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Final Thesis Report 2011, SEIT, UNSW@ADFA 1 Particle Packing; An Effective Approach to Optimized Design of Ultra High Strength and Self Compacting Concretes Thomas H. Bleeck 1 University of New South Wales at the Australian Defence Force Academy Optimum mix design depends to a large extent on the density values and grain size distribution of the ingredients. UNSW@ADFA possesses instruments that allow the study of grain size as well as the specific gravity values of concrete constituents. This project develops an algorithm that optimizes the proportions of concrete ingredients based on particle size distributions and mix design grading requirements. I. Introduction eveloping concretes with a reduced cement content is desirable because it is cheaper and less cement produced is more beneficial for the environment due to the high levels of pollution that result. CO2, SO2 and NO2 are byproducts of cement production. The energy required to produce cement compared to aggregate is approximately 1300 and 8 kW h/t respectively, highlighting the desire to reduce the amount of cement required in concrete (Mehta, 1986). Some of the complexity of concrete mix design comes from the contrasting effects the quantities of materials has on the characteristics of the concrete. A simple answer of adjusting the mix design to use less cement and more aggregate may not be feasible as it will result in the concrete not meeting the strength requirements, being as durable, as well as the workability of the mix being compromised. Due to this the inclusion of industrial by products such as fly ash, silica fume and slag is introduced because of the favorable reactions with cement and their effect on bonding with the aggregates. The effect of fly ash, silica fume etc. are related to their shape, size and pozzolanic activity. For example, fly ash normally has spherical shape and smaller size than Portland cement, which can result in a continuous size grading and self-compactness together with the other components. An approach which is being developed is to optimize the particle packing of aggregates and powders in the concrete mix design with the aim to increase the aggregate proportions used by minimizing the number of voids and increasing the density of the concrete. By improving the packing of aggregates the properties of the concrete such as strength, modulus of elasticity, creep and shrinkage can be improved (Neville, 1995). By effectively increasing the amount of aggregate that is used in a mix the goal of reducing the cement content is also reached. (Amirjanov & Sobolev, 2008) The benefits of particle packing have been researched for many years but it has only been in recent years with the aide of computer programs that optimization algorithms have been developed. The need for a user friendly way to calculate the optimal proportions of each concrete ingredient was identified. The algorithm that has been developed using MATLAB and is a Non-Dominated Sorting Genetic Algorithm, NSGA-II (Ray, Singh, Isaacs, & Smith, 2009). The algorithm that has been developed optimizes the proportions of each solid ingredient so that the mix design grading is the closest fit to the ideal grading. The data that is required is the particle size distributions of each ingredient and the grading specifications for the mix design. Much research, both experimental and theoretical has also been done into the important effect aggregate grading has on the properties of the concrete. The features of this algorithm are its ease of use and the ability to add multiple constraints depending on the mix requirements as well as the speed and accuracy of results when compared to other methods, such as trial and error and graphical approach. Examples of the constraints that can be applied are volumetric ranges for individual materials as well as easily adjusting the desired grading of the mix. From this algorithm concrete mix designs can be developed that are able to further investigate the benefits 1 ZEIT4500, Engineering Project and Practical Experience D

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Page 1: 534-2791-1-PB (1)

Final Thesis Report 2011, SEIT, UNSW@ADFA

1

Particle Packing; An Effective Approach to Optimized Design of Ultra

High Strength and Self Compacting Concretes

Thomas H. Bleeck1

University of New South Wales at the Australian Defence Force Academy

Optimum mix design depends to a large extent on the density values and grain size

distribution of the ingredients. UNSW@ADFA possesses instruments that allow the

study of grain size as well as the specific gravity values of concrete constituents. This

project develops an algorithm that optimizes the proportions of concrete ingredients

based on particle size distributions and mix design grading requirements.

I. Introduction

eveloping concretes with a reduced cement content is desirable because it is cheaper and less cement produced is more beneficial for the environment due to the high levels of pollution that result. CO2, SO2 and NO2 are byproducts of cement production. The energy required to produce cement compared to aggregate is approximately 1300 and 8 kW h/t respectively, highlighting the desire to reduce the amount of cement required in concrete (Mehta, 1986). Some of the complexity of concrete mix design comes from the contrasting effects the quantities of materials has on the characteristics of the concrete. A simple answer of adjusting the mix design to use less cement and more aggregate may not be feasible as it will result in the concrete not meeting the strength requirements, being as durable, as well as the workability of the mix being compromised. Due to this the inclusion of industrial by products such as fly ash, silica fume and slag is introduced because of the favorable reactions with cement and their effect on bonding with the aggregates. The effect of fly ash, silica fume etc. are related to their shape, size and pozzolanic activity. For example, fly ash normally has spherical shape and smaller size than Portland cement, which can result in a continuous size grading and self-compactness together with the other components. An approach which is being developed is to optimize the particle packing of aggregates and powders in the concrete mix design with the aim to increase the aggregate proportions used by minimizing the number of voids and increasing the density of the concrete. By improving the packing of aggregates the properties of the concrete such as strength, modulus of elasticity, creep and shrinkage can be improved (Neville, 1995). By effectively increasing the amount of aggregate that is used in a mix the goal of reducing the cement content is also reached. (Amirjanov & Sobolev, 2008) The benefits of particle packing have been researched for many years but it has only been in recent years with the aide of computer programs that optimization algorithms have been developed. The need for a user friendly way to calculate the optimal proportions of each concrete ingredient was identified. The algorithm that has been developed using MATLAB and is a Non-Dominated Sorting Genetic Algorithm, NSGA-II (Ray, Singh, Isaacs, & Smith, 2009). The algorithm that has been developed optimizes the proportions of each solid ingredient so that the mix design grading is the closest fit to the ideal grading. The data that is required is the particle size distributions of each ingredient and the grading specifications for the mix design. Much research, both experimental and theoretical has also been done into the important effect aggregate grading has on the properties of the concrete. The features of this algorithm are its ease of use and the ability to add multiple constraints depending on the mix requirements as well as the speed and accuracy of results when compared to other methods, such as trial and error and graphical approach. Examples of the constraints that can be applied are volumetric ranges for individual materials as well as easily adjusting the desired grading of the mix. From this algorithm concrete mix designs can be developed that are able to further investigate the benefits 1 ZEIT4500, Engineering Project and Practical Experience

D

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of particle packing as well as the impact replacing the cement content with materials such as fly ash or silica fume has on the packing density as well as overall characteristics of the concrete

II. Project Outline

A. Aims • Investigate current research into reducing cement content in concrete mix design. • Develop a user friendly algorithm that easily optimizes the proportions of materials to obtain the desired grading specifications of the mix design.

III. Literary Review The following section looks into the previous work completed on mix designs with a focus on SCC. The review will also give a summary of each of the essential concrete ingredients (aggregate and cement) as well as the main pozzolanic products that are now regularly included in concrete mix designs. The purpose of this is to deliver an understanding into the benefits as well as negative effect that they have on the major characteristics of concrete. It was from this literacy review that the benefits of optimizing the particle packing became apparent. From this the need for an easy to use algorithm was identified as none are readily available for use in mix designs.

Aggregate Aggregates make up to 75% of the overall concrete volume in some cases and both fine and coarse making it a vital component of concrete. Higher percentages of aggregates offer many benefits to the characteristics of a concrete mainly, economical due to its cheap cost when compared to other ingredients such as cement, reducing the creep and shrinkage whilst increasing durability (Neville, 1995, p. 108). Aggregate is a major contributor to the compressive strength of a concrete, due to its previously mentioned high volume percentage. Reducing the number of voids results in more water being able to act as a lubricant between the particles. (Brouwers & Radix, 2005) This results in less water required in the overall mix design and the water/cement ratio being reduced. Lowering the water/cement ratio leads to an increase in the strength and durability of the concrete. (Neville, 1995, p. 174) In lowering the water/cement ratio to increase strength in standard concrete mix designs workability is sacrificed. Using a larger sized aggregate can also reduce the water/cement ratio. This is due to the smaller surface area that is required to be wetted per unit mass. This has been proven with aggregate sizes up to 38.1 mm. (Neville, 1995, p. 174) Nichols found that there is an optimum maximum aggregate size for varying cement contents. The significance of 38.1 mm aggregate was found again with aggregates larger than this having a reduced compressive strength after 28 days. (Nichols e.g 19—as cited by Neville, 1995, p. 175) The surface area of aggregates is important as it dictates the amount of cement that is required to cover its area, therefore a smaller surface area requires less cement and hence less water. (Neville, 1995, p. 158) It is important to ensure that water content is increased with specific surface area of the aggregate, as neglecting this will lower the strength of the concrete. (Newman & Teychenne, 1954) A measure of sphericity can be done to determine the roundness of the particles. Sphericity is the ratio of the particle surface area to its volume. Angular particles with a high ratio of surface area to volume increase the water demand of the mix design in order to not sacrifice workability. Grading of aggregates by sieve analysis allows grading charts to be produced which give a visual on the spread of fine and coarse aggregates. Grading allows the packing of the aggregate to be more efficient as it allows specifications to be set. However these limits must consider the aggregate that is available locally and as narrow limits increase so does the overall cost. There are several factors that must be considered when attempting to define an optimum gradation. However it must be noted that the easier it is to pack particles of different sizes together also results in the smaller particles requiring less force to be dislodged. This can cause the concrete to segregate when hardened. (Neville, 1995, p. 156) Economically it is desirable that aggregates inhabit the maximum volume possible as well as the higher strength that can be gained with a higher density of aggregates. (Neville, 1995, p. 157) The trade off in mixing with the maximum density is that the workability is sacrificed. Ideal grading curves have been suggested by numerous researches and will be discussed in detail later. Traditional grading curves are effective in setting gradings for traditional concrete mixes where particles smaller than 150µm are not required to be as accurately measured as

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SCC. For particles with sizes less than 150µm the relationship between the mix design and specific surface is not clear, as these particles do not require wetting in the same way as larger particles. (Glanville, Collins, & Matthews, 1947) Overall the grading of aggregates is vital due to its effect on the workability of the concrete, impact on water/cement ratio, controlling the segregation as well as improving the strength, shrinkage and durability of hardened concrete. (Neville, 1995, p. 163) The bulk density of the particles also affects and is in turn affected by the packing. Bulk density is defined as the mass of aggregate which will fill a container of a given unit volume. The bulk density can be an indicator of the level of packing that is achieved in a given aggregate. An aggregate with a range of different shapes and sizes achieves a denser packing than an aggregate with a single sized particle. Adding smaller particles to fill the voids created when larger particles pack together increases the bulk density of an aggregate. (Neville, 1995, p. 127) A high bulk density is aimed for in this project as it results in fewer voids and hence requires less cement to fill the voids. (Neville, 1995, p. 128) (Lay, 2003) The voids ratio of the aggregates when in saturated and surface dry condition can be calculated in the following equation: 𝑣𝑜𝑖𝑑𝑠  𝑟𝑎𝑡𝑖𝑜 = 1 − !"#$  !"#$%&'

!"#$%&'  !"#  !"#$%&%"#×!"#$  !"##  !"  !"#$% (Neville, 1995, p. 128) (1)

Fineness of cement: The fineness of cement is proportional to the total surface area of the cement particles. The specific surface area is of major importance that affects the rate and extent of hydration, which starts at the surface of cement particles. So the total surface area of the cement represents the area available for hydration. Hydration of cement does not fully penetrate all cement particles especially when those particles are too large (references). Therefore, a high amount of large cement particles would restrict the full process of hydration which then reduces the strength development of the concrete. (Neville, 1995, p. 21). Fly Ash: The first benefit of fly ash as is the case with aggregates and alternate cementitious materials such as silica fume and slag is that energy and resources are saved compared to cement. The benefits of spherical particles were discussed in the packing of coarse aggregates and the principles are the same with fly ash and any other particle added to a concrete mix. Fly ash particles have a natural spherical make up and a very high fineness, these properties result in an improvement in workability in fresh concrete mixes containing fly ash. Fly ash generally has a diameter between less than 1µm and 100µm and the specific surface is usually 250-600 m2/kg, as determined using Blaine method. In contrast to aggregates the relatively high specific surface area is a desirable property as it results in fly ash being readily available for reaction with calcium hydroxide. (Neville, 1995, p. 85) The addition of fly ash to concrete results in tighter packing, with the fly ash particles fitting in between cement particles and increase in overall strength. The improved packing also reduces the permeability of the concrete. (Neville, 1995, p. 651) The pozzolanic reaction that occurs in fly ash is slow compared to the hydration of cement, and this means that a concrete containing fly ash has a lower strength initially compared to traditional cement only concrete. (Neville, 1995) Fly ash reduces the bleeding capacity and water demand of the concrete due to the spherical shape of the particles. (Neville, 1995, p. 654) The reduction of water demand incrases with the addition of fly ash up to 20% of cemenitious volume. (Helmuth, 1987)

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Figure 1: Fly Ash (United States Department of Transportation - Federal Highway Administration)

Silica Fume The specific gravity of silica fume is generally 2.20, compared to Portland cement of 3.15. Silica particles are extremely small ranging between 0.03 and 0.3µm. Specific surface cannot be determined using Blaine apparatus. Nitrogen adsorption indicates a specific surface of 15 000 -20 000 m2/kg, compared to ordinary Portland cement of 200 – 500 m2/kg. Low bulk density 200 to 300 kg/m3 (Neville, 1995, p. 87) The addition of silica fume to concrete mixes improves the durability and increases the strength as well as reducing the cost by reducing the cement content required. The high level of silica doxide improves the pozzilanic reactions. (Bubshai, Tahir, & Jannadi, 1996). In using silica fume as a partial replacement for cement, it reduces the initial strength (1-3 days) but improves the ultimate strength. Ground Granulated Blast Furnace Slag Chemically, slag is a mixture of lime, silica and alumina, the same oxides that make up cement but in different proportions. Slag can be used as a raw material with limestone for manufacture of Portland cement in the dry process, which is economically advantageous. (Neville, 1995, p. 79) It can also be used on its own with the presence of an alkali activator as a cementitious material as slag is a hydraulic material. (Douglas, 1992)

Figure 2: Particle Size Distribution of Cement, Ground Granulated Blast Furnace Slag, Silica Fume and Fly Ash using Mastersizer 2000.

Figure 2 shows the Particle Size Distributions of Portland Cement, Ground Granulated Blast Furnace Slag, Fly Ash and Silica Fume was determined using laser diffraction technology. Previously it was very difficult to find the PSD of such materials due to the small particle sizes, as seen above 90% are smaller than 100µm. With this new laser diffraction equipment it will be possible to further investigate the effect that increasing the content of fine particles has on improving the concrete properties and further reducing the cement content required. Self-compacting concrete Self-compacting concrete is designed to optimize the packing of aggregates so that the volume of cement and powders can be reduced. This results in a highly workable, medium strength and low cost concrete. By optimizing the packing, a higher percentage of finer sands and industrial by products such as fly ash and slag can be used. Fly ash and slag have been proven to improve the workability and durability of concrete. (Su & Maio, 2003) One of the main aims in achieving the densest packing possible is to reduce the cement content required to fill the voids. Self-compacting concrete was initially developed in Japan in 1988 by Okamura (Okamura, 1997)to achieve durable concrete structures. SCC is more durable because it can be compacted into all areas of buildings framework under its own weight without the need of external vibration. The concrete must also be able to resist segregation when flowing through the zones congested with reinforcing steel bars. To

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achieve the required flowability of the concrete with reduced water/cement level, a super-plasticiser (SP) is needed. The method developed by Okamura in 1986 was pioneering in the development of SCC, however they have now been further developed. The empirical method employed a set fine to coarse aggregate ratio with the water to binder and super-plasticiser amounts adjusted to achieve the required workability. The method was based on set proportioning of coarse and fine aggregate and then the workability required achieved by adjusting the super-plasticiser and water/cement ratios. Whilst this method achieves SCC properties, it was overdesigned for strength and thus had high cement content. This high paste content increases the cost of concrete as well as results in more shrinkage. Simultaneously adjusting the water to binder ratio and the SP dosage makes it difficult to determine the required values respectively. Okamura and Ouchi’s method known as the ‘Japanese Method’ was further developed by Edamatsu et al. (2003), by adding rules regarding the volume of coarse and fine aggregate used as well as the water to powder ratio and SP amount. Okamura and Ozawa, SCC method was designed to be implemented easily by ready mix concrete plants. The method involves the coarse aggregate content being fixed at 50% of the solid volume, Fine aggregate fixed at 40% of the mortar volume, water to powder ratio is assumed as 0.9 to 1.9, depending on the properties of the powder and the super-plasticiser and final water to powder ratio are determined so as to ensure self compactability. (Okamura & Ouchi, 2003)This method results in a higher strength than designed for due to the high cement volume. The ‘Chinese Method’ was developed by Su et al. in 2001 and was further developed by Sue and Miao in 2003. This took an alternate approach to the ‘Japanese method’ with the packing of aggregates being determined first and then the voids filled with paste for the mix design. The aggregate content was determined by the packing factor (PF). Research by Su et al (Su, Hsu, & Chai, 2001) and Su and Miao (Su & Maio, 2003) developed a new mix design for SCC known as the ‘Chinese Method’. This method varied from the original Japanese method of Okamura and Ozawa, in that it starts with the packing of aggregates and does not have a set percentage of aggregates to be used. The benefits of this method are both cost saving and improving the overall packing of the concrete. The method is favorable because the high amount of aggregate used improves the strength, stiffness, permeability, creep and drying shrinkage. The packing factor of aggregates is the vital element of this method. Packing factor is defined as: 𝑃𝐹 = !""!#$%&  !"#$%&'  !"  !""#$"!%$  !"#$%  !"#$%!&'"(

!""!#$%&  !"#$%&'  !"  !!!"#  !""#$"!%$ (1)

The procedures of measuring the bulk densities before and after compaction are defined in ASTM C29, with the compacted bulk density measured by the rodding procedure and the loose bulk density by the shovel procedure. A higher PF means a greater amount of aggregate used, reducing the binders, which reduces the workability and strength, whereas a smaller PF results in more binders used and therefore more drying shrinkage and higher cost. As shown in the graphs below, all of the PF tested met the required workability tests for SCC and the resultant strength was higher than designed for in all cases at 28 days. The high cement content in the ‘Chinese’ mix design was addressed in the second method published in 2003 (Su & Maio, 2003). Despite the mixes being overdesigned in terms of strength, the cement content used is significantly less than in conventional concrete mixes. The advantage of this method over the ‘Japanese method’ is that the cement volume is reduced, which saves on cost as well as improving the technical performance of the concrete while applying the highest possible aggregate percentage. The increase in aggregate improves the strength, stiffness and impermeability, and reduces shrinkage. The better packing of the aggregate is achieved by using a higher percentage of sand and less gravel, reducing the number of voids. The disadvantage in the increased aggregate percentage is the reduced paste available which results in less fluidity. The authors of the ‘Chinese method’ did not explain how they arrived at the value of the optimum sand to aggregate ratio or packing factor. An improvement on determining the cement content can be made the ‘Chinese method’. The equation used is as follows:

(2) With C being the cement content (kg/m3 ) f’c being the compressive strength of concrete at 28 days (MPa) and x is the compressive strength provided by each kg of cement, in MPa. The values given for ‘x’ to determine the compressive strength of each kg of cement ranges from 0.11-0.14 MPa which results in 120kg difference for each extreme for a 60MPa concrete.

aggregate, PF is the packing factor, the ratio of mass ofaggregates in the mixture to that of loosely packed stateaccording to ASTM C-29, 1.14–1.22 for FC [14], VAf=VAis the volume ratio of fine aggregate to total aggregate.

Step 2: Calculation of cement content

Cement is regarded as the primary provider of thecompressive strength of concrete. However, concretewith too much cement is neither economical nor dura-ble. The proposed method suggests using minimum ce-ment content for strength requirement. If a compressivestrength of x MPa at 28 d is expected for each kilogramof cement used, the cement content will be

C ! f 0c

x"3#

where C is the cement content (kg/m3), f 0c is the specified

compressive strength of concrete at 28 days (MPa), x isthe compressive strength provided by each kilogram ofcement, in MPa, 0.11–0.14 MPa (15–20 psi) for FC usedin Taiwan [14].

Step 3: Selection of water/cement ratio

The ‘‘required average compressive strength f 0cr’’ must

first be determined from the specified strength f 0c and

variation on concrete strength during the production inthe ready-mixed concrete plant. This can be done ac-cording to the method suggested by ACI 319-95 [15] asfollows:

f 0cr ! max"f 0

c $ 1:34S; f 0c $ 2:33S % 35# "MPa# "4#

where S is the standard deviation (MPa).The relationship between f 0

cr at 28 d and water/cementratio for FC was obtained from previous experiments[16] and is presented on Fig. 2; this relationship is similarto that proposed by ACI 211.1 [9]. However, the selectedwater/cement ratio must satisfy both the strength andthe durability criteria. Due to the lack of data on the

durability of FC, the values can be taken from ACI211.1 [9] in this study.

Step 4: Calculation of mixing water content required bycement

The content of mixing water required by cement canthen be obtained using

Wc !Wc

C

! "

C "5#

where Wc is the content of mixing water required bycement (kg/m3), Wc=C is the water to cement ratio byweight.

Step 5: Calculation of FA and GGBS contents

To obtain the required workability and segregationresistance, FA and GGBS are used to increase the bin-der content. Then the paste volume of Pozzolanic ma-terials (Vpp) can be calculated as follows:

Vpp ! 1% Aco

"1000GAc#% Afo

"1000GAf#% C"1000Gc#

% Wc

"1000Gw#% Va % n

"C $ P #"1000Gsp#

"6#

where Vpp is the volume of FA and GGBS paste, GAc isthe specific gravity of coarse aggregates, GAf is the spe-cific gravity of fine aggregates, Gc is the specific gravityof cement, Gw is the specific gravity of water, Gsp is thespecific gravity of superplasticizer (liquid), Va is the aircontent (%), P is the amount of FA and GGBS (kg/m3),n is the dosage of SP based on binder content (%).

In order to get the FA and GGBS paste with water/binder ratio of Wf=F and Ws=S as flowable as the cementpaste, flow tests (ASTM C230) should be carried out. Ifthe total amount of pozzolan materials (FA and GGBS)in FC is P, where FA occupies A% and GGBS occupies1% A%, the adequate ratio of these two materials can beestablished through testing or according to previousexperience [16].

Vpp ! 1

!

$ Wf

F

"

A%P

"1000Gf#$ 1

!

$ Ws

S

"

& "1% A%# P"1000Gs#

"7#

where Gf , Gs, Gc, Wf=F , Ws=S and A% can be obtainedfrom tests.

Let Eq. (6) equals Eq. (7), the total amount of Po-zzolanic materials P in FC can be obtained. Hence, FAcontent (F) and GGBS content (S) can be calculated asfollows:

F ! A%P "8#

S ! "1% A%#P "9#Fig. 2. Relation between compressive strength and water to cementratio.

N. Su, B. Miao / Cement & Concrete Composites 25 (2003) 215–222 217

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Figure 2 shows the optimum ratio of sand to coarse aggregate for achieving the smallest void fraction for the three mixtures used. The effect the finer particles (0-1mm) have on decreasing the void fraction is evident (Brouwers & Radix, 2005).

Figure 3 (Brouwers & Radix, 2005)

Brouwers and Radix build on the ‘Chinese method’ and attempt to achieve an optimal packing of aggregates by deriving a relationship between packing and specific surface area of each powder and the water required for flowability and slumps. For a majority of concrete mix designs a grading curve is selected for the aggregates. However for SCC which are designed with a significantly higher proportion of fine particles the traditional grading curves are not applicable as they typically have a minimum particle size of 150µm. Andreasen and Andersen (Andreasen & Andersen, 1930) developed an approach to determining a continuous particle size distribution with the densest packing. Funk and Dinger (Funk & Dinger, 1994) to further optimize the PSD for particles of sizes smaller than 500µm modified this model, referred to as modified Andreasen and Andersen model (Brouwers & Radix, 2005). Brouwers and Radix demonstrated that the ‘Chinese method’ closely follows the modified A&A model. By achieving a more efficient and dense packing it allows more water to be available to act as lubricant for the solids, resulting better fluidity. This is achieved by adjusting the amounts of 3 different types of sand. In normal concrete, design codes stipulate a continuous grading in order to achieve a tight packing, however Fuller S-curves are not suited to SCC due to the high volume of fine particles below 500µm in the case of SCC. If a Fuller grading curve is applied to SCC with fine particles the concrete becomes less workable and poor in cement content. Andreasen and Andersen derived an equation (Equation 3) to model the optimum packing as follows (Brouwers & Radix, 2005):

(3) With q being a parameter between 0 and 1 adjusted with the particle size to gain the optimal packing. (Andreasen & Andersen, 1930) found that optimal packing occurred when q = 0.37, a Fuller curve is modeled with q =0.5. P is the fraction that can pass the sieve with opening D, and Dmax is the maximum particle size of the mix. The more powders in the mix the smaller is q. Funk and Dinger developed the following modified A&A equation to take into account the minimum particle size, as opposed to 0 being the minimum in the standard A&A curve.

(4)

is reduced by a constant factor, about 75–80%. In Section 8this reduction is compared to the compaction of powderswhen they are combined with water to form paste.

Furthermore, Fig. 3 reveals that all sand/gravel mixesattain a minimum void fraction with sand/gravel (mass) ratiosof 40/60 to 60/40 (both in loose and compacted condition).The coarser the sand, the higher the most favourable sandcontent (as a smaller volume of the concrete will thencomprise paste). Fine sand (0–1mm) attains aminimum voidfraction when its content is 40%, medium sand (0–2 mm) at50%, and coarse sand (0–4 mm) at 60% in combination withgravel. In loose condition this minimum void fractionamounts to 30%, after compaction to about 23%. In theexperimental part later-on attention will be paid to uSCC thatcan be achieved in fresh SCC. The experiments with sand andgravel reported here give an indication which contents willyield a minimum void fraction.

The mass and volume of the aggregate per m3 of concretenow reads:

Va !Ma

qa; Va ! 1" uSCC

! "

m3 #3$

The second step is the computation of the cement content.The required cement content follows from the desiredcompressive strength. The Chinese Method assumes a linearrelation between the cement content and compressivestrength ( f Vck). Accordingly, the mass and volume of cementfollow from:

Mc !fckVx;Vc !

Mc

qc#4$

The value of x appeared to range from 0.11 to 0.14 N/mm2 per kg OPC/m3 concrete [7]. Later, during theexperiments, the value of x will also be determined for

the slag blended cement used here (Table 1). As Su et al.[6] and Su and Miao [7] used a mix of OPC (200 kg/m3

concrete) and granulated slag, slag blended cement isemployed here.

The quantity of water for the cement and the filler (thepowders, Fig. 1) is based on the flowability requirement.The water needed for these powders follows from flowspread tests with the Haegermann flow cone, executedanalogously to Domone and Wen [13]. Ordinary tap water isused as the mixing water for the present research. For thevarious water/powder ratios the slump (d) and relativeslump (Cp) are computed via:

d ! d1 % d2

2;Cp !

d

d0

# $2

" 1 #5$

In Fig. 4 the relative slump Cp is set out against thewater/powder mass ratio (Mw/Mp) for cement, fly ash andlimestone powder. A straight line is fitted and theintersection with the y-axis (Cp=0) yields the watercontent whereby no slump takes place, i.e. the watercontent that can be retained by the powder. From Fig. 4for instance follows that for cement flow is possible ifMw/Mc>0.33.

Flowing requires Cp>0, and when powders are com-bined, and the water/powder ratio such that Cp of eachpowder is equal. The mass and volume of water per m3 ofconcrete thus becomes:

Mw ! acCp % bc! "

Mc % afCp % bf! "

Mf ; Vw

! Mw=qw; Vf ! Mf=qf #6$

The coefficients ac, bc, etc., follow from the fitted lines inFig. 4, which are crossing each other. This is a consequenceof the fact that the relative slump is related to the mass ratio

0.15

0.20

0.25

0.30

0.35

0.40

0.45

0 10 20 30 40 50 60 70 80 90 100

Percentage sand / coarse aggregate

Void

frac

tion

Mixture sand 0-1 mm before compactionMixture sand 0-1 mm after compactionMixture sand 0-2 mm before compactionMixture sand 0-2 mm after compactionMixture sand 0-4 mm before compactionMixture sand 0-4 mm after compaction

Fig. 3. Void fraction of sand (3 types)/gravel mixes, before and after compaction at various sand contents (m/m) in sand/gravel mixes.

H.J.H. Brouwers, H.J. Radix / Cement and Concrete Research 35 (2005) 2116–2136 2119

ether polymer with lateral chains. The dry matter is related tothe total amount of powder by:

MSP ! n Mc "Mf# $ ! n qcVc " qfVf# $ #9$

Practical values of n are 0.4–1.7%. The amount of fillerfollows by combining Eqs. (6)–(9):

Vf !/SCCm3 % Vair % 1" acCp " bc " dmSPInI

qcqSP

! "

1" afCp " bf " dmSPInIqfqSP

#10$

The filler volume decreases with the increasing relative slump(Cp). The water/cement ratio follows from:

w=c ! Mw

Mc! qwVw

qcVc

!qw acCp " bc

# $

Vc " qw afCp " bf# $

Vf

qcVc#11$

With increasing Cp the w/c increases. Also increasing fillervolume augments the w/c, as this volume also requires water,whereas the cement content remains the same. According toDutch Standards, however, the w/c is limited to a maximumvalue, prescribed by the prevailing Durability Class (Table 2a).In the Japanese Method, Cp!0 is approached as much aspossible, in what follows (Sections 4 and 5), for the ChineseMethod Cp ranges from 1 to 2.

Now, the volumes of aggregate, cement, air, super-plasticizer, filler and water in the concrete are known. Theamount of mixing water follows from Eq. (6), wherebyaccount is taken from the water (free moist) present inaggregate and superplasticizer:

Mw; t ! acCp " bc# $

Mc " afCp " bf# $

Mf

% 1% dmsp

# $

IMSP % 1% dma# $IMa #12$

In this section, masses and volumes of the concreteingredients are determined. The solids, aggregate andpowders, consist of gravel, sand, filler and cement. In thenext section the PSD of each component and the ideal PSDand packing of the entire solids mix will be analysed.

3. Packing theory

The Japanese and Chinese Methods do not pay attentionto the PSD of the aggregates. It is however known that theviscosity of slurry becomes minimal (at constant water

content) when the solids have tighter packing [10]. Whenparticles are better packed (less voids), more water isavailable to act as a lubricant between the particles. In thissection the effect of grading and packing on workability isaddressed.

For ‘‘normal concrete’’, most design codes requirecontinuous grading to achieve tight packing. Continuousgrading curves range from 250 Am to a maximum particlesize (Fuller curve). For modern concretes, such as HighStrength Concrete and SCC this Fuller curve is less suited.This curve is applicable to materials with a particle sizelarger than 500 Am. Applying this grading curve to materialswith fine constituents results in mixes that are poor incement and that are less workable. The Dutch StandardNEN 5950 [14] therefore requires a minimum content offine materials (<250 Am) in normal concrete (Table 2b). Asthe content and PSD of fine materials (powder) cannot bedetermined properly with the Fuller curve, it is less suitedfor SCC as a large part of the solids consist of powder.

Actually, the packing theory of Fuller and Thompson[15] represents a special case within the more generalpacking equations derived by Andreasen and Andersen [9].According to their theory, optimum packing can be achievedwhen the cumulative PSD obeys the following equation:

P D# $ ! D

Dmax

% &q

#13$

P is the fraction that can pass the sieve with opening D,Dmax is maximum particle size of the mix. The parameter qhas a value between 0 and 1, and Andreasen and Andersen[9] found that optimum packing is obtained when q!0.37.

The grading by Fuller is obtained when q =0.5. Thevariable q renders the A&A model suitable for particle sizessmaller than 500 Am. In general, the more powders (<250Am) in a mix, the smaller the q that best characterizes thePSD of the mix [11]. To validate the hypothesis of tightpacking and the application of the A&A model, the PSD ofthe Chinese Method is analysed. In Fig. 6 the PSD of theaggregates are graphically depicted, based on the sievingdata given by Su et al. [6] and Su and Miao [7]. As no sieveinformation is provided for the powders, it is not possible todepict the PSD down to 1 Am. But the PSD of the entiresolid mix is corrected for this powder content, which isknown. In Fig. 6 also the grading curves of Fuller and A&A(with q =0.3) are depicted.

Fig. 6 reveals that the Chinese Method seems to followthe grading curve of the A&A theory with q =0.3. With the

Table 2a

Maximum w/c ratio for each Durability Class (NEN 5950 [14])

Durability Class 1 2 3 4 5a 5b 5c 5d

w/c 0.65 0.55 0.45 0.45 0.55 0.50 0.45 0.45

w/c with air

entrainment

0.55 0.55

Table 2b

Minimum amount of fine material per m3 of concrete (NEN 5950 [14])

Largest grain size

(Dmax) [mm]

Minimum vol. fraction fine

material (<250 Am) in concrete

8 0.140

16 0.125

31.5 0.115

H.J.H. Brouwers, H.J. Radix / Cement and Concrete Research 35 (2005) 2116–2136 2121

available ingredients in The Netherlands and their PSD’s(Fig. 2), it will be difficult to compose a mix that canapproach this A&A curve to the same extent. Fig. 6confirms that the grading curve of A&A better accountsfor powders than the grading curve of Fuller. From thecurves in Fig. 6 it furthermore follows that about 20% of theparticles are finer than 75 Am, whereas, according to Fuller,only 5.5% are smaller than 75 Am. As the A&A modelaccounts for powders (<250 Am) better, it is better suited fordesigning SCC. A continuous grading of all solids(aggregate and powders) will result in a better workabilityand stability of the concrete mix.

The A&A model prescribes a grading down to a particlediameter of zero. In practice, there will be a minimumdiameter in the mix. Accordingly, a modified version of the

model is applied that accounts for the minimum particle sizein the mix (Funk and Dinger [10]). This modified PSD(cumulative finer fraction) reads:

P D! " # Dq $ Dqmin

Dqmax $ D

qmin

!14"

whereby Dmin is the minimum particle size in the mix. Formany years the same equation is also used in miningindustry for describing the PSD of crushed rocks [16].

In a Fdouble-logarithmic_ graph, the A&A model resultsin a straight line, whereas the modified A&A model resultsin a curve that bends downward when the minimumdiameter is approached. In Fig. 7 both curves are givenfor q =0.25 and Dmin=0.5 Am. In the next sections, for the

0

10

20

30

40

50

60

70

80

90

100

0.01 0.1 1 10 100

Particle size (D) [mm]

% C

umul

ativ

e fin

er (M

/M)

Su et al. [6]

Su and Miao [7]

A&A (eq. (13)), Dmax = 19 mm, q = 0.3

Füller (eq. (13)), Dmax = 19 mm, q = 0.5

Fig. 6. Analysis of actual PSD of aggregates used by Su et al. [6] and Su and Miao [7].

0.1

1

10

100

0.1 1 10 100 1000 10000 100000

Particle size (D) [µm]

% C

umul

ativ

e fin

er (V

/V)

Modified A&A model (eq. (14)), Dmax = 16 mm, Dmin = 0.5 µm, q = 0.25 A&A model (eq. (13)), Dmax = 16 mm, q = 0.25

Fig. 7. Cumulative finer volume fraction according to A&A model (Eq. (13)) and modified A&A model (Eq. (14)).

H.J.H. Brouwers, H.J. Radix / Cement and Concrete Research 35 (2005) 2116–21362122

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7

Figure 4 (Brouwers & Radix, 2005)

Brouwers and Radix demonstrated that from the sieve analysis presented in the ‘Chinese method’, particle size distribution closely follows A&A curve as opposed to a Fuller curve, this is shown in Figure 3 above (Brouwers & Radix, 2005). The 3 mixes developed by Brouwers and Radix were designed to follow the modified A&A curve, which was closely achieved. Brouwers and Radix used 3 different sands, 0-1mm, 0-2mm and 0-4mm and even though all 3 combinations closely followed the modified A&A -curve they could be improved to achieve a denser packing. A possible way of improving the gradation of the aggregate is to have a greater overlapping of aggregate sizes, e.g. 0-1mm, 0-2mm, 2-4mm and 4-8mm. By achieving a grading that follows the modified A&A curve even closer, it will improve the workability and stability of the concrete. Brouwers and Radix also demonstrated the benefits of having a higher percentage of fine sand (0-1mm) in the aggregate with the mix with higher percentage of fine sand following the desired grading line more closely. This resulted in the mix showing better resistance to segregating and higher workability, whilst reducing the powder content required as well as SP dosage, compared to the ‘Chinese method’ (Su & Maio, 2003). The mix with the highest percentage of fine sands had the highest compressive strength, possible due to the tighter packing achieved. The fine and medium sands also had a beneficial effect on the water penetration resistance. Other researchers proposed other methods of mix design for SCC. These generally, have not presented any solution of substantial importance. For example; a mix design method has been proposed by Aggarwal et al. in 2008 does not improve on the ‘Chinese method’ or Brouwers and Radix’s (AGGARWAL, AGGARWAL, GUPTA, & SIDDIQUE, 2008). This method is an empirical one and does not focus on the benefits that have been shown in achieving optimal grading’s of aggregates and only results in a SCC with a max compressive strength of 31.54MPa at 28 days and this was achieved using a high amount of cement compared to alternative designs.

Figure 5 (Bosiljkov, 2003)

available ingredients in The Netherlands and their PSD’s(Fig. 2), it will be difficult to compose a mix that canapproach this A&A curve to the same extent. Fig. 6confirms that the grading curve of A&A better accountsfor powders than the grading curve of Fuller. From thecurves in Fig. 6 it furthermore follows that about 20% of theparticles are finer than 75 Am, whereas, according to Fuller,only 5.5% are smaller than 75 Am. As the A&A modelaccounts for powders (<250 Am) better, it is better suited fordesigning SCC. A continuous grading of all solids(aggregate and powders) will result in a better workabilityand stability of the concrete mix.

The A&A model prescribes a grading down to a particlediameter of zero. In practice, there will be a minimumdiameter in the mix. Accordingly, a modified version of the

model is applied that accounts for the minimum particle sizein the mix (Funk and Dinger [10]). This modified PSD(cumulative finer fraction) reads:

P D! " # Dq $ Dqmin

Dqmax $ D

qmin

!14"

whereby Dmin is the minimum particle size in the mix. Formany years the same equation is also used in miningindustry for describing the PSD of crushed rocks [16].

In a Fdouble-logarithmic_ graph, the A&A model resultsin a straight line, whereas the modified A&A model resultsin a curve that bends downward when the minimumdiameter is approached. In Fig. 7 both curves are givenfor q =0.25 and Dmin=0.5 Am. In the next sections, for the

0

10

20

30

40

50

60

70

80

90

100

0.01 0.1 1 10 100

Particle size (D) [mm]

% C

umul

ativ

e fin

er (M

/M)

Su et al. [6]

Su and Miao [7]

A&A (eq. (13)), Dmax = 19 mm, q = 0.3

Füller (eq. (13)), Dmax = 19 mm, q = 0.5

Fig. 6. Analysis of actual PSD of aggregates used by Su et al. [6] and Su and Miao [7].

0.1

1

10

100

0.1 1 10 100 1000 10000 100000

Particle size (D) [µm]

% C

umul

ativ

e fin

er (V

/V)

Modified A&A model (eq. (14)), Dmax = 16 mm, Dmin = 0.5 µm, q = 0.25 A&A model (eq. (13)), Dmax = 16 mm, q = 0.25

Fig. 7. Cumulative finer volume fraction according to A&A model (Eq. (13)) and modified A&A model (Eq. (14)).

H.J.H. Brouwers, H.J. Radix / Cement and Concrete Research 35 (2005) 2116–21362122

dolomite aggregate. Since the fineness modulus of crushedsand is usually very close to or even exceeds the JUS (formerYugoslav standard) standard upper limit value equal to 3.6,quartzite sand having a fraction of 0–1 mm is traditionallyadded to compensate the lack of fine material in the crushedsand. Quartzite sand deposits are limited to a few locations,and these supplies are nearly exhausted. The efficientreplacement of this sand by an easily available viscosityagent (VA) would thus be very desirable.

The aim of the work reported in this paper was toinvestigate the influence of two high purity LFs on thefresh properties and strength characteristics of SCC mixes.One was finely ground limestone, and the other waslimestone dust. SCC mixes were prepared using poorlygraded, crushed limestone aggregate and a VA, and theircement contents ranged from 380 to 390 kg/m3. Standardtests were carried out according to JUS standards.

2. Materials

PC designated CEM II/A-S 42.5R (EN 197), with aclinker mineralogical composition (Bogue) of C3S = 64%,C2S = 15%, C3A= 9% and C4AF = 9%, and with up to 15%of ground-granulated blast furnace slag was used. Thecement had a relative density of 3.08 g/cm3. The finelyground limestone (LF-C) contained 99.6% CaCO3 in theform of calcite and 0.4% quartz (SiO2), and the limestone dust(LF-L) contained 100% calcite. The texture of the parent rockwas predominantly sparitic (Dcalcite grains >10 mm) for theLF-C, andpredominantlymicritic (1mm<Dcalcite grains < 4mm)for the LF-L. The two LFs had a relative density of 2.75g/cm3.

The PSDs of LF-C, LF-L and PC, obtained by a laserscattering technique (MICROTRAC-FRA9200), are shownin Fig. 1. The parameters of the fitted RRSB distributionwere n = 0.9 and x0 = 12.7 mm, n = 0.88 and x0= 6.3 mm, andn = 0.99 and x0 = 19.0 mm for LF-C, LF-L and PC, respect-ively. The Blaine specific surface areas of LF-C and PC, andthe calculated specific surface areas (CS) of LF-C and LF-Lare given in Table 1. As indicated, LFs are finer and better

graded than PC, and of the two fillers, LF-L is better gradedand much finer than LF-C. However, considering theparticle shapes of LFs, the difference does not seem to besignificant (Fig. 2).

The used coarse (4–16 mm) and fine (0–4 mm, S1)aggregates consisted of crushed limestone with an averagecompressive strength of the parent rock of approximately200 MPa. The coarse aggregate was a combination of 4–8and 8–16-mm fractions, for which the highest dry roddedbulk density was obtained. For the purposes of comparison,an SCC mix without VA was prepared with sand (S2) thatwas a combination of 80%vol of S1 sand and 20%vol of anatural, 0- to 1-mm quartzite sand. With this combination,optimum dry rodded particle packing was obtained at thelowest quartzite sand content. The grading and physicalcharacteristics of the aggregates are shown in Table 2.

A polycarboxylate-based product with a solid content of34% was used as an SP. It is produced by a Sloveniancompany (TKK Srpenica). The VA used was a polysacchar-ide type admixture with 5% of active ingredient, produced byMAPEI.

3. Test methods and criteria for the fresh concrete mixes

The test methods used for the evaluation of the workabil-ity of SCC mixes were selected from those developed byother authors [19]. They were as follows: slump flow test, V-funnel test, CBI L-box test and filling vessel test. The testingprocedures and apparatus were those presented by Takada etal. [20], with one exception: for the V-funnel test, a 10-lfunnel with the dimensions given by Domone et al. [21] wasused. As an additional test, air content was also determined.

The following criteria for satisfactory self-compactingbehaviour were adopted on the basis of the author’s ownexperience, as well as recommendations from other authors[21,22]: a slump flow of between 650 and 750 mm, a V-funnel time of between 5 and 15 s, an H2/H1 blocking ratioin the L-box test greater than 0.8, and a filling ratio in thefilling vessel test greater than or equal to 90%.

4. Mix design and proportioning

The general method proposed by Okamura and Ozawa[23] was followed for the mix design of SCC mixes. Thismethod generally leads to concrete with a higher paste

Table 1Specific surface area of fillers and PC

Blaine (m2/kg) CS (m2/cm3)

PC 373 –LF-C 372 2.222

LF-L –a 2.705a Inappropriate test method due to the presence of agglomerated

particles.

Fig. 1. PSD of fillers and PC.

V.B. Bosiljkov / Cement and Concrete Research 33 (2003) 1279–12861280

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Using a finely ground limestone filler can greatly improve the particle packing and the amount of mixing water required can be significantly reduced. Increasing the amount of finely ground limestone mixed with cement improved the packing significantly and the deformability of the paste was also improved (Bosiljkov, 2003). The PSD of the Portland cement used, finely ground limestone (LF-C) and limestone dust (LF-L) is shown in figure 4 above (Bosiljkov, 2003). This can be attributed to the limestone being finer and better graded than cement. The PSDs were obtained using a laser scattering technique (Bosiljkov, 2003). Achieving a better packing density with the added limestone allows more water to be released and improves the flowability of the concrete. Yahia et al. recommended a cement and limestone range of between 23% and 29% of mortar volume for a w/c ratio of 0.35. This range varies with the w/c ratio (Yahia, Tanimura, & Shimoyama, 2005). The addition of fly ash improves the viscosity of the fresh concrete whilst reducing the amount of cement used. (Xie, Liu, Yin, & Zhou, 2002) The optimum Blaine surface area of fly ash was found to be approximately 500-600 m2/kg and a content of 30-40% of total cementitious materials for the optimal workability and water demand. When the fly ash content is no more than 40% of all cementitious materials the compressive strength is not significantly reduced at 28 day tests. (Xie, Liu, Yin, & Zhou, 2002) also demonstrated the benefits of a higher sand ratio for improving workability and obtaining a smaller compressive strength difference between SCC and ordinary concrete. It was found that the sand to total aggregate ratio is optimal at 44% and cannot be less than 40% as shown in Figure 5 below (Shen, Yurtdad, Diangana, & Li, 2009). Using this method, SCC with the required properties in the fresh state and compressive strengths of 60-80MPa and cementitious material not less than 500 kg/m3 was achieved.

Figure 6 (Shen, Yurtdad, Diangana, & Li, 2009)

A mix design method of SCC designed for pre-cast industry was proposed by Shen et al in 2009. This method focused on optimizing the packing density of aggregates by using the PF, a modified formula compared to the ‘Chinese method’, and also incorporated optimizing the sand to aggregate ratio. The quantity of binders used was calculated using the Bolomey formula, which differed from the ‘Chinese method’, and that of Brouwers and Radix. The Bolomey formula calculates the binder/water ratio based on the following equation:

(5)

With fc28 the compressive strength of SCC at 28 days, fcem the compressive strength of the cement at 28 days, B/W is the ratio of water to binder and G is the coefficient relating to the properties of aggregate such as the maximum diameter and shape of gravel (Shen, Yurtdad, Diangana, & Li, 2009). The super-plasticiser was found by setting a flow spread in a mortar test. (Shen, Yurtdad, Diangana, & Li, 2009) The maximum packing density was based on the experimental method of Brouwers and Radix to determine the void fraction of aggregates according the ASTM C29 procedure on measuring the bulk density of aggregates before and after compaction. The PF is then defined as the compacted bulk density to the loose bulk density of the aggregates the same as in the ‘Chinese method’. This method also allows for extra aggregates needed to replace the sand filling the voids in the gravel as well as the lubrication of the grains making the aggregate more compact. Flow spreads of pastes were selected to be similar to those defined in the mortar tests. Table 1 is a

(passing ability H2/H1 ‡ 0.80 with three rebars, where H1is the depth of concrete immediately behind the gate, andH2 is the mean depth of concrete at the end of horizontalpart of L-box), and SR2 (segregated portion £ 15%) as therules of verification for fresh SCC. Notice that the SCCshould also comply with the durability requirements pre-scribed by European standard EN 206–1 (AFNOR 2005b).

2.1. Aggregates

2.1.1. Compaction of aggregatesIf the aggregates are packed in a better way, there will be

more paste to decrease the friction between the grains of theaggregates. Therefore, the optimal compaction level consistsof finding the maximum packing density of aggregates. Anexperimental method (Brouwers and Radix 2005) has beenproposed to determine the void fraction of aggregates ac-cording to the American Society for Testing and Materials(ASTM) standard C29/C29M (ASTM 2003). In fact, theminimum void fraction corresponds to the maximum pack-ing density of the aggregates.

The ASTM standard C29/C29M defines the procedures tomeasure the bulk density of aggregates before and aftercompaction: the loose bulk density is measured by theshovel procedure, and the compacted bulk density by therodding procedure. Thus, the loose and compacted densityof aggregates can be determined experimentally by varyingthe mass ratio of sand to aggregates from 0% to 100%.Fig. 1 shows an example of this evolution for the aggregatesused in this paper. A zone around the peak of the regressioncurve ‘‘after compaction’’ is found, and the optimum massratio of sand to aggregates (S/A) is equal to the mean valueof this zone. Notice that the two extreme points (0% and100%) of the curve ‘‘before compaction’’ correspond, re-spectively, to the loose bulk density of gravel rg and sandrs.

2.1.2. Packing factorThe packing factor (PF) is defined by Su et al. (2001) as

the ratio of compacted bulk density rcompact to loose bulkdensity rloose of the aggregates. However, Su et al. do notindicate how they determine the experimental value of PF

and assume a predefined value. In this study, PF is calcu-lated by choosing the value corresponding to the optimumratio of sand to aggregate (S/A). The compacted bulk densityand loose bulk density of the aggregates at the point of opti-mum ratio S/A are therefore initially found, and PF can becomputed as follows:

!1" PF #rcompact

rloose

PF is used to calculate the quantity of aggregates in SCC.

2.1.3. Quantity of aggregatesThe first stage of the proposed method is to calculate the

quantity of aggregates. The volumes of loose sand and loosegravel are denoted Vs and Vg, respectively (in a unit volume1 m3). Their bulk densities were measured in Sect. 2.1.1, sotheir masses are ms = rsVs and mg = rgVg. To determine Vsand Vg (step 1 in Fig. 2), two equations can be established:

!2" rsVs

rgVg $ rsVs# Rs=a

!3" Vs $ Vg # 1

where Rs/a is the optimum mass ratio of sand to aggregate.After the sand and gravel are mixed (step 2 in Fig. 2), as

the sand fills the voids in the gravel, the total volume of ag-gregates will be lower than the unit volume. Va is designatedas the volume of aggregates including the voids. Subse-quently, due to the lubricating effect of the paste which de-creases the friction among the grains in the blendingprocess, the aggregates will become more compact, so addi-tional aggregates Maa should be added to make the volumeof aggregates Va unchangeable (step 3 in Fig. 2). By usingthe definition of PF, the final mass of aggregates Ma can beobtained as follows:

!4" Ma # PF%ms $ mg& # PF%rsVs $ rgVg&

The mass of additional aggregates can be obtained as Maa =(PF – 1)(ms + mg). The total paste volume Vp can be cal-culated as follows:

Fig. 1. Example of experiment to determine density of aggregates by varying the ratio of sand to aggregates. R2, coefficient of determination..

Shen et al. 1461

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comparison between the compositions estimated by the Japanese and Chinese SCC methods and the proposed method by Shen et al for a SCC with a compressive strength of 50MPa. (Shen, Yurtdad, Diangana, & Li, 2009) Table 1 (Shen, Yurtdad, Diangana, & Li, 2009)

IV. Particle Packing Models The packing of particles is a significant importance to the benefits it has on the characteristics of concrete. Research into particle packing has been undertaken since the since the early 20th century by Feret 1892 Fuller and Thompson 1907 (Amirjanov & Sobolev, 2008). The complexity of particle packing in concrete is due to the random nature of the properties of the aggregates and powders such as their size, shape and surface texture. There are several different particle packing models and theories that have been developed over the last 100 years, such as Furnas, Toufar, Dewar and Fuller and Thompson. Packing Models can be categorized as either monodisperse systems or polydisperse systems (Funk & Dinger, 1994). Monodisperse systems are the packing of equal size particles or such as spheres, because of the random sizes of concrete materials polydisperse packing in the most relevant. Polydisperse systems are characterised by mixes contain particles of different shapes and sizes and are packed either regularly or randomly. Polydisperse mixtures can be further classified into discretely distributed and continuously distributed. Continuously distributed particle size distributions (PSD) show the greatest pertinence to concrete development and is packing due to the wide range of particle sizes being considered. The total volume of voids in concrete is reduced when the range of particle sizes is as large as possible (Neville, 1995). The ultimate aims in concrete particle packing are to: •achieving densest mix possible; and in turn

•minimise the number of voids between particles

•Increase the aggregate volume and in turn reducing cement content used without sacrificing the concrete fresh or hardened properties.

Achieving a minimum void fraction of the concrete mix reduces the cement content required and increases the amount of free water available to act as the lubricant hence reducing the water to cement ratio required in concrete mix (Neville, 1995). The degree of packing the concrete mix can be calculated the packing factor (Equation 2). By increasing the packing factor of the concrete mix will result in a denser concrete with less cement required. The packing of monosized particles will not be discussed in this paper as it is not as relevant to concrete particle packing. A figure of monosized size packing is shown below in Figure 7.

Variation of the coefficient g with respect to the ratio W/Bfor SCC10–SCC50 is shown in Table 1. It can be deducedthat the compressive strength at the age of 1 day dependson the type of cement and the ratio W/B. The coefficient gis approximately 0.62–0.71 for cement B when W/B variesfrom 0.52 to 0.40; the coefficient g for cement A is system-atically lower and shows greater variation of 0.32–0.49when W/B varies from 0.59 to 0.44. The experimental datafor g can afford useful information for the subsequent mixdesign of SCC concerning compressive strength at an earlyage.

4.4. ComparisonsTable 3 shows a comparison between the compositions

estimated by the Japanese and Nan Su methods and thoseobtained by the proposed method. The comparison is madefor an SCC with a compressive strength of around 50 MPaat 28 days. The composition obtained by the proposedmethod corresponds to that of SCC30 (Table 1).

For the Japanese method, the coarse and fine aggregatescan be calculated according to the fixed empirical values. Arange of 0.8–1.0 for the water to powder ratio (by volume)and 0.9%–1.3% for the dosage of superplasticizer are pro-posed in this method, so average values of 0.9 and 1.1% areused to obtain the quantity of mixing water and superplasti-cizer, respectively. In addition, as the Japanese method doesnot indicate how to determine the binder composition to ob-tain the strength, the same W/B ratio as that of the proposedmethod is used (W/B = 0.52). Therefore, the contribution ofadditions to the compressive strength is taken into account.

For the Nan Su method, it is not clear how to calculatePF, and therefore a PF calculation formula proposed byChoi et al. (2006) is used. The quantity of cement is propor-tional to the compressive strength, with a coefficient of0.14 MPa/kg. Cement type I was used by Su et al. (2001)and Su and Miao (2003) in their studies. Thus, it was judi-cious to find a W/C ratio corresponding to this type of ce-ment and allowing a concrete strength of about 50 MPa tobe obtained. According to Kim et al. (2002), a value of0.40 can be used. As the quantity of cement is known, thewater needed for cement can be determined according tothe W/C ratio. The quantity of limestone powder is deter-mined from Figs. 3 and 4 on the condition that the cement

and limestone pastes have the same flowability. The supple-mentary water required by the limestone powder is added tothe total amount of mixing water. The quantity of the super-plasticizer should be determined at the point of saturation,so it cannot be estimated without experimentation.

Compared with the Japanese method, the Nan Su methodand the proposed method give lower paste contents andgreater quantities of sand. Furthermore, the quantity of pastecalculated by the proposed method was the lowest of thethree methods but still satisfied the requirements of SCC forthe fluidity and segregation resistance. In the same way, theproposed method required the lowest amount of cement.

5. ConclusionsThis study aimed to contribute to the development of the

mix-design method of self-compacting concrete (SCC). Theproposed mix-design method enables the packing density ofaggregates to be optimized and ensures good fluidity of theSCC. The following conclusions are drawn from the resultsobtained.

(1) The composition estimated by the proposed method sa-tisfied the requirements of SCC in the fresh state, sothis method is validated by the experiments.

(2) The compressive strength of SCC estimated by calcula-tion agreed well with that obtained from testing. Theproposed mix-design method of SCC enables, with thematerials used in this study, a compressive strength offrom 10 to 50 MPa at the age of 1 day to be obtained.Therefore, this method is applicable to the precast indus-try.

(3) The optimum ratio of sand to aggregate (S/A) and thepacking factor (PF) are two important parameters for thedesign of SCC. In this work, the value for the optimumratio S/A is 0.52–0.60, and the value of PF is from 1.10to 1.14.

(4) Generally, the dosage of superplasticizer for SCC is dif-ficult to estimate. In the proposed method, however, thequantity of superplasticizer can be determined by theflow spread test on the paste and mortar. Therefore,there is no need to carry out many trial mixes on theSCC itself.

(5) The coefficient g, which represents the ratio of compres-sive strength at 1 day to that at 28 days, is 0.32–0.49 or0.60–0.70 according to the type of cement and the ratioW/B in this work. This coefficient is useful in practice.Knowing the compressive strength at 28 days from theBolomey formula, the compressive strength at 1 day canbe estimated using the coefficient g.

(6) Compared with the Japanese method and the Nan Sumethod, the proposed method required a lower quantityof paste, indicating more aggregates and a lower quantityof cement in a unit volume.

ReferencesAFGC. 2008. Recommendations for use of self-compacting con-

crete. Association Francaise de Genie Civil (AFGC), Paris.AFNOR. 1996. Beton pret a l’emploi (standard XP P 18–305). As-

sociation Francaise de Normalisation (AFNOR), Paris.AFNOR. 2001. Ciment — Partie 1: composition, specifications et

criteres de conformite des ciments courants (standard NF EN

Table 3. Comparison between the compositions estimated by theJapanese and Nan Su methods and those from the proposedmethod for a compressive strength of 50 MPa.

Japanesemethod

Nan Sumethod

Proposedmethod

Coarse aggregate (kg) 742 751 789Fine aggregate (kg) 763 996 1006Cement (kg) 349 357 310Limestone powder

(kg)295 126 96

Mixing water (kg) 197 166 174Superplasticizer (kg) 7.4 — 5.3Air content (L) 15 15 15Paste volume (L) 432 341 323

aCannot be estimated without experiments.

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Figure 7: Monosized Particle Packing model

The discrete approach is based upon a set of particles with a distinct defined sizes such as a mix of golf and basketballs (Furnas 1928).The discreet approach uses the size ratio, s between the course and fine aggregate ratios larger than 2 :1 are recommended the densest packing (Furnas 1928). An example of a discrete model packing is shown below. This approach is simpler mathematically but has major drawbacks in that there are very few aggregates that have natural bimodal discrete distributions. Because of this discrete modeling is unrealistic for concrete technology. The unrealistic nature of the packing comes as the particles cannot be randomly mixed and follow the discrete model. Each material is required to be pack separately into densest arrangement. This approach is therefore artificial and then not suited to concrete mix design application.

Figure 8: Schematic illustration of the influence of the size ratio s on the packing fraction PF of discrete bimodal mixtures in a unit cell. (Husken, 2010) Continuous graded particle packing. A continuous size distribution is more applicable to the concrete mix design as it accounts for the large particle size ranges and includes all of the possible sizes of aggregates used. Research into continuously greater particles distribution has been undertaken since the early 20th century. This work demonstrated that the grading of concrete mixers influence the properties of both fresh and hiding concrete (Amirjanov & Sobolev, 2008). This research also demonstrated the benefits of a continuous type grading panel properties such as strength due to the void ratio being reduced. One of the most commonly used ideal grading models is the modified Andreasen and Andersen equation (Equation 5) which was initially proposed in 1931 (Husken, 2010). This model was also the basis for the Fuller curve when the distribution q equal to 0.5. The initial model was modified in 1994 by Dinger and Funk to include a minimum particle size as well is the maximum that was initially included this model. It has been concluded to be the most suitable for the packing of concrete materials (Smith & Haber, 1995). Because of this the modified Andreasen and Andersen ideal grading model was selected as the most appropriate to be used in the optimal proportioning in the materials in concrete mix. A mix with a lower distribution modulus, q will result in a fine aggregate mix whereas a high q value will result in a course mix. By increasing the distribution modulus q the packing factor and compressive strength is shown to decrease (Husken, 2010).

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Figure 9: Compressive strength of designed aggregate mixes for varying distribution modulus q (Husken, 2010). The Fuller grading curve (Equation 6) only consider the aggregates used in the concrete and not the particles finer than 125µm, such as cement. The fine particles have a significant impact on the concrete properties as well is the degree of packing of the overall mix and therefore must be considered (Funk & Dinger, 1994). This fact further strengthens the use of the modified Andreasen and Andersen model with its inclusion of the minimum particle size. By considering the optimal packing of the fines (particles smaller than 125µm), in the mix design the overall packing degree of the concrete is able to be improved and less cement can be used (Husken, 2010). As previously mentioned denser packing microstructure of the fines leads to a lower water requirement to achieve the desired workability which also results in better properties of the hardened concrete (Neville, 1995). Research by Husken further demonstrated improvements in strength of the concrete by incorporating fines into the overall grading of concrete mixes. This further validates the use of the modified Andreasen and Andersen equation and the advantages it has over many mix design codes using the Fuller curve which only considers the grading of aggregates. Huskens mixes that were graded using the modified Andreasen and Andersen model resulted in higher packing fraction and compressive strength. The mix considered the grading of cementitious materials as well as the aggregates were able to successfully reduce the cement content, further of great demonstrating benefits of optimising the particle packing.

Figure 10: Comparison of Modified A&A model Eq.5 and original A&A model.

In conclusion the ideal of an ‘ideal grading curve’ has been commonly utilized in modern mix designs and the benefits have been shown (Neville, 1995). However there are no universally accepted mathematical models for the ideal grading curve. It has also been shown that different concrete types have varying characteristics and therefore not one grading model is suitable for all concretes. From current research the modified A & A equation appears to be the best suited as it considers the entire grading of all solid ingredients and is practical in nature when compare to discrete based packing models. Whilst the distribution modulus has been found to be optimal when q = 0.37, experiments can be further undertaken to see how it influences concrete properties such as workability. A continuous particle size distribution has been concluded to be the most relevant to improving concrete properties.

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V. Methods to obtain a type grading A type grading is defined as the grading specifications for the concrete mix design. As previously stated there is no ideal type grading but the benefits of aggregate grading has on the concrete properties has been shown (Neville, 1995). Such methods of obtaining the required grading for a mix design include, trial and error, graphical methods such as Rothfuch’s, manually or analytically utilizing a computer. Using graphical and manual methods is possible when only considering coarse and fine aggregates, but it is still time consuming and the graphical method an estimate. Because of the need to experiment on the influence all concrete materials have on the mix design such as cement and fly ash, utilizing computer software is necessary. These methods consider the volumetric proportions of each material passing set sieve sizes and can be easily represented graphically as seen in Figure 10 below. After each of the materials optimal proportions are calculated to best fit the specified type grading the specific gravities are used to calculate the relevant masses for the mix design.

VI. Optimisation Algorithm A need for an easy to use method to calculate the optimized proportions of desired materials in a concrete mix was identified from the literature review. The graphical and trial and error methods of obtaining the proportions of materials so that it meets the grading requirements of the mix design is not suitable for mix designs with a large particle size range. The methods are essentially rough estimates and are difficult to solve when a large number of aggregates are used. Such algorithms have been already been developed but are not readily available or are very complicated to understand (Hüsken & Brouwers, 2008) (Amirjanov & Sobolev, 2008) (Sivilevicius, Podvezko, & Vakriniene, 2011). By using the least squares method the problem is set up as follows:

• mix design solid ingredients, Ij for j=1,2,…,m • particle sizes/sieve sizes, Si i=1,2,…,n • total % passing ith particle/sieve size, pij • target grading distribution, piT • optimal proportion of each ingredient, Pj

𝑚𝑖𝑛 ( 𝑝!"𝑀! − 𝑝!")! = 𝑝!"𝑀! − 𝑝!"!

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A MATLAB coded optimization algorithm was utilized to solve this problem (Ray, Singh, Isaacs, & Smith, 2009). Figure 11 shows the grading curves of several generations of the algorithm highlighting how the accuracy is increased with the greater the number of generations as the mix design curve obtains a closer fit to the target grading. The larger area between generation 11 and the target grading can clearly be seen.

Figure 11: Comparisons of accuracy of the fit of multiple generations

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The main goal of allowing the algorithm to be easy to use was achieved by developing a user guide that accompanies the code. This user guide can be found in Annex A of the full report for this project. The algorithm requires the user to provide the particle size distributions of the materials used in the mix design. From this the data is easily imported into MATLAB and then the desired constraints can be added. The constraints which initially hold the greatest importance are as follows:

• Volumetric Constraint: that the sum of the volumetric proportions is less than 1. This can be adjusted to be less than 1 to account for non-solid ingredients such as air, water and admixtures.

• Non-negativity constraint such that no ingredient can have a volumetric proportion less than zero and hence the volume total cannot be less than zero.

• Minimum and maximum individual ingredient proportions. Such as minimum cement content. • Ratios between ingredients.

Validation of the algorithm The result generated from the new algorithm was compared to the results of Sivilevicius, Podvezko and Vakriniene. This research determined the optimal grading of a hot mix asphalt mixture with 7 different materials. The algorithm developed without the specific constraints set by Sivilevicius, Podvezko and Vakriniene had a fit that matched the results of the model and can be seen below in figures 9 and 10.

Figure 12: PSD of materials and the composed asphalt mix

Figure 13: Target and mix grading comparisons

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Table 2: Comparison of two optimisation models

VII. Future Research

By utilizing the algorithm and new laser diffraction technology, such as Mastersizer 2000 it is possible to measure the PSD of materials and then import them into the optimization algorithm. From this mix designs can be developed to that utilize the particle packing benefits discussed in this paper in an attempt to further reduce the cement requirements of a mix design. The Andresen and Andersen packing model can also be further verified by investigating concretes which follow its ideal grading curve and comparing them to design standards grading curve requirements. The impact that the distribution modulus, q has on the concrete properties can also be tested by modifying the mix design proportions accordingly. This will further test the work by Husken that suggested that increasing the distribution modulus q the packing fraction and compressive strength is shown to decrease. This algorithm will also be able to further test how different size ranges for materials change the packing of a concrete and build on the work by Brouwers that suggest that possible way of improving the gradation of the aggregate is to have a greater overlapping of aggregate sizes. It is recommended that using the new laser diffraction technology to investigate the effect materials such as silica fume, fly ash and slag have on the overall packing of the concrete and how the finer particles influence concrete mix designs that have lower cement content. This research will allow for mix designs to be developed with the aim of reducing the cement content whilst improving concrete properties which will be a positive step in concrete development.

VIII. Conclusions The benefit of optimizing the particle packing of all the concrete ingredients to achieve the greatest density

has been well documented. Whilst there is still no universally accepted mathematical model for the densest packing arrangement, the Andreasen and Andersen is identified as the most relevant and effective for concrete. Concrete mix designs which utilize the Andreasen and Andersen grading curve have resulted in lower cement requirements without sacrificing the strength of workability of the concrete. From the literature review the need for an easy to use algorithm to optimize the proportions of each concrete material based upon their particle size distributions was identified. This algorithm was developed allowing for future research to further investigate the benefits of optimizing the particle packing has on concrete properties as well as being the basis for new mix designs.

Sieve  size  (mm)Target  Grading  Total  %  Passing  

Model  A                              Total  %  Passing  

New  Algorithm  Total  %  Passing

31.5 100 98 10022.4 95 95 9716 69 73 7411.2 54 50 518 44.5 46 455 36 36 362 27.5 28 28

0.71 22 21 220.25 15 13 130.09 6 8 8

R2 0.9954437 0.995005

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Acknowledgements

I would like to thank my thesis supervisor A/Prof Obada Kayali who has guided and inspired me to complete this project. His expertise and willingness to help at all times was especially helpful as the thesis journey throughout the year has been up and down, so the constant encouragement was much appreciated. I would also like to thank A/Prof Ruhul Sarker for his initial help in understanding how optimization problems are solved and providing me with valuable guidance. I would like to especially thank Dr. Tapabrata Ray, who kindly provided me with the MATLAB code that he had developed to be adapted to the optimization problem in this project, without his help I would not have been able to complete it. I would also like to thank James Baxter for his technical support when working in the laboratory and always making time to help was much appreciated. To my beautiful girlfriend Nicole, who supported me throughout the entire project and always reminded me that I was always going to be successful in the end and was always to my stresses, you have been amazing and thank you. Final thanks go to my close friend Matthew whose testing and constructive comments for the algorithm user guide was instrumental in the final user guide.

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Douglas, E. (1992). Properties and durability of alkali-activated slag concrete. ACI MAterials Journal, 89(5), 509-16. Funk, J., & Dinger, D. (1994). Predictive Process Control of Crowded Particulate Suspension, Applied to Ceramic

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