Edgar Chuta
email: edgarchuta@gmail.com

Johan Colin
email: jcolin@estp-paris.eu

Jena Jeong
email: jjeong@estp-paris.eu

The impact of the water-to-cement ratio on the surface morphology of cementitious materials

Keywords: Lightness, Surface roughness, Aesthetic concrete, Cementitious Materials, Water-to-cement ratio Highlights

In the present work, we have studied the impact of the variation of the water-to-cement (W/C) ratio on the roughness and lightness in cementitious materials surfaces. For this purpose, we have manufactured cement pastes and mortars in 4*4*16 cm 3 metal molds. We have used a spectrocolorimeter to determine the lightness of the surfaces and a digital microscope to measure their roughness. The terms lightness L * were used to characterize the color and the coefficients of the surface development R S to characterize the roughness. From our results, we have observed the increase of surface lightness when the W/C ratio increases, as well as the decrease of the roughness with the increase of the W/C ratio. Thus, there is an inverse relationship between lightness and roughness. On the other hand, the presence of sand in the mortars generates rougher and darker surfaces than in cement pastes. This phenomenon could be due to the absorption coefficient of the sands that absorb the water and therefore reduce the amount of water present in the pastes, thus generating darker surfaces.

Introduction

In recent years, concrete technology has advanced very rapidly, improving both the quality of use and the mechanical performance of the concrete [START_REF] Peter | Lea's Chemistry of Cement and Concrete[END_REF][2] [3] [START_REF] Wang | Mechanical properties of high performance concrete reinforced with basalt fiber and polypropylene fiber[END_REF]. The manufacture of concrete has benefited from innovations thanks to the addition of admixtures [START_REF] Stecher | Novel concrete superplasticizers based on phosphate esters[END_REF] [START_REF] Sathyan | Influence of superplasticizer family on the durability characteristics of fly ash incorporated cement concrete[END_REF] and the improvement of production tools [START_REF] Berodier | Robust production of sustainable concrete through the use of admixtures and in-transit concrete management systems[END_REF] [8] [START_REF] Agust-Juan | Potential benefits of digital fabrication for complex structures: Environmental assessment of a robotically fabricated concrete wall[END_REF] [START_REF] Sanjayan | 3D Concrete Printing Technology[END_REF]. As well as the technological advances, the aesthetic interest has become an important issue [START_REF] Bissonnette | Concrete surface engineering[END_REF] [START_REF] Sadowski | Multi-scale metrology of concrete surface morphology: Fundamentals and specificity[END_REF]. From the gray or texture variation of a concrete surface, it is possible for any observer to recognize a good product, to recognize if a surface has defects and if these defects could generate aesthetic or structural problems in the long term. Thus, the aesthetic improvement not only makes the appearance of the concrete more aesthetic but also protects it against the aggressions coming from the environment [START_REF] Collectif | Protection des bétons par application de produits la surface du parement, Guide technique[END_REF]. Depending on the environment, coatings or weather conditions to which the concrete is exposed, the concrete skin can protect against the carbonation [START_REF] Ferrer | Service life of structural lightweight aggregate concrete under carbonation-induced corrosion[END_REF] [START_REF] Li | Predicting carbonation depth for concrete with organic film coatings combined with ageing effects[END_REF] or protect the steel against corrosion [START_REF] Jiang | Degradation of steel-to-concrete bond due to corrosion[END_REF] [START_REF] Song | Inexpensive and non-fluorinated superhydrophobic concrete coating for anti-icing and anti-corrosion[END_REF]. The surface of the raw concrete usually has many surface defects which undergo different forms of damage during their service life and are visible to the naked eye due to variations in color or texture [START_REF] Geoffray | Résultats et recommandations du projet national CALIBE: La maîtrise de la qualité des bétons[END_REF] [19] [START_REF] Girish | Quantifying changes in surface characteristics of concrete due to progressive deterioration[END_REF] [START_REF] Md | Concrete damage in field conditions and protective sealer and coating systems[END_REF]. Through a survey or study of the different degradation phenomena, its durability could be evaluated [START_REF] Inłs | Methodology for service life prediction of architectural concrete facades[END_REF].

The concrete surface is defined by the skin of concrete which is different from its core. It is the face of the element of construction designed to remain apparent and which can be the subject to numerous mechanical or chemical treatment [23]. This concrete surface is usually composed of fine elements (cement and sand) which are surrounded by the coarse aggregates (aggregates that make up the concrete skeleton) due to the wall effect [START_REF] Vénaut | La pratique des ciments mortiers et béton[END_REF] [START_REF] Zheng | Aggregate distribution in concrete with wall effect[END_REF]. The concrete skin is formed during the process of concreting, when the fresh concrete is poured into a given mold. The contact of fresh concrete with the wall of the mold gives rise to the formation of a concrete-formwork interface [START_REF] Bouharoun | Characterization of the interface between fresh concrete and formwork[END_REF] [START_REF] Caro | Influence of the nature of the demoulding agent on the properties of the formwork -concrete interface[END_REF].

Once hardened, the concrete skin corresponds to the first few millimeters of concrete from the surface [START_REF] Chamseddine | Caractérisation des propriétés de la peau des bétons de structures[END_REF] and at the same time, to the micro-roughness and the brightness of the surfaces which during the demolding gives the form of formwork [START_REF] Martin | Étude de la texture de la surface coffrée des parements verticaux en béton[END_REF]. The hardened concrete skin can be divided into 3 layers and their compositions are different from the core. The skin has one first layer of cement paste about 0.1 mm, then a mortar layer about 5mm and finally a layer of concrete about 30 mm [START_REF] Kreijger | The skin of concrete composition and properties[END_REF]. Kreijger also finds, that the porosity in the concrete skin is greater compared to its core.

If we compare the modulus of elasticity between the center and the concrete surface, there is a difference of 6 GPa whatever the type of formwork it is [START_REF] Chamseddine | Caractérisation des propriétés de la peau des bétons de structures[END_REF].

The concrete appearance quality (defects, color or texture) is a phenomenon of the surface of the concrete [START_REF] Strehlein | Dark discoloration of fair-face concrete surfaces -transport and crystallization in hardening concrete[END_REF],

where 99% of the visual perception of the concrete surface is due to the first 100 to 200 µm layers [START_REF] Martin | Étude de la texture de la surface coffrée des parements verticaux en béton[END_REF]. This variation of the surface color and texture of the concrete generally depends on the finest concrete component such as fine aggregates (≤ 1mm [START_REF] Tfb | La teinte gris du béton[END_REF] or ≤ 4mm [START_REF] Vénaut | La pratique des ciments mortiers et béton[END_REF]), the cement [START_REF] Betocib | Les bétons à base de ciment blanc: Prescriptions Techniques[END_REF], mineral additions, pigments [START_REF] Betocib | Les bétons apparents Prescriptions techniques[END_REF] [START_REF] López | Color stability in mortars and concretes. part 1: Study on architectural mortars[END_REF], the amount of water formulation [START_REF] Tfb | La teinte gris du béton[END_REF][36] [START_REF] Trub | Sécrétion de chaux et teinte grise du béton[END_REF], type and form-work roughness [START_REF] Martin | Étude de la texture de la surface coffrée des parements verticaux en béton[END_REF] [36] [START_REF] Garg | Enhancement in the quality of near surface concrete using some formwork liners[END_REF], the type and quantity of oil used [39] [START_REF] Hurd | Avoiding arguments over architectural concrete[END_REF], the vibration time [START_REF] Grampeix | Vibration des bétons[END_REF], and the environmental conditions before and after demolding [START_REF] Strehlein | Dark discoloration of fair-face concrete surfaces -transport and crystallization in hardening concrete[END_REF]. For example, concrete samples stored at high temperatures will give a lighter surface and darker surface if they are stored at low temperatures. In the same way, in a very high humid environment, surfaces will be darker compared to a sample kept at low humidity [START_REF] Strehlein | Dark discoloration of fair-face concrete surfaces -transport and crystallization in hardening concrete[END_REF] (Figure 1). The above measured phenomena can be explained via multiple reflection inside water layer over a rough surface [START_REF] Lekner | Why some things are darker when wet[END_REF] due to the humidity of the environment.

Another factors that could determine the variation of texture and color are the different types of minerals resulting from the hydration of cement such as calcite and C-S-H. Thus, there could be more calcite in light areas and more C-S-H in dark areas, with a slightly higher sulphur content in the dark areas [START_REF] Lallement | Hétérogénéités de teinte des parements en béton : caractérisation et identification des mécanismes[END_REF] [START_REF] Lemaire | Contribution a la maîtrise de la qualité des parements de béton, Contribution to the control of the aesthetic quality of the concrete surfaces[END_REF]. The increase in percentage of iron content in the concrete skin, leads to the decrease of lightness according to different types of cement [START_REF] Izoret | Paramètres physiques du contrôle de la qualité des parements: une approche phénoménologique[END_REF]. Recently, there are several scientific papers that study concrete appearance. For example, color stability in architectural mortars [START_REF] López | Color stability in mortars and concretes. part 1: Study on architectural mortars[END_REF], morphological evolution of the surface of lightweight concrete [START_REF] Sadowski | Morphogenesis in solidification phases of lightweight concrete surface at early ages[END_REF], microstructural properties of the skin of concrete [START_REF] Sadowski | The effect of surface treatment on the microstructure of the skin of concrete[END_REF], evaluation of concrete surfaces using different methods [START_REF] Lemaire | Evaluating concrete surfaces using an image analysis process[END_REF], etc.

Even if there are a lot of research papers in the literature, some relevant parameters, i.e., water-to-cement ratio (W/C) for lightness of concrete has not been well studied yet. In fact, studies about this subject are qualitative, and in some cases the results are different. For example we have on the one side, observations that say that the hardened concrete manufactured with Portland cement, becomes clearer if the formulation W/C ratio is higher [START_REF] Trub | Sécrétion de chaux et teinte grise du béton[END_REF] [48], while on the other side, the hardened concrete becomes darker if the formulation W/C ratio is higher [START_REF] Izoret | Paramètres physiques du contrôle de la qualité des parements: une approche phénoménologique[END_REF].

Moreover, about the variation of texture or roughness, on the one hand, more compact and smooth area are found in dark zones, and some hollow and fault area in light zone [START_REF] Lallement | Hétérogénéités de teinte des parements en béton : caractérisation et identification des mécanismes[END_REF]. On the other hand, according to [START_REF] Izoret | Recherche associative atilh: Caractérisation de la teinte des parements pra-91-03[END_REF], the dark surface is rather rough compared to the light zone (smooth). In addition, the increase in the W/C ratio seems to generate smoother surfaces according to [START_REF] Izoret | Paramètres physiques du contrôle de la qualité des parements: une approche phénoménologique[END_REF].

Consequently, there are conflicting observations on the variation of lightness and roughness based on the W/C ratio in concrete. So, our goal in this article, is to study the impact of the variation of W/C on the roughness and lightness of cement pastes and mortars surfaces.

The organisation in our paper is following: First of all in section two, we will list the equipment to be used to measure the roughness and lightness of our cement samples, and then the methods that will allow us to measure them. Next in section three, we will detail the experimental program for the manufacture of specimens of cementitious materials that will allow us to determine our objectives. As a fourth section, we will present our results according to the variation in lightness and surface roughness depending on the W/C ratio. Our observations will be analyzed visually first, and then confirmed with the use of the spectrocolorimeter for lightness variation and the analog microscope for roughness. In the fifth section we will study the evolution of the lightness of surfaces of cementitious materials when they are manufactured in successive layers, as it is in the real case of concrete manufacturing. Finally, as a last section, we will analyze the results obtained and develop our conclusions.

Materials and methods

Lightness measurement

The color classification is based on three criteria: lightness, tint (or hue) and saturation (intensity) [START_REF] Lemaire | Evaluating concrete surfaces using an image analysis process[END_REF]. At this point you should not confuse, lightness with brightness. Lightness (perceived reflectance) concerns the objective side of visual experience while brightness (perceived luminance) concerns the subjective side [START_REF] Gilchrist | Lightness and brightness[END_REF].

The color perception of an object is governed by three factors: the nature of the illumination (illuminating light source), the optical properties of the object (the reflection or transmission of light by the object) and the response of the human eye (observer) [START_REF] Broadbent | Colorimetry, methods[END_REF].

To characterize the colors of lights as seen by the human brain, the CIE (Commission Internationale de l'clairage) have developed basic standards and procedures of metrology in the fields of light and lighting. One of these color systems is the CIELAB color space using tristimulus values X, Y, Z of the color stimulus and X n , Y n , Z n tristimulus values of the reference white object color stimulus [START_REF] Buckley | CIELAB for Color Image Encoding (CIELAB, 8-Bit; Domain and Range, Uses)[END_REF]. The L * a * b * space is used to measure the color of objects in virtually all areas (e.g. food [START_REF] Larran | Use of digital images to estimate cie color coordinates of beef[END_REF]). L * denotes lightness, while a * and b * are the chromaticity coordinates that indicate the direction of the colors: a * is the redness and b * is the yellowness of object. The lightness takes a value between 0 (black) and 100 (white) and can be calculated [START_REF] Sève | Science de la couleur: aspects physiques et perceptifs[END_REF]. Parameters a * and b * have not been considered for this work, because they are small and do not vary significantly. These variations of a * and b * can be less than 3 points of the gray scale ranging from a very light gray (level 1) to a dark gray (level 7) [START_REF] Lemaire | Contribution a la maîtrise de la qualité des parements de béton, Contribution to the control of the aesthetic quality of the concrete surfaces[END_REF].

In practice, the variation of the lightness (gray variation) can be evaluated using a scale of 7 gray levels according to french standard P18-503 and inspired by the work of the W29 committee of CIB [55]. In our case, visual analyzes of the specimens were performed in a standard laboratory (T = 20 ± 2 • C and HR = 45 ± 5), with good lighting conditions because of linear LED lamps. The observation distance was one meter, perpendicular to the observed surface of the specimens. To measure the lightness variation of our samples, we will use the Minolta CM-508i spectrocolorimeter (Figure 2a), with an embedded dual beam light source providing uniform illumination of the object during measurements. The data is calculated based on the standard illuminant D 65 which is the average daylight. In Figure 2b) the diffuse illumination (1) with 8-degree viewing angle, on the surface measured (∅ 11 mm) is carried out under standardized conditions set by CIE. The surface returns part of it, only the light reflected perpendicular to the surface ( 2) is recovered by an optical fiber and analyzed using the colorimetric calculator [START_REF] Lallement | Hétérogénéités de teinte des parements en béton : caractérisation et identification des mécanismes[END_REF]. The spectrocolorimeter measures the light reflected by an object for each wavelength, which takes into account the properties of the surfaces to restore the light energy that varies in a scale from 0 (black) to 100 (white) [START_REF] Minolta | Analyse des couleurs, parlons clair[END_REF]. It is important to keep in mind that if the difference is greater than 3 points of lightness according to [START_REF] Lallement | Hétérogénéités de teinte des parements en béton : caractérisation et identification des mécanismes[END_REF] or 2 points according to the standard NF P 18-503 in gray variation, the experimental lightness variations (∆L * ) between two specimens, is different one from the other.

Roughness measurement

Any morphological analysis of concrete firstly is visually inspected to know its appearance (e.g. the appearance of a concrete surface according to the P 18-503 standard [START_REF] Vanhemelsdaele | Définition d'un mode opératoire pour la caractérisation de l'homogénéité de teinte et de texture d'un parement en béton[END_REF]). After a visual inspection, the methods used to characterize concrete surface morphology are typically based on 2D profile measurements [58] [59]. But in recent years, the use of 3D topography [START_REF] Siewczynska | Method for determining the parameters of surface roughness by usage of a 3d scanner[END_REF] [61] [START_REF] Sadowski | Evaluation of the height 3d roughness parameters of concrete substrate and the adhesion to epoxy resin[END_REF] has become very popular because three-dimensional analysis of the surface has important advantages [START_REF] Rousseau | Physique des solides et morphologie des surfaces[END_REF].

In our case, to characterize the roughness of cementitious materials surfaces, we will use the coefficients of the surface development [START_REF] Siewczynska | Method for determining the parameters of surface roughness by usage of a 3d scanner[END_REF] in percentage (R s ) that corresponds to the micro-topography of the surface in 3D. It is defined as the surface analogous to the blaine specific surface of a powder [START_REF] Izoret | Paramètres physiques du contrôle de la qualité des parements: une approche phénoménologique[END_REF]. To calculate the coefficients of the surface development we will use (1):

R s = S m S g * 100 (1)
Where S m is the measured surface area and S g is the geometric area or the orthogonal area to the plane.

Chemical characterization SiO2 Al2O3 Fe2O3 CaO MgO SO3 K2O Na2O

S-Cl-CO2 Autre 20 5 3,2 64,5 0,8 3,1 0,79 0,25 0,01 0,07 1,1 1,18 To measure the roughness of our samples, we will use the Keyence VHX-2000E digital microscope from "Le Laboratoire de Mcanique et Technologie"-LMT ENS Cachan (Figure 3). The image captured by the camera is displayed in real time on a built-in LCD, capable of covering a magnification range of 0.1x to 5000x. This system is particularly useful in research and development, quality control, failure analysis and manufacturing [START_REF] Keyence | Srie vhx-6000 microscope numrique catalogue[END_REF]. In our case, we will make our measurements of the measured surface area with a magnification of 200x.

Presentation of materials and samples

In this part, we will study the variation of the lightness and the roughness of the hardened surfaces of cement pastes and mortars by making several samples and by varying the W/C ratio. The type of cement used is the CEM I 52.5 N manufactured in Lumbres, France. The chemical characteristics of the cement are described in Table 1. The purpose of this study is to determine the relationship between lightness and W/C ratio at first. After that, we determine the relationship between the roughness of a hardened surface and the W/C ratio. Additionally is observed the variation of the surface porosity of cementitious materials as a function of the variation of the W/C ratio.

We have made cement pastes and mortars in a standardized metal rectangular mold of 4*4*16 cm 3 . The W/C ratios of the our specimens are described in Table 2 and Table 3. We use the "D ÉMOULAGE 80" (FBC lubrifiants in France) as a release agent. Two pieces of special 20x30 cm 2 paper towels and approximately 10 mL of release agent for each mold have been used to oil our molds. Once the molds are oiled, we begin to prepare the mixtures to manufacture our specimens. The cement pastes and mortars are prepared in the laboratory using a mixer with a bowl volume of 5 litres. For the cement paste, we add the cement and water to the bowl and immediately start the mixer at low speed for 1 minute and then stop the mixer for 90 s. Remove with a squeegee all the cement paste adhering to the walls and place it in the middle of the bowl. Restart the mixer at high speed for 1 minute. The mortar specimens were manufactured according to standard NF EN 196-1. After the last mix (cement pastes and mortars),

we immediately pour the fresh materials into the metal molds. The pastes are cast in a single layer and the mortars are cast in two layers; then they are compacted by the jolting apparatus. The samples are covered with a glass plate to prevent evaporation. After 24 hours, cement pastes and mortars are then removed from the mold and placed in a temperature (T) and relative humidity (RH) controlled room (T = 20 ± 2

Measurement of lightness and roughness during 28 days at hydration

The lightness and roughness program measurement is following:

1. The gray variation of the hardened cement paste and mortar samples were first observed by the naked eye during 28 days after demolding, in a daily basis by three observers.

2. To confirm visual observations on the variation of the lightness as a function of time and W/C ratio, we take 6 measurements of the cement paste and mortar surface for each W/C ratio with the spectrocolorimeter in the Figure 2. The measured surfaces were randomly selected.

3. Lightness obtained with the spectrocolorimeter will be plotted as a function of time (1 to 28 days after demolding) and W/C ratio (at 28 days). From the obtained figures we will describe and analyze the results.

4. After 28 days, with the "Keyence" digital microscope in the Figure 3, 3D images were obtained to describe and measure the surface roughness. The geometric surface was 1.6048 mm 2 . We have taken 7 measurements of the cement paste and mortar surface area for each W/C ratio. Measured surfaces were chosen randomly and they didn't have apparent surface porosities visible to the naked eye. In the illustrations obtained in 3D, the red color represents the highest part of the roughness profile and the blue color represents the lowest part.

Mortars

5.

From the 3D images we can describe the variation of the roughness as a function of water-to-cement ratio.

6. The measured developed surface(R s ) obtained with the digital microscope will be plotted and analyzed as a function of water-to-cement ratio.

7. Finally, from our results, we can plot, describe and analyze the variation of the roughness as a function of the variation of lightness in cement pastes and mortars.

Results

Naked eye observation of samples

First of all, we will observe the gray variation (lightness or darkness) during the 28 days after demolding between our specimens on the cement pastes surfaces as a function of W/C ratio. This comparison to the gray variation has been inspired by the work of the W29 committee of CIB.

On the first day of demolding, we observe that the surfaces of all samples of hardened cement pastes are still wet.

Especially P050 paste seems more wet and darker compared to the others. Within 2 days after demolding, the wet on the surface of the cement paste seems to disappear completely. After 28 days (Figure 4a), the P030 paste is dark with small clear areas. The P035 seems less dark than the previous one, with some light areas. The P040 looks a lot like the previous one. The P045 seems clear with some dark areas. Finally the P050 is more clear with small dark areas. The porosity variation in cement paste surfaces is also changing with increasing W/C ratio (Figure 5). The P030 paste has large pores of about 4 mm. P035 has smaller pores than the previous one with pores of about 1 mm. The P040 has small pores and fewer than the previous one, with pores around 1 mm. P045 has very small and fewer pores.

Finally the paste P050 seems smooth and does not seem to have visible pores. Therefore, We find that the surface of the P050 paste is the lightest and the P030 paste is the darkest. So visually, cement paste lightness increases with increasing W/C ratio. On other hand, some paste surfaces have white spots, they are generally close to the surface pores. These white spots may be the product of the phenomenon known as surface lime secretion [START_REF] Tfb | La teinte gris du béton[END_REF]. Now, we will compare the gray variation in mortar samples (Figure 6a): On the first day of demoulding, surfaces of all hardened mortar samples are still wet, M060 mortars appear wetter and darker than other samples. After about 2 days, the humidity of the surface of the mortars seems disappear completely. After 28 days (Figure 6b), the mortar M040 appears more dark with black spots which represent surface pores. The M045, M050 and M055 mortars seem to have the same color but a little clearer to M040. Finally, the M060 mortar is much brighter than the others with a smoother surface and no pore presence. Therefore, it is observed that the surface of the M060 mortar is the lightest and the M040 mortar is the darkest. The presence of pores on mortar surfaces varies as a function of water-to-cement ratio also. The M040 mortar surface contains many pores about 4 mm in diameter. M045 mortar contains pores of about 3 mm. Mortars M050 and M055 contain pores of plus or minus 2 mm. Finally, the mortar M060 contains small pores of less than 1 mm. Using the spectrocolorimeter (Figure 2a), we proceed to measure the lightness variation in cement paste surfaces during 28 days after having been demolding. According to the figure (Figure 8a) we can see the following:

Lightness measurement via spectrocolorimeter

1. We have two areas on the variation of the lightness of cement paste surfaces: a first zone (I) where the lightness increases rapidly during 4 days and a second zone (II) after 4 days where the lightness continue to increase very slightly to finally remain almost constant.

2. On the day of demoulding, the lightness of all cement pastes is very low and almost the same. The lightness varies between 62 and 66.

3. P050 paste on the first day is dark. But after 4 days, it becomes clearer than the others and continues until 28 days.

4. P045 and P050 paste lightness are almost similar, with a difference in the order of ∆L * = 1.41 after 28 days (∆L * must be greater than 2 minimally to be considered different).

5. After 28 days, we find that the P050 cement pastes are lighter than the others, and that the P030 pastes are the darkest.

Next, we will describe the lightness variation in mortar surfaces during 28 days according to the Figure 9, we can see the following: 2. On the first day, the lightness of all mortars are low and varies between 54 and 62.

3. M060 mortars on the first day is very dark compared to the others. After 2 days, they become clearer than the others.

4. M050 and M055 mortar lightness are similar, with a difference of ∆L * = 0.17, after 28 days.

5. After 28 days, we find that M060 mortars are lighter than the others, and the M040 mortars are the darkest.

According to our results, we found 2 zones of lightness variation in cementitious materials, i.e. zone I where the surface is wet and dark at the beginning, which over time lightness increases rapidly, and zone II where lightness remains stable. According to the literature, when a surface is covered by water boundary (wet), the light beams that arrive on the surface, will absorb it. So there would be less light beams in the area for arriving to our eyes. As a result, we see the material darker [START_REF] Lekner | Why some things are darker when wet[END_REF]. Thus, according to our observations, the increase of the lightness of the first zone could be due to the drying of cementitious materials and the second zone when the drying is finished.

Based on the above results, we will draw the lightness variation as a function of water-to-cement ratio at 28 days in cement pastes and mortars. It will allow us to determine the influence of sand on the lightness of the cement paste.

According to the Figure 10, we can observe the lightness variation in our hardened specimens after 28 days (dry surfaces). After 4 days, the surface lightness of our samples did not vary considerably for the pastes and after 2 days in the case of the mortars, as we can see in Figures 8 and9. Firstly, the tendency of the two curves, hardened cement pastes and mortars, is literally the same. This means that the increase of W/C ratio always leads to an increase in lightness. Secondly, mortars are darker than cement pastes with the same W/C ratio (∆L * > 2). Thirdly, P040 pastes are similar to those of M045 mortars, and it is the same, between P050 pastes and M060 mortars. According to the literature, the surface appearance (skin) of cementitious materials is a phenomenon that depends on the finest concrete components (cement and fine sand). So, the appearance of the surface of the hardened mortar could be represented by the layer of hardened cement paste present in the mortar. In this case, we could consider that the W/C ratio of the P040 cement paste was similar to the W/C ratio of the cement paste of the M045 mortar, thus, there is a difference of 0.05% of water. This difference can be explained by the absorption of water by the sand. As is known in the literature, the absorption coefficient in natural sands varies between 1.2 and 1.5 [65][66]. This would result in a decrease in the W/C ratio of the cement paste in the mortar, and thus a decrease in lightness. In this way, we can say the same about the difference between P050 cement and M060 mortar.

Finally, we can say that the loss of lightness in the hardened mortars can be due to the absorption of the sand in the fresh state. These differences between pastes and mortars are very significant when comparing it visually. The visual perception of objects depends not only on the lighting, but also on each observer. For example between P050 (Figure 4b) and M050 (Figure 6b), it appears that the M050 mortar is darker than the P050 cement paste. In order to reduce these differences in visual perceptions, the use of the colorimeter allows us to measure them objectively.

Variation of surface roughness of hardened cement pastes and mortars at 28 days

For this purpose we use the "Keyence" digital microscope. The geometrical measuring surface is 1.6048 mm 2 .

We take 7 measurements of the cement paste facing area for each W/C ratio chosen randomly. Surfaces did not have apparent surface porosity which can be recognized by the naked eye.

In the Figure 11, we show the 2D and 3D morphology for cement pastes roughness. In the 2D images, we see that the P030 paste has a more heterogeneous appearance compared to the P050 paste. This difference could be due to the morphology difference or crystallographic agglomerations on the surface. From the 3D image, we can clearly see this For cement mortars (Figure 12), we can see a clear difference between the M040 and the M060. The M040 mortar has a heterogeneous morphology, while the M060 mortar has a more homogeneous surface in 2D. This difference is clearly seen in the 3D images. The M040 mortar a present surface with many peak and with a maximum peak height of 152 µm, while in the M060 mortar the surface is flat, with a maximum profile height of about 27 µm.

From our results showed in 3D, we observe that the surface texture (roughness in cement pastes and mortars)

decreases with the increase of the W/C ratio. This result at 28 days is detailed in Table 4 and drawn in Figure 13.

Cement Pastes S m (mm 2 ) S g (mm According to Table 4, we can see the difference of R S between P030 and P050 (0,53%), as well as between M040 and M060 (1,123%). These percentage differences are small. However, these differences are very significant about According to the 3D analysis and Figure 13, we confirm that the increase of the W/C ratio in the cementitious materials leads to the reduction of the developed surface (roughness). Secondly, the roughness of the mortars are much more important concerning to the cement pastes. Moreover, the roughness of the mortar is not only very important comparing to the cement paste, but also decreases faster when the W/C increases. Finally, the standard deviation of the first two W/C values of mortars is very large, which can be explained by the amount of sand and the porosity in the mortars. This roughness or heterogeneity of the surface of the mortars thus implies a great difference between the one and the other made by the microscope.

Proposal of relation between lightness and roughness

Once determined the variation of lightness and roughness as a function of water-to-cement ratio. From our data we can plot the lightness variation as a function of the roughness. These results will allow us to know the influence of roughness on lightness. From Figure 14, we can conclude that a weak roughness gives surfaces rather clear. So, we deduce that the presence of sand in cement pastes generates an increase in roughness, which in turn also generates a decrease in lightness. As we had previously described, the enormous roughness in mortars comparing to the cement paste, would be due to the sand.

Evolution of lightness in cement pastes and mortars two layers.

For this study we have manufactured cement paste and mortar samples. The goal of these tests is to determine the variation of lightness due to the effect of waiting time about one hour between two layer and lightness variation.

To achieve this goal, samples P050 and M050 were chosen. Because this W/C ratio of 0.50 belongs not only a standardized formulation, but also, the roughness is quiet similar between two samples (Figure 13). Cement pastes and mortars were manufactured as described in section 3.1. After the last mix, fresh materials are introduced into the metal mold. The samples were made in two successive layers. Each layer is approximately about 2 cm of high. The second layer has been poured one hour after the first layer. After 24 hours, cementitious materials are removed from the mold and placed in a temperature and humidity controlled room. The visual observations that we have identified are the following:

For cement pastes, a color difference between the two layers were observed on the first day (Figure 15a). e.g. the lower layer appears slightly darker than the upper layer. After 40 days, the difference in color becomes less identifiable between the two layers, even if the upper layer remains slightly darker than the lower layer (Figure 15b). For mortars, a slight difference in color between the two layers were observed after the first day. This may be due to the presence of humidity. After 48 days, the color difference becomes less identifiable between the two layers.

In cement pastes, a dividing line between the two layers is easily recognized. These lines are clearer than the rest of the sample. In fact, during the concrete manufacture, when concrete is manufactured, once the fresh concrete is installed, it is compacted by vibration. The vibration allows an optimal filling of the fresh concrete in the molds, making the air and water rise to the surface during vibration. Once the first layer has been compacted, there is a layer of water that remains on the surface [23][41]. When we add the second layer of fresh cement paste, that layer of water from the first layer of concrete is trapped between the two layers, which generates an increase in water (W/C ratio).

This difference in W/C ratio would mean the increase in surface color once hardened. In mortars this phenomenon is not observed, this would be due to the filling conditions. The mortars were vibrated for 60 seconds, causing the water layer of the first surface to mix completely throughout the sample, as well as the presence of sand would help this process.

From these observations, we can see that the number of manufacturing layers in pastes has a greater influence than in mortars, about the variation in color surface.

Conclusions

The aim of this work was to confirm or refute the observations found in the literature regarding the variation in lightness and surface roughness of cementitious materials as a function of water-to-cement ratio. For this purpose, several samples of cement pastes and mortars were made in a standardized rectangular metal mould of 4*4*16 cm 3 .

We used a spectrocolorimeter to measure the lightness and a digital microscope to measure the roughness. From our experimental tests we observed the following for pastes and mortars :

• The variation in lightness is proportional to the W/C ratio (between W/C=0.3 and 0.5 for pastes and 0.4 and 0.6 for mortars). These results confirm the observations obtained by [START_REF] Trub | Sécrétion de chaux et teinte grise du béton[END_REF] and [START_REF] Cimbeton | La maîtrise esthétique des parements en béton[END_REF], but are different from the observations of [START_REF] Izoret | Paramètres physiques du contrôle de la qualité des parements: une approche phénoménologique[END_REF].

• The surface roughness of the materials also depends on the W/C ratio. Therefore, an increase in the W/C ratio leads to a decrease in roughness. This means that there is an inverse relationship between W/C ratio and roughness. These results have the same tendency observed by [START_REF] Izoret | Paramètres physiques du contrôle de la qualité des parements: une approche phénoménologique[END_REF], but different from the observations made by [START_REF] Lallement | Hétérogénéités de teinte des parements en béton : caractérisation et identification des mécanismes[END_REF].

• Surface pore sizes decrease with increasing W/C ratio. The surface becomes finely porous and compact. These observations are the same as those found by [START_REF] Tfb | La teinte gris du béton[END_REF] • In the first days the lightness increases very quickly (all this due to loss of humidity), and after 2 or 3 days the lightness remains almost constant.

From our results, we have observed that the formulation of W/C ratio in cementitious materials influences the variation in lightness and roughness. Thus, we have determined that light reflection is more important when the surface of the material is smooth, so the surface becomes lighter, unlike a rough surface. Then, the surface roughness of a material determines the surface lightness. According to the open literature [START_REF] Strehlein | Dark discoloration of fair-face concrete surfaces -transport and crystallization in hardening concrete[END_REF], the roughness of a surface defines how light is reflected. A flat surface produces specular reflection and a rough surface produces diffuse reflection (rough surfaces that tend to reflect light in all directions). According to our results concerning cementitious materials, we can say that a flat surface would generate a specular reflection that would appear less dark to the observer. Instead, a rough surface that would generate diffuse reflection would appear darker to the observer.

Acknowledgements

This work was funded by EFB (Ecole Franaise du Bton). A special thanks to Laurent Izoret for his permanent collaboration in this research.

Figure 1 :

 1 Figure 1: Effect of atmospheric conditions on the appearance of the facing

Figure 2 :

 2 Figure 2: (a) Colorimeter Minolta CM508i b) Diagram representing the measuring head[START_REF] Lallement | Hétérogénéités de teinte des parements en béton : caractérisation et identification des mécanismes[END_REF] and c) lightness of the seven zones of the French reference scale[START_REF] Lemaire | Evaluating concrete surfaces using an image analysis process[END_REF]

Figure 3 :

 3 Figure 3: a) Digital microscope "Keyence" to LMT-Cachan and b)developed surface coefficient

Figure 4 :

 4 Figure 4: Variation of the lightness surface of cement pastes (a) at 24 hours and (b) at 28 days

Figure 5 :

 5 Figure 5: Variation of the pore size in cement pastes as a function of water-to-cement ratio: (a) P030 and (b) P050 at 28 days

Figure 6 :Figure 7 :

 67 Figure 6: Variation of the lightness surface of mortars (a) at 24 hours and (b) at 28 days

Figure 8 :

 8 Figure 8: Spectrocolorimeter measurements of the lightness of cement pastes

Figure 9 :

 9 Figure 9: Spectrocolorimeter measurements of the lightness of mortars during 28 days

Figure 10 :

 10 Figure 10: Variation in cement pastes and mortars lightness as a function of water-to-cement ratio at 28 days

Figure 11 :

 11 Figure 11: Images of surfaces with 200x magnification of cement pastes in 2D (a) P030 and (b) P050, and in 3D, (c) P030 and (d) P050

Figure 12 :

 12 Figure 12: Images of surfaces with 200x magnification of cement mortars in 2D (a) M040 and (b) M060, and in 3D (c) M040 and (d) M060

Figure 13 :

 13 Figure 13: Variation of the average roughness of pastes and mortars as a function of water-to-cement ratio

Figure 14 :

 14 Figure 14: Variation of the lightness as a function of the surface roughness

Figure 15 :

 15 Figure 15: Variation of lightness in cement pastes as a function of the waiting time in the same sample: (a) First day after demolding and (b) 40 days after demolding

Figure 16 :

 16 Figure 16: Variation of lightness in cement mortars as a function of the waiting time in the same sample: (a) First day after demolding and (b) 40 days after demolding

Table 1 :

 1 Chemical composition of cement CEM I

  • C and HR = 45 ± 5) for 28 days.

	Cement Pastes P030 P035 P040 P045 P050
	Cement (gr)	1500 1500 1500 1500 1500
	Water (gr)	450	525	600	675	750
	W/C	0.30	0.35	0.40	0.45	0.50

Table 2 :

 2 Cement pastes specimens manufactured.

Table 3 :

 3 Mortars specimens manufactured.

Table 4 :

 4 Average values of developed surfaces (R s ) of cement pastes and mortars.

			2 )	R s (%)	Mortars S m (mm 2 ) S g (mm 2 ) R s (%)
	P030	1.6152	1.6048	100.644	M040	1.6245	1.6048	101.224
	P035	1.6099	1.6048	100.320	M045	1.6105	1.6048	100.356
	P040	1.6088	1.6048	100.247	M050	1.6067	1.6048	100.118
	P045	1.6068	1.6048	100.127	M055	1.6082	1.6048	100.210
	P050	1.6067	1.6048	100.114	M060	1.6064	1.6048	100.101