalities between levels spacing: with the voltages given by the simplified ideal model, the middle level is only 29.5% of the full dynamic range, while both external spacings are 35%. With the realistic model voltages, all the spacings are close to 33.3%.

PAM-4 BER MEASUREMENTS

The experimental setup consists in two parts. For the optical part, an O-band external cavity laser emits light at 1.31µm wavelength, the beam is then amplified through a semiconductor optical amplifier (SOA) before being coupled in and out of the chip (coupling losses are about 5dB per grating coupler). At the receiver side, light is amplified with a praseodymium amplifier and split by a 3 dB directional coupler, one half of the power feeds a 40GHz photodiode followed by a 35GHz travelling wave amplifier and the resulting signal is sent to the error counter of a BER tester, while For this experiment, the power received on the photodiode is swept from -8.5 dBm to 0.5 dBm. The peak-to-peak voltages are set to 7 V on the first arm and 4V on the second one to almost use the full dynamic range and obtain equally-spaced levels. The resulting BER curve is plotted in Fig. 6. It can be seen from Fig. 6(b) that the link BER is under the hard-decision forward error correction (HD-FEC) threshold of 3.8×10 -3 for a received power of -6dBm, under the KP4-FEC threshold of 2.2×10 -4 for a received power of -3.4dBm and reaches a value as low as 1.54×10 -6 for a received power of 0.5dBm. The transitions in the eye diagram (Fig. 6(a)) suggests that these results could be further improved by increasing the MZM bandwidth.

CONCLUSION

To fulfill the increasing spectral efficiency requirements in intra-datacenter data-communications, IM-DD PAM-4 modulation format is considered as an interesting choice, and silicon photonics is a well-suited technology. It is possible to use a simple and flexible silicon MZM structure to optically generate four intensity levels out of two binary NRZ electrical signals with different amplitudes, removing the need for power hungry DACs within the electrical driving systems. However, this PAM-4 generation method requires conveniently tuned driving voltage amplitudes.

After introducing an O-band silicon MZM, a realistic model for the MZM transmission was presented, taking account of the phase shifters static properties. This model was compared to a simpler one based on an ideal lossless MZM and a significant difference was highlighted between the two. At last, a demonstration of a 20Gb/s O-band PAM-4 transmission was performed, with a measured BER under the HD-FEC threshold of 3.8×10 -3 for a received power of -6dBm and reaching a value as low as 1.54×10 -6 for a received power of 0.5dBm.

2. 1

 1 Figure 1. (a) Schematic top view of the dual-drive MZM, each phase shifter can be driven independently through coplanar travelling-wave electrodes, and thermal heaters controlled with a DC voltage can be used to tune the operating point. (b) Schematic cross section of one phase shifter, the carrier depletion regime in the PN junction is used to achieve phase modulation along the rib waveguide.

Figure 2 .

 2 Figure 2. (a) Experimental change in the effective refractive index of the mode as a function of the DC applied reverse voltage on the phase shifter. (b) Corresponding change in the VL efficiency product as a function of the DC applied reverse voltage on the phase shifter.

Figure 4 .

 4 Figure 4. Normalized Electro-Optical transmission spectrum of the MZM (S21), the measured bandwidth is 17 GHz (3dB-bandwidth in the optical domain).

Figure 5 .

 5 Figure 5. PAM-4 transmission levels resulting from the application on the realistic silicon MZM model of peak-to-peak voltages given by (a) the ideal lossless MZM model (8.3V on one arm and 5.34V on the other) and (b) the realistic silicon MZM model (8V on one arm and 4.72V on the other).

  the other half is sent to a 25 GHz real time oscilloscope displaying the eye diagram in real time. For the electrical part, two complementary 10 Gb/s 2 15 -1 pseudo-random binary sequences are first generated, one of them is delayed by 200 ps thanks to an RF delay line. Both signals are then amplified by means of tunable gain RF amplifiers and a 4 V reverse DC voltage is added on each line with bias tees to bias the PN-junction. At the output, both lines are terminated with 50 Ω loads after DC blocks. The gain of the RF amplifiers is used to tune independently the peak-to-peak voltages applied on each arm of the MZM.

Figure 6 .

 6 Figure 6. (a) 20 Gb/s PAM-4 opened eye diagram at 0 dBm received power. (b) 20Gb/s PAM-4 BER against received power. The silicon MZM is driven with VPP1=7V and VPP2=4V in both figures.

ACKNOWLEDGMENT

This work was supported by the European project Cosmicc (H2020-ICT-27-2015-688516).


Antonio R Hidalgo-Muñoz

Christophe Jallais

Myriam Evennou

Daniel Ndiaye

Fabien Moreau

Maud Ranchet

Romain Derollepot

Alexandra Fort

Hemodynamic responses to visual cues during attentive listening in autonomous versus manual simulated driving: A pilot study

Keywords: attention, auditory stimuli, distraction, driving simulator, fNIRS

Emerging automation technologies could have a strong impact on the allocation of drivers' attentional resources. The first objective of this pilot study is to investigate the hemodynamic responses evoked to relevant visual stimuli in manual and autonomous driving.

The second aim is to examine how the inclusion of a secondary task (attentive listening to a broadcast) modulates these hemodynamic responses in both driving situations. Frontal, temporo-parietal and occipital activations were recorded using a functional Near-InfraRed Spectroscopy (fNIRS) system. Event-related analysis was used to determine whether visual cue processing (specifically, the lighting of a lead vehicle's brake-lights) could induce different brain responses depending on the driving mode and on the presence or absence of a competing task. Mind-wandering as reported by the participants was more pronounced during autonomous compared to manual driving. Our results showed an increase in the OxyHb concentration in the right temporo-parietal and occipital areas during manual compared to autonomous driving, suggesting greater allocation of attentional resources for processing visual cues in the first condition. Finally, an event-related decrease in right frontal activity during autonomous driving when listening was observed, suggesting that attentional resources were more focused on the secondary task than on monitoring the driving scene.

Introduction

Manual driving is a demanding cognitive and physical task, the performance of which could be affected by distraction and inattention [START_REF] Fort | Attentional demand and processing of relevant visual information during simulated driving: A MEG study[END_REF][START_REF] Lemercier | Inattention behind the wheel: How factual internal thoughts impact attentional control while driving[END_REF]. Driver distraction can be caused by everyday, concurrent tasks involving interactions with an object [START_REF] Caird | Does talking on a cell phone, with a passenger, or dialing affect driving performance? An updated systematic review and meta-analysis of experimental studies[END_REF] or by external stimuli unrelated to the driving context. Concerning inattention, it can be defined as a decrease in attentional resources allocated to driving because of thoughts unrelated to the driving task, either voluntary thoughts directed towards a goal (e.g., problem solving), ruminations (Jallais, Gaubaude and Paire-Ficout, 2014) or mindwandering [START_REF] Smallwood | The Science of Mind Wandering: Empirically Navigating the Stream of Consciousness[END_REF][START_REF] Baldwin | Detecting and quantifying mind wandering during simulated driving[END_REF].

New automation technologies and advanced driver-assistance systems in cars can facilitate distraction and inattention. As they carry out several tasks, such as speed regulation or collision risk warning, these systems may change the division of attentional resources by reducing the attentional demand of the driving task and thus increasing the driver's proneness to distraction [START_REF] Xu | Functional connectivity analysis of distracted drivers based on the wavelet phase coherence of functional near-infrared spectroscopy signals[END_REF] or inattention. Given the safety consequences of distraction and inattention in both manual (see Galéra et al. 2012) and autonomous driving, when the driver is expected to take over (see [START_REF] Navarro | Neuroergonomics of Car Driving: A Critical Meta-Analysis of Neuroimaging Data on the Human Brain behind the Wheel[END_REF], it is crucial to understand how distraction may affect information processing in both conditions. To be able to assess how distraction and inattention can modulate information processing during autonomous driving, that is when no driving performance is required, the use of neuroimaging techniques is of great interest.

As the driving task involves a large range of perceptual and cognitive processes (e.g., perception, selection, anticipation, planning, decision-making and motor coordination), this activity recruits a large cerebral network. In a meta-analysis of functional magnetic resonance imaging (fMRI) studies, [START_REF] Navarro | Neuroergonomics of Car Driving: A Critical Meta-Analysis of Neuroimaging Data on the Human Brain behind the Wheel[END_REF] identified what they call a "common cardriving circuit" composed of the cerebellum (motor coordination), the bilateral extra-striate cortex (visual selective attention and visual processing), the right middle temporal gyrus (visual motion processing), the precuneus (visuospatial information processing), the left anterior part of the insula (high level cognitive control and attentional processes), the right posterior cingulate gyrus (topographical memory), the right dorsomedial part of the thalamus (corticocortical interactions) and motor areas.

Distraction and inattention have been examined using neuroimaging techniques. [START_REF] Allen | The balanced mind: the variability of task-unrelated thoughts predicts error-monitoring[END_REF], using blood-oxygen-level-dependent (BOLD) activity, found that medial prefrontal cortex (mPFC) activity increased when thoughts unrelated to the task increased, whilst dorsal region activity decreased when the individual engaged with the task. In the driving context, [START_REF] Just | A decrease in brain activation associated with driving when listening to someone speak[END_REF] showed, also using fMRI, that listening to statements and judging their veracity decreases activity in a parietal lobe region involved in spatial processing compared to a driving without listening to the statements. Similarly, using magnetoencephalography (MEG), Fort el al., (2010) examined how a distractive listening task affects neuronal processing of driving-relevant visual information (traffic light or direction). They observed that divided attention entails a reduction in top-down attention for visual processing. This reduction results in decreased activity in the dorso-lateral prefrontal cortex linked to selection and top-down attention [START_REF] Corbetta | Control of goal-directed and stimulus-driven attention in the brain[END_REF] and in the occipital areas linked to perceptual processing. In addition, these authors observed an increase in activity in the posterior parietal region involved in attentional shifting [START_REF] Vandenberghe | Functional specificity of superior parietal mediation of spatial shifting[END_REF]. Despite their interest, both techniques (fMRI and MEG) require that participants keep head movements to a minimum. Moreover, fMRI requires participants to lie down. These constraints limit immersion in simulated driving.

The recent deployment of functional near infrared spectroscopy (fNIRS) offers a new possibility for investigating brain responses in more naturalistic settings such as driving [START_REF] Unni | Assessing the driver's current level of working memory load with high-density functional near-infrared spectroscopy: a realistic driving simulator study[END_REF]. However, few studies have compared cognitive workload during manual and autonomous driving using fNIRS. [START_REF] Sibi | Monitoring driver cognitive load using functional near infrared spectroscopy in partially autonomous cars[END_REF] aimed to determine the cognitive workload variation in drivers utilizing vehicles with different levels of automation. They found that autonomous driving decreases frontal activation compared to manual driving, suggesting a lower cognitive load during autonomous driving. This reduced load is a concern as it has been suggested that intermediate levels of automation that require unexpected take-over can unsettle drivers if they are not ready to resume control [START_REF] Arakawa | Psychophysical assessment of a driver's mental state in autonomous vehicles[END_REF].

Although the purpose of the studies on the topics mentioned above was to evaluate brain activation while driving and executing secondary tasks, the event-related paradigm to investigate hemodynamic responses to visual cues has been scarcely considered. On the other hand, the influence of attentive listening as a distractive task in manual and autonomous driving has not been studied yet. Most studies using fNIRS whilst driving investigated the prefrontal cortex (Liu et al., 2016) even though driving involves a large neural network as reported above. Therefore, the objective of this study is twofold. The first aim is to investigate the hemodynamic responses evoked to relevant visual stimuli in manual and autonomous driving. The second aim is to examine how the inclusion of a secondary task (attentive listening to a broadcast) modulates these hemodynamic responses in both driving situations.

It is hypothesized that autonomous driving allows greater mind-wandering than manual driving, which is more attentionally demanding. Thus, mind-wandering should decrease the available attentional resources to process visual cues during autonomous driving compared to manual driving. When performing a secondary task during autonomous driving, although mind-wandering should decrease, the attention would be oriented to this secondary task (distractive task) and contribute to decreasing the attentional resources to process visual cues. Hence, a difference between mind-wandering and conducting a secondary task during autonomous driving should be reflected in increased activity in the brain areas underlying processing of the secondary task and decreased evoked response amplitude in the prefrontal cortex [START_REF] Fort | Attentional demand and processing of relevant visual information during simulated driving: A MEG study[END_REF][START_REF] Allen | The balanced mind: the variability of task-unrelated thoughts predicts error-monitoring[END_REF].

To test these hypotheses, we designed an experiment using a car simulator while recording event-related hemodynamic activity using fNIRS. Since frontal, temporo-parietal and occipital areas are recruited during the driving task and for multitasking, cortical activity was measured in these regions.

Materials and method

Participants

A total of 12 healthy, French-speaking volunteers 20 -43 years of age (mean = 29.3 ± 7.6, 6 males, one left-handed) from The French Institute of Science and Technology for Transport, Development and Networks (IFSTTAR) were recruited for the experiment. All participants had normal auditory acuity, normal or corrected-to-normal vision and no history of a neurological or psychological disorder (according to self-report). A valid driving license for at least 3 years was required (10.8 ± 8 years). This study was approved by the French ethical committee (Comité de protection des personnes Sud-Est1, reference number: 2018-A01202-53). All subjects gave written informed consent in accordance with the Declaration of Helsinki.

Simulation and driving tasks

The driving simulator was equipped with a steering wheel, a turning indicator, an accelerator and a brake pedal. An interactive visual scene of a suburban driving environment was projected onto three screens covering an angle of 150°. Participants were comfortably seated in a car seat approximately 80 cm from the central screen (24") and asked to avoid abrupt head movements. Two different driving activities were required:

-For the manual driving sessions, the participant was instructed to drive in a suburban environment and follow a car that joined the lane. There were no oncoming vehicles, and overtaking was not allowed. The participant had to try and keep a speed of 70 km/h and brake when they saw brake lights from the car in front. The scenario finished with an oral message to park. -For the autonomous driving sessions, the participant was asked to start driving the vehicle and delegate control to the autonomous system by taking their hands off the steering wheel and their feet off the pedals as soon as a sound alert was emitted to trigger autonomous driving. During autonomous driving, the vehicle drove automatically, and the participant was asked only to pay attention to the driving environment and the brake lights from the lead car. No driving action from the participant was needed for autonomous driving. The vehicle drove and braked in an autonomous way, uninterrupted. The scenario finished with an oral message to park manually.

Auditory stimuli

The auditory stimuli consisted of 8 radio broadcasts 2 minutes in length extracted from the Internet (creative commons license) that dealt with different topics, such as history, literature and science. In each broadcast, a main narrator (gender parity among the broadcasts) talks about a particular topic in an informal style. The emotional content of the stimulus was assessed by an adaptation of the Geneva Emotion Wheel [START_REF] Scherer | What are emotions? And how can they be measured?[END_REF], where the intensity of different feelings (happiness, energy, serenity, compassion, anger, boredom, fear, anxiety and sadness) were self-rated by the participants. In addition, the participants' task engagement was evaluated using a Likert scale (from 0: no interest/boring to 5: very interesting) to check the possible influence of boring or interesting content on brain activation [START_REF] Horrey | Distraction and task engagement: How interesting and boring information impact driving performance and subjective and physiological responses[END_REF].

To ensure that the participant listened attentively to the broadcasts, they were informed that they had to answer three questions about the content of each broadcast when it ended. The responses were scored with 0, 0.5 or 1 point (always evaluated by the same experimenter) according to their accuracy. The broadcasts were randomly selected for each condition to avoid repetition.

Mind-wandering assessment

The tendency for mind-wandering was assessed at the beginning of the experiment by the French version of the Mindful Attention Awareness Scale (MAAS) [START_REF] Jermann | Mindful Attention Awareness Scale (MAAS): Psychometric properties of the French translation and exploration of its relations with emotion regulation strategies[END_REF]. The MAAS is a 15-item scale designed to assess a core characteristic of dispositional mindfulness, namely, open or receptive awareness of and attention to what is taking place in the present [START_REF] Brown | The benefits of being present: mindfulness and its role in psychological well-being[END_REF].

The proportion of attention allocated to the driving task and the proportion of thoughts unrelated to the tasks (driving and listening) considered as mind-wandering were estimated by each participant for each driving session. The participants were instructed to indicate the percentage of thoughts related to driving, to the broadcast (for dual-task condition) and "other thoughts".

Experimental design

After the lead vehicle joined the lane, ten braking actions had to be executed for each driving session. The lead vehicle braked with a random inter-stimulus duration between 7 and 10 s and the participant had to brake as quick as possible to avoid to reach the car. Manual and autonomous driving activities (described in section 2.2), were carried out with and without listening to broadcasts and were considered the dual task and single task, respectively.

Two sessions 2 minutes in length for each factor combination were presented (manual or autonomous conditions for the driving factor and dual task or single task for the listening factor), i.e., 2 sessions × 2 factors × 2 levels = 8 driving sessions (see an example for a participant in Fig. 1). The order in which the driving conditions were presented was counterbalanced. In the case of dual-task conditions, the participant had to answer orally the three questions about the broadcast content just after it ended. Then, after each session, the participant answered the question about the proportion of thoughts related to each task or unrelated to them (mind-wandering) in approximately 15 seconds in writing by indicating the percentage (%). Then, the participant had 30 seconds to recover a resting state. After the first run (consisting in 4 driving sessions), there was a break if participant needed it.

fNIRS recording

A NIRScout device (NIRx Medical Technologies) was used for fNIRS data acquisition. The system has 16 sources and 24 detectors (22 of them included in this study) that receive wavelengths of 760 and 850 nm recorded at 3.9 Hz to compute OxyHb and DeoxyHb concentrations, respectively. Optode placement choice was based on the recommendations of [START_REF] Morais | fNIRS Optodes' Location Decider (fOLD): a toolbox for probe arrangement guided by brain regions-of-interest[END_REF] to cover auditory, frontal and occipital areas and constrained to keep an appropriate source-detector distance of 3 cm, resulting in 41 channels as depicted in Fig. 2.

A calibration was performed for each participant to check each optode's signal quality to guarantee an acceptable gain level. Dark noise analysis assured a low luminosity pollution for the measures.

fNIRS signal processing

The fNIRS signals were analyzed using NirsLAB toolbox version 2017.6 [START_REF] Xu | nirsLAB: a computing environment for fNIRS neuroimaging data analysis[END_REF]. A band pass filter of 0.01 -0.5 Hz was applied to discard cardiac activity, respiratory signals and high frequency noise. Spike artifacts and discontinuities were removed with STD thresholds of 3 and 5, respectively. Averaged oxygenation concentrations were computed using the modified Beer-Lambert law for each epoch [START_REF] Villringer | Near infrared spectroscopy (NIRS): a new tool to study hemodynamic changes during activation of brain function in human adults[END_REF]. The event related responses were computed within 7 s segments after the stimulus (brake lights), and a maximum of 30 points were sampled to define the curves. The application of a jitter (variable inter-stimuli interval duration) prevented spurious periodic artefacts in the event-related responses. The approach to study the evoked hemodynamic responses can be considered a rapid event-related study where the inter-stimuli intervals may be shorter than the response elicited [START_REF] Amaro | Study design in fMRI: basic principles[END_REF].

Given the short segments in the study, the mean signal value was the most representative parameter for information linked to brain area activation compared to the maximal peak value.

An exploratory analysis (paired Student's t-tests) was performed to determine the most relevant channels. However, given that current fNIRS systems do not let an adequate spatial resolution (a distance about 3 cm between source and detector is required) to study constricted brain regions, an exhaustive brain topological study was out of the scope of this paper. Therefore, to avoid the influence of individual differences in placement accuracy and to reduce the artefacts linked to basal blood flow, the channels were grouped in different clusters and the averaged signals computed for further statistical analysis.

Statistical analysis

Sphericity was first checked for the OxyHb and DeoxyHb values by means of Mauchly's test. Greenhouse-Geisser correction was applied if the sphericity assumption was not met.

A two-way analysis of variance (ANOVA 2×2), the first factor representing the driving activity (manual and autonomous) and the second one referring to the concurrent listening task (single and dual task), was performed for each variable for every group of channels according to the scheme showed in Fig. 1. Post-hoc analyses (LSD correction) were carried out to disentangle significant interactions.

All statistical analyses were carried out using SPSS 25.0 software.

Results

Auditory attention assessment

Listening attention was assessed by answers to three questions for each broadcast. Given that there are two dual task sessions for each driving condition (see Sec. 2.5), the maximal score was 6 for each condition. There were no significant differences in attention during autonomous (4.3 ± 1.3 correct answers) and manual driving (4 ± 1.4) conditions (p = .61). The correlation between attention scores in each condition was not significant (r = .01, p = .8).

Mind-wandering scores

Figure 3 shows the percentage of thoughts related to the driving task or driving environment for manual and autonomous driving. The thoughts linked to the broadcast content (only for the dual task conditions) and other thoughts considered mind-wandering were also considered. As depicted in Fig. 3, attention payed to the driving context was higher for manual driving, even if the participant was instructed to pay attention to the lead vehicle during autonomous driving. As expected, listening to a broadcast decreased the mindwandering linked to other thoughts. The averaged MAAS scores of the 12 participants was 3.29 (standard deviation = 1.02), which is similar to the results presented for the French population norm by [START_REF] Jermann | Mindful Attention Awareness Scale (MAAS): Psychometric properties of the French translation and exploration of its relations with emotion regulation strategies[END_REF]. None of the participants was considered outliers according to MAAS results. A significant correlation was found between the MAAS score and performance in the listening task during autonomous driving (r = -.671; p = .034), indicating that individuals with a higher MAAS score were less accurate in answering questions in the autonomous driving condition. Regarding the interest level, no significant main effect (p = .078) was found despite the average score generally being higher for dual task conditions.

Brain activation analysis

Main effects: driving and listening

Concerning the OxyHb mean values, a main effect of driving mode was found in the temporo-parietal area of both hemispheres (left: F(1,11) = 7.06; p = .022; ɳp 2 = 0.391 and right: F(1,11) = 8.44; p = .014; ɳp 2 = 0.434) that showed higher activation for manual driving than for autonomous driving.

Regarding the DeoxyHb mean values, a main effect of driving mode was found for the right frontal area (F(1,11) = 8.63; p = .013; ɳp 2 = 0.440) and for the left tempo-parietal region (F(1,11) = 5.61; p = .037; ɳp 2 = 0.338) that showed, in contrast to OxyHb values, higher concentrations in autonomous driving.

No main effect of listening was found for OxyHb or DeoxyHb.

Interaction: driving and listening

An interaction between driving mode and listening was significant for both frontal areas (left: F(1,11) = 6.91; p = .023; ɳp 2 = 0.386 and right: F(1,11) = 8.46; p = .014; ɳp 2 = 0.435), the right temporo-parietal area (F(1,11) = 6.46; p = .027; ɳp 2 = 0.370) and the occipital area (F(1,11) = 6.44; p = .028; ɳp 2 = 0.369).

To disentangle the origin of these interactions, post-hoc analyses were performed, and the results are illustrated in Figures 4, 5 and6. The mean values of OxyHb and DeoxyHb following the visual cue (illumination of the brake light on the lead vehicle) was computed over 30 points. The results revealed that activation of the right temporo-parietal (p = .013) (Fig. 4) and occipital (p = .011) (Fig. 5) areas are higher in manual driving compared to autonomous driving in the dual task condition (when the listening task competes). Figures 4 shows an earlier amplitude peak for the occipital region during manual driving (between 3 and 4 s after stimulus presentation) than for right temporo-parietal regions (between 4 and 5 s) as depicted in Fig. 5.

A similar result to this one was found in the right frontal area (Fig. 6) where the activation decreases significantly in autonomous driving in the dual task condition compared to ST (p = .038).

MD-DT

AD-DT Concerning DeoxyHb, an interaction between driving mode and listening was also found in the right frontal region (F(1,11) = 4.93; p = .048; ɳp 2 = 0.310). The post-hoc analysis showed a significant difference between manual and autonomous driving in the single task condition (p = .006).

Discussion

As mentioned, the present work aims to investigate the hemodynamic responses evoked to relevant visual stimuli in manual and autonomous driving in a car simulator and to analyze how the inclusion of a secondary task (attentive listening to a broadcast) modulates these hemodynamic responses in both driving situations. For these aims, the fNIRS signal was recorded from frontal, temporo-parietal and occipital areas. We conducted an event-related analysis of the brain activation following illumination of a lead vehicle brake light according to 4 conditions: single-versus dual-task combined with manual versus autonomous driving. The main results were 1) a higher score of reported mind-wandering during autonomous driving as a single task than as a dual task (when attentive listening was required), 2) higher OxyHb concentration for manual driving compared to autonomous driving in the bilateral temporo-parietal and occipital regions, and 3) an interaction in the activation of frontal areas is found between driving and listening conditions due to the higher activation during autonomous driving as a single task compared to autonomous driving as a dual task including attentive listening (which is not significant for manual driving).

Mind-wandering in manual and autonomous driving

During manual driving, the driver must pay attention to the stimuli present in the environment and process them to respond properly. This process should reduce the natural tendency to let the mind wander, as subjectively stated (Fig. 3). In the dual task conditions, attentional resources must be shared for the two tasks (manual driving and listening to a broadcast) leading to higher cognitive workload. This sharing may lead to a decrease in mindwandering [START_REF] Zhang | Relationship between workload and mind-wandering in simulated driving[END_REF]. Hence, people with a higher tendency to let their minds wander (as scored by MAAS) can have comparable performance to people with a weaker tendency to let their minds wander. By contrast, during autonomous driving, correlational analyses suggest that people who scored higher in MAAS had some free attentional resources to let their minds wander, leading to lower performance in the listening task (Sec. 3.2).

Driving effect: manual vs autonomous

As expected, higher brain activation, as measured by OxyHb concentration, were found for manual driving compared to autonomous driving (see Figs. 4 to 6 and section 3.3) in the bilateral temporo-parietal and occipital regions. This result could be related to processing visual information and spatial attention and the basal low mental workload in autonomous driving situations [START_REF] Sibi | Monitoring driver cognitive load using functional near infrared spectroscopy in partially autonomous cars[END_REF]. These cognitive processes are not needed in autonomous driving where vigilance and quick reactivity are the most important needs only when a take-over is required [START_REF] Casner | The challenges of partially automated driving[END_REF]. However, contrary to [START_REF] Sibi | Monitoring driver cognitive load using functional near infrared spectroscopy in partially autonomous cars[END_REF], differences in the frontal regions were not evidenced between manual and autonomous driving for the present event-related paradigm. This difference may be due to the contribution of mind-wandering when attentional resources are not needed to drive [START_REF] Berthié | The restless mind while driving: drivers' thoughts behind the wheel[END_REF].

Distraction effect: attentive listening to a broadcast

In this study, distraction was generated with a dual-task condition consisting of attentive listening. Surprisingly, we did not manage to show a general impact of the listening task on brain activation, OxyHB or DeoxyHb, regardless of the brain areas considered. Nonetheless, the brain area linked to auditory processing has been successfully studied using fNIRS [START_REF] Plichta | Auditory cortex activation is modulated by emotion: a functional near-infrared spectroscopy (fNIRS) study[END_REF]. Indeed, [START_REF] Salo | Brain activity associated with selective attention, divided attention and distraction[END_REF] suggest that auditory distraction can be measured in a restricted area and would elicit activity enhancements only in the auditory cortex. Arguably, it would have been expected to find significant differences in temporo-parietal regions. However, during single-task driving (where there was no broadcast), there were auditory stimuli linked to driving (motor noise), which could have hidden the listening effect of the dual task.

On the other hand, in their experimental design, Salo et al., 2017 included a stream of synchronous tones and gratings where no verbal processing was needed. If verbal information is presented, there are several factors that influence brain activation besides sensorial processing, such as how interesting the information is for the listener [START_REF] Horrey | Distraction and task engagement: How interesting and boring information impact driving performance and subjective and physiological responses[END_REF] or the emotional content [START_REF] Spreckelmeyer | Combined perception of emotion in pictures and musical sounds[END_REF]. Even if in the present study interest and emotional content were controlled to avoid these effects, the temporal variations in these components could have an impact on the averaged measures and hide the listening effect.

Interaction of driving and attentive listening

The significant interaction between driving and listening conditions can be explained by higher activation in dorso-lateral prefrontal areas in autonomous driving for the single task compared to the dual task. This event-related activation change can be explained by greater proneness to mind-wandering in autonomous driving (without listening) due to the monotony of this task where no driving action is needed [START_REF] Berthié | The restless mind while driving: drivers' thoughts behind the wheel[END_REF].

Higher mind-wandering would decrease frontal activation during the time segments preceding the visual cues (brake lights), which are considered the baseline for the next event. This result agrees with [START_REF] Durantin | Characterization of mind wandering using fNIRS[END_REF], who showed that OxyHb level faded before the target stimuli in mind-wandering situations as assessed by the sustained attention to response task (SART). Hence, OxyHb level would be consequently higher after the stimulus since it measures relative oximetric brain variations. Nevertheless, we must be cautious in drawing such conclusions because inter-stimuli intervals are short and instantaneous mind-wandering is not guaranteed. Another possible explanation, not exclusive, would be that this decreased activation in the dorso-lateral prefrontal area would be due to the distractive task, as observed by Fort el al., (2010) in a driving simulator study using MEG.

The decreased activation in frontal areas in the dual task could suggest that brake lights act as distractors that interfere with the listening task. This explanation would agree with the conclusions drawn from the study by [START_REF] Ozawa | Distraction decreases prefrontal oxygenation: a NIRS study[END_REF] that showed decreased OxyHb in the prefrontal cortex associated with distraction. In the present study, this effect is observed only in autonomous driving, which is a monotonous supervision task. By contrast, for the manual driving situation, driving is always the main task, even if auditory stimuli are broadcasting. Therefore, attention would be more focused on the visual driving environment than on the broadcast, such that event-related responses show increased OxyHb in the occipital area reflecting visual processing of the brake lights.

However, note that, for instance, [START_REF] Nosrati | Event-related changes of the prefrontal cortex oxygen delivery and metabolism during driving measured by hyperspectral fNIRS[END_REF] showed an increase in prefrontal brain activation whilst performing different driving tasks, such as right and left turns (with pedestrians and traffic), in the presence of auditory distractors. This discrepancy with our results might be explained by the different attentional demands of the driving tasks used. Right and left turns are highly demanding tasks compared to our braking task (without traffic or pedestrians), which can be easily automated by the drivers. In addition, the secondary tasks used were different and may have created different attentional demands. Further studies are needed to better understand the potential interactions between the demands of the main task and the demands of the secondary task.

Brain hemodynamic responses in highly automated vehicles

The weaker activation of the right prefrontal cortex, for OxyHb, in autonomous compared to manual driving together with the higher activation in the right temporo-parietal and occipital regions in manual compared to autonomous driving while listening suggest that visual cues related to the driving environment at a high level of automation could act as distractors. The incorporation of sophisticated assistance systems on board the vehicles leads us to reconsider the definition of "driving performance" and the concept of "main" and "distractive" tasks. This reconsideration is particularly true whilst driving autonomous vehicles, when secondary tasks, or even sleeping, could be allowed depending on the automation level [START_REF] Casner | The challenges of partially automated driving[END_REF]. In this context, users might consider the warnings to take-over as distraction from another task different from driving. This context would be particularly relevant during the first use of an automated vehicle, as the warnings have to be learned to be associated with adequate action, and they are not processed automatically.

Limitations of the study

This study has some limitations. The inter-stimuli intervals are presumably shorter than the hemodynamic response duration, leading to a rapid event-related approach [START_REF] Amaro | Study design in fMRI: basic principles[END_REF]. Hence, a study with longer windows is desirable to better establish the response latency and to avoid response overlap. Regardless, artefacts would be present in every condition without biasing the results.

Finally, despite the power analysis yielding more than 0.8 power, the results of this pilot study were obtained using a small sample. Therefore, further studies to replicate these results are needed to reinforce their interpretation and to generalize our results. In addition, cognitive and attentional processes might be partially dependent on individual characteristics, such as age, capability or expertise, and these characteristics should be considered for each population.

Conclusions

.

Our results suggest that visual cues (brake lights of a lead vehicle) are differently processed during manual versus autonomous driving. Besides, during autonomous driving, listening to a broadcast influences the attentional processing of these visual cues. To our knowledge, this study is the first study that showed that visual cues from the driving environment in an autonomous vehicle can be considered distractors and measured the related brain activation using fNIRS.

In future works, the emotional content of the broadcast could be manipulated to check the influence of the limbic system on fNIRS responses to distractors. Furthermore, the computation of features representing temporal variation in longer segments of hemodynamic signals could be used as input to classifiers to determine driver distraction episodes using fNIRS.

Figure 1 :

 1 Figure 1: Example of driving session order for one participant. In each session of 2 minutes, 10 braking action are expected. MD = manual driving; AD = autonomous driving; ST = single task; DT = dual task.

Figure 2 :

 2 Figure 2: (a) Probe setup (optode positions) according to the 10-20 system. (b) Channel clustering for brain area analysis. Of note, frontal channels were separated into two regions according to laterality. Red channels were utilized for visual representation of the grand average signals (see Figs. 4 and 5).

Figure 3 :

 3 Figure 3: Percentage of thoughts related and unrelated to the tasks in each of the 4 conditions. MD: Manual Driving; AD: Autonomous driving; ST: single task; DT: dual task.

  Figure 4: (a) Interaction between driving mode and listening for OxyHb in the right temporoparietal region. ST: Single task. DT: Dual task (with listening). (b) Grand average (including 12 participants, mean ± standard error) hemodynamic responses from right temporoparietal region in DT by manual (MD) or autonomous (AD) driving condition, and the mean ± standard error inter-subject of OxyHb (red lines) and DeoxyHb (blue lines) are represented for the channel between C6 and CP6 (amplitude (mM) × 10 -4 ).


J Saliba

F Grondin

M Matallah

A Loukili

H Boussa

Modelling of basic creep effect on concrete damage at a mesoscale level

Keywords: Creep, mesoscopic model, concrete

In its service-life concrete is loaded and delayed strains appear due to creep phenomenon. Some theories suggest that micro-cracks nucleate and grow up when concrete is submitted to a high sustained loading, which contribute to make the concrete weaker. Thus, it is important to understand the interaction between the viscoelastic deformation and damage in order to design reliable civil engineering structures. Several creep-damage theoretical models have been proposed in the literature. However most of these models are based on empirical relations applied at the macroscopic scale. Coupling between creep and damage is mostly realised by adding some parameters to take into account the microstructure effects. In the author opinion, the microstructure effects can be modelled by taking into account the effective interactions between the concrete matrix and the inclusions. In this paper, a viscoelastic model is combined with an isotropic damage model. The material volume is modelled by a Digital Concrete model which takes into account the "real" aggregate size distribution of concrete. The results show that stresses are induced by strain incompatibilities between the matrix and aggregates at mesoscale under creep and lead to cracking.

INTRODUCTION

Deformation and fracture of concrete are associated with very complicated progressive failure. Tensile creep is an important issue especially in the case of special concrete structures. The effects of high stress levels on the longterm behaviour of concrete are important with reference to delayed strains, residual strength and permeability. Three main mechanisms were recognized for tensile creep [START_REF] Bissonnette | Tensile creep of concrete: study of its sensivity to basic parameters[END_REF][START_REF] Garas | Multi-scale investigation of tensile creep of ultrahigh performance concrete for bridge applications[END_REF]: water seepage, viscous shear and microcracking. On one hand, creep deformations relax the stresses generated by autogenous shrinkage and thermal dilation at early ages [START_REF] Bissonnette | Tensile creep at early ages of ordinary, silica fume and fiber reinforced concretes[END_REF][START_REF] Altoubat | A new look at tensile creep of fiber reinforced concrete[END_REF]. On the second hand, creep includes a detrimental substantial component of microcracking [START_REF] Cook | The tensile creep and fracture of desiccated concrete and mortar on water sorption[END_REF]. It is usually accepted that the failure process under a sustained load is associated with the development and growth of microcracking [START_REF] Rossi | Investigation of the basic creep of concrete by acoustic emission[END_REF][START_REF] Bazant | Cohesive crack with rate-dependent opening and viscoelasticity: I.mathematical model and scaling[END_REF][START_REF] Barpi | Lifetime evaluation of concrete structures under sustained post-peak loading[END_REF]. Thus, understanding the behaviour of concrete requires the detailed assessment of creep and the part of damage. Coupling between the viscoelastic behaviour and damage is mostly realised by a classical approach in which a time dependent growth of damage is considered [START_REF] Omar | Déformations différées du béton : Etude expérimentale et modélisation numérique de l'interaction fluageendommagement[END_REF][START_REF] Mazzotti | Nonlinear creep, Poisson's ration, and creep-damage interaction of concrete in compression[END_REF][START_REF] Reviron | Coupling between creep and cracking in tension[END_REF][START_REF] Torrenti | Coupling between leaching and creep of concrete[END_REF]. In the author opinion, the microstructure effects can be modeled by taking into account the effective interactions between the concrete matrix and the inclusions. The multi-scales approach was found very useful for the evaluation of material characteristics affected by the material characteristics of the components. Thus, the mesoscale modelling presents many advantages in the understanding of the fracture process and the corresponding effect of concrete heterogeneities [START_REF] Grassl | Meso-scale approach to modelling the fracture process zone of concrete subjected to uniaxial tension[END_REF][START_REF] Lopez | Meso-structural study of concrete fracture using interface elements. I: numerical model and tensile behaviour[END_REF]. In addition it allows giving new elements for the comprehension of complex phenomena as the behaviour of concrete under confinement [START_REF] Dupray | A mesoscopic model for the behaviour of concrete under high confinement[END_REF], temperature effect [START_REF] Grondin | Multi-scales modelling for the behaviour of damaged concrete[END_REF], sulphate attack [START_REF] Idiart | Chemo-mechanical analysis of concrete cracking and degradation due to external sulfate attack: A meso-scale model[END_REF] ... In order to have more information on the behaviour of concrete under creep, coupling between a viscoelastic model and an isotropic damage model is operated and a Digital Concrete model is used to take into account the microstructure heterogeneities. In the first section, the non linear viscoelastic model for the creep behaviour is presented. Then, the model parameters are determined by experimental tests on mortars under direct tensile creep. Finally, the numerical results obtained for direct tensile creep and flexural creep tests at the mesoscopic scale are compared to experimental measurements.

The numerical model

The non-linear viscoelastic model

The volume V of a heterogeneous material is formed by two media: a matrix defined by the medium V m and inclusions defined by the medium V i . With the objective to model the damage due to creep of cement-based materials, phases have a damage elastic behaviour. A constant load F is applied on one of the surface boundary of V. This load implies local displacements fields ( ) u y , local strain fields ( ) y ( )

( ) ( , ( )) : ( ) ( ) ( ) p v y C y y y y y σ ε ε ε ε = - - ɶ (1
where 0 ( ) C y ɶ is the initial stiffness of the material phases considered isotropic and linear elastic. Stresses are defined along a finite set of directions defined by unit vectors n [START_REF] Fichant | Isotropic and anisotropic descriptions of damage in concrete structures[END_REF]:

( ) 3 2 1 (1 )
(1 ) ( )

t i ij j t t ij i k kl l d n n d n n n σ σ τ σ σ = - = - - ∑ (3)
Where σ and τ represent the normal and tangential components of the local stress fields and d the scalar value of the isotropic damage which depends only on the elastic strain:

( )

0 0 1 exp e d t d e d B ε ε ε ε   = - -   (4)
where t B represents a damage parameter to control the slope of the strain softening constitutive relation in function of the width h of the element and 0 d ε the strain threshold from which damage begins and is defined as the ratio between the tensile strength and the Young's modulus ( 0 /

d t f E ε = ).
The original version of the model has been modified in order to take into account the plasticity part in the fracture energy dissipation. The Nadai criterion has been replaced by two Drucker-Prager yield functions. One to limit the tensile regime and the second to limit the compression and the compression-compression regime:

( ) ( ) ( ) ( ) ( ) ( )      - - + = - - + = 0 1 2 0 1 2 ~w p w I J F w p w I J F ij c ij c c ij t ij t t σ β σ α σ β σ α (5)
where c α , t α , c β and t β are four parameters in function of the relationship between the tensile limit stress and the compression one and the relationship between the bi-axial compressive state and the uni-axial one. The hardening law is considered as linear plastic:

( ) 0 . w p q p w = + ( 6
)
where q is a model parameter, p is the effective plastic strain and 0 w represents the elastic domain in the stress space. The viscoelastic strain is defined by Kelvin-voigt chains. With those elements, the stress history does not have to be stored for the calculation of creep strain [START_REF] Saliba | Study of creep-damage coupling in concrete by acoustic emission technique[END_REF]. For a Kelvin-voigt unit i, the basic strain evolution is given by:

( ) ( ) ( ) v v v v t k t t η ε ε σ + = ɺ ɶ (7)
Where ( ) v t εɺ represents the derivative of the elementary basic creep strains, v k the stiffness and v η the viscosity of the Kelvin voigt unit.

The creep process occurs only in the undamaged part of the material and the effective stresses are linearized for each time step. The local total viscoelastic strains are obtained by solving analytically the differential equations and are expressed as:

1 1 1 n n n n v v v v v v n v n a b c ε ε ε ε σ σ + + + ∆ = -= + + ɶ ɶ (8)
Where n v ε is the viscoelastic strain vector at time-step number n and , ,

v v v
a b c depend upon material parameters.

The total viscoelastic strain is deduced from the sum of all the elementary viscoelastic strains.

( ) ( )

1 1 i n v i t t ε = + = Ε = ∑ (9)

Digital concrete model

The Digital Concrete Model has been developed with the aim to have a 'realistic' representation of cement-based materials by taking into account the random size distribution of heterogeneities. So, for previous applications on the behaviour of concrete, the concrete microstructure was represented as a multi-phases material with successions of three material phases (cement paste, pores, aggregate of various sizes) spatially distributed in a random way. Each phase is characterized by a set of physical and geometrical parameters as: the volume fraction, the unit size (aggregate or pore diameter), physico-mechanical properties. A specific algorithm has been developed to make a spatial and random distribution of these phases on the basis of a F.E. grid. Details are given in [START_REF] Grondin | Multi-scales modelling for the behaviour of damaged concrete[END_REF]. Simulations on Representative Elementary Volume (REV) allow defining the REV dimensions and the finite element size chosen in accordance with the material characteristics and the problem type. Generally the REV dimensions are taken equal to four times the highest inclusion diameter and the finite element size is equal to 0.8 time the smallest inclusion diameter. Calculations have been performed to check the stability of results with these dimensions for different inclusions distributions. The presented model is implemented in the finite element code CAST3M. Mechanical and basic creep parameters were identified from an experimental campaign performed in GeM laboratory.

3 Experimental identification of material parameters

Materials properties

Concrete and mortar specimens were mixed with Portland cement CPA-CEMII 42.5, crushed limestone aggregate distributed in fine sand, with a maximum size of 5 mm and a density of 2570 kg/m 3 and crushed gravel of size 5 to 12.5 mm with a density of 2620 kg/m 3 . A superplasticizer agent (Glenium 27) with a quantity of 1.9 kg/m 3 has been added for the workability of concrete. The same constituents were used for mortar. Table 1 shows the mix quantities of constituent materials for mortar and concrete. The mixtures were characterized by a water-to-cement ratio of 0.56. Three-point bending tests were realised on concrete beams with the dimensions 100 * 200 * 800 mm 3 [START_REF] Saliba | Study of creep-damage coupling in concrete by acoustic emission technique[END_REF]. Tensile tests were realised on cylinder specimens φ110x500 mm 2 .

Experimental procedures

All tests are performed in a climate controlled chamber at 50 % of relative humidity and temperature of 20°C. For creep tests, the exchange of moisture is prevented by a double layer of self-adhesive aluminium paper.

The flexural creep tests are performed on frames (Figure 1b) with a capacity ranging from 5 to 50 KN. The load is applied by gravity with a weight and counterweight system and the displacement is measured at midspan (Figure 1). Three-point bending creep tests are realized on notched specimens. Specimens are loaded in creep at 70% and 85 % of the maximum load (F max ). The maximum load is measured in fracture tests with specimens at 28 days controlled with the crack mouth opening displacement (CMOD).

Tensile tests are conducted in a 100 kN capacity electromechanical machine. For each specimen, two thick steel plates are fixed on the top and on the bottom using high modulus and strength epoxy. Two rings are fixed on the specimen with three screws. Three LVDT with an accuracy of ±3 µm are placed on the rings at 120°. The relative displacement between the two sections is measured on a base of 280 mm at the central zone. A general view of the experimental setup is provided in figure 1a. The load is applied with a constant rate of 0.2 kN/s; so that the maximal strength occurred at about 1 minute. During each test, load, LVDT displacement and load cell displacement are measured and recorded up to final failure with a data acquisition system. Two specimens are loaded in creep at 85 % and 70% of the maximum load.

Measurement of the concrete components properties

Concrete is modelled by a two-phase material considering aggregates embedded in the mortar matrix. So, the mechanical properties of mortar and aggregates have to be determined separately. Two mortar specimens are submitted to rupture at the age of two months to measure the maximum load to be considered in creep tests. In this study, we consider that the matrix governs the viscoelastic behaviour of concrete. So, the basic creep parameters are also determined based on tensile creep tests on mortar. A constant load is maintained for 30 days at 70% and 85% of the maximal strength. The Kelvin-Voigt parameters of the viscoelastic model are then calibrated to give a calculated total strain evolution of mortar, performed for an uniform mortar volume, comparable to the measurements (Figure 2). The displacement rate is very fast in the first few days of loading (primary creep) and then stabilizes (secondary creep). Creep strain begins then to decrease in time indicating that shrinkage increases. The same behavior was observed by Reinhardt and Rinder [START_REF] Reinhardt | Tensile creep of high-strength concrete[END_REF] and Rossi et al. [START_REF] Rossi | Basic creep behavior of concretes investigation of the physical mechanisms by using acoustic emission[END_REF]. Creep strain for aggregates is considered equal to zero. The direct tensile test does not allow measuring the postpeak regime. The fracture energy (G f ) for each constituent is also given by the literature [START_REF] Borderie | Approche mésoscopique du comportement du béton, Apport de la représentation géométrique[END_REF]. For aggregate, the mechanical characteristics are obtained from the literature. A Young's modulus of 60 GPa and a tensile strength of 6MPa are considered [START_REF] Granger | Comportement différé du béton dans les enceintes de centrales nucléaires analyse et modélisation[END_REF]. All the parameters that are used at the mesoscopic scale are summarized in table 3.

E (GPa) 0 ν t f (MPa) f G (J/m²) 1 v k (GPa) 2 v k (GPa) 3 v k (GPa) v η (GPa.

Application on concrete at the mesoscale

The considered mesoscale for modelling the behaviour of concrete is the scale at which the material can be observed as a set of coarse aggregates embedded in a mortar matrix. Here, coarse aggregates are inclusions of a size greater than 5 mm while mortar matrix is a mixture of finer aggregates and a cement paste. The aggregate volume represents 37% of the total volume of concrete. The stability of results depending on the size of the specimen and the maximal diameter of the inclusion was performed in a recent study [START_REF] Grondin | Multi-scales modelling for the behaviour of damaged concrete[END_REF] and was respected here (L/Dmax>4).

Table 3: The aggregate size distribution of concrete φ (mm) 5 6.25 8 10 12.5 f V (%) 3 7 11 14 2

Creep behaviour in tension

The imposed constant load is equal to 70% or 85% of the maximal strength of concrete calculated by a fracture test. Figure 3 shows the macroscopic stress-strain curve obtained by the numerical simulation in comparison with experimental results. A good correlation is obtained and the post-peak region is very brittle as in the experimental tests. The numerical simulation and the experimental creep tests are presented in Figure 4. The numerical creep strain obtained with the digital concrete model is lower than creep strain for mortar specimen wish is expected as the aggregate do not creep. The specimens loaded at 85% fail after few days and the crack is localized at the end of the specimen. This failure may be due to stress concentration at both extremities. In addition, while concrete specimens fails, mortar specimens do not show any damage; thus the failure can be associated to the presence of the interfacial transition zone which is characterized by weak mechanical properties that should be simulated in the future for a real representation of this behaviour. Figure 5 shows the damage localisation for concrete specimens loaded at 70% and 85%. The specimens loaded at 70% show little damage localized at the mortar-aggregate interface. The same result is obtained for the specimen loaded at 85% however the damage intensity is more important. This damage is due to the load application at the beginning and begins to increase with creep.

Structural response on a three-point bending test

Numerical simulations are performed on concrete submitted to a three-point bending creep test and results are compared to experimental results analysed in a previous study [START_REF] Saliba | Study of creep-damage coupling in concrete by acoustic emission technique[END_REF]. Only half of the beam is analysed (100*200*400 cm 3 ) due to a central symmetry around the notch. A regular mesoscopic mesh related to the middle part of the concrete specimen is generated and two homogeneous concrete blocks are attached to the left end of the beam with progressively larger mesh to avoid stress concentration (Figure 6). Numerical simulations are performed under stress plane conditions. The same parameters determined above are used for the mesoscopic mesh. For the homogeneous part, the parameters are determined by direct tensile test on homogenous concrete specimens. Creep compliance is assumed equal in compression and in tension which is in accordance with experimental evidences for mature concrete [START_REF] Brooks | A comparaison of creep, elasticity and strength of concrete in tension and in compression[END_REF]. A fracture test is performed to determine the maximal flexural strength (Figure 7). Calculated results of the typical load-CMOD curve are compared with experimental results. The evolution of local damage is also visualized in the material microstructure (Figure 8). The damage is localized at the front of the notch at the beginning of the test.

Then cracks begin to join up together and cracks propagate in the mortar matrix. The proposed model is also suitable for the computations of creep damage in bending. In Figure 9 deflection-time curves are plotted for different load to peak load ratios. The macroscopic behaviour of concrete under creep loading is characterized by a progressive degradation of the material stiffness. This behaviour is caused by the growth and coalescence of micro-cracks in the concrete microstructure (Figure 10). That means that the mechanical properties of concrete are gradually and locally degraded under creep. Further, we assume that the concrete specimen collapses when a long continuous crack develops at the bottom of the specimen and at the same time the maximum axial strains of the elements along the main crack are higher than the corresponding ultimate strain. This work has allowed highlighting the nucleation of micro-cracks in the concrete microstructure under a sustained load which contribute to the weakness of concrete observed in a recent work [START_REF] Saliba | Study of creep-damage coupling in concrete by acoustic emission technique[END_REF].

ACKNOWLEDGEMENT

This study has been performed in the project MEFISTO which is supported by the French National Research Agency (ANR -Agence Nationale pour la Recherche) in the program "Villes Durables" (Sustainable Cities) under grant number VD08_323065.

ε

  and local stress fields ( ) y σ in each point y of V which are linked by the following behaviour law:

  stiffness tensor of the material phases depending on the strain of phases, ( ) p y ε the local plastic strain fields and ( ) v y ε the local viscoelastic strain fields. The chosen damage model is the isotropic model developed by Fichant et al.[START_REF] Fichant | Contiuum damage modeling: approximation of crack induced anisotropy[END_REF]. It allows to represent the unilateral effect and to obtain objective results independently of the length of the finite elements by controlling the fracture energy. This model is a simplified version of the microplan model of Bazant and Ozbolt[START_REF] Bazant | Nonlocal microplane model for fracture, damage, and size effect in structures[END_REF] and is based on the relation between the total stress and the effective stress ( ) y σɶ of the material defined by:

Figure 1 :

 1 Tensile creep test setup (a) and general view of the flexural creep frame (b).

Figure 2 :

 2 Figure 2: Tensile creep strain of mortar specimens loaded at 70% and 85%.

Figure 3 :Figure 4 :

 34 Figure 3: Stress -strain relationship in tension and comparison with experimental results.

Figure 5 :

 5 Figure 5: Localisation of damage in concrete specimens loaded at 70% and 85% of the maximal strength.

Figure 6 :Figure 7 :

 67 Figure 6: Meshing of the concrete beams under three point-bending tests.

Figure 8 :

 8 Figure 8: Localisation of damage in concrete beams at 86, 100 of the maximal strength and 5% of the post peak region under three point bending test.

Figure 9 :Figure 10 :

 910 Figure 9: Deflection-time curves of concrete beams in flexion for different stress to strength ratios

Table 1 :

 1 Concrete and mortar mixtures proportions.

	Constituents	Dosage for concrete (Kg/m3)	Dosage for mortar (Kg/m3)
	Gravel: G5/12,5 mm	936.0	-
	Sand: 0/5 mm	780.0	1270.0
	Cement: CEMII 42.5	350.0	550.0
	Water	219.5	330.0

Table 2 :

 2 Model parameters for mortar and aggregates


Alexis Pinet

Thuy Linh Nguyen

Guillaume Bernadat

Bruno Figadère

Laurent Ferrié

Synthesis of 3,5-Disubstituted 1,2-Dioxolanes Through the Use of Acetoxy-Peroxyacetals

The synthesis of acetoxy-endoperoxyacetal derivatives allowed the formation of functionalized 3,5-disubstituted-1,2dioxolanes through the formation of reactive peroxycarbenium species under Lewis acid mediation. The introduction of a neutral nucleophile such as allylsilanes, silanes, or silyl enol ethers was accomplished with moderate to good yields. The two studied Lewis acids, TiCl4 and SnCl4, gave contrasted results. The higher diastereoselectivity towards the trans diastereomer in experiments with TiCl4 as Lewis acid was explained by a faster degradation of the cis isomer product, conducting generally to lower yields. A rationalization of this result was supported by calculation.

Organic peroxides are uncommon moieties for natural products. 1 Nevertheless, this pharmacophore is often source of potent biological properties due to the relative reactivity of peroxides. Besides the famous anti-malarial agent, artemisinin, isolated from Artemesia annua plant, 2 many other organisms produce peroxide containing natural products. Particularly, plakinic acids, isolated from sponges Plakortis sp., exhibit a fatty acid structure with a 1,2-dioxolane ring between positions 3 and 5 (Figure 1). 3 Another characteristic of plakinic acids is that the 1,2-dioxolane ring is 3,3,5,5-tetra-substituted. More recently, we investigated the synthesis of simpler analogues of mycangimycin, 3 a new peroxide isolated from Streptomyces sp. living in symbiosis with insect Dendrocton frontalis. 3 Mycangimycin has a very similar structure compared to plakinic acids but beside its highly conjugated fatty chain, the 1,2-dioxolane ring is only 3,5-disubstituted (Figure 1). This difference of structure is detrimental for the synthesis of this compound. Indeed, the substitution pattern present in the dioxolane ring of plakinic acids facilitates the preparation of such compounds due to the enhanced stabilization of intermediate carbenium or radical species necessary to provide the expected structure. 3 Precursor of 3,5-tetrasubstituted dioxolane rings can also be double bonds though peroxymercuration, 3 and here again, the substitution of starting olefins for mycangimycin derivatives is detrimental to the reactivity of the required olefin. For these reasons, relatively few examples of preparation of 3,5-disubstituted 1,2dioxolanes are found in the literature. 6 Peroxycarbenium ions have emerged as a powerful tool for the synthesis of organic peroxides. 3 Nevertheless, the synthesis of 3,5-disubstituted 1,2-dioxolanes from the corresponding peroxyacetals is still an issue due to a reduced stabilization of the oxycarbenium ion as intermediate. Moreover, disfavoured withdrawing effect by induction of one oxygen atom to the other at the peroxide moiety reduces the ability to stabilize the peroxycarbenium compared to a classical acetal. Indeed, we planned to use in early experiments some reported methodologies from Dussault et al. 8b to perform the nucleophilic addition to peroxyacetal such as methoxyperoxyketal 6, which has been prepared from hemiperoxyketal 4 by acid mediated metathesis with MeOH. 3 However, to our disappointment, we were unable to prepare entity 7 from hemiperoxyacetal 5 (prepared from cyclopropanol by oxidative ring opening with triplet oxygen, see supporting information) and any simple alcohol. By analogy with tetrahydrofurans, we decided to activate the cyclic peroxyacetal as acetate, due to its known excellent leaving group ability.

In the first attempts, we experienced issues to obtain acetate 8 under classical conditions involving pyridine and Ac2O, but only decomposition was observed, which can explain that a similar structure was scarcely reported. 10 Fortunately the preparation of such a compound was possible by using Lewis acid-catalysed acetylation condition. With rare earth triflates such as Yb(OTf)3, we obtained expected acetate 8 in high yield. It is worth noting that stability of this compound is pretty high compared to THF acetate derivatives due to a reduced stabilization of the peroxycarbenium compared to THF oxycarbeniums, and thus compound 8 can then be generally purified by flash chromatography on silica gel without notable decomposition. A Sakurai reaction between peroxyacetal 8 and allyltrimethylsilane 9 was then investigated, searching optimized reaction conditions. Dichloromethane was found to be the most suited solvent for this reaction. TMSOTf or BF3• OEt2 were ineffective promoters for this transformation, converting only small amounts of starting material (Table 1, entries 1 and 2). In contrast, SnCl4 and TiCl4 were far more promising. Indeed, SnCl4 gave a high isolated yield of dioxolane 10 (Table 1, entry 4) at -40 °C. At lower temperature (entry 3), the reaction hardly proceeded with recovery of starting material after one hour. Extended reaction time did not improve significantly the yield and/or the diastereoselectivity. At higher temperature, the yields also decreased due to some degradations (Table 1, entries 5 and6). The observed diastereoselectivity is moderated, in contrast to those observed on 2,4-disubstituted THF derivatives. 11 This limited selectivity could be attributed to a competition between two conformers of the peroxycarbenium species. We also turned our attention to TiCl4; similarly to SnCl4 the reaction must be conducted at -40 °C (Table 1, entry 8) rather than -78 °C (Table 1,entry 7). However, in contrast to SnCl4, diastereoselectivity for 1,2-dioxolane 10 was largely improved up to 85:15, albeit with a lower yield. To explain this enhancement, we suspected reaction product 10 to endure a selective degradation of the cis isomer, therefore enriching the proportion of trans isomer but decreasing overall yield. Indeed, this hypothesis was confirmed by adjusting the number of equivalents of TiCl4 to the reaction mixture. Increasing the stoichiometry of TiCl4 to 1.1 equivalent decreased the yield but increased diastereoselectivity to 91:9 (Table 1,entry 9), while decreasing the amount of TiCl4 to 0.7 equivalent improved the yield but decreased diastereoselectivity of 10 to 70:30 (Table 1,entry 10)

Scheme 2. Partial degradation of dioxolane 10 using reduced amount of TiCl4 under the reaction conditions of a Sakurai reaction

An additional experiment allowed us to confirm our hypothesis by applying Sakurai reaction conditions to dioxolane 10 with a reduced amount of TiCl4 (0.4 equivalent). After 30 min, the reaction mixture was quenched and purified to afford starting material in 56% recovered yield but with an improved diastereoselectivity in favour of the trans compound (from 70:30 to 84:16, Scheme 2).

The mechanism of this TiCl4 catalyzed degradation was further investigated and some major degradation products were identified. A TiCl4 catalysed Kornblum-DeLaMare rearrangement 12 of dioxolane 10 afforded compounds 12 and 13 on one hand (Scheme 3, top route). On the other hand, TiCl4 mediated fragmentation of dioxolane 10 also afforded aldehyde 14 and ketone 15 from intermediate 11a. Under Sakurai reaction conditions, reactive species such as aldehyde 14 was converted into allyl adduct 18 (Scheme 3, bottom route). Presumably, a similar process occurred from intermediate 11b as well, but the expected degradation products were not produced in sufficient amount and also due to their relative volatility for some of them, side products 14, 16, 19, 20 and 21 were only observed from GC/MS analysis of the crude material and were not isolated. The mechanism of this fragmentation is not completely clear on our system, since the possibility of a retro-aldol reaction from 1,3-hydroxyketones 12 and 13 cannot be completely excluded. However a similar fragmentation was studied on 3,3,4-trisubstituted 1,2-dioxolanes with TiCl4, affording ketones and aldehydes with migration of an alkyl group, an hydrogen or a deuterium. 13 An analogous fragmentation was also observed in one of our previous work, where a bicyclic peroxyketal afforded a ketoester under triflic acid activation. 4 These two examples show that a retro-aldol process might not occur since it cannot explain the formed product. Here, the migration of the proton from position 3 or 5 to the position 4 of the 1,2-dioxolane ring is probably concomitant with the peroxide bond and carboncarbon bond cleavage (Scheme 3). Origin of the enhancement of the diastereoselectivity by degradation in the presence of TiCl4 in favour of trans compound was then investigated at the B3LYP/ (6-31+G(d,p), LanL2DZ) 13 level of theory (Pople's basis set for organoelements and Los Alamos effective core potential for metallic centers). We focused our study on one of the two possible TiCl4 mediated Kornblum-DeLaMare rearrangements, leading to intermediate 23 from dioxolane 22, a simplified model of dioxolane 10 (Figure 2). Transition states starting from diastereoisomers cis-22 and trans-22 were localized on the potential energy surface. First attempts to search a pathway for the transition state from cis/trans-22 and TiCl4 only were unsuccessful. Introduction of a proton acceptor under the form of an additional chloride anion, which is likely to be found in the reaction medium, allowed the rearrangement to occur. The difference of activation energy ΔΔE ‡ between the two diastereomers was found to be 2.2 kcal/mol, in favour of isomer cis-22. This result is consistent with our observation about a faster degradation of cis-10 compared to trans-10 with TiCl4 and subsequent enrichment of this latter. The energy for [cis-22+TiCl4+Cl -] is higher by 3.7 kcal/mol compared to the trans isomer, probably due to steric interactions between the two alkyl groups at the backside of the 1,2-dioxolane ring, squeezed by TiCl4 and chlorine placed on the front face. In contrast, the transition state for cis-22 is only 0.7 kcal/mol higher due to the free field for proton trapping by chlorine anion at the front face of the dioxolane ring. In the meantime, a steric congestion exists between chlorine and one alkyl group in the transition state for trans-22, demanding more energy (2.9 kcal/mol) to perform the reaction (Figure 2). Table 3. Use of various peroxyacetals 40-45 and peroxyketal 46 in the Sakurai reaction with allyltrimethylsilane 9. We then turned our attention to the nature of the nucleophile being able to react on endoperoxyacetal 8. The use of various allylsilanes proved to be successful (Table 2, entries 1-6). The selective degradation of cis diastereoisomer with TiCl4 gave always better trans selectivity. Enol ethers were also screened as potent nucleophiles (Table 2, entries 7-10). The cis diastereoisomer was obtained as major product, although TiCl4 mitigated this result due to a selective degradation of cis diastereoisomer. Cyanide 29 was a very effective nucleophile with SnCl4 as well as azide 30 giving expected products 37 and 38 with excellent yields but no control of the diastereoselectivity. TiCl4 was not able to improve this result, resulting only in decreased yield (Table 2, entries 11-13). Reduction of the endoperoxyacetal is also possible with triethylsilane 31, producing 3-monosubstituted dioxolane 39 (entries 14 and 15).

Next, we explored substrates 40-46 (easily obtained as compound 8, see Supporting Information) in the Sakurai reaction with allylsilane 9. In order to improve the diastereoselectivity of the reaction, bulky dioxolanyl acetates 40-42 were studied (Table 3, entries 1-6). Unfortunately, these substrates did not improved diastereoselectivity compared to acetate 8 (Table 1), and a selective degradation of cis product was still observed when was used TiCl4 in most of the cases. Nevertheless, high steric congestion of the tert-butyl group for compound 42 seemed to suppress degradation of product 49, affording high yield of it using both Lewis acid. Benzyl substituted and protected alcohols are compatible in this reaction leading to good yield with SnCl4 and improved trans diastereoselectivity with TiCl4, as expected (Table 3, entries 7-11). Ketal derivative 46 was also examined with our protocol (Table 3, entries 13 and 14). Due to the improved stabilization of the peroxonium species with the methyl group, compound 46 proved to be unstable and could not be isolated cleanly. The crude material was used directly in the Sakurai reaction, meaning that the yield was calculated over two steps. Product 53 was obtained with a good selectivity with both SnCl4 and TiCl4. This result is comparable in yields (over 2 steps) with Dussault's procedure, meaning our methodology is not only limited to endoperoxyacetals. 7e,15 In conclusion, we developed a new method for the formation of 3,5-disubstituted 1,2-dioxolanes through the use of acetoxyperoxyacetals and the formation of peroxycabenium intermediate species under SnCl4 or TiCl4 activation. The formation of acetoxyperoxyacetal by using a Lewis acid catalysis proved to be essential for their formation and allowed a sufficient reactivity for further functionalization. SnCl4 and TiCl4 were found to be the best Lewis acids screened so far. A wide variety of substrates and nucleophiles were compatible with the reaction conditions. A variation of results was observed between these two reagents: SnCl4 generally gave good yields but moderate selectivities, while TiCl4 furnished higher selectivity towards the trans products but generally lower yields. In this case, a TiCl4 mediated decomposition of the newly formed products takes place, where the cis-disubstituted dioxolane seems to decompose faster than the trans isomer, explaining improved selectivities and lower yields thus observed. Calculation about towards one degradation pathway could rationalize why cis-1,2-dioxolanes decompose more easily under treatment with TiCl4.

Figure 1 .

 1 Figure 1. Artemisinin, plakinic acids and mycangimycin Scheme 1. Activation of endoperoxy-ketals and -acetals.

  Scheme 3. Identification of TiCl4 mediated degradation products of dioxolane 10.

Figure 2 .a

 2 Figure 2. Energy profiles of the TiCl4 mediated Kornblum-DeLaMare rearrangements of model compound cis and trans-22 at the B3LYP/(6-31+G(d,p), LanL2DZ) level of theory. Electronic energy along the coordinates is represented in kcal/mol relative to [trans-22+TiCl4+Cl -]. A chloride anion was used as a base to scavenge the proton freed in the reaction.Table 2. Addition of various nucleophiles to peroxyacetal 8 a

a

  Reaction conditions: 40-46 (1 equiv.), TiCl4 or SnCl4 (0.9 equiv.), allyltrimethylsilane(3 equiv.) in CH2Cl2 at -40 °C. b Isolated yield. c Diastereoselectivities were determined by 1 H NMR. d Yield calculated over 2 steps from hemiperoxyketal precursor of acetate 46.

Table 1 . Screening of Lewis acid, stoichiometry and temper- ature on the Sakurai reaction between acetoxyperoxyketal 8 and allylTMS 9.

 1 .

	Entry	Lewis acid	Equiva-lent	Temperature	Yield a (%)	dr b (trans:cis)
	1	TMSOTf	0.1 or 1	-78 °C to rt	<10	nd c
	2	BF3.OEt2	1.0	-78 °C to rt	19	nd c
	3	SnCl4	0.9	-78 °C	13 d	50:50
	4	SnCl4	0.9	-40 °C	80	65:35
	5	SnCl4	0.9	0 °C	31	78:22
	6	SnCl4	1.0	rt	-e	-e
	7	TiCl4	0.9	-78 °C	7 d	75:25
	8	TiCl4	0.9	-40 °C	47	85:15
	9	TiCl4	1.1	-40 °C	30	91:9
	10	TiCl4	0.7	-40 °C	60	70:30

a Isolated yield. b Diastereomeric ratios were determined by 1 H NMR. c Not determined. d 50% of recovered starting material. e Decomposition.

AUTHOR INFORMATION Corresponding Author

* E-mail: laurent.ferrie@u-psud.fr ORCID Laurent Ferrié: 0000-0002-1171-205X Bruno Figadère: 0000-0003-4226-8489 Guillaume Bernadat: 0000-0001-8955-0364

Notes

The authors declare no competing financial interest.

ACKNOWLEDGMENT

A.P. thanks the MESRI for a PhD fellowship, L.N. the USTH for a financial support. We thank Karine Leblanc and Jean-Christophe Jullian (BioCIS, Châtenay-Malabry) for HRMS analysis and NMR services, respectively. Leo Goehrs from Alionis is gratefully thanked for the donation of computing hardware.