Feng Zhang

Prof Yu-Jun Cui
email: yu-jun.cui@enpc.fr

Nathalie Conil

Jean Talandier

Effect of fracture voids on the swelling behaviour of Callovo-Oxfordian claystone

Keywords: COx claystone, Fracture voids, Swelling behaviour, Sealing

The Callovo-Oxfordian (COx) claystone has been considered as a possible host rock for deep geological repository of high-level radioactive waste in France.

When constructing the repository, it is unavoidable to generate a fractured zone in the vicinity of excavated repository walls. In the assessment of the repository performance, it is important to investigate the role of the fractures on the swelling capacity of COx claystone and to further characterize the fractured zone evolution. In this study, the effect of fracture voids on the swelling behaviour of COx claystone was investigated by simulating the fracture voids with a space created by a limited amount of grains sandwiched between claystone disks, and by performing a series of swelling tests in oedometer under a low vertical stress (0.05 MPa) and swelling pressure tests under constant-volume condition. Results showed that, with water infiltrating into the sample with fracture voids, the grains collapsed before the swelling of claystone disks.

The whole sample was composed of swelling zones corresponding to the claystone disks with higher dry density than the expected final value, and of compression zones corresponding to the initial fractures with lower dry density. Moreover, the axial strain and swelling pressure decreased as the fracture void increased. The maximum fracture voids that might be fully filled by the swelling of COx claystone (sealing) were found to be 5.14% -7.65% without considering the long-term creep contribution in the field condition.

Introduction

The Callovo-Oxfordian (COx) claystone has been considered as a possible host rock for deep geological disposal of high-level radioactive waste by the French Radioactive Waste Management Agency (ANDRA) thanks to its favorable properties such as low permeability and diffusion coefficient, high retention capacity for radionuclides [START_REF] Andra | Synthesis -evaluation of the feasibility of a geological repository in anargillaceous formation[END_REF]. In order to assess the reliability of the host rock as a geological barrier for radioactive waste confinement in field condition, an underground research laboratory (URL) was constructed at a depth of 490 m in the 150 m-thick formation of COx claystone in Bure, France [START_REF] Armand | Short-and long-term behaviors of drifts in the Callovo-Oxfordian claystone at the Meuse/Haute-Marne Undergroud Research Laboratory[END_REF]. As excavation of the underground repository in this formation induced shear and tensile fractures, a damaged zone around the galleries was created with fractures smaller than 1 mm [START_REF] Armand | Geometry and properties of the excavation-induced fractures at the Meuse/Haute-Marne URL drifts[END_REF]. A part of this zone is normally unsaturated during the construction and exploitation of the galleries due to ventilation. It becomes progressively saturated with the up-take of underground water. Under the effect of water infiltration, the COx claystone in the fractured zone is expected to swell and to close the excavation-induced fractures, leading to a significant reduction of water transmissivity. Thereby, in the assessment of repository performance, it is important to account for the swelling behaviour of the COx claystone with fractures.

The swelling behaviour of COx claystone under the effect of fractures has been scarcely reported in literature, mainly because of the difficulty related to the sampling of fractured samples in field [START_REF] Armand | Geometry and properties of the excavation-induced fractures at the Meuse/Haute-Marne URL drifts[END_REF], as well as the relatively large variability of natural COx claystone in terms of dry density and mineralogy (Conil et al., 2018;[START_REF] Zhang | Assessment of swelling pressure determination methods with intact Callovo-Oxfordian claystone[END_REF]. On the-other hand, the self-sealing behaviour of fractured COx claystone has been widely investigated by means of gas/water permeability tests in the laboratory and in the field condition [START_REF] Davy | Permeability of macro-cracked argillite under confinement: gas and water testing[END_REF][START_REF] Zhang | Damage and sealing of clay rocks detected by measurements of gas permeability[END_REF][START_REF] Zhang | Experimental evidence for self-sealing of fractures in claystone[END_REF][START_REF] De La Vaissière | Gas and water flow in an excavation-induced fracture network around an underground drift : A case study for a radioactive waste repository in clay rock[END_REF][START_REF] Auvray | Self-sealing of claystone under x-ray nanotomography: a newly-developed triaxial compression cell[END_REF]. It was found that the gas/water permeabilities of strongly fractured COx claystone sample significantly decreased after water re-saturation, indicating a relatively high self-sealing capacity of COx claystone. This point was confirmed by the X-ray tomography technique [START_REF] Ando | Analysis of COX self sealing behaviour from x-ray computed tomography images[END_REF][START_REF] Giot | Self-sealing of claystone under X-ray nanotomography[END_REF][START_REF] Di Donna | Self-sealing capacity of argillite samples[END_REF]. Moreover, the swelling behavior of compacted sealing/backfilling materials in the presence of artificial fractures was also widely reported in literature [START_REF] Wang | Experimental study on the swelling behaviour of bentonite/claystone mixture[END_REF][START_REF] Wang | The effects of technological voids on the hydro-mechanical behaviour of compacted bentonite-sand mixture[END_REF][START_REF] Bian | Voids effect on the swelling behaviour of compacted bentonite[END_REF][START_REF] Jia | Effects of a simulated gap on anisotropic swelling pressure of compacted GMZ bentonite[END_REF]. Results show that the swelling pressure decreased as the fractures increased. Basically, the sealing of fractured claystone is a complex long-term hydro-mechanical process, which is controlled by many factors such as the extent and intensity of fractures, the swelling capability of claystone as well as the boundary conditions (e.g., the stress state, the build-up backfill pressure).

From a practical point of view, well understanding the swelling behaviour of COx claystone with the presence of fractures is helpful in analyzing the self-sealing process in the fractured zone.

In this study, a series of swelling tests were performed in oedometer on COx claystone with different fracture voids either under a low vertical stress (0.05 MPa) or under constant-volume condition, the fracture voids being simulated by a limited quantity of COx claystone grains of defined sizes, sandwiched between COx claystone disks. For comparison and further analysis, the results from the swelling and compression tests performed by [START_REF] Zhang | Assessment of swelling pressure determination methods with intact Callovo-Oxfordian claystone[END_REF] on intact COx claystone samples were considered. After the tests under constant-volume condition, the water content and dry density profiles were determined, allowing further interpretation of the swelling behaviour of COx claystone samples with fracture voids. Emphasis was put on the initial fracture void on the swelling and swelling pressure as well as the maximum fracture voids that might be sealed by COx claystone swelling, which are key questions in the assessment of deep geological repository performance of nuclear waste disposal.

Materials and methods

Materials

Undisturbed COx claystone samples were extracted at 490 m depth from the Underground Research Laboratory (URL) at Bure in France, following the direction parallel to the bedding plane that was found to be parallel to the ground surface through observation of a piece of COx claystone immersed in water. They were then covered by foil and conserved in a fully confined cell (T1), preventing water loss and soil rebounding [START_REF] Conil | How rock samples can be representative of in situ condition: A case study of Callovo-Oxfordian claystone[END_REF]. At 490 m depth, the average mineralogical composition is [START_REF] Armand | Short-and long-term behaviors of drifts in the Callovo-Oxfordian claystone at the Meuse/Haute-Marne Undergroud Research Laboratory[END_REF]: 50-55 % clay minerals, 20% tectosilicates, 20-25% carbonates and 3% other minerals (subordinate pyrite and iron oxides). The clay minerals composition contains 55% I/S (interstratified illite-smectite), 30% illite and 15% kaolinite and chlorite.

The synthetic water used in this study had the same chemical composition as the pore water of COx claystone from the ANDRA URL in Bure (Table 1).

Preparation of samples

In this study, five cores (EST56054, EST56056, EST56062, EST57173 and EST57175) with 300 mm length and 80 mm diameter were used. After opening the COx claystone from the confined cell (T1) in the laboratory, a cylinder with 50 mm diameter was drilled in the direction perpendicular to the bedding. Then, this cylinder (50 mm diameter) was cut with a scroll saw machine to prepare disks with 5 mm height for samples with fracture voids. The fracture voids for samples with two, three and four disks were simulated with a defined space created by COx claystone grains of defined sizes between the disks of 5 mm height each (see Fig. 1). The grains were obtained by crushing intact COx claystone and passing through different sieves, and their mass was kept less than 1% of the whole sample in order to minimize its effect on the global swelling behaviour of the sample. The fracture void of the sample was defined as the volume of fractures divided by the volume of the whole sample (including the volume of disks and fractures).

Experimental methods

The swelling tests on the samples with fracture voids under 0.05 MPa vertical stress were performed in a conventional oedometer. The inner surface of the metallic cell was smeared with silicone grease in order to minimize the side friction during the swelling tests, following ASTM D2435-96. The experimental programs are shown in Table 2. Two tests were performed on samples with two disks (CS(2 disks)01-02), five tests on samples with three disks (CS(3 disks)01-05) and two tests on samples with four disks (CS(4 disks)01-02), the height of each disk being 5 mm. The crushed COx grains respectively passing through sieves of 0.2-0.25, 0.315-0.4, 0.5-0.63, 0.63-0.8 and 0.8-1.0 mm were used, allowing creation of the fracture voids ranging from 1.78% to 10.68% (see Table 2). Note that swelling tests under different vertical stresses (CS(1 disk)01-04) and compression test (SC(1 disk)01) on intact samples with a height of 10 mm (see Table 2) were performed by [START_REF] Zhang | Assessment of swelling pressure determination methods with intact Callovo-Oxfordian claystone[END_REF]. To facilitate the sample installation in the oedometer cell, an initial small gap corresponding to a void ratio of 0.015 -0.02 (see Table 2) was kept between the sample and the oedometer cell. In further analysis, these initial gaps are regarded as space allowing soil free swelling [START_REF] Zhang | Assessment of swelling pressure determination methods with intact Callovo-Oxfordian claystone[END_REF]. However, for the samples with fractures, due to the difficulty of calculating the void ratio corresponding to initial gaps, these initial gaps together with the fractures created by grains contributed to the initial fracture voids as well as the global void ratios. Moreover, the void ratio corresponding to the filter paper thickness (0.09 mm) was equal to 0.009. Thus, the effect of such small void ratio on the swelling behaviour during wetting was ignored.

It is worth noting that to facilitate the synthetic water infiltration, the top, bottom and lateral surfaces of sample were covered with filter papers. With water infiltration from the bottom of the cell (the water head was about 0.5 m), water will go through the filter papers into the bottom, and then through the lateral filter paper to the fractures and the top surface, prior to the disks. Thereby, the adopted water infiltration condition was close to the field condition: water mainly infiltrates into fractures prior to being adsorbed by claystone. The axial displacement was monitored using a LVDT (Linear Variable Differential Transformer), and the deformation was considered as stabilized when the axial strain rate was less than 5×10 -4 /8 h (AFNOR, 1997).

The swelling pressure was determined by the constant-volume method, and the experimental setup is presented in Fig. 2. The sample covered with filter papers was placed between two porous stones in a stainless cell with a diameter of 50 mm. The synthetic water was infiltrated from the bottom of the cell and a force transducer was mounted to measure the axial force/swelling pressure. The experimental program is shown in Table 3. Three tests were performed on samples with two disks (CV(2 disks)01-03), two tests on samples with three disks (CV(3 disks)01-02) and one test on sample with four disks (CV(4 disks)01). The initial fracture voids varied from 2.44% to 7.65% (Table 3). Note that the swelling pressure test CV(1 disk)01 on intact sample with a height of 10 mm was performed by [START_REF] Zhang | Assessment of swelling pressure determination methods with intact Callovo-Oxfordian claystone[END_REF]. When the swelling pressure was stabilized, the test was considered as completed [START_REF] Villar | Influence of temperature on the hydro-mechanical behaviourof a compacted bentonite[END_REF].

It is worth noting that the sealing of excavation-induced fractures (smaller than 1 mm) is a complex long-term hydro-mechanical process [START_REF] Armand | Geometry and properties of the excavation-induced fractures at the Meuse/Haute-Marne URL drifts[END_REF], which is controlled by many factors such as the extent and intensity of fractures, the swelling capability of claystone as well as the boundary conditions (e.g., the stress state). This is the reason why the different grain sizes (0.2-0.25 mm, 0.315-0.4 mm, 0.5-0.63 mm, 0.63-0.8 mm, 0.8-1.0 mm) and the different quantities of disks (2, 3 and 4), as well as the two boundary conditions (constant-stress 0.05 MPa and constant-volume condition) were considered in this study.

After the swelling tests under constant-volume condition, the samples were extracted from the oedometer cell and then divided into several layers (see Fig. 1). For the sample with two disks (Fig. 1a), layers 1, 2 included the top and bottom disks, respectively, while layer 1.5 included the top and bottom disks, and the fracture voids in between. Corresponding definitions were adopted for the samples with three and four disks (Figs. 1b and1c). Each layer was then cut into small pieces for the water content and dry density determinations. The water content was determined by oven drying the samples at 105℃ for 24 h and the dry density was determined by immersing the samples into a non-wetting hydrocarbon liquid called Kerdane [START_REF] Delage | Suction and in-situ stresses of deep Boom clay samples[END_REF][START_REF] Tang | Experiment evidence on the temperature dependence of desiccation cracking behavior of clayey soils[END_REF][START_REF] Tang | Desiccation and cracking behaviour of clay layer from slurry state under wetting-drying cycles[END_REF][START_REF] Zhang | Effect of degree of saturation on the unconfined compressive strength of natural stiff clays with consideration of air entry value[END_REF]. Accordingly, the water content and dry density profiles were determined following the definitions of layers shown in Fig. 1.

All the tests were performed at a controlled temperature of 20 ± 1°C.

Experimental results

Fig. 3 shows the results from tests CS(1 disk)01-04 on intact samples [START_REF] Zhang | Assessment of swelling pressure determination methods with intact Callovo-Oxfordian claystone[END_REF]. It can be observed that the axial strain slowly increased in the first 0.001 day (1.4 min), then quickly increased till approximately 0.3 day (432 min). Afterwards, the axial strain slowly increased until stabilization. In addition, the stabilized axial strain decreased with the increase of vertical stress. Fig. 4a presents the compression curve from test SC(1 disk)01 on intact sample [START_REF] Zhang | Assessment of swelling pressure determination methods with intact Callovo-Oxfordian claystone[END_REF]. It appeared that, upon wetting, the sample swelled under a low vertical stress of 0.05 MPa. After the swell completion, further compression gave a normal consolidation curve (NCL) that allowed determination of the compression index in the range of stress from 2 to 16 MPa (Cc = 0.0366). In addition, by approximating each curve with two straight lines, the yield stress σ ' y was determined, equal to 0.55 MPa, as indicated by the arrow in this figure. For further analysis, the compression curve shown in Fig. 4a was used to determine the oedometric modulus Eoed as follows:

= - = -ℎ = -1 + (1)
where hi and e0 are respectively the initial height and void ratio of the sample, dεv, dh and de are respectively the volumetric strain, height and void ratio changes under an increment of vertical stress dσv. GMZ01 bentonite: with the increase of vertical stress, the Eoed decreased at the beginning and then linearly increased when the stress was higher than the yield stress in a logarithmic scale. These observations suggest that the Eoed is a good indicator of soil yielding. Moreover, a linear relationship between the oedometric modulus and the vertical stress was obtained after yield.

The results from tests CS(2 disks)01-02 on samples with fracture voids are shown in Fig. 5 in terms of axial strain versus time (Fig. 5a) and void ratio versus time (Fig. 5b). For comparison, the result from test CS(1 disk)01 on intact sample [START_REF] Zhang | Assessment of swelling pressure determination methods with intact Callovo-Oxfordian claystone[END_REF] was also presented. It is worth noting that when the axial strain was positive, the decrease/increase of axial strain referred to the decrease/increase of the magnitude. By contrast, in case of negative value, the decrease/increase of axial strain referred to the increase/decrease of the magnitude. It appeared from Fig. 5a Finally, the axial strain slowly increased until stabilization. Moreover, the higher the initial fracture void, the larger the initial collapse and the smaller the final axial strain at stabilization, suggesting the significant effect of fracture voids. The results identified in Fig. 5b show that, for intact sample, the void ratio increased all the time, while for samples with fracture voids, the void ratio decreased in the first 0.001 day (1.4 min), then increased until stabilization. Moreover, the higher the initial fracture void, the larger the final void ratio at stabilization. The results from tests CS(3 disks)01-05 and tests CS(4 disks)01-02 on samples with fracture voids are presented in Fig. 6 and Fig. 7, respectively. For comparison, the result from test CS(1 disk)01 on intact sample [START_REF] Zhang | Assessment of swelling pressure determination methods with intact Callovo-Oxfordian claystone[END_REF] was also presented. As for samples with two disks shown in Fig. 5, it is observed that: i) for samples with fracture voids, the axial strain (or void ratio) decreased during the initial collapse stage, then increased until stabilization; ii) the higher the initial fracture void, the larger the final void ratio and the smaller the final axial strain at stabilization.

The maximum void that could be filled by claystone swelling corresponded to the one at which the total swelling part was equal to the total collapse part. For its determination, all the axial strains corresponding to the total collapse and swelling parts, as well as the total axial strains were determined from the curves of axial strain versus time shown in Figs. 5a, 6a and 7a. Taking test CS(2 disks)01 as an example (see Fig. 5a): i) during hydration, water flowed into the fracture voids, leading to a collapse of grains up to -0.84% at approximately 0.001 day (1.4 min); ii) the total axial strain at stabilization being 1.29%, the axial strain related to the total swelling of disks was thus calculated to be 2.13% (equal to 1.29% -(-0.84%)). For other tests (CS(2 disks)02, CS(3 disks)01-05 and CS(4 disks)01-02), the total axial strains and the corresponding collapse and swelling parts were determined in the same manner, and the results are presented in Fig. 8. It appeared that, with increasing initial fracture void, the total axial strain and the collapse part significantly decreased, while the swelling part slightly decreased, revealing the significant effect of fracture voids. In addition, the fracture void at which the swelling part was equal to the collapse part (also zero total axial strain) could be also determined from Fig. 8. Due to the scatter of the test data, it appeared necessary to introduce two curves to define the upper and lower limits for the total axial strain, as indicated in Fig. 8. The maximum fracture voids that could be filled by the swelling of disks were thus estimated at 5.14%-7.65%.

This suggests that only the fracture voids smaller than 5.14%-7.65% can be sealed by claystone swelling. The range of this maximum fracture void implies the variability of claystone in terms of mineralogy and dry density [START_REF] Conil | How rock samples can be representative of in situ condition: A case study of Callovo-Oxfordian claystone[END_REF][START_REF] Zhang | Assessment of swelling pressure determination methods with intact Callovo-Oxfordian claystone[END_REF]. It should be however noted that this conclusion does not consider the long-term creep contribution in the field condition. Afterwards, the swelling pressure slowly increased until stabilization. For the samples with fracture voids, the swelling pressure decreased in the first 0.001 day (1.4 min),

showing a collapse feature. Afterwards, the swelling pressure slowly increased up to approximately 0.006 day (8.6 min), then quickly increased up to 0.3 day (432 min).

Finally, the swelling pressure slowly increased until stabilization. Moreover, the stabilized swelling pressure decreased as the initial fracture void increased, suggesting a significant effect of fracture voids [START_REF] Wang | Experimental study on the swelling behaviour of bentonite/claystone mixture[END_REF][START_REF] Wang | The effects of technological voids on the hydro-mechanical behaviour of compacted bentonite-sand mixture[END_REF].

Figs. 10a-10f present the water content and dry density profiles (following the definitions of layers in Fig. 1) of samples with fracture voids wetted under constant-volume condition. For comparison, the expected final dry densities here calculated using the total mass of COx solids (including the disks and the grains)

divided by the volume of the whole sample at the end of the test (including the disks and the fracture voids) were also presented. It appeared that, for samples with two disks (Figs. 10a-10b), larger water contents and lower dry densities were found at position 1.5 that included the top and bottom disks as well as the fracture void in between, as compared with the values at position 1 (top disk) and position 2 (bottom disk). In addition, with increasing initial fracture void, the water contents for positions 1, 1.5 and 2 increased, while the dry densities for positions 1 and 2 decreased.

Moreover, the measured dry densities for disks (represented by the full numbers 1 and 2) were larger than the expected final one, showing the significant effect of fracture voids. The similar phenomena were observed for samples with three and four disks (Figs. 10c-10f): i) larger water contents and lower dry density were found for disks sandwiching fracture voids, as compared with the values for disks only; ii) with increasing initial fracture void, the water contents for disks, and for disks sandwiching fracture voids increased, while the corresponding dry densities decreased; iii) the measured dry density of disks were larger than the expected final one.

Discussion

During the hydration of sample with fracture voids, the synthetic water flowed into the fracture voids first. As a result, the grains were fully hydrated and subsequently collapsed, leading to a decrease of axial strain and swelling pressure before 0.001 day (1.4 min), as shown in Figs. 5, 6, 7 and 9. Afterwards, the disks started to swell (after 0.001 day (1.4 min) in Figs. 5, 6, 7 and 9), and the sample showed swelling (at which the sample with a dry density larger than the expected final state, was subjected to further swelling with a decrease of dry density over time) and compression zones (where the sample with a dry density lower than the expected final state, was subjected to compression with an increase of dry density over time), in agreement with test results on MX80 bentonite by [START_REF] Bian | Voids effect on the swelling behaviour of compacted bentonite[END_REF]. Examination of the dry density profiles in Figs. 10b, 10d and 10f showed that the disks corresponded to the swelling zones, while the initial fracture voids corresponded to the compression zones.

Thereby, the decrease of axial strain of swelling part with initial fracture void identified in Fig. 8 represented the compression of grains by the swelling of disks.

The larger the initial fracture void, the larger the compression of swollen grains. This explained the decrease of the total axial strain (Fig. 8) and the swelling pressure (Fig. 9) with the increase of initial fracture void.

For further analysis, all the results of samples with fracture voids under constant-volume condition were replotted in Fig. 11 in terms of the measured swelling pressure versus the expected final void ratio. The expected final void ratio was calculated using the total volume of voids (including the voids in the disks and fracture voids) divided by the total volume of solids (including the solids in the disks and grains). For comparison, the evolution of swelling pressure with the void ratio of intact COx claystone samples (tests CS(1 disk)01-04 listed in Table 2 and CV(1 disk)01 listed in Table 3) is also presented. It is worth noting that the swelling line determined by the swelling tests on intact COx claystone samples defined the swelling limit: the samples upon wetting from the same initial state stopped at this limit, whatever the stress path followed [START_REF] Zhang | Assessment of swelling pressure determination methods with intact Callovo-Oxfordian claystone[END_REF]. It appeared that at the same swelling pressure, higher void ratio was found for the samples with fracture voids.

This might be due to the fracture voids that were not fully filled at stabilization of swelling. This deduction was confirmed by the swollen grain distributions on the surface of disk after test CV(3 disks)02 (see Fig. 12, obtained by camera): the swollen grains distributed in an inhomogeneous fashion and the inter-grain voids could be clearly identified, indicating that the initial fracture voids created by grains were not fully filled. If the void ratio corresponding to the fracture voids that were not filled was subtracted from the global void ratio, the relationship between the swelling pressure and the void ratio was expected to be similar to that for intact samples. To verify this point, the variation of swelling pressure with the average void ratio of disks (average value of disks calculated from the dry density values after the tests shown in Table 3) were considered and the results are presented in Fig. 13. It appeared that at the same swelling pressure, the void ratios of disks were close to those on the swelling line, confirming that the difference identified in Fig. 11 was due to the fracture voids which were not fully filled. In that case, the transmission of total swelling pressure in the fracture voids zone was controlled by the swollen grains. It is worth noting that the slightly higher void ratio of disks observed in Fig. 13 could be partly attributed to the rebound while extracting the samples from the oedometer cell. It could be also due to the natural material variability in terms of mineralogy and dry density [START_REF] Conil | How rock samples can be representative of in situ condition: A case study of Callovo-Oxfordian claystone[END_REF][START_REF] Zhang | Assessment of swelling pressure determination methods with intact Callovo-Oxfordian claystone[END_REF].

For further analyzing the compression of swollen grains under constant-volume condition, the oedometric modulus Eoed defined in Eq. ( 1) was considered. As mentioned previously, the void ratio of grain was not measured after the swelling test, which rendered the calculation of oedometric modulus Eoed of grain by Eq. ( 1) difficult. Note however that the compression of swollen grains approximately corresponded to the swelling of disks under constant-volume condition: i) the swelling pressure generated by the disks' swelling was approximately equal to the value that was imposed to the grains' compression; ii) the corresponding axial displacement of the disks' swelling was equal to that of the grains' compression.

Moreover, the void ratios of the disks and grains before hydration were also the same, equal to the initial value e0. Thus, the oedometric modulus Eoed of grains was approximately equal to the value of disks for simplicity. Taking test CV(2 disks)01 as an example, the oedometric modulus Eoed of grains was determined as follows: i) the swelling pressure at the start of disks' swelling and the corresponding void ratio were firstly determined. With water infiltration, the grains collapsed and the swelling pressure quickly decreased from the initial stress of 0.059 MPa to the lowest value of 0.0389 MPa at approximately 0.001 day (1.4 min) (Fig. 9), where the disks could reasonably be regarded to start to swell and the corresponding void ratio was determined (0.2098, average value of top and bottom disks calculated from the dry density before the test); ii) the swelling pressure at stabilization and the corresponding void ratio of disks were determined afterwards. The stabilized swelling pressure was 0.346 MPa, and the corresponding void ratio of disks was determined (0.2533, average value of top and bottom disks calculated from dry density after the test in the Eoed of grains was lower than that deduced from the normally consolidated line (NCL). This could be attributed to the fracture voids that were not fully filled (Fig. 12), which did not enable the compression of swollen grains to obey the one-dimensional K0 condition. It could be logically deduced that the Eoed of grains would be closer to that deduced from NCL if the quantity of grains or the stress during hydration increased. Following up this logic, the line of Eoed versus vertical stress was extrapolated to the NCL. A stress 1.56 MPa was obtained at the intersection of the two lines. This stress corresponds to the value which theoretically verifies the one-dimensional K0 compression. In that case, the fracture voids are expected to be totally filled.

Conclusions

In this study, the effect of fracture voids on the swelling behaviour of COx claystone was experimentally investigated by performing swelling tests either under 0.05 MPa vertical stress or under constant-volume condition. At the end of swelling tests under constant-volume condition, the water content and dry density profiles were determined. The results obtained allow the following conclusions to be drawn. Table 1. Salts used for synthetic water preparation

List of Tables

  Fig. 4b plots the Eoed versus vertical stress in a logarithmic scale. It appeared that, upon loading below 0.5 MPa stress (close to the yield stress 0.55 MPa), the Eoed decreased as the vertical stress increased. By contrast, beyond the yield stress 0.55 MPa, the Eoed linearly increased. This is consistent with the results reported by Nguyen et al. (2013) on Boom clay and by Ye et al. (2014) on

  that, for the intact sample (CS(1 disk)01), the axial strain increased with time until stabilization. For samples with fracture voids (tests CS(2 disks)01-02), the axial strain decreased in the first 0.001 day (1.4 min), showing a closing trend of fractures due to collapse of COx claystone grains. Afterwards, the axial strain slowly increased up to approximately 0.006 day (8.6 min), then quickly increased till 0.3 day (432 min).

Fig. 9

 9 Fig. 9 shows the results from tests CV(1 disk)01, CV(2 disks)01-03, CV(3

Fig. 1 .Fig. 2 .Fig. 3 .Fig. 4 .Fig. 5 .Fig. 6 .Fig. 7 .Fig. 8 .Fig. 9 .Fig. 10 .Fig. 11 .Fig. 12 .Fig. 13 .Fig. 14 .Fig. 4 .Fig. 5 .Fig. 6 .Fig. 7 .Fig. 10 .

 1234567891011121314456710 Fig. 1. Schematic diagram of samples with fracture voids: (a) two disks, (b) three disks, (c) four disks Fig. 2. Layout of the constant-volume cell Fig. 3. Axial strain versus time for intact samples Fig. 4. Compression test SC(1 disk)01 on intact sample: (a) void ratio versus vertical stress, (b) oedometric modulus versus vertical stress Fig. 5. Results of samples with fracture voids wetted under 0.05 MPa from tests CS(2 disks)01-02, together with those of intact sample from test CS(1 disk)01: (a) axial strain, (b) void ratio Fig. 6. Results of samples with fracture voids wetted under 0.05 MPa from tests CS(3 disks)01-05, together with those of intact sample from test CS(1 disk)01: (a) axial strain, (b) void ratio Fig. 7. Results of samples with fracture voids wetted under 0.05 MPa from tests CS(4 disks)01-02, together with those of intact sample from test CS(1 disk)01: (a) axial strain, (b) void ratio Fig. 8. Total axial strains and the corresponding collapse and swelling parts versus initial fracture void for samples with one, two, three and four disks Fig. 9. Evolution of swelling pressure under constant-volume condition Fig. 10. Water content and dry density profiles for samples with fracture voids after swelling tests under constant-volume condition: (a) water content profile (two disks), (b) dry density profile (two disks), (c) water content profile (three disks), (d) dry density profile (three disks), (e) water content profile (four disks), (f) dry density profile (four disks) Fig. 11. Comparison of swelling pressure between intact samples and fractured samples with consideration of fracture voids Fig. 12. Distribution of grains on the disk surface after test CV(3 disks)02 Fig. 13. Comparison of swelling pressure between intact samples and disks in fractured samples without consideration of fracture voids Fig. 14. Variation of oedometric modulus with vertical stress

  Fig. 11. Comparison of swelling pressure between intact samples and fractured samples with consideration of fracture voids

Table 3

 3 Eoed of grains under 0.346 MPa stress was estimated at 8.54 MPa. For other tests (CV(2 disks)02-03, CV(3 disks)01-02 and CV(4 disks)01), the Eoed of grains was estimated in the same manner, and the results are shown in Fig.14. For comparison, the results of Eoed that was determined from oedometer test shown in Fig.4bare also presented. It appeared that: i) the Eoed of grains was lower than that of intact sample; ii)

); iii) the Eoed corresponding to the swelling of disks was finally calculated ((0.346 MPa -0.0389 MPa) × (1 + 0.2098) / (0.2533 -0.2098) = 8.54 MPa). Thus, the

Table 2 .

 2 Test program for samples wetted under constant-stress condition and compression test

Table 3 .

 3 Test program for samples wetted under constant-volume condition

	List of Figures

During the hydration of COx claystone samples with fracture voids, the grains collapsed first while in contact with water. Afterwards, the disks started to swell and the whole sample presented swelling zones corresponding to the claystone disks and compression zones corresponding to the initial fracture voids.

The axial swelling strain and swelling pressure decreased as the initial fracture void increased. The correlation between the swelling pressure for sample with fracture voids and the expected final void ratio was found to be higher than that of intact sample, which was explained by the fact that the fracture voids were not fully filled.

The maximum fracture voids that might be fully filled or sealed by the swelling of COx claystone were found to be 5.14% -7.65% without considering the long-term creep contribution in the field condition.


Arnault Lassin
email: a.lassin@brgm.fr

Sylvain Guignot
email: s.guignot@brgm.fr

B Madé

Philippe Blanc
email: p.blanc@brgm.fr

Selection of thermodynamic properties for zeolite minerals

Keywords: zeolites, thermodynamic properties, underground storage

In the context of deep underground nuclear waste repositories, safety has to be assessed over long periods of time (100 000 years, usually). At the European level, repository concepts may use various types of physical barriers to prevent the release of toxic elements into the geosphere. Among those materials, clay minerals do represent an important contribution, for the engineered barrier made of bentonite, or for the surrounding geological host rock, which may include a large amount of clays. Gaucher et al. (2004) showed that the contact with cement based materials, used for repository underground facilities could induce mineralogical transformations in both sides of the cement / clay interface, producing zeolite minerals. Those 3D framework silicates are stabilized in alkaline environments and were found in many experiments where clay minerals were put in contact with alkaline solution (Gaucher and Blanc, 2006).

Assessing the stability of those minerals over long periods of time is thus of importance for risk assessment calculations. Thermodynamic properties are essential for such applications and within the framework of the Thermochimie project (Giffaut et al., 2014), much efforts have been devoted to filling in gaps in thermodynamic databases in general and for zeolites in particular (Blanc et al., 2015). The current selection establishes the consistency within the selections for clay, zeolites and cement phases (Blanc et al., 2015). However, since then several studies have been published, aiming to investigate the thermodynamic properties of such minerals, like the work proposed recently by Ma and Lothenbach (2020a) and Ma and Lothenbach (2020b), for example. Such studies allow completing the Thermochimie database for the properties estimated in the previous selection, or for the minerals which can not be included, given the lack of data in the literature. Furthermore, the determinations carried out by Ma and Lothenbach (2020a) and Ma and Lothenbach (2020b) enlighten the necessity to distinguish zeolites which have been equilibrated with porewaters over thousands of years and phases freshly precipitated, presenting higher solubilities. This work presents and illustrates the guidelines followed for the new selection of zeolites thermodynamic data. Illustrations are provided, along with comparisons with recent determinations.

ACKNOWLEDGEMENTS

Financial support from the French National Radioactive Waste Management Agency (ANDRA), from the Thermochimie consortium and from the French Geological Survey (BRGM) is gratefully acknowledged. Blanc, P., Vieillard, P., Gailhanou, H., Gaboreau, S., Marty, N., Claret, F., Madé, B., Giffaut, E., 2015. ThermoChimie database developments in the framework of cement/clay interactions. Applied Geochemistry 55, 95-107. Gaucher, E.C., Blanc, P., 2006. Cement/clay interactions -A review: Experiments, natural analogues, and modeling. Waste Management 26, 776-788. Giffaut, E., Grivé, M., Blanc, P., Vieillard, P., Colàs, E., Gailhanou, H., Gaboreau, S., Marty, N., Madé, B., Duro, L., 2014. Andra thermodynamic database for performance assessment: ThermoChimie. Applied Geochemistry 49, 225-236. Ma, B., Lothenbach, B., 2020a. Synthesis, characterization, and thermodynamic study of selected Na-based zeolites. Cement and Concrete Research 135, 106111. Ma, B., Lothenbach, B., 2020b. Thermodynamic study of cement/rock interactions using experimentally generated solubility data of zeolites. Cement and Concrete Research 135, 106149.


Yi Hong

Frédéric Soulignac

Adélaïde Roguet

Chenlu Li

Bruno J Lemaire

Rodolfo Scarati Martins

Françoise Lucas

Brigitte Vinçon-Leite

Impact of Escherichia coli from stormwater drainage on recreational water quality: an integrated monitoring and modelling of urban catchment, pipes and lake

Keywords: Escherichia coli, Recreational water, Urban stormwater drainage, Integrated monitoring and modelling, Process based modelling, Buildup and washoff

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

Introduction

In recent years, recreational waterbodies are increasingly attractive and frequented in urban areas. This worldwide trend requires minimum standards for achieving and maintaining high water quality at all times to ensure the protection of public health. In accordance with the European Bathing Water Directive (Directive 2006/7/EC), the concentration of faecal pathogens has to be monitored in order to take appropriate management actions in case of non-compliance with the requirements. Present in the gut microbiota of humans and warm-blooded animals, Escherichia coli (E. coli) is commonly used as an index of faecal contamination [START_REF] Deltares ; Edberg | Escherichia coli: the best biological drinking water indicator for public health protection[END_REF] which indicates the presence of pathogens causing gastrointestinal infections [START_REF] Who | Guidelines for safe recreational water environments[END_REF]. Depending on the risk of infection, the Directive 2006/7/EC classifies bathing waters as excellent, good, sufficient or insufficient.

In spite of the growing concerns for maintaining the required quality of the bathing waters, the impacts of several pollution sources are still poorly controlled, particularly the pollution from urban stormwater discharges. In many municipal areas, urban stormwater is conveyed in separated sewer systems and discharged directly to receiving waters without any treatment. The typical levels of E. coli in stormwater greatly exceed the existing recreational water guidelines [START_REF] Marsalek | Urban Wet-Weather Flows: Sources Of Fecal Contamination Impacting On Recreational Waters And Threatening Dringking-Water Sources[END_REF], this may degrade the bathing water quality and even cause severe public health risks, especially during heavy precipitation periods.

The distribution and fate of E. coli released into the urban lakes can be generally described as a combination of die-off and dilution [START_REF] Mclellan | Distribution and Fate of Escherichia coli in Lake Michigan Following Contamination with Urban Stormwater and Combined Sewer Overflows[END_REF][START_REF] Mccarthy | Intra-event variability of Escherichia coli and total suspended solids in urban stormwater runoff[END_REF]). However, it is still unfeasible to track the spatial-temporal distributions of this faecal indicator organism with monitoring data. Many modelling approaches have been reported in scientific literature for simulating the transport and fate of E. coli in recreational waters. Existing models can be mainly categorized into two classes: the data-driven approaches and the deterministic models. The data-driven models, for example, Artificial Neural Networks (ANN) [START_REF] Kashefipour | Neural networks for predicting seawater bacterial levels[END_REF][START_REF] He | Water quality prediction of marine recreational beaches receiving watershed baseflow and stormwater runoff in southern California, USA[END_REF], random forest [START_REF] Parkhurst | Indicator bacteria at five swimming beaches-analysis using random forests[END_REF][START_REF] Jones | Hydrometeorological variables predict fecal indicator bacteria densities in freshwater: data-driven methods for variable selection[END_REF], and other regression based models [START_REF] De Brauwere | Modeling Fecal Indicator Bacteria Concentrations in Natural Surface Waters: A Review[END_REF][START_REF] Brooks | Predicting recreational water quality advisories: A comparison of statistical methods[END_REF] attempt to relate E. coli concentrations with various environmental factors such as rainfall, solar radiation, water temperature, salinity, population density, etc. Although acceptable results are reported using these methods, their performance will continue to be questionable if they are applied to extrapolate patterns outside the range of case-specific measured data, and they cannot reproduce the spatial-temporal dynamics of E. coli processes. The deterministic models aim to fully capture the changing dynamics for describing the complex interactions between catchments, rivers and water bodies (e.g. [START_REF] Bedri | An integrated catchment-coastal modelling system for real-time water quality forecasts[END_REF][START_REF] Huang | Integrated hydro-bacterial modelling for predicting bathing water quality[END_REF]. Nevertheless, most published deterministic models are focused on coastal bathing waters. Very limited research exists for urban catchments and their receiving lakes. Moreover, the fate of E. coli is mainly simulated by using a constant decay rate, rare studies have considered the mortality of E. coli.

In this context, this paper proposes an integrated deterministic and spatially distributed urban catchment -lake model for simulating the generation, transport and mortality processes of E. coli from an urban catchment including the drainage network to a receiving recreational lake. Two widely used models are comprised in the modelling system, including (i) the sub-catchment based and one-dimensional sewage network model SWMM (Rossman 2010), and (ii) the three-dimensional model Delft3D (Deltares 2016). This integrated modelling chain is tested for an urban catchment and its related recreational lake located in the Great Paris region. Extensive hydrodynamic and water quality data from detailed monitoring survey are used for model calibration and validation.

Materials and methods

Study area description

The study area is located in the South-East of Paris (Créteil, Val-de-Marne, France) (Fig. 1a), consists of an urban catchment of 95 ha and a recreational lake of 42 ha (Lake Créteil) (Fig. 1b). The study catchment is a typical urbanized area in the Paris region, characterized by its high population density (≈ 8,000 inhabitants/km²) and low surface permeability (about 10 % of the areas are permeable surfaces). The average slope is approximately 2%. During rainfall events, stormwater runoff is collected by a separated drainage system. The total length of the network is 17.6 km, with a single outlet on the eastern side of Lake Créteil (Fig. 1c). Besides, a flow valve is installed at the end of the stormwater sewers to divert dry weather flow into the wastewater networks, avoiding the discharge of waste water from cross-connections between the separated pipes.

The receiving waterbody, Lake Créteil, is an important outdoor leisure centre in the Paris region (boating, sailing, angling, etc.), with a park of 0.62 km² on the western bank of the lake. Apart from the stormwater drainage of the urban catchment, Lake Créteil is mainly fed by groundwater which flows from the Marne river to the Seine river (Fig. 1a), due to a 1-meter difference in the normal levels of the navigation reaches [START_REF] Soulignac | Performance Assessment of a 3D Hydrodynamic Model Using High Temporal Resolution Measurements in a Shallow Urban Lake[END_REF]. The lake water level can be regulated by a fixed gate on the western bank. The mean depth of Lake Créteil is 4.5 m, with the southern part deeper than the northern part, reaching a maximum depth of 6.5 m. The total volume of the lake is about 1.9×10 6 m 3 .

Since the boundary conditions of Lake Créteil are well controlled with constructed isolation dams, the E. coli patterns in the receiving water body are strongly influenced by the stormwater drainage of the connected urban catchment. This study area is therefore specifically suited for assessing the impact of stormwater quality on urban lakes.

Sampling methodology 2.2.1. Measuring equipment in stormwater sewer

From Oct. 10 th to Nov. 5 th 2013, hereafter referred to as the sewer monitoring period, a monitoring and auto-sampling system is set up at the downstream end of the main stormwater sewer, before it divides into two parallel pipes towards the outlet. Water depth and water flow rate are recorded at a 2-min time step. An autonomous controller is connected both to a flow meter (Mainstream IV, Hydreka Inc.) which measures water depth and mean flow velocity, and to an auto-sampler (HACH Sigma SD900). The discharge is then automatically estimated by considering water height, flow velocity and pipe shape. When the sewer water depth is higher than 0.15 m, the controller receives a positive signal to activate its "water height flag", and starts to count the water volume registered by the flow meter. If the "water height flag" remains activated, the controller sends positive signals to the auto-sampler for sampling 125 mL water at 64 m 3 water volume interval. Water samples gathered during a rainfall event are mixed and stored in a large container, then collected on the following day of every rainy day, and reserved at 4°C up to 4 hours prior to laboratory processing. This approach allows to collect representative stormwater flow samples of each rainfall event.

Lake Créteil monitoring

Lake Créteil is equipped with high-frequency monitoring sensors and a meteorological station (PME Inc, LakeESP) from May 12 th , 2012 to Jan. 31 th 2014, hereafter referred to as the lake monitoring period. Meteorological variables such as wind speed and direction, precipitation, air temperature, air pressure, relative humidity (Vaisala, WXT520) and net radiation (Kipp and Zonen NR Lite2) are measured every 30 seconds. Since the study area is quite small (< 1 km 2 ), which corresponds to only one grid of a typical C-band radar (1 km resolution) and dozens of grid cells of an X-band radar in Paris region (250 m resolution) [START_REF] Paz | Rain gauge networks' limitations and the implications to hydrological modelling highlighted with a X-band radar[END_REF], rainfall is considered as homogeneous within the Créteil basin. The underwater chain is equipped with temperature sensors (NKE, SP2T) at different depths, also with a sampling time-step at 30 seconds. These datasets and the measured lake bathymetry are used for the hydrodynamic modelling of the lake [START_REF] Soulignac | Performance Assessment of a 3D Hydrodynamic Model Using High Temporal Resolution Measurements in a Shallow Urban Lake[END_REF].

E. coli concentration measurement

During the sewer monitoring period, on-site experiments are carried out in Lake Créteil at station S, C and O (Fig. 1b) on the following day of each rainfall, to collect water samples for laboratory analysis.

E. coli concentrations of the collected lake and sewer water samples are enumerated by the microplate method, according to the French standard method NF ISO 9308-3. Raw or diluted samples are spread in 96-wells microplates containing a dehydrated culture medium. After an incubation period of 48-72 h at 44 °C ± 0.5 °C, the microplates are examined under ultraviolet light at 366 nm. The results are expressed as the Most Probable Number (MPN), which is a statistical estimate of the density of microorganisms. The detection limit of <0.075 MPN ml -1 water sample is estimated. Moreover, a monthly E. coli monitoring program of Lake Créteil is performed from January 2012 to December 2013 [START_REF] Roguet | Importance of Local and Regional Scales in Shaping Mycobacterial Abundance in Freshwater Lakes[END_REF], which covers the lake monitoring period.

Event-based and continuous simulations

Using rainfall intensity measurements at every 30 seconds, different rainfall events can be identified by dry period intervals longer than 90 minutes, meaning no rain intensity data recorded during 90 minutes. And a valid rainfall event should have a total water depth more than 1 mm. Based on these criteria, four different rainfall events can be recognized for the sewer monitoring period. Event-based simulations are performed for these rainfall events, calibrated and validated by using the continuous measurements of stormwater sewer discharge, E. coli event-mean-concentration (EMC) of stormwater sewer flow, and the E. coli concentration at three points in Lake Créteil on the following day of each event. In addition, a continuous simulation is performed for the lake monitoring period with the calibrated parameters, monitored water temperature at different depths and monthly E. coli concentration in the lake are used to evaluate the model performance. Simulation periods, comparison measurements for assessing model performance, and characteristics of the studied rains are illustrated in Table 1.

Model description 2.3.1. Overview of the integrated modelling system

The integrated modelling system consists of three separated components: the urban catchment component, the 3D lake hydrodynamic component, and the 3D lake water quality component. Urban catchment processes are simulated by the SWMM model (Rossman 2010). Faeces of urban animals (dogs, cats, birds, etc.) are considered to be continuously accumulated on urban surfaces (roads, roofs, sidewalks, etc.) in dry-weather periods (build-up). During rainfall events, these pollutants are removed with surface runoffs (wash-off), and then transported in the stormwater drainage network into the receiving lake. The in-lake processes are simulated with the Delft3D modelling suite (Deltares 2016), respectively hydrodynamics by the FLOW module and E. coli transport and mortality processes with the WAQ module.

Python scripts are developed in order to automatically link the different modelling components by interfacing the involved state variables. However, feedback among different components, such as a downstream condition in the stormwater outlet due to the lake water level, are not permitted yet by the current version of modelling. A schematic of the integrated model is presented in Fig. 2.

Figure 2.

Scheme of the integrated modelling system

Urban catchment component

The urban catchment is divided into 21 sub-catchments according to the administrative divisions of residential, commercial and industrial zones. The surface runoff of each sub-catchment is simulated with a non-linear reservoir because of the simplicity and robustness of this approach. The surface storage is taken into account as an initial hydrological loss. The impervious area represents 40% -80% of different sub-catchments, and the infiltration in pervious areas being described by the [START_REF] Green | Studies on Soil Phyics[END_REF] equations. Rainfall-runoff routing is solved by coupling the continuity equation with the Manning equation. Water flow in sewer networks is computed by 1D kinematic wave equations with finitedifference scheme. Whereas, ponding is not allowed for the manholes since it is not an issue for the study period, and this research focuses on E. coli simulations under normal rains.

The build-up and wash-off processes of E. coli are calculated at the scale of each sub-catchment. The build-up during a dry period follows an exponential growth curve (Eq. 1), and the wash-off rate depends on the runoff discharge and the amount of the remaining substances at each time-step (Eq. 2) (Rossman 2010).

_ 1 1 ⁄ ! " # 2
Where:

_ is the mass of E. coli accumulated on the surface during a dry period (MPN m -2 );

%&' is the time of dry weather periods (days); is the maximum possible build-up of E. coli (MPN m -2 );

( is build-up constant rate (day -1 ); ⁄ is the wash-off rate (MPN m -2 h -1 );

! is the wash-off coefficient (mm -1 );

) is the wash-off exponent (-); q is the runoff flux rate over sub-catchment (mm h -1 );

is the remaining E. coli at each time step (MPN m -2 )

For E. coli routing, the pipes are considered as continuously stirred tank reactors (CSTR). The concentration of E. coli in pipes at the end of a time step is found by integrating the conservation of mass equation over this time step.

3D lake modelling

The Delft3D-FLOW model (Deltares 2016) solves the Navier-Stokes equations for an incompressible fluid, under the shallow water and the Boussinesq assumptions. The system of equations consists of the horizontal equations of motion, the continuity equation, and the transport equation of heat. This set of partial differential equations in combination with an appropriate set of initial and boundary conditions is solved on a finite difference grid with current velocities defined on cell faces and scalar variables at cell centres. Following the settings in [START_REF] Soulignac | Performance Assessment of a 3D Hydrodynamic Model Using High Temporal Resolution Measurements in a Shallow Urban Lake[END_REF], the horizontal surface of Lake Créteil is meshed with 981 Cartesian cells of 20 m × 20 m, and the Z-model is used with 18 horizontal layers of height 33 cm. Monitored values of wind direction and speed, air temperature, relative humidity, and precipitation, as well as the recorded values of hourly incident solar radiation and cloud cover at the nearest weather station located at Orly Airport, 10 km west of the lake, are used to force the simulations.

Water level variations are neglected, as they never exceeded 3% of the water height over a simulation period.

The transport and fate of E. coli in the lake are simulated with Delft3D-WAQ (Deltares 2016). For modelling purpose, it is supposed that E. coli is a stand-alone substance: (i) it is present only in the water column, (ii) it does not accumulate in the sediment or resuspend from it, (iii) it does not grow in the water, and (iv) only the transport and mortality processes are simulated. These hypotheses simplify the real-world processes, making the physically-based modelling of E. coli dynamics possible for urban lakes. Processes of E. coli in Lake Créteil is computed by advection-dispersion-mortality equation (Eq. 3). In each cell of the 3D model, advection-dispersion of E. coli is computed by the conservation of mass equations (please refer to (Deltares 2016) for more details), while the mortality of E. coli is related with temperature and solar radiation (Eq. 4 -5).

• >? • @ , • A0 • 1 C•D E • F 5
Where:

is the concentration of E. coli in a 3D-cell (MPN m -3 ) kmb is the basic mortality rate of E. coli (d -1 ); ktmrt is the temperature coefficient of the mortality rate (-); T is the water temperature (°C); kmrd is the radiation dependent mortality rate (d -1 ); 7 &% is the radiation related mortality constant (m² W -1 d -1 )

DL is the fraction of daytime in 24 hours (-); @ , is the fraction of UV-radiation as derived from visible light (-); A ; is the daily solar radiation as visible light at the water surface (W m -²); E is the background extinction of UV-radiation (m -1 );

H is the water depth (m);

Model calibration and uncertainty analysis

Calibration of SWMM model are first performed for hydraulic/hydrologic parameters, and then for build-up/wash off parameters. The Nash-Sutcliff efficiency coefficient (NSE) [START_REF] Nash | River flow forecasting through conceptual models part I -A discussion of principles[END_REF] is used to assess the model performance (Eq. 6). NSE can range from ∞ to 1. An efficiency of 1 (NSE = 1) corresponds to a perfect match of modelled discharge or E. coli concentration to the observed data.

IJK A simple and robust bisection approach is applied to estimate the optimized value of each parameter.

Given the initial interval of each parameter, the bisection method cuts the interval into two halves and check which half interval has the larger NSE value. This method keeps cut the interval in halves until the resulting interval is small, the optimized parameter value can be then approximately equal to any value in this final interval. When calibrating one parameter, we fix other parameters to their optimal values or the mid-point of the initial interval if the calibration is not performed yet.

For urban catchment hydrological simulations, we calibrate the manning's n roughness and the initial loss for impervious and pervious surfaces, respectively. The initial intervals for these parameters and other default values of hydraulic/hydrologic parameters can be referred to (Rossman 2010). Initial intervals of E. coli build-up and wash-off parameters are shown in Table 2.

An exploratory uncertainty analysis is performed to represent the impacts of wash-off/build-up parameters on E. coli concentration. Since simulations for the integrated water quality modelling is computational expensive (particularly for the 3D lake module), a stochastic parameter sampling approach is repeated for ten simulations of each event-based modelling and the continuous modelling.

The analysed parameters are considered as uniformly distributed in the initial intervals defined in Table.

2. For each rains, we randomly pick-up ten parameter sets in these intervals and implement simulations.

The uncertainty of the analysed simulation period can be then expressed by the 95% confidence interval of the simulated E. coli concentrations.

Results

Water flow and E. coli concentration at drainage outlet

The hydraulic/hydrologic and build-up/wash off parameters of the SWMM model are calibrated for the rain of 10/14/2013, and then validated with the other three rainfall events, as well as the sewer monitoring period (10/10 -11/05/2013). The optimized n-manning values are 0.015 for impervious areas and 0.15 for pervious areas, and the initial loss is 0.5 mm for impervious areas and 2 mm for pervious areas. Optimized build-up and wash-off parameter values of E. coli are shown in Table 2.

! mm -1 Wash-off coefficient 1.0 -3.0 2.0 ) - Wash-off exponent 1.0 -2.0 1.1

Water flow simulations at stormwater outlet

As seen in Fig. 3, the performance of the water flow simulation was quite satisfactory (NSE > 0.7 for all rainfall events). The hydrological dynamics in urban catchment is correctly represented by the SWMM model. The model can be then used for event-based and long-term simulations of E. coli dynamics.

Event mean concentrations of E. coli

As shown in Fig. 4, the simulated EMC of E. coli can correctly represent the measured values at the drainage outlet for the four sampled rainfall events. This consistent result confirms the validity of using the presented modelling approach for simulating the generation and transfer of faecal contaminants in urban catchment. Following thermal-hydro dynamics of the receiving waterbodies, the discharged E.

coli may lead to the degradation of water quality in potential bathing areas of the lake. Confirming the necessity to evaluate the impacts of stormwater drainage on recreational water quality in urban areas.

However, it can be noted that the modelling uncertainty of E. coli is significant in stormwater sewer flows. Uncertainties related to build-up and wash-off parameters can be up to two orders of magnitude, while the analytical uncertainty of measured values is less than one order of magnitude. These results suggest that further field studies could be operated in order to reduce the initial intervals of parameter values. Moreover, the reliability of this modelling approach could be tested for different urban catchments.

Long-term variations of E. coli in stormwater sewers

Long-term simulations are performed for the period from May 12 th , 2012 to Jan. 31 th , 2014, using the optimized parameters. Water flow rate and E. coli fluxes are computed at 5 second time-step, simulated results are reported every two minutes. Rainfall intensity, water volume and E. coli mass from stormwater drainage are shown in Fig. 5.

The stormwater discharge entering Lake Créteil can be up to 1 × 10 4 m 3 per day for heavy rain periods, it is negligible compared to the total water volume of the lake, which is approximately 2 × 10 6 m 3 . However, during rain events, the total influx of E. coli into the lake is at a maximum of 4 × 10 13 MPN per day. Considering the EU "good water quality" threshold (1000 MPN/100 mL) with a homogeneous distribution assumption, this limit is consistent with 2 × 10 13 MPN of E. coli in the entire lake. Showing that the urban stormwater discharge may impact the microbial quality of the lake. In that case, insight into the distribution of E. coli from stormwater sewer discharge is required for a good management of urban bathing water quality.

Hydrodynamics and E. coli distribution in Lake Creteil

Coupling the SWMM model and Delft-3D model at a two-minute time-step, the hydro-thermal dynamics and E. coli transport in Lake Creteil are simulated. Simulations are performed with the calibrated values of drag coefficient (0.0015) and Secchi depth (1 m) presented in [START_REF] Soulignac | Performance Assessment of a 3D Hydrodynamic Model Using High Temporal Resolution Measurements in a Shallow Urban Lake[END_REF]. Forcing variables such as wind direction and speed, air temperature, relative humidity, precipitation, solar radiation and cloud cover are defined according to in-situ monitoring and recordings of the nearest weather station. The background concentration of E. coli in the lake is set to 5 MPN/100 mL based on the average E. coli concentration over a monthly monitoring of the points S, C and O. Since very few measured data is available for defining E. coli characteristics in Lake Creteil, water quality parameters are defined following Deltares (2016) (Table 3).

Measured and simulated water temperature

An accurate simulation of water temperature thermal stratification and mixing of water column is required for water quality modelling in the lake. In order to verify the model performance, its ability to reproduce the water temperature and the thermal regime was assessed. In Fig. 6, the hourly mean profiles of observed water temperature in the middle of Lake Creteil (Point C) are compared with the simulation results for the period from 05/12/2012 to 01/31/2014. The Mean Absolute Error (MAE, Eq. 7) between simulated and measured temperature at different depths are calculated for the three monitoring points (S, C, O), shown in Table . 4.

[K 1 / \ | J ^ ^ | _ ^P 7
Where / refers to the number of simulated-measured temperature data pairs; J ^ and ^ represent the simulated and measured water temperature, respectively. According to Table . 4, for this simulation period of 20 months, the MAE between simulated and measured water temperature is varied from 0.4 to 0.7 °C at the three points and different depths, indicating a good modelling performance for representing the thermal dynamics of the lake. Water temperature is slightly better reproduced in the middle of the lake (Point C), and worse reproduced on the surface water (0.5 m). This phenomenon is because of the water condition is more stable in the middle of the lake, where is less influenced by stormwater inflows (Point S), outflows (Point O), and fluctuations on the water surface caused by wind and human activities. In Fig. 6, several stratifications are observed during the study period. The stratification period varies from a few hours to several days. Alternations between stratification and mixing are correctly reproduced by the model. These results confirm that the present modelling approach is suitable for representing the spatial and temporal variations of the lake's hydro-thermal regime.

Spatial-temporal distribution of E. coli in Lake Creteil

Simulated E. coli concentrations at the three monitoring points are compared to the measurements for the events of October 14 th , 16 th , 20 th , and November 3 rd , 2013 (Fig. 7). Since on-site samplings in the lake are performed on the following day at 10:00 am of each rainy day, simulated values at the corresponding time are analysed. For each event, using outputs from the ten urban catchment simulations, the uncertainty of E. coli simulations at the three points in the lake (S, C, O) can be assessed. These results are shown in Fig. 7. As shown in figure 7, the E. coli concentration decreases with the distance from the stormwater outlet (S>C>O). The simulated E. coli concentration with optimized parameters are within the confidence interval of the measured values for all the studied rainfall events. Moreover, both simulations and observations are under the EU threshold for a "good water quality" of bathing water (1000 MPN/100 mL) the day after rainfall events. In this case, lake water quality could recover the good quality threshold for bathing on the day after rains. However, modelling uncertainties are important, particularly for E.

coli concentration at the point S, which could overpass the EU threshold. Nevertheless, comparing to stormwater sewer flow simulations (Fig. 4), the uncertainty of E. coli modelling in the lake is decreased. This result is due to the fixed water quality parameters for the 3D lake modelling. In order to estimate the duration and range of the impacts of stormwater discharge, and to ensure the safety of bathing water, spatial and temporal distribution of E. coli in the lake is required. To this end, E. coli dynamics in Lake Creteil after the rain of 10/14/2013 is presented as an example (Fig. 8).

As shown in Fig. 8, the central part of the lake close to the sewer outlet always indicates higher E. coli levels than the rest of the lake, and it is strongly affected by the stormwater discharge. In a range of 500 m of the sewage outlet, the E. coli concentration remains over 10 times higher than the good water quality threshold (1000 MPN/100 ml) 3 hours after the end of the rain. After 6 -12 hours, the E. coli are mostly homogeneously distributed in a range of 1 km to the stormwater outlet. While it takes about 24 hours for the entire lake to return to a low E. coli concentration level. Besides, as the wind direction is mainly from the south during the simulation period, it can be observed that the spread of E. coli towards the north of the lake, particularly after 6 hours, because of advection process. Moreover, it can be noted that the north and the south border of Lake Creteil are slightly impacted by the stormwater drainage, where the water quality remains at a good level all the time.

Long-term variations of E. coli in the lake

For the lake monitoring period (05/12/2012 -01/31/2014), simulated monthly mean concentration of E.

coli with 95 % confidence intervals, are compared with the monthly observations at the three points (S, C, O) of the lake (Fig. 9). According to Fig. 9, as expected, the E. coli concentrations are higher at the points closer to the stormwater sewer outlet (S>C>O). Moreover, it can be noted that most observed values are within the 95 % confidence intervals of the simulated concentrations. These promising results prove the validity of the present modelling approach. Nevertheless, as shown in Fig. 8, the E. coli concentration in the lake can change significantly within 24 hours, monthly comparisons cannot fully capture the effectiveness of this integrated model. Due to the monthly monitoring setup (always the same day of the month at 9 -11 am), not all of the measured E. coli concentration can represent the impact of stormwater discharges. Therefore, in order to evaluate the model performance, we only compare the measured values within two days after rains, with the optimized E. coli hourly simulations at 10:00 am of the sampling dates. Using all the simulated and measured E. coli concentration at the three sampling points (S, C, O), scatter plot of the simulations against the observations is presented in Fig. 10. As indicated in the figure, the simulated E. coli concentrations represent correctly the observed values. The Pearson's correlation coefficient is calculated from all the simulations and observations at the three sampling points (S, C, O), resulting r=0.89, p-value = 8.7 × 10 -6 . This encouraging result confirms the validity of the presented modelling approach for simulating the impacts of E. coli from stormwater drainage to urban lakes. However, as presented in Fig. 10, only 5 among the 20 monthly observations have rains within 48 hours before the sampling dates, a few observed E. coli concentrations in the lake were significantly higher than the background concentration (5 MPN/ 100 ml) during dry weather periods. This phenomenon implies that the microbiological contaminants from sources other than urban stormwater sewer flows may exist.

Discussion

On the use of integrated modelling for bathing water management

Regulated methods for monitoring E. coli concentrations take several days from sample collection [START_REF] Deltares ; Edberg | Escherichia coli: the best biological drinking water indicator for public health protection[END_REF], nevertheless, The EU Bathing Water Directive (EU 2006) requires the provision of appropriate and prompt information to the public, especially in relation to predictable extreme events. Hence, at sites where water quality is affected by the short-term deterioration, results from water quality samples do little to inform the public, particularly for forecasting. The modelling approach is suitable for analysing the impacts of stormwater drainage on bathing water, where the water quality could be degraded immediately after rainfall events.

Many existed studies applied data-driven (or black-box) models to estimate E. coli dynamics (e.g. de [START_REF] De Brauwere | Modeling Fecal Indicator Bacteria Concentrations in Natural Surface Waters: A Review[END_REF][START_REF] Brooks | Predicting recreational water quality advisories: A comparison of statistical methods[END_REF]. In these models, the output variable is assumed to be a linear or non-linear function of several input variables, and the optimal values for coefficients associated with each of these variables are sought. The main advantage of these models is their ease and flexibility of use, allowing them to be applied for short-term and real-time predictions. Nevertheless, the model reliability and predication performance depends on the complexity of input variables and accessibility of enough data, relevant explanatory variables are extremely site-specific. For instance, [START_REF] Francy | Predictive Models for Escherichia coli Concentrations at Inland Lake Beaches and Relationship of Model Variables to Pathogen Detection[END_REF] reported that the relations between bacterial concentrations and environmental parameters in Lake Erie differed from year to year, and therefore they suggest using at least two years of data for model calibration. [START_REF] Frick | Nowcasting and Forecasting Concentrations of Biological Contaminants at Beaches: A Feasibility and Case Study[END_REF] also suggest that these models should be updated and validated regularly in order to account for the changing conditions that would not be covered in the original calibration. The performance of these models varies widely, de Brauwere et al. ( 2014) reviewed several black box models, and found the R 2 ranges from 0.29 to 0.99, emphasizing their extreme case-sensitivity. Since black-box models do not include mechanic relationships, they cannot be used for in-depth understanding of the system, and cannot be repeatedly applied for different case studies or under changeable conditions, such as land-uses changes and different management strategies.

Deterministic (or white-box) models are capable of investigating the spatial and temporal dynamics of E. coli in aquatic systems. An important fraction of the freshwater studies is concerned with catchments, often in rural areas. A significant number of studies used the Soil and Water Assessment Tool (SWAT) (e.g. [START_REF] Chin | Watershed-Scale Fate and Transport of Bacteria[END_REF][START_REF] Cho | Modeling metal-sediment interaction processes: Parameter sensitivity assessment and uncertainty analysis[END_REF], and the USEPA-developed Hydrological Simulation Program-FORTRAN (HSPF) (e.g. [START_REF] Benham | MODELING BACTERIA FATE AND TRANSPORT IN WATERSHEDS TO SUPPORT TMDLS[END_REF]. These models use a decay term of E. coli depends on solar irradiation. Besides catchment models, some studies developed stream, river, or estuary section models. For instance, [START_REF] Bedri | An integrated catchment-coastal modelling system for real-time water quality forecasts[END_REF], [START_REF] Huang | Integrated hydro-bacterial modelling for predicting bathing water quality[END_REF] couple catchment and coastal models for assessing E. coli distributions on coastal beach areas. However, no existing research integrates urban stormwater discharge model with 3D lake modelling for estimating E. coli distributions in urban bathing water. Moreover, uncertainty analysis was barely done in these studies. This is mainly due to the complexity of model set-up and configuration, high uncertainty of pollution sources, expensive computational costs, and scarcity of case studies with validated results.

In the present study, deterministic models are used because of the limited availability of in-situ measurements. Only a few water samples are collected for measuring E. coli concentration in the lake, even less samplings are performed after rains. According to the monthly observations, E. coli concentration are generally under 500 MPN/100 ml for all the three monitoring points, showing a good water quality (Fig. 9). On the contrary, simulation results indicate that the E. coli concentration can easily overpass this value at a 1-km range of the stormwater outlet within 24 hours after rains (Fig. 7). These modelling approach can thus provide more details for the public to make an informed choice on whether and where to use the bathing water. Although the uncertainties linked with parameter values, pollution sources (e.g. waterfowl, cross connection during rains, etc.) and E. coli mortality processes could be further discussed, this paper originally challenges the new field of integrated urban catchmentpipe-lake modelling for assessing the impact of stormwater discharge on lake water quality with reasonable assumptions. Moreover, the satisfied modelling performance emphasizes a promising potential for the improvement of urban bathing water quality management.

Future outlook for urban bathing water quality modelling

In order to promote the use of urban bathing water quality modelling in an operational context, considerations for future development can be generally outlined in two aspects: (i) improving the reliability of models by introducing new processes, datasets and calibration approaches; (ii) extending the functionalities of models for practical issues by integrating with socio-economic modules and computer techniques.

The modelling improvements can be considered on the following aspects. First, processes describing pathogenic contaminants from diffuse sources, such as combined sewer overflows, bird feces, human activities, can be introduced by coupling with distributed urban catchment models (e.g. [START_REF] Hong | Integrating atmospheric deposition, soil erosion and sewer transport models to assess the transfer of traffic-related pollutants in urban areas[END_REF][START_REF] Hong | A new approach of monitoring and physically-based modelling to investigate urban wash-off process on a road catchment near Paris[END_REF][START_REF] Refsgaard | Système Hydrologique Europeén (SHE): review and perspectives after 30 years development in distributed physically-based hydrological modelling[END_REF]. Second, the description of faecal indicator bacteria (FIB) decay processes can be advanced benefitting from the newly developed rapid bacterial monitoring techniques, by analysing high-frequency measurements of FIB on a time scale of hours or even minutes. Third, more sophisticated calibration and uncertainty analysis could be addressed to enhance the reliability of present model, for instance, an efficient and robust approach developed by Hong et al. ( 2019) could be applied to this complex integrated model with limited computational efforts. Finally, as various field studies have reported significant proportions of FIB attached to suspended particles [START_REF] Pachepsky | Escherichia Coli and Fecal Coliforms in Freshwater and Estuarine Sediments[END_REF], it may be useful to distinguish the different dynamics of free FIB and those attached to particles: adsorption-desorption processes can be described by appropriate kinetic laws, and calculate settlingresuspension processes with settling velocity and erosion formulations. In addition, hybrid models coupling physically-based hydrodynamic models with data-driven ecological models is an appropriate approach for certain cases (e.g., [START_REF] Hellweger | Ensemble modeling of E. coli in the Charles River, Boston, Massachusetts, USA[END_REF].

On the other hand, current study uses a single rainfall station as the precipitation forcing for the small Créteil urban catchment (95 ha), which may not sufficient for urban hydrological simulations at larger scales. [START_REF] Ochoa-Rodriguez | Impact of spatial and temporal resolution of rainfall inputs on urban hydrodynamic modelling outputs: A multi-catchment investigation[END_REF][START_REF] Souza Ba De | Multi-hydro hydrological modelling of a complex periurban catchment with storage basins comparing C-band and X-band radar rainfall data[END_REF] indicate that high spatial and temporal resolutions are required for urban hydrologic applications. [START_REF] Müller | Temporal rainfall disaggregation using a multiplicative cascade model for spatial application in urban hydrology[END_REF] show that the usage of a single rain gauge and hence spatial uniform rainfall leads to an overestimation of flood events. This overestimation will lead to an overestimation of E.coli load in the lake resulting from the surface runoff. In order to improve the reliability and accuracy of the present modelling approach, the usage of available high-resolution x-band radar data for Paris region [START_REF] Paz | Rain gauge networks' limitations and the implications to hydrological modelling highlighted with a X-band radar[END_REF]) is a perspective for future studies of urban bathing water quality modelling.

To be extensively used, simulation results need to be rapidly accessible by managers and public, moreover, models should help providing relevant information to make strategic management decisions regarding socio-economic benefits. In perspective, integrated assessments coupling with hydroecological simulations can bring together knowledge from a variety of disciplinary sources to solve complex real-world problems. Such as using the quantitative microbial risk assessments (QMRAs) for assessing the infection risk from recreational water use, and the cost-benefits assessments for evaluating the gains of maintaining the natural bathing water quality. In addition, scenario simulations with the participation of urban water managers and stakeholders can be proposed to evaluate outcomes of different management strategies.

Conclusion

In many municipal areas, urban stormwater sewers are directly connected to receiving water bodies without any treatment, this may degrade the quality of natural bathing waters, and even cause severe public health risks. In this paper, we developed an integrated urban catchment-pipes-lake modelling approach, to simulate the impacts of E. coli from stormwater sewer flows on recreational water quality.

To our knowledge, it is the first time such an integrated and spatial distributed approach is developed and applied for urban bathing water quality.

The modelling system couples two widely used models, including SWMM (Rossman 2010) and Delft3D (Deltares 2016), to simulate E. coli processes such as generation, transport and mortality from an urban catchment including the drainage network to a receiving recreational lake. This integrated modelling approach is tested for an urban catchment and its related recreational lake located in the Great Paris region.

Hydrological and E. coli build-up/wash-off parameters of SWMM are calibrated and validated for four rainfall events and a 25-day period. The comparison of measured and simulated E. coli event mean concentration (EMC) at stormwater drainage outlet shows a good modelling performance. The hydrothermal dynamics and E. coli transport in Lake Creteil are simulated by using default parameter values. Simulated E. coli concentrations at three monitoring points are within the confidence intervals of the measurements for the studied rains. Spatial-temporal analysis of E. coli distribution in the lake shows that in a range of 500 m of the stormwater sewer outlet, E. coli concentration remains at a very high level during three hours after rains, while it takes about 24 hours to return to a good water quality level.

A 20 months-simulation is then performed for analysing long-term variations of E. coli in the lake.

Comparing the measured and simulated water temperature at different depths of the lake, the modelling system can correctly reproduce the hydro-thermal dynamics of Lake Créteil. Moreover, simulated E. coli concentrations at three monitoring points are compared with monthly observations. The good coherence between simulated and measured values confirms the validity of the present modelling approach.

A stochastic parameter sampling approach is applied for preliminarily assessing uncertainties of E. coli simulations related to wash-off/build-up parameters. Uncertainties of E. coli concentration in stormwater sewer flows can be up to two orders of magnitude, while it is decreased for E. coli simulations of the lake, yet still significant. These results suggest that field studies could be operated in order to optimize the initial intervals of parameter values, and the reliability of this modelling approach could be further discussed.

In order to improve the reliability of the present modelling approach, future development can be carried out by introducing new processes, datasets and calibration approaches. We also aim to extend the model functionalities for practical issues by integrating real-time prediction system, socio-economic assessments and participatory scenario simulations.

Figure 1 .

 1 Figure 1. (a) Location of the study area in Créteil, France. (b) Zoomed-in view of the urban catchment, recreational lake, storm sewer system, monitoring and sampling points.

Figure 3 .

 3 Figure 3. Water flow simulations at stormwater drainage outlet. Simulations (solid blue line) are compared with continuous measurements (red astericks). Parameters are calibrated for the event of 10/14/2013 (a), and validated for the event of 10/16/2013 (b), 10/20/2013 (c), 11/03/2013 (d), and a long period from 10/10 to 11/05/2013 (e).

Figure 4 .

 4 Figure 4. Event Mean Concentration (EMC) of E. coli in stormwater sewer flows, for rains of 10/14 (I), 10/16 (II), 10/20 (III) and 11/03/2013 (IV). Simulated EMC (blue bars) are compared with the measurements (red bars). Error bars indicate the modelling uncertainty related to parameter values (blue bars), and the analytical uncertainty of measured values (red bars).

Figure 5 .

 5 Figure 5. (a) Observed hourly rainfall intensity, simulations of (b) daily stormwater discharge entering Lake Créteil, and (c) daily total influx of E. coli entering Lake Créteil.

Figure 7 .

 7 Figure 7. Simulated (coloured bars) and observed (white bars) E. coli concentrations at the three points (S, C, O) in Lake Creteil on the following day at 10:00 am for rains of 10/14 (I), 10/16 (II), 10/20 (III) and 11/03/2013 (IV). Error bars indicate the modelling uncertainty related to parameter values, and the analytical uncertainty of measured values, respectively.

Figure 8 .

 8 Figure 8. Spatial and temporal distribution of E. coli in Lake Creteil after the rainfall event of Oct. 14 th , 2013. E. coli concentration of the surface water are presented. Wind direction distribution during the 24 hours are shown as well.

Figure 9 .

 9 Figure 9. Simulated monthly mean concentration of E. coli with the 95% confident intervals, and the monthly observations at the three points in Lake Creteil (S, C, O). Simulation period is from 05/12/2012 to 01/31/2014 (please note the that the y-axis range of different graphs differs).

Figure 10 .

 10 Figure 10. Scatter plot of simulated and observed E. coli concentration on different sampling dates.

Table . 1

 . Simulation periods, comparison measurements for assessing model performance, and characteristics of the studied rains.

	Simulation period	Comparison measurements	Rains	Precipit ation depth	Duration	Calibration / Validation
			10/14/2013 4.8 mm 1.3 Hours Calibration
	Sewer monitoring period: 10/10 -11/05/2013 (Event-based simulations)	Stormwater sewer discharge; E. coli EMC of the lake after rains; stormwater sewer flow; E. coli concentration in	10/16/2013 3.4 mm 1.4 Hours Validation 10/20/2013 5.9 mm 0.4 Hours Validation
			11/03/2013	11.7 mm	8.2 Hours Validation
	Lake monitoring
	period: 05/12/2012 -01/31/2014 (Continuous	Lake water temperature at different depths; Monthly E. coli concentration in the lake;	05/12/2012 -01/31/2014	1046 mm	628 Days Validation
	simulation)

Table . 2

 . Initial intervals and optimized values of the build-up and wash-off parameter for E. coli.

	Symbol	Units	Definition	Initial interval	Optimized value
		SI3 (	Maximum possible build-up of E. coli	10 10 -10 16	10 14
	(	day -1	Build-up constant rate	0.6 -2.0	1.2

Table . 3

 . Parameters for modelling E. coli dynamics.

	Symbol	Units	Definition	Value
	T U , T W	m² s -1	Dispersion coefficient of E. coli in horizontal directions;	1
	T X	m² s -1	Dispersion coefficient of E. coli in the vertical direction;	10 -7
	kmb		Basic mortality rate of E. coli	0.8
	ktmrt	-	Temperature coefficient of the mortality rate	1.07
	Y kmrd	3 3 ( Z	Background extinction of UV-radiation Radiation related mortality constant	0.08 0.086

Table . 4

 . Mean absolute error (MAE) of water temperature at Points S, C, O, and at different depths.

	Points	0.5 m (°C)	1.5 m (°C)	2.5 m (°C)
	S	0.68	0.58	0.59
	C	0.47	0.42	0.40
	O	0.55	0.51	0.52

Figure 6 Hourly mean profiles of observed and simulated water temperatures in the middle of Lake Creteil (Point C), from May 12 th , 2012 to Jan. 31 th 2014.

Acknowledgements

This work was funded by the ANR-ANSWER project (No. ANR-16-CE32-0009) and the ANR-PULSE project (No. ANR-10-CEPL-0010). The DSEA (Direction des Services de l'Environnement et de l'Assainissement) and the DGST (Direction Générale des Services Techniques), of the Departmental Council of the Val-de-Marne district, financed the equipment and monitoring of the storm sewer of Lake Creteil with a flowmeter. The DGST of Créteil City provided the authorizations and the street signalization equipment that were necessary to conduct the storm sewer study in the lake. The author would like to thank the experimental team for data collection and equipment maintenance, in particular Viet Tran Khac, Mohamed Saad and Philippe Dubois.

Availability of data and materials:

The source code and data of the SWMM-Delft3D integrated modelling platform can be obtained for free. Please contact Dr. Brigitte Vincon-Leite, LEESU, MA 102, Ecole des Ponts, AgroParisTech, UPEC, UPE, Champs-sur-Marne, France, email : bvl@enpc.fr ;

Author Contributions:

Yi Hong, Brigitte Vinçon-Leite and Bruno J. Lemaire conceived of the presented idea. Yi. Hong, Chenlu Li and Frédéric Soulignac developed the theory and performed the computations. Frédéric Soulignac, Adélaïde Roguet, Rodolfo Scarati Martins, and Françoise Lucas carried out the on-site experiments and provided data. Yi Hong wrote the first draft. All authors discussed the results and contributed to the final manuscript.

Competing Interests:

The authors declare no conflict of interest. Ethical Approval: The authors declare that the manuscript has not been published previously. Consent to Participate: All authors voluntarily to participate in this research study. Consent to Publish: All authors consent to the publication of the manuscript.