Concrete, from a Centuries-Old Construction Material to Modern Particle-Based Composite Concepts

Abstract

Chapter 7 is focusing on the material of prime engineering relevance, concrete. The major part of the world’s infrastructure is realized in concrete. Moreover, in many high-rise buildings concrete has been employed. The relatively low production costs render possible using high safety factors. As a result, the composition of concrete is governed traditionally by empirical laws. This has been laid down in a large number of practical building codes that confront the structural engineer with selection procedures more than with design requirements on the basis of particulate and hydraulic characteristics of the material. In such procedures, the aggregate’s sieve curve is required to fall within defined, relatively wide boundaries. The selection of the water to cement ratio (w/c) is also part of such procedures. This factor significantly influences the material’s strength and durability capabilities as well as (partly) provides for proper consistence, involving among other things the capacity to readily fill up the mould during compaction by vibration and enrobe the steel reinforcement completely without a loss of homogeneity. As a consequence, the building code includes requirements for the fresh state in terms of specified slump and flow classes.

Economic and technical demands of relatively recent date have led to material developments that required better insight into the engineering mechanisms of material behavior. This has stimulated extensive experimental and computer simulation research efforts. Concrete is a so-called particulate material on different levels of its microstructure. On meso-level, densely packed aggregate particles build up a skeleton of the material. This skeleton provides concrete with its load-bearing capacity in compression, since aggregate grains are generally relatively strong and stiff. On micro-level, the aggregate structure is stabilized by the hydraulic cementitious particulate binder that hardens after mixing with water. Tensile stresses are conventionally taken by steel reinforcement, not discussed herein.

The strength and durability of the matured concrete depends upon packing density on both levels of the microstructure and on the complicated details of the (cement) chemistry involved. Concrete performance is at least partly relying on packing phenomena although not explicitly incorporated into the selection procedures of the building code. However, such phenomena play a significant role in research aiming at the development of new categories of concrete with specifically upgraded performance. As an integral part of present day concrete technology, particle packing therefore forms the hard-core of this chapter. Packing on the two levels of the microstructure together with the chemistry involved in the maturation of the binder leads to a process of pore de-percolation. Durability of the material is depending of course on the resulting complex spatial structure of highly tortuous and partly continuous pores so this issue is also discussed in this chapter. Again, traditionally, durability research is based on experimental approaches, whereby short term tests are employed, requiring extrapolation of the results.

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7.1 Introduction

Concrete is a particulate cementitious material. Mortars and concrete are the fundamental components of much of the construction industry in the world. For daily definition purposes, a concrete is a cementitious material containing aggregates of sizes greater than 5 mm, whereas a mortar is a cementitious material containing aggregates of smaller sizes.¹ The term “mortar” comes from the Latin mortarium, the name given to the trough in which the material was mixed, as in “mortar and pestle”. In fact, the Romans had a rudimentary but highly effective concrete made of a volcanic ash sourced from Pozzuoli on the slopes of Mt. Vesuvius and slaked lime, hence the term Pozzolanic cement. Cement technology goes back even further, to the Ancient Greeks and Mesopotamian civilizations preceding them, but it was the Romans that developed concretes sufficiently to construct concrete-filled walls, known as “opus caementicium”, cementitious terracotta flooring, “opus signinum” and even used their concretes in building the famous Pantheon in Rome, which still stands today, a testament to their skills. However, it was the patenting of Portland cement by Leeds-based Joseph Aspdin in 1824 that led to the development of the reliable, high-strength concretes and mortars that are used throughout the world today. Named Portland cement because of its similarity in appearance to the highly-admired building stone from Portland Bill in Dorset, it is manufactured by heating slurry of limestone or chalk with clay in a kiln, and grinding the resultant clinker to a fine powder and adding gypsum. Development of building structures in concrete in the Netherlands dates back to around 1900; first standards for regulating all aspects of this industry are from 1912. Regularly, these standards were upgraded, whereby the last decade the standards in the European Union were attuned to each other.

The particulate nature of concrete and mortars extends to different levels of the microstructure [18, 44, 51, 53]. Concrete is made up of a hydraulic matrix and (mostly) hard inclusions. Aggregate occupies at least three-quarters of the volume of concrete, so dominantly governs properties in the fresh and in the hardened state, as well as material costs [15, 64]. The aggregate builds up the load-bearing skeleton in concrete engineering structures subjected to compression; most of the tension is taken up by the reinforcement of steel bars and fibres (see Sect. 7.3.4). However, it also reduces global shrinkage deformations and size of the cracks developed due to shrinkage and differential settlements. Fine cement particles and water, together forming the paste, are added to the aggregate to give the fresh, green concrete mixture a proper workability² as well as to allow for the necessary chemical reactions later on for connecting the aggregate particles strongly together (see Sect. 7.2). This fresh concrete mixture is prepared on site or transported to the building side to be poured into the mould. Mostly it is thereupon compacted by vibration to fully fill the mould and enrobe the steel reinforcement bars. Vibration can be avoided when self-compacting concrete is employed (see Sect. 7.6.1).

Concrete is a relatively cheap building material. Hence, design can be crude. High safety factors are applied, leading to material capabilities significantly above expected working stresses. The economic pressure for doing research so that material behavior could be better exploited is as a consequence low. In fact, the conventional design practice is reduced to a selection procedure to fulfill the requirements for the desired construction (see Annex 7A). Empirical relationships form the basis of this procedure, which includes making choices of:

• The relevant exposure class in relation to corrosion risks by the environment;

• The intended life time of the construction;

• Compressive strength class in relation to aforementioned requirements;

• Consistence in terms of slump or flow classes of the fresh concrete in relation to desired workability. Note that higher slump and flow values (see Sect. 7.5) allow easier filling of moulds, though at the expense of concrete strength and durability. Therefore, chemical admixtures often replace part of the water required for adequate consistence.

The result of this procedure leads to a specification that forms the contract between the user and the producer of the concrete. Conformity testing is used to check whether the delivered concrete complies with the specification. Once accepted and used to realize the full-scale structure, testing is still relevant for checking the specification itself. During construction, this can involve testing of workability of the fresh material. Next, specimens are made for checking the grade. Moreover, cores can be drilled from the realized structure to test its ultimate quality.

Conventional concrete technology is based on empiric relationships between composition and behavior. In more recent times it was realized however that better insight would be fundamental for systematic material improvement. Hence, materials science aspect became more apparent in experimental research efforts. This is a time-consuming, laborious and thus expensive approach, however. As a result, research has been undertaken during the past decades to correlate empirical findings with computer simulation data. Concrete is a particulate material on different levels of its structure. So, packing phenomena and porosity are the main issues in such studies, because packing density is directly related to strength, whereas porosity is related to its underlying durability properties.

Aggregate properties encompass grading, shape, surface texture, stiffness, volumetric density and toughness. For the concrete properties, the amount of aggregate is an important parameter. Aggregate is classified according to size as coarse (river gravel or crushed rock) or fine (sand). The sieve curve represents the volume-weighed size distribution of gravel and sand and of the aggregate mixture (the so called grading). The impact of the particle size distribution on packing density has been widely investigated [15]. Optimum and possible ranges of sieve curves have been recommended. Practical concepts have been incorporated in building codes. Considering it from engineering and economic viewpoints, concrete containing a larger amount of aggregate that is more densely packed is cheaper, has lower porosity and shrinkage, and will lead to better performance. Therefore, aggregate mixture design plays an important role in concrete technology of advanced cementitious composites.

Shape of aggregate has been recognized for a long time as an important factor [15, 17, 23, 37]. It has an enormous influence on workability of fresh concrete. Aggregate grains with angular shape (crushed rock versus aggregate of fluvial origin) reduce workability; higher friction between the paste and aggregate require paste content to be increased for maintaining proper workability conditions, at the expense of increased costs. Rougher aggregate surface can impart a better adhesion between aggregate and paste. So, mechanical interlock and increased friction at rougher surfaces can contribute to improving strength, even in flexure. Therefore, high performance concrete also requires careful selection of aggregate [1, 23, 37]. Because of inherent complications in defining shape and in its experimental assessment, an explicit and universal approach is still missing. The influence of particle shape on workability has been implemented in practical construction field by requiring “enough vibration at appropriate workability levels”.

Packing also plays a role on micro-level, where cement blending has become a popular way to generate high performance cementitious materials. Grading has been demonstrated on this level to be of paramount importance for yielding optimum material performance. As an example, reference can be given to successful blending experiments in which a gap-graded inert mineral admixture was combined with Portland cement (PC) [14]. This similarly holds for concrete with finer fillers such as limestone powder, quartz flour, rice husk ash, or other inert fillers [6].

Particle packing and product porosity are closely related through a complicated, highly tortuous structure of partly connected pores after maturation [11, 42, 49]. Thus, this chapter will deal with these phenomena, particularly because of relatively recent advanced cementitious material developments, exploiting gained insight into aggregate and cement grain packing in the fresh state and its consequences for strength and durability. These advanced cementitious composites will be discussed later on. Of course, cementitious materials derive their capabilities from hydraulic properties. So, the next section will pay attention to elementary notions of cement chemistry.

7.2 Elementary Cement Chemistry

The clinker and the non-hydrated Portland cement are formed from limestone at high temperature (1,450 °C) in the cement kiln. In order to achieve the desired setting qualities in the finished product, a quantity (2–8 %, but typically 5 %) of calcium sulfate (usually gypsum or anhydrite) is added to the clinker and the mixture is finely ground to form the finished cement powder. This is achieved in a cement mill. The grinding process is controlled to obtain a powder with a broad particle size distribution, in which typically 15 % of the particles is smaller than 5 μm and 5 % exceeds 45 μm. Typically, the control is based on size distribution measurements by laser diffraction. Mostly, however, the fineness of the ultimate cement is specified by the specific surface area (Blaine number), which is the total particle surface area per unit mass. The rate of initial reaction (up to 24 h) of cement on addition of water is directly proportional to the specific surface area. Typical values are 320 ~ 380 m²/kg for general-purpose cements and 450 ~ 650 m²/kg for “rapid-hardening” cements.

Cement Chemist Notation (CCN) has been introduced to simplify the chemical formulas (Table 7.1). It is a “short-hand” way of writing the formulas of oxides of calcium, silicon and other elements.

Table 7.1 Typical oxides in Portland cement in CCN

The typical composition of Portland cement clinker is presented in Table 7.2. Hence, the four compounds referred to as C₃S, C₂S, C₃A and C₄AF are known as the main phases of Portland cement. The phase composition of particular cements can be quantified through a complex set of calculations known as the Bogue Formula.

Table 7.2 Typical constituents of Portland clinker plus gypsum

The first two phases C₃S and C₂S are crystalline and directly react with water to form calcium silicate hydrate (C₃S₂H₃) and calcium hydroxide (CH) in the paste

$$ 2{\mathrm{C}}_3\mathrm{S}+6\mathrm{H}\to {\mathrm{C}}_3{\mathrm{S}}_2{\mathrm{H}}_3+3\mathrm{CH} $$

(7.1)

$$ 2{\mathrm{C}}_2\mathrm{S}+4\mathrm{H}\to {\mathrm{C}}_3{\mathrm{S}}_2{\mathrm{H}}_3+\mathrm{CH} $$

(7.2)

The cement hydrates are primarily responsible for the strength of the concrete, in addition to the aggregates. CH forms crystals in the pores, thus decreasing porosity, but does not contribute to strength. The first reaction Eq. 7.1 is much faster than Eq. 7.2, so contributes disproportionately to early strength. In fact, hydration products formed in hardened cement pastes are very complicated, because many of these products have nearly the same formula and some are solid-solutions with overlapping formula. Different reactions produce different amounts of heat, so the various cements available on the market have different compositions to fulfill specific requirements, such as low-heat cement for voluminous concrete structures such as a dam.

There are five main types of Portland cements according to ASTM C150-2009 [74] (Table 7.3). The composition may vary within limits.

Table 7.3 Typical composition of basic five Portland cements

Type I is the most common used Portland cement, the so called general purpose cement. It is commonly used for general construction especially when making precast and precast-prestressed concrete that is not to be in contact with soils or ground water. C₃A content shall not exceed 15 %.

Type II is intended to have moderate sulfate resistance with or without moderate heat of hydration. This type is meant for general construction that is exposed to moderate sulfate attack, e.g. when the concrete is in contact with soils and ground water with high sulfur content. This type of cement costs about the same as Type I. In view of its properties, Type II Portland cement is the major general purpose cement in Northern America. C₃A content shall not exceed 8 %.

Type III has relatively high early strength. This cement is similar to Type I, but ground finer, typically to a specific surface 50–80 % higher than Type I. The gypsum level may also be increased somewhat. The increased surface area leads to faster hydration reactions. Thus, the concrete obtains a higher compressive strength in a much shorter time that types I and II, but somewhat at the expense of the long-term strength. It is usually used for precast concrete manufacture, where high 1-day strength of concrete allows fast turnover of molds. It may also be used in emergency construction and repairs and construction of machine bases and gate installations.

Type IV Portland cement is generally known for its low heat of hydration. The percentages of C₂S and C₄AF are relatively high and C₃S and C₃A are relatively low. Maximum content of C₃A is 7 % and the maximum content of C₃S 35 %. This causes the heat given off by the hydration reaction to develop at a slower rate. However, as a consequence the strength of the concrete develops slowly. After 1 or 2 years the strength is higher than the other types after full curing. This cement is used for very large concrete structures, such as dams, which have a low surface to volume ratio.

Note: Portland-pozzolan cements and ground granulated blast furnace slag cement additionally offer cheaper and more reliable alternatives and are widely used in Europe.

Type V is used where sulfate resistance is important. This cement has a very low C₃A content with a maximum of 5 %, which accounts for its high sulfate resistance. Also, C₄AF + 2C₃A content cannot exceed 20 %. This type is used in concrete that is to be exposed to alkali soil and ground water sulfates, which react with C₃A causing disruptive expansion. It is unavailable in many places although its use is common in the western United States and Canada. As with Type IV, Type V Portland cement has mainly been supplanted by the use of ordinary cement with added ground granulated blast furnace slag or tertiary blended cements containing slag and fly ash.

Concrete today is no longer a 1:2:4 issue for the ratio of cement: fine aggregate (sand): coarse aggregate (gravel). Concrete has many chemicals added to it besides the basic ingredients, aggregate, cement and water. The chemicals are e.g. retarders to control the setting time, plasticizers for workability, slump retention admixtures for ready mixed concrete and mineral admixtures for durability, like micro silica, fly ash or slag. Chemical and physical properties of ingredients decide the concrete properties, both in plastic and hardened form.

7.3 Packing Phenomena

7.3.1 Introduction

Proper particle packing is essential for good concrete strength and durability. Thus, this phenomenon has been given serious attention, particularly in recent decades, both experimentally and analytically (e.g. [44]). Extensive information on packing is also available outside concrete technology. Of course, particle packing on meso- as well as micro-level dominates also the characteristics of the pore network structure formed during maturation of the concrete. Pores will reduce strength; however, they also render possible the diffusion of water during drying and give access to harmful components from the outside during application in the matured state. The gradual de-percolation phenomenon in the hardening paste between the aggregate grains is a very complicated phenomenon. Hence, analytical and experimental ways to approach the problem can be extremely sophisticated.

With the rapid development of computer facilities, computer simulation of particle packing has become an economic and reliable alternative. In this chapter we make reference to various approaches employing such computer simulation facilities. This requires considering this way of tackling the problems in more detail, because reliability lies in the very details. Concrete technology has witnessed some sort of autonomous development in this respect. Primarily methods of random sequential addition (RSA) of mostly spherical particles have been developed, thereby making use of random generators. In [59], the authors have indicated how in the mid-seventies of the previous century the development of such an RSA system that was based on a sintering mechanism was started at Delft University of Technology. A continuation was based on mutual sliding along the surfaces of interfering spherical particles when compressed in a container of gradual reducing size. A first version was used to predict wall effects in fiber concrete [48]. A new start in the nineties of the previous century, initiated by fast computer developments, led to the SPACE system used in part of this chapter [44]. SPACE, however, is a discrete element method (DEM). Recently, an even more advanced DEM was developed, based on arbitrary-shaped particles. This so-called HADES system is also used in this chapter [15, 54, 60]. These analogue DEMs are in the frontier of research on virtual cementitious systems in the concrete technology field.

Up till now, in concrete technology, predominantly random sequential addition (RSA) systems were in vogue [3, 53, 54]. Outside of concrete technology, only rarely such systems are being used. Herein, particles are placed from large to small on preconceived Poisson field positions [71]. If this leads to physical violations (overlap), the last generated particle is rejected. The number of rejections increases dramatically at moderate volume fractions, making this generation process very time-consuming. However, a fundamental limitation is that particles are more evenly distributed than in practice [54, 66]. Material properties depending on the dispersion of the particles, so called structure-sensitive properties [53], will, therefore, be poorly represented by RSA systems. In contrast to RSA systems, DEM are based on concurrent algorithms that reflect the particle interferences when they are poured into a container (either with a cement matrix or not). Static DEM [66] are based on locally shifting the interfering particles. Dynamic solutions have all particles moving inside the container. SPACE [44, 58] and HADES [15] belong to this most advanced category. For a critical discussion on RSA versus DEM, also offering the proper references of the aforementioned publications, see [54]. Dispersion of aggregate or cement particles is far more realistic in DEM than in RSA approaches [15, 66], as confirmed by experiments. Hence, structure-sensitive properties can only reliably be simulated by DEM. This also holds for the pore percolation process in both cement and concrete.

In the concrete technology field, the simulated fresh cement structure is hydrated, the principles for which are mostly derived from [28]. This is reasonably straight forward for spherical particles [44, 59], but would be quite complicated in systems with arbitrary shaped binder particles, such as pursued by HADES. An example of a cement paste consisting of spherical particles (pocketed between aggregate grains) and hydrated by aforementioned principles (described in [44, 55]) is shown in Fig. 7.1.

Fig. 7.1

Section of a cube of relative young cement paste with w/c = 0.25, in the horizontal direction pocketed between aggregate grain surfaces, simulated by DEM system HADES. Top and bottom surfaces are periodic, simulating a situation of more remote aggregate grain surfaces in the vertical direction. Cement is supposedly only to be composed of C₃S (alite). Un-hydrated cement nuclei are in red, gel produced by hydration of C₃S in blue, calcium hydroxide CH in green and pores in black

7.3.2 Packing of Aggregate Grains in Concrete

As stipulated, at the heart of concrete making is the design of particle mixtures. Aggregate of fluvial (or sea) origin or crushed rock has to fulfill a specified series of criteria. The hydrated cement in which the aggregate grains will be dispersed provides an alkali environment with high pH value. Aggregate, the mineralogical composition of which is such that the so called alkali-silica reaction may occur, should be avoided. This reaction leads to local expansion that can cause large-scale crack formation and spalling at concrete surfaces. Extensive damage has occurred in concrete practice before this mechanism was identified.

In the framework of this book, the most characteristic feature of concrete–like materials is grading. Therefore, more explicit attention will be paid to this phenomenon. The basic idea of finding an “ideal” aggregate mixture is illustrated in Fig. 7.2. Nevertheless, in normal practice, the locally available aggregate is employed when the actual grading curve falls within the borders indicated in the building code.

Fig. 7.2

Ordered bimodal (left) and tri-modal packed structure of spheres (right) [15]

The largest particles leave voids that should ideally be filled up by the fraction of next smaller particles (Fig. 7.2 left bimodal, right tri-modal mixture). Such a concept already renders this possible, demonstrating the effect of (bimodal) grading on packing density (Fig. 7.3).

Fig. 7.3

Maximum packing density versus composition of bimodal mixtures for different 3D spherical particle size ratios obtained by a RSA packing system (D _s and D _l : sieve sizes of large and small particles, respectively) [15]

Thereupon, the next fraction of even smaller particles fills up the voids left in the packing system, and so on. In the literature of the past century, numerous approaches to this packing problem have been developed (see also Sect. 2.2). The “classical” systems are described in [76]. The Fuller curve is renown, leading to near-optimum density in the case of continuously graded mixtures (so, encompassing all sieve fractions). It is governed by the parabolic curve ${\mathrm{P}}_{\mathrm{d}}=100\sqrt{d/D}$, where P _d is the volume percentage of particles passing through the sieve with opening d and D is the maximum grain size in the mixture. In a more generalized version, the square root is replaced by the ith root, whereby the value of i should be adapted to the field of application and the production method (explicitly involving compaction) [35]. Concrete building codes generally define upper and lower bounds between which the sieve curves of the aggregate should be situated. This is in line with the uncertainty in analytical approaches but is also of economic significance; a local aggregate of which the sieve curve falls inside the delineated area for proper mixtures is cheaper than one composed of separate sieve fractions.

Figure 7.4 shows the packing densities of mixtures of river gravel with different grading, which are determined in a prescribed/standardized way in 8-liters cylinders. Additionally, maximum volume density of mixtures with similar grading has been determined by DEM using the SPACE system that is based on spherical grains. The particle size distributions (PSDs) of mixtures A ~ F cover the 1 ~ 32 mm range. The finenesses of mixtures are increasing from mixture A to mixture F. The PSD of mixture D is corresponding to the Fuller curve. Obviously, correspondence between experiments and simulation is satisfactorily. These tests indeed point out that mixtures close to the so called century-old Fuller PSD (mixtures D and E) have near optimum grading.

Fig. 7.4

Comparison of the packing density at the jammed states of different mixtures of river gravel aggregate and of SPACE-generated spherical aggregates with similar grading characteristics [44]

Shape is an important parameter for particle packing as well as for properties of concrete. Two typical real aggregates are depicted in Fig. 7.5, revealing aggregate of fluvial origin (river gravel) to have rounded edges, whereas crushed rock aggregate has sharp edges. Crushed rock aggregate tends to reduce consistence and packing density compared to aggregate of fluvial origin. Figure 7.6 shows different density distributions of bimodal packing of different type of aggregate. Particle shape directly influences packing densities of mixture in all proportions. This influence is also illustrated by the mono-size particle packing simulation using HADES in Fig. 7.7, where different types of aggregate are simulated from spherical (of fluvial origin) to tetrahedron-like (crushed rock) shapes. The effect of grain shape on optimum packing density is evident. Packing densities are influenced by different shape parameters such as facet number and sphericity in the simulation. “Shape” of particles comprises different aspects such as aspect ratio, angularity, surface roughness and specific surface area and, thus, is hard to define unambiguously. Different approaches have been developed for its assessment [15, 17].

Fig. 7.5

Particles of crushed rock (left) and of river gravel aggregate (right) [15]

Fig. 7.6

Maximum packing density versus composition of bimodal mixtures for different aggregate types (shapes) obtained by dry packing experiments (D _s and D _l : sieve sizes of small and large particles, respectively)

Fig. 7.7

(top) Examples of dense random packing of mono-size particles with shape of (a) tetrahedron, (b) hexahedron, (c) octahedron and (d) sphere, respectively; (bottom) maximum packing density versus (left) facet number and (right) sphericity of 3D particles shown above [15]

Optimum mixture proportioning is basically focusing on achieving maximum density. This will promote strength and durability of the final product. This can also be achieved with discontinuous mixtures (designed on the basis of gap-grading). This could lead to somewhat higher strength than obtained with continuously graded mixtures (containing the same volume fraction of aggregate) [76]. We will see later that in the design of (ultra) high performance concrete (UHPC/HPC) this principle is exploited as to aggregate and binder alike.

But optimization must as well focus on properties of the fresh state. For, the concrete mixture’s consistence should allow proper compaction of the material to fully exploit strength and durability potentialities. Also, fresh mixture’s mobility should be large enough to correctly enrobe steel reinforcement. If not, composite behavior will be endangered as well as reinforcement corrosion promoted. On the other hand, mobility should be limited so that large-scale segregation of aggregate particles by vibration during compaction is prevented. As stated earlier, in the design of mixtures use is preferable made of local aggregates that should just fulfill the requirements of the building code. Optimization of grading would increase material costs; this is only relevant for special purpose concretes.

7.3.3 Packing of Binder Particles in Concrete

Hence, proper packing of aggregate is only an obvious design problem for advanced cementitious composites. Particularly in HPC and UHPC also packing of the binder should be carefully designed. It has been experimentally demonstrated that partial replacement of the Portland cement by an inert mineral admixture (carbon black) could lead to higher strength levels, particularly at early age, provided the carbon black is finer than the cement [14]. Then, closer particle packing causes increased (van der Waals) physical forces that more than compensate for the reduced chemical ones. In [6] it was demonstrated experimentally and by SPACE simulation that partial replacement (up to 25 %) of Portland cement by fine-grained rice husk ash was only efficient when the size ranges of mineral admixtures and of the cement were gap-graded. The significant effect of gap-grading by fine-grained rice husk ash has also favorable effects on pore size distribution (Fig. 7.8) and will therefore also influence durability in a positive way [61]. Also, the use of the pozzolanic mineral admixture silica fume as partial replacement of the Portland cement significantly improves concrete strength and density [2]. So, this gap-graded binder solution combines chemical as well as physical effects (see also Sect. 2.2).

Fig. 7.8

Volume-based pore size distribution functions for plain PC and gap-graded blended PC (BPC) for both the interfacial transition zone (ITZ) and bulk (middle zone: MZ)

Hydration is influenced by particle shape because of the surface-volume ratio effect [7]. So, aggregate and binder particles should be simulated with proper shape characteristics. Conventional hydration models are mostly based on the assumption of spherical cement grains [28, 44, 70]. But it may introduce serious biases as compared to the surface-volume ratio witnessed with real cement grains, as revealed by X-ray micro-tomography (μCT) [13]. This will also affect the microstructure evolution and properties [7]. After a series of shape analyses, [15] proposed two shape alternatives, i.e. flat ellipsoids and a sort of octahedrons, for a more realistic hydration system. Two example simulations with surface area to volume (S-V) curves corresponding to experimental findings are depicted in Fig. 7.9. It proves that these two shapes reflect more realistic S/V curves and, consequently, could better predict hydrated cement paste properties.

Fig. 7.9

(left) S-V-relationships of a group of cement grains by flat ellipsoids (left top), respectively, polyhedra (left bottom). Experimental data are due to [13]. Corresponding simulated structures are displayed at the right [15]

Figure 7.10 may finally demonstrate that a section pattern of a simulated cube of octahedron cement grains shows visual similarity with a section of real cement paste. Hence, for this type of cement this would be the proper shape for simulation of fresh cement grains.

Fig. 7.10

(a) a section of the simulated structure (1,000 octahedron grains in 10 ~ 50 μm range); (b) a 2D section of a real fresh cement structure (Cement-133) obtained by μCT; w/c = 0.35 (Source: http://visiblecement.nist.gov/cement.html. Note that the real particle size range is wider than the one used for the simulation (courtesy NIST))

Experiments have revealed inter-particle forces (van der Waals forces, electrostatic forces, etc.) are crucial for packing of cement grains, especially in the drying state [16, 69]. Figure 7.11 presents experimental data on the packing of different powders under dry as well as in wet conditions [16]. The wet packing method can reduce the inference of inter-particle forces and thus lead to higher packing density. Particle packing is also affected by particle size distribution. Although inter-particle forces can be dramatically reduced by the wet packing method [69], the internal cement structure may still reveal patch formation despite the addition of a superplasticizer [51]. This can only be simulated by DEM-based systems, of course.

Fig. 7.11

Packing densities of different powder types under different conditions (wet or dry) [69]. For details of the packing procedures, see [16]; LF encompasses a wide particle size distribution; CEM I 52.5 and CEM I 42.5 are Portland cements with higher and lower fineness, respectively

7.3.4 Packing of Fibers in Concrete

Mechanical behavior of fiber reinforced concrete depends among other things on pull-out resistance of the “short” fibers and shearing of the fibers over the crack edge. This has been modeled to determine the efficiency factors of the fiber reinforcement. In design, the fiber packing is assumed isotropic uniformly random (IUR). However, in reality it is influenced locally by large aggregate grains and the mold. Eventually, segregation can occur by compaction under vibration. Hence, the resulting packing can be highly anisometric, as illustrated by the X-ray radiography image of a research-size specimen shown in Fig. 7.12 [56]. See also [19].

Fig. 7.12

(top) Location of vertical slices prepared of prismatic steel fiber reinforced concrete (SFRC) specimen (1,000 × 200 × 50 mm) containing 1.72 % by volume of hooked-end fibers. X-ray radiographs were prepared of all slices of which an example is presented at the bottom; this reveals steel fiber dispersion to be highly anisotropic [47] (Courtesy Heron)

A practical assumption introduced by the first author is that the actual fiber dispersion can be considered a summation of a 3D random dispersion (hence, IUR), a planar distribution (referred to as 2D) and a linear one (1D) [45]. This renders possible deriving also the geometric efficiency factors of the fibers in orthogonal directions as a summation of contributions due to 3D, 2D and 1D fiber systems. Estimates of the orthogonal stress transfer capabilities at ultimate {σ(x), σ(y), σ(z)} of SFRC specimens subjected successively in the respective coordinate directions to tensile loading are [25, 63]

$$ \begin{array}{l}\sigma (x)={\sigma}_m\left(1-{V}_f\right)+\eta (x)a{\tau}_f{V}_f\\ {}\sigma (y)={\sigma}_m\left(1-{V}_f\right)+\eta (y)a{\tau}_f{V}_f\\ {}\sigma (z)={\sigma}_m\left(1-{V}_f\right)+\eta (z)a{\tau}_f{V}_f\end{array} $$

(7.3)

in which σ _m stands for the tensile strength of the plain mortar and τ _f is the presumably uniformly distributed shear strength between fiber and cementitious matrix. a and V _f stand for the fiber aspect ratio (slenderness) and volume fraction, respectively. η(x), η(y) and η(z) are the fiber orientation efficiency factors in the respective coordinate directions. The product aV _f τ _f is generally referred to as the fiber factor. Obvious ways to enhance the fiber factor are limited, since too slender fibers (say, a > 100) cause “balling” and increased fiber content is undesirable because of economic demands. Shortly after ultimate loading the matrix contribution is exhausted. Thereupon, a steady decline in post-peak load-bearing capacity is found due to pulling-out of the fibers, as shown in Fig. 7.13. Hence, even low volume fractions of fiber reinforcement lead to a more gradual degradation of the overstrained concrete structure.

Fig. 7.13

Stress–strain curve in direct tension of SFRC specimens (50 × 200 × 1,000 mm, shown at the top of Fig. 6.11 and containing 1.72 % by volume of 30 × 0.4 mm hooked fibers). Observations are due to 150 mm clip gauges spanning the main crack. For further experimental details, see [47] (Courtesy Heron)

So far, the discussion implicitly focused on steel fibers; however a variety of fibers is employed in practice (glass, carbon, wood, rice husks, polypropylene, PVC, etc.). Further, hybrid systems are applied whereby different types of material are combined or fibers of the same material are employed but of different sizes. In the latter case, the micro-fibers control the early stages of crack formation in the pre-peak range, whereas the macro-fibers do so in the post-peak range. Microfibers require modifications in the mixing procedure to prevent “balling” of the fibers [62]. Fibers of natural origin (wood, rice husks, sisal, coconut fibers) require reduction in the alkalinity of the matrix to extend service life. This is possible because use is limited to sheets without steel reinforcement (that would otherwise easily corrode at reduced alkalinity). Glass (even of high quality) also suffers degradation in the high alkaline environment in concrete.

The effect of compaction by vibration and of the flow of the fresh mix into the mould on actual packing characteristics of the fibers has received major interest, because of economic impact. The external layer of SFRC is different due to this so called wall effect. This can have significantly impact on (surface) crack control capacity. The analytical approach is basically similar to the one for the bulk case. Detailed information can be found in the international literature [52].

The design equation resulting from Eq. 7.1 with η(x) = η(y) = η(z) = 1/3 is [46]

$$ {\sigma}_c={\sigma}_m\left(1-{V}_f\right)+\frac{1}{3}a{\tau}_f{V}_f $$

(7.4)

This is the tensile strength of the SFRC material, which is governed by a large number of fibers intersecting the macro-crack that resulted from crack coalescence and crack concentration inside the fracture process zone. At a critical crack opening, the contribution by the matrix will be exhausted and only the load-carrying capacity of the fibers is left. In the pre-ultimate domain crack openings are small and fibers cannot be assumed fully de-bonded, so a reduction factor has to be added for interfacial stress transfer. Additionally, the small cracks in this domain are to different degrees out of plane with the forthcoming macro-crack. This leads to an additional strength reduction factor, β. So, the resulting stress in the pre-ultimate domain is given by

$$ {\sigma}_c={\sigma}_m\left(1-{V}_f\right)+\frac{1}{3}\upbeta a{\tau}_f{V}_f $$

(7.5)

with β < 1.

This renders possible making the transfer to special concretes (HPFRCC and ECC) discussed in Sect. 7.6. High quality cementitious composites are very brittle and thus require fiber reinforcement. The advanced cementitious materials reveal strain hardening. Hence, post peak strength (after exhausting the matrix contribution) should exceed that of the pre-ultimate material strength. This leads according to Eqs. 7.4 and 7.5 to a critical volume fraction V _fcrit given by

$$ {V}_{fcrit}>\frac{\sigma_m}{\frac{1}{3}a{\tau}_f\left(1-\upbeta \right)} $$

(7.6)

Substitution of practical values of the parameters in Eq. 7.6 (a = 75; σ _m   = τ _f ; β = 0.15) [26] demonstrates that significantly higher volume densities are required to provide concrete with strain hardening capacity. Note that in conventional SFRC, V _f is around 1 % by volume.

The development of SFRC basically started after the Second World War. In the early 1980s a new SFRC material was introduced by Lankard that revealed strain hardening, i.e., “slurry infiltrated fiber concrete” (SIFCON) [27]. Fibers were packed in a mold, whereupon the cementitious slurry was poured into it. Up to 20 % by volume of fibers were employed. Of course, the reinforcement structure was strongly an-isometric. Modern engineered cementitious composites (ECC) is a scientific engineering approach to achieving strain hardening in cementitious composites. For a somewhat more elaborate historical description, see [24], presenting also the proper references to the aforementioned articles.

7.3.5 Wall Effect in Particle Packing

A final phenomenon that should be discussed in this connection is the wall effect. Aggregate near the mould and cement close to the aggregate grain surface will reveal size segregation. Both gradient structures have effects on properties [12, 18, 41, 44]. Volume fraction increases in both cases away from the wall. Near the mould, the mixture is therefore relatively rich of cement paste leading to increased shrinkage and possible surface cracking. Near the aggregate surface, we have a similar phenomenon: more inter-particle space and thus larger porosity. However, as a consequence the degree of hydration is higher (see Fig. 7.14). The wall effects are different in different components of the concrete or in evaluation parameters and they are influenced by design factors (e.g. w/c) (see Figs. 7.15 and 7.16). Both effects selectively influence the formation of certain chemical compounds (like large calcium hydroxide CH crystals).

Fig. 7.14

Wall effects in degree of hydration over the ITZ in a model (virtual) concrete after 10-h and 100-h of hydration [18]

Fig. 7.15

Volume fraction of different phases versus distance to aggregate surface (at the left) for model cement at 100-h’s hydration. ITZ’s extent for unhydrated cement seems exceeding the one for porosity [18]

Fig. 7.16

Gradients in volume fraction, V _V (left) and specific surface area, S _V (right) of unhydrated cement grains in fine-grained (497 m²/kg) SPACE-generated model cement for five different values for w/c. It is seen that ITZ’s thickness for volume density and specific surface area increase at higher w/c [15]

This holds for normal concrete. When fine mineral admixtures (e.g., silica fume) are used to replace part of the Portland cement and a proper amount of superplasticizer is added for achieving the required consistence level at low w/c, the fine mineral admixture particles will fill up the open spaces between the cement particles, as depicted by Fig. 7.1. Van der Waals forces will be increased to such a degree that the strength level of the interfacial transition zone (ITZ) can exceed the one in bulk (Fig. 7.17). Note that λ is the mean free spacing, defined as the mean value of uninterrupted surface-to-surface distances between all neighbouring particles. λ ⁻³ is supposedly associated with local (van der Waals-based) bond capacity [44]. The result of this size segregation phenomenon is that the traditionally high crack initiation capacity in ITZs, which provides concrete in compression with a certain degree of toughness, is eliminated. Under high compressive stresses, the material more-or-less explodes in the brittle mode because of the high crack energy release rate. This is the basis for the development of HPC and UHPC. To compensate for the loss of toughness, fibres are added to such materials. This may lead as an example to high performance steel fibre reinforced cementitious composites (HPSFRCC).

Fig. 7.17

Disproportional bond strength increase in the ITZ remains through hydration process. Quite extensive ITZ can be observed (declining at higher w/c) [18]

It is argued in the literature that size segregation might be stimulated by the so called Brazil Nut Effect (BNE) [50] (Fig. 7.18). BNE is a hot item in advanced journals, where the “normal” BNE, i.e., the migration of large particles to the top (so, against the gravity force) of a finer-grained mixture is distinguished from the reversed BNE and the horizontal one; both with respect to the gravitation direction. Research has been conducted showing volumetric density of the migrating particle(s) with respect to that of the rest of the mixture and the size ratio of the two particle systems involved to be leading parameters in whether we can expect dealing with one of these concepts (Fig. 7.19). Some supporting evidence in concrete technology is published in [50], also providing the proper references of the abovementioned contributions to the BNE.

Fig. 7.18

HADES simulation (video snapshots) of size segregation during vibration at container bottom (Brazil Nut Effect) [57]. (Reproduced with permission. Copyright Springer)

Fig. 7.19

Phase space for particle properties. Each symbol represents one experiment. Shaker amplitude is 1:91 cm and frequency 1:67 Hz. Mechanisms were also depending on the area percentage of filling the horizontal disk with the glass beads (segregation was not observed at lower values) [39] (Courtesy Prof. Rehberg)

7.4 Porosimetry

7.4.1 Assessment of 3D Pore Geometry

The particulate nature of concrete extends into the micro-level, where binder particles disperse in the watery environment in the fresh state of the material. Packing details of the binder change with reducing w/c. Such packing details directly influence the structure of the hydrated material and so also the de-percolation process that governs pore space in the matured material. In addition to the aforementioned w/c, the design of the binder can involve partial replacement of the Portland cement (PC) by a mineral admixture. When the latter is finer than the PC, this can give rise to significant physical contributions (due to van der Waals forces) to the strength of the material. So even inert components have been demonstrated effective [14]. The fineness of the PC (expressed in Blaine number, or specific surface area) is another design parameter influencing the packing details of the binder, and thus of the pores in the matured material [44].

Continuous pores are the way harmful substances can reach the interior of the concrete or the reinforcement steel. So, durability relies on limitation of percolated porosity. Porosity is the space resulting after the hydration products are formed. This is obviously depending on cement particle characteristics, such as size distribution and dispersion. What conventionally is experimentally determined by quantitative image analysis (QIA) is porosity and 2D pore size distribution (PoSD) [53, 67]. Nevertheless, the most popular approach is Mercury Intrusion Porosimetry (MIP). This is a 3D method but offers information orders of magnitude away from more realistic approaches [9, 67], as revealed by Fig. 7.20 (see also section “Mercury Penetration Technique” in Chap. 3).

Fig. 7.20

Comparison of MIP and QIA pore size distribution plots for 28 days old cement paste (w/c = 0.4) containing air voids [9, 18] (Reproduced with permission; copyright Elsevier)

The 2D pore size distribution obtained in sections cannot easily be transformed into a 3D PoSD function. This can directly be proven by considering sections of a dispersion of mono-size spherical particles with size D. The section reveals circles of different sizes, the diameter of which is defined by x. The probability density function of x is [20, 45]

$$ f(x)=\frac{x}{D\sqrt{D^2-{x}^2}} $$

(7.7)

So, this is different from the Dirac-like probability density function of the spheres. Even average 2D section size of the spheres ($\overline{x}=\pi D/4$) differs from the 3D particle size. So, with first order stereology (classical way of quantitative image analysis), 3D properties of pores cannot be obtained.

Still, 3D information can be obtained on 2D material sections [18, 49, 54]. Of course, sampling is the hot issue in that case. In Fig. 7.20 the star volume measurement technique is illustrated [18]. A random point x on a pore section at the left is provided by a “star” as sketched at the right. A pike in the star represents the unobstructed length, l _i, in the direction of viewing to the nearest perimeter of the pore. A local estimate of 3D pore volume, v*, is obtained by the given formula in Fig. 7.21. A large series of such observations on random points at pore sections can be used for constructing a cumulative PoSD.

Fig. 7.21

2D schematic drawing of the star of the pores, defined as the volume of the light grey zone v* averaged for all points x in the pore space. The distribution (histogram) of the star volume as x spans the pore space gives insight into the pore size distribution [18]

Another approach is indicated in Fig. 7.22. The digitized image of a field as part of a section reveals pores in black. In this image the mathematical morphology operator “opening” is applied, meaning subsequent erosion and equivalent dilation within a given opening size, which removes areas smaller than this opening size. By doing this operation at increasing opening sizes, an area-based pore size distribution is obtained, which equals the cumulative 3D volume-based pore size distribution in view of isotropy [18].

Fig. 7.22

Opening distribution by structuring elements of increasing sizes gives a sort of size classification. By opening with a square 0.9 μm structuring element, the lower circled region is removed; hence, this local branch area is contributing to the size range < 0.9 μm [18]

A recently published application is presented in Fig. 7.23 [53]. Two different concretes (N is produced with some sodium chloride) are investigated and opening distribution curves and derivative curve (PoSD) are displayed at the bottom.

Fig. 7.23

SEM micrographs of concrete specimens N (a) and D (produced with some sodium chloride, b) and the results due to application of the opening operator on area fraction of porosity (c) and on the derivative of the opening distribution (d). Lower values of porosity and critical pore size (horizontal value at the top of the curve) are found for N (normal) concrete (d) [53] (Reprinted with permission; copyright Elsevier)

7.4.2 Assessment of Pore Topology and Geometry

Analysis of random section is not sufficient to get information on pore percolation, of course. This is however a major feature underlying durability issues of concrete [68]. The most trivial approach is by serial sectioning and 3D reconstruction. This can only be realized economically by computer simulation. Ye [70] developed the necessary algorithms in HYMOSTRUC3D, a sequential random addition system. This has unrealistic cement particle dispersion. Moreover, Ye filled up the pore system by spheres of increasing radii starting from a pre-determined point. This leads to a biased cumulative PoSD [18]. Hence, [8] employed SPACE to more realistically disperse the cement particles in the fresh state, whereupon he implemented the particle system in HYMOSTRUC3D [70]. To reduce computer time, the computer cement was significantly coarser than actual cement with a Blaine value (specific surface area) of 300 m²/kg. This should be kept in mind when extrapolating his findings, of which Fig. 7.24 presents an example for a relatively low w/c (so, HPC). It depicts, at the left, the decline in total porosity in the ITZ (aggregate grain surface at the left). At the right, the steeper decline is shown of the percolated fraction of total porosity [8, 50].

Fig. 7.24

Total porosity (a) and percolated fraction of porosity (b) inside the ITZ. The involved w/c is 0.3, the (ultimate) degree of hydration is 0.748 and cement fineness is 300 m²/kg [8]. Results obtained by serial sectioning and 3D reconstruction (Reprinted with permission; copyright Elsevier)

Of engineering significance is the conclusion that in this low w/c range, so for HPC, percolated porosity seems restricted to the ITZs around aggregate particles. These are (partly) connected (percolated) in the dense random packing state of the aggregate. Hence, also for global pore percolation the designed aggregate skeleton would play a major role. Research into the aggregate parameters influencing ITZ percolation [4] revealed the sieve curve and particle shape exerting such influences. Also the ITZ width is obviously an important factor. This is governed by particulate features of the binder (cement fineness, w/c, grain distribution), so can also be influenced by design. Figure 7.25 [72] shows influences of volume fraction (V _V ) and PSD (Fuller distribution or equal volume fraction (EVF) distribution) on the chloride diffusivity of concrete. Chloride diffusivity is linearly decreased with increasing packing density of aggregate due to the increase of pore tortuosity and reduction in paste content. Concrete with Fuller PSD has a better resistance to chloride diffusion. The newest porosimetry research gives answer to the question whether ITZ percolation (that occurs increasingly at higher packing densities) would be intimately related to chloride diffusion. This was suggested by Fig. 7.24b that only reveals part of the ITZ liable to pore percolation; the latter is a necessary condition for transport though pores in concrete.

Fig. 7.25

Effect of aggregate gradation on chloride diffusivity of concrete [72] (Reproduced with permission; copyright Ice Publ.)

Figure 7.26 is obtained by so called double random multiple-tree structuring (DRMTS), derived from ‘Rapidly exploring Random Tree’ (RRT) algorithms used in robotics [55, 60]. The two ITZ zones at the left and right cannot easily be distinguished from the central zone! Numerous dead-end pores branch off main pore trunks that directly connect external free surfaces of the specimen (e.g. top and bottom). All these connections modify the pore network almost into one pore tree, offering numerous transport routes. This is revealed by Fig. 7.27, which presents the gradient in continuous porosity between two adjacent aggregate grains underlying Fig. 7.26 and the continuous porosity in a specimen with periodic boundaries representing a cement pocket with remote aggregate grain surfaces.

Fig. 7.26

Exploration by DRMTS approach of the pore tree system in virtual hydrated cement paste with w/c = 0.2 at hydration time of 1,440 h (2 months); fresh cement paste was simulated by HADES and casted in 100 μm cubes with two rigid (left and right) and four periodic surfaces. Finally, it was hydrated by CEMHYD [3] system [55] (Reproduced with permission; courtesy Prof. El-Batahgy)

Fig. 7.27

Gradient structures in connected pore volume at two different boundary conditions, of which the green one obtained from Fig. 7.18 [55] (Reproduced with permission; courtesy Prof. El-Batahgy)

Consequence of Fig. 7.27 as compared to Fig. 7.24b is that outside the narrow zone of direct connections between top and bottom surface of the specimens (parallel to the aggregate grain surfaces at the left and right) along pore “trunks”, connections are established between the pores branching far off the main trunks. This will provide a significant contribution to bulk paste and not just to the ITZs. This is supported by only modest effects sorted by ITZ percolation on transport-based phenomena [72].

Generally speaking, this porosimetry research may convincingly demonstrate that particle packing design on both meso-level (aggregate) and on micro-level (cement paste) govern the details of the pore structure in cementitious materials, and, thus, the hydraulic properties of the material. This consequently extends to the durability performance of cementitious composites in engineering structures of the built environment.

7.5 Workability or Consistence

Fresh concrete is also called “Green Concrete”. It is a stage of concrete in which concrete is in the plastic state that allows the material to be molded. The general notion to describe the state of fresh concrete is workability or consistence; this is the ease with which concrete will flow and can be compacted without loosing its homogeneity, or integrity.

Factors affecting concrete workability are:

• Water cement ratio

• Amount and type of Aggregate

• Amount and type of Cement

• Weather conditions

  • Temperature

  • Wind

• Chemical Admixtures

• Sand to Aggregate ratio

The particulate notions concern the aggregate mixture design, the selection of the type of aggregate and the design of the binder. Firstly, increased internal surface area of the aggregate negatively influences consistence. Secondly, blending the cement by a fine mineral admixture like silica fume dramatically increases internal surface area, so requires the use of a water reducing agent or superplasticizer. Hence, chemical admixtures are very important in modern concrete technology.

The consistence following from the material design can be checked in a lot of different ways, of which the slump-flow test is a very popular one. In general, the slump flow test is very similar to the standard ASTM C143/C143M (2010) [73] slump test, whereby the sagging of the top surface of the concrete cone is measured as depicted in Fig. 7.28. For that purpose, Abram’s cone is placed in the center of the slump flow board, either in the normal orientation (large opening down) or inverted (small opening down). It is filled in one lift (no rodding or other consolidation) with concrete, taking care that the sample is well mixed and not segregated in the sampling process. The cone is then raised in 3 ± 1 s to a height of 230 ± 75 mm (9 ± 3 in.), allowing the fluid concrete to flow onto the slump flow board. The slump flow is the diameter of the resulting concrete “patty” obtained from the average of measuring the greatest diameter and diameter perpendicular to this direction. Large differences between the two diameters indicate a non-level surface, which must be corrected. The result is reported to the nearest 10 mm (half-inch). Self Compacting Concrete (SCC) generally has slump flow of 560–760 mm (22–30 in.). DEM can be employed for the simulation of the slump-flow test as an example shown in Fig. 7.28.

Fig. 7.28

Set up (left in mm) and (right) stages in the slump test as simulated by a DEM system (HADES) [57] (Reproduced with permission; copyright Springer)

As stipulated, a very wide range of other tests are being employed for similar purposes (Table 7.4), in some cases also involving reinforcement bars as obstruction. See [21] for a complete survey of such methods all standardized in relevant building codes. Two examples, simulated by computer, are presented in Fig. 7.29 for SCC. Table 7.4 gives a survey of methods standardized for SCC only. The fresh concrete has been modeled using a particle-based computational fluid dynamics (CFD) system. The elements of the simulation use physical properties to control their behavior and can interact with each other and react according to impulses, forces and accelerations. Such approaches make it possible correlating outcomes of the various tests in vogue for concrete.

Table 7.4 List of test methods for workability properties of SCC [21]

Fig. 7.29

Simulations of SCC in a U-shaped test (left) and in an L-Box test (right) by a particle-based computational fluid dynamics method

7.6 Special Concretes

As argued above, the packing design is getting more crucial for modern material developments, such as self-compacting concrete (SCC), HPC and UHPC and engineered cementitious composites (ECC). In the higher performance domain the inclusion of various combinations of short fibers is common. Their packing is also a popular subject of research, because the assumption of isotropic uniform randomness (IUR), as it is generally adopted in design, can be far off reality. Design of the fiber reinforcement thus depends on the effect of such packing details on stress transfer capability over cracks introduced in the material body during maturation and as a result of external loading.

7.6.1 Self Compacting Concrete

Self compacting (also called self-leveling or self-consolidating) concrete is a concrete which compacts itself; there is no further compaction by vibration required. Making concrete structures without vibration has been done in the past, e.g., the placement of concrete under water. Mass concrete, and pile concrete can be successfully placed without vibration. But these concretes are generally of lower strength and it is difficult to obtain consistent quality. Modern application of self-compacting concrete (SCC) is focused on high performance, and thus a better and more reliable and uniform quality [5].

Recognizing the lack of uniformity and complete compaction of concrete by vibration, researchers at the University of Tokyo, Japan, started in late 1980s to develop self compacting concrete, a concrete that did not require vibration to achieve full compaction [29]. The utilization of self compacting concrete started growing rapidly. By the year 2000, SCC had become popular in Japan for prefabricated products and ready mixed concrete [30]. Of course, SCC also spread through Europe and USA.

Self compacting concrete has been described as “the most revolutionary development in concrete construction for several decades”. It has proven to be beneficial from the following points:

• Faster construction

• Improved durability

• Reduction in site manpower

• Better surface finish

• Easier placing

• Safer working environment.

SCC is a relative newcomer to the building industry, when one considers the length of time concrete has been in use. The development of a variety of admixtures has allowed the production of a type of concrete that is more cost effective as it reduces construction time significantly, it does not require vibration, compaction and in many cases finishing either. However, the latter is highly dependent on multiple factors, including mix design. In the framework of this chapter it can therefore be stressed that particle packing is also a major phenomenon in SCC [43].

Mix design principles are similar as for normal concrete: successive particle fractions fill up the openings in the skeleton of larger grains. To do so efficiently, generally gap-graded size fractions are employed. Between the fine sand and the Portland cement, a fine powder fraction is added, together indicated as “powder” in Fig. 7.30. Due to deviating significantly from “normal” concrete, special guidelines for designing and testing SCC have been developed [36, 40, 75, 77].

Fig. 7.30

Scheme of compositions of normal concrete and SCC (after [31]); C cement, W water, S sand, G gravel (Reproduced with permission; copyright JCI)

As with any field that has practical applications, there are multiple theories relative to mix design and it is quite likely that in the field none of these are applied exactly as written. Practice tends to uncover the impracticalities of theories. However, the mix design methods used in the field and in practice are beyond the scope of this book as it would require discussion with many concrete producers, who would likely be reticent to reveal they do not abide to the letter by the design process. There are three basic variables that have been recognized by all experts as affecting the properties of fresh concrete, namely the properties of the mortar, the ratio of coarse aggregate in the whole mix, and the use of super-plasticizing admixtures to improve fluidity and workability. As with traditional concrete, the mortar will have a serious impact on the final result. The ratio of sand in the mortar will determine the degree of workability/consistence as well as segregation resistance. The super-plasticizer’s main role is to improve workability and the quality and quantity used will be the main factors that determine its flowability.

• The rational mix design method [32]

This is one of the simplest methods and was developed in 1995 in Japan, being based on the fact that self compacting concrete is affected by the proportions of the various materials as well as their quality. The fundamental principle is that the aggregate content is fixed – both coarse and fine – so that the flowability can be achieved only through the variation of the superplasticizer ratio.

• Linear optimization mix proportioning [10]

This type of mix design method for self compacting concrete was developed in the UK as a result of research done to judge whether the materials available were suitable for use in SCC. The method is based on the rational mix design method but also incorporates linear optimization to improve on the initial design method. This may appear as a more complex method but the formulas can be entered into a spreadsheet that allows for the use of linear optimization.

• Model for SCC [34]

This is a method that was designed in the field to meet the rigors and specifications of various construction projects. It includes such stages as determining the void content, blocking criteria, mortar proportions and concrete proportions. All these criteria are fulfilled according to the requirements of the project in question, considering strength, durability and so on.

Trial and error methods are often applied in addition to some theory or model on proper mix design, to find optimum basic mixtures for SCC. Further refinement of the SCC composition depends on the project itself, viz. local conditions and requirements. An example of a successful commercial basic mixture for SCC is given in Table 7.5.

Table 7.5 Basic composition of a successful mixture for SCC [www.leyde.com/England/…/BETONAC-SCC.pdf]

7.6.2 High and Ultra High Performance Concrete and Steel Fiber Concrete

Design of the particle mixture is a crucial stage in the development of HPC and UHPC. Large aggregate is excluded (maximum aggregate size is of the order of 1 mm in UHPC), and the finer particle ranges are gap-graded, so packing density is increased, aiming for exclusion of defects in the hardened material. w/c is reduced, in UHPC to 0.2 ~ 0.25, accepting that due to water shortage part of the cement cannot contribute to hydration, but will do so to packing density. High-quality cements are blended by silica fume that is considerably finer than the cement. Furthermore, limestone powder or glass powder is added [65]. Short organic (polypropylene, poly-vinyl alcohol (PVA)) and metal (steel or carbon steel) fibers are added to raise the tensile strength [30]. UHPC like the Lafarge-produced Ductal [33] that has been developed in the past decades has very low porosity and displays very low shrinkage and creep. At densities up to 2,600 kg/m³, compressive strength can be up to 100–250 MPa and a direct tensile strength in the 5–10 MPa range. UHPC is therefore advertised as a material with properties between concrete and steel.

Figure 7.31 presents compressive strengths values of UHPC revealing the influence of the proportion of fine sand in the mixes (specified in detail in [65]). The packing parameters have obvious influence on the compressive strength as also demonstrated by Figs. 7.3 and 7.6. The choice of the type of superplasticizer is additionally shown of paramount importance [65]. The amount of superplasticizer in the fine-grained mixtures provided them with self compacting properties, despite the low value of w/c (0.2). This shows the gradual transfer from one type/class of special concretes into another one. It is also common to classify such mixtures in the category of HPSFRCC, high performance steel fiber reinforced cementitious composites.

Fig. 7.31

28-days compressive strength of concrete (f _c) containing different proportions of sand A (d _max = 0.2 mm) in sand B (d _max = 0.8 mm)

Fiber reinforcement modifies material behavior of normal concrete fundamentally. When normal concrete is subjected to tensile stresses it will crack due to its low tensile strength. Cracking on micro-level generally starts at the surface of the aggregate grains. This may even occur in the so called virgin state, before the material is subjected to any external loading. However, once subjected to such loadings, these interface cracks start coalescing and soon a major crack will cut the specimen in halve. Fibers provide the material with a residual strength after cracking. Residual strength will depend on volume fraction, on fiber geometry, orientation and dispersion (also, on fiber packing!), on the cementitious matrix and on the production conditions (in particular on compaction by vibration). Hence, fiber reinforced concrete is another commodity. Relevant information can be obtained from the vast international literature, encompassing thousands of papers.

7.6.3 Engineered Cementitious Composites

The application of dispersed short fibers has led to the gradual development of HPFRCC and Ultra HPFRCC (UHPFRCC); names adopted by Naaman and Reinhardt since the early 1990s [26]. This also gave rise to the development of engineered cementitious composites (ECC) by Li and co-workers [22], Ductal at Lafarge [33] and by Rossi and co-workers [37]. The latter developed the principle of the multi-scale concept into Multi-Scale Cement Composites (MSCC), which contain three steel fiber geometries totaling more than 10 % by volume aimed for structural use without traditional reinforcement. Specifically, CEMTEC _multiscale has been developed for elements in bending. Modulus of Rupture (MOR) values of around 50 MPa have been recorded in experiments [38].

Basically, ECC can be resorted under the category of (U)HPFRCC. Quite obviously, this also involves ECC with self-compacting capabilities. Self-compacting engineered cementitious composite (ECC) was developed by optimizing the micromechanical parameters, which control composite properties in the hardened state, and the processing parameters that govern the rheological properties in the fresh state. In the development concept of self-compacting ECC, micromechanics is adopted to properly select the matrix, fiber, and interface properties to exhibit strain hardening (generally attributed as pseudo-strain hardening) and multiple cracking behavior in the composites. With the selected ingredient materials, the self-compactability of ECC is then realized by the controlled rheological properties of fresh matrix and the uniform dispersion of fibers. The controlled rheological properties of fresh matrix, including deformability, flow rate, and self-compactability is a result of adopting an optimal combination of a superplasticizer and a viscosity agent. According to the measurements of slump flow and the self-placing test result, the ECC developed is proven to be self-compacting. Flexural tests demonstrate that the mechanical performance of self-compacting ECC is insensitive to the externally applied consolidation during placing.

The same reasoning holds for ECC in general. It is based on ingredients similar to those of FRC or HPFRC and contains only 2 % by volume or less of discontinuous fibers. Micromechanical optimization or composite constituent tailoring leads to desired performance characteristics of ECC. This explicitly involves pseudo-strain hardening resulting from multiple cracking. Structural elements subjected to bending can reveal behavior similar to that of steel (Fig. 7.32). Therefore, the approach is also denoted as “Performance Driven Design Approach” [22].

Fig. 7.32

ECC material in pure bending reveals large deformations due to multiple cracking [22] (Courtesy Prof. Li)

Generalizing, the conclusion can be drawn that the optimum packing of particle ranges and of fibers is an integral element of this performance-driven design approach in the field of concrete technology as far as special concretes are at issue.

7.7 Conclusions

Concrete has a particulate nature on different structural levels. Hence, particle packing is a relevant phenomenon in the fresh as well as in mature states. Nevertheless, design was never strictly based on packing principles; it was merely at the background of building code requirements. A vast literature exists in concrete technology that was for a long time predominantly of a trial and error nature. Concrete is a relatively cheap material, dramatically impeding the necessity of designing with safety factors slightly higher than unity. This had similar repercussions for the nature of research. The development of special concretes in competition with other types of material has somewhat changed the scene. Packing has been re-discovered as the fundamental basis for a particulate material such as concrete. Moreover, with the fast development of computer facilities, numerical simulation offers an economic and efficient approach to concrete research. Equally, an extensive literature on packing phenomena allows for a quick start. Unfortunately, during the past decades the RSA method has been developed for that purpose in concrete technology. This hampers the wide-spread employment of superior DEM. Proper DEM is based on a concurrent algorithm that has direct reflections of particle interaction in normal concrete during production. These are therefore more reliable for assessments of structure-sensitive properties that are primarily of engineering relevance, such as those related to strength and durability. An important property is therefore concrete porosity.

DEM used to simulate and study particle packing problems is reflecting modern material developments in concrete technology. Packing principles, which are underlying particulate materials such as concrete, were never explicitly employed in design. However, the development of the advanced concrete composites during the past several decades was only possible on the basis of insight into packing phenomena. This chapter pays therefore special attention to this more recent history of concrete technology. It shows the transformation of this, centuries-old construction material, to far more sophisticated cementitious composites by employing the scientific packing principles also exploited in other material disciplines.

7.7.1 Definitions, Abbreviations and Symbols

Concrete	Cementitious material containing aggregates of sizes larger than 5 mm (or 4.76 mm)
Consistence	Ease of fresh (green) concrete to flow and be compacted without loosing its homogeneity and integrity (note that there are different methods for its determination)
Mortar	Cementitious material containing aggregates of sizes smaller than 5 mm (or 4.76 mm)
Porosity	For concrete: final space left in between the particles after compaction; note that different pore sizes may influence different characteristics, such as strength and diffusion of water and other compounds
Workability	See consistence
A	Aluminum oxide in CCN notation
ASTM	American Society for Testing Materials
BNE	Brazil nut effect
C	Calcium oxide in CCN notation
CCN	Cement chemist notation
CFD	Computational fluid dynamics
CUR	Civieltechnisch Centrum Uitvoering Research en Regelgeving (Dutch Civil-technical Centre for Execution of Research and Regulation)
DEM	Discrete element method
DRMTS	Double random multiple-tree structuring
ECC	Engineered cementitious composites
EN	European standard
F	Ferric oxide in CCN notation
HADES	HAbanera’s Discrete Element Simulator
HPC	High-performance concrete
HPFRCC	High-performance steel fiber reinforced cementitious composites
ITZ	Interfacial transition zone
IUR	Isotropic uniform randomness
MSCC	Multiscale cementitious composite
MOR	Modulus of rupture
PC	Portland cement
PSD	Particle size distribution
PoSD	Pore size distribution
PVA	Polyvinyl alcohol
QIA	Quantitative image analysis
RRT	Rapidly exploring random tree algorithm
S	Silicon dioxide in CCN notation
$\overline{\mathrm{S}}$	Sulfur trioxide in CCN notation
SCC	Self-compacting concrete
SEM	Scanning electron microscopy
SFRCC	Steel fiber reinforced cementitious composites
SIFCON	Slurry infiltrated fiber concrete
SPACE	Software Package for the Assessment of Compositional Evolution
UHPC	Ultra-high-performance concrete
UHPFRCC	Ultra-high-performance steel fiber reinforced cementitious composites
UHPP	Ultra-high-performance paste
a	Aspect ratio (=slenderness) of fibers
d	Sieve opening
d max	Maximum sieve opening (=size) of sand
D	Maximum grain size in the mixture
D l	Sieve opening (=size) of large mono-size particles
D s	Sieve opening (=size) of small mono-size particles
f c	28-days compressive strength of concrete
l i	Distance from random point in pore to its perimeter (in section)
P d	Volume percentage of particles passing through the sieve with opening d
S	Surface area
V	Volume
V f	Volume fraction of fibers
V fcrit	Critical volume fraction of fibers (leading to strain hardening)
V V	Volume fraction of particles
ν*	Pore volume
w/c	Water/cement ratio
β	Strength reduction factor for fiber reinforcement
η	Geometric efficiency factor of fiber reinforcement
λ	Mean value of uninterrupted surface-to-surface distances between all neighbouring particles
σ c	Tensile strength of fiber reinforced concrete
σ m	Tensile strength of plain concrete
τ f	Friction resistance between fiber and cement matrix

Annex 7A

7.1.1 Selection Procedure to Fulfil Construction Requirements

In normal practice, the design issue is reduced to finding proper economic solutions in the given situation (using e.g. local aggregates) through the use of building codes (see bibliography). It is therefore more a selection procedure than a scientific design operation. First, the procedure involves selection of the relevant exposure class (Table 7.6).

Table 7.6 Main exposure classes

The next selection step regards the intended life time for the construction (Table 7.7).

Table 7.7 Intended working life time

The next selection step concerns the required strength of the cover layer on the main reinforcement. With smaller thicknesses (still exceeding the prescribed minimum for the relevant part of the construction), a higher concrete grade would be required to guarantee proper life time of the construction in the relevant environmental conditions (Table 7.8). A higher concrete grade has negative impact on economy of the full structure; a thicker cover layer does not always require increasing thickness of the structural element.

Table 7.8 Compressive strength classes for conventional concrete

The fresh concrete also sets building code requirements, which specify a range of slump and flow classes for consistence (Table 7.9). Higher slump or flow values as alternatives make filling of the mould easier, but cause a reduction in concrete quality, if done by water addition. Then, not just strength is reduced but also durability is negatively affected. So, once grade is selected, this cannot be the way. Instead of water, chemical admixtures are employed. These, however, increase material costs.

Table 7.9 Target values for consistency of fresh concrete