Marianne Horoyan

Anne-Marie Benoliel

Christian Capo

Pierre Bongrand

Localization of calcium and microfilament changes in mechanically stressed cells

Localization of calcium and microfilament changes in

mechanically stressed cells.

Living cells have a basic capacity to change their shape and move through the surrounding milieu (1). It is an obvious requirement that these processes be regulated. For example, if a cell sends a large lamellipodium towards some region of interest, due to the finiteness of membrane area and constancy of cell volume (2), some negative signal must limit the protrusive activity in order to avoid useless loss of energy. Also, when a cell hits a solid obstacle, this encounter must be perceived in order to initiate a direction change, even if the foreign surface is not recognized by specific membrane receptors. Finally, in multicellular organisms, it is necessary that the components of tissues endowed with a mechanical function be able to respond to exogeneous forces : thus, it is well known that arterial walls can modify their tension in response to variations of the blood pressure.

It is therefore not surprising that many authors reported on the ability of various cells to respond to mechanical stimulation. The migratory activity of isolated corneal cells was enhanced by the application of tension (3). Mechanical loading of chicken chondrocytes increased DNA and glycosaminoglycan synthesis (4). Fluid shear forces were found to induce the formation of stress fibers in human endothelial cells (5). When blood leukocytes were sucked into glass micropipettes, they displayed erratic deformations of the mechanically induced protrusion within several tens of seconds (6). Finally, turbulent but not laminar shear stress increased the turnover of vascular endothelial cells in vitro [START_REF] Davies | Proc. Natl. Acad. Sci[END_REF].

However, the mechanisms by which mechanical stimuli generated diverse cell responses remain incompletely understood. Indeed, stretch-activated cationic channels were demonstrated in vascular endothelial cells [START_REF] Lansman | [END_REF]9) or epithelial cells (10), but no direct link was demonstrated between ionic fluxes and modifications of cell behavior. In the present work, we took advantage of fluorescent labeling and digital image processing to localize calcium and microfilament changes in rat basophil leukaemia (RBL) cells subjected to mechanical aspiration in glass micropipettes. It is concluded that the imposed stress induced transient and local calcium rises with a participation of intracellular calcium stores, together with cytoskeletal changes. However, both events were not always spatially correlated, which strongly suggested that unidentified biochemical events were involved in cell responses.

MATERIALS AND METHOD

Cells. Rat basophil leukaemia cells (RBL-2H3)) were from Dr. Metzger's laboratory (NIH, Bethesda, MD (11)). They were kindly provided by Dr. J. Kanellopoulos (Institut Pasteur, Paris). They were cultured in RPMI 1640 medium (Flow laboratories, GB) buffered with 20 mM HEPES, pH 7.2 and supplemented with 10 % fetal calf serum, 2 mM L-glutamin, 100 U/ml penicillin and 100 µg/ml streptomycin. They were detached from culture dishes with 2.5 % trypsin, then washed and maintained in RPMI 1640 medium.

Fluorescent labeling. Calcium monitoring was achieved by loading cells with 1 µM Fura2/AM (12) supplied by Calbiochem (La Jolla, CA) for 30 minutes at 37°C in a solution of 20 mM HEPES, 1 mM CaCl 2 , 1 mM MgCl 2 , 5 mM KCl, 10 mM glucose, 135 mM NaCl,1 % bovine albumin, pH 7.4 (labeling buffer). They were then washed and used immediately in the same buffer.

Polymerized actin was revealed as described by Barak et al. (13) by fixing cells for 20 minutes with 3.7 % paraformaldehyde in phosphate buffer at room temperature, then labeling samples by another 20 minute incubation in phosphate buffer containing 10 U/ml 7-nitro-benz 2-oxa-1,3 diazoyl phallacidin (NBDphallacidin, Molecular Probes, Eugene, OR) and 100µg/ml lysophosphatidylcholine (Sigma).

Microscopical observation. Cells (10 6 /ml) were deposited as 50 µl aliquots on glass coverslips (22x32 mm 2 ) on the stage of an inverted IMT2 Olympus microscope equipped with a Lhesa 1036 video-amplified camera (Lhesa, Cergy Pontoise, France) with dual output. The sensitivity was 0.0015 lux. The first output was connected to a monochrome monitor (Zenith model ZVM 1230-EA) through a videotape recorder (Toshiba DV |90F) and a video timer/character generator (CG-C7S, JVC, Japan) allowing time reading with 0.1 second accuracy. The second output was connected to a PCVision+ digitizer (Imaging Technology, Woburn, MA) mounted on a PC20-III (IBM compatible) computer (Commodore business inc.). This performed real time digitization with 512x512 pixel resolution and 8-bit accuracy. The digitizer output was connected to a CDD-1402E multisync color monitor (Sony, Japan), allowing coded display with 256x256x256 colors. Images were stored on a floppy disk or a hard disk for delayed analysis. The linearity of light intensity determinations was checked as previously described [START_REF] André | [END_REF]. The microscope was modified by removing excitation filters from the blocks provided by the manufacturer and mounting combinations of excitation and neutral filters on a custom-made bar replacing the shutter used to switch off fluorescence illumination. It was thus possible to switch the excitation wavelength manually within about one second, allowing pH (15) and calcium monitoring by determination of the ratio R between fluorescence intensities obtained with two different illumination frequency domains. A laboratory-written software allowed superposition of two cell images with optimum correlation (in order to correct for a possible cell displacement during filter change), background subtraction and pixel-per-pixel intensity ratio calculation. Grynciewicz's formula (12) was used to calculate local calcium concentrations as follows :

(Ca 2+ ) i = K d (R -R min )/(R max -R) L
where K d is the affinity constant for association between fura-2 and calcium under intracellular ionic conditions (this was taken as 224 nM ( 12)). R min and R max are the ratios between fluorescence intensities at low ( 340 nm) and high (380 nm) excitation wavelength, these parameters were equal to 1.11 and 7.74 respectively under standard observation conditions (50 W mercury burner, 40X DPlanapo-UV objective). Parameter L is the ratio between fluorescence intensities measured at high wavelength excitation (380 nm) at high and low calcium concentration respectively and was equal to 0.21. Parameters R min , R max and L were obtained by studying cells incubated in buffer containing calcium and 1µM calcium ionophore ionomycin (Calbiochem), with or without an excess of EGTA to chelate free calcium.

Micropipette aspiration. We used the same methodology as was selected in a previous study made on macrophage deformability (16). Briefly, glass micropipettes were drawn out of capillary tubes (0.85 mm inner diameter ; Terumo, Tokyo, Japan) with a vertical pipette puller (David Kopff instruments, Tujunga, Ca) and enlarged to about 4 µm diameter by frontal shock against a smooth glass surface. They were then connected to a water-filled U tube manometer allowing pressure stabilization and reading with a few mm H 2 0 accuracy. Pipettes were held with a de Fonbrune type C pneumatic micromanipulator (Beaudouin, Paris) stuck on the microscope stage with a two-sided adhesive tape. The equilibrium pressure was determined by observation of the movements of free particles near the pipette mouth. Calcium monitoring was performed by subjecting Fura-2-loaded cells to a constant sucking pressure of 5 cm H 2 O for 4 minutes at 37°C (using a heating stage). The cytosolic calcium concentration was measured at regular intervals of about 15 seconds. Cells were then fixed and stained with phallacidin without being removed from the pipette. In other experiments, cells were subjected to sequential steps of aspiration with pressures of 2, 5 and 10 cm H 2 O (i.e. 196, 490 and 980 Pa) for 30 seconds each under continuous recording. The protrusion length was measured subsequently.

RESULTS

Mechanical stress induces a transient calcium rise in RBL cells.

Thirty-two cells were loaded with fura|2 and sucked into micropipettes with a negative pressure of 980 Pa. This induced the formation of a cylindrical protrusion of about 5-10µm length within a few seconds (figure 1). Intracellular calcium distributions were measured immediately before aspiration, and at regular intervals of 20-50 seconds for the following four minutes. Data were stored on floppy disks, and delayed analysis was performed with coded color display (figure 1C) or digital representation (figure 2). In most cells, aspiration caused a rapid calcium rise : indeed, whereas the maximum local concentration of free calcium was 75 nM±5.8 nM Standard Error (range 1-323) on resting cells, this rose to 269 nM±49.5 nM S.E. (range 74-1088) ten seconds after aspiration and returned to the initial value within about 3 minutes (figure 3). Further, 21 cells displayed a relative increase of the maximum local calcium concentration higher than 30 % ten seconds after the beginning of aspiration, whereas no such increase was found on ten control cells that were observed for 4 minutes. Hence, what we observed was a consequence of the inflicted stress, not spontaneous calcium fluctuations.

Cytosolic calcium increase cannot be solely ascribed to an increase of membrane permeability.

The simplest interpretation of our findings might be that membrane stretch resulted in substantial permeability A cytosolic calcium rise was visible in the same cell region 40-60 s after the onset of aspiration with a maximum level higher than 800 nM in the protrusion (C). Calcium concentrations were displayed with a color-coded scale.

Fig. 2. Calcium distribution in a mechanically aspirated cell.

A micropipet-aspirated cell was studied for fluorescence distribution after formation of a small protrusion (arrow). Using the ratio between fluorescence intensities measured with two different excitatory conditions, the local calcium concentration was calculated for each pixel and expressed as nanomoles.

increase, with subsequent calcium influx due to the high difference between extracellular and intracellular electrochemical potential of calcium ions. In order to test this possibility, we compared the calcium changes displayed by cells subjected to mechanical stress in calcium-containing and calcium-deprived media. As shown in table 1, similar calcium increases were observed under both experimental conditions. However, calcium rises were somewhat delayed in presence of an extracellular calcium chelator. Hence, some release of intracellular calcium stores must contribute the observed rise of cytosolic calcium.

Local calcium increase is often but not always located in regions of highest membrane tension.

If cell calcium increases were initiated by local membrane stimulation, they might be expected to occur primarily at sites of maximum stress, i.e. near the pipette mouth or the protrusion tip (where the radius of curvature was highest). As shown on table 2, this occured in nearly two thirds of observed cells, but some cells displayed definite calcium rise only at distance from the pipette tip. The most usual patterns of calcium distribution are exemplified in figure 4.

Table 1 Influence of extracellular calcium on cytosolic calcium rise in stressed cells

Maximum calcium level (nM) at time

Sucking cells into micropipettes resulted in cytoskeletal reorganization.

It was of interest to know whether the calcium rise we detected in stretched cells was associated to some structural or functional change. Since cytoskeletal elements are expected to play a role in cell deformation, we compared the distribution of polymerized actin in resting and deformed cells. Fourteen cells were stained with NBD-phallacidin after micropipette aspiration. All of them displayed a clearcut localized fluorescence accumulation (as exemplified in figure 1). Comparison between control and stressed cells (table 3) strongly suggested that i) no substantial actin polymerization was triggered by micropipette aspiration, since both groups of cells displayed similar labeling intensity, and ii) the apparent fluorescence concentration we reported was indeed a consequence of cell deformation, since the highest fluorescence intensity was substantially (50 %) and significantly (P<0.001 according to Student's t test) higher in these cells than in controls (table 3). Thirty two cells were sucked into micropipettes and monitored for intracytoplasmic calcium distribution. Ten and sixty seconds after the onset of aspiration, most cells (26/32 and 23/32 respectively) displayed a local cytoplasmic rise as shown. Eleven control cells and fourteen cells that had been subjected for 4 minutes to micropipette aspiration were fixed and microfilaments were stained with NBD-phallaciding. Mean cell fluorescence and maximum pixel fluorescence were then recorded under the same conditions. Mean values are shown (using arbitrary units) ± Standard Error.

Table 3 Mechanical stress induces a local concentration of polymerized actin in mechanically stressed cells

Table 4

Colocalization of cytosolic calcium rise and local microfilament accumulation in micropipette-aspirated cells.

Localization of calcium rise

Calcium rise and cytoskeletal accumulation do not always occur in the same cell region.

An absolute correlation between the localization of calcium rise and cytoskeletal accumulation in individual cells would be strongly suggestive of the existence of a direct link between both events. However, as shown on table 4, there was no strict correlation between both phenomena. Hence, calcium changes migth not be the only parameter involved in cytoskeletal reorganization.

Intracellular calcium changes do not substantially affect cell deformability.

Despite the aforementioned conclusions, in view of previous evidence on the regulation of cell cytoskeleton (17,18), it was reasonable to expect a direct relationship between intracellular calcium changes and alterations of cell deformability. This point was addressed by comparing the deformability of cells with high and low intracytoplasmic calcium. RBL cells were thus subjected to micropipette aspiration i) in control medium, ii) in presence of 10 -6 M ionomycin and iii) in presence of 10 -6 M ionomycin and 5 mM EGTA. The latter two procedures resulted in rapid rise and lowering of intracytoplasmic calcium level, as demonstrated with Fura 2 monitoring (not shown). However, as shown on table 5, both procedures induced only moderate although significant (P<0.01) decrease of cell deformability.

DISCUSSION

The goal of this work was to analyze cell responses to exogeneous stress. The first and quite unambiguous conclusion was that mechanical stress induced a complex biochemical response in rat basophilic leukaemia cells. Indeed, whereas the increase of membrane permeability induced by membrane stretchning (8, 9, 10) might be viewed as some kind of transient leakage, our finding that stress induced a cytosolic calcium rise in a medium containing a chelator of this cation implies that intracellular calcium stores were mobilized, suggesting the occurrence of a cascade of intracellular events (19). A possible mechanism would be the formation of inositol trisphosphate as a consequence of phospholipase activation, with subsequent release of nonmitochondrial calcium [START_REF] Muallem | Proc. Natl. Acad. Sci[END_REF]. Note that it is not inconceivable that mechanical tension per se might activate membrane-embedded phospholipases, since a remarkable activation of these enzymes could be triggered by a reduction of about one dyne/cm of the surface pressure of a lipid layer [START_REF] Demel | [END_REF], which is the same order of magnitude as the mechanical tension induced on the cylindrical wall of a protrusion of 2 cm radius by a sucking pressure of 1000 Pa. Another point of importance concerning calcium measurements must be emphasized : Twodimensional fluorescence images represent a convolution between three-dimensional fluorescence distributions and the point spread function of the optical system. Hence, what we called "local calcium concentration" was in fact the mean of calcium concentrations in an extended region of space. It is therefore possible that very localized and moderate calcium rises were missed in some cells.oeüIt must also be pointed out that the results we presented are in line with the previous finding by Maxfield and colleagues [START_REF] Kruskal | Proc. Natl. Acad. Sci. (USA)[END_REF] that spreading of human neutrophils was immediately preceded by a calcium spike. Our data support the view that this might be related to a change of the plasma membrane tension, a possibility that was indeed considered by the authors [START_REF] Kruskal | Proc. Natl. Acad. Sci. (USA)[END_REF].

A second conclusion is that mechanical stress induced a cytoskeletal response in RBL cells. Indeed, all micropipette-aspirated cells displayed a topological reorganization of polymerized actin as visualized with NBD-phallacidin. Since in thirteen cells out of fourteen a local actin concentration was found in the protrusion or near the pipette tip, an attractive hypothesis would be that there was a call for polymerized actin in the region of aspiration (i.e. near the pipette tip), resulting in a flow of blocks of gelled actin filaments that were sometimes stopped near the pipette mouth, resulting in local concentration increase. This view is consistent with qualitative observations made on the deformation of human melanoma cells [START_REF] André | [END_REF]. The local calcium increases we described might result in separation of these blocks following local disruption of the gelled microfilament network, possibly due to gelsolin activation (18,[START_REF] Hartvig | Cell physiology of blood Gunn[END_REF]. This view would be consistent with the lack of absolute correlation we reported between the localization of calcium spikes and cytoskeletal concentration.

Thirdly, our results strongly suggest that cells responded to exogeneous stress by active mechanical yield. Indeed, deeply perturbing cell cytoskeleton regulation by maintaining high or low value of cytoplasmic calcium resulted in moderate but significant decrease of cell deformability (table 5). It must be pointed out that increased cell stiffness was expected after calcium lowering [START_REF] Miller | [END_REF]26), not calcium increase [START_REF] Hartvig | Cell physiology of blood Gunn[END_REF], supporting the view that cytoskeletal regulation is not solely dependent on calcium ions. Further work is therefore required to correlate cell response to mechanical stress with other local events such as pH changes or protein phosphorylations. Clearly, only a detailed analysis of local cellular phenomena can allow a precise understanding of the mechanism of cell shape regulation.

Fig. 1 .

 1 Fig. 1. Calcium and cytoskeletal changes induced by mechanical aspiration of RBL cells.A single cell was sucked into a micropipet, thus inducing the formation of a visible protrusion (A). Calcium was measured repeatedly, and the cell was fixed 4 min later and stained with NBD-phallacidin to reveal microfilaments. Microscopical examination revealed a local concentration of polymerized actin in the protrusion (B). A cytosolic calcium rise was visible in the same cell region 40-60 s after the onset of aspiration with a maximum level higher than 800 nM in the protrusion (C). Calcium concentrations were displayed with a color-coded scale.

Fig. 3 .

 3 Fig. 3. Kinetics of cytosolic calcium rise in mechanically stressed cells. Twenty-two individual cells were sucked into a micropipet at time zero, and the maximum local calcium concentration was measured at regular intervals. mean values are shown. vertical bar length is twice the SE.

Fig. 4 .

 4 Fig. 4. Localization of calcium rise in mechanically stressed cells. the cytosolic calcium concentration was uniformly lower than 200 nM in resting cells (A). After aspiration, local calcium rises could be detected at distance from the pipet tip (B), in the cell protrusion (C), or near the pipet tip (D), with maximum values higher than 500 -1000 nM.

  cells were subjected to micropipette aspiration for 4 minutes under calcium monitoring, then fixed and stained with NBD-phallacidin. All cells displayed local microfilament accumulation, and ten of them exhibited a local calcium rise. The localization of both events is shown.

Table 2 Localization of calcium rise in stressed cells

 2

	Time		Number of cells with		Total
	(second)		calcium rise		No calcium rise	cell
		in protrusion near pipette tip	far from		number
				pipette
	10	3	14	9	6	32
	60	7	9	7	9	32

Table 5 Influence of calcium rise on the deformability of RBL cells Length of the protrusion induced by a pressure of

 5 Cells were sucked into micropipettes with increasing pressure for steps of 30 seconds each, and the length of the protrusion obtained after each step was measured. Mean values are shown ± Standard Error. The significance of the influence of ionomycin or ionomycin and EGTA was calculated with Student's t test and indicated in brackets. NS means : not significant at the 0.05 confidence level.

	Number of tested

Author for correspondence -Current mail address (2009) : pierre.bongrand@inserm.fr

-Mechanical Cell Stimulation -Horoyan et al.

-Mechanical Cell Stimulation -Horoyan et al.

-Mechanical Cell Stimulation -Horoyan et al.

Acknowledgment. This work was supported by the INSERM (CJF 89-07).


Miguel Angel Mejía-Morales
email: miguel-angel.mejia-morales@inrae.fr

Emmanuel Mignot
email: emmanuel.mignot@insa-lyon.fr

André Paquier
email: andre.paquier@inrae.fr

Darius Sigaud
email: darius.sigaud@inrae.fr

Sébastien Proust
email: sebastien.proust@inrae.fr

Impact of the porosity of an urban block on the flood risk assessment: a laboratory experiment

Keywords: laboratory experiment, urban flood risk, urban block porosity, LSPIV technique

Physical modelling of urban flooding usually considers that the flow is concentrated in the streets, assuming that urban blocks and individual buildings are non-porous structures. This assumption is open to criticism, as potential lateral flow exchanges through openings in the walls of an urban block (e.g. gates, windows and doors) are likely to modify the flow pattern in the block and adjacent streets. This paper reports an experimental study conducted on a 5.4 m long and 3.2 m wide physical model, representing a rectangular urban block and four surrounding streets. The focus of the study was on investigating the lateral flow exchange processes between the porous urban block and its adjacent streets during flooding for a variable urban block porosity. Eight porosity values were studied, keeping the same boundary conditions. A porosity equals zero, i.e. a flow around a non-porous block, served as a reference flow situation. For each porosity value, the impact of

Introduction

According to [START_REF] Unisdr | The human cost of natural disasters: A global perspective[END_REF], flood events increased by 39% from 2004 to 2013 with respect to the previous decade. The damage to goods and people caused by these events is particularly significant in urban settlements, mainly because of the high population density and the value of the assets.

As reported by United Nations et al. (2019), the number of people living in urban areas worldwide is increasing, and it is estimated that, by 2050, it will be the case for two thirds of the world's population. Therefore, developing methodologies to assess the urban flood hazard and the associated risk with higher precision is particularly relevant. Flood hazard is usually described by flow depth, flood extent, flow ve-locity, flood wave propagation, flood duration and the water's rising rate (de Moel et al., 2009). Among these, the most common parameters are the local velocity and flow depth, used for the prediction of building damage (e.g. [START_REF] Jakob | Vulnerability of buildings to debris flow impact[END_REF][START_REF] Lo | Building vulnerability to debris flows in Taiwan: a preliminary study[END_REF][START_REF] Maiwald | Damage and loss prediction model considering inundation level, flow velocity and vulnerability of building types[END_REF]Milanesi et al., 2018), instability of parked and transit vehicles (e.g. [START_REF] Shu | Incipient velocity for partially submerged vehicles in floodwaters[END_REF][START_REF] Xia | Formula of incipient velocity for ooded vehicles[END_REF]Xia et al., , 2014b;;[START_REF] Teo | Experimental studies on the interaction between vehicles and floodplain flows[END_REF][START_REF] Kramer | Safety criteria for the trafficability of inundated roads in urban floodings[END_REF][START_REF] Martínez-Gomariz | A new experiments-based methodology to define the stability threshold for any vehicle exposed to flooding[END_REF][START_REF] Gómez | Experimental and Numerical Study of Stability of Vehicles Exposed to Flooding[END_REF], and people's instability (e.g. [START_REF] Karvonen | The use of physical models in dam-break flood analysis[END_REF][START_REF] Jonkman | Human Instability in Flood Flows 1[END_REF]Russo et al., 2013;[START_REF] Chanson | Human body stability in floodwaters: The 2011 flood in brisbane cbd[END_REF]Xia et al., 2014a;[START_REF] Milanesi | Pedestrian hazard criteria for flooded urban areas[END_REF][START_REF] Martínez-Gomariz | Experimental study of the stability of pedestrians exposed to urban pluvial flooding[END_REF][START_REF] Arrighi | Hydrodynamics of pedestrians' instability in floodwaters[END_REF][START_REF] Arrighi | Preparedness against mobility disruption by floods[END_REF].

Urban flood studies are then more often conducted to quantify the spatial distribution of velocity and flow depth to establish flood hazard and risk maps (e.g. [START_REF] Chen | Integrated urban flood vulnerability assessment using local spatial dependence-based probabilistic approach[END_REF][START_REF] Costabile | Is local flood hazard assessment in urban areas significantly influenced by the physical complexity of the hydrodynamic inundation model[END_REF][START_REF] Galuppini | A unified framework for the assessment of multiple source urban flash flood hazard: the case study of monza, italy[END_REF].

However, studying flood events in an urban environment remains a challenge, because it requires incorporating various topographical details in the flooding model (e.g. buildings, street furniture and vehicles, sewage system, subway), and the latter must account for the complex interplay between flow and topographical and hydraulic singularities (e.g. interaction with fixed and mobile obstacles, streets-sewer network or streets-buildings flow exchanges).

Among the tools used to study these events, numerical modelling is the most widely used method, especially two-dimensional (2-D) modelling (e.g. [START_REF] Mignot | Comparison of numerical and experimental simulations of a flood in a dense urban area[END_REF][START_REF] Soares-Frazão | Two-dimensional shallow-water model with porosity for urban flood modelling[END_REF][START_REF] El Kadi Abderrezzak | Modelling flash flood propagation in urban areas using a two-dimensional numerical model[END_REF][START_REF] Guinot | Multiple porosity shallow water models for macroscopic modelling of urban floods[END_REF][START_REF] Bazin | Computing flooding of crossroads with obstacles using a 2d numerical model[END_REF], since: (i) flows within the urban area are too complex for 1-D models; (ii) the involved horizontal geometrical length-scales are often large compared to flow depths; and (iii) studies using 3-D modelling demand a high computational cost (Paquier et al., 2019).

However, the scarcity of detailed and reliable data on real-world urban flood events represents a drawback to the calibration and validation of these models [START_REF] Macchione | Extracting quantitative data from non-conventional information for the hydraulic reconstruction of past urban flood events. a case study[END_REF]. In this context, laboratory physical models are a convenient alternative, especially useful, for investigating flow patterns in complex geometries under controlled conditions [START_REF] Finaud-Guyot | Experimental insight for flood flow repartition in urban areas[END_REF].

They can provide reliable information and detailed observations at local scale, and can also be used as a benchmark tool for the calibration of numerical models.

Although real-world urban blocks and individual buildings include openings (e.g. doors, windows, gates, fences) and interior spaces (e.g. gardens, courtyards, parking lots), most experimental urban flood studies consider them as non-porous structures through which the flow cannot enter (e.g. [START_REF] Ishigaki | Hydraulic model tests of inundation in urban area with underground space[END_REF][START_REF] Araud | Modeling Flood in an Urban Area: Validation of Numerical Tools Against Experimental Data[END_REF][START_REF] Finaud-Guyot | Experimental insight for flood flow repartition in urban areas[END_REF]. However, to the best of the authors' knowledge, no study has proved that the impact of the exchanges between the street network and urban blocks on the flow characteristics is negligible, and accordingly, has to be discarded. In general terms, very few studies are dedicated to the flows entering buildings during floods, except for the study of [START_REF] Zhou | Experimental assessment of building blockage effects in a simplified urban district[END_REF] reference flow situation with a porosity equal to zero. The main aim was to assess the impact of a variable block porosity on flow depths, velocities and flow patterns in the streets and block, and on the lateral discharges through each opening. Risk maps for pedestrians in the streets and block were then deduced from the flood hazard assessment. Section 2 outlines the experimental methodology including the description of the physical model, the measurement techniques, the flow cases studied, and the flood risk criterion for pedestrians. Section 3 reports the impact of porosity on the measured flow features (water depth and velocity, exchange discharges, horizontal secondary flow cells). Section 4 discusses its impact on the related flood risk to pedestrians inside the block and in the neighbouring streets. The main conclusions are eventually drawn in section 5.

Methodology

Experimental set-up

The physical model for the study of flood risk, termed MURI, is a 5.4 m long and 3.8 m wide rectangular tilting platform, which comprises three longitudinal streets and three transverse streets, and represents an urban district (Figure 1.A). For this study, the working zone was reduced to 5.4 m × 3.2 m, focusing on a single 1.56 m long and 0.96 m wide rectangular block and four surrounding streets (upstream, downstream, right and left) of equal width, b = 0.15 m (Figures 1.B and 1.C), with two discharge inlets (upstream end of the right and left streets) and 4 discharge outlets (downstream end of all streets). The sidewalls of the block and streets are made of transparent plastic and the platform bed is made of grey PVC. The model bed slope in the longitudinal direction (aligned with the x-axis), S 0x , was set at 0.12%, and the slope in the lateral direction (aligned with the y-axis), S 0y , at zero. No building or furniture was placed within the block to maximize any potential flow through it. The porosity of the urban block walls was varied by changing the number of openings along them (with a maximum of three in each wall).

Each opening was 6 cm wide and 8 cm high, and the free-surface flow always remained below the opening top.

The total inlet discharge, Q in T = 6.5 l s -1 , was partitioned between the inflow in the right (Q in 1 = 4.5 l s -1 ) and left (Q in 2 = 2.0 l s -1 ) streets, as shown in Figure 1.C. Each inlet discharge was adjusted with an independent valve-flowmeter system, with a standard error of 3% of the flow rate. A honeycomb plastic grid was placed at the entrance of each street to straighten out the flow. At the outlet of each street, the flow fell into an outlet tank, the outlet discharge was then monitored using an electromagnetic flowmeter (OPTIFLUX 2000 by KROHNE). The four outlet discharges are denoted as 1.C. At the downstream end of each street, a vertical tail weir enables flow depths in the street network to be controlled. In the present study, the weir heights were set to get a higher flow depth in the right street than in the left street, making easier a transverse flow through the porous block (the weir height w = 4 cm at outlet 1, while w = 3 cm at outlets 2, 3 and 4).

Q out 1 , Q out 2 , Q out 3 and Q out 4 as depicted in Figure
The scale ratio in the horizontal plane, λ xy , equals 50, and the vertical scale ratio, λ z , equals 10. The model then represents in the real-world an urban block of 78.0 m × 48.0 m and 7.5 m wide streets, with 3 m wide gates, and flow depths of about 0.60 m. This difference in scale ratios leads to a distorted-scale model with a distortion ratio λ xy /λ z = 5, which ensures: i) greater flow depths, allowing greater accuracy during measurements, and ii) larger Reynolds numbers, improving the dynamic similarity with the prototype [START_REF] Chanson | Hydraulics of open channel flow[END_REF].

Measuring techniques

To answer all questions raised in section 1, the measuring devices had to be set to access: (i) the flow depth fields in the streets and within the urban block, (ii) the discharge within each street reach, (iii) the discharge entering or leaving the urban block through each opening and (iv) the velocity field over the whole measuring domain. Following subsections detail the corresponding measurement methods.

Flow depth

The 2-D field of flow depth, d, was obtained using an Ultrasonic distancemeasuring Sensor (US), with an accuracy better than 0.3 mm and reproducibility better than 0.5 mm (BAUMER UNDK 20I6914/S35A). The estimated flow depth uncertainty equals 0.65 mm. The US is fixed on a mechanical gantry system moving along both longitudinal (x-axis) and transverse (y-axis) directions. Each measurement was taken at a sampling rate of 50 Hz for 50 s (time convergence tests were carried out to define the appropriate acquisition duration, see Appendix A.1). The spatial interval between two measurements in the streets was equal to 5.0 cm and 6.5 cm in the streamwise and spanwise directions (3 measurements in the street cross-section), respectively, and around 12.0 cm along both directions within the urban block.

Porous urban block

Q out 1 Q out 2 Q out 3 Q out 4

Velocity

The flow velocity in the water column was measured using an Acoustic Doppler Velocimeter (ADV) with a side-looking probe (NORTEK Vectrino +). Its accuracy is of 0.5% of the measured value. The three instantaneous velocity components (u x , u y , u z ) were measured at each point at a sampling rate of 100 Hz for 100 s in the streets and 200 s within the urban block. These acquisition durations were defined based on time convergence tests of the ADV' signal, under various flow conditions, as presented in Appendix A.2.

Water was seeded with polyamide powder (VESTOSINT R ), with an average particle diameter of 55 µm to increase the signal-to-noise ratio. The WinADV software was used to process the ADV raw data, including a filtering step based on the despiking technique proposed by [START_REF] Goring | Despiking acoustic doppler velocimeter data[END_REF]. The sampling standard errors for the time-averaged local velocity components, U x , U y and U z are 0.20 cm s -1 (∼ 0.4%), 0.06 cm s -1 (∼ 1.5%) and 0.10 cm s -1 (∼ 3.7%), respectively in the streets (these errors were estimated based on 20 times series of 100 s each at the same measuring point at 3 different locations), and 0.13 cm s -1 (∼ 2.0%), 0.05 cm s -1 (∼ 23.3%) and 0.04 cm s -1 (∼ 10.5%), respectively within the urban block (20 times series of 200 s at 1 location).

The surface velocity in the streets and within the block was measured using the Large Scale Particle Image Velocimetry technique (LSPIV). In previous studies, this technique proved to be reliable for a laboratory use (e.g. Muste et al., 2000;[START_REF] Kantoush | Lspiv implementation for environmental flow in various laboratory and field cases[END_REF], being able to accurately measure small velocities in shallow-depth flows [START_REF] Meselhe | Large scale particle image velocimetry for low velocity and shallow water flows[END_REF], and to properly distinguish large-scale and small-scale flow structures [START_REF] Fujita | Large-scale particle image velocimetry for flow analysis in hydraulic engineering applications[END_REF]. Wood shavings with diameters ranging from 1 to 4 mm were used as free-surface tracers. This light and pale material sharply contrasted with the dark grey colour of the model bed. A video camera (Panasonic, HC-V770) was placed 2.8 m above the experimental set-up, with the optical axis perpendicular to the model bed. The spatial resolution of the camera was 1920 px × 1080 px, with a recording rate of 25 frames per second. In It should be mentioned that seeding the flow at only one location to measure surface velocities over the entire domain was found to be inappropriate.

In this case, a large seeding generates clogging in small velocity areas and along the main streets, while a limited seeding does not deliver sufficient tracers in the upstream (transverse) street and within the urban block. The best procedure arising from preliminary tests was actually to perform various videos with different seeding locations for a given flow case (a procedure only possible under steady flow conditions). Seeding the flow at the entrance of the right and left streets, a first video recorded the tracer movements in the right, left and downstream streets. Seeding at the entrance of the upstream street, a second video recorded the tracers in this street. Last, seeding the flow near the block openings (on the street side), a third video was taken to measure surface velocity within the urban block. Application of the LSPIV technique was then performed in each of these three areas independently, and the resulting surface velocities were finally plotted on the same map.

The agreement in velocity magnitude and velocity direction at the intersections of the three zones gave confidence in the quality of the surface velocity measurement.

Finally, to validate the surface velocity results, the velocity measured by LSPIV was compared to ADV velocity. Two types of ADV velocity data were considered here: near-surface velocities and depth-averaged velocities.

Within the block, the fair agreement of the LSPIV velocities with these two types of ADV velocity data proves that flow is mainly two-dimensional (see figure B.16 in Appendix B). In the streets, although velocity magnitude and recirculating flow areas are adequately captured by LSPIV, the results in some areas near the crossroads appear to be less accurate, mainly due to the presence of strong flow depth fluctuations. In addition, the slight decrease in velocity when approaching the walls in some areas was not observed either (see figure B.17 in Appendix B). Overall, the velocities obtained with the LSPIV technique in the streets are slightly lower than the near-surface ADV data, mainly due to the clogging of the tracers. A video of the tracers' motion used for LSPIV will be available on a web site before publication.

Discharge

The flow velocity within the water column was measured at 9 to 10 elevations (depending on flow depth) and at 15 lateral positions across the wetted area in a street. The discharge in a street reach was then computed by integrating the ADV velocity data across the street as follows:

Q st = b 0 d 0 U x dz dy, for x-axis-oriented streets (1)
or

Q st = b 0 d 0 U y dz dx, for y-axis-oriented streets (2)
where Q st is the discharge in the street reach, U x and U y are the local timeaveraged velocity components along the x-axis and y-axis, respectively. We should keep in mind that the inlet and outlet discharges were measured in the pumping loop system using electromagnetic flowmeters. Then, based on the mass conservation law at each crossroad and each opening, the number of cross-sections over which the discharge had to be computed by Equation 1or 2 from the ADV data was set just sufficient to assess the discharge within each street reach and through each opening. Additional cross-sectional ADV measurements were performed to compute discharges (with Eq. 1 or 2) and verify that they were in agreement with discharges obtained using the mass conservation law.

While the velocity field was measured as close as possible from the bed, lateral walls and free-surface, areas along all four boundaries of a street crosssection remained blind with no available velocity measurement. To estimate the discharge in Equation 1 or 2, an extrapolation of the measured velocity field was thus required with a slip condition applied at the free-surface and a no-slip or an average between slip and no-slip conditions applied along the bed and lateral walls (for details, see Appendix C).

Finally, it should be reminded that the estimate of the discharge at a given cross-section in a street network remains a challenging task, even though innovative techniques tend to arise [START_REF] Finaud-Guyot | Experimental characterization of various scale hydraulic signatures in a flooded branched street network[END_REF]. Preliminary tests were conducted to compare the discharge estimated by Equation 1or 2 with the discharges measured by the electromagnetic flowmeters, located upstream of the inlet tanks and downstream of the outlet tanks, obtaining an average error of 1.5%. Therefore, although the method requires assumptions to cover the blind zones near the boundaries (bed, walls and flow surface), as well as the inconvenience of using an intrusive instrument (ADV) in a narrow cross-section, the results seem to be fairly reliable.

Flow conditions and experimental cases

The experiments were conducted under steady flow conditions and subcritical regime. The hydraulic boundary conditions, i.e., inflow discharges and heights of the tail weirs, were kept constant from one porosity value to another.

The porosity along each wall was defined as:

ψ = N • L op L i ; i = {x, y} (3)
where ψ is the wall porosity, N is the number of openings along the wall, L op is the length of the opening and L i is the total length of the wall. The flow cases and the associated porosity values are reported in Table 1. Only symmetrical distributions of the wall porosity were considered: the same value along right and left streets; and the same along the upstream and downstream streets.

The case C00-00 with a non-porous block, as mostly considered by previous works in the literature, serves as a reference flow situation. The extreme case 100-100, without urban block, represents an urban configuration of a main square. In between, a small porosity (a single opening along a wall) and a large porosity (three openings along a wall) are both studied with six cases featuring the same porosity along face-to-face walls, along x-axis direction (C00-04 and 00-12), y-axis direction (C06-00 and C19-00), and finally along both directions (C06-04 and C19-12).

Table 1: Values of the wall porosity ψ (Eq. 3), and number of openings along each wall, N , for the eight flow cases. Over the past 50 years, several studies have been conducted with real people to estimate their threshold of instability in flood flows (e.g. [START_REF] Foster | Stability of children on roads used as floodways[END_REF][START_REF] Takahashi | Experimental study on people's safety against overtopping waves on breakwaters[END_REF][START_REF] Karvonen | The use of physical models in dam-break flood analysis[END_REF][START_REF] Jonkman | Human Instability in Flood Flows 1[END_REF]Russo et al., 2013;[START_REF] Martínez-Gomariz | Experimental study of the stability of pedestrians exposed to urban pluvial flooding[END_REF], with real people and using a concrete monolith representing a real-size person (e.g. [START_REF] Abt | HUMAN STABILITY IN A HIGH FLOOD HAZARD ZONE[END_REF], using scale models (e.g. Xia et al., 2014a), which is a more conservative approach that may well represent the lower limit of people's stability, or by observations made during real flood events (e.g. [START_REF] Milanesi | Pedestrian hazard criteria for flooded urban areas[END_REF]. The results of each study showed a significant scatter, and this was of course expected, as the instability threshold can be influenced by many parameters defining human beings (e.g. the weight, height, age, strength, skills, psychological characteristics), as well as the conditions (e.g. experimental set-up, protective equipment, clothing of subjects) and methodology (e.g. subject standing or walking, criteria for instability) carried out in the various studies. • Low, very few pedestrians exhibit instability (up to 2% of the total data set).

• Moderate, some pedestrians exhibit instability (up to 20% of the total data set).

• Significant, many pedestrians exhibit instability (up to 50% of the total data set).

• High, most pedestrians exhibit instability (above 50% of total data set).

The estimate of the local level of risk for pedestrians requires to firstly pass the results from the physical model scale to the real-world prototype scale, using Froude similarity, F r m = F r p [START_REF] Chanson | Hydraulics of open channel flow[END_REF][START_REF] Heller | Scale effects in physical hydraulic engineering models[END_REF], we have the following ratios:

U p U m = λ 1 2 z
for velocity (4)

d p d m = λ z for flow depth (5)
where subscripts m and p correspond to the model and the prototype respec-

Measured flow features

Flow depth

Figure 3 shows the spatial distribution of flow depth, d, in the streets and urban block for all cases. Putting aside the case without block (C100-100), the flow depth ranges from 5 cm to 7.5 cm (0.50 m -0.75 m in the prototype) for all flow cases. The largest flow depths are observed in the right street, due to both the high inflow discharge in this street and the backwater effect due to the 4 cm high tail weir located at the outlet of this street (Figure 1.C.). Inside the urban block, as the free-surface is almost horizontal, the flow depth slightly increases along the x-axis due to the longitudinal bed slope of the model.

Interestingly, the flow depth within the urban block can differ from the flow depth in the adjacent streets. In the right street, the flow depth is higher than in the block (up to 10% at x = 3.25 m for cases with a porosity along the upstream and downstream block walls only, i.e. cases C06-00 and C19-00). In contrast, the flow depth can be smaller in the downstream street than in the block, e.g. by 14% at y = 0.30 m for cases with a porosity along the right and left block walls only (C00-04 and C00-12).

Figure 4 shows the relative difference in flow depth, ∆d, for each case with respect to the reference case (C00-00), defined as:

∆d = d -d ref d ref × 100 (6)
where d ref refers to the flow depth of the reference case, C00-00. In the streets surrounding the urban block, the relative difference in flow depth, ∆d, can reach up to -7% in the right street and 12.5% in the downstream street (case All the discharge values are shown as a percentage of the total inlet discharge (Q in T = 6.5 l s -1 ). In the streets, the direction of the flow is the same for all cases, i.e. from upstream to downstream in the two longitudinal streets, and from right to left in the two transverse streets. In contrast, the direction of the exchange flow through the openings may vary from one case to another.

Discharges and bulk-velocity in the streets

Regarding the discharge magnitude, when using case C00-00 as a reference flow situation, Figure 5 shows that the change in porosity: i) significantly affects the discharges in the streets surrounding the urban block; ii) significantly affects the discharge entering the block, which logically increases with an increasing porosity; and iii) hardly alters the outlet discharges, putting aside the extreme case without block (C100-100).

The relative differences in discharge in the streets, ∆Q st , with respect to the reference flow case, are shown in Figure 6. They are computed at the upstream end of the four surrounding streets. The relative difference ∆Q st increases with block porosity, for instance, for cases C00-04 and C00-12, ∆Q st = -40% and -70%, in the upstream street, ∆Q st = -24% and -36% in the left street, and ∆Q st = 6% to 10% in the right street, respectively.

The same tendency is observed when comparing cases C06-00 and C19-00, or cases C06-04 and C19-12. The exchange discharges through the block openings also increase with the porosity (see Figure 7). However, no tendency arises for the intrusion discharge as a function of the porosity. For instance, if we compare 3 pairs of cases where the porosity is increased by 200%, the increase in discharge is 107% from C00-04 to C00-12, 830% from C06-00 to C19-00 and 70% from C06-04 to C19-12.

It is also interesting to investigate the influence of the porosity distri-bution for a fixed total number of openings along the block walls. For two openings (cases C00-04 and C06-00), Figure 7 indicates that the discharge through the urban block is greater, by approximately 240%, with openings in the right and left walls than with openings in the upstream and downstream walls. The same result holds for 6 openings, when comparing cases C00-12 and C19-00, with a higher exchange discharge of 40% when the openings are located in the left and right streets. Hence, the exchange discharge between streets and block does not depend only on the porosity value. This is a more complex process, depending on the location of the openings, the flow orientation through these openings, the flow circulation within the block, and flow depths and discharges in the surrounding streets.

Finally, when moving away from the block, the outlet discharges are hardly affected by a change in porosity, the flow distribution among the four outlets is rather constant from one case to another, when putting aside the extreme case without block (C100-100), as shown at the top right of Figure 5.

The maximum variation with respect to the reference case remains limited to around 2%. To verify whether this was due to the imposed weir heights, additional experiments were conducted (for detailed information see Appendix D), by changing the hydraulic boundary conditions (inflow discharge distribution between left and right streets, and the height of the weirs) and the longitudinal and transverse slopes. The results obtained are similar as in the main experiment: the urban block porosity does not significantly impact the discharge distribution among the four outlets. The latter is mainly driven by the presence of the urban block, irrespective of the porosity value of its walls. The bulk velocities in the streets for the six cases with a porous block are now compared with those of the reference case. Figure 8 shows the relative difference in bulk velocity (∆U x b and ∆U y b , as appropriate) for all the streets. In the streets surrounding the block, the bulk velocities considerably vary with respect to the reference case, and this variation increases with an increasing porosity. Among the six cases presented in the figure, for all the streets, the larger velocity difference from the reference case corresponds to cases with greater porosity, i.e. cases C00-12, C19-00 and C19-12. The biggest differences are observed in the upstream street, with maximum differences between 65 and 70% for cases C00-12, C19-00 and C19-12. As the variation in flow depth in the streets with respect to the reference case is limited (Section 3.1), the significant variation in velocity observed here is mainly due to the variation in discharge in the streets.

Surface velocity and recirculation flow patterns

Figure 9 shows the spatial distribution of the time-averaged surface velocity magnitude, U s , along with the time-averaged streamlines, in all accessible areas. For all cases, the surface velocity magnitude ranges from 0 to about 60 cm s -1 (0.0 -1.9 m s -1 at the prototype scale). The highest velocity magnitude is observed in the right street due to the high inflow discharge at the entrance of this street. The velocity in the left street is three to four times lower. The upstream street exhibits one or two recirculating flow areas (depending on the flow case) induced by the shearing with the flow in the right street, and on average, the flow along this street is the slowest among all the streets. The downstream street is characterized by a wide range of velocity magnitude (from 0 to 50 cm s -1 ), with the highest velocities mainly located along the right wall, opposite to the block under study. Besides, the velocity magnitude within the urban block is significantly smaller than in the streets, about 20 cm s -1 maximum (0.63 m s -1 at the real-world prototype scale), a third of the maximum velocity on the streets.

Within the urban block, from two to five recirculating flow areas can be observed. The spatial distribution and the size of the recirculating flow cells are mainly driven by the direction of the jets through the openings. For instance, case C00-04 shows two cells, nearly symmetrical, on each side of the entering jet. In contrast, case C06-00 (with the same number of openings but aligned with the longitudinal direction) shows a main recirculating flow cell and a smaller secondary one on the right side upstream. These results are in agreement with those presented in several studies on shallow reservoirs (e.g. Vertical shaded bands indicate the location of the openings along the urban block walls. [START_REF] Dewals | Experimental and numerical analysis of flow instabilities in rectangular shallow basins[END_REF][START_REF] Dufresne | Classification of flow patterns in rectangular shallow reservoirs[END_REF][START_REF] Goltsman | Flow pattern of double-cavity flow at high reynolds number[END_REF]. The difference in the flow pattern between C00-04 and C06-00 is partly due to the length-width ratio of the reservoir, which is higher for C06-00, and to the exchange flow rate magnitude (three times higher for C00-04). A similar trend is observed for cases C00-12 and C19-00, with the same number of openings, but along opposite axes: case C00-12 exhibits two main recirculation cells (one larger than the other), plus three small recirculation cells driven by the jets through the right wall; however, C19-00, exhibits a single recirculation cell and three much smaller ones, two upstream and one downstream.

Finally, case C06-04 comprises two main recirculation cells and a small one upstream, while case C19-12 comprises two main recirculation cells and three small ones next to the right wall. As expected the higher number of openings increases the number of recirculation cells. We can thus conclude that the flow pattern inside the urban block depends on its length-width ratio (length = main jet direction), the magnitude of the jets, the number of openings (porosity value) and their locations (porosity distribution).

In absence of urban block (case C100-100), two recirculating flow cells of similar size are generated. Contrary to what is observed within the block, here the flow velocity in the recirculation cells does not decrease as drastically compared to the streets velocity, mainly in the downstream cell. Amongst all cases, here is where the highest average velocities are found.

Flood risk to pedestrians

Assuming that the surface velocity (calculated with LSPIV) is equal to the depth-averaged velocity (valid assumption according to figures shown in the Appendix B), using the spatial distribution of local flow depth and applying the Froude similarity detailed in Eqs. ( 4) and ( 5), a 2-D map of flood risk level for pedestrians was built for each flow case (Figure 10). This enables to assess the impact of the urban block porosity on the risk level.

The latter is defined by the criteria proposed in Figure 2.

For each flow case, the flood risk ranges from low to high, the highest risk being located in the right street due to the high velocity and flow depth along this street. The risk level is also important in the downstream street near the right sidewall, with strong flow velocities (even in absence of block, as it is the main path of the high-speed stream as previously mentioned). In contrast, the level of risk inside the block is small due to the very low velocity in this open area.

Figure 10 also shows that block porosity can enhance flood risk level at one specific location while reducing it at another. For instance, when comparing C00-12 with C00-00, the risk decreases in the upstream street but increases in the right street. This same tendency is observed in these streets, to a greater or lesser extent, for the other cases, except for case C19-00, where a local increase in the level of risk is predicted in the vicinity of the openings in the upstream street. For the other streets, only limited and local differences in the level of risk are predicted, mainly in the vicinity of the openings, as for instance, in the downstream street of case C19-12, whit a higher level of risk. Within the urban block, the modifications of the level of risk are mainly due to changes in velocity, since flow depths are almost the same throughout the area for all cases. The areas of greatest risk occur near the openings along the incoming flow jets. Therefore, the impact of porosity on the flood risk increases when porosity increases, but this is spatially limited to to the vicinity of the openings.

Conclusions

Urban flood flows were experimentally investigated on a 5.4 m long and 3.2 m wide physical model, representing a rectangular urban block and four adjacent streets. The focus of the study was on assessing the effects of the porosity of the urban block walls (openings such as gates, windows and doors) on the spatial distribution of flow depth and velocity in a street network of limited spatial extent. The effect of the block porosity on the flood risk to pedestrians was also estimated.

Eight flow cases have been studied: a reference case with a non-porous urban block; six cases varying the porosity value and the spatial distribution of the porosity along the block walls; and an extreme case without block. For each case, the flow depth and surface velocity were measured in the streets and within the block. The discharge in each street reach and the exchange discharges between block and streets were also measured.

Block porosity was found to have a small influence on the spatial distribution of flow depths. In the streets surrounding the block, the average difference in flow depth (compared to the reference case) is approximately of 1.5%, and the maximum difference of 12%. When moving away from the block, these two percentages fall at 1% and 3%, respectively. It should be noted that the flow depth can strongly vary from either side of a block wall, i.e. between the block and the street: from -14% (smaller flow depth in the street) to +10% (higher flow depth in the street). This result questions the common practices to consider the flow level in the building equal to that in the adjacent street to estimate the potential damages of a flooding scenario.

The impact of the block porosity is far more significant on the local bulk velocity and discharges in the streets surrounding the block (changes in flow discharge up to 70% compared with the reference case). Inside the block, the value and distribution of the porosity have a significant influence on the flow pattern. The number and size of the recirculating flow cells are mainly driven by the magnitude and locations of the exchange inflows and outflows between street and block. However, when moving further away from the block, the influence of the porosity is limited, similar to that observed for flow depths, and could therefore be neglected.

Last, the variation of block porosity was found to modify the flood risk to pedestrians only locally near the openings, both in the street and block.

As a result, if assessing the flood risk at the scale of a building entrance (one address) is required, it is recommended to take into account the porosity of the buildings and urban blocks when performing risk maps. When assessing the risk at a more global scale, present results seem to indicate a limited impact of the porosity; still this result will have to be confirmed by further studies. per second the velocity field of two cases (C19-12 and C100-100), with increasing durations (from 10 s to 180 s) and averaging in time the surface velocity over the entire area. The convergence criterion was the duration where the velocity difference for each point of the velocity field with respect to the velocity of the total recording time (t = 180 s) is equal or less than 1 cm s -1 , for at least 80% of the total number of points in the measuring grid.

The time-averaged velocity difference for each point in the velocity field was computed with the following expression:

| ∆U s (n (t) ) |= | 1 n (t) n (t) i=1 u i - 1 n (t=180) n (t=180) i=1 u i | (A.
3)

The convergence was obtained earlier within the block, after 10 s (as

indicated

  , who represented buildings as square aligned and staggered obstacles, over a plain, with square open windows, and the study of Sturm et al. (2018), who represented them as real-world building shapes, over a floodplain, with open windows and doors. As the lateral flow exchanges between urban blocks and streets have been little studied, we took a closer look on these physical processes based on a laboratory experiment. It was conducted using a tilting physical model termed MURI (Maquette Urbaine pour l'étude du Risque d'Inondation, i.e. urban model for the study of flood risk), at the Hydraulics and Hydro-morphology Laboratory of INRAE centre Lyon-Villeurbanne, France (Figure 1.A). The focus was on the exchanges between one single porous urban block and four adjacent streets (Figures 1.B and 1.C). The openings in the urban block walls stand for wide gates. Eight values of porosity were studied, including a

Figure 1 :

 1 Figure 1: (A) General overview of the urban model for the study of flood risk, MURI (B) Zoom on the urban block with adjustable porosity (in picture the largest possible porosity). (C) Sketch and dimensions of the experimental set-up with the largest possible porosity, i.e. with 12 openings, as for case C19-12 (top and side view).

  addition to natural light, four led lamps with an adjustable light intensity were used along with light diffusion screens to light up the set-up. The free Fudaa-LSPIV software co-developed by EDF/INRAE was used to process the videos and compute the time-averaged surface velocities. The required recording duration was 60 s (see time convergence tests of the 2-D distribution of time-averaged velocity in Appendix A.3).

  Risk criterion for pedestrians For each flow case, the local flow depth and depth-averaged velocity together (hazard) with the vulnerability of pedestrians to flooding enable the risk level to be assessed. The vulnerability was determined based on the Product Number, P N = U d, where U is the depth-averaged velocity magnitude and d the flow depth.

  [START_REF] Cox | Australian rainfall and runoff revision project 10: appropriate safety criteria for people[END_REF] proposed vulnerability curves based on people instability data sets available at that time. However, in the last 10 years additional studies have been carried out, mainly exploring conditions of instability in shallow flow with high velocities, common during floods in urban areas (e.g.Russo et al., 2013; Xia et al., 2014a;[START_REF] Martínez-Gomariz | Experimental study of the stability of pedestrians exposed to urban pluvial flooding[END_REF]. These studies, as well as experiences acquired and observations made by[START_REF] Chanson | Human body stability in floodwaters: The 2011 flood in brisbane cbd[END_REF], suggest that the people's instability in urban areas during floods begins at lower flow depths and velocities than those reported in previous studies. Therefore, following a procedure similar to that performed by Cox et al. (2010), a new criterion of the risk to pedestrians during flooding in urban areas is proposed based on the available experimental data and field observations on people's instability, and on various guidelines for the safety of people during flooding. Three Product Number thresholds are proposed: first, P N = 0.3 m 2 s -1 , defines the lower limit of people's stability according to Xia et al. (2014a) and Abt et al. (1989) (results obtained using the concrete monolith), up to d = 0.7 m, based on the curve for critical self-evacuation proposed by Ishigaki et al. (2009) and up to U = 2.0 m s -1 , based on the limit of people's stability at small flow depths found by Russo et al. (2013) and Martínez-Gomariz et al. (2016); second, P N = 0.7 m 2 s -1 , is the upper limit ofXia et al. (2014a) results and where the first signs of people's instability begin for studies conducted by[START_REF] Abt | HUMAN STABILITY IN A HIGH FLOOD HAZARD ZONE[END_REF],[START_REF] Takahashi | Experimental study on people's safety against overtopping waves on breakwaters[END_REF] and[START_REF] Karvonen | The use of physical models in dam-break flood analysis[END_REF], up to d = 0.9 m and up to U = 2.70 m s -1 , which represents approximately the mid-point in the range of velocities found for people' instability at small flow depths found by Russo et al. (2013) and Martínez-Gomariz et al. (2016); and third, P N = 1.0 m 2 s -1 , corresponds to approximately the 50% limit of instability cases of the total data set, up to d = 1.2 m, proposed by Cox et al. (2010), being the largest flow depth tested in the available data series, and up to U = 3.5 m s -1 , which is approximately the upper limit of people's stability at shallow flow according to Russo et al. (2013) and Martínez-Gomariz et al. (2016), i.e. above this limit almost all pedestrians exhibit instability. All these vulnerability curves are shown in the flood risk diagram for pedestrians, Figure 2, and they define four flood risk levels, which are as follows:

Figure 2 :

 2 Figure 2: Proposed flood risk diagram as a function of the product number, P N = U d, defining four levels of risk for adult pedestrians. Based on available experimental data and field observations on people instability, and recommended guidelines for the safety of people during floods.

Figure 3 :

 3 Figure 3: Flow depth d in the streets and within the urban block for all flow cases.

Figure 4 :

 4 Figure 4: Relative difference in flow depth, ∆d (Eq. 6), in the streets, with respect to the reference case C00-00. Cool colors indicate areas where flow depths are greater than in the reference case, while warm colours indicate areas where flow depths are smaller.

Figure 5

 5 Figure5shows an overview of the discharges in the streets and urban block for all cases. The inlet and outlet discharges (monitored by electromagnetic flowmeters) are indicated by shaded boxes; the discharges computed using Equation (1) or (2) are highlighted in purple and blue colours, depending on the considered extrapolation method, detailed in Appendix C (no-slip condition or an average between slip and no-slip conditions); and the discharges computed from the mass conservation equation are highlighted in orange colour. In the middle of the block, the intrusion discharge is highlighted in pink, obtained as the average between the sum of discharges entering (green arrows) and leaving (red arrows) the block along with the corresponding uncertainty that includes the errors coming from the measuring instruments (electromagnetic flowmeter and ADV) and from the discharge computation method. The uncertainty was estimated as half the difference between entering and leaving discharges. Due to additional ADV measurements, several values can be obtained; the largest one is shown in Figure5.

Figure 5 :

 5 Figure 5: Discharges in the streets, urban block, and inlet and outlet discharges for all flow cases. All the discharge values are presented as a percentage of the total inlet discharge, Q in T = 6.5 l s -1 . The inlet and outlet discharges (measured with the electromagnetic flowmeters) are indicated by shaded boxes. The discharges computed from Eq. (1) or (2) are indicated by purple and blue boxes, depending on the boundary condition used to compute them, an average between slip and no-slip and no-slip, respectively. The discharges deduced from mass conservation are highlighted in orange colour. The intrusion discharge in the block and the associated uncertainty are highlighted in pink colour.

Figure 6 :

 6 Figure 6: Relative difference in discharge with respect to the reference case, ∆Q st , at the upstream end of each street surrounding the urban block (i.e. at x = 3.09 m for the right and left streets and at y = 0.15 m for the upstream and downstream streets).

Figure 7 :

 7 Figure7: Flow rate through the urban block for six flow cases, as a percentage of the total inflow discharge, Q in T = 6.5 l s -1 .

Figure 8 :

 8 Figure 8: Relative difference in bulk velocity with respect to the reference case, ∆U xb and ∆U yb , in the longitudinal direction (x-axis) and transverse direction( y-axis), respectively.

Figure 9 :

 9 Figure 9: Time-averaged surface velocity magnitude, U s , and streamlines in the streets and within the urban block (derived from LSPIV data).

Figure 10 :

 10 Figure 10: Flood risk maps for adult pedestrians, for each flow case, obtained by scaling flow depths and velocities at the real-world prototype scale using Froude similarity (Eqs. 4 and 5), and with λ z = 10.

  Figure A.12: Time convergence of the time-averaged streamwise velocity at 14 various locations. Convergence is reached when %Error ≤ ± 3%. The shaded area indicates the range ± 3%.

  Figure A.13: Time convergence of the time-averaged surface velocity difference, ∆U s , for various recording durations, from 10 s to 120 s, for cases C19-12 and C100-100. Convergence is reached when | ∆U s | ≤ 1 cm s -1 and % Frequency ≥ 80%.

Figure D. 19 :

 19 Figure D.19: Discharge distribution at the different outlets for each set of experiments, values shown as a percentage of the total inlet discharge (Q in T = 6.5 l/s.). The set of experiments A corresponds to the experiments detailed in the paper.

Table D .

 D 2: Characteristics of the additional sets of experiments. A is the original set of experiments in this paper. of Height of the weir, w (cm) Inflow (%) S 0x S 0y experiments Out 1 Out 2 Out 3 Out 4 Q in 1 -Q in 2 (%) (%)

														1.65
														+ _
			0.78		0.86 + _				1.47 + _		1.79 + _
			+ _					1.27
								+ _
	Set A + _ 0.60 0.25 + _ 0.25 + _ 0.25 + _	4 + _ 0.54 0.83 + _ 0.94 + _	3	0.14 + _ 0.27 + _ 0.59 + _	3	3 + _ 0.87 0.54 + _ + _ 0.62	0.96 + _ 1.14 + _ 1.23 + _	+ _ 0.35 0.94 + _ + _ 0.63	0.97 + _ 1.01 0.98 + _ + _
	B	A	0	B	0	C	0	D	0	E	70 -30	F	0.12 0.00 G
	C		0		0		0		0		90 -10
	D		4		3		3		3
											70 -30
	E		0		0		0		0
														1.02 0.20
	F		4		3		3		3
											90 -10
	G		0		0		0		0
								56

Acknowledgements

The authors acknowledge the financial support offered by the French National Research Agency (ANR) for the project DEUFI (under grant ANR-18-CE01-0020).

to identify thresholds of a person's stability in a flow. Water Resources Research 52, 7793-7805. doi:10.1002/2016WR019182. Milanesi, L., Pilotti, M., Belleri, A., Marini, A., Fuchs, S., 2018 The time convergence of the US signal was tested by performing 13 independent flow depth measurements at various locations (in the streets, within the block and in specific areas with significant fluctuations in flow depth, such as crossroads). Each measurement was carried out for 400 s at a sampling rate of 50 Hz. For each measurement, the time-averaged flow depth over each partial acquisition duration was computed and compared to the time-averaged flow depth over the total acquisition duration (t = 400 s), as:

where d i is the instantaneous flow depth and n (t) is the number of samples at time t. Then, the appropriate acquisition duration was defined as the time, t, for which ∆d(n (t) ) is lower than 0.3 mm (accuracy specified by the manufacturer). As shown in Figure A.11, this duration was 50 s.

Appendix A.2. ADV velocity data

The time convergence of the ADV velocity data was tested by measuring for 600 s at a sampling rate of 100 Hz. Although the ADV is capable of measuring the three velocity components (u x , u y , u z ), we focused on the horizontal components (u x , u y ), which are used to compute the discharge in the streets and also to be compared with the velocities obtained via LSPIV.

Velocity measurements were performed at 14 locations (eight in the streets and six within the block) and for various cases (with the porous block, nonporous block and no block). We considered time convergence criterion of 3%, equal to the value of the standard error observed for the inlet discharge. The percentage error of the time-averaged velocity for each partial acquisition duration was obtained with the following expression:

where u i is the instantaneous velocity. In general, the convergence was obtained earlier in the streets (blue curves, Figure A.12) than within the block (red curves), therefore two appropriate acquisition durations were proposed, 100 s for the ADV measurements within the streets and 200 s within the block.

Appendix A.3. Surface velocity using LSPIV technique

To evaluate the appropriate video recording duration for the LSPIV technique, convergence tests were established by recording at a rate of 25 frames dition assumes an average of the previous two. Discharges computed using these three conditions (from 0.5 l s -1 to 3.0 l s -1 in different streets) were compared with the discharge readings given by the electromagnetic flowmeter. At the free-surface, the slip boundary condition is systematically applied, while for the other boundaries (bed and lateral walls), the appropriate condition is selected according to the following criteria:

• No-slip boundary condition for the cross-sectional velocity distributions where the largest velocity magnitude is concentrated in the center and it decreases towards the boundaries, see With the variability, we can notice that for all the sets the impact of the porosity on the outlet discharge distribution is relatively low, the largest variation is ± 1.79% at outlet 1 in the set of experiments F.