A Cherouat*'

J L Billoet

S Belhous

TWO COMPONENT FINITE ELEMENT MODEL FOR THE SIMULATION OF SHAPING OF PREPREG WOVEN FABRIC

Two Component Finite Element Model for the Simulation of Shaping of Prepreg Woven Fabric

Abel Cherouat, Jean-Louis Billoët, Sid Belhous

INTRODUCTION

Continuous fibre reinforced composites are now firmly established engineering materials for the manufacture of components in the automotive and aerospace industries. They offer design engineers enormous opportunities for introducing new design concepts whilst reducing costs. In this respect, preimpregnated gives flexibility in the composite shaping and is already playing an important role in increasing the use of advanced composites. The ability to define, in advance, the ply shapes and material orientation allows engineers to optimize the composite structural properties of the part for maximum strength, maximum material utilization and maximum lay-up efficiency.

The formulation of the new efficiency numerical models for the simulation of the composite shaping processes should make it possible to reduce the time needed to manufacture of complex pieces and to optimize costs in an integrated design approach. Actually, the preimpregnated composite corresponds to a structure composed of the combination of the yarn network and resin membrane. Some models are proposed to homogenize elastic properties of a composite material and to simulate the deformation of these materials by forming process. Geometrical and micro-macro mechanical approaches are proposed in the literature to simulate the transformation of fabrics during the draping process [START_REF] Cherouat | Simulation numerique de l'emboutissage des tissus de fibres de verre par la methode des elements finis[END_REF], [START_REF] Gelin | [END_REF] and [START_REF] Blanlot | ICCE/3 New Orleans USA[END_REF]. It is difficult to globally characterise, by homegeneous methods, the behaviour of this fabric without losing mechanical characteristics. The new numerical finite element model developed at a mesostructural level permits to take into account the various mechanics of physics of the mechanical transformation of prepreg fabrics during the shaping process, namely large angular variations of yarns, viscoelasticity of resin and evolution of possible damages in yarns. The different advantages of this modelling is first to give the ability to obtain a very good material orientation of yarns and consequently to introduce good data in the pre-processing of the calculation of the 1 final piece after polymerization, secondly to give the mechanical limits of the fabric during the forming process and to limit the falls of the fabric thanks to a better definition of the flat form. The forming process of prepreg woven fabric usually includes complex mechanisms which can have a significant effect on mechanical properties of the finished product.

The overall behaviour of prepreg composite is based on a finite strain membrane model and must take fabric weaving (geometrical undulation of yarns), fibre properties and resin behaviour into account. The development of a numerical model for prepreg woven fabric behaviour can be defined as : l. the most appropriate weaving of the reinforcements for the forming process, 2. fibre positions in the composite structure, 3. the holding force of the composite during the forming deformation, and 4. the state of impregnated fabric (wrinkling, folding, fibre damage and resin strains).

The proposed model is described by meso-structural approach for finite strains and geometrical non linearities. The bi-component finite elements for modelling prepreg fabric behaviour are based on an association of 3D membrane finite elements representative of resin behaviour and truss finite elements representative of warp and weft fibres behaviour. The efficiency of the proposed model resides in the simplicity of its numerical formulation and the performance of its mechanical approach.

MESO-STRUCTURAL FINITE ELEMENT APPROACH

It is easily shown that a large rotation of the fibres is followed by straightening phenomena which intervene in the kinematic transformation of fabrics during the shaping deformation and determine the aptitude of prepreg woven fabrics to make up complex shapes. The shaping operation is strongly affected by the fabric behaviour, which is different from that of a conventional sheet metal. The simulation of the shaping process is based on the numerical and mechanical approaches specific to the composite reinforced fabric behaviour. The meso-structural model is a 'biphase model' in which the elastic fibre and viscous resin components are treated separately. The fibres are assumed to be embedded in the resin and move with inter-fibre shear deformation. The proposed finite element makes it possible to model the deformation of composite fabrics by taking into account the various dominating mechanisms in the physics of the mechanical transformation of fabrics such as geometrical non linearity (large displacements and finite rotations of fibres), material non linearity (viscoelastic behaviour of resin in shearing, variation of fibres due to weaving of fabric) and contact with friction between tools and prepreg material.

In the numerical model, the behaviour of the fabric is represented by structural truss finite elements corresponding to the behaviour of warp and weft fibres and the resin is modelled by 2D membrane finite elements (Figure 1). The interaction effects and friction phenomena between fibres are negligible. The proposed bi-component finite elements can take into account geometrical non linearities such as large displacements and finite rotations of fibres, material non linearities such as viscoelastic behaviour of resin in shearing and undulation of fibres due to the weaving of fabric. A co-rotational formulation associated with rigid body rotation, derived from the polar decomposition, is used to describe the kinematic motion and the deformation mechanism that woven material undergo during shaping process. The constitutive equations for finite-strains use objective derivatives. In a above equations the rotation rate of the local frame in which a simple derivative would give objective derivative is defined by Green-Naghdi's co-rotational formulation. To characterise the objective behaviour of the fabric, the stretching tensors are written in the rigid body rotation frame as ( 7)

Using Kirchhoff's and Green-Naghdi's tensor stress, the stress rate in the fibre and the resin can be written at any time by :

The internal vector load is defined by summation of elementary forces which are function of Cauchy's stresses, material surface area S and normal vector to the surface n s ! j fib res = L f (f fR ii s dS fib res st

j resin = J (f m R ii s dS s• fibres re sin (9)
The behaviour of prepreg woven fabric in a non-polymerized phase is obtained by superimposing the membrane behaviour of the resin and the behaviour of each fibre in the material frame :

Before deformation

-comp -"" J -mR-d "" J -JR -dS "" J -JR -dS f -L.J (J n,. s + L.J (J warpns + L.J (J weftns elts s• warp sf weft sf To validate the proposed approach for the mechanical behaviour of the prepreg woven fabric and the computational finite element modelling, some numerical simulations were carried out . The laying-up of prepreg fabric on a non developable surface was built inside our laboratory in order to cover hemispherical surface (Figure 4) [START_REF] Blanlot | ICCE/3 New Orleans USA[END_REF]. The numerical simulation is carried out with Abaqus software using an explicit formulation. With the numerical simulation, we can visualize fibre orientations and ply shapes after the forming process and predict manufacturing problems.

After deformation

1. SIMULATION OF LA YING-UP SHAPING PROCESS

An initially square non polymerized woven fabric made of carbon fibre (3SO x 3SO mm) is draped on a hemispherical surface (r = 120 mm). Eight loaded springs are used to maintain the fabric during the shaping transformation. The formability of composite fabric during the laying-up process is tested by using two directions of fibres ±4S0 (Figure Sa) and 0° (Figure Sb). The final experimental shapes for a 300 mm displacement of the mould are shown in Figure 6a for (-4S0 ,+4S0) fabric deformation and in Figure 6b for (0°,90°) fabric deformation. We can notice that these shear angles values are very large (>40°) along the diagonal line for the (0°,90°) fabric on Figure 8 and along the median line for the (-4S0,+4S0) fabric Figure 7. These numerical results show that the proposed finite element model takes into account the highly anisotropy of fabric behaviour.

SIMULATION OF DEEP DRAWING PROCESS

An initially square blank (280 x 280 mm) and a circular blank (r = 140 mm) made of a glass fibre are shaped into a square box (Figure 9). The forming process of composite fabric usually includes large angular variation of the warp and the weft directions which can have a significant effect on the mechanical properties of the finished product. Results of simulations of the shaping operation are shown in Figure 10. Figures 11 and12 show the shear angles of the fibres for three sets of radius (5, 10 and 15 mm) for the punch. These radii mainly influence the maximum values of the angular variations of the fibre directions. The square blank leads to shear angles greater than 80° which values cannot be used for the fabric. On the contrary, the circular blank leads to shear angles smaller than 60° and the shaping operation appears to be possible.

CONCLUSION

A numerical mesostructural approach is proposed for modelling the behaviour of the preimpregnated composite fabric. Numerical examples show the concordance of the computed final shapes and relative distorsions between fibres with experimental ones. The numerical results of shaping processes (deep drawing and laying-up) prove the validity of the proposed formulation. The numerical tool is an efficient means of evaluating factors related to manufacturing process and an efficient help to design a preforming sequence for manufacturing fabric reinforced composites. It is possible to detect the main defects occurring during the shaping deformation in order to obtain good, quantitative information on the forming process and to pre-determine the mechanical properties of the composite parts and tool shapes. Extensions of the numerical model have been carried out with a view to take the viscoelasticity of the resin and the undulation of fibres into account.

FourFigure 1 .)

 1 Figure 1. Two-component finite element for the simulation of mechanical behaviour of woven fabric 3. MODELLING OF PREPREG WOVEN FABRIC BEHAVIOUR Large angular variations of yarns, viscoelasticity of resin and evolution of damage in yarns are the main mechanical mechanisms which control the shaping process of impregnated fabric. The kinematic transformation of impregnated material in large displacements and finite strains is based on the following assumptions : Al : Non-sliding inter-fibre during the shaping process can be experimentally observed by the following transformation of aligned straight lines drawn on the fabric. For each point of continuum material the current position is defined in current configuration by X fibres = X re sin = F X fibres = F X re sin

Figure 2 .Figure 3 .

 23 Figure 2. Geometrical transformation of fibre-resin linkage points

Figure 4 .Figure 6 .

 46 Figure 4. Laying up on the hemisphere

Figure 8 .

 8 Figure. 7. Angles between yams on the median ±45°

Figure 9 .

 9 Figure 9. Trial of punch-drawing

  Figure//. Angles between yarns on the circular diagonal Figure 12. Angles between yarns on the diagonal square


J Laigaard

I Farreras-Alcover

S Joye

L Laguerre

Data mining corrosion and failure in cable stays

Cable stays may be sensitive to water ingress in the lower anchorage, which may induce severe corrosion. The corrosion may occur even though strands are protected by a multi-barrier system comprising main HDPE cable tubes, strand individual HDPE sheathing and waxing and galvanization of strand wires. The reason for this is that parallel strand systems are anchored by wedges inducing a wound in the zinc, which with water ingress may initiate a corrosion process increasing the risk of strand failure in time. Motivated by this, this paper presents firstly the details of the ultrasonic testing method (Uscan) used to classify strand wires of cable stays according to different levels of corrosion defects. The rates of false positives and false negatives of the techniques are quantified for the case study presented, given that some cable stays where replaced and were subject to exhaustive testing and visual inspection. Then, data from 10 years of ultrasonic tests are used to explore correlation patterns in corrosion levels at different scales including strand, cable stays and system of stays in a bridge. This has led to an improved understanding of the corrosion condition of the considered cable stays. A histogram technique is presented as means of a systematic data quality check to compare data from different testing campaigns. A regression model to predict the tensile resistance of a strand/cable stay based on the condition classification from the ultrasonic tests is presented. Model parameters quantify the resistance associated with different wire conditions. The results from different ultrasonic testing campaigns in time can be used to estimate the resistance of the cable stays via the proposed model. This, supplemented with design loads and other sources of information, can be used to inform strategies for managing deteriorating cable stays. Finally, lessons learnt from the present case-study and recommendations to manage corroding cable stays are discussed.

INTRODUCTION

Modern cable stay bridges have parallel strands cables individually anchored by wedges. Each strand is individually sheathed with PEHD, each wire coated with zinc and the interstices filled with wax. The whole strand bundle is then encased in an outer general duct. Figure 1 shows a typical parallel strand concept. This cable stay concept, which has existed since the mid-nineties, generally provides very good protection against corrosion. Nevertheless, in several cases, corrosion problems have been observed in the lower cable stay anchorages. At this location the galvanization protection may be partly affected by wedge indentation, water can ingress and accumulate due to cavities in wax/grease injection, thereby the conditions for getting a corrosion cell at this location exist. On top of this, mechanisms such as corrosion fatigue and galvanic corrosion may also be present. All these mechanisms enhance corrosion and thus risk of broken wires. When assessing the condition of strands, different sources of data should ideally be combined to maximize the information about corrosion. Such sources may comprise:

-Visual inspection (anomalous behavior of the structure, signs of corrosion, broken wires / strands, water ingress etc.) -Chemical analysis (water samples, wire samples) -Maintenance records -Non-Destructive Tests (NDT), see Ciolko et. al (1997) for an overview focusing on prestressing steel strands in concrete bridges, and monitoring methods (endoscopic, ultrasonic, acoustic emission, magnetic etc.) -Mechanical test results of dismantled elements 2 ULTRASONIC TESTING

Method and approach

The ultrasonic method presented here, Uscan® is a patented non-destructive testing service that applies to detect flaws in steel wires and strands, see [START_REF] References Laguerre | Method for detecting a defect in a metal wire of a set of metal wires, in particular for an anchoring area of a civil engineering structure[END_REF] and [START_REF] Laguerre | Non destructive evaluation of seven-wire strands using ultrasonic guided waves[END_REF]. The ultrasonic guided wave reflectometry applied to stay cables or prestressing cables (Uscan®) has been developed by Gustave Eiffel University (UGE) and Sixense.

The system is applicable to T15,7 strands (7x5mm wires) with wedge anchoring. These strands have been widely used for decades as pre-stressing active reinforcements or as stay cables.

The technique is based on the generation of an ultrasonic guided wave into any constitutive wire of the strand from the accessible end of the tested wire. The ultrasonic guided wave interacts with possible flaws. The analysis of the reflected wave features gives information about the flaw severity and its location along the wire. The technique is based on the fact that once an ultrasonic wave is sent from the tip of a steel wire, a reflected signal is generated once it encounters a crack/break along the wire. These reflected signals will be recorded by the system and analysed by a qualified engineer. The wave is generated/detected by an ultrasonic transducer held in contact with the prepared wire end. The inspection ranges from several decimeters to a few meters, which is usually the nonaccessible zone of the anchorage, where the corrosion and crack probability is the highest because of possible water presence, reduced strand protection or higher tensile stress.

The defect can either be corrosion, fatigue cracking or wire break.

The ultrasonic wave is tuned according to the type of tendons: individually sheathed strands, strands poured in cement grout or individual parallel wires Analysis of the signal wire by wire leads to a classification of each wire between green, orange, or red status as detailed below.

-Green: the signal has no or very low amplitude reflections.

-Orange: the signal has some reflections with significant amplitudes indicating a potential defect along the wire.

-Red: the signal has a high amplitude reflection indicating a potential failure along the wire.

The system has been initially developed for stay cables with 7 wires T15,7 strands individually sheathed and for a short distance detection within the anchorage of the cable. More recently the technology has been enhanced to be applied on cement grouted prestressing cables. The characteristics of those cables is to have bare strand casted in cement grout. This environment requires more power and different frequencies for the ultrasonic wave.

Uncertainty and bias in ultrasonic testing

The UScan® process depends on the preparation quality of the strand ends. The end surface must be flat and orthogonal to the axis of the strand. Sixense uses dedicated cutting and grinding tools to carefully achieve this preparation. Once prepared, an accurate positioning of the transducer and the application of a coupling material is required for good reliability.

The data presented below focusses on on-site Us-can® measurements performed on typical stay cables with Parallel Wire System (T15.7, 7 wire strands, individually sheathed) of a given bridge. A comparative analysis has been made between the wire condition classification derived from Uscan measurements and the real state of the wires observed after the dismantling of the stay cables.

Visual observations of corrosion after cable dismantling have been classified into 7 levels which have then been qualitatively grouped in 3 levels to match the three classification levels of Uscan measurements. Table 1 shows the detection outcomes and Table 2 shows the results and rate in terms of compared wires. Even if the results shows inevitable false positive and negative errors, they show good correlation on the measurement of "green" classified wires (80%) which reveals the accuracy of the methodology by assessing the global health of the cable. The below data mining approach allows to go further in the interpretation.

DATA MINING CORROSION AND FAILURE

IN CABLE STAYS

Data

Uscan tests for a typical cable stay bridge provide records with categorization of condition into undamaged, significantly corroded/damaged, and broken wires. Data records exist for each wire and can be aggregated at a 7-wire strand and at a stay levels. For modern long-span cable-stayed bridges, the amount of data records may be of several thousand records for each ultrasonic measurement campaign of all cable stays wires.

Data mining approach

The interpretation of large amounts of NDT and monitoring data for translation into meaningful condition status is a challenge which should not be underestimated. An effective approach to overcome such challenge is to pursue systematic data mining, where key dimensions/parameters are extracted and used for identifying and presenting patterns related to corrosion degradation and failure based on physical mechanisms.

The following has been investigated in our data mining approach: -Data reliability -Change in degradation over time on a strand and stay level -Degradation patterns in individual strands, i.e. undamaged, corroded, broken -Degradation patterns in a cable stay cross section -Global degradation over time -Spatial distribution of the global degradation -Correlation with other data sources, i.e., tensile test results.

For the data mining approach, three parameters have been considered:

(1) Number of green, orange, and red wires at a strand level from the processed Uscan dataset.

(2) A strand damage indicator developed to quantify the damage of each strand. This has defined as:

𝐷𝐼 𝑖 = 𝑛 𝑂,𝑖 + 10 ⋅ 𝑛 𝑅,𝑖 (1)
where 𝐷𝐼 𝑖 is the damage indicator of the i th strand and 𝑛 𝑂,𝑖 and 𝑛 𝑅,𝑖 are respectively the number of orange and red wires in the strand.

(3)

Parameters to estimate the tensile resistance of wires, strands and cable stays as a function of Uscan records, refer to section 3.7.

Data sanity

Before doing the actual data mining, it is necessary to carry out some basic quality assurance checks. This is to ensure only good quality data is considered when doing the actual condition assessment. This data sanity check comprises several layers:

-Repeatability of results when doing testing on site.

That is, being sure that the ultrasonic probe provides the same results by repeating tests on the same wire.

-Check the stability of results from the ultrasonic data processing by sensitivity analyses with respect to the applied data processing strategy. -Checking that overall data consistency over time.

One way of doing this is to check the data for accumulation of corrosion/failures over time. It is well-known that corroded wires do not repair themselves and hence corrosion damage should accumulate and condition deteriorate over time.

Figure 2 shows an example of a verification of data consistency over time. This is done by observing the change of the damage indicator defined by equation (1) between different years. The difference of this indicator between two measurements campaigns is used to quantify if corrosion has progressed by considering all tested strands as one statistical population. Results are represented in a histogram that can be interpreted as follows:

-In case of no deterioration from year to year the distribution of changes in DI follows a narrow Normal distribution equivalent to the statistical uncertainty of the Uscan method. -In case of deterioration the histogram may be expected to follow a positive skewed distribution. Any negative skewed distribution suggesting a decrease in the deterioration should not be expected and would suggest an unintended bias error in the measurement or data processing carried out.

Strand cross section -degradation patterns

A significant part of the interpretation of Uscan data is to correlate and understand the existence of any corrosion patterns both at individual strand and at cable stay cross sections. The existence of such patterns has been investigated by analyzing Uscan data for strands on a cable-stayed bridge for different testing campaigns spanning a decade. The analyses are based on comparison of data from consecutive years looking for wire degradation, which either remains or accumulates in strands. Degradations that disappear or become smaller suggest that the pattern is not genuinely correlated with corrosion. Examples of such inspection results are given in the following.

No general pattern has been found regarding which wires in a strand tend to corrode first, except for that the central wire which will most likely never become the first wire to corrode in a strand cross section.

Table 3 shows typical identified degradation patterns in strands. With a repeatability between different Uscan campaigns of approximately 65 to 90 %, the typical pattern is clusters of two to three corroded wires. The existence of a single corroded wire only can be found with a repeatability of 50%. A broken wire can be found with almost a repeatability of 100% but such a case will very rarely be found without corrosion of adjacent wires in the strand. In some cases, visual observations of the strand ends done when removing the anchorage cap to perform Uscan tests become part of the interpretation of Uscan data. One important finding has been that, in some cases, the central wire of a strand is found to be missing over time. In such cases, Uscan data shows that this only occurs when at least two of the surrounding wires have corroded, hence suggesting the failure of the strand. Figure 3 shows the mechanism.

Cable stay cross sectiondegradation patterns

The degradation observations of all strands in a cable stay cross section may also reveal patterns of corrosion, as the corrosion mechanism may depend on water ingress into the cable stays and their anchorages.

To characterize these patterns, Uscan data was investigated by dividing strand locations into horizontal layers (Figure 4). This was done to investigate if corrosion of the strands at the lowest layers was more significant than at other locations, thereby indicating an accumulation of water ingress in those layers. To explore the existence of such a pattern, the damage indicator DI for each strand was used to calculate the average DI of each layer, refer to Figure 5. From this figure, there is no indication of a pattern associated with higher corrosion levels at the lowest layers (i.e. layers 8 or 9) resulting potentially from water accumulation. Consequently, the origin of the detected corrosion in a cable cross section is likely to be related to local circumstances, such as voids and cracks in the applied wax injection in the anchorage.

Global bridge degradation patterns

Another pattern of interest with respect to corrosion degradation of cable of stays relates to the spatial location of the cable within the global cable stay configuration of the bridge.

This has been investigated by inspecting the Uscan data by using the DI damage indicator from equation (1) and then plotting the DI values for strands in a map with the stay number on vertical axis and the strand number on the horizontal axis. Figure 6 shows an example plot of a bridge for the Uscan results translated into DI as described above. DI values below 10 are represented in orange and indicate up to 7 corroded wires of a strand, whereas strands containing one or more broken wires are plotted in red. Strands containing DI of 0 (all 'green' wires) are represented in green.

It shall be noted that the data presented correspond to ultrasonic testing campaigns performed at different years (i.e. not all cable stays are tested in a single measurement campaign). Hence this figure does not reflect the current state of the stay system. This highlights the need for indicating the year associated to each Uscan data as older campaigns are inherently less reliable, given the irreversible nature of the corrosion degradation process. Figure 6 clearly suggests that some cable stay positions are more prone to corrosion degradation than others. The final cause for this cannot be concluded but it may relate to increase ambient exposure of some cable stays or that some cable stays have been installed in a more adequate way than others at the time of construction. The final answer cannot be given alone based on Uscan data and require some further investigations utilizing data from e.g. visual inspections. Figure 6. Distribution of DI damage indicator on all cable stays of bridge. Orange dots are strands with up to 7 corroded wires. Red dots are strands with a least on broken wire and green dots correspond to strand with only 'green' wires. Cable stays are listed vertically, whereas strands identification number for a given cable stay are listed horizontally indicating strand 'layer' identities.

Regression model for strand tensile resistance prediction based on Uscan data

Performing ultrasonic testing prior to stay replacement and subsequent laboratory tensile testing of selected strands kept in their wedges in the lower anchorage offers a precious dataset that can be used to explore the correlation between Uscan color classification and strand tensile resistance.

The above has been explored by assessing different regression models considering the number of green, orange and red wires in a strand as explanatory variables and the tensile resistance of a strand obtained from laboratory tests as the predictive variable. In the present study, the dataset considered to derive the predictive regression models consisted of 34 strands covering a range of different degradation conditions and for which both Uscan color classification (green, orange, red) before removal of the stays and laboratory tensile test results were available.

Figure 7 shows the tensile test results of the dataset considered in the regression model presented below. Green dots represent strands with only 'green' (Uscan colour classification) wires, orange dots represent strands with only 'green' and 'orange' wires and red dots represents strands with at least one 'red' wire. (2)

or, more compactly:

𝑓 𝑡𝑢,𝑖 = 𝑓 𝑟𝑔 ⋅ 𝐴 𝑠𝑡 7 (𝛼 𝐺 ⋅ 𝑛 𝐺,𝑖 + 𝛼 𝑂 ⋅ 𝑛 𝑂,𝑖 + 𝛼 ′ 𝐺 ⋅ 𝑛 𝐺,𝑖 ′ + 𝛼 𝑂 ′ ⋅ 𝑛 𝑂,𝑖 ′ ) (3)
where 𝑓 𝑡𝑢,𝑖 is the predicted tensile resistance of the i th anchored strand tested in laboratory, 𝑓 𝑟𝑔 is the resistance class of the strands (e.g. 1770 MPa), A st is the area of a strand, 𝑛 𝐺,𝑖 and 𝑛 𝑂,𝑖 are the number of green and orange wires in a strand with no red wires and 0 otherwise, 𝑛 𝐺,𝑖 ′ and 𝑛 𝑂,𝑖 ′ are the number of green and orange wires in a strand with at least one red wire and 0 otherwise and 𝛼 𝐺 , 𝛼 𝑂 , 𝛼′ 𝐺 , 𝛼′ 𝑂 are the model parameters associated respectively with 𝑛 𝐺,𝑖 , 𝑛 𝑂,𝑖 , 𝑛 𝐺,𝑖 ′ and 𝑛 𝑂,𝑖 ′ . The parameters 𝛼 can be regarded as factors associated with the wire tensile resistance for a given UScan condition category (red, orange), with 0 meaning no resistance and 1 full theoretical resistance.

It is noted that strands with a missing central ('king') wire are considered to have no tensile resistance, as confirmed during laboratory forensic analysis. This is not described by equations ( 2) nor (3) but should be considered when predicting strand tensile resistances.

Model parameters are estimated by least squares multiple linear regression. Table 4 summarizes the obtained model parameters. For model simplicity and physical interpretation ease, the resistance of red wires has been imposed to be 0. Furthermore, the model considers two group of strands separately: i) strands where Uscan indicates the presence of at least one 'red' wire (likely broken) ii) and other strands (i.e., strands without 'red' wires).

The obtained model parameters show that for both strand groups, the resistance associated with 'green' wires is close to 100% of the theoretical (99% and 108% respectively), as expected. The estimated model parameters reveal a differential behavior for 'orange' wires for each of the two strand groups. For strands with no 'red' wires, orange wires are associated with 83% of their theoretical resistance, whereas for strands with at least one 'red' wire, the same parameter decreases to 23%. From a physical perspective, this is as expected given that the 'orange' Uscan classification is inherently associated with a degree of variability, ranging from a wire where corrosion is in its preliminary stages to a corroded wire close to failure.

The presence of 'red' wires in a strand should therefore be regarded as an indicator of an advanced corrosion process that is translated into a lower resistance of 'orange' wires compared to strands with less advanced corrosion process that have not yet resulted into wire ruptures.

Figure 8 shows model resistances versus model predictions. Apart from an evident outlier (caused by the non-detection of broken wires in a strand by Uscan), the regression model predicts strand resistance as a function of Uscan color classification of strand wires with a Mean Absolute Error (MAE) of 6.4% and a R 2 of 0.80 when considering all 34 strands as a training dataset.

The effect of Uscan false positives / negatives has been assessed by correcting Uscan color classification according to the visual observations performed in laboratory. At a strand level, which is the level used by the predictive regression model, the false positive/negative Uscan rates do not affect significantly the model parameters, the R 2 nor MAE of the models. In order to assess the uncertainty of the model parameters, the dataset consisting of 34 samples has been randomly divided 25 times into an 80%-20% training / prediction datasets. The mean, standard deviation (Std) and the resulting coefficient of variation (CoV) of the different model parameters is shown in Table 5. As expected, the model parameters with highest uncertainty (CoV) are 𝛼′ 𝑂 and 𝛼 𝑂 , which are the models parameters describing the resistance of orange wires for strands with at least one 'red' wire and with no 'red' wires respectively. For a cable stay with N strands, the resulting tensile resistance can be estimated by the below equation: (4) which can be re-written as:

𝐹 = 𝑁 ⋅ 𝑓 𝑟𝑔 ⋅ 𝐴 𝑠𝑡 ⋅ 𝛼 (5)
with

where F is the estimated tensile resistance of a stay with N strands and 𝛼 is the cross section condition factor relating to the capacity of the stay (or effective cross section), with 0 meaning no tensile resistance and 1 equivalent to the theoretical resistance associated with the nominal cross section.

It is worth noting that the model presented in equations (2), (3), ( 4) and ( 6) estimates the tensile resistance at a given point in time (time where Uscan test was obtained) and that elongations at different wire ruptures are not modelled.

When using the model, it is critical that new Uscan data is associated with the same testing and data processing principles as the Uscan results used for deriving the model. As such, any improvement/change on the underlying Uscan data-processing routines to classify wires into categories (colors) shall be applied retrospectively to all historical data, especially to the dataset used to derive the predictive regression model. Otherwise, this would introduce a bias in the predictive variables of the regression model.

Quantitative degradation estimation over time

The results obtained from different ultrasonic testing campaigns can be used to estimate the resistance of the stay cables by using equations 4 to 6. This is illustrated in Figure 9, where the condition factor 𝛼 is plotted versus time for different stay cables. Figure 9 shows that stay 1, and to a lesser extent stay 4, present an ongoing degradation pattern and will be investigated in more detail and with higher frequency than other stays which appear relatively stable.

CONCLUDING REMARKS

The present paper has presented a data mining methodology to assess corrosion and failure of wires from parallel stranded stay cables. It relies on multiple data sources including ultrasonic test results (prevalent data source), visual inspection in laboratory of strands from several replaced cable stays and results from tensile test performed in laboratory from some of the replaced strands.

A histogram statistical approach has been developed to check different ultrasonic campaigns performed at different points in time. It can be successfully used to verify the consistency of ultrasonic test results under the assumption that corrosion is a nonreversible process and thereby its development can either remain constant or increase in time. This allows identifying campaigns with non-reliable results, which deserve further data processing before they can be used in condition assessment.

The statistical analysis of ultrasonic test records has enabled to characterize corrosion patterns at different levels including strand, stay and globally on the stay system of a bridge. On a strand level, no clear pattern exists regarding the position of the wires to corrode first. On a stay anchorage level, no correlation has been found between corrosion levels and lower location of the strands, suggesting water accumulation in lower strand layers. On a bridge level, some cable stays have been associated with higher corrosion levels. The final cause for this cannot be concluded but it may relate to increase ambient exposure of some cable stays or that some cable stays have been installed more adequately than others during construction

In addition, the presented case study provided an opportunity for validation of the Uscan ultrasonic technique, as some of the stays of the bridge were replaced allowing visual inspection of all wires. In this regard, part of the replacement program included a thorough testing and inspection campaign to gain knowledge about the condition of the cable stays and about the methods used to assess them. Hence, visual observations of all the wires from the replaced stays were compared with ultrasonic Uscan results. This enabled to quantify and document the rates of false positives and false negatives at a wire level. The results show good accuracy of the technology with a correlation on the measurement of "green" classified wires of 80%. As cable stay anchorages are inaccessible for inspection of signs of wire corrosion, it is worth to be noted that ultrasonic testing currently appears to be the only method able to provide some reliable indications about the condition (corrosion / rupture) of wires.

Another result obtained as part of the data mining exercise has been the development of a regression model that can be used to predict the tensile resistance of a strand/cable stay based on the condition classification from the ultrasonic Uscan technique ('green', 'orange' and 'red'). Model parameters were estimated to quantify the resistance associated with different color-classified wires. In the case-study presented, 'green' wires are roughly associated with unchanged resistance, whereas 'orange' wires have a different behavior depending on whether they are located in a strand with advanced corrosion (i.e., with at least an identified wire rupture, 'red' wire) or not. For the former case, the wire resistance is 23% of the theoretical case; this increases to 83% for 'orange' wires in a strand with no detected wire ruptures. For physical consistency and model simplicity, broken ('red') wires were modelled to have no resistance.

The developed model can be used to estimate the criticality of the different cable stays considering design loads and ultrasonic testing. Such an approach, which is not a formal safety assessment in itself, can be used to inform future testing, inspection, and replacement strategies.

Although not discussed in the paper, acoustic emission is also an important tool for managing stay cables affected by corrosion. By nature, acoustic emission and ultrasonic testing are complementary. This is because ultrasonic testing provides a corrosion condition assessment in terms of corroded and broken wires at a given point in time, whereas acoustic emission detects wire ruptures incrementally, i.e. only from the time when a monitoring system is commissioned. Thereby, the combination of both techniques maximizes the benefit to the operator/owner of the bridge. For instance, acoustic emission can trigger ultrasonic testing campaigns and thereby optimize their frequency. The number of wire breaks detected between two ultrasonic testing campaigns can be compared with acoustic emission results, thereby increasing confidence in the stay condition assessment.

A key aspect of the case study presented has been the performance of visual inspection and laboratory tests of some of the replaced cable stays in addition to ultrasonic testing, which has enabled to quantify the reliability of the ultrasonic technique and link this with stay cables tensile resistance estimates. It is believed that similar approaches would greatly benefit the future condition assessment of bridges with similar corrosion degradation mechanisms, and for which stay replacements are planned. This requires a thoughtful definition of the testing objectives associated with the replacement operation, careful de-tensioning of the cable stays to allow representative laboratory testing and a full traceability of all stay elements from the bridge to the laboratory.

Figure 1 .

 1 Figure 1. Top left: parallel strands anchored by a wedge. Top right: system of strands with individual sheathing and stay sheathing. Bottom: components of parallel strand stay system.

Figure 2 .

 2 Figure 2. Histogram of changes in strand damage indicator DI. Example results.

Figure 3 .

 3 Figure 3. Left) Typical corrosion pattern (DI) in a strand with central wire (wire 7) missing. "Green" means intact wire, "Orange" corroded; and "Red" broken wire. Numbers refer to DI damage indicator (2). Right) Mechanism of lost central wire.

Figure 4 .

 4 Figure 4. Division of cable anchorage in up to nine horizontal layers of strands.

Figure 5 .

 5 Figure 5. Average damage indicator DI considering data for all cable stays of a bridge. In this case, maximum DI occurs in layer no. 6.

Figure 7

 7 Figure 7 Strand tensile resistance versus elongation at first wire rupture for tested strands considered in the regression model.

Figure 8 .

 8 Figure 8. Measured (in laboratory) versus predicted tensile strand resistance.

  𝐺 ⋅ 𝑛 𝐺,𝑖 + 𝛼 𝑂 ⋅ 𝑛 𝑂,𝑖 + 𝛼 ′ 𝐺 ⋅ 𝑛 𝐺,𝑖 ′

Figure 9 .

 9 Figure 9. Cross section condition factor 𝛼 for selected cable stays over seven years.

Table 1 .

 1 Detection outcomes

			Uscan Measurements
			Green	Orange	Red
		Level 1,2,3	Correla-	False	False
	*V.O.	(green) Level 4,5,6 (orange)	tion No detec-tion	alarm Correla-tion	alarm False alarm
		Level 7	No detec-	No detec-	Correla-
		(red)	tion	tion	tion
	* Visual observation.
	Table 2. Achieved probability of detection based on
	324 samples analyzed.
		Results		Total number of wires
	Conform (OK)	765	79%
	False alarm (FA)	79	8%
	No detection (ND)	127	13%

Table 3 .

 3 Repeatability of degradation patterns between different Uscan campaigns.

	Degradation pattern	Repetability of pat-
		tern
	Single corroded wire (no cluster)	50-100 %
	Cluster of two corroded wires	65-100 %
	Cluster of three corroded wire	90-100%
	Broken wires	100-100%

Table 4 .

 4 Model parameters.

	𝛼 𝐺	𝛼 𝑂	𝛼′ 𝐺	𝛼′ 𝑂
	0.99	0.83	1.08	0.23

Table 5 .

 5 Model parameters uncertainty. 𝛼 𝑂 , 𝛼′ 𝐺 , 𝛼′ 𝑂 are the model parameters associated respectively with 𝑛 𝐺,𝑖 , 𝑛 𝑂,𝑖 , 𝑛 𝐺,𝑖 ′ and 𝑛 𝑂,𝑖

	Parameter*	Mean	Std.	CoV
	𝛼 𝐺	0.99	0.0093	0.9%
	𝛼 𝑂	0.83	0.073	9%
	𝛼′ 𝐺	1.08	0.08	7%
	𝛼′ 𝑂	0.23	0.15	65%

*𝛼 𝐺 , ′ .


Jeremy Borderieux

Jean-Claude Gégout

Josep M Serra-Diaz

High landscape-scale forest cover favors cold-adapted plant communities in agriculture-forest mosaics

Keywords: Temperate forests in France Major taxa studied: Forest vascular plants plant community, landscape ecology, forest fragmentation, global warming, forest inventory, mesoclimate, microclimate

Aim:

The ongoing climate warming is expected to reshuffle understory plant-community composition by increasing the occurrence of warm-adapted species at the expense of coldadapted species. Previous studies have evidenced a warming Community Temperature Index (CTI) over time. However, data indicate that the local tree canopy can partly explain an observed lag between understory plant CTI and climate warming rates, though landscapescale forest cover effects have not yet been investigated. Here, we test the hypothesis that the amount of forest cover in the landscape lowers local CTI.

Introduction

Climate change and land-use change are the main drivers of past and current plant diversity.

These drivers and their interaction are leading to shifts in species distribution, the extinction of the most vulnerable species, and a reshuffling of existing communities [START_REF] Franklin | Global change and terrestrial plant community dynamics[END_REF][START_REF] Kuhn | Highlighting declines of cold-demanding plant species in lowlands under climate warming[END_REF][START_REF] Pecl | Biodiversity redistribution under climate change: Impacts on ecosystems and human well-being[END_REF][START_REF] Thomas | Extinction risk from climate change[END_REF]. The flora of the forest understory makes up 80% of forest vascular plant diversity and plays a key role in many ecosystem functions [START_REF] Landuyt | The functional role of temperate forest understorey vegetation in a changing world[END_REF]. Likewise, understory flora is being increasingly considered in forest management decisions in the face of climate change [START_REF] Blondeel | The need for an understory decision support system for temperate deciduous forest management[END_REF][START_REF] Gilliam | The Ecological Significance of the Herbaceous Layer in Temperate Forest Ecosystems[END_REF][START_REF] Landuyt | The functional role of temperate forest understorey vegetation in a changing world[END_REF], and in global forest conservation and restoration efforts [START_REF] Stanturf | Contemporary forest restoration: A review emphasizing function[END_REF].

The influence of free-air temperature (the macroclimate) on understory communities is buffered by the cover of local overstory trees [START_REF] De Lombaerde | Maintaining forest cover to enhance temperature buffering under future climate change[END_REF][START_REF] Godefroid | Spatial variability of summer microclimates and plant species response along transects within clearcuts in a beech forest[END_REF][START_REF] Maclean | Microclimates buffer the responses of plant communities to climate change[END_REF][START_REF] Zellweger | Forest microclimate dynamics drive plant responses to warming[END_REF]. Tree cover in temperate forests creates an understory microclimate characterized by cooler maximum temperatures and warmer minimum temperatures. Microclimate depends on local stand conditions, but is also driven by broader scale factors. Topography for example is an important factor that can influence temperature through elevation, aspect, cold air pooling, as is macroclimate, which is determined by drivers such as latitude, solar radiation and distance to the coast. The effect of local tree cover on the understory microclimate and species communities is increasingly under study; however, less is known about the effect of landscape-scale forest cover on understory composition.

The forest habitats in central European landscapes have typically undergone intensive logging in the past, which has resulted in the current mosaic of forest patches of different sizes. These patches, where forest understory species may persist under existing tree cover, are embedded in an extensive agricultural matrix (IES, 2013). The influence of landscapescale forest cover on the regional climate is still under debate and is currently the subject of many studies, since forest cover at the landscape scale involves two processes pulling in opposite directions. On the one hand, temperatures may increase with increasing forest cover because a forest's albedo is lower than other land cover types like grasslands and croplands. This warming effect is most apparent in cooler seasons, when forests do not retain the snow cover and release a latent heat flux at night. On the other hand, forests have a cooling influence during warmer seasons, stemming from their higher evapotranspiration, which directly cools the air and promotes cloud formation [START_REF] Bonan | Forests and Climate Change: Forcings, Feedbacks, and the Climate Benefits of Forests[END_REF][START_REF] Hesslerová | Daily dynamics of radiation surface temperature of different land cover types in a temperate cultural landscape: Consequences for the local climate[END_REF][START_REF] Pokorny | Solar energy dissipation and temperature control by water and plants[END_REF]. The growing season is a critical period for both annual and perennial cold-adapted species. One could therefore expect that landscape-scale forest cover could benefit plant species by cooling the hotter and drier (mean and extreme) conditions in spring and summer that could induce the dieback of vulnerable species. In those landscapes, the community could also be comprised of coldadapted species because they can outcompete the warmer-adapted species located at their cold edge of their distribution [START_REF] Sanczuk | Competition mediates understorey species range shifts under climate change[END_REF]. Highly forested landscapes could also influence plant-community composition and favor cold-adapted species through other means. For example, large forest patches in central Europe historically grow on low-nutrient soils unsuitable for agriculture, and are less influenced by fertilization from nearby croplands than small forest patches [START_REF] Bergès | Past landscape explains forest periphery-to-core gradient of understorey plant communities in a reforestation context[END_REF]. This is relevant as the coldadapted species in Europe are also adapted to poorer soil conditions [START_REF] Ewald | The calcareous riddle: Why are there so many calciphilous species in the Central European flora?[END_REF]. Taken together, these two characteristics increase the potential for highly forested landscapes to conserve cold-adapted species.

In this study, we investigated the role of forest cover in the surrounding landscape on plotscale (i.e. local) plant-community composition in agricultural-forest mosaics in the temperate biome. We carried out pairwise comparisons of forest plots with contrasted landscape-scale forest cover (1km area), and used community temperature index (CTI) as a proxy for community adaptation to climate. CTI is calculated as the average thermal optimum of the recorded species of a plot. The thermal optimum of a species is estimated from a species maximum probability of occurrence along the temperature gradient and therefore reflects the climate that the species experiences in its biogeographic area. CTI may be used to compare a species' or a community's tolerance to the warming climate; a large difference between the current climate and a species' optimum can be an early warning sign of local or regional extinctions [START_REF] Kuhn | Highlighting declines of cold-demanding plant species in lowlands under climate warming[END_REF].

We hypothesized that (1) plant communities surrounded by highly forested areas would have a lower CTI than those located in landscapes with little forest cover; that (2) there would be a pure landscape-forest cover effect, which, (3) together with soil factors, would explain the differences in CTI.

Materials and methods

a. Overview

We used floristic surveys from the French National Forest Inventory (NFI) and a 20-meter resolution forest cover map to test the influence of forest cover in the surroundings on local Community Temperature Index (CTI). This CTI aggregated the thermal optima of every species on a given plot, thus reflecting the mean climatic preference of the community. We used pairwise comparisons to reveal differences in the CTI (ΔCTI) of geographically close plots (<5 km from each other) with contrasting landscape-scale forest cover (high vs. low forest cover, calculated within a 1-km-radius area) in a French temperate lowland forest.

We then used a linear model to analyze the effect of bioindicated soil conditions, local canopy cover, distance to the forest edge, and difference in landscape-scale forest cover on ΔCTI. We tested the robustness and the relationship between ΔCTI and landscape-scale forest cover by repeating the analysis at different landscape-forest-cover thresholds to separate high vs. low landscape-scale forest cover.

b. Floristic surveys and landscape-scale forest cover.

We extracted plant-community data from the French National Forest Inventory (NFI). NFI surveys are based on a 1km-by-1km grid sampling scheme. One tenth of the grid nodes (equally-distanced plots) are surveyed each year to ensure spatial and temporal representativeness for French forests. We extracted our study plots from the NFI surveys from 2005 to 2019.

Each NFI plot has a circular nested design where different variables are measured at varying radii from the plot center. The floristic surveys used in our study were performed within a 15-meter-radius circle (area = 709 m 2 ).The taxonomy of the described flora was standardized to the Euro+ Med PlantBase taxonomy (Euro + Med, 2006). We removed tree species and the other main woody species from our data, since the presence of trees in the understory is sensitive to management, and because woody species respond more slowly to environmental factors than do herbaceous forest species. We also removed species that had not been identified to the species level. NFI canopy cover data is estimated at the plot level through visual observation of the light intercepted by the canopy within a 25-meter-radius circle; cover cannot exceed 100%. We extracted the mean annual temperature (hereafter MAT) for each plot from a model calibrated with 214 French weather stations [START_REF] Piedallu | Soil and climate differently impact NDVI patterns according to the season and the stand type[END_REF]. We extracted elevation from a 25m-resolution digital elevation model produced by the National Geographic Institute (BD_topo).

We obtained the landscape-scale forest cover for each plot by computing the percentage of forest cover in the surrounding 1km-radius area. We selected a 1km radius to capture the immediate surroundings of the plots and to compensate for the fuzziness (± 250 m) of the coordinates the NFI provides to protect private property. This 1km radius is coherent with remote sensing studies that have shown an effect of forest cover on regional climate at a 5km-by-5km scale [START_REF] Li | Local cooling and warming effects of forests based on satellite observations[END_REF][START_REF] Prevedello | Impacts of forestation and deforestation on local temperature across the globe[END_REF]. Forest cover data were obtained from 'BD_Foret V2', a 20m-resolution forest map [START_REF] Ign | BD Forêt version 2[END_REF]. This map was produced through photo interpretation of infrared images and adheres to the definition of a forest established by the Food and Agriculture Organization (FAO), i.e. a surface area exceeding 0.5 ha with more than 10 % tree cover. Lastly, we used the boundaries of the BD_Foret V2 map to compute the distance to the nearest forest edge for a few plots, for which the true coordinates were available (the 2006 to 2011campaign).

c. Calculating Community Temperature Index and soil conditions bioindication

We calculated CTI as the mean of the thermal optima of all the non-tree vascular plant species occurring in the plot. The species' thermal optima were extracted from the ClimPlant database [START_REF] Vangansbeke | ClimPlant: Realized climatic niches of vascular plants in European forest understoreys[END_REF]. This database provides thermal optimum estimates based on distribution atlases and the 10km-resolution 1971-2000 climate data of WorldClim v2 [START_REF] Fick | WorldClim 2: New 1-km spatial resolution climate surfaces for global land areas[END_REF] at the European scale. The database covers the entire distribution of the species we recorded, thus providing us with an accurate estimation of their thermal optima. For the 844 different species recorded, we obtained 508 species' thermal optima. On average, a plot hosted 13 (s.d. 7.4) species with a known thermal optimum, representing 78% (s.d. 13%) of the studied species of a plot. Species with no thermal optimum were mostly rare or endemic species.

To go beyond climate, we also selected soil pH and nutrient availability as possible explanatory variables for, differences in CTI between plots with high and low landscape forest cover. This step was critical since evolutionary adaptation may create a correlation between climate and soil preferences for plant species. For instance, cold-adapted species are generally also adapted to acidic soils [START_REF] Ewald | The calcareous riddle: Why are there so many calciphilous species in the Central European flora?[END_REF][START_REF] Szymura | Bioindication with Ellenberg's indicator values: A comparison with measured parameters in Central European oak forests[END_REF]. The litter in cold forests is more likely to have slow biotic activity (low temperature, low nutrients conifer needles), which reduces nutrient cycling and availability [START_REF] Osman | Forest Soils[END_REF]. By including soil information, we were also to able to isolate the contribution of climate factors to CTI.

We extracted species pH indicator values from the EcoPlant database [START_REF] Gégout | EcoPlant: A forest site database linking floristic data with soil and climate variables[END_REF], a phytosociological database linking floristic surveys and soil analyses. We extracted species nitrogen and light requirements, respectively Ellenberg N and L, from [START_REF] Ellenberg | Zeigerwerte von Pflanzen in Mitteleuropa[END_REF], a large survey of expert knowledge on plant ecology. We assigned a pH indicator value and an Ellenberg N and L value to respectively 512, 429 and 453 species, encompassing 92%, 61% and 69% of the total occurrences in our dataset. We then calculated the bioindicated (inferred from the flora) pH, nitrogen availability and light at each plot by averaging the indicator values of the species present without weighting by abundance [START_REF] Carpenter | How robust are community-based plant bioindicators? Empirical testing of the relationship between Ellenberg values and direct environmental measures in woodland communities[END_REF]. To improve the reliability of our soil bioindication, we maximized the number of species used in our calculations by including all the species possible, even those without a thermal optimum value.

d. Study area, plot selection, and geographical pairing of the plots

Our study site was located in the French temperate broadleaf and mixed-forest biome where 31% of the land cover is forested (IGN, 2019). The climate is oceanic to continental (with larger temperature amplitudes) and the MAT ranges from 8 to 11°C (Météo France weather stations; [START_REF] Piedallu | Soil and climate differently impact NDVI patterns according to the season and the stand type[END_REF]. The study area included mountain ranges, but the strict selection procedure described hereafter mainly focused on lowland areas characterized by alternating expanses of croplands, grazing land and deciduous forest patches of different sizes.

We selected NFI plots exclusive to this biome, and refined our selection with two criteria:

(1) the plots had to be forested -as opposed to open land or recent clear-cuts, and (2) to ensure the quality of the CTI value, the plots had to host more than five species for which thermal optimum information was available.

The plots with more than 80% of forested area within a 1km radius (251 ha) were classified as "forested" (F) and those with less than 30% (94 ha) were classified as "non-forested" (NF). We selected pairs of "forested" vs. "non-forested" plots based on two constraints: [START_REF] Chen | Microclimate in Forest Ecosystem and Landscape Ecology: Variations in local climate can be used to monitor and compare the effects of different management regimes[END_REF] the distance between the plots was <5 km, and (2) the elevation difference was <50 m.

These criteria allowed us to minimize the macroclimatic differences between plots. In order to give the same weight to each plot, a given plot was only included in one pair. We used an algorithm to maximize the number of possible pairs respecting the two constraints: we first paired isolated plots, then paired the plots with many neighbors (see the Data Availability section for codes). This process resulted in a larger sample size of paired plots, although the mean distance between the plots of a pair was not minimized. F and NF plots were similar in terms of macroclimatic mean annual air temperature, with a mean average difference of only 0.06 C° across all plots (Table 1). The plot-scale basal area and canopy cover differed by 2.1 m²/ha and 0.6%, respectively (Table 1). Average pH and mean Ellenberg N values differed between the two landscape classes: they were higher in NF than in F plots by 0.8 and 0.9, respectively (Table 1).

e. Statistical analyses

We used a Wilcoxon ranked test to test whether the difference in CTI (hereafter ΔCTI)

between the F and the NF plots was significantly different from 0.

To test whether variables other than the difference in landscape-scale forest cover (F vs NF) could explain ΔCTI, we used a linear model with ΔCTI as the dependent variable, and the pairwise differences of the other candidate factors as independent variables. The variables tested were bioindicated pH, mean Ellenberg N and L indices, year of survey, elevation and MAT. A stepwise AIC (Akaike Information Criterion) procedure determined the final model when the addition or the deletion of a variable did not reduce the AIC by more than 2 points (Akaike, 1974).

We also tested for canopy cover and distance to the forest edge, two determinants of understory microclimate [START_REF] Meeussen | Microclimatic edge-to-interior gradients of European deciduous forests[END_REF][START_REF] Zellweger | Forest microclimate dynamics drive plant responses to warming[END_REF]. Canopy cover values were only available for 1,940 pairs, and distance to the forest edge for 309 pairs.

Consequently, we ran the variable selection procedure on the complete dataset (2,012 pairs) without these two variables. We then fitted the selected model with the addition of the canopy cover or the distance to the edge variable to the appropriate subset of the complete dataset. We thus obtained three models: the model for the complete dataset, the canopy cover model, and the distance-to-forest-edge model.

The model formulation is summarized in equation ( 1),

∆𝐶𝑇𝐼 = 𝑖𝑛𝑡𝑒𝑟𝑐𝑒𝑝𝑡 + 𝛽 𝑖 * ∆ 𝑖 + 𝜀 (1)
where ΔCTI is the CTI of the F plot minus the CTI of the NF plot for each plot pair; Δi is the subtraction of an explanatory variable i for the same F-NF pair, and ε is the error term of mean 0, following a normal distribution. βi is the fitted parameter testing the effect of Δi.

Any significant difference of a parameter from 0 was assessed with a Wald test. The interest of this formulation is that all the covariables (Δi) are differences. If these covariables are set to 0, the intercept represents the effect of a difference in landscape forest cover (F vs NF) per se, all other environmental variables considered.

To quantify the effect the predictors had on ΔCTI, we computed effect size by multiplying the fitted parameter βi by the mean of Δi. For example, a difference Δi can be strongly correlated with ΔCTI at the pair level, but have no effect on overall ΔCTI because Δi is close to 0.

We checked for residual normality, absence of collinearity among the predictors, homoscedasticity and independence from the other variables not included in the models [START_REF] Zuur | A protocol for data exploration to avoid common statistical problems[END_REF]. The above requirements were met for all of the models tested.

We further assessed the robustness of our results by testing different thresholds to separate the F vs. NF classes. Specifically, we ran the above-mentioned analysis (2.d, 2.e) with a varying threshold for F plots. This threshold ranged from [30% -50%] of forest cover in the 1km radius to [80% -100%] by increments of 5%. The NF plot classification was kept constant [0% -30%]. This resulted in a total of eleven assessments of landscape-scale forest effects.

All analyses were performed with the R software v 3.6.1 (R Core Team, 2019) and the 'sf' [START_REF] Pebesma | Simple Features for R: Standardized Support for Spatial Vector Data[END_REF], 'raster' [START_REF] Hijmans | raster: Geographic Data Analysis and Modeling[END_REF] 'data.table' [START_REF] Dowle | data.table: Extension of `data.frame[END_REF], 'ggplot2' [START_REF] Wickham | Ggplot2[END_REF] and 'ggspatial' [START_REF] Dunnington | ggspatial: Spatial Data Framework for ggplot2[END_REF] packages.

Results

The plots in forested landscapes (F) had an average CTI 0.26°C lower than the plots in nonforested landscapes (NF) (P<0.001). The difference in CTI between F and NF plots was highly variable (0.81°C s.d.). In 63% of the plot pairs, F plots had a lower CTI (the difference was negative), and for 17% of the pairs this difference was more than -1°C (Fig. 2). Conversely, for 37% of the plot pairs, the F plots had a higher CTI, and the difference was more than +1C° for 6% of the pairs. Differences in CTI ranged from -3.5°C to +3.0°C (Fig. 2). We found only minor effects, that is significant but negligible effects, (effect size < 0.03°C)

for ΔElevation, ΔMAT, ΔEllenberg L and ΔYear on pairwise differences in CTI (Table 2).

However, the effects of ΔBioindicated pH and ΔEllenberg N had more importance on ΔCTI:

-0.24°C and 0.11°C, respectively (Table 2). This greater effect size was caused by the important difference between the F and NF plots for the two soil parameters (Table 1). In our subset of species, thermal optimum was positively correlated, with low statistical significance, with the pH indicator value (coefficient: 0.16, P<0.10, Fig. S1, Table S3).

Thermal optima and N Ellenberg values were not correlated (P=0.40, Table S3). We found a significant effect of local canopy cover on ΔCTI. This effect however contributed marginally (effect size=0.001°C) to lower CTI in F plots because F and NF plots had on average the same local canopy cover (Table 1, Table S1). We found no significant effect of distance to forest edge on ΔCTI (P=0.42, Table S2). It should be noted that these two results

do not imply that canopy cover or distance to forest edge are unrelated to CTI. Rather, they

showed that the balance of those variables created by the pairwise selection successfully reduced their effect size to be negligible.

We fitted our linear model with only pairwise differences as a predictor. As a result, setting the differences to 0 meant that the model compared the F and NF categories with all other factors considered to be equal. Thus, the significant intercept we found indicated a decreased in CTI in F plots not explained by any other factors than the difference in landscape classification (NF vs F, Table 2). The lower CTI in the F plots was robust to different F-NF classification thresholds (e.g. highly forested landscapes, Fig. 3) but lower CTIs were especially apparent in landscapes with >70% total forest cover. Effect sizes of the other factors playing a significant role were also robust to changes in NF-F classification thresholds. The decrease in ΔCTI and the contribution of the other factors to it were linear, we did not detect a saturation effect of increasing landscape-scale cover effect.

Figure 3: Difference in CTI between a "forested" and a "non-forested" plot (black line) as a function of how much total forest cover surrounds a "forested" plot. A negative value means that the forested plot has a cooler community. Colored lines are the contribution (effect sizes) of the most important drivers of this difference. Effect sizes were computed by multiplying the fitted parameter of a driver to the mean of its difference between "forested" and "non-forested" plots. The number of plot pairs for each analysis is shown. Minor effects are significant predictors but with negligible effect size. Minor effects are: year of the survey, elevation, mean annual temperature and Mean Ellenberg L.

Discussion

Our results indicate that the CTI of vascular plants in forest understories is 0.26°C lower in forested landscapes than in unforested landscapes. This result can be compared with the recent community thermophilization rates (increasing CTI over time) of ca. 0.1°C per decade found in temperate forest plant communities [START_REF] Dietz | Windstorm-induced canopy openings accelerate temperate forest adaptation to global warming[END_REF][START_REF] Martin | Short-term climateinduced change in French plant communities[END_REF][START_REF] Richard | The climatic debt is growing in the understorey of temperate forests: Stand characteristics matter[END_REF], and with recent air-temperature warming rates of ca. 0.26 °C per decade (2002 to 2018) in our study area [START_REF] Dietz | Windstorm-induced canopy openings accelerate temperate forest adaptation to global warming[END_REF]. We found a significant spatial pattern for the CTI of forest understory plants equivalent to three decades of thermophilization, or one decade of macroclimatic warming. By controlling for canopy cover and distance to forest edge, we show that the lower CTI in highly forested landscapes is explained by differences in soil conditions (pH and nutrient content) that favor cold-adapted species. The structure of our sampling allowed us to observe a landscape-scale forest cover cooling on CTI per se.

In our study, bioindicated soil characteristics (Ph and nutrient content) drove 50% of the difference in CTI between F and NF plots (0.13°C). In landscapes with less than 30% forest cover, the understory plant communities in our plots were characterized by species requiring nutrient-rich soils and high pH, and by nitrophilous species. These species had higher thermal optima, thus creating a significant (albeit weak) correlation between soil and climate preference (Fig. S1, Table S3). On average, soil pH and mean N Ellenberg values were respectively 0.8 and 0.9 lower in F plots (Table 1). These differences may have affected the CTI, as an increase of 1 in a pH indicator value increases the thermal optimum of a species by 0.16 C° (Table S3). Correlations of thermal optimum and soil preferences have been documented before [START_REF] Ewald | The calcareous riddle: Why are there so many calciphilous species in the Central European flora?[END_REF], they may results from adaptation of to poor soils found of cold forests [START_REF] Osman | Forest Soils[END_REF].

Landscape forest cover was therefore linked to local soil conditions we observed in the F and NF classes (Table 1). In addition, pH and nitrogen are both very sensitive to past agricultural practices. Small forests are more likely to be younger forests growing on past agricultural lands in our study region, as shown by historical maps made in cir. 1750 [START_REF] Vallauri | Les forêts de Cassini. Analyse quantitative et comparaison avec les forêts actuelles[END_REF]. The smaller (and generally younger) forests display high nutrient loads because they are located on former agricultural lands, and conversely, the larger forests historically grow on less fertile soils [START_REF] Bergès | Past landscape explains forest periphery-to-core gradient of understorey plant communities in a reforestation context[END_REF]. Furthermore, smaller forest patches and forest edges are more affected by horizontal fertilization from nearby fields, and by atmospheric N deposition [START_REF] Bergès | Past landscape explains forest periphery-to-core gradient of understorey plant communities in a reforestation context[END_REF]. Agricultural mosaics make up most European forests' immediate surroundings (IES., 2013). Our findings could therefore be applied in most temperate European forests, where the species pool and agriculture mosaics are similar .

The remaining effect of 0.13°C at the intercept of the model represents an effect that none of the other included variables explained, and which can be attributed to the difference in landscape forest cover. The lower CTI in the forested landscapes implies that the species therein have biogeographic origin of cooler climate. Such species can be present due to legacy effects; cold-adapted species are associated with old-growth forests [START_REF] Bodin | Shifts of forest species along an elevational gradient in Southeast France: Climate change or stand maturation[END_REF][START_REF] Dupouey | La Végétation des forêts anciennes[END_REF][START_REF] Ewald | The calcareous riddle: Why are there so many calciphilous species in the Central European flora?[END_REF]. The remnants of old growth forests in France tend to be large forests that fall into our definition of forested landscapes [START_REF] Vallauri | Les forêts de Cassini. Analyse quantitative et comparaison avec les forêts actuelles[END_REF].

Cold-adapted forest species also have limited dispersal capacity [START_REF] Dupouey | La Végétation des forêts anciennes[END_REF]. The larger forests in the landscapes with high forest cover could favor species with low dispersal capacity since connectivity is increased in large, closely-knit forest habitats [START_REF] Saura | Forest landscape change and biodiversity conservation[END_REF]. We cannot exclude the possibility that parts of our results originate from the temporal dynamic of CTI, that is, thermophilization, as our study is set in a fixed time span and could be a snapshot of different thermophilization rates [START_REF] Richard | The climatic debt is growing in the understorey of temperate forests: Stand characteristics matter[END_REF].

In our analyses, we controlled for microclimatic effects. We carried out balanced plot pairing and added two well documented determinants of forest microclimate -immediate canopy cover and distance to forest edge -to our sub-models [START_REF] Chen | Microclimate in Forest Ecosystem and Landscape Ecology: Variations in local climate can be used to monitor and compare the effects of different management regimes[END_REF][START_REF] De Frenne | Global buffering of temperatures under forest canopies[END_REF][START_REF] Meeussen | Microclimatic edge-to-interior gradients of European deciduous forests[END_REF]. The effect of the landscape-scale forest cover remained significant with these controls. This indicates that landscape-scale forest cover may have a cooling effect on regional temperatures, with a subsequent effect on the understory. Forests have higher evapotranspiration than other land cover types such as cropland and grasslands, thereby lowering the air temperature and promoting cloud formation. The forest cover can cool the regional climate during the growing season [START_REF] Bonan | Forests and Climate Change: Forcings, Feedbacks, and the Climate Benefits of Forests[END_REF][START_REF] Hesslerová | Daily dynamics of radiation surface temperature of different land cover types in a temperate cultural landscape: Consequences for the local climate[END_REF][START_REF] Pokorny | Solar energy dissipation and temperature control by water and plants[END_REF], and this service is critical for the survival of understory plants , especially cold-adapted species, during the hot summer months. Indeed, the conditions in the understory depend on local stand structure, but also on the regional climate (De Frenne et al., 2021).

Our results show a large variability in CTI differences between the F and NF plots (Fig. 1).

Indeed, 37% of the F plots had a higher CTI than the NF plots. This is most likely due to sampling conditions. CTI is sensitive to changes in community composition when the number of occurrences is low. Furthermore, though we selected geographically close plots with contrasting landscape-scale forest cover to balance the environmental and stand variables of the two large classes F and NF for the whole dataset (Table 1), some individual pairs no doubt differed in stand conditions (e.g. canopy cover). Such conditions influence the microclimate [START_REF] De Frenne | Microclimate moderates plant responses to macroclimate warming[END_REF] and this contributed to the large variability in differences we found in the full sample. Finally, we do not exclude the possible impact of other landscape such as water bodies, urbanized areas, complex edge structures or topographic elements that could significantly influence climate and community dynamics [START_REF] Meeussen | Microclimatic edge-to-interior gradients of European deciduous forests[END_REF].

Our study relied on plant species indicator values but their use is controversial since indicators can be poorly correlated with actual measurements as they are sometimes derived from expert knowledge [START_REF] Marrec | Can flora predict forest microclimate[END_REF][START_REF] Szymura | Bioindication with Ellenberg's indicator values: A comparison with measured parameters in Central European oak forests[END_REF]. We strengthened our analysis by including the pH indicator value from [START_REF] Gégout | EcoPlant: A forest site database linking floristic data with soil and climate variables[END_REF], which was calibrated with soil measurements and a floristic survey database. We maintain that it was useful to include these indicator variables in our study as a proxy for excess fertilization from nearby previous and current agricultural activities. Similarly, we combined Ellenberg L (light) values, when available, and canopy cover data (in one of the sub-model) to better account for canopy density and light conditions.

We used the mean of the recorded understory thermal optima as our response variable. The thermal optima in ClimPlant were computed from distribution maps and grids of macroclimatic temperature [START_REF] Vangansbeke | ClimPlant: Realized climatic niches of vascular plants in European forest understoreys[END_REF]. These indices are valuable to infer the biogeographic origin of a species. We interpreted cooler CTI within a highly forested landscapes as a regional cooling favoring those species. However, the potential of CTI to infer direct microclimatic temperature is limited [START_REF] Marrec | Can flora predict forest microclimate[END_REF], future research including microclimatic measurements or analysis of readily available weather station data, will be critical to further elucidating the climatic versus soil effects contributing to the persistence of cold-adapted species observed in our study.

Current climate warming is likely to have particularly harmful effects on cold-adapted species, which may escape regional warming by retracting to climate refugia with locally cooler and more suitable microclimates [START_REF] Corlett | Will plant movements keep up with climate change?[END_REF][START_REF] Hylander | Climate adaptation of biodiversity conservation in managed forest landscapes[END_REF][START_REF] Kuhn | Highlighting declines of cold-demanding plant species in lowlands under climate warming[END_REF]. For forest species, these climatic refugia can be topographic (e.g. cold air pooling) [START_REF] Stark | Microclimate-based species distribution models in complex forested terrain indicate widespread cryptic refugia under climate change[END_REF], dense forests [START_REF] Frey | Spatial models reveal the microclimatic buffering capacity of old-growth forests[END_REF] or even hedgerows in open landscapes [START_REF] Vanneste | Contrasting microclimates among hedgerows and woodlands across temperate Europe[END_REF]. Our study highlights that highly forested landscapes also promote the presence of cold-adapted species, a refugia that is expected to last as the buffering capacity of forest will stay constant or increase with climate change [START_REF] De Lombaerde | Maintaining forest cover to enhance temperature buffering under future climate change[END_REF]. Our results however should not be used to undermine the importance of small forest patches in agriculture mosaics [START_REF] Valdés | High ecosystem service delivery potential of small woodlands in agricultural landscapes[END_REF]. Forests in landscapes with limited forest cover harbor on average warm-adapted species, which are more suited to the warmer climate and are more resilient in the face of disturbances. that could rapidly remove the forest buffering capacity [START_REF] Christiansen | Changes in forest structure drive temperature preferences of boreal understorey plant communities[END_REF][START_REF] Hylander | Climate adaptation of biodiversity conservation in managed forest landscapes[END_REF]. In addition, our results (Fig. 3) show a linear decrease, without saturation, in CTI with increasing landscape-scale forest cover, as a result, any amount of forest cover in the landscape can have an effect on CTI. This implies that landscape-scale forest cover diversity also matters for understory plant diversity by providing a set of different soil and thermal conditions for a variety of species. Acknowledging such heterogeneity and the potential refugia of large forests is one of the keys to successful forest biodiversity conservation at the landscape scale [START_REF] Hylander | Climate adaptation of biodiversity conservation in managed forest landscapes[END_REF]. We acknowledge that part of the difference in CTI could be driven by the colonization of warm-adapted generalist species in edges and low forested landscapes. We chose to emphasize the presence of cold-adapted species in "forested" plots as they are the most threatened by climate change, and are most discussed in recent conservation literature [START_REF] Hylander | Climate adaptation of biodiversity conservation in managed forest landscapes[END_REF]. In addition, our regional cooling interpretation complement the current literature on the potential protection forest microclimate offers in the warm edge of the distribution of cold-adapted species (De Frenne et al., 2021;[START_REF] Sanczuk | Competition mediates understorey species range shifts under climate change[END_REF].

Current land use changes will likely drive changes in forest cover and forest distribution [START_REF] Doelman | Exploring SSP land-use dynamics using the IMAGE model: Regional and gridded scenarios of land-use change and land-based climate change mitigation[END_REF][START_REF] Ellis | Land Use and Ecological Change: A 12,000-Year History[END_REF]. We demonstrate that the mean thermal optimum of an understory plant community is sensitive to the amount of forest around it. Large forest masses harbor on average more cold-adapted species, and landscapes with forest patches of contrasting sizes may provide a suite of opportunities for different species. As the climate continues to warm, guaranteeing the availability of both forested and diverse landscapes will be key to ensuring biodiversity protection and ecosystem adaptation and resilience in the near and distant future.

Akaike , H. (1974). A new look at the statistical model identification. IEEE Transactions on Automatic Control, 19 [START_REF]Data Availability French National Forest Inventory data are freely available through the Institute for Geographic and Forest Information[END_REF], 716-723. https://doi.org/10.1109/ TAC.1974.1100705

Figure 1 :

 1 Figure 1: (a) Map of the study area, dots are the centroids of each National Forest Inventory plot pair, background map is a 1km resolution forest cover map of France (IGN, 2019), brown inset indicates the location of the (b) map. (b) Close-up map of a plot pair, dots are the NFI plots, circles are the surrounding area used to compute the percentage of forest cover in the landscape, and dark green is the forest cover at a 20m resolution. Basemaps credits: OpenStreetMap

Figure 2 :

 2 Figure 2: Distribution of the difference in Community Temperature Index (CTI, °C) for all plot pairwise differences (n= 2,012). A negative difference means that the forested plot in the pair displayed a cooler CTI. The solid vertical line represents the mean of this difference, the dashed vertical line indicates no pairwise difference (0 °C).

Table 1 :

 1 Environmental characteristics of Forest (F) versus non-forest (NF) plots. Mean of environmental, landscape and stand variables per plot classification (5 th and 95 th quantiles in parentheses). Landscape forest cover is estimated within a 1km radius around the plot.

	LANDSCAP	NUMBER	MEAN	ELEVATIO	LANDSCAP	LANDSCAP	MEAN	BIOINDICATE	BASAL	CANOP
	E OF THE	OF	ANNUAL	N (M)	E FOREST	E FOREST	ELLENBER	D PH	AREA	Y
	PLOT	PLOTS	TEMPERATUR		COVER	COVER (%)	G N		(M²/HA	COVER
			E (°C)		(HA)				)	(%)
	NON-		11.00			19.9			24.7	78.3
	FORESTED		(9.68-	252 (61-	62 (19-	(6.2-	5.3 (3.4-	6.2 (4.6-	(4.6-	(30-
	(NF)	2012	12.91)	633)	92)	29.2)	6.7)	7.2)	49.7)	100)
	FORESTED		10.94			89.4			22.8	78.9
	(F)		(9.69-	262 (71-	281 (254-	(80.8-	4.4 (2.7-		(5.2-	(30-
		2012	12.81)	639)	312)	99.4)	5.9) 5.4 (4-6.8)	42.6)	100)

Table 2 :

 2 Linear model results relating differences in Community Temperature Index (CTI) to different drivers. Coefficients (Estimate), Standard errors, P-values, effect size of the parameter, and adjusted R² for the linear model predicting the pairwise difference in CTI. Effect sizes were computed by multiplying an estimate by the mean pairwise difference of the corresponding parameter (except for the intercept).

	PARAMETERS	ESTIMAT	STD. ERROR P-VALUE EFFECT SIZE	R²
		E
	INTERCEPT ΔELEVATION ΔMAT	-0.133 0.00274 0.279	0.024 0.00082 0.086	<10 -4 <10 -4 0.0013	-0.13 0.027 -0.016	0.12 2
	ΔELLENBERG L	-0.199	0.019	<10 -4	0.0074

Acknowledgments

The authors are grateful to the French institute for geographic and forest information (IGN) for providing the NFI data and the French forest cover map (BD forêt V2). The authors thank Jean-Daniel Bontemps and Jonathan Lenoir for their fruitful comments. JB was funded by a joint AgroParisTech and Région Grand-Est grant (grant number 19_GE8_01020p05035) and JMSD was funded by the ANR-JCJC SEEDFOR (ANR-21-CE32-0003). JMSD acknowledges the support from from NASA for UConn's Ecological Modeling Institute (#80NSSC 22K0883). The authors are thankful to Vicki Moore for reviewing the language.

Supplementary materials