Characterization of Plant-Based Aggregates

Chapter 2 Characterization of Plant-Based Aggregates Bio-based aggregates present characteristics which are very different from the mineral aggregates typically used in concretes, for which there are standardized tools and techniques for characterization. In this chapter, the aggregates examined come from the stem of plants cultivated either for their fibers (hemp, flax, etc.) or for their seeds (oleaginous flax, sunflower, etc.). In all cases, our aim is to enhance the value, as aggregates for construction materials, of co-products from the stem which have, hitherto, hardly been used (if at all). Cultivation of these plants solely for the purposes of production of aggregates would not be advisable either from an economic or an environmental point of view: the cost of such materials would prove significant in relation to, e.g., mineral aggregates – the price of which is steadily increasing as resources become less readily available – and their production would mobilize agricultural land for nonfood purposes. In the case of fibrous plants, it should be noted that this latter point is compensated by the fact that cultivation of such plants contributes to balanced land management and constitutes a beneficial component in cereal crop rotation. Owing to the structure of the stem of the plant they are made from, such aggregates are generally malleable, elongated and highly porous with a low apparent density. Within the finished product, they do not play the part of a rigid skeleton, as do mineral aggregates in hydraulic concretes, but are instead very flexible, and for large quantities, their compactness in the material depends on the compacting performed during the implementation stage. They can also absorb large amounts of water and prevent potential hydraulic reactions of the binder used due to water competition. Chapter written by Vincent PICANDET. 2 Bio-aggregate-based Building Materials, Chapter 2, pp 27–73 Hence, the characterization of these aggregates, which is crucial to a proper apprehension of the quality of the materials in which they are incorporated, requires adaptations to be made to the techniques usually employed for mineral aggregates, or the devising of new characterization procedures. Following a brief description of the microstructure of these particles, based on current studies aimed at enhancing the value of hemp shiv, flax shiv and sunflower stems, a study relating to characterization of particle size distribution is detailed in the case of hemp shiv. Measurements of the bulk density and compressibility of the hemp shiv are also presented. Finally, the water-absorbing capability of these aggregates is illustrated by a few very simple tests. 2.1. Microstructure of the shiv particles 2.1.1. Structure of the stem of fibrous plants In a transversal cross-section, going from the outside toward the center of the stem, which often forms a hollow cylinder (see Figures 1 and 2), the different cellular tissues making up the plant are composed as follows [CRO 05; BOU 06]: - Epidermis: this constitutes the stem’s protective layer, and is the area in which exchanges with the surrounding environment take place. - Primary fibers: these are associated with the primary phloems, running from the primary meristem. The primary fibers are distinguished from the wood fibers by their length, a very slender cell wall and a particular chemical composition. - Phloem: this is the tissue that channels elaborated sap, which is a solution rich in glucides such as saccharose, sorbital and mannitol. - Secondary fibers: these are generated from the cambium. - Cambium: this enables the stem to grow thicker, which is referred to as secondary growth. The cambium originates from the procambium – a tissue derived from the primary meristems (creating the primary vascular bundle). Cambial activity, therefore, is responsible for the production of the secondary xylem which is the main element in the central part of the stem. - Meristem: this is a biological tissue comprising non-differentiated (or slightly differentiated) cells forming an area of growth where cell division takes place. We usually distinguish the primary meristems, which ensure the growth of the stem in Characterization of Plant-Based Aggregates, written by Vincent PICANDET 3 terms of length, from the leaves or roots and the secondary meristems, which are responsible for the transversal growth of the organs of certain plants. - Xylem: this ensures the plant’s uprightness, and the transport of minerals – functions performed respectively by the the fibers. and vessels. Figure 2.1. Transversal cross-section of a hemp stem halfway up In the case of hemp, the part assimilated to the cortex containing the epidermis and the fibers represents barely 10% of the cross-section of the stem. Conversely, the secondary xylem, assimilated to the woody part, represents over 85% of the cross-section of the stem [FID 08]. Hemp shiv comes from this part of the stem. The inner layer of the hollow stem is made of a material that is more translucent than the woody part. These cells located at the heart of the stem constitute the primary xylem – the site of cell multiplication in the process of the plant’s growth. 4 Bio-aggregate-based Building Materials, Chapter 2, pp 27–73 a) b) c) d) Figure 2.2. View, under a trinocular microscope, of the transversal cross-section of thin slivers of hemp stem 2.1.2. SEM observation of hemp shiv particles Cross-sections were taken of the woody part of the stem of a hemp plant and observed under a SEM (Scanning Electron Microscope) at various levels of magnification both along and across the stem (see Figure 2.3). These observations confirm the highly porous nature of this material, which accounts for its excellent capacity to absorb and retain water. It is made up of capillaries, formed by the cell walls and oriented longitudinally (i.e. in the direction of the stem). The width of these capillaries is variable, but on the transversal views they appear to be connected, end-to-end, to one another. Characterization of Plant-Based Aggregates, written by Vincent PICANDET a) b) c) d) 5 Figure 2.3. SEM observations of hemp shiv: transversal (a and c) and longitudinal (b and d) views The process of defibration produces hemp shiv particles from the woody part of the stem, named as shiv, which are elongated along its axis. The porosity of these particles is also mainly oriented along the same axis. These pores have a diameter that essentially varies between 10 and 50µm and a length of around 80µm (see Figure 2.3d). 2.1.3. Chemistry of the cell walls Plant aggregates are made up of cell walls – remnants of the cells that make up the plant from which they are taken. These lignocellular walls are composed primarily of cellulose, hemi-celluloses and lignin in varying proportions depending on the species of plant and the position or function of the cell within the plant’s structure. For instance, a fiber is created by a cell which is elongated and whose metabolism has focused entirely on the creation of the cell wall. 6 Bio-aggregate-based Building Materials, Chapter 2, pp 27–73 Mass % Cellulose HemiLignins celluloses 12 28 Hemp shiv [GAR 98] 48 Hemp shiv[VIG 96] Hemp fibers [GAR 98] Hemp fibers [VIG 96] Hemp fibers [SED 08] Hemp fibers [TRO 08] Flax shiv [FEN 89] Flax shiv [BUR 07] Flax shiv [COX 99] Flax fibers [SAI 02] Sunflower stalk [JIM 93] Marrow-less sunflower [JIM 93] Marrow-less sunflower [KHR 96] Sunflower marrow [YIN 07] 44 18 55 Pectins Ash Wax 6 2 4 28 4 2 1 16 4 18 4 3 55 16 4 14 4 1 56.1 10.9 6 20.1 - 7.9 58.7 14.2 6 16.8 53 34.2 46 78 13 21.3 26.2 6 24 30.2 23.1 5 - >2 1.2 3.1 2 - 42.1 29.7 13.4 5.9 7.9 1 38.6 22.8 16.2 - 12.2 - 41.4 30 18.3 - 8.9 - 47.4 9.4 3.5 6 20.4 - 4.3 - Table 2.1. Mass fractions of the main categories of constituents of plant cell walls Cell walls also contain various aromatic compounds associated with lignins, pectins, waxes, fats or lipids and ash or mineral compounds which can be extracted by calcination [AKI 10]. Cellulose, hemi-celluloses and lignin, in that order, are the three most abundant types of natural polymers [BUR 08]. Table 2.1 gives a non-exhaustive overview of some values found in the existing body of literature for the distributions of the primary constituents of the cell walls in plants likely to produce aggregates for use in construction materials, which have now been studied to a relatively advanced level. This category includes two fibrous plants – hemp and flax – and an oily plant – sunflower – for which the data were obtained by Vincent Nozahic [NOZ 12]. Characterization of Plant-Based Aggregates, written by Vincent PICANDET 7 2.1.3.1. Cellulose Cellulose is primarily a linear polymer of glucose [NEL 00]. The way in which glucose is linked or arranged to form this linear polymer determines the properties of the particular cellulose. Generally, the glucose can be arranged in a crystalline manner, giving rise to a stable, hydrophobic polymer with excellent mechanical stress resistance. Cellulose is present in the cell walls in the form of microfibrils (between 2 and 20nm in diameter and 100-400nm in length), constituting a mechanically-resistant linear structure [AKI 10]. A number of different models of the arrangement of these microfibrils in the cellulosic fiber may be envisaged, while in other parts of the cell wall, cellulose may also be present in a less ordered form than the crystalline state mentioned above, with significant differences in terms of physical properties and functions. In the case of fibrous plants, cellulose is essentially present in the cortical fibers, the role of which is to improve the rigidity of the stem. These long fibers constitute the main added value of the plant. 2.1.3.2. Hemicellulose After cellulose, hemicelluloses are the second most omnipresent carbohydrate in plant cell walls. The term “hemicelluloses” covers many different polysaccharides which are rather heterogeneous because of their origin and therefore their composition and their structure or arrangement. Hemicelluloses are not linear polymers, and in cell walls they are generally linked with pectins, aromatic compounds or cellulose [AKI 10]. They are often compared to a matrix component, which can be present in the lamellae that hold the cell walls in fibrous tissues together, and in the primary and secondary cell wall, which is finer and rich in cellulose, where they serve as the link between cellulose and lignin [FOC 92]. It should be noted that hemicelluloses are relatively hydrophilic, and contain glucides which are potentially water-soluble. If included in an aqueous solution, the quantities and solubility of the polysaccharides likely to interact with, e.g., a paste of mineral binder, altering the kinetics of its binding and the binding itself, are highly variable. However, care should be taken when envisaging this option. 2.1.3.3. Lignin The aromatic ring is the basic chemical component in lignin and other aromatics. These compounds are extremely diverse and are present in various forms within the plant and the cell walls. Three main groups of lignins can be distinguished [BUR 08]: softwood lignin (gymnosperms), e.g. conifers; hardwood lignin (angiosperms), and lignin from herbaceous plants. This latter group is beginning to 8 Bio-aggregate-based Building Materials, Chapter 2, pp 27–73 attract an increasing amount of interest in R&D, because it is a renewable material produced in an annual cycle, and can be provided, primarily by the annual production of biomass. The lignin largely conditions the properties and treatment of bio-sourced materials. Hence, lignin is the compound which, indirectly, plays a capital role in the development of the market for these materials [BUR 08]. The estimated quantity of lignin is often relative to the measuring method used, and there may be an appreciable difference in the amounts reported in the literature, even for the same material [AKI 10]. Lignin also provides protection against the development of bacteria and pathogenic microbes that are harmful to the cell walls [AKI 08]. The nature and amount of the lignin present in the different parts of the plant have a significant impact on the effectiveness of retting procedures applied to fibrous plants, and also, more generally, on the durability or biodegradability of materials made from the plant. In partnership with cellulose, lignin gives the plant a rigid structure, enabling it to stand upright. In the cell walls, lignin is closely associated with hemicelluloses and cellulose. Covalent bonds are formed between lignin and hemicelluloses, and it is associated with the cellulose by the intermediary of the hemicelluloses [AKI 10]. In the case of fibrous plants – mainly flax or hemp – most of the lignin is to be found in the tissues in the center of the stem, containing the xylem and the other cell walls serving to channel water and sap [AKI 96]. Flax or hemp shiv obtained by defibration come from this so-called “lignified” part of the plant (see Table 2.1). 2.1.3.4. Pectin Pectins, much like hemicelluloses, are water-soluble and include many different components which are present in cell walls. Of these, galactose and rhamnose are the most representative of pectins. In fibrous plants they are often present in small quantities, but they are located strategically in the plant’s tissues. Pectins, in juxtaposition to hemicelluloses, constitute the polysaccharide matrix in the different tissues of the plant and in the fibers [AKI 10]. It should be noted that retting of fibrous plants causes degradation of the pectins by the action of bacteria and mold, thereby enabling the fibers to be separated from the non-fibrous part of the plant. 2.1.3.5. Waxes, fats and lipids These hydrocarbons are of different sorts, but share the peculiarity of being insoluble in water [NEL 00]. The biological functions they perform are also diverse. Fats and oils are the main forms of energy storage for many living organisms. Phospholipids and sterols are structural components in membranes. Other lipids play various roles, including enzymatic functions, pigmentation, etc. Biological waxes are esters, comprising long chains of alcohols. The proportion of these constituents Characterization of Plant-Based Aggregates, written by Vincent PICANDET 9 is relatively low in fibrous plants, but may be higher in grasses (bagasse and cereals) [AKI 10]. Lipids are particularly important on the external wall of plants, and around the fibers. In addition, the accumulation of wax on the cuticle forms a protective barrier against dehydration and the entry of infection agents into the plant. During the retting of fibrous plants, the epidermis of the stem separates from the fibers and the lignified central part. Flax shiv, like hemp shiv, contains only very small amounts of wax. 2.1.3.6. Ash The quantity of insoluble mineral matter can be determined by a number of methods, the results of which are fairly congruous, overall. The quantity of ash in fibrous plants is generally low, whereas in grasses it may be significantly higher – particularly in rice or wheat straw, whose silica (SiO2) content is higher. Yet fibrous plants – particularly flax and hemp – contain greater quantities of heavy metals such as lead (Pb), copper (Cu), zinc (Zn) and cadmium (Cd) [AKI 10]. The capacity of these plants to accumulate these heavy metals can, furthermore, be exploited to depollute some soils [LIN 02]. 2.1.4. Density and porosity, in the case of hemp shiv The densities and porosities measured on two types of hemp shiv [NGU 10a], “HS” (Hemp Shiv) and “FHS” (Fibrous Hemp Shiv), presented in Figure 2.4 (see section 2.2), are summarized in Table 2.2. The apparent density when loose and dry is measured on the basis of a cylindrical volume 160mm in diameter and 320mm in height, in which the loose dry hemp shiv is poured. The apparent density of the particles was measured on the basis of a straight section of stem, the area of which was determined by image analysis and the measured height. This figure, given as an indicative value, is underestimated in that the hemp shiv particles probably have a greater density [CEY 08; CER 05], owing to the stresses undergone during the defibration process and the stress of confinement when they were conditioned and kept in a 20kg sack. A value of 300kg.m-3 would, at first glance, seem to constitute a more meaningful density of the particles used. It would represent a decrease of the intra-granular porosity but a slight increase in the inter-granular porosity as reported in Table 2.2. The apparent density of the solid phase is determined by a pycnometer, using toluene as filling fluid. 10 Bio-aggregate-based Building Materials, Chapter 2, pp 27–73 From these measurements, we deduce the following porosity values: - total porosity: φtotal = 1 – ρV/ρS - intra-granular porosity: φintra = 1 – ρP/ρS - inter-granular porosity: φinter = 1 – ρP/ρV It should be noted that when long fibers are present in hemp shiv, as is the case of fibrous shiv, these fibers make up a significant proportion of the loose volume, and largely contribute to the increased inter-granular porosity. Although the apparent density of the dry particles is probably underestimated, the intra-granular porosity proves to be very high, which accounts for the excellent absorbent quality of this material. ρL apparent density loose and dry [kg.m ] -3 ρP apparent density of the dry particles [kg.m-3] ρS apparent density of the solid phase [kg.m ] φtotal, total porosity φintra, intra-granular porosity φinter, inter-granular porosity -3 HS FHS 112 71 256 256 1460 1440 92% 95% 82% 82% 56% 72% Table 2.2. Densities and porosity of the hemp shiv under examination 2.2. Particle Size Distribution (PSD) At present, no norm exists to cover the PSD of bio-sourced aggregates. They are different in many respects from the mineral aggregates traditionally employed in hydraulic concretes – which rounder, very unyielding with low porosity and considerably denser – for which methods of characterization, mainly by sieving, have been defined and are employed in the published standards. Yet the industrial implementation either on-site or in a precast factory necessitates a better characterization of these aggregates to stay abreast of the quality of the finished materials. Characterization of Plant-Based Aggregates, written by Vincent PICANDET 11 2.2.1. General characteristics of aggregates made from fibrous plants Hemp straw and flax straw is composed of very long and not heavily lignified cortical fibers surrounding a woody part (very heavily lignified short fibers) at the center of the stem [CRO 05], corresponding to the part which, while the plant was growing, carried the sap. The cortical fiber, rich in cellulose, represents the main value of this agricultural product [BOU 06]. During the process of defibration, the straw is ground, usually using a hammer mills. The woody part is detached from the fibers, and shredded into small pieces to form hemp or flax shiv. In the case of hemp, 100kg of straw, when ground, yield around 30kg of fiber, 60kg of hemp shiv and 10kg of dust [BOU 06; BEV 09; BRU 09]. Although it is the main constituent, hemp shiv is merely a co-product of the exploitation of hemp. Its main use up until now has been in animal litter or horticultural straw. The term “hemp shiv” is currently used to denote aggregates from the stem of the hemp plant which may be very varied, as they come from agricultural products that are subject to weather hazards and obtained using various post-harvest processes. Flax shiv, for its part, present still more disparate characteristics, particularly due to the larger variety of species that can be grown. In addition, the implementation processes employed generally tend to (prefer) these particles, and therefore – depending on the overall shape of the particles – give rise to a tangible anisotropy of the material, particularly in terms of its thermal characteristics [ELF 08; NGU 10b]. 2.2.2. Fiber content When the plant is felled, it may be left on the ground for a variable length of time so that retting will facilitate the process of defibration. The advance of this process, the dampness of the straw and the regulations of the grinders used affect the size of the particles obtained when the straw is ground [MAN 04; MIA 11]. Also, the defibration performed may be more or less vigorous, and the fiber content in the hemp shiv or the flax shiv may be variable. 12 Bio-aggregate-based Building Materials, Chapter 2, pp 27–73 a) HS Hemp shiv b) FHS shiv Figure 2.4. Hemp shiv under investigation, laid out in a spread 7cm in diameter The study presented below is based on the example of two types of hemp shiv: a hemp shiv gained from an advanced process of defibration with very few residual fibers, denoted HS, and another gained from a partial process of defibration, containing a significant amount of short cortical fibers (shorter than 4cm), denoted FHS. It is very easy to distinguish these two hemp shiv with the naked eye, as shown in Figure 2.4. 2.2.3. Methods for characterizing the PSD Two methods can be easily employed to study the PSD of the hemp shiv, each with advantages and drawbacks: The conventional method of sieving with dry particles enables us to take measurements directly on a sample of a few hundred grams. The limitations of this method are due to the elongated shape of hemp shiv particles, and their low density, which render sieving less appropriate and unreliable [IGA 09]. 2D image analysis of particles spread out over a flat surface gives us access to more information. Thereby, the width and length of each particle detected can be measured. However, this method is more complex and requires samples no larger than a few grams. The precision of the results produced is therefore limited by the representativeness of the sample and by the only dimensions obtained for the aggregates by projection onto a plane. Characterization of Plant-Based Aggregates, written by Vincent PICANDET 13 2.2.3.1. Sieving method Sieving was performed on dry material, so that the finest particles could separate from the others. Sieves with standardized square mesh were used, as was a mechanical siever for the study of soils and mineral aggregates (NF ISO 3310.1 – ASTM E-11-95). In order to obtain repetitive results, the vibration time was extended to an hour for a 200-gram sample and for 5 consecutive sieves. The apertures of the sieves used ranged from 10 to 0.315mm as follows: 10; 8; 6.3; 5; 4; 3.15; 2.5; 2; 1.25; 1; 0.63 and 0.315mm. PSD analysis by sieving assumes that all the particles are practically spherical in shape, and pass through a square aperture when their diameter is less than the side of the square. For flat or elongated particles, such as hemp shiv particles, this point is developed in further detail in section 2.2.5.3. The particles may either pass through the sieve in the direction of their length (see Figure 2.20) or (stay back) if they are positioned across the aperture. In the latter case, these particles may also block the passage of particles located above them. Generally speaking, increasing the time taken over sieving helps to reduce the relative differences of the refused particles obtained for each sieve. On the basis of several tests, the precision of the results, i.e. the evaluation of the particles retained in each sieve, was evaluated at ±15% with the series of sieves used. These uncertainties are illustrated in Figure 2.6. Globally we observe that the PSD of the two hemp shiv under study (apart from fibers), are relatively close. Figure 2.5. Pellets of fibers formed with the first sieves (4 and 5mm) When fibers are present, sieving can be used to complete the separation of the fibers from the hemp shiv. Indeed, the fibers tend to form pellets in the first sieves – see Figure 2.5. Also, when the fiber and the hemp shiv are still linked, the vibrations of the sieve are enough to detach them. Generally, the amount of fibers in the hemp shiv tested varies between 1 and 15% of the mass. For instance, this fiber content was evaluated as being between 12% and 15% in the case of the fibrous hemp shiv 14 Bio-aggregate-based Building Materials, Chapter 2, pp 27–73 (FHS) as shown in Figure 2.4. The PSD presented below do not take account of these free fibers. Yet even in the case of hemp shiv obtained by an advanced process of defibration, a detailed examination of the aggregates shows that a small amount of short fibers may still be found attached to a few hemp shiv particles, even after the stages of sieving performed, for at least 30 minutes. Figure 2.6. Cumulative size distribution obtained by sieving 2.2.3.2. Image-analysis method This method requires good-quality sampling, in that only a finite amount of material can reasonably be analyzed. A classic method of quartering can be applied to a 20kg sack of hemp shiv and repeated as many times as need be. The representativeness of the sample selected is the key element guaranteeing the relevance of the results produced. 2.2.3.2.a. Acquisition of a digital image Image analysis is based on a two-dimensional observation of particles spread out over a flat surface. In this study, the images were obtained with a conventional scanner generally used to digitize documents. This technique offers the advantage of avoiding any distortion of the image which might occur if a camera were used. The scanner can acquire a color image or an image converted into 8-bit grayscale that Characterization of Plant-Based Aggregates, written by Vincent PICANDET 15 can be processing by an image-analysis program such as “Image Tool” or “ImageJ”, which are freely accessible online. The particles are spread out so that they do not overlap or touch. This requires very detailed attention, because the particles are fine and in these conditions it is difficult to avoid some overlap. Certain algorithms can be used to deal with this problem at the image-processing level [SHA 06], but with the aim of simplifying the procedure of analysis and increasing the precision of our measurements [IGA 09a] [IGA 09b], we limited ourselves to a procedure of rather dispersed distribution, requiring a greater number of images to be analyzed and a case-by-case verification of potential overlaps of particles. As the hemp shiv under investigation is light in color, a dark background was used in order to obtain a maximum degree of contrast. The grayscale image was processed at a resolution of 600 DPI (dots per inch) on both the vertical and horizontal axes. This corresponds to a constant scale factor of 0.04233mm per pixel. This scale factor can be verified by calibration. On an A4 surface, i.e. 210 × 297mm2, the image produced in an uncompressed format occupies around 35MB of memory. The precision of the measurements can further be improved by increasing the resolution, but this is limiting because of the time needed for the scanner to transfer the data and for the storage and processing of the multiple images. Image analysis requires a binarized image, which necessitates prior thresholding of the grayscale image. This is the trickiest step in this method, particularly if a large number of fine particles (of less than 0.5mm width) are present. Automatic thresholding procedures may be available, but there will be a halo effect, to a greater or lesser degree of severity, around the particles identified. The halo effect tends to decrease the level of gray of the pixels on the outer boundary of the lightest objects. Incorrectly adapted thresholding may therefore contribute to an artificial increase of the size of these objects and consequently, noticeably over- or underestimate (depending on whether the background is dark- or light-colored) the relative size of the smallest objects detected [NGU 10a; IGA 09b]. Yet this problem can be greatly assuaged by manual thresholding to process the image. The lower bound of the threshold can be adjusted so that this halo effect is contained in a band approximately 1 pixel in width around each object. Appropriate thresholding should cover the surface of the objects needing to be detected as precisely as possible. The quality of this thresholding can be verified using small “standard” objects the same color as the particles we wish to detect. Generally, in the case of light-colored particles on a dark background, the upper threshold is fixed at the maximum, i.e. 255, and the lower threshold is between 60 16 Bio-aggregate-based Building Materials, Chapter 2, pp 27–73 and 90. In our case, in order to create the most apt binarized image, the value of this lower threshold was set at 80 for all the images processed. Hemp shiv also contains dust of organic or mineral origin, usually less than 2% of the weight of the particles passing through the 0.315mm sieve. The tail of distribution toward the finest particles is difficult to quantify using image analysis. Such a task would require additional observation, on a microscopic scale, of finest sieved sample. Next, therefore, it is useful to define a detection threshold, i.e. a minimum projected area of the objects to be processed, so as to take account only of the hemp shiv particles and avoid dust particles represented by merely a few pixels. In the case presented here, only the particles whose area is greater than 0.08mm2 (i.e. objects represented by at least 45 pixels) and width greater than 0.1mm (i.e. over 2 pixels across) were taken into account for the PSD analysis. Other processing operations can also be carried out with a view to preparing the images before analysis. One such operation, which involves producing an erosion of a given number of pixels followed by an operation of expansion of the object by adding the same number of pixels onto its boundary, can help eliminate dust particles and fibers which are not representative of the hemp shiv particles needing to be identified. This operation is referred to as an opening operation, because it may lead to the de-compartmentalization of cavities, separated by thin boundaries, which may be contained in the objects. By way of example, its effect is illustrated in Figure 2.10 for a thickness of 2 pixels. 2.2.3.2.b. Measurements of length and parameters of shape of the objects Image analysis gives us access to far more information than does sieving. For each particle detected, its projected area and the perimeter of that projected area are directly measured and recorded. Other more elaborate parameters, such as the minimum convex area surrounding the object (see Figure 2.7), can be used to define different formal parameters to help better characterize the particles. Of these, the convexity ratio, χ (also called “solidity”) [MOR 00], defined as the object’s projected area over the convex area surrounding that object, reveals the form of the particles. Perfectly convex particles have a convexity ratio of 1. In this study, we labeled particles with a convexity ratio of less than 2/3 as non-convex (see section 2.5.1). Similarly, the convexity of the particles can also be estimated by looking at the ratio of the projected area to the product of the length by the width of the identified Characterization of Plant-Based Aggregates, written by Vincent PICANDET 17 object (Area/(Length × width)) when this measurement is not embedded in the software tool being used. Minor Axis Projected are of the object Smallest enclosing circle Minimum convex area encompassing the object Width* Major axis Boundary of the object Length* Figure 2.7. Evaluation of the convex area and the maximum Féret diameter Observation of different types of ground-up straw shows that the resulting particles have irregular and angular forms due to the microstructure of the plant, oriented along the axis of the stem and to the (tearing) action that can sometimes be caused by hammer mills, for instance. In this scenario, the shapes of the finest particles therefore tend to be polygonal and convex, whereas the shapes of the coarsest particles tend to diversify to include non-convex particles [BIT 09a]. 18 Bio-aggregate-based Building Materials, Chapter 2, pp 27–73 Overall, in the case of convex and non-convex particles gleaned from ground straw, the method for determining the length based on the diameter of the smallest enclosing circle or maximal caliper (which some writers also refer to as the Féret diameter) is fairly representative of the length of the object [IGA 09a]. Hence, the length can be directly quantified using this maximum diameter, defining the major axis of the projected area (see Figure 2.7). Figure 2.8. Hemp shiv particles after binarization of the image, classified on the basis of biases in the analysis which will cause protuberances due to tearing and to remaining connected fibers 2.2.3.2.c. Determination of the particle size The measurement of the length and width of these particles may be subject to different definitions, depending on the representativeness of these dimensions in the case of the type of object needing to be analyzed. The width can be defined and measured using Image Tool, as the maximum length along the minor axis, perpendicularly to the major axis. This is denoted as “width*” in Figure 2.7 and Figure 2.9. For around 2600 analyzed particles contained in a 4g sample of HS hemp shiv, Figure 2.11 gives a view of the logarithmic scale of the widths in comparison to the lengths analyzed. This method leads to a slight overestimation with rectangular shapes, because it is the diagonals that are identified as the lengths. However, the overestimation of the lengths therefore also applies, to the same degree, to the widths, so that the elongation of the particles, ε (the ratio of length to width of the particles) – a parameter which we shall study later on – remains the same. Overestimation is also important in the case of non-convex particles, because the measured width starts from the major axis even if this axis lies outside the object. The width can also be defined, and measured using ImageJ, as the minimal Féret diameter or minimal caliper, i.e. the minimum distance between two parallel straight lines (or planes) encompassing the object, or indeed as the width of the narrowest rectangle (or parallelepiped) containing the object – see Figure 2.9. This method could lead us to suppose that the estimation of the width is correct in the case of rectangular particles. However, in the case of hemp shivs, the short fibers still connected and the particles (destroyed) by grinding give rise to outcrops from the Characterization of Plant-Based Aggregates, written by Vincent PICANDET 19 projected areas and ultimately cause an overestimation of the widths obtained by way of this method. In order to iron out some of the (protuberances) of the objects studied (see Figure 2.8) and analyze them using geometric forms deemed to be representative, other methods exist. Such methods consist of adjusting the basic geometric shapes (rectangles, ellipses, triangles, polygons, etc.) to the objects detected [IGA 08; BIT 09a] so as to determine their length, and above all their representative width. Of these, in the case of hemp shiv, an ellipse can be adjusted so that its center of gravity corresponds to that of the object and its projected area is identical to that of the object. The lengths and widths of the object are therefore defined respectively in accordance with the large and small radii of the adjusted ellipses (see Figure 2.9). Smallest rectangle containing the object (Minimum Féret Diameter) Fitted ellipse (Small diameter) Boundary of the object : (Perimeter / Area) Fitted ellipse (Large diameter) Major Axis (Length*) (Maximum Féret Diameter) Diameter of the smallest enclosing circle (Width*) Maximum length perpendicular to the major axis Figure 2.9. Lengths and widths analyzed 20 Bio-aggregate-based Building Materials, Chapter 2, pp 27–73 a) b) c) Figure 2.10. Analysis of a hemp shiv particle approximately 20mm in length: a) grayscale scanned image; b) image after thresholding; c) image after operation of opening of 1 pixel followed by adjustment of an ellipse, facilitating the evaluation of its length and width It should be noted that with rectangular shapes, the adjustment of an ellipse also leads to an overestimation of the lengths and widths in identical proportions, so that the elongation of the particles, ε, again remains unchanged. For the same images obtained with a 4g sample of CP hemp shiv, the widths on the basis of the lengths analyzed by adjustment of an ellipse on each object detected (around 2600 – see section 2.5.1) are represented on Figure 2.12. Of these point clouds, two general categories of particles may appear: the particles representative of hemp shiv, for which the corresponding point cloud is centered around a width of around 2mm. and dust or micro-fibers, for which the point cloud seems to be truncated by the threshold selected. Of the various characteristics that are measured, the elongation seems critically important, because it will condition the orientation of the granular arrangement and the anisotropy of the finished materials. For the same sample, it is represented as a function of the projected area of each particle when the lengths are measured from the major and minor axes in Figure 2.14 and when they are evaluated on the basis of the diameters of the adjusted ellipses in Figure 2.13. The point cloud is primarily clustered around a straight line denoting a constant length-to-width ratio. For an elongation on a logarithmic scale, the points appear to be distributed in accordance with a normal law. In these figures, therefore, we have considered the geometric mean of the elongation of each particle weighted by its area, notated as ε gm, and the Characterization of Plant-Based Aggregates, written by Vincent PICANDET 21 corresponding standard deviation, notated as σgm, in order to calculate the confidence intervals for the different segments of the projected area in question. In Figure 2.14, it appears that the smallest particles, with a projected area of less than 0.4mm2 may contain short fibers (shorter than 5mm) which are not straight. These particles noticeably increase the average elongation of the particles contained in the smallest intervals of projected area when the lengths and widths are measured in accordance with the major and minor axes. Overall, for these two methods of analysis, there does not appear to be any significant change in elongation with the projected area of the particles. Over all the particles identified, the average value of this elongation is near to 4, with a geometric standard deviation of around 1.5. The impact of the dimensional approach to particle analysis on the results is presented in greater detail in section 2.6.2. Width* [mm] 10 1 0.1 0.1 1 10 100 Lenght* [mm] Figure 2.11. Length and width of hemp shiv particles evaluated by the major and minor axes of the projected area 22 Bio-aggregate-based Building Materials, Chapter 2, pp 27–73 Width [mm] 10 1 0.1 0.1 1 10 100 Lenght [mm] Figure 2.12. Length and width of hemp shiv particles evaluated by adjustment of an ellipse over the projected area Figure 2.13. Elongations of hemp shiv particles evaluated along the major and minor axes of the projected area Characterization of Plant-Based Aggregates, written by Vincent PICANDET 23 Figure 2.14. Elongations of the hemp shiv particles evaluated by adjustment of an ellipse over the projected area 2.2.4. PSD analyses Various types of distribution, or probability density, of size of particles may be deduced from these tests, depending on whether they are distributed in accordance with their number or with their projected area. However, so as to be meaningfully representative of potential granular packing and to be comparable with the analyses obtained by sieving, this analysis should be performed on the basis of a distribution of the volume of the particles. 2.2.4.1. Frequency distribution Distributions on the basis of the number of particles can be performed directly from the raw data from the image analysis step. However, this type of distribution is very sensitive to the number of the smallest particles, and particularly to their detection threshold. In the study presented, we set a detection threshold based on the projected area of the particles equal to 0.08mm2. Yet clearly, the material contains even smaller particles which will not be taken into account when counting the particles. Such a distribution based on the relative cumulative number of particles passing through a sieve of a given size, denoted as N% in Figure 2.15, therefore depends heavily on this detection threshold. 24 Bio-aggregate-based Building Materials, Chapter 2, pp 27–73 2.2.4.2. Area fraction distribution (projected area) Image analysis also gives us access to the projected area of each particle detected: Ai. The influence of the finest particles on the PSD can therefore be weighted by this criterion, so as to consider a distribution by the cumulative projected area of the particles whose considered size is less than a given value. The distribution of cumulative passing can be directly calculated on the basis of the sum of the projected areas of n particles, arranged in order of increasing size, for a total number of N particles detected, whose total area is AT. The cumulative distribution by increasing size, PA(X ≤ xn), similar to the “cumulative passing” obtained by sieving (see Figure 2.6), can then be written as: PA (X ≤ x n ) = ∑ ∑ n i=1 N Ai A i=1 i = 1 AT ∑ n i=1 Ai [2.1] where X is the considered size of the particles and PA(X ≤ xn) the proportion of the projected area accounted for by particles smaller than the nth particle of size xn. The cumulative distributions PA(X ≤ xn) and the distributions of size based on the area of the particles are therefore annotated (A%) in the figures. 2.2.4.3. Mass fraction distribution The PSD curves are usually traced on the basis of the results obtained by sieving, i.e. on the basis of a mass distribution. If Mi is the mass of the particle i, the distribution PM(X ≤ xn) is directly calculated from the cumulative mass of the n smallest particles passing through a sieve of given size out of a total of N particles of mass MT: PM (X ≤ x n ) = 1 MT ∑ n i=1 Mi [2.2] where X is the considered size of the particles and PM(X ≤ xn) the proportion of the mass of particles smaller than the nth particle of size xn. 2.2.4.4. Relation between area fraction- and mass distributions In order to be able to compare the results obtained by sieving and by image analysis, a distribution of the size of the particles in relation to their mass must be considered – that is, we must consider a distribution of type PM(X ≤ xn) for both the width and length.. Characterization of Plant-Based Aggregates, written by Vincent PICANDET 25 If the apparent density of the particles is independent of their dimensions, PM(X ≤ xn) can also be written in accordance with the volume Vi of each particle and their total volume VT. Supposing that the particles are similar in shape, ei denotes the average thickness over the whole of the projected area of each particle, i.e. their third dimension (inaccessible by 2D image analysis), and the volume of each particle can be considered to be the product of its projected area, Ai, by its average thickness, ei: Vi = eiAi. PM (X ≤ x n ) = 1 VT ∑ i=1 Vi ≅ n ∑ ∑ n e .A i i=1 i N [2.3] e .A i i=1 i From hereon in, many complementary tests can be performed; yet it is not easy to approximate the thickness ei of each particle. It can only be supposed that since the particles are simply and freely spread out over a plane, this average thickness is less than the width of each particle. The thickness of the woody part in the stem varies noticeably, depending on the climatic conditions, the date of harvesting and the density of the plantation [SCH 06] on the one hand, and then depending on the height of the particular section within the stem [RAH 10], increasing from the apex toward the base. However, the process of defibration is applied to all the cropped straw, giving rise to multidirectional grinding. As observed for different types of ground straw, the general shape of the particles does not seem to be affected by the diameter of the stems being ground [NGU 10a; IGA 09a] whereas the size of the particles produced depends essentially on the process of grinding itself and on the settings used [BIT 09a]. Figure 2.11 shows that in this case, the average elongation ratio of the particles is, overall, independent of the particles’ projected area. This observation can be supposed to extend into the third dimension: the average ratio of width to average thickness, Φ = ei/li, may also be reasonably assumed to be constant. If the density of the particles is identical, with a similar shape irrespective of their size – i.e. if they are generally homothetic and their volume Vi can be approximated by Φ Aili, the mass distribution of the particles can be deduced from the projected area Ai and the width li of the particles by the following relation: PM (X ≤ x n ) ≅ ∑ ∑ l .Ai ⎛ ei ⎞ ≅ Φ (const.) ⎟ ⎜ if l l .Ai ⎝ i ⎠ i=1 i n i=1 i N [2.4] It is in view of this hypothesis that the cumulative distributions PM(X ≤ xn) and distributions of size based on the mass of the particles are annotated as (M%) in figures hereafter. 26 Bio-aggregate-based Building Materials, Chapter 2, pp 27–73 It should be noted that the cumulative distribution PM(X ≤ xn) depends neither on the value of the apparent density of the particles, ρa, nor on Φ . Because PM(X ≤ xn) is sensitive to the largest particles, this distribution may be considerably different from PA(X ≤ xn) in the case of a spread distribution. It is interesting to note that if all the particles had the same thickness, the approximation of the cumulative distribution by mass, PM(X ≤ xn), defined in equation [2.3], would be equivalent to PA(X ≤ xn) defined in equation [2.2]. Figures 2.15 and 2.16 illustrate the difference observed between the cumulative distributions based on the number of particles, the projected area and the supposed mass of the particles, for both the width and length of the particles. In addition, the standard distributions of particle size represented in Figure 2.17 confirm the uni-modal nature of the area fraction (A%) and mass fraction (M%) distributions for the width and length of the particles. Figure 2.15. Cumulative size distribution of “CP” hemp shiv obtained by sieving, considering a mesh-size measuring d and 21/2d in the sieves, and frequency distributions (N%), in area fraction (A%) and mass fraction (M%) obtained by image analysis from the lengths and widths of the hemp shiv particles evaluated along the major and minor axes of the projected area of the particles Characterization of Plant-Based Aggregates, written by Vincent PICANDET 27 Figure 2.16. Cumulative size distribution of “CP” hemp shiv obtained by sieving, considering a mesh-size measuring d and 21/2d in the sieves, and frequency distributions (N%), in area fraction (A%) and mass fraction (M%) obtained by image analysis from the lengths and widths of the hemp shiv particles evaluated by adjustment of ellipses on the projected areas of the particles 28 Bio-aggregate-based Building Materials, Chapter 2, pp 27–73 Figure 2.17. PSD in mass fraction of “CP” hemp shiv obtained by sieving, considering a mesh-size measuring d and 21/2d in the sieves, and density of distributions in area fraction (A%) of the widths, and mass fraction (M%) of the widths and lengths obtained by image analysis from the dimensions evaluated by adjustment of ellipses on the projected areas of the particles 2.2.5. Comparison of the results obtained by image analysis 2.2.5.1. Impact of the selection of the particles to be analyzed The detected area and minimal width of the particles needing to be analyzed constitute the first parameter when selecting which particles to analyze. In the wake of the defibration process, the hemp shiv particles may have varied shapes, which deviate from the ellipsoidal or parallelepipedic shapes to which it is possible to compare them. Short fibers may still be attached, and the tearing action to which the stem is subjected leads to very varied shapes that are sometimes difficult to qualify in terms of representative length and width. Thus a minimum convexity ratio can be set in order to discount particles whose shape differs too greatly from the conventional shapes which can be correctly analyzed. Figure 2.18 therefore presents the effect of this selection on the distribution of the widths of the same sample containing: 2600 particles whose area is greater than 0.08mm2 with a convexity Characterization of Plant-Based Aggregates, written by Vincent PICANDET 29 coefficient χ, greater than 0; 2460 particles with χ > ½; 2300 particles with χ > ⅔; and 1980 particles with χ > ¾. There is a noticeable effect is visible on frequency distributions, for the finest particles, while the differences become very small for area fraction distributions, and insignificant for mass fraction distributions. It should be noted that the same observation can be made as regards the distributions of the lengths, with differences reduced still further. 100% Convexity > 0 Cumulative percentage passing [%] 80% Convexity > 0.5 Convexity > 0.63 60% N% Convexity > 0.75 A% 40% M% 20% 0% 0.1 1 Width [mm] 10 Figure 2.18. Threshold effect of the convexity-to-width ratio of the ellipses adjusted to the projected areas of the particles being analyzed The results presented in this study relate to particles whose area is greater than 0.08mm2, width greater than 0.1mm and convexity ratio greater than 2/3. It should be noted that this final condition, here applied operationally in order to shed light on the results presented, disqualifies less than 12% of particles detected (300 in this case) out of the sample tested, and therefore has little significant influence on the progression of the analyses. The influence of the threshold concerning the minimum area of the particles taken into consideration in the analyses has also been studied. At the resolution selected – 23.6 pixels/mm (600 DPI) – it does not seem representative to consider objects whose surface area is less than or equal to 0.08mm2, i.e. we look at particles represented by at least 45 pixels – notably to study the overall shape of the particles, for instance. When this threshold is increased in iterative steps, up to ten times this initial value (i.e. up to 0.8mm2), the number of particles taken into account decreases significantly, but we do not see a significant difference in the distributions of observed sizes in area fraction and mass fraction. Increase it still further, and slight 30 Bio-aggregate-based Building Materials, Chapter 2, pp 27–73 differences appear, primarily on the distributions of width of the particles. In reality, for the hemp shiv being studied, it still seems possible to consider only those particles whose area is greater than or equal to 1mm2 to perform a simplified but representative PSD study. However, a lower threshold is preferable, wherever possible. 2.2.5.2. Impact of the method of analysis The measurement of the length and width of these particles may be subject to different definitions depending on the representativeness of these dimensions in the case of the type of object needing to be analyzed – see Figure 2.9. Three different analytical methods have been applied to the same images, and the distributions of lengths and widths are presented and compared in Figure 2.19. 1) Maximum length along the major axis (or maximum Féret diameter) and maximum length along the minor axis, perpendicular to the major axis, denoted as “Major/Minor axes”. 2) Maximum and minimum Féret diameter, i.e. minimum distance between two parallel lines (or planes) encapsulating the object, denoted as “Féret”. 3) Large and small diameter of an ellipse adjusted so that its center of gravity corresponds to that of the object and its projected area is identical to that of the object, denoted “Ellipse”. It is clear that the distribution of the length is hardly sensitive at all to the analytical method employed. It should be noted, however, that the first two methods lead to theoretically-identical results for the length, even if two different programs are used to measure it. Notably, there is no significant difference between the distributions of lengths analyzed by methods 2 and 3 using the same program. The widths, for their part, are more sensitive to the analytical method used. This point develops differently depending on the nature of the particles studied, particularly in the case of different food grains [IGA 09c]. In the case of hemp shiv, however, the discernible difference is relatively small, and this difference is comparable for both types of distribution shown in Figure 2.19, in terms of the area fraction (A%) and mass fraction (M%). Characterization of Plant-Based Aggregates, written by Vincent PICANDET 31 100% Cumulative percentage passing [%] Ellipse (A%) Major/Minor Axis (M%) 80% Féret (A%) Width (A%) Ellipse (M%) 60% Width (M%) Major/Minor Axis (M%) Féret (M%) 40% Lenght (A%) Lenght (M%) 20% 0% 0.1 1 10 100 Size [mm] Figure 2.19. Impact of the analytical method on the distribution of widths and lengths of the objects (projected areas of the particles) analyzed As mentioned in section 2.2.3.2.c, adjustment of ellipses to the projected areas of the hemp shiv particles enables us to iron out some of the remaining short fibers, supple and slight in terms of volume in comparison to the woody particles to which they are still attached, which are more rigid and voluminous, that we are seeking to identify. This method, leading to the smallest estimated widths, was therefore selected for the continuation of the study here presented. 2.2.5.3. Comparison with the results obtained by sieving As presented in Figures 2.15 and 2.16, the cumulative distributions of the particles are, overall, closer to the curve of cumulative passing obtained by sieving, considering the width, rather than the length. This implies that the particles are capable of passing through the sieves in a direction perpendicular to the meshes, and that the sorting of the hemp shiv when the particles are sieved is done primarily on the basis of the width rather than the length of the particles. If we assume that the particles are ellipsoidal, elongated and flat in shape, when these particles can pass lengthways through the sieves, their width may be oriented along the diagonals of the square holes (see Figure 2.20). In this case, only those particles whose width is greater than 21/2d are caught by a sieve whose mesh size measures d. 32 Bio-aggregate-based Building Materials, Chapter 2, pp 27–73 Elliptical particle projected in the direction of its length (large diameter) Sieve opening : d (mm) d Particle Width 2 d, diagonal of the opening Sieve mesh Thickness of the particle Figure 2.20. Cross-section of the largest elliptical particle able to pass through the sieve, in the direction of its length and along the diagonal of the square hole Figure 2.21 shows that the distribution of the cumulated mass widths (M%) is very similar to the distribution obtained by considering the diagonal of the square opening in the sieves, 21/2d mm instead of the mesh size i.e. the side of the square opening, measuring d mm. This indicates that the majority of the particles are oriented along the diagonal of the opening when they pass through the sieves. As Figure 2.22 confirms, the size-per-mass distribution of the particles is also that which corresponds most closely to the results obtained by sieving. Yet this is slightly more skewed toward fine particles. This may be due to some of the finer particles being retained in the sieve, particularly in the last and finest sieves, whose meshes are finer than 1.25mm. Characterization of Plant-Based Aggregates, written by Vincent PICANDET Figure 2.21. Comparison of the width cumulative distributions in terms of area fraction and mass fraction obtained by image analysis and by sieving, considering the side of the square opening d and its diagonal 21/2d 33 34 Bio-aggregate-based Building Materials, Chapter 2, pp 27–73 Figure 2.22. Comparison of the width distributions in mass fractions by image analysis and by sieving, considering the diagonal of the square opening 21/2d 2.2.6. Characterization of the geometry of the particles 2.2.6.1.. Average elongation The elongation of the particles can lead to an anisotropy in the material, owing to the preferred orientation that their implementation usually causes, and to the orientation of the microstructure and porosity within these particles. In view of their respective volume, the elongation of the largest particles will have a greater impact on the general properties of the material than will the smaller particles. The average elongation of the particles, ε , therefore needs to be weighted by the volume of each particle and can be written as follows: ε= ∑ N ∑ i=1 Vi N i=1 Li li Vi ≅ ∑ ∑ N i=1 N Li A i l Ai ( si V ≅ Φ l A ) i i [2.5] i i=1 i The estimations of lengths are essentially identical no matter what the analytical method, whereas for the width the estimations exhibit a slight difference (see Figure 2.19). Consequently, for the sample of hemp shiv under consideration, the average elongation varies between 3.93 (adjustment of the ellipse) and 3.65 (Féret diameters), with 3.85 (major/minor axes). The geometric means of the elongation are very similar to these values for all cases (see section 2.2.3.2.c), with an associated standard deviation of less than 1.54. 2.2.6.2. Average flatness The average ratio of the particles’ thickness to their width, Φ , can be considered an indicator of the flatness of the particles. It can be evaluated if the mass or total volume of the particles being analyzed is known [KWA 99]. Φ= ∑ i=1 li Ai VT N = ρa ∑ i=1 li Ai MT N [2.6] In our case, the mass of the sample is known, and the apparent density of the particles ρa can be estimated [NGU 10a; CEY 08]. We shall consider the apparent Characterization of Plant-Based Aggregates, written by Vincent PICANDET 35 density ρa of the particles to be approximately 300kg/m3, in the case at hand; Φ ≅ 1/3 if the dimensions are estimated on the basis of adjusted ellipses. In that the widths estimated differ slightly depending on the analytical method in question, the value of Φ will be slightly smaller when the widths are estimated as being greater. For instance, Φ ≅ ¼ when length and width are measured in accordance with the major and minor axes. 2.2.7. Characterization of the PSD 2.2.7.1. Means and standard deviations The arithmetic mean of the size (width or length) of the particles, weighted by their area or mass, and the associated standard deviation, can be used to gain an overall characterization of the PSD. The standardized degrees of skewness and kurtosis relative to the 3rd- and 4th-order moments of distribution can also be calculated. However, in that the distributions can be approximated by a normal law according to a scale of logarithmic size, the weighted geometric mean Xgm and its associated standard deviation σgm, defined in the two equations below, appear to be more relevant when seeking to characterize the distribution, as in the case of numerous distributions of particle sizes obtained from the comminution of the stems of different herbaceous plants [ASA 06; BIT 09a; BIT 09b; MIA 11] or organic dusts [IGA 09b]. ⎛ ∑ M i ln ( x i ) ⎞ X gm = exp ⎜ ⎟⎟ ⎜ ∑M i ⎝ ⎠ ⎛ ⎜ σ gm = exp ⎜ ⎜ ⎝ [2.7] ∑ M ( ln ( x ) − ln ( X ) ) ∑M i i gm i 2 ⎞ ⎟ ⎟ ⎟ ⎠ [2.8] 2.2.7.2. Graphic methods Different sizes corresponding to representative fractions of cumulative passing such as D95, D90, D84, D75, D60, D50, D30, D25, D16, D10, and D5 are classically used to determine different parameters which are supposed to characterize the PSD. In 36 Bio-aggregate-based Building Materials, Chapter 2, pp 27–73 particular, the mean, the standard deviation, the skewness and the kurtosis, on the basis of a normal law, can be approximated from these different values [FOL 74]. Other parameters can also be used, with the aim of evaluating the uniformity and the extent of the PSD at hand. Among the commonly-used dimensionless coefficients, the Hazen coefficient or coefficient of uniformity, Cu = D60/D10 and the coefficient of curvature Cc = D302/D10D60 can be used, although the nomenclature employed to qualify mineral aggregates is not directly applicable to the current case. 2.2.7.3. Distribution models The maximum amount of information can be obtained if a distribution model is adjusted to the PSD under investigation [DJA 97]. Different laws exist that are based on semi-infinite variables. Usually, basic models with two parameters – one relating to the average size and the other to the extent of the distribution – are used. 2.2.7.3.a. Log-normal distribution Given the uni-modal nature of the distributions presented and apparently symmetrical according to a logarithmic scale of size, the Log-Normal law seems obvious as a first approach [LIM 01]. Its distribution function of the lengths X is written as follows: ⎛ ln ( x ) − ⎞ ⎤ 1⎡ ⎢1 + erf ⎜ ⎟⎥ 2 ⎢⎣ ⎝ σ 2 ⎠ ⎥⎦ PLog.N (X ≤ x) = [2.9] where μ and σ are the parameters needing to be identified, and erf(x) denotes the Gauss error function. It should be noted that eμ and eσ reciprocally represent the weighted geometric mean and the associated standard deviation, which can both also be calculated on the basis of the whole dataset including each particle identified, and denoted as Xgm and σgm (see Table 2.3). The probability density of this distribution function is written thus: PLog.N (x) = ⎡ ⎛ ln ( x ) − ⎞2 ⎤ exp ⎢ − ⎜ ⎟ ⎥ xσ 2π ⎣⎢ ⎝ σ 2 ⎠ ⎥⎦ 1 [2.10] The mode, ModeLog.N, or dominant value (i.e. the value which is most represented in the size considered in the population of objects under investigation) is obtained on the basis of the maximum of this latter function: ModeLog.N = e(μ−σ²)mm. The arithmetic mean of the size, or expected value, ELog.N, is written as: Characterization of Plant-Based Aggregates, written by Vincent PICANDET ⎛ σ2 ⎞ E Log.N = exp ⎜ + ⎟ 2 ⎠ ⎝ 37 [2.11] and its associated standard deviation is given by: σ Log.N = E Log.N exp ( σ 2 ) − 1 [2.12] 2.2.7.3.b. Rosin-Rammler distribution When the size distribution relates to particles or fragments obtained by grinding, one of the other models used most frequently in the existing body of literature is the Rosin-Rammler model [DJA 97], particularly in the case of biomass, [ALL 03; ALL 04; BIT 09b; BIT 11]. The distribution function of this model, identical to the Weibull distribution, can better represent skewed distributions [ROS 33]: ⎡ ⎛ x ⎞k ⎤ PRR (X ≤ x) = 1 − exp ⎢ − ⎜ ⎟ ⎥ ⎣⎢ ⎝ ⎠ ⎦⎥ [2.13] ⎡ −ln (1 − P (X ≤ x) ) 1k ⎤ RR ⎢⎣ ⎥⎦ [2.14] where λ and k are constants relating respectively to the dimension of the 63.2th percentile of the distribution function and to the tightening of the distribution. This distribution function has the advantage of exhibiting a reciprocal function which can be used to directly calculate the dimensions corresponding to a given cumulative fraction. x = The median size of the particles DRR(50) corresponds to P(X ≤ x) = 50% and is equal to λ.ln(2)1/kmm. The probability density derived from the Rosin-Rammler distribution function can be written as follows: PRR (x) = k⎛x⎞ ⎜ ⎟ ⎝ ⎠ k −1 ⎡ ⎛x⎞ exp ⎢ − ⎜ ⎟ ⎢⎣ ⎝ ⎠ k ⎤ ⎥ ⎥⎦ The mode of this distribution, ModeRR, is written: [2.15] 38 Bio-aggregate-based Building Materials, Chapter 2, pp 27–73 ⎛ k −1 ⎞ ModeRR = ⎜ ⎟ ⎝ k ⎠ 1 k [2.16] The arithmetic mean of the size, or its expected value ERR, is: ⎛ 1⎞ E RR = Γ ⎜1 + ⎟ ⎝ k⎠ [2.17] where Γ(x) denotes the gamma function. The associated arithmetic standard deviation is given by: σ RR = 2 ⎛ 2⎞ 2 Γ ⎜1 + ⎟ − E RR ⎝ k⎠ [2.18] 2.2.7.3.c. Adjustment of the distribution laws The aforementioned two distribution models can easily be adjusted to the area fraction and volume fraction distributions – see Figure 2.23. They encompass each of the distributions, in width or length. Overall, the distributions are better represented by a log-normal law – particularly for the smallest values. These two models can also be adjusted for data obtained by sieving, but with far fewer points (see Figure 2.21). Using a “least-squares” method, the correlation coefficient R2 is mentioned in each of the cases studied in Table 2.3. The values deduced from the parameters of these models can thus be used to give a fairly accurate overall characterization of the PSD under study. The standardized distributions and the superposition of probability density functions of these models are shown in Figure 2.22 in the case of sieving, considering the diagonal of the square opening, i.e. 21/2d, and in Figures 2.24 and 2.25 for the distributions by area fraction and mass fraction respectively. Overall, these different figures show that these two models describe the distributions observed fairly well. The Rosin-Rammler model is better at describing the PSD obtained by sieving of the finer particles, because it takes account of greater skewness toward fine particles. The log-normal law, for its part, is better at describing the distributions obtained by image analysis and corresponds more closely to the modes observed. Characterization of Plant-Based Aggregates, written by Vincent PICANDET Figure 2.23.Comparison of the models adjusted to the cumulative distributions of width and length in area fraction and mass fraction Figure 2.24.Comparison of the models adjusted to the distributions of width and length in area fraction 39 40 Bio-aggregate-based Building Materials, Chapter 2, pp 27–73 Figure 2.25. Comparison of the models adjusted to the distributions of width and length in mass fraction 2.2.7.3.d. Values characteristic of the present case The values of the different parameters characteristic of the distributions are recapped in Table 2.3. Of these parameters selected and to qualify the distributions, in that these distributions are fairly well represented by a log-normal model, the geometric mean Xgm and its associated standard deviation σgm, which correspond respectively to the values of eμ and eσ for a long-normal distribution described in equation [2.9], seem fairly representative of the PSD presented – particularly as regards the description of the granular packing that they are likely to cause. The comparison of these values, juxtaposed in Table 2.3, enables us to fully appreciate the representativeness of the adjustments made. 41 Characterization of Plant-Based Aggregates, written by Vincent PICANDET Sieving Width 1/2 d 2 d (A%) (M%) Log-Normal, see equation [2.9] R2 μ σ ModeLog.N = e(μ−σ²) [mm] Length (A%) (M%) 0.99998 0.99998 0.99963 0.99902 0.99931 0.99916 0.595 0.942 0.701 0.914 2.039 2.197 0.396 0.396 0.480 0.465 0.537 0.539 1.55 2.19 1.60 2.01 5.76 6.74 Rosin-Rammler, see equation [2.13] R2 0.99997 0.99998 0.99342 0.99393 0.99385 0.99241 2.13 3.01 2.38 2.88 λ [mm] k 2.98 2.98 2.62 2.87 D50 1.86 2.63 1.98 2.48 see equation [2.14] [mm] ModeRR see equation [2.16] 1.86 2.63 2.07 2.54 [mm] Arithmetic mean and standard deviation [mm] Eam 1.65 2.33 2.21 2.68 0.65 1.77 1.02 1.15 σam ELog.N 1.96 2.77 2.26 2.78 see equation [2.11] σLog.N 0.81 1.14 1.15 1.37 see equation [2.12] ERR 1.88 2.69 2.11 2.57 see equation [2.17] σRR 0.69 0.98 0.87 0.97 see equation [2.18] Geometric mean and standard deviation [mm] 9.22 10.71 2.35 2.42 7.28 8.60 7.89 9.21 8.69 10.04 4.58 5.00 8.87 10.41 5.13 6.04 8.17 9.50 3.70 4.18 Xgm 1.45 2.06 1.99 2.45 7.58 8.85 e = D50 Log.N σgm 1.81 2.56 2.02 2.50 7.68 9.00 1.71 1.71 1.61 1.55 1.72 1.67 e 1.49 1.49 1.62 1.59 1.71 1.71 μ σ Dimensionless coefficients Cu 1.97 1.97 2.09 2.09 2.29 2.29 Cg 1.03 1.03 0.97 0.98 1.02 0.93 42 Bio-aggregate-based Building Materials, Chapter 2, pp 27–73 Table 2.3. Calculated and adjusted parameters of the PSD exhibited in the case of the hemp shiv under investigation The correspondence of these values and standard deviations obtained is excellent, while the geometric means obtained are in accordance with the distributions obtained by image analysis, and differ slightly for the distributions obtained by sieving. This difference may be due to some of the finer particles being retained in the sieve, particularly in the last and finest sieves, whose meshes are finer than 1.25mm. It is also interesting to note that the geometric standard deviations, for the area fraction or mass fraction weighted variables, are very similar for both the widths and lengths. This confirms the generally homothetic nature of the geometry of the particles. Finally, as regards geotechnical parameters using the dimensionless coefficients Cu and Cg, these PSD (in mass fraction) would be qualified as uniform, and therefore incorrectly graded or too well sorted to be used in a concrete mix. 2.2.8. Conclusions The image analysis method, based solely on 2D observations, can be used to gain a precise measurement of the length of the hemp shiv particles and, to a lesser extent, when these particles retain connected fibers, of their width. Various image analysis algorithms can be used to determine their width, such as the minimum Féret diameter or the measurement of the small diameter of an adjusted ellipse. Many different shape parameters are available, and a large number of particles can be identified to deliver statistically robust results. The near-constancy of the average elongation of the particles for the different surface intervals considered, obtained on the basis of the 2D analysis, suggests that the particles generally have a homothetic shape in 3D, i.e. a quasi-constant average flatness. In addition, according to this basic hypothesis, image analysis allows us access to the average elongation ε and the average flatness Φ of the particles which are likely to cause significant anisotropy in the materials, in that the modes of implementation or casting of the materials including hemp shiv tend to orient these particles. If we also consider this hypothesis, the comparison between sieving and image analysis shows that the square-mesh sieves conventionally used for mineral aggregates separate the hemp shiv particles, elongated and flat, essentially on the basis of their width. Furthermore, given how thin they are in comparison to their width, the hemp-shiv particles pass through the sieves if that width is less than the diagonal of the square holes. Hence, conventional sieving offers an initial approach to the distribution of the width of the particles. Notably, it enables us, if need be, to separate the cortical Characterization of Plant-Based Aggregates, written by Vincent PICANDET 43 fibers remaining after the defibration operations, and also to evaluate the amount of finer particles, or dust depending on the definition adopted, contained in the hemp shiv. Sieving can also be used to supplement the image analysis techniques presented herein. From a practical point of view, therefore, image analysis can be performed very easily with basic office materials, a flatbed scanner (or digital camera) and a modern computer. The software packages, which are freely available online, can be used in their basic, default configurations. Experience shows us, in the case of the hemp shiv under investigation, that a detection threshold for the particles set between 0.08 and 0.8mm2, with no special discrimination between the particles in view of their convexity, yields similar results: with no significant differences in terms of the distributions either of area fraction or of mass fraction. In addition, it is sufficient to sample 4g of material obtained by successive stages of quartering to provide reliable and reproducible results. The distributions obtained by sieving and image analysis, for their width or length, cumulative in terms of area or mass, are uni-modal and can be accurately approximated using a classic log-normal law. The weighted geometric mean and the associated standard deviation therefore constitute the main representative parameters with regard to the granular packing and to the overall properties induced in the materials, to characterize this type of PSD. 44 Bio-aggregate-based Building Materials, Chapter 2, pp 27–73 2.3. Compactness and compressibility Unlike mineral aggregates, usually employed in hydraulic concretes, aggregates made from plant particles and highly deformable and cannot provide the material with a rigid skeleton. The apparent density ρV of loose dry hemp shiv (see Table 2.2 and section 2.1.4), can be significantly increased by the application of confining stress. The application of such stress is sometimes necessary for storage and/or transport. Applied upon implementation or casting, it can help greatly reduce the porosity in the elaborated material and increase its mechanical resistance [NGU 09]. Axial stress applied [MPa] 1.5 1 FHS exp. FHS fitted model 0.5 HS exp. HS fitted model 0 50 150 250 350 450 Equivalent bulk density of dry hemp shiv [kg.m-3] Figure 2.26. Change in the apparent density of loose dry hemp shiv as axial stress is applied in the cylinder A compacting test is performed in a steel cylinder with an internal diameter of 160mm and a height of 320mm. The stress is applied axially by a piston sliding into the cylinder. Compacting is performed by a hydraulic press with a capacity of 500kN. The movement of the piston and the force applied are recorded. The forcedisplacement curve for both types of aggregates is recorded and expressed as Figure 2.26, plotting axial applied stress against equivalent bulk density of dry hemp shiv. For this test, the hemp shiv was humidified so that its water content was 100%, so that the test would be representative of the mechanical behavior of the hemp shiv 45 Characterization of Plant-Based Aggregates, written by Vincent PICANDET at the time when it is cast. This in fact corresponds to its water content at the moment of mixing during the manufacture of blocks destined for prefabrication by controlled compacting in the fresh state of hemp concrete [NGU 09; NGU 10a]. Figure 2.26 demonstrates that the apparent density of loose hemp shiv becomes greater than that of the uncompressed shiv once stress of 0.7MPa is applied. The inter-granular porosity is then probably reduced, but, in view of the deformability of the shiv particles , no information can be gleaned from these tests about the intergranular porosity in the compressed bulk. In order to characterize the compressibility of, hemp shiv in bulk, a basic model with two parameters, σo and k, described by equation [2.19], inspired by models frequently used in the study of compacting of different biomasses [EMA 07], was used. It directly links the stress applied to the hemp shiv, σ, to the equivalent bulk density of dry hemp shiv in its initial state, ρVo, and to that in the stressed state ρV. ⎛ρ -ρ ⎞ σ = σ o ⎜ V Vo ⎟ ⎝ ρ Vo ⎠ k [2.19] This model fairly accurately describes the experimental behavior observed within the range of stresses applied. The values of the parameters σo and k are recapped in Table 2.4. The parameter k, which relates to compressibility, indeed appears greater in the case of fibrous hemp, FHS, because it exhibits greater relative deformation under equal stress. ρVo [kg.m-3] σo [MPa] k (compressibility) [-] HS 112 0,38 1,3 FHS 71 0,13 1,8 Table 2.4. Fitted parameters of the compressibility model to the cases under investigation here 2.4. Water absorption capacity In order to determine the water absorption capacity of the hemp shiv and its absorption kinetics, measurements were taken from 100g samples of completely dry shiv. They were dried beforehand at 60°C until a uniform weight was reached, before being immersed in water for different periods of time: 1, 2, 5, 10, 30 and 60 minutes, and then 24 hours and 48 hours. The mass of the sample at a given time enables us to determine the degree of water absorption, which is expressed as the 46 Bio-aggregate-based Building Materials, Chapter 2, pp 27–73 ratio between the sample’s weight gain at that particular moment and its initial dry weight. The absorption kinetics, measured by sequential weighing after immersion in water, is similar for both aggregates, HS and FHS: very fast. The loose dry aggregates absorb 50% of their maximum water capacity in less than a minute [NGU 10a], which suggests significant competitiveness in terms of water mobilization between the loose aggregates and the lime during casting and setting. As an indication, we note that after 48 hours of immersion, the absorption of the HS aggregates reache 400% and that of the FHS aggregates 350%. Water Absorption [%] 300 200 HS 100 FHS 0 0 10 20 30 Time [minutes] Figure 2.27. Change in water content of hemp shiv over increasing time of immersion The fibers contained in the Fibrous Hemp Shiv are probably less hydrophilic because of their less porous structure. Hence, although the inter-granular porosity is greater in the case of FHS, the kinetics and absorption capacity are less than in the case of HS, which contains very few fibers. Water absorption capacity plays a very important role for the formulation and casting of hemp concrete. This hydrophilic property of the shiv conditions the use of hydraulic binders. Indeed, it means that hemp shiv will be in competition with the binder to mobilize water, thereby altering the hydration of the binder which may need to react with the water. 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