A review on mixture design methods for self compacting concrete

A review on mixture design methods for self compacting concrete Construction and Building Materials 84 (2015) 387–398 Contents lists available at ScienceDirect Construction and Building Materials jour.

A review on mixture design methods for self-compacting concrete

Caijun Shi⇑, Zemei Wu, KuiXi Lv, Linmei Wu

College of Civil Engineering, Hunan University, Changsha 410082, China

h i g h l i g h t s

Five mixture design methods for SCC based on different principles are reviewed

Feature and flow chart of mixture design procedure for each method is presented

Advantages and disadvantages of each method is compared

It provides valuable suggestions for choosing appropriate design method for SCC

a r t i c l e i n f o

Article history:

Received 1 January 2015

Received in revised form 13 March 2015

Accepted 16 March 2015

Keywords:

Self-compacting concrete

Mixture design method

Classification

Advantages and disadvantages

a b s t r a c t

Mixture design is a very important step in production and application of concrete Many mixture design methods have been proposed for self-compacting concrete (SCC) This paper presents a critical review on SCC mixture design methods in publications Based on principles, those methods can be classified into five categories including empirical design method, compressive strength method, close aggregate packing method and methods based on statistical factorial model and rheology of paste model The procedures, advantages and disadvantages of each method were discussed The most appropriate method should

be chosen according to actual situations to obtain high quality SCC with satisfactory properties

Ó 2015 Elsevier Ltd All rights reserved

Contents

1 Introduction 387

2 Mixture design methods 389

2.1 Empirical design method 389

2.2 Compressive strength method 390

2.3 Close aggregate packing method 391

2.4 Mixture design method based on statistical factorial model 393

2.5 Mixture design method based on rheology of paste model 395

3 Conclusions 397

Acknowledgement 397

References 397

1 Introduction

Self-compacting concrete (SCC) is a special type of concrete

which can be placed and consolidated under its own weight

with-out any vibration effort due to its excellent deformability, and

which at the same time is cohesive enough to be handled without

segregation or bleeding The concept of SCC was first proposed by Okamura in 1986, and the prototype was first developed by Ozawa

at the University of Tokyo in 1988[1,2] SCC has many advantages over conventional concrete, including: (1) eliminating the need for vibration; (2) decreasing the construction time and labor cost; (3) reducing the noise pollution; (4) improving the filling capacity of highly congested structural members; (5) improving the interfacial transitional zone between cement paste and aggregate or reinforcement; (6) decreasing the permeability and improving http://dx.doi.org/10.1016/j.conbuildmat.2015.03.079

0950-0618/Ó 2015 Elsevier Ltd All rights reserved.

⇑ Corresponding author Tel./fax: +86 731 8882 3937.

E-mail address: cshi@hnu.edu.cn (C Shi).

Contents lists available atScienceDirect Construction and Building Materials

j o u r n a l h o m e p a g e : w w w e l s e v i e r c o m / l o c a t e / c o n b u i l d m a t

the durability of concrete, and (7) facilitating constructability and

ensuring good structural performance[3,4]

Concrete mixture design is a selection of raw materials in

optimum proportions to give concrete with required properties

in fresh and hardened states for particular applications Different from conventional concrete, a quality SCC should have three key properties[5]: (1) filling ability – the ability to flow into the form-work and completely fill all spaces under its own weight; (2) pass-ing ability – the ability to flow through and around confined spaces between steel reinforcing bars without segregation or blocking; (3) segregation resistance – the ability to remain homogeneous both during transporting, placing and after placing In addition to good self-compactability, designed SCC also should meet the require-ments for strength, volume stability and durability of the hardened concrete at the same time[6] Due to those obvious advantages, SCC has been a research focus for many years Five North American conferences [7–9], seven RILEM conferences [10–12] and three symposiums on design, performance and use of SCC [13–15]have been held so far

It has reported that factors including composition of raw mate-rials, incorporation of chemical and mineral admixtures, aggregate, packing density, water to cement ratio (W/C) and design methods has significant effects on properties in terms of rheology, strength, shrinkage and durability of SCC[16–19] Hu and Wang[20]showed that graded aggregate could considerably reduce yield stress and viscosity of concrete The increased paste volume could enhance the rheological properties of SCC[21,22] SCC designed using modi-fied Brouwers’ method exhibited satismodi-fied workability with recom-mended dosage of high range water reducer[19] With the world moving toward to sustainable development, waste materials such

as fly ash (FA), rice husk ash (RHA), crushed limestone powder [23], waste glass powder[24,25], recycled and tire rubber aggre-gates have been used in SCC[26–28] It is reported that the strength

of SCC improved with the increasing content of superplasticizer

Table 1

Summary of existing mixture design methods for SCC in the literatures.

Empirical design

method

Okamura, and Ozawa 1995 Fix coarse and fine aggregate first, and then obtain self-compactability by adjusting W/B and

superplasticizer dosage

[34] Edamatsa, Sugamata,

and Ouchi

2003 Use mortar flow and mortar V-funnel testing to select the fine aggregate volume, volumetric water-to-powder ratio and superplasticizer dosage

[36]

Domone 2009 For a given set of required properties, make the best estimation of the mixture proportions, and then

carry out trial mixes to prove

[38]

Compressive

strength

method

Ghazi, and Al Jadiri 2010 Based on the ACI 211.1 method for proportioning conventional concrete and the EFNARC method for

proportioning SCC

[39]

Dinakar, Sethy, Sahoo 2013 Use GGBS in SCC based on the strength requirements and consider the efficiency of GGBS [33] Close aggregate

packing method

Hwang, and Tsai 2005 Use Densified Mixture Design Algorithm (DMDA), derived from the maximum density theory and

excess paste theory

[42]

Petersson, Billberg, and Van

Su, Hsu, and Chai 2001 Use packing factor (PF) to control the content of fine and coarse aggregate in mixture proportion [44] Sedran, and De Larrard 1996 Use software to design SCC based on the compressible packing model (CPM) [46] Shi, and Yang 2005 Use a combination of the excessive paste theory and ACI guidelines to design self-consolidating

lightweight concretes

[3] Sebaibi, Benzerzour,

Sebaibi, and Abriak

2013 Based on FN EN 206-1 standard, compressible packing mode (CPM) and packing factor (PF) [47]

Kanadasan and Razak 2014 Integrate the actual packing level of aggregate and paste volume into the proportioning method based

on the particle packing to obtain the final mixture design

[48]

Statistical factorial

model

Khayat, Ghezal, and Hadriche

1999 Obtain a statistical relationship between five mixture parameters and the properties of concrete [49]

Ozbay, Oztas, Baykasoglu, Ozbebek

2009 Design in a L18 orthogonal array with six factors, namely, W/C ratio, water content (W), fine aggregate

to total aggregate (S/a) percent, fly ash content (FA), air entraining agent (AE) content, and superplasticizer content (SP)

[52]

Bouziani 2013 Useful to evaluate the effect of three types of sand proportions (river sand, crushed sand and dune

sand), in binary and ternary systems, on fresh and hardened properties of SCC

[53]

Rheology of paste

model

Saak, Jennings, and Shah

2001 Avoid segregation of the aggregates as a critical design parameter, then a new segregation-controlled design methodology is introduced for SCC

[54]

Bui, Akkaya, and Shah 2002 Expand Saak’s concepts to include the effects of aggregate (and paste) volume ratio, particle size

distribution of the aggregates and fine to coarse aggregate ratio, to propose a new paste rheology model

[55]

Ferrara, Park, and Shah 2007 Steel fiber-reinforced self-compacting concrete based on the paste rheology model [57]

YES NO

Air content: 4-7%

Coarse aggregate content: the ratios of the coarse

aggregate volume to solid volume is 0.50

Fine aggregate content:

V funnel testing using coarse aggregate

VW/VP: mortar flow testing

SP dosage: mortar V-funnel testing

Measured properties >

required ones˛

SCC

Fig 1 Mixture design procedure proposed by Edamatsa.

(SP) when 10% RHA was incorporated[29] Economical SCC could be

successfully developed with 28-day compressive strengths from 26

to 48 MPa with incorporation of 40–60% FA[30] In addition, Long

et al.[28]indicated that the incorporation of rubber aggregates

sig-nificantly influenced yield stress of fresh SCC specimen and the

compressive strength at 28 days, depending on the size distribution

and volume percentage of the rubber aggregate

As a vital step to the production of concrete, many researchers

from all over the world have done a lot of researches on mixture

design of SCC, and proposed a variety of mixture design methods

based on different principles or control parameters Mixture design

methods or guidelines for SCC have been promulgated with wide

applications in many countries and regions However, there is a lack

of uniform criterion, specific design parameters or factors to evalu-ate the SCC design process, which makes it difficult to compare the effectiveness of different design methods and properties of SCC This paper classified the mixture design methods of SCC into five cate-gories based on their design principles The procedures, advantages and drawbacks of each method were presented and compared It is the purpose to review the progresses and to provide valuable scien-tific bases for selection of suitable mixture design methods of SCC

2 Mixture design methods There are many mixture design methods for SCC Domone[38] and Petersson [43] presented a model respectively in 1996 In

1999, the Laboratory Central des Ponts et Chausses (LCPC) [46] developed an approach on the basis of the BTRHEOM rheometer and RENE-LCPC software Su et al [44] introduced a coefficient called packing factor (PF) to adjust the relative content of aggre-gate and paste Hwang [42] et al proposed a densified mixture design algorithm, which was derived from the maximum density theory and excess paste theory Saak et al.[54]used rheology of paste model for the design of fiber-reinforced SCC Ghazi et al [39]developed a new method capable of proportioning SCC mix-tures with specified compressive strength Recently, Sebaibi et al [51] proposed a new mixture design method based on the European standard (EN206-1), the Chinese method and the optimization of the granular packing Moreover, there are some modified mixture design methods based on those existed methods [31–33] The existing mixture design methods for SCC in the litera-tures are summarized inTable 1 Based on the design principles, those methods can be classified into five categories: empirical design method, compressive strength method, close aggregate packing method, methods based on statistical factorial model and rheology of paste model The following sections discuss these methods in details

2.1 Empirical design method Empirical design method is based on empirical data involving coarse and fine aggregates content, water and cementitious

Flowability test of cement paste:

Determine water demand;

Determine optimum SP dosage

Flowability test of cement mortar:

Determine optimum sand content

Metakaolin mortars Control mortar

Absorption of mortar mixtures

Setting time test

Compressive strength of mortar mixtures: Determine the optimum replacement level of powder mortars

Flowability & filling ability of mortar mixtures: Determine optimum SP dosage and replace different level of pozzolan

Control Concrete Optimum MK Concrete

Fresh tests of concrete mixes:

Slump flow cone, V-funnel box, L-box, and segregation sieve

Accepted results according to typical acceptance criterion for SCC

Fig 2 Flow chart of mixture design procedure of the approach proposed by Khaleel (modified based on Ref [37] ).

Coarse aggregate content Vca

Fine aggregate content:

Vfa(%)=0.45(100-Vca)

Paste volume: Vpa(%)=100-Vca-Vfa

Trial concrete mixtures

Materials information

Specify concrete properties: Filling ability, passing ability and Segregation resistance

Recommend

values

W/P and SP dosage:

the spread and V-funnel tests

Fig 3 Mixture design procedure of UCL method.

material contents and superplasticizer dosage to determine the

ini-tial mixture proportions The best estimates of the mixture

propor-tions for required properties are carried out through several trial

mixes and adjustment

Okamura et al.[1,34] proposed a mixture design method for

SCC based on experiences The design procedure included the

fol-lowing aspects: (1) coarse aggregate content in the concrete was

fixed at 50% of the solid volume; (2) fine aggregate content was

fixed at 40% of the mortar volume; (3) water-to-powder ratio

was assumed between 0.9 and 1.0 by volume, depending on the

properties of the powder; (4) superplasticizer dosage and the final

water-to-powder ratio were determined so as to ensure

self-compactability

This approach is very easy to follow, but there were no

parame-ters describing the properties of aggregate In order to obtain

higher workability and moderate viscosity, higher dosage of

super-plasticizer must be used, which could result in retarding of

con-crete and increases the cost of SCC as well Although this method

is based on experiences, it is a simple approach for designing SCC

Edamatsa[35,36]improved the method by fixing fine aggregate

ratio, volumetric water-to-powder ratio and superplasticizer

dosage.Fig 1shows the mixture design procedure Compared with

Okamura’s approach, this method can be applicable to powder

materials and aggregates of various qualities However, further

work is required to characterize the properties of raw materials,

including the compactability between powder materials and

superplasticizers

Khaleel et al.[37]proposed a design method, which was similar

to Edamatsa’s approach, for self-compacting metakaolin concrete

with coarse aggregates of different properties The mixture design procedure is shown in Fig 2 Experiments were conducted on paste, mortar and concrete to facilitate the mixture design process

It is indicated that this method was good in production of SCC with coarse aggregate of different properties The use of metakaolin in concrete can not only a good choice for utilization of wastes but also enhance properties of SCC

Domone et al.[38]also proposed a method based on experience and understanding of the behavior of SCC named UCL method The method estimated the mixture proportions for a given set of required properties, then adjusted it by trial mixes The mortar fraction of concrete was tested using spread and V-funnel tests

to determine the water-to-powder ratio and superplasticizer dosage.Fig 3shows the procedure of this method In this method, only standard tests for fresh concrete are needed and other compli-cated tests such as rheology behavior of mortar or concrete are avoided

A significant advantage for the empirical design method is its simplicity However, intensive laboratory testing is needed to obtain compatible behavior for available constituents and satisfac-tory mixture proportions Besides that, changes in raw materials will need intensive re-testing and adjustments

2.2 Compressive strength method This type of method determines cement, mineral admixtures, water and aggregate contents based on required compressive strength Ghazi et al.[39]proposed a straightforward method for SCC mixture design based on ACI 211.1 [40] method for

YES

NO Measured properties>required ones

6 Fine aggregate content 5 Powder content

2 Maximum weight of water and air content

3 W/C, water and cement contents

4 Gravel content

SCC

1 Required compressive strength of SCC

?

Fig 4 Mixture design procedure of the method proposed by Ghazi.

Table 2

SCC compressive strength versus W/C (Table 3 in Ref [39] ).

YES

NO

Select components Fix the total powder

or cementitious content

Fix the GGBS percentage and calculate efficiency

of GGBS at 28 days

Determine water content of mixture

Determine sand/total aggregate ratio using standard gradation curves

Determine superplasticizer dosage

Determine final mixture composition Trial mixtures and tests

on SCC properties

Check with EFNARC guidelines Re-design mixture

Go for the development of SCC

proportioning conventional concrete and EFNARC[41]method for

proportioning SCC In this method, the coarse aggregate content

depended on the maximum aggregate size (MAS) and fineness

modulus of the fine aggregate The water content was determined

based on both the maximum aggregate size and concrete strength

The W/C and the water-to-powder volume ratios were determined

by the compressive strength of concrete Its brief flow chart is

shown inFig 4

The original ACI 211.1 method covers the design of compressive

strength from 15 to 40 MPa However, this method expanded

com-pressive strength range from 15 to 75 MPa for SCC, with maximum

W/C as shown inTable 2 This method also needs to use some

rele-vant tables in reference[39]

Dinakar et al [33] proposed a method for SCC containing

granulated blast-furnace slag (GGBS) using efficiency factor The

method consisted of five steps as shown inFig 5 The total powder

content was fixed in the first step, the percentage of slag was fixed

based on the strength required The efficiency factor (k) was

deter-mined for the same percentage with the equation proposed in the

second step In the third step the water content required for SCC

was determined and the coarse and fine aggregates were then

determined using appropriate combined aggregate gradation

curves of DIN standards Finally the self-compactability of the fresh

concrete was evaluated through the slump flow measurement

and flowability through V-funnel testing, and passing ability

through L-box testing

Using the proposed method and established efficiency values for GGBS, SCC with strengths range from 30 to 100 MPa at GGBS replacement levels from 20 to 80% could be developed This method considered the efficiency of pozzolanic materials and pre-sented a way for using high volume replacements up to 80% for

30 MPa

The compressive strength method presents a clear and precise procedure to obtain specific quantities of ingredients and mini-mizes the need for trial mixtures In addition, the proposed method takes into consideration the gradation of fine and coarse aggre-gates or the contributions of pozzolanic materials to the properties

of concrete However, one of its weekness is that it requires adjust-ments to all ingredients like sand, coarse aggregate, superplasticiz-ers and water, to achieve an optimal mixture proportion

2.3 Close aggregate packing method This type of mixture design method determines mixture pro-portions by obtaining ‘‘the least void’’ between aggregates based

on packing model first, then applying pastes to fill the void between aggregates

Hwang et al.[42]proposed a method based on the Densified Mixture Design Algorithm (DMDA) The effects of three types of aggregate packing (primitive, dense, gap gradation) on void within aggregates and the property of produced concrete were investi-gated [42] The primitive packing type used sand to fill the void between coarse aggregate, and then used fly ash to fill the void between aggregates as shown inFig 6 Dense packing type used the standard sieves of 3/8 in, Nos 4, 8, 16, 30 and 50 to separate aggregates into different sizes, and the remained fine particle was omitted Then followed the similar packing procedure of the primitive packing type as shown in Fig 6by iterative filling the coarse particle with finer one from 3/8 in to No 50 and finally filled with fly ash to wholly pack the aggregates Results indicated that the dense-graded curves were quite close to the Fuller’s curve, as shown inFig 7

DMDA was derived from the maximum density theory and excess paste theory, and was the durability design concept to achieve minimum water and cement content by applying fly ash Fig 6 The procedure of aggregate packing (modified based on Ref [42] ).

Select proper material source;

Obtain material information

Calculate the least void VV

NO

YES

Obtain the maximum density by iterative packing of aggregate

Calculate the volume of aggregate Vagg

Assign volume of paste amount VP=nVV

Determine the SP and water content

SCC

Measured properties>required ones?

to fill the void between aggregates and cement paste to attain ‘‘the

least void’’ The procedure of this method is shown inFig 8 The

SCC designed by the DMDA is high flowable, cost-effective and

dur-able It overcomes concrete problems due to shape, particles

dis-tribution, gap gradation of aggregates and large amount of

cement paste However, there is very little information concerning

the passing ability through reinforcement and segregation

resistance

Petersson et al.[43]proposed a mixture design method for SCC

based on a relationship between the blocking volume ratio and

clear reinforcement spacing to fraction particle diameter ratio

This method considered concrete as a solid aggregate phase in a liquid paste phase formed by powder, water and admixtures The paste fills the void in the aggregate matrix and provides a lubricat-ing layer around each particle In this method, the risk of blocklubricat-ing was calculated using the following equation

where Vaiis the volume of aggregate group i and Vabiis the blocking volume of aggregate group i By using Eq.(1) together with the blocking criteria, the minimum paste volume for different gravel

to total aggregate ratios can be calculated The procedure of this method is shown inFig 9

This method is notable for its importance but is not that easy to apply It enables to design mixtures for a specific bar spacing with sufficient lubrication between aggregates However, there are no adequate methods to justify uniformity of the mixture

Su et al [44,45] proposed a mixture design method for SCC using a packing factor (PF) The principal consideration of the method was to fill the paste of binders into voids of loosely piled aggregate framework The packing factor (PF) of aggregate is defined as the mass ratio of tightly packed aggregate to that of loosely packed aggregate Thus the content of fine and coarse aggregates can be calculated as follows:

where Wris the content of coarse aggregates in SCC (kg/m3); Wsis the content of fine aggregates in SCC (kg/m3); WrLis the unit vol-ume mass of loosely piled saturated surface-dry coarse aggregates

in air (kg/m3); WsL is the unit volume mass of loosely piled satu-rated surface-dry fine aggregates in air (kg/m3); S/a is the volume ratio of fine aggregates to total aggregates, which ranges from 50

to 57% The procedure of this method is shown inFig 10 [45] This method is simple and uses a smaller amount of binders PF determines the aggregate content and influences the strength, flowability and self-compacting ability However, how to

NO

YES

Construction Criteria Void Content Blacking Criteria

Paste Volume

Coarse aggregate content,

SP dosage

Wanted SCC

Mortar volume

Measured properties>required ones?

Fig 9 Mixture design procedure of the method proposed by Petersson (modified

based on Ref [43] ).

Water content Wc

Fly ash content F GGBS content S

Cement content C

SP dosage

Packing factor PF

Water to cement ratio Wc/C

Fine aggregate content Af

Coarse aggregate content Ac

Pozzolanic paste volume Vpp

Water content Ws

Water content Wf

Total water content W

determine the optimum sand to aggregate ratio or the packing

fac-tor is not explained These two values are assumed empirically to

carry out the mixture design

Sedran et al.[46]proposed a method based on the compressible

packing model (CPM), which is the third generation of packing

models developed at LCPC CPM first calculated virtual packing

density of solid particles with different particle size distributions

according to the packing structure; then through the compaction

index K, the relationship between virtual packing density and

actual packing density was established in different packing

pro-cess Finally, a nonlinear equation was solved to get the actual

packing density In this method, a BTRHEOM rheometer and a

RENE-LCPC software were needed to be used together for SCC

design The procedure of this method is shown inFig 11 [46]

The method focuses on optimizing the granular skeleton of

con-crete from the viewpoint of packing density Sometimes, it could

result in very low paste content, causing a rapid loss of slump flow

and blockage while pumping Besides, it is difficult for others to use this method without purchasing the software

Shi et al.[3] proposed a method for self-consolidating light-weight concretes (SCLCs), using a combination of the excessive paste theory and ACI guidelines for the design of conventional structural lightweight concrete Glass powders and ASTM Class F

fly ash were added to produce excessive paste to increase the flowability and segregation resistance of the concrete The proce-dure of this method is shown inFig 12 The designed SCLC mix-tures exhibited good flowability and segregation resistance Sebaibi et al.[47]proposed a method based on the compressible packing model[46], the method proposed by Su[44]and the EN 206-1 standard In this method, RENE-LCPC software was used to optimize the composition of SCC The Eqs.(2) and (3)were used

to calculate the content of coarse and fine aggregates respectively The paste amount of pozzolanic materials was calculated using the

NF EN 206-1 The procedure of this method is shown inFig 13 The W/C was selected accoring toFig 14

The SCC designed with the method contains more aggregate but less binder The ratio of fine aggregate to mortar volume was 60%, which was higher than the value of 40% proposed by Okamura Then a concrete mixture designed by the proposed method requires a smaller quantity of binder, rather higher ratio of fine aggregate to mortar volume

Kanadasan et al [48] used the particle packing concept to ensure the fresh and hardened properties of SCC incorporating waste product of palm oil clinker aggregate The actual packing level of aggregate and paste volume were integrated into the method The flow chart for the mixture design procedure is shown

inFig 15 The results indicated that the mixture design could be employed not only for palm oil clinker but also for a variety of combinations of aggregate It not only helps to conserve the natu-ral resources but also promotes sustainability in preserving the environment

2.4 Mixture design method based on statistical factorial model This method is based on the effects of different key parameters such as the contents of cement and mineral admixtures, water-to-powder ratio, volume of coarse aggregate, and dosage of SP etc on workability and compressive strength of fresh and hardened SCC Reasonable ranges for each parameter are determined, and mixture proportion is calculated according to mixture design of conven-tional concrete

Khayat et al.[49,50]proposed a statistical factorial model by selecting five key mixture parameters to design SCC The five key parameters were the cementitious material content (CM), the ratio

NO

YES

Half saturation amount of SP Initial combination of binders

Measure the water demand

Run RENE-LCPC to optimize the mixture proportion

Adjust water content to gain the target viscosity

Adjust SP dosage to gain suitable slump flow;

Check with general criteria

Check rheological behavior

Measured properties>required ones ?

Fig 11 Mixture design procedure of the method proposed by Sedran (modified

based on Ref [46] ).

YES

NO

Determine the void volume in the dry binary aggregate mixtures according to ASTM C29

Determine optimum combination of coarse and fine aggregates

Determine cement content and W/C according to strength requirement and ACI 211.2,

Determine volume of excess paste through experiment

Determine mineral admixtures content

SCLCs

Measured properties>required ones?

of water to cementitious materials (W/CM), the concentrations of

high-range water reducer (HRWR), viscosity-enhancing agent

(VEA) and the volume of coarse aggregate (Vca) Statistical factorial

design models were used to derive design charts which correlate

input mix-design variables to output material properties, mainly

consisting of the measurements of fresh state properties as well

as the compressive strength The resulting understanding of the

interaction between the key parameters can be used for both mix

optimization and quality control

Sonebi[51]used statistical factorial model to design medium

strength SCC containing fly ash In his experiment, a factorial

design was carried out to mathematically reflect the influence of five key parameters on filling and passing abilities, segregation and compressive strength, which are important for the successful development of medium strength SCC incorporating pulverised fuel ash (PFA) The parameters were the contents of cement and PFA, water-to-powder (cement + PFA) ratio (W/P) and dosage of

SP The responses of the derived statistical models are slump flow, fluidity loss, Orimet time, V-funnel time, L-box, J-Ring combined to the Orimet, J-Ring combined to cone, rheological parameters, segregation and compressive strength at 7, 28 and 90 days Twenty-one mixes were prepared to derive the statistical models, and five were used for the verification and the accuracy of the developed models The results showed that medium strength SCC with 28-day compressive strengths of 30 to 35 MPa could be achieved by using up to 210 kg/m3of PFA

Ozbay et al.[52] analyzed mixture proportion parameters of high strength self-compacting concrete (HSSCC) by using the Taguchi’s experiment design method for optimum design Mixtures were designed using L18 considering six factors including W/C, water content (W), fine aggregate to total aggregate percent (S/a), fly ash content (FA), air entraining agent (AE) content and superplasticizer content (SP) One of the advantages of the Taguchi method is that it minimizes the variability around the tar-get when bringing the performance value to the tartar-get ones Another advantage is that the optimum working conditions deter-mined from the laboratory can also be reproduced in full scale production

Use Rene-LCPC to calculate the experimental packing density of the binary mixture

YES

NO

Calculate fine and coarse aggregate content, according to (2) and (3)

Calculate cement

content: C=fc’/0.14

Select W/C according

to Fig 14

Calculate silica fume:

SF/(SF+C)=0.10 And (W/b)max=0.45 Use marsh cone to obtain the

optimum dosage of SP

SCC

Measured properties>required ones?

Fig 13 Mixture design procedure of Sebaibi’s method.

0

10

20

30

40

50

60

0.2 0.3 0.4 0.5 0.6 0.7

W/C

Age 28d

Fig 14 Relationship between compressive strength and water-to-cement ratio.

YES NO

Select materials Physical characterization tests Determine of aggregate

substitution ratio

Measure particle packing:

Void volume; Particle packing

Select of correction lubrication factor Determine aggregate and

cement content

Determine paste volume

Determine water and additional powder content

Verification test - Trial mix Excess paste effect

Check with

Bouziani et al [53] developed a mixture design method to

evaluate the effects of three types of sand including river crushed

and dune sand, in binary and ternary combinations, on properties

of fresh and hardened SCC A simplex-lattice mixture design with

three factors and five levels was carried out All other SCC

compo-nents (coarse aggregate, cement, addition, superplasticizer and

water) were kept constant The simplex-lattice design is a space

filling design that creates a triangular grid of combinations, as

shown in Fig 16, where the number of combinations (C) is

expressed by the following equation:

where q is the number of factors and m is the number of levels When three factors and five levels are considered, the number of combinations to be treated is 21

A mathematical model describing the effects of three sands and their combinations on given property can be established using this approach A second-degree model was used with three non-independent variables (proportions of RS, CS and DS) and five levels, as expressed as follows:

Y ¼ b1 RS þ b2 CS þ b3 DS þ b4 ðRS  CSÞ þ b5 ðRS  DSÞ

The model’s coefficients (bi) represent the contribution of the associate variables on the response Y, which were determined by

a standard least-square fitting using statistical software Although this method is accurate and avoids extensive repeated experiments,

it refers to specialized statistics knowledge, which makes it difficult for people to follow without this basic knowledge

The factorial design approach is valid for a wide range of mix-ture proportion and provides an efficient means to determine the influence of key variables on SCC properties Such understanding can facilitate the test protocol required to optimize SCC, hence reduce the effort necessary to optimize specified concrete to secure balance between various variables affecting flowability, deforma-bility, stability and strength However, establishment of statistical relationships needs intensive laboratory testing on available raw materials

2.5 Mixture design method based on rheology of paste model Saak et al.[54]developed a ‘‘rheology of paste model’’ to design SCC The method proposed that the rheology of the cement paste

Fig 16 Illustration of the simplex-lattice design with three factors (RS, CS and DS)

and five levels (Fig 1 in Ref [53] ).

If no OK

Adjusted

Adjusted Unsatisfactory

Fresh SCC

Solid phase (fine and coarse aggregates)

Design and Construction criterion

Liquid phase (cement, air and admixtures)

Criteria for liquid phase (paste model)

Criteria for solid phase (aggregate blocking model)

Water to binder ratio, Minimum paste volume, Coarse - total aggregate ratio

Final mixture proportion (High performance and economic efficiency)

Concrete trial

Paste rheology

Adjust W/B

or paste volume

Superplasticizer

matrix largely dictated the segregation resistance and workability

of fresh concrete, given a specified particle size distribution and

volume fraction of aggregate The applicability of the method is

tested by measuring the flow properties of fresh concrete

Additionally, it is proposed that a minimum paste yield stress

and viscosity must be exceeded to avoid segregation under both

static (rest) and dynamic (flow) conditions, respectively

Bui et al.[55]extended Saak’s concepts to include the effects of

aggregate (and paste) volume ratio, particle size distribution of the

aggregates and fine to coarse aggregate ratio These factors,

together with the aggregate shape, influence the void content

and the average diameter of the solid skeleton particles The

aver-age diameter of the solid skeleton particles is defined as:

dav¼

P

idimi

P

imi

ð6Þ

where diis the average diameter of aggregate fraction i and miis the

mass of that fraction

A minimum volume of cementitious paste is needed to fill the

voids between the aggregate particles and create a layer

envelop-ing the particles, thick enough to ensure the required deformability

and segregation resistance of concrete Hence, the average

aggre-gate spacing dss[56], defined as twice the thickness of the excess

paste layer enveloping the aggregates:

dss¼ dav

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

1 þ Vpaste Vvoid

Vconcrete Vpaste

3

s

 1

ð7Þ

This can be hence regarded as an indicator of the degree of sus-pension of the given solid skeleton The rheological properties of the paste (yield stress and viscosity) have to be optimized with respect to the average aggregate diameter and as a function of the aggregate spacing The procedure of this method is shown in Fig 17

The paste rheology model and criteria related to aggregate spac-ing and average aggregate diameter can be applied for different coarse-to-total aggregate ratios, cement contents, and water-to-binder ratios as well as different contents and types of fly ash The paste rheology model can reduce the extent of laboratory work and materials used, and provide the basis for quality control and further development of new mineral and chemical admixtures Farrara et al.[57]proposed a method for steel fiber-reinforced SCC based on the paste rheology model The applicable fibers are treated as an ‘‘equivalent spherical particle’’ fraction, with 100% passing fraction at an equivalent diameter, deq-fibers, defined through the specific surface area equivalence:

deq-fibers¼ 3Lf

1 þ 2L f

d f

cfiber

Optimally graded solid skeleton for the given paste/solid ratio

Select raw materials for cement paste

Select fine and coarse aggregate, and fibers

Model for rheological behavior

of cement paste:

Mini-cone flow test: rheometer test

Optimal grading of solid skeleton:

Average diameter of particle: dav Measure void ratio: Vvoid

Assess paste volume ratio Vp Assess solid volume ratio Vsolid

Assess correlation between cement paste rheology, solid skeleton gradation and paste/solid volume ratio

Identify allowable values of dss for self-compactability

Select paste/solid volume ratio

Identify optimum rheological properties

of cement paste and select its composition

Mix-design of SCSFRC

Average spacing of solid particles dss

Fig 18 Flow chart for mixture design of SCSFRC (modified based on Ref [57] ).