Hossein Davarzani
email: h.davarzani@brgm.fr.

Romain Aranda

Stéfan Colombano

Fabien Laurent

Henri Bertin

Experimental study of foam propagation and stability in highly permeable porous media under lateral water flow: diverting groundwater for application to soil remediation

Keywords: Foam, saturated zone, soil pollution, high permeability, 2D tank Highlights

Foam propagation and stability in highly permeable porous media, encountered in soil pollution applications, are still challenging. Here, we investigated the application of foam for blocking the aquifer to divert the flow from a contaminated zone and, therefore, ease the remediation treatments. The main aim was to better understand the critical parameters when the foam is injected into a highly permeable aquifer with high groundwater flow velocity (up to 10 m/day). A decimetric-scale 2D tank experimental setup filled with 1 mm glass beads was used. The front part of the 2D tank was made of transparent glass to photograph the foam flow using the light-reflected method. The water flow was generated horizontally through injection and pumping points on the sides of the tank. The pre-generated foam was injected at the bottom center of the tank. Water streamlines (using dye tracing) and water saturation were investigated using image interpretation. Results show that 100% of the water flow was diverted during the injection of the foam. Foam stability in porous media depends significantly on the horizontal water flow rate. Recirculating water containing the surfactant increases foam stability. The main mechanism of destruction was identified as the dilution of the surfactant in water. However, the head-loss measurements showed that despite foam destruction, the relative permeability of the water phase in the media remained quite low. Injection of foam increases the radius of gas propagation, thanks to foam's high viscosity, compared to a pure gas injection case. These results are new highlights on the efficiency of foam as a blocking agent, showing that it can also serve as a means for gas transport more efficiently in porous media, especially for soil remediation applications.

Introduction

Foams have multiple applications in soil remediation. In recent research, three different foam uses were studied: vectorization, desorption and mobilization, and blocking foams. For each foam technology, new formulations must be considered (surfactant and its concentration, additives, gas) to adjust the properties of the foam to its application. Vectorization foam is used to transport a specific additive for an in situ chemical remediation. Foams can transport nanoparticles [START_REF] Sheng | Enhanced Oil Recovery Field Case Studies[END_REF], calcium polysulfide [START_REF] Zhong | Enhanced remedial amendment delivery to subsurface using shear thinning fluid and aqueous foam[END_REF], bacteria for aerobic biodegradation [START_REF] Choi | Enhancement of aerobic biodegradation in an oxygen-limiting environment using a saponin-based microbubble suspension[END_REF], or hydrogen [START_REF] Maire | Targeted delivery of hydrogen for the bioremediation of aquifers contaminated by dissolved chlorinated compounds[END_REF]. Desorption and mobilization foams use the surfactant properties of the foam to desorb pollutants and push them to a recovery well. Recent laboratory studies have been carried out to assess how foam behaves in porous media for shallow contaminated soil remediation [START_REF] Couto | Remediation of sandy soils using surfactant solutions and foams[END_REF][START_REF] Dicksen | Mobility of Foam in Heterogeneous Media: Flow Parallel and Perpendicular to Stratification[END_REF][START_REF] Mulligan | Remediation with surfactant foam of PCP-contaminated soil[END_REF]. Several studies have focused on the remediation of soils contaminated by DNAPL, such as trichloroethylene (TCE) [START_REF] Jeong | A micromodel analysis of factors influencing napl removal by surfactant foam flooding[END_REF][START_REF] Jeong | Micromodel study of surfactant foam remediation of residual trichloroethylene[END_REF][START_REF] Rothmel | Surfactant foam/bioaugmentation technology for in situ treatment of TCE-DNAPLs[END_REF].

Foam as blocking or diverting agents acts to reduce fluid flow in a high permeability zone of heterogeneous porous media. This blocking effect is possible thanks to the high viscosity of the foam and its gas fraction, reducing the mobility of water in the injected area. Foams formed in the different layers of soil are not identical; in general, stronger foam is generated in the layers of higher permeability, partially blocking these layers. This helps to homogenize flows between different layers. This is one of the main advantages of foam as a non-Newtonian fluid.

A few authors have studied foam in the laboratory with the objective of a blocking application [START_REF] Aranda | Experimental study of foam flow in highly permeable porous media for soil remediation[END_REF][START_REF] Bertin | Foam placement for soil remediation[END_REF][START_REF] Kovscek | Foam mobility in heterogeneous porous media[END_REF]Portois et al., 2018a;Portois et al., 2018b]. Blocking more permeable areas also redirects recovery fluids to less permeable areas [START_REF] Wever | Polymers for enhanced oil recovery: A paradigm for structure-property relationship in aqueous solution[END_REF]. The reason is related to bubble stability and the capillary pressure [START_REF] Khatib | Effects of Capillary Pressure on Coalescence and Phase Mobilities in Foams Flowing Through Porous Media[END_REF]. Layers with high permeabilities have larger pores and therefore lower capillary pressure. Low capillary pressure means that the foam bubbles will not break as easily in these layers. In addition, small bubbles in more permeable layers will reduce gas mobility and divert the flow of water in these layers [START_REF] Rossen | Simplified Mechanistic Simulation of Foam Processes in Porous Media[END_REF]. The foam generated for blocking applications must be very stable to withstand flow over potentially long periods. The main phenomenon for foam coalescence in porous media is related to the capillary pressure introduced generally as a critical value [Kovscek et al., 2007]. The capillary pressure in porous media is a function of water saturation and surfactant concentration. Surfactant concentration, as well as foam quality, also significantly influence foam stability in porous media [START_REF] Wang | An evaluation of surfactant foam technology in remediation of contaminated soil[END_REF].

More recently, [START_REF] Aranda | Experimental study of foam flow in highly permeable porous media for soil remediation[END_REF] investigated the properties of foam generated using an alpha-olefin sulfonate surfactant and nitrogen for flow-blocking purposes in a very high permeable porous medium (> 10 -10 m 2 ). A packed column was used to study the impact of different parameters such as the foam generation method and the pre-generated foam permeability on the foam blocking properties. Foam flow in highly porous media behaves with two regimes: a weak foam flow followed by a strong foam flow. These two distinct flow regimes were more significant when the foam was generated by the co-injection technique (surfactant and gas). They found that a pre-generated foam is a good option for blocking the highly permeable zone. This pre-generated foam showed non-Newtonian, shear-thinning behavior [START_REF] Aranda | Experimental study of foam flow in highly permeable porous media for soil remediation[END_REF]Omirbekov et al., 2020a;Omirbekov et al., 2020b].

The final goal of this study was not to redirect the groundwater flows in areas of low permeability but rather to block an entire area upstream of the area to be remedied. The final goal was to divert or slow down underground flows and to isolate the saturated zone which is under chemical treatment (Fig. 1). The increase in the residence time inside this zone should facilitate the implementation of in situ remediation techniques in the saturated zone (chemical vectorization and treatments). At the end of the remediation processes, the foam will have to be destroyed naturally to allow underground flows naturally. Finally, the pilot site on which these technologies will potentially be applied has very high permeability (from 10 -10 to 10 -8 m²). Thus, one of the main novelties of the present work is to study the blocking effect of foam in highly permeable porous media.

At the microscopic scale, foam has been studied in micro-models to examine the generation and destruction of gas bubbles through their direct visualization and thus establish a predictive model of bubble size distribution in the foam [START_REF] Géraud | Lamella division in a foam flowing through a two-dimensional porous medium: A model fragmentation process[END_REF]. On a macroscopic scale, foam flow has been studied in homogeneous and heterogeneous media. Foam propagation in 2D tanks has been studied recently by some authors [START_REF] Bertin | Foam placement for soil remediation[END_REF][START_REF] Bouzid | Enhanced remedial reagents delivery in unsaturated anisotropic soils using surfactant foam[END_REF][START_REF] Forey | Use of saponin foam reinforced with colloidal particles as an application to soil remediation: Experiments in a 2d tank[END_REF][START_REF] Longpré-Girard | 2d sandbox experiments of surfactant foams for mobility control and enhanced lnapl recovery in layered soils[END_REF] using different configurations to focus on the effect of heterogeneity and/or the presence of pollutant. They showed the importance of several physical parameters like permeability contrast, presence of pollutant, and surfactant formulation on the foam propagation and stability. To our knowledge, there is a lack of information in the literature concerning the study of foam flow and stability under water flow conditions in a decimetric-scale 2D setup.

The setup presented here combines dye tracing, mass balance calculation, and a photographic analysis technique to assess foam flow and saturation values in the porous medium.

Fig. 1. Schematic illustration of the foam injection process for groundwater flow diverting

The objective of the present research work was to study foam injection in the presence of a flow of water to assess its potential as a blocking fluid for diverting flow from a polluted area.

Although the real situation occurs in a 3D geometry, to simplify the problem and to visualize better the foam flow using an imaging technique, all experiments were carried out in a 2D tank.

The propagation and the stability of the foam were studied in a reference case with a water flow of different velocities, as well as 10 m/day, according to the groundwater flow rate in a real polluted site. Additional experiments were carried out to study the influence of the nature of the water flow and its velocity on the propagation and stability of the foam.

Materials and fluids

Porous media

In all 2D tank experiments, 1 mm glass beads were used for the study. These glass beads, supplied by Dutscher ® , were the same as those used in [START_REF] Aranda | Experimental study of foam flow in highly permeable porous media for soil remediation[END_REF]Omirbekov et al., 2020b]. The porous media obtained using these glass beads have an average permeability of 8.4 × 10 -10 m² and an average porosity of 0.37. The transparency properties of glass beads allow good visualization of flows and saturation levels by image analysis.

Surfactant solution and gas

Building upon the results in [START_REF] Aranda | Experimental study of foam flow in highly permeable porous media for soil remediation[END_REF]Omirbekov et al., 2020b], a solution of alpha-olefin sulfonate surfactant (AOS) concentrated at 4×CMC was used for the experiments.

The surfactant solutions were always prepared the same day or the day before starting the experiments to avoid possible aging effects. In addition, further surface tension measurements were made on the stock solution to ensure that the CMC value (1.8 g/L) had not changed over time. The results show that the CMC was not changed for more than a year after opening the product. The gas used to generate the foam was N2 supplied by Air Liquide © (purity> 99.99%).

Carbon dioxide, supplied by the same provider (purity> 99.7%), was also used to prepare the foam pre-generator.

Experimental setup and procedure

Foam pre-generation

The pre-generator consists of a porous medium made of calibrated glass beads of 0.1 mm diameter contained in a PVC column of 10 cm effective length as presented in [START_REF] Aranda | Experimental study of foam flow in highly permeable porous media for soil remediation[END_REF]. The porous medium porosity of the pre-generator column was 0.38 with a permeability of 1.1 × 10 -11 m².

2D tank setup

Two tanks of small (S) and medium (M) sizes were used in this study. The geometric characteristics of the porous media contained in these tanks are presented in Table 1. 2D tanks are composed of a central volume to contain the porous medium. On the two sides of this volume are two cavities separated from the central volume by two 250 µm metal grids allowing fluids to flow but fine enough to contain the porous medium. The cavities insure an almost vertical homogeneous pressure inside the 2D tank. The dimensions of 2D tank and the length of the cavities are specified in Table 1. The assumption was made that the flows in the tanks were two-dimensional. To support this hypothesis, the ratios between the effective height of the saturated porous medium and its width are also presented in Table 1. The tanks have a central injection point on their lower part through which the foam is injected. The M tank also has side connection points for connecting pipes and generating lateral water flows. The experimental setup is presented in Fig. 2. It consists of a primary circuit (foam injection), a secondary circuit (lateral flow of water), and a tertiary circuit (pumping of excess water). In the primary circuit, the nitrogen and the surfactant solution are co-injected into the foam pre-generator column, the gas using a Brooks ® Delta Smart II mass flowmeter (precision: ± 0.34 mL.min -1 ), and the liquid by an Ismatec ® Reglo ICC peristaltic pump (precision: ± 0.063 mL.min -1 ). The co-injection system used a Swagelok ® Tee connector. The fluids left the pre-generator in the form of foam. This foam flowed to a 4-way valve which directed it either to a beaker while awaiting stabilization, or to the tank to begin injection. The circuit pipes were made of PVC and had an inside diameter of 0.635 cm.

The secondary circuit consisted of four pipes and an Ismatec ® Reglo ICC peristaltic pump with four independent channels. This circuit allows deionized water to be injected into the inlet (or left) cavity of the tank. This injection was carried out by two pipes, the ends of which were located at the top and bottom of the cavity (S tank) or at two lateral connection points (M tank)

to create as homogeneous a flow as possible. Likewise, two pipes pumped water from the outlet (or right) cavity, symmetrically to the water injection pipes. To maintain a constant lateral flow, the pumping rate in all four pipes was the same. The tertiary circuit was made up of two pipes and an Ismatec ® Reglo ICC peristaltic pump. The two ends of the pipes were placed at the water/air interface in the two cavities, directly in the cavity (S tank) or attached to a connection point (M tank). This circuit was used to pump excess water from the cavities. When foam was injected into the tank, it occupied a volume replacing water that should be pumped by the tertiary circuit to a beaker placed on a Sartorius ® MSE8201S balance (precision: ± 0.1 g). From

the measured mass, one can deduce the volume occupied by the foam during the injection.

Fig. 2. Experimental 2D tank setup for foam injection and stability study. 2D tank was filled with 1 mm glass beads. The water flows horizontally and pre-generated foam is injected from a bottom center hole (small tank dimensions: =43.5 cm, H=25 cm, h=20 cm and =2 cm; medium tank dimensions: =51 cm, H=35 cm, h=30 cm and =1.8 cm).

Photos were taken using a Nikon ® D850 camera with a 105 mm focal length lens installed on a tripod. The camera was placed in the central axis of the tank, as close as possible but at sufficient distance to capture the entire tank. A Broncolor ® Litos projector was placed above the tank, slightly in front of the device, and off-center. The placement above the tank avoids the reflection of the projector on the 2D tank glass. The slight offset ensured that images were not obstructed by the projector foot. A Scuadra XpoGrey ® element representing standard gray levels was attached to the tank to allow the photographs to be calibrated. During the first photography tests, these standards served to verify that white was not overexposed (brightness value = 255) or underexposed black (brightness value = 0). The photos were taken in a darkroom to overcome variations in exterior light.

Experimental procedures

The 2D tanks were slowly filled up to height H with glass beads to obtain a homogeneous stack. Deionized water was then injected through the injection point at the bottom of the tank at a rate of 2.0 mL/min. The homogeneity of the glass beads and the low injection speed keep water flow stable. Due to very low capillary effects, no air bubbles trapped in the medium were observed. The tank was saturated with water up to an effective saturated height h listed in Table 1 and shown in Fig. 2. The unsaturated zone helps to prevent the lateral flow of water at the surface. All experiments are referenced in Table 2 with the size of the associated tank and the type of lateral flow.

The type of lateral flow was changed in some experiments. The lateral flow is of type "open"

when the deionized water is injected continuously. The experimental setup has been modified so that the pipes of the secondary flow operate in a closed circuit. This means that the fluid pumped into the outlet cavity is directly reinjected into the inlet cavity (instead of deionized water). A flow of this "closed" type allows water to be reused in the tank with a surfactant that has been diluted beforehand and carried away by the lateral flow. Finally, some experiments were simply carried out without activating the secondary circuit. In this case, there is no lateral flow in the tank ("without flow" case). This corresponds to the ideal case where there is no groundwater flow and foam should be in its maximum stability value. It can help to better understand the effect of the lateral flow on foam flow behavior which is one of the main objectives of this work. The pre-generator column was first filled with the porous medium (0.1 mm glass beads).

Then CO2 was injected into the column followed by deionized water, and finally the AOS surfactant solution at a concentration of 4×CMC. Since a pre-generator column is used for several experiments, it is initially filled with destroyed foam (gas and surfactant solution) as the experiment is initialized.

Following the same procedures as described in [START_REF] Aranda | Experimental study of foam flow in highly permeable porous media for soil remediation[END_REF], gas and surfactant solution are co-injected into the pre-generator directing the foam to the effluent beaker using the 4-way valve. This achieves a steady-state foam flow in the pre-generator column guaranteeing that the foam quality is 85% and the total flow rate is 4 mL/min. The objective of this preliminary step is to generate a strong foam repeatable for each experiment inside the pregenerator. The steady-state was achieved when the pressure signal before the pre-generator became stable. At the same time, the second circuit was activated to generate a lateral flow with a flow velocity of 10 m/day. The tertiary circuit was also activated to pump out any water excess before the start of the experiment. To confirm the homogeneity of the lateral flow, a tracing test was carried out with a solution of bromcresol green (BCG) at 1 g.L -1 . The dye is injected into the inlet left cavity and its flow is photographed. Finally, when all the flows are stable and the foam is ready to be injected, a first (zero) photo is taken. The foam was injected into the 2D tank by changing the 4-way valve. At the end of the injection period, the 4-way valve was turned to direct the foam to the effluent beaker. The primary circuit (injection) was stopped but the secondary and tertiary circuits were left active to study the stability of the foam over time.

A new tracing is done at the end of the experiment to visualize the impact of the foam on the lateral flow. The duration of the injection was not the same for all the experiments. Some injections had to be stopped earlier because of some experimental constraints.

Image Analysis

To use the data acquired by photography, the images must be processed and interpreted. The final objective of this approach is to define a relationship between light intensity and liquid saturation. To achieve this, we used the light reflection methods (LRM) (see [START_REF] Alazaiza | A review of light reflection and transmission methods in monitoring non-aqueous phase liquid migration in porous media[END_REF]).

Image treatments

First, a global area of interest (AOI) was defined to obtain the mean grey value necessary to associate with the water saturation. This area is smaller than the 2D tank glass surface to remove the shadows that appear near the edges. Before any treatment step, it is important to choose the appropriate analyzing wavelength. The authors recommend working in monochrome [START_REF] Flores | A simplified image analysis method to study lnapl migration in porous media[END_REF]; however, the technical limitations in the laboratory made it necessary to use white light during the experiments. As the foam is white, its intensity is approximately equal in all monochrome spectra. Consequently, the choice was made to work on shades of gray. The photographs are therefore converted into a 8-bit format to obtain 255 shades of grey. The gray level was calculated using = ( + + ) 3 ⁄ where I is the light intensity (-), between 0 and 255. There are many other methods described in the literature for converting RGB color images to grayscale [START_REF] Câdík | Perceptual evaluation of color-to-grayscale image conversions[END_REF]. The most appropriate technique should be chosen according to the set objective (aesthetics, contrast, highlighting a particular color, etc.).

Many pixels may have under or over brightening. To correct this effect, it is essential to create small meshes where the intensity of the pixels will be averaged. The first step is to determine the optimal size of this mesh. For simplicity, these meshes will be square. The optimal size should be chosen as small as possible to get the most accurate information possible, but large enough to avoid pixel order variations. The primary analysis showed that the microscopic variations in intensity stabilize at an area of 8,836 px², or a small mesh of 94 pixels per side.

In the photographs, the lighting may also not be perfectly uniform in the horizontal and vertical directions. To correct this lack of uniformity, the global mean intensity over AOI is calculated on an image before injecting foam (reference image) where the 2D tank is fully saturated with water = 1 ( = 0). Each analysis of a series (for one experiment) of photos will be based on its reference image. The matrix is defined for each mesh such that = -!" with !" the mean intensity over each small mesh. This uniformization gives a unified gray corresponding to = 1. However, the difference between the global average value over AOI and the original average value of each small mesh !" is kept for the rest of the analysis.

Finally, the intensity is linearly corrected using the standard black and white of the image

= 255 % & -! ' "(&) -! ' * ( 1 )
where is the corrected intensity of each small mesh. The coefficient 255 changes the value of the intensity to a scale of 0 to 255 as initially to obtain more meaningful values. Technically, this coefficient is unnecessary for image analysis. "(&) and ! ' are the standard white and black intensities of the analyzed image, and & the uniform intensity of each mesh is calculated as below using the variations in the intensity of the image zero .

+ = "(&) -! ' ,"(&) -, ! ' ( 3 )
where ,"(&) and , ! ' are the standard black and white intensities of the image zero.

Calibration of the intensity-saturation relationship

The optical density was used to estimate water saturation from grayscale images of a 2D

tank [START_REF] Flores | A simplified image analysis method to study lnapl migration in porous media[END_REF][START_REF] Kechavarzi | Multispectral image analysis method to determine dynamic fluid saturation distribution in two-dimensional threefluid phase flow laboratory experiments[END_REF]. It has been shown that the optical density can be related to water saturation using a linear function [START_REF] Colombano | Thermal and chemical enhanced recovery of heavy chlorinated organic compounds in saturated porous media: 1d cell drainage-imbibition experiments[END_REF][START_REF] Luciano | Laboratory investigation of DNAPL migration in porous media[END_REF][START_REF] O'carroll | Infiltration of PCE in a system containing spatial wettability variations[END_REF][START_REF] Philippe | Experimental study of the temperature effect on two-phase flow properties in highly permeable porous media: Application to the remediation of dense nonaqueous phase liquids (DNAPLs) in polluted soil[END_REF]. In the case of light reflection methods, the transmitted and received energy flux can be associated with the measured reflected light intensity , and the light intensity reflected by a perfect white surface & [START_REF] Flores | A simplified image analysis method to study lnapl migration in porous media[END_REF][START_REF] Kechavarzi | Multispectral image analysis method to determine dynamic fluid saturation distribution in two-dimensional threefluid phase flow laboratory experiments[END_REF][START_REF] Schincariol | On the application of image analysis to determine concentration distributions in laboratory experiments[END_REF]. Therefore, the optical density (OD) can be calculated as

-. = -log 2 % & * ( 4 )
Then the water saturation can be calculated according to a linear relationship = 3-. + 4

( 5 )

The coefficients α and β are then calculated from two calibration images where the saturations are known. For high precision and simplicity, the photos used were at = 0.15 (value of liquid saturation in the foam just after injection) and = 1. To visualize the results of this analysis, the meshes were colored according to their gray intensity. This visualization imposes a discretization of intensities and saturations. For this study, the saturation slices [0; 0.1], [0.1; 0.3], [0.3; 0.5], [0.5; 0.7], [0.7; 0.9], [0.9; 1] were used and associated with a color scale from white to blue.

Method validation

To validate this method, the volume of gas in the tank calculated from the image analysis was compared to that calculated from the mass measurements of the excess water. For this comparison, an experiment without lateral flow was used to eliminate errors due to a difference between the injection and pumping rates generating the lateral injection. During injection, the gas occupied a volume equal to the volume of water leaving the tank from which the volume of injected surfactant solution is subtracted. From imaging, the volume of gas in the tank was deduced from the saturation values calculated from the light intensity considering the 2D tank volume and porous medium porosity. The calibration performed on this experiment gave the values 3 = -2.90, 4 = 6.40 and = 70.

Results and Discussions

Foam flow and its blocking effect

This section discusses the results obtained for the reference case (lateral flow of 10 m/day),

i.e., the propagation of the foam front, the ability to block the lateral flow, and the stability of the foam in the porous medium after stopping the injection.

Fig. 4 shows the results of the tracings carried out before and after injection into the S tank (experiment #1). Before injection, the tracer flows quite uniformly across the 2D tank. The broadening of the shape is due to the diffusion of the tracer in the porous medium. After the foam injection is complete, the tracer flows around the strong foam. The lateral flow of water is therefore completely diverted by the strong foam. In this case, the foam injection was extended so that it reached the unsaturated zone of the tank. The photos show that the water level rises upstream to allow water to flow over the foam.

Stability

After the end of the foam injection, its temporal stability was investigated. During this phase of the experiment, a lateral water flow was maintained in the tank. Fig. 6 shows the changes of gas volume over time in the tank, obtained by imaging. After a short delay, the gas volume decreased and reached a limit value corresponding to the remaining gas volume in the tank once all the strong foam is destroyed. It is interesting to note that the gas volume decreased little during the destruction of the strong foam (from 1150 mL to 955 mL).

83% of the gas supplied by the flow of foam, therefore, remains trapped in the porous medium, either at the initial location of the foam or above it by buoyancy. The photo of the tank after foam destruction shows a gas saturation distribution that is much more homogeneous than at the end of the injection. The tracing tests carried out at the end of the destruction of the foam show that the flow is slowed down in the foam injection zone but that it passes through this zone again (see Fig. 7). The delay before the start of the destruction of the foam seems to be related to the surfactant concentration. Indeed, during the first moments of the stability phase, the surfactant solution is sufficiently concentrated to guarantee the stability of the foam. With the phenomenon of advection-diffusion at the interface, the concentration of surfactant in the solution decreases below the CMC, which promotes foam coalescence.

By taking photos, it is also possible to measure the height of the water in the inlet and outlet cavities. The height differences correspond to the pressure drop required to generate the lateral flow in the porous medium due to foam propagation in the pore space. This pressure drop corresponds to a reduction in the average mobility of water in the tank. This reduction can be presented as a resistance factor 9: "!) , !) (-) as below:

9: "!) , !) ( ) = ∆ℎ( ) ∆ℎ & &) (6)
where ∆ℎ & &) (m) is the difference in water height due to the lateral flow before the foam injection and ∆ℎ(m) is the difference in water height due to the lateral flow at time t.

The temporal evolution of resistance factor 9: "!) , !) is presented in Fig. 8 for experiment #6. During the foam injection phase, RF increases as gas was invading the tank. Water mobility is logically reduced because of the space occupied by the strong foam, which diverted the lateral flow. After stopping foam injection, RF continued to increase slowly compared to the foam injection stage. Consequently, water mobility continued to decrease despite the destruction of the strong foam because a large part of the gas supplied by the foam remained present in the tank. In addition, the gas that escaped from the strong foam, after foam coalescence, rose toward the surface and became trapped in pores. Thus, the gas saturation and its distribution increased in this zone above the strong foam and remained high in the zone previously occupied by the strong foam. Thus, the average mobility in the tank decreased during the coalescence of the strong foam. Strong foam strictly diverts water flow during the injection phase but is gradually destroyed after the injection is stopped. After this destruction, the mobility of water greatly decreases due to the homogenization and distribution of gas saturation in the 2D tank. The lateral flow generates more pressure difference to flow into the tank after the foam is destroyed. Thus, the foam retains its blocking properties even after its destruction. The main interest of the foam for blocking an area could therefore be a means of transporting gas in a porous medium in a homogeneous manner thanks to its high viscosity. Once the zone is occupied by the foam, it can be destroyed to be replaced by the trapped gas, which will maintain a low relative permeability and can be trapped in pores for a longer time.

Influence of lateral flow type

To study how the type of lateral flow influenced foam propagation and stability, the injections were stopped at a time corresponding to the same water mass measured at the outlet of the tank to have the same gas saturation in the tank. After the foam injection was stopped, the lateral water flow was continued at the same velocity as during the injection. Fig. 9 shows the photos taken during the stability phase. Time zero corresponds to the end of the foam injection. Three different weak foam patterns were observed during the three types of flow at the end of foam injection (t=0). These patterns were systematically observed for each of the

Influence of lateral flow velocity

Experiments were carried out in the M-tank to assess the influence of the lateral flow velocity. Four experiments (numbers 4, 5, 6, and 7) were carried out with lateral flow velocities of 5, 7.5, and 10 m/day and one experiment without any lateral flow. The results are presented below. To quantify the foam volume, the radius of influence (ROI) of the foam is defined as the geometric mean of the lateral radius 9 ( and the vertical radius 9 E as 9-= F9 ( 9 E . To complete the analysis of the shape of the foam, the aspect ratio AR is defined as G9 = 9 ( 9 E ⁄ .

Only the shape of the strong foam zone will be discussed. Strong foam can be visually distinguished from weak foam and gas bubbles by the regularity of its shape as well as its color very close to white, indicating a high gas saturation. The areas of the tank where weak foam or gas bubbles flow have irregular shapes are difficult to qualify geometrically (Fig. 10). However, because of the coalescence phenomena, part of the volume of injected gas escapes and is not included in the strong foam mass. Thus, the ROI follows a power law with an exponent less than 0.5 (0.44 -0.47), depending on the coalescence rate. The coalescence rate should be higher for higher lateral flow velocity; therefore, the exponent for the ROI factor is slightly lower. However, the precision of experiments does not allow us to see a significant difference between low lateral flow velocities (0 and 5 m/day) and high ones (7.5 and 10 m/day).

The aspect ratios are plotted in Fig. 12 for different water lateral flow velocities. The aspect ratios are just above 1 at the beginning of the injection and decrease with time to reach the direction at the beginning of the injection can be attributed to bottom wall effects. This means that the elongation of the half-ellipse is more horizontal at the beginning of the injection and tends to a half-circular form at the end. These results show that gravity has no significant impact on strong foam propagation. This confirms the results obtained in [START_REF] Aranda | Experimental study of foam flow in highly permeable porous media for soil remediation[END_REF], which

show that in the case of the flow of a strong foam in a porous medium, the viscous forces are dominant over the gravitational forces. The lateral flow rate tends very slightly to increase the aspect ratio. However, because the random pathway of foam (preferential paths) in the 2D tank, it is difficult to obtain more precise results. To study the influence of the lateral flow speed on the stability of the foam, the injections were stopped at the same mass measured at the outlet of the tank. After the foam injection was stopped, the lateral flow was continued at the same velocity as during the injection. Fig. 13 shows photos of the tanks, according to the time elapsed since the stopping of their respective foam injections. The lateral flow velocity has a significant impact on the stability of the strong The results of these analyzes are presented in Fig. 14. Since the initial gas volumes vary slightly, the volumes are presented in the form of relative gas volume equal to the ratio between the gas volume at time t and the gas volume measured at the end of the injection (t=0). The measurement error due to the difficulty to delimit the boundary between the strong foam zone and the exterior leads to values greater than 1 in the limit of 5%. For the 10 m/day experiment, the volume of gas remaining in the final state tank is quite high compared to the other experiments. However, the relevance of this graph lies in the destruction phase and not only on the value of the volume of gas in the final state. First of all, in the absence of lateral flow, the foam zone is stable during the time of the experiment. In presence of lateral flow, the foam zone remains stable for a time that depends on the velocity. These times are around 30, 12, and 5 hours for 5, 7.5, and 10 m/day lateral water velocity, respectively. This delay is attributed to the time necessary to reduce the surfactant concentration below the CMC by an advection-diffusion phenomenon. The velocity of the flow primarily affects the time before decreasing the volume of gas. There is no significant difference in destruction speed between experiments after this time limit is reached.

Since the advection and dispersion of surfactant are proportional to the velocity of the flow, the latter accelerates the loss of surfactant, and coalescence is initiated more quickly. When the surfactant concentration decreases, the strong foam coalesces starting with the areas with low surfactant concentration, i.e., the foam/water interface and in particular the sidewall on the upstream side of the lateral flow.

Conclusions

We studied the behavior of the foam flowing in a highly permeable porous medium in the presence of a lateral flow of water using 2D tank setups. The influence of this flow and its velocity on the propagation and stability of the foam have been studied in detail.

A flow of strong foam, in the form of a semi-circular semi-ellipse, and a weak foam around it followed by the free gas flow occurred during the foam injection. The quasi-circular shape of the strong foam shows its viscosity and the domination of viscous effects over gravity effects.

The weak foam, on the other hand, flows toward the top of the tank, indicating a lower viscosity.

Lateral flow creates an asymmetry in the weak foam pattern by inhibiting coalescence on the upstream side of the strong foam.

Tracing tests showed that all of the lateral flow was diverted by the strong foam during its injection thanks to its high viscosity. Stability tests have shown that all of the strong foam is destroyed within a few tens of hours. A low lateral flow rate helps to delay the onset of foam coalescence. We found that the coalescence is mainly controlled by the phenomenon of advection-diffusion of the surfactant in the 2D tank. It is expected that, when the surfactant concentration decreases below the critical micelle concentration (CMC), the strong foam begins to coalesce. Foam destruction decreases its viscosity and generates trapped and free-gas that escapes from the strong foam zone upwards towards the top of the tank. This increases gas saturation and its distribution in the area above the strong foam reducing water's mobility in the porous medium.

The foam, therefore, has a double blocking effect: the first is a strict and direct blocking effect caused by the viscosity of the strong foam, and the second is a relative and indirect blocking effect caused by the homogenous distribution of the gas phase in the porous medium.

The gas remains trapped in the porous medium and slows the flows if these are generated by a constant pressure head as is the case with unconfined aquifers.

These results shed new light on the efficiency of foam as a blocking agent, showing that it can also serve as a means of transporting gas more efficiently in porous media, especially for soil remediation applications.

Acknowledgments

This study was performed as part of the "Famous" project. The authors would like to thank ADEME for co-funding the project under the GESIPOL program and BRGM/DEPA and Solvay France for providing the Ph.D. grant for Romain Aranda. We gratefully acknowledge the financial support provided to the PIVOTS project by the "Région Centre -Val de Loire" and the European Regional Development Fund.

Fig. 3

 3 Fig. 3 presents the temporal evolution of the volume of gas in the tank, calculated by measuring the mass and estimated by imaging. Error bars represent 5% of the value calculated by imaging. The values calculated by the two techniques are similar within only 5% of error. It is therefore concluded that the imaging analysis technique allows estimation of the saturation in the tank within ± 5%.

Fig. 3 .

 3 Fig. 3. Gas volume in the tank as a function of time, calculated by mass measurement and estimated by imaging. Error bars represent 5% of the value calculated by imaging.

  attributed to low mobility of strong foam due to its high viscosity and low relative permeability. Therefore, water flows around the foam zone as seen in Fig.4. These results demonstrate that the foam can divert the flow of water, acting as a blocking fluid.

Fig. 4 .

 4 Fig. 4. Traces before and after injection of foam. The tracer is identified by the hatched area. 2D tank S (# 1). Top: Before injection (15 minutes between each photo). Bottom: After injection (5 minutes between each photo).

Fig. 5 .

 5 Fig. 5. Time evolution of the foam zone submitted to a lateral water flow (V = 10 m/day). 2D tank M (Experiment #6).

Fig. 6 .

 6 Fig. 6. How gas volume changes in the tank after the end of the injection. Tank M (Experiment #6).

Fig. 7 .

 7 Fig. 7. Tracing after foam destruction. The tracer is identified by the hatched area (15 minutes between each photograph). Tank S (Experiment # 1).

Fig. 8 .

 8 Fig. 8. Mobility reduction over time (Experiment #6).

Fig. 9 .

 9 Fig. 9. Influence of the type of flow (open flow: free surfactant water flow, closed flow: recirculating outlet flow, and without lateral flow) on the foam patterns during the stability phase. Time after the end of the injection.With an open flow, the strong foam is quickly destroyed. In contrast, the destruction of the foam is much more limited in the case of a closed flow. For an experiment without flow, only

Fig. 10 .

 10 Fig. 10. Example of the form of foam propagation. The strong foam is visually identifiable by itswhite color and regular shape.

  the radius of influence are presented in Fig.11for different water lateral flow velocities. The dynamics of the radius of influence follow an evolution close to a power-law function. In the theoretical case where no coalescence phenomenon would occur, the radius of influence would evolve according to a relation of the type 9-= H√ , by geometric definition (for a constant the foam injection rate). The maximum theoretical value for H when the whole foam volume would be converted into strong foam can be calculated byH = J KL MNwith O injection flow rate and P porous medium porosity.

Fig. 11 .

 11 Fig. 11. Influence of the lateral flow velocity on the temporal evolution of the radius of influence.

  one at the end of the injection. The elongation observed in the horizontal

Fig. 12 .

 12 Fig. 12. Influence of lateral flow velocity on aspect ratio over time.

Fig. 13 .

 13 Fig. 13. How foam patterns change during the stability phase for different flow velocities (Time step 20 hours).

Fig. 14 .

 14 Fig. 14. Influence of lateral flow velocity on relative gas volume over time after the end of the injection.

Table 1 .

 1 Characteristics of the porous medium contained in the different tanks.

					Tank		Cavity
		Effective	Total	Saturated height	width		length
	2D tank	length [cm]	height [cm]	ℎ [cm]	[cm]	ℎ	[cm]
	Small (S)	43.5	25	20	2.2	0.11	2.0
	Medium (M)	51.0	35	30	4.0	0.13	1.8

Table 2 .

 2 Summary of the experiments carried out in the 2D tank.

	Experiment number 2D tank	Lateral	water	Lateral	flow
			flow type		velocity
	1	S	Open		10 m/day
	2	S	Without flow	-
	3	S	Closed		10 m/day
	4	M	Open		5 m/day
	5	M	Open		7.5 m/day
	6	M	Open		10 m/day
	7	M	Without flow	-

& = !" + + ( 2 )where +(-) presents the correction for the possible variation between photographs


Camille D'hervilly
email: c.dhervilly@gmail.com

Isabelle Bertrand

Yvan Capowiez

Camille Béral

Léa Delapré-Cosset

Claire Marsden
email: claire.marsden@supagro.fr

Seasonal variations in macrofauna distribution according to the distance from a herbaceous strip in a Mediterranean alley cropping plot

Keywords: herbaceous strip, soil macrofauna, alley cropping, earthworm, agroforestry, market gardening

In alley cropping systems, herbaceous strips planted with trees are added into cropped fields.

These systems could provide a favorable habitat for many organisms, producing shade in summer and litter in autumn, but their impacts on soil macrofauna are poorly studied, with most samplings limited to one date and therefore one season only. This study investigated the seasonal variations in the spatial distribution of soil macrofauna in a Mediterranean alley cropping plot. We sampled three different shading treatments: a strong shading treatment with lightly-pruned trees, a light shading treatment with pollarded trees, and a no-shade treatment without trees in the herbaceous strips. We measured the density of macrofauna individuals classified into different taxonomic and functional groups by the extraction of 25*25*25 cm soil cores in the herbaceous strip (with or without trees), and in the crop alley at 1 m and 2.5 m from the herbaceous strip. We found a similar response of macrofauna density to the distance from the herbaceous strip for all shading treatments. However, this response was strongly dependent on the season. In spring, just after soil tillage, most soil macrofauna presented higher densities in the herbaceous strip than in the crop alley, except for plant feeders. In early summer, this trend was mostly visible for earthworms, Diplopoda and adult Coleoptera. In autumn, higher densities in the herbaceous strip than in the crop alley were only significant for anecic and endogeic earthworms, while other macrofauna categories presented similar densities at all distances from the herbaceous strip, due to an increase in macrofauna density in the crop alley. These large seasonal variations in spatial distribution of soil macrofauna highlight the importance of temporal repetitions when studying community responses to agroforestry system design and management. The mechanisms by which population densities increased in the crop alley a few months after soil perturbation require further investigation.

Introduction

We are facing a global decrease in biodiversity, partly associated with landscape simplification and with current dominant agricultural practices [START_REF] Habel | Mitigating the precipitous decline of terrestrial European insects: Requirements for a new strategy[END_REF][START_REF] Mclaughlin | The impact of agricultural practices on biodiversity[END_REF]. Agroforestry, or the association of trees and agriculture, can promote an increase in animal biodiversity in cropped fields, because of the addition of new and more diverse habitats [START_REF] Jose | Agroforestry for ecosystem services and environmental benefits: an overview[END_REF]. For example, agroforestry has been shown to impact positively the presence of birds and of pollinator insects compared to simplified agricultural areas [START_REF] Udawatta | Agroforestry and biodiversity[END_REF]. Its impacts on soil dwelling fauna have been far less studied, especially in the Mediterranean zone, and so far work has focused mainly on earthworms or organisms of the soil surface such as adult carabids [START_REF] Marsden | How agroforestry systems influence soil fauna and their functions -a review[END_REF].

In addition to its purely conservational value, soil-dwelling fauna performs essential roles in ecosystem functions, and increases in its diversity and density could improve the multifunctionality of agricultural land [START_REF] Bender | An Underground Revolution: 23 Biodiversity and Soil Ecological Engineering for Agricultural Sustainability[END_REF]. Among them, litter-feeders (mainly earthworms, woodlice and millipedes) contribute to the decomposition of organic matter and to associated nutrient turnover through litter comminution and modification of microbial activity in their guts and fresh feces [START_REF] Barrios | Soil biota, ecosystem services and land productivity[END_REF][START_REF] David | The role of litter-feeding macroarthropods in decomposition processes: A reappraisal of common views[END_REF][START_REF] Frouz | Effects of soil macro-and mesofauna on litter decomposition and soil organic matter stabilization[END_REF], and to carbon storage in old feces [START_REF] Frouz | Effects of soil macro-and mesofauna on litter decomposition and soil organic matter stabilization[END_REF][START_REF] Wolters | Invertebrate control of soil organic matter stability[END_REF]. Some earthworms incorporate fresh organic matter into the mineral soil, where it can be protected from degradation and contribute to carbon storage [START_REF] Bossuyt | Protection of soil carbon by microaggregates within earthworm casts[END_REF], which has also been shown for millipedes [START_REF] Filser | Soil fauna: Key to new carbon models[END_REF]. Conversely, earthworms feeding on stabilized particulate organic matter contribute to mineralize it [START_REF] Lavelle | Soil invertebrates and ecosystem services[END_REF]. Earthworm activity can also improve soil structure by the creation of burrows, soil decompaction and the creation of an organo-mineral horizon [START_REF] Lavelle | Large-scale effects of earthworms on soil organic matter and nutrient dynamics To cite this version : Large-Scale Effects of Earthworms on Soil Organic Matter and Nutrient Dynamics[END_REF]. In addition, the regulation of the invertebrate community by animal feeders is increasingly studied for pest control [START_REF] Holland | Semi-natural habitats support biological control, pollination and soil conservation in Europe[END_REF], and is performed by organisms living in the soil (Chilopoda, most larvae of Coleoptera, etc) or dependent on the soil for their larval stage or overwintering (insect predators at their adult stage) [START_REF] Geiger | Hibernation of predatory arthropods in semi-natural habitats[END_REF]. The soil can also host larvae of future crop pollinators. Practices promoting soil fauna abundance and diversity should thus be favored in a context of reduction of chemical inputs.

In alley cropping agroforestry, trees are organized in rows in order to facilitate crop management practices along alleys. A strip of around 2 m wide is uncultivated below the trees, and an associated understory vegetation is initially sown or appears spontaneously, mostly herbaceous. The lack of disturbance, permanent soil cover and source of additional food resources from this non-exported vegetation creates a specific habitat in these herbaceous strips. They are an overwintering site for most surface-dwelling invertebrates living in alley cropping systems [START_REF] Boinot | Distribution of overwintering invertebrates in temperate agroforestry systems: Implications for biodiversity conservation and biological control of crop pests[END_REF], present higher earthworm densities than crop fields and crop alleys [START_REF] Cardinael | Spatial variation of earthworm communities and soil organic carbon in temperate agroforestry[END_REF], and host high densities of woodlice [START_REF] D'hervilly | Sown understory vegetation strips impact soil chemical fertility, associated microorganisms and macro-invertebrates in two temperate alley cropping systems[END_REF][START_REF] Pardon | Gradients in abundance and diversity of ground dwelling arthropods as a function of distance to tree rows in temperate arable agroforestry systems[END_REF][START_REF] Pardon | Juglans regia (walnut) in temperate arable agroforestry systems: effects on soil characteristics, arthropod diversity and crop yield[END_REF] and millipedes [START_REF] Pardon | Gradients in abundance and diversity of ground dwelling arthropods as a function of distance to tree rows in temperate arable agroforestry systems[END_REF]. This herbaceous strip could particularly be a reservoir of macrofauna, i.e. soil fauna larger than 2 mm, then able to disperse towards the crop alley over wider distances than mites or springtails, for example. However, proof is still lacking that the herbaceous strip really benefits the establishment of diverse and abundant communities in the crop alley, as studies of spatial heterogeneity in alley cropping systems are scarce and show contrasting results. For example, no variation in earthworm density was found in crop alleys with the distance from the herbaceous strip by [START_REF] Cardinael | Spatial variation of earthworm communities and soil organic carbon in temperate agroforestry[END_REF], while earthworm density was negatively impacted by herbaceous strip proximity in some sites [START_REF] D'hervilly | Sown understory vegetation strips impact soil chemical fertility, associated microorganisms and macro-invertebrates in two temperate alley cropping systems[END_REF][START_REF] Rivest | Variation of soil microbial and earthworm communities along an agricultural transect with tree windbreak[END_REF]. In addition, the effect of the distance from the herbaceous strip is also probably influenced by tree properties, as they determine the quantity and quality of litter added in the crop alley and the strength and range of the microclimate effect. For example, woodlice and millipede activity were positively affected by old but not young tree row proximity in one study [START_REF] Pardon | Gradients in abundance and diversity of ground dwelling arthropods as a function of distance to tree rows in temperate arable agroforestry systems[END_REF], and a gradient in earthworm density from the tree to the center of the crop alley was found in a Canadian system for some tree species only [START_REF] Price | Spatial and temporal distribution of earthworms in a temperate intercropping system in southern Ontario, Canada[END_REF]. Finally, most studies rely on one single sampling season, while conceptually, dynamic exchanges between herbaceous strips and crop alleys can be expected to depend on the period of the year, driven by adverse or favorable properties of the crop alley or by soil organism life cycles affected by climatic conditions. This study aims to determine the seasonal variations of soil macrofauna distribution according to the distance from a herbaceous strip (HS) for different shade treatments in an alley cropping plot. We made the hypotheses that (i) HS can be a specific shelter for macrofauna, leading to higher faunal densities in HS than in crop alleys; (ii) this bimodal density distribution is particularly visible during certain seasons when conditions are not favorable for soil fauna in the crop alley, and replaced by a gradient-type distribution during other seasons due to soil macrofauna dispersal from the HS towards the crop alley; and (iii) this HS shelter effect is less visible in the presence of strongly-shading trees than in the presence of lightlyshading trees or without trees, as tree-induced changes in microclimate and in litter and soil organic matter presence may render crop alley conditions more favorable for soil macrofauna.

Methods

Site description

The study took place in an experimental alley cropping plot of 2,250 m 2 located near Vézénobres in the South of France (44.058 N,4.111 E), included in a wider alley cropping site. The climate is Mediterranean (temperature of 15.2 °C and 760 mm of precipitation per year on average, French Institute of Meteorology Météo France). The soil is on recent alluvial deposits, loamy in the first 25 cm depth with a pH of around 8, 16 % of CaCO3 and a CEC of 9.5 cmol + kg -1 on average (basic soil properties are detailed in Table 1 and Table S1 in the Supplementary resources). These soil properties were determined at the beginning of the sampling in 2018. Texture was analyzed on decarbonated soil sieved at 2 mm. Bulk density was determined with the cylinder method (dry weight of soil sampled in 100 cm 3 cylinders).

Soil organic carbon content was measured with an elemental analyser (Thermo Fisher Scientific Flash 2000) on soil sieved at 2 mm and ground at 250 µm.

Hybrid walnut trees (Juglans nigra L. x Juglans regia L.) spaced 10 m apart were planted in 1995. Cereal and legume crops were grown with conventional practices between the tree rows until 2010 (mostly wheat and rapeseed, with some fallow periods). Since then, the plot has been converted to organic farming.

The experiment was set up in 2015, after a year of sunflower cultivation with reduced tillage and no fertilizer, followed by a cover crop. The experimental plot was divided into three shade treatments of 750 m 2 each (Fig. 1a). In the strong shade treatment (shade ++), trees were only lightly pruned as usually done in agroforestry systems (mean diameter at breast height of 0.37 ± 0.07 m in 2017). In the light shade treatment (shade +), trees were strongly pruned to obtain pollarded trees (mean diameter at breast height of 0.33 ± 0.08 m in 2017).

Pruning took place in February 2015 and again in February 2018. In the last treatment, no tree was present (no shade), as trees initially present had been removed in 2011. Each treatment consists of three 8 m-wide and 25 m-long crop alleys and their adjacent herbaceous strips (HS), planted with trees in treatments shade ++ and shade + (Fig. 1a). HS are 2 m wide, covered with spontaneous vegetation and mowed about twice a year in each treatment (characteristics of the vegetation are detailed in Table 1 andTable S1 in the Supplementary materials). Each crop alley is made up of 5 mulched raised beds (with rameal chipped wood on 2 to 3 cm width or hay on 7 cm width alternating each year), about 90 cm wide and 20 cm high, parallel to the HS (Fig. 1b). In each shade treatment, the three crop alleys are managed as a rotation of 3 vegetable crops (carrots, tomatoes and lettuces), meaning that in a given year only one crop alley in each shade treatment is planted with tomatoes. The order of rotation of the different vegetables between the different crop alleys is the same for all shade treatments. Soil was rotary tilled and beds formed at the beginning of the experiment in 2015, and then soil was always rotary tilled after carrot production. After tomatoes or lettuces, beds were only consolidated with a hoe. Fertilization was similar for all productions, with the addition of ricinus oil cakes in 2015 (250 kg ha -1 ), and 2016 (400 kg ha -1 ), and of poultry manure in 2017 and 2018 (560 kg ha -1 each year). No pesticides were used except in 2018 when slug pellets were applied (Ferramol at 0.08 kg ha -1 ). Crops are drip irrigated during summer.

Sampling design and plot management during sampling

Macrofauna samplings took place in April (16 th to 23 rd ) i.e. spring, June (18 th to 22 nd ) i.e. early summer and November (14 th to 21 st ) i.e. late autumn of 2018 to take into account seasonal variability. Rainfall during the year of the experiment was of 166 mm (January), 59 mm (February), 72 mm (March), 90 mm (April, first sampling), 101 mm (May), 4 mm (June, second sampling), 20 mm (July), 56 mm (August), 19 mm (September), 257 mm (October) and 226 mm (November, last sampling, Bellegarde weather station, monitoring data from the INRAE CLIMATIK platform managed by the AgroClim laboratory of Avignon, Francedata).

No sampling was carried out during late summer because the rainfall was very low, thus limiting the chance of finding soil macrofauna. Only the crop alleys planted with tomatoes were sampled in order to ensure homogeneous management practices. In these crop alleys, raised beds were rotary tilled in March and covered with a 2 to 3 cm-thick layer of ramial chipped wood obtained from walnut prunings. Different varieties of tomato plants previously grown in the nursery were planted a week after the first sampling (1.6 plants per m²). Each crop alley received two top dressings of poultry manure in March and in April after tomato plantation, for a total of 560 kg ha -1 . Tomato plants were drip-irrigated from June (before our sampling date) to mid-September. The previous crops in these crop alleys were lettuces (2015), tomatoes (2016) and carrots (2017). HS were mowed after the June sampling date and at the end of summer. In tomato beds, manual weeding was regularly performed until the end of September, when tomato harvesting stopped.

Sampling was designed in order to investigate the effect of the distance from the HS in different shading conditions. Macroinvertebrates were sampled along transects perpendicular to the HS with three distances from the HS (0 m i.e. in the middle of the HS, 1 m from the HS border i.e. in the closest tomato bed to the HS, and 2.5 m from the HS border i.e. in the next tomato bed) (Fig. 1b). For each shade treatment (shade++, shade + and no shade) and at each sampling season, each of the three distances from the HS was sampled eight times (eight transects were made), meaning 24 samples were taken for each shade treatment for a given season (72 samples per season all treatments combined, thus 216 samples in total). All samples were taken in the same crop alley for a given shade treatment as only one crop alley was planted with tomatoes in each shade treatment, and as no replication of the shade treatments was available on this experimental plot. In the treatments with trees (shade ++ and shade +), four of these transects started at an HS sampling position located 1m from the nearest tree, and four others started at an HS sampling position located 5m from the nearest tree (Fig. 1b).

Macroinvertebrate sampling

At each sampling point, macroinvertebrates were hand sorted from soil blocks of 25*25*25 cm (adapted from [START_REF] Anderson | Tropical soil Biology and Fertility, a handbook of methods -second edition[END_REF]. Earthworms were kept alive in water, and then counted and determined at species level under laboratory conditions, and classified into the three main ecological categories anecic, endogeic and epigeic following [START_REF] Bouché | Stratégies lombriciennes[END_REF].

Other macroinvertebrates were kept in ethanol, and then counted and determined under laboratory conditions. Chilopoda were determined at order level, while insects and Diplopoda were determined at family level when possible. Count values obtained were expressed as densities (individuals per m 2 ). As ants presented a wide variation in their densities (due to their properties as social insects), ant density was separated in three density classes (no individuals found, between one and 240 individuals per m 2 , and more than 240 individuals per m 2 ). This classification was chosen to make a distinction between no ants present, few ants presents (240 individuals per m² refers to 15 individuals found in a soil block, abundance after which ant counts always reached high numbers of individuals which could not be counted precisely), and probable ant hill. A feeding group was attributed to each category of macrofauna when possible. Diplopoda, Isopoda and larvae of Diptera were classified as litterfeeders. Araneae, Chilopoda, Staphylinidae and larvae of Carabidae, Staphylinidae and Cantharidae were classified as animal-feeders. Elateridae, Curculionidae and larvae of Lepidoptera, Elateridae, Curculionidae and Melolonthinae were classified as plant-feeders, although they consume different parts of the plants. Anecic earthworms were classified at 50 [START_REF] Bernier | Earthworm feeding activity and development of the humus profile[END_REF], while endogeic earthworms were all classified as soil-feeders and epigeic earthworms were all classified as litter-feeders.

Statistical analyses

To investigate the effect of the distance from the HS within the different seasons and shade treatments, macroinvertebrate density (grouped in taxonomic and feeding groups, as well as ecological categories anecic, endogeic and epigeic for earthworms) was analyzed using generalized linear models fitted by quasi Poisson law (with a log link function). These analyses were not run for each earthworm species individually, as most species did not account for enough individuals. Distance from the HS (0, 1 or 2.5 m), shade treatment (shade ++, shade + or no shade) and season (April, June or November) and their interactions were used as fixed factors. Significant effects were determined by type II F tests and followed by pairwise comparisons (Tukey). Significance level was set to 5 %. As no significant difference was found for macrofauna density between transects distant 1 m and 5 m from the tree in the shade treatments with trees (shade ++ and shade +), all transects were treated as simple replicates, whatever their distance from the tree (data not shown). Analyses were run using R statistical software (version 3.6.2) (R Core Team, 2019) with packages lme4 [START_REF] Bates | Fitting Linear Mixed-Effects Models Using lme4[END_REF], car [START_REF] Fox | An R Companion to Applied Regression[END_REF] and emmeans [START_REF] Lenth | Litter N-content influences soil millipede abundance, species richness and feeding preferences in a semi-evergreen dry forest of Guadeloupe (Lesser Antilles)[END_REF]. Ant density classes were analyzed with a cumulative link model, using the ordinal R package [START_REF] Christensen | ordinal -Regression Models for Ordinal Data[END_REF].

Species richness (i.e. number of different species) and the Shannon diversity index were calculated for earthworms at species level (vegan package in R, [START_REF] Oksanen | Vegan: ecological diversity[END_REF], and analyzed using generalized linear models (species richness) or analyses of variance (Shannon index) with the same fixed factors season, distance from the HS and shade treatment.

Variations in macrofauna community composition between distances from the HS and shade treatments were evaluated with a principal component analysis using densities in taxonomic groups at order or family level when possible (packages FactoMineR and ggplot2 in R) [START_REF] Lê | FactoMineR: An R Package for Multivariate Analysis[END_REF][START_REF] Wickham | ggplot2: Elegant Graphics for Data Analysis[END_REF] for each season. Groups with too few individuals (median equal to 0) were excluded from the analysis. Earthworms were separated into the ecological groups anecic, epigeic and endogeic to account for their different behaviors. In order to account for large differences in density between taxonomic groups, data were standardized to the maximal density measured for each taxonomic group (maximal margin method of function decostand, vegan package in R, [START_REF] Oksanen | Vegan: ecological diversity[END_REF].

Results

Macrofauna community composition

Identified macrofauna were mostly earthworms (17 ± 12 % standard deviation, 32 ± 17 % and 29 ± 15 % of macrofauna individuals in the no shade, shade + and shade ++ treatments respectively), Chilopoda (9 ± 9 %, 10 ± 10 % and 20 ± 16 % respectively), Diplopoda (21 ± 12 %, 13 ± 10 % and 4 ± 6 % respectively) and Coleoptera (26 ± 13 %, 17 ± 16 % and 21 ± 18 % respectively). Formicidae represented up to an estimated 82 % of all individuals in some samples (while their mean contribution was estimated to 12 ± 19 %, 10 ± 16 % and 7 ± 14 % in the no shade, shade + and shade ++ treatments respectively) (Table S2 in the Supplementary materials).

The principal component analysis based on macrofauna density in the different taxonomic groups shows variable patterns with the season. In April and June, the principal component analysis mostly isolates sampling points of the HS from those of the tomato beds along the first axis (representing 23 % of the variance in April and 25 % of the variance in June) (Fig. 2a and Fig. 2b). In April, it is explained by more epigeic and anecic earthworms, Julidae and Isopoda in the HS than in the tomato beds. In June, it is explained by more epigeic earthworms, Julidae and Staphylinidae in the HS than in the tomato beds. The separation of sampling points from the different shade treatments is much less clear, and takes place along axis 2, which explains a lower part of the variance (16% in April, 15 % in June) (Fig. 2a and Fig. 2b). In the opposite, the separation between the HS and the tomato beds is not clear in November, where it is driven by component 2 (16 % of the variance, Fig. 2c), while the first component (22 % of the variance) clearly isolates the shade treatments from one another, especially the no shade treatment from shade ++. There were particularly more Polydesmidae and Elateridae larvae in the no shade treatment compared to other treatments, while the shade ++ treatment is additionally characterized by lower densities of endogeic earthworms and of Julidae compared to other treatments. The tomato beds at 1 m or 2.5 m from the HS could not be separated at any season.

Macrofauna density in taxonomic groups

The response of macroinvertebrate density to the distance from the HS was similar in all shade treatments (Table S3 in the Supplementary materials, significant interaction between distance from the HS and shade treatment for Diplopoda only, and probably due to large differences in densities between shade treatments, see Fig. S1 in the Supplementary materials). However, macrofauna density was different between shade treatments, with especially lower densities in shade ++ compared to other treatments for most taxonomic groups (except Chilopoda, cf Table S2 in the Supplementary materials).

The effect of the distance from the HS on macroinvertebrate density varies with the taxonomic group and the season, as shown in Table 2 and Table S3 in the Supplementary materials (significant effect of the interaction between the distance from the HS and the season for Lumbricidae, Diplopoda, Isopoda, Chilopoda and adult Coleoptera). At all seasons, earthworms presented significantly higher densities in the HS compared to the tomato beds (1 and 2.5 m from the HS), and ants presented higher densities in the HS compared to 2.5 m from the HS (Table 2). Diplopoda presented higher densities in the HS than 2.5 m from the HS in April, and higher densities in the HS compared to all tomato beds (1 and 2.5 m from the HS) in June, but not in November. Isopoda presented higher densities in the HS than in the tomato beds (1 and 2.5 m from the HS) in April only. Adult Coleoptera presented higher densities in the HS compared to 1 m from the HS in April, and compared to both 1 and 2.5 m from the HS in June, while no difference was found in November. In the opposite, Chilopoda presented higher densities at 1 m from the HS than in the HS in November, while no difference was found at other seasons. Dermaptera and Coleoptera larvae did not vary significantly with the distance from the HS at any season (no significant effect of the interaction between distance from the HS and season or of the distance from the HS alone, Table S3 in the Supplementary materials). No significant difference between 1 and 2.5 m from the HS was found for any season or taxonomic group. The attenuation of differences in macrofauna density between the HS and the tomato beds in November is due to a significant increase in macroinvertebrate density at this season compared to April and June in the tomato beds but not in the HS for earthworms, Diplopoda, Isopoda and Chilopoda (Table 2).

Earthworm diversity

Seven species of earthworms were found in all shade treatments (Table 3). Earthworm diversity varied with the distance from the HS (Table 3). Species richness was higher in the HS than both 1 and 2.5 m from the HS in April and June, and than 2.5 m from the HS in November. The Shannon index presented a significant decreasing gradient from the HS to 2.5 m from the HS for all seasons.

The response of earthworm density to the distance from the HS varies with their ecological category (Fig. 3). Anecic earthworms presented higher densities in the HS compared to 1 and 2.5 m from the HS at all seasons, especially due to Aporrectodea nocturna (Table 3).

Endogeic earthworms presented higher densities in the HS compared to 1 and 2.5 m from the HS in April and June, but only compared to 2.5 m from the HS in November, especially due to Allolobophora chlorotica and to Aporrectodea rosea. Epigeic earthworms (all of Lumbricus castaneus species) presented higher densities in the HS compared to 2.5 m from the HS in April, and compared to both 1 and 2.5 m from the HS in June, but no significant difference was found anymore in November for epigeic density between distances from the HS, because of a large increase in epigeic density in the tomato beds between June and November.

Feeding groups

The distribution of macrofauna in the plot varies according to the feeding group considered (Fig. 4). Litter-feeders presented higher densities in the HS compared to tomato beds in April and June, but not in November (Fig. 4a). This result was mostly driven by litter-feeding earthworms and Diplopoda. Soil-feeding earthworms presented higher densities in the HS than in the tomato beds at all seasons (Fig. 4b). Animal-feeders presented higher densities in the HS than in the tomato beds in April only (Fig. 4d). Animal-feeders were mostly Chilopoda, especially in June and November. Plant-feeders presented a different pattern from other groups, with a significantly lower density in the HS compared to the tomato beds in April (Fig. 4c). Plant-feeders were mostly Coleoptera larvae, of which a huge proportion consisted of Elateridae (85 % ± 27 %).

Discussion

Constant patterns of macrofauna distribution throughout seasons

Throughout all seasons, HS macrofauna communities were characterized by higher densities of litter-feeders but similar Dermaptera and Chilopoda densities, compared to communities found in the tomato beds.

Earthworms presented higher densities in the HS compared to both tomato beds at all seasons, especially due to anecic earthworms. Higher earthworm densities in HS than crop alleys were also found by [START_REF] Cardinael | Spatial variation of earthworm communities and soil organic carbon in temperate agroforestry[END_REF] in France and [START_REF] Rivest | Variation of soil microbial and earthworm communities along an agricultural transect with tree windbreak[END_REF] in Québec for different alley cropping plots mostly cultivated with cereals and legume crops, and by [START_REF] Crittenden | Earthworm assemblages as affected by field margin strips and tillage intensity: An on-farm approach[END_REF] in the Netherlands for herbaceous margins of fields cultivated with cereals and tuber crops. Anecic earthworms live in permanent burrows in the soil. HS were probably a favorable habitat to them as they were not subject to soil perturbation, while anecic earthworms were probably negatively impacted by the repeated destruction of their burrows and the lack of adequate food resources and protection against predators at the soil surface in the tomato beds [START_REF] Chan | An overview of some tillage impacts on earthworm population abundance and diversity -implications for functioning in soils[END_REF]. Aporrectodea nocturna, the main anecic earthworm species found in this study, is in particular known to reuse its burrows intensively [START_REF] Capowiez | Differences in burrowing behaviour and spatial interaction between the two earthworm species Aporrectodea nocturna and Allolobophora chlorotica[END_REF].

In addition, endogeic earthworms always presented higher densities in the HS than 2.5 m from the HS. Endogeic earthworms were probably strongly impacted by the recent rotary tillage as they live and feed inside the soil. Similarly, ants also presented higher densities in the HS than 2.5 m from the HS at all seasons. Anthills were probably repeatedly destroyed by intensive tillage in the tomato beds. In agreement with us, [START_REF] Boinot | Distribution of overwintering invertebrates in temperate agroforestry systems: Implications for biodiversity conservation and biological control of crop pests[END_REF] found more activity density of ants in the tree row than in the crop alley in mature alley cropping systems cultivated with cereals in the south of France. In spatially structured systems like the one studied here, spatial differences in soil properties (e.g. higher soil organic carbon concentrations and stocks under tree rows such as often found in agroforestry systems (Cardinael et al., 2017)) could contribute to explaining locally higher densities of earthworms. However in our case, basic soil characteristics, including organic matter content, did not vary according to sampled positions (Table 1), therefore differences in macrofauna communities are more likely related to other changes in habitat characteristics caused by vegetation structure and management practices.

Dermaptera and Chilopoda density did not vary between HS and crop alleys at any season.

Similarly, Smith et al. (2008b) did not find significant differences in Chilopoda abundance between grass margins and the adjacent wheat crop in England. These organisms are able to move quite fast and could have recolonized tomato beds more rapidly than other soil-dwelling organisms such as earthworms and larva after tillage. While adult Coleoptera have a faster dispersal, particularly flying Staphylinidae, they did not present the same pattern, probably because they use different habitats for living and feeding.

Seasonal variations in macrofauna distribution

Despite a constant general trend, this study reveals some seasonal variations in the differences between HS and tomato bed macrofauna communities, which could be due to climatic variations or to crop management. In April, most soil macrofauna was probably negatively impacted by the recent soil perturbations in the tomato beds. Smith et al. (2008b) indeed found that soil scarification reduces macrofauna density, but that populations recovered within a season after soil scarification. In the present study, these macrofauna categories seem to have recovered in November, or even in June for Isopoda. The recovery in November could have been amplified by the interruption of weeding and of other management, allowing the colonization of tomato beds by herbaceous vegetation, probably providing food and habitat usually not found in crop alleys for soil macrofauna. In addition, November 2018 was a particularly rainy month, which could have favored macrofauna activity. More generally, Mediterranean regions are affected by strong climate variability: spring is not always a favorable season as it can sometimes be too dry, summer is generally very dry and hot, and intense rainfall events can occur in autumn, with variable timing and amplitude. Endogeic macrofauna is very sensitive to such variations in rainfall and temperature, with a limited activity in summer, and as found in this study a potential increase in activity in autumn. The herbaceous strip could act as a refuge in unfavorable seasons, by buffering climatic conditions compared to the exposed crop alley. In addition, some soil macrofauna taxa require different habitats at different periods of the year. In spring, macrofauna is probably found in the places where it overwintered, i.e. probably buffered habitats such as the HS. In summer, macrofauna concerned by aestivation (such as epigeic and anecic earthworms) is probably not present in places submitted to high temperatures and fast desiccation such as the crop alley, with little plant cover of the soil, low bulk density and fragile structure due to rotary tillage. The specific effect of the climatic conditions versus agricultural practices, particularly soil tillage, is however difficult to determine as each agricultural practice is strongly associated with the season.

Epigeic earthworms and isopods are usually present at very low densities in tilled soils, probably because of the reduction in adequate shelter and food at the soil surface [START_REF] Hassall | Sheltering behavior of terrestrial isopods in grasslands[END_REF][START_REF] Pelosi | Earthworm community in conventional, organic and direct seeding with living mulch cropping systems[END_REF]. Higher densities of isopods in tree rows compared to crop alleys have already been found in spring similarly to us in both young and old sites with cereals or tuber crops in Belgium and France [START_REF] D'hervilly | Sown understory vegetation strips impact soil chemical fertility, associated microorganisms and macro-invertebrates in two temperate alley cropping systems[END_REF][START_REF] Pardon | Gradients in abundance and diversity of ground dwelling arthropods as a function of distance to tree rows in temperate arable agroforestry systems[END_REF], and isopods have been shown to hibernate in tree rows in mature alley cropping plots in the south of France [START_REF] Boinot | Distribution of overwintering invertebrates in temperate agroforestry systems: Implications for biodiversity conservation and biological control of crop pests[END_REF]. Epigeic earthworms have also been shown to be mostly present in tree rows in spring in France [START_REF] Cardinael | Spatial variation of earthworm communities and soil organic carbon in temperate agroforestry[END_REF][START_REF] D'hervilly | Sown understory vegetation strips impact soil chemical fertility, associated microorganisms and macro-invertebrates in two temperate alley cropping systems[END_REF] or in field margins in July [START_REF] Crittenden | Earthworm assemblages as affected by field margin strips and tillage intensity: An on-farm approach[END_REF] compared to the neighboring crop. In addition, higher densities of Diplopoda were also found in tree rows than in adjacent crops by [START_REF] Pardon | Gradients in abundance and diversity of ground dwelling arthropods as a function of distance to tree rows in temperate arable agroforestry systems[END_REF]. However, our study demonstrates that Isopoda, epigeic earthworms and Diplopoda can be present in the crop alley at similar densities to those of the HS in autumn, their establishment being probably favored in our case by the shelter provided by ramial chipped wood presence at the soil surface of the tomato beds. Tomato bed irrigation in June probably further favored early colonization by isopods, limiting the usual adverse conditions of the summer. Surprisingly, it did not favor epigeic earthworms whose presence was mostly restricted to the HS in June, although they are known to be positively affected by increases in soil humidity and litter presence at the soil surface [START_REF] Bouché | Stratégies lombriciennes[END_REF]. Temperatures were probably too high for epigeic earthworm activity in summer, and ramial chipped wood was probably a more interesting resource for Isopoda than for epigeic earthworms.

Adult Coleoptera were mostly Staphylinid beetles and Carabids in our study. [START_REF] Andersen | Densities of overwintering carabids and staphylinids (Col., Carabidae and Staphylinidae) in cereal and grass fields and their boundaries[END_REF]Smith et al. (2008b) found respectively more Carabid and Staphylinid beetles or more Coleoptera in field margins than in the cereal crop fields (in Norway and England respectively), similarly to what we found in April and June. The higher densities of adult Coleoptera in the HS than in the tomato beds in April and June could be due to additional prey for the animal-feeders in the HS as usually described for margin habitats [START_REF] Landis | Habitat management to conserve natural enemies of arthropod pests in agriculture[END_REF]. It could also be due to their behavior, as most of them feed at night (Martin-Chave et al., 2019a), and could use the HS as a shelter during the day. Contrary to our hypothesis, no significant difference was found between distances 1 m and 2.5 m from the HS for macrofauna density at all seasons. However, we only investigated the HS close vicinity, due to the limited size of our experimental plot (crop alleys were only 8 m wide), which could have hidden some effects. For example, Smith et al. (2008a) found higher macrofauna density up to 3 m from field margins compared to the middle of the field in England. However, while the HS presented higher endogeic earthworm density than both tomato beds in April and June, endogeic earthworm density was only significantly higher in the HS than 2.5 m from the HS in November, suggesting a positive effect of HS vicinity on endogeic earthworm density in November. A positive effect of tree row proximity on earthworm density has already been suggested by [START_REF] Price | Spatial and temporal distribution of earthworms in a temperate intercropping system in southern Ontario, Canada[END_REF]. A possible explanation is that most macrofauna dispersed from the HS to at least 2.5 m from the HS in the crop alley in November, but that this dispersion was more limited for endogeic earthworms, whose movements are slowed as they are restricted to the soil.

Plant-feeding Coleoptera larvae presented higher densities in the tomato beds than in the HS in April, and no differences between distances from the HS at other seasons. These Coleoptera were mostly wireworms (Elateridae), known to be detrimental to crops, which could explain their preference for the crop alley. However, wireworms are usually destroyed directly or indirectly by tillage [START_REF] Parker | The biology and management of wireworms (Agriotes spp.) on potato with particular reference to the U[END_REF], which was performed only a month before the first sampling season. Wireworms could have been located deeper in the soil in March during tillage, or soil cover by ramial chipped wood could have limited their predation after exposure at the soil surface. In addition, the use of rotary tillage could have made it easier for them to dig into the loose soil (particularly low bulk density in the crop alley).

Overall, the seasonal and spatial patterns observed in this study reflect taxon-specific responses to a complex combination of variations in climatic conditions and management practices in a spatially-structured agricultural system. The well-known impacts of soil perturbation on soil fauna in agricultural systems (e.g. van Capelle et al., 2012) could be partially alleviated by the inclusion of herbaceous strips, allowing the recovery of some macrofauna taxa in crop alleys at certain seasons.

Variations between shade treatments

We expected to find more homogeneous macrofauna densities relative to the distance from the HS in the strong-shade treatment (shade ++) than in the light shade (shade +) and no shade treatments, as we expected that the more homogeneous tree shading and litter inputs would attenuate the habitat differences between HS and raised beds. However, we found no effect of the shade treatment on the spatial distribution of macrofauna within the plot. Shade treatments most likely influenced all distances from the HS homogeneously, as soil macrofauna density and community composition differed between shade treatments at a general level, especially in November. Increased shade has been found to increase soil macrofauna density in tropical systems [START_REF] Martius | Microclimate in agroforestry systems in central Amazonia: Does canopy closure matter to soil organisms?[END_REF]), but has rarely been studied in temperate or Mediterranean systems. [START_REF] Pardon | Gradients in abundance and diversity of ground dwelling arthropods as a function of distance to tree rows in temperate arable agroforestry systems[END_REF] investigated the effect of herbaceous strips with or without trees at field edges in Belgium, and found a higher woodlice density in the presence of trees and no difference for millipedes, while in our study both were positively impacted in the absence of trees (no shade treatment). In our study, higher shade led to a lower macrofauna density for most macrofauna, Chilopoda excepted. This was particularly visible in November, possibly related to a delayed and cumulative impact on populations of the shade that appeared around the end of May. Similarly, Martin Chave et al. (2019b) found a lower activity density of the main Carabidae in the strong shade treatment compared to lighter shade treatments in September in the same experimental plot. The strong shade treatment (shade ++) was shown to buffer temperature variations in this same study (Martin-Chave et al., 2019b). A strong shade could have lowered temperature too much during the day in November, attenuating the positive impact of autumn on macrofauna activity. The soil environment was also probably strongly modulated by the soil cover by tree leaves and the limited herbaceous vegetation biomass observed in November in the strong shade treatment (shade ++). This would have further created buffered microclimate conditions in this treatment, and induced strong differences in litter quality and quantity between shade treatments, which has been shown to modulate soil macrofauna abundance and diversity [START_REF] Lenth | Litter N-content influences soil millipede abundance, species richness and feeding preferences in a semi-evergreen dry forest of Guadeloupe (Lesser Antilles)[END_REF][START_REF] Vohland | Distribution patterns of the litter macrofauna in agroforestry and monoculture plantations in central Amazonia as affected by plant species and management[END_REF]. Interestingly, earthworms and Dermaptera presented higher densities in the light shade treatment (shade +) than in both strong shade (shade ++) and no shade treatments, meaning the observed trends are not only the results of a variation of shade and of the inputs of tree litter. While these results on the shade treatments seem interesting, it is important to note that there was no replication of the shade treatments in this experiment.

Observations of the differences between shade treatments are thus limited to hypotheses, and should be the focus of future investigations. However, the fact that the same effect of the distance from the HS was observed for three different shade treatments is relevant as it indicates that uncropped herbaceous strips are a possible reservoir of soil macrofauna in spring and summer, independently of the presence and management of trees on these strips.

Conclusions

Herbaceous strips were shown to present higher macrofauna density and earthworm diversity compared to nearby tomato beds whatever the shade treatment. This finding confirms the important role of non-perturbed herbaceous strips to preserve dense and diverse macrofauna communities across fields, including in alley cropping systems. However, this study reveals the importance of considering seasonal variations when studying soil macrofauna in alley cropping systems. The maximal seasonal activity was found to be in autumn, while most samplings in crops usually take place in spring, and patterns of macrofauna distribution in the plot could be quite different according to the season. The role of the season itself versus of the management practices (especially soil tillage) in these differences is hard to determine as both vary simultaneously, and requires further investigations with limited soil perturbation, such as zero tillage experiments, or the comparison of different crop managements. A possible 1 Table 1 Vegetation and soil properties (of the 0-25 cm soil layer) in each shade treatment, at different distances from the herbaceous strip (HS) (mean ± standard deviation). Vegetation was collected in squares of 50*50 cm and oven-dried at 40 °C during a week for dry biomass determination. the different distance from the HS for all seasons combined when the answer was similar for all seasons (no significant effect of the interaction between season and distance from the HS in Table S3 of the Supplementary materials) (Tukey test, p-value < 0.05). Bold values and letters underline significant differences between distances from the HS for the taxonomic group and season concerned. For Formicidae, a cumulative link model was used. distance from the HS for all seasons combined when the answer was similar for all seasons (no significant effect of the interaction between season and distance from the HS in Table S3 of the Supplementary materials) (Tukey test, p-value < 0.05). Bold values and letters underline significant differences between distances from the HS and seasons for index concerned. (endogeic) 0 m 0.00 ± 0.00 4.00 ± 4.00 8.00 ± 8.00 1 m 0.00 ± 0.00 2.00 ± 2.00 2.00 ± 2.00 2.5 m 0.00 ± 0.00 0.00 ± 0.00 1.33 ± 1.33 Aporrectodea caliginosa S.

(endogeic) 0 m 0.00 ± 0.00 0.00 ± 0.00 3.33 ± 3.33 1 m 0.00 ± 0.00 0.00 ± 0.00 1.33 ± 1.33 2.5 m 0.00 ± 0.00 0.00 ± 0.00 1.33 ± 1.33 Species richness 0 m 2.9 ab 3.3 ab 3.9 a

1

Figure captions Fig. 1 .

 captions1 Figure captionsFig. 1. Experimental plot (a) and sampling design (b). This sampling design was repeated for each shade treatment (no shade = no trees, shade + = strongly-pruned trees, shade ++ = lightly-pruned trees), and for each season (April, June and November of 2018). HS stands for herbaceous strip.

Fig. 2 .

 2 Fig. 2. Graphical representations of principal component analyses computed with macroinvertebrates at order or family level (when possible), for (a) April data, (b) June data and (c) November data. Earthworms were additionally separated by ecological categories. Individuals are identified by their distance from the herbaceous strip in the representations on the left, with red circles for 0 m, orange triangles for 1 m and yellow squares for 2.5 m. Individuals are identified by their shade treatment in the representations on the right with dark blue circles for the no shade treatment, light blue squares for shade + treatment, and medium blue triangles for shade ++ treatment. Ellipses represent confidence intervals at 95 % around barycenters. Only variables with a cos 2 > 0.5 are represented.

Fig. 3 .

 3 Fig. 3. Mean values of earthworm density for each earthworm ecological category at each season and each distance from the herbaceous strip (HS). Different letters indicate significant differences between distances from the HS for a given earthworm category and season (Tukey test, p-value < 0.05) after generalized linear models fitted with a quasi-Poisson law. Error bars are the standard error of the mean for each earthworm ecological category.

Fig. 4 .

 4 Fig. 4. Mean values of densities of litter-feeders (a), soil-feeders (b), plant feeders (c) and animal-feeders (d) at each season and distance from the herbaceous strip (HS). Different letters indicate significant differences between distances from the HS for the given season and

Table 2

 2 Mean values of macro-invertebrate densities (individuals per m 2 ) for each distance from the herbaceous strip (HS) and each season for the three shade treatments combined. Mean values were obtained from linear generalized models fitted with a quasi-Poisson law. Values are back-transformed from the logarithmic scale used for analyses. Different lower case letters indicate significantly different values between the means for a given taxonomic group (Tukey test, p-value < 0.05). Different upper case letters indicate significantly different values between

		No shade			Shade +			Shade ++
	Distance from the HS	0 m	1 m	2.5 m	0 m	1 m	2.5 m	0 m	1 m	2.5 m
	Texture (clay /	103 ± 2 /	105 ± 2 /	104 ± 4 /	114 ± 3 /	112 ± 6 /	110 ± 7 /	112 ± 4 /	110 ± 5 /	107 ± 2 /
	silt /	410 ± 3 /	410 ± 11 /	405 ± 12 /	383 ± 15 /	379 ± 18 /	377 ± 22 /	386 ± 7 /	379 ± 14 /	373 ± 7 /
	sand, g kg -1 )	471 ± 6	469 ± 8	475 ± 8	490 ± 11	496 ± 24	500 ± 30	484 ± 7	491 ± 18	502 ± 9
	Bulk density (g cm -3 )	1.26 ± 0.08	1.07 ± 0.04	1.11 ± 0.04	1.27 ± 0.09	1.10 ± 0.05	1.13 ± 0.05	1.32 ± 0.06	1.11 ± 0.07	1.17 ± 0.04
	pH (in water)	8.2 ± 0.0	8.2 ± 0.0	8.2 ± 0.1	8.1 ± 0.1	8.2 ± 0.0	8.2 ± 0.0	8.1 ± 0.1	8.3 ± 0.1	8.2 ± 0.0
	Soil organic carbon (%)	1.5 ± 0.2	1.7 ± 0.3	1.6 ± 0.2	1.9 ± 0.1	2.0 ± 0.2	1.7 ± 0.1	2.0 ± 0.2	1.9 ± 0.1	1.8 ± 0.2
	Gravimetric water content	27 ±3 /	30 ± 3 /	28 ± 1 /	28 ± 1 /	29 ± 1 /	27 ± 0 /	24 ± 4 /	26 ± 1 /	25 ± 2 /
	(April/ June/	24 ± 2 /	32 ± 4 /	30 ± 3 /	23 ± 3 /	29 ± 3 /	26 ± 3 /	25 ± 2 /	26 ± 2 /	24 ± 1 /
	November, %)	29 ± 2	33 ± 3	32 ± 2	27 ± 1	28 ± 1	27 ± 1	25 ± 1	26 ± 1	25 ± 1
	Vegetation biomass (April /	120 ± 94 /	2 ± 6 /	2 ± 4 /	42 ± 37 /	0 ± 0 /	0 ± 0 /	64 ± 62 /	0 ± 0 /	0 ± 0 /
	June /	629 ± 304 /	77 ± 90 /	62 ± 56 /	426 ± 75 /	191 ± 282 /	79 ± 72 /	404 ± 220 /	14 ± 20 /	24 ± 19 /
	November, g m -2 )	391 ± 243	125 ± 150	27 ± 30	233 ± 135	22 ± 27	13 ± 16	65 ± 31	6 ± 9

Table 3

 3 Mean values ± standard deviation of the density of each earthworm species (individuals per m 2 ), and mean values of earthworm diversity indices from generalized linear models (fitted by quasi Poisson law for species richness, and normal law for Shannon index). Different lower case letters indicate significantly different values between the means (Tukey test, p-value < 0.05). Different upper case letters indicate significantly different values between the different

category to which the median value belongs (between 0, 0 to

and more than 240 individuals m -2 )

synonymy Nicodrilus nocturnusBouché, 1972 (Briones et al.,

2009)

Acknowledgements

We wish to thank members of the Eco&Sols research unit and of the University of Avignon who helped with the field and identification work, especially Maé Podechard and Ninon Claude. We are grateful to Nancy Rakotondrazafy, Jean-Marc Souquet and Romain Domingo for the help in associated soil analyses, and to Delphine Mézières and Sébastien Boinot for the help in plant identification. We thank Denis and Virginie Florès for their kind permission to sample their field. This work was supported by the French foundation La Fondation de France.