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.

Construction and Building Materials 84 (2015) 387–398 Contents lists available at ScienceDirect Construction and Building Materials journal homepage: www.elsevier.com/locate/conbuildmat Review 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 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 Introduction Mixture design methods 2.1 Empirical design method 2.2 Compressive strength method 2.3 Close aggregate packing method 2.4 Mixture design method based on statistical factorial model 2.5 Mixture design method based on rheology of paste model Conclusions Acknowledgement References Introduction Self-compacting concrete (SCC) is a special type of concrete which can be placed and consolidated under its own weight without any vibration effort due to its excellent deformability, and which at the same time is cohesive enough to be handled without ⇑ Corresponding author Tel./fax: +86 731 8882 3937 E-mail address: cshi@hnu.edu.cn (C Shi) http://dx.doi.org/10.1016/j.conbuildmat.2015.03.079 0950-0618/Ó 2015 Elsevier Ltd All rights reserved 387 389 389 390 391 393 395 397 397 397 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 388 C Shi et al / Construction and Building Materials 84 (2015) 387–398 Table Summary of existing mixture design methods for SCC in the literatures Classification Authors Year Main features Refs Empirical design method Okamura, and Ozawa 1995 [34] Edamatsa, Sugamata, and Ouchi Domone 2003 Fix coarse and fine aggregate first, and then obtain self-compactability by adjusting W/B and superplasticizer dosage Use mortar flow and mortar V-funnel testing to select the fine aggregate volume, volumetric water-topowder ratio and superplasticizer dosage For a given set of required properties, make the best estimation of the mixture proportions, and then carry out trial mixes to prove Conduct in three phases, i.e paste, mortar and concrete Based on the ACI 211.1 method for proportioning conventional concrete and the EFNARC method for proportioning SCC Use GGBS in SCC based on the strength requirements and consider the efficiency of GGBS [39] Use Densified Mixture Design Algorithm (DMDA), derived from the maximum density theory and excess paste theory Mainly based on the void content and the blocking criteria [42] 2009 Khaleel and Razak 2014 Compressive strength method Ghazi, and Al Jadiri 2010 Dinakar, Sethy, Sahoo 2013 Close aggregate packing method Hwang, and Tsai 2005 Petersson, Billberg, and Van Su, Hsu, and Chai Sedran, and De Larrard Shi, and Yang 1996 Sebaibi, Benzerzour, Sebaibi, and Abriak Kanadasan and Razak 2013 Khayat, Ghezal, and Hadriche Ozbay, Oztas, Baykasoglu, Ozbebek Statistical factorial model Rheology of paste model 2001 1996 2005 [38] [37] [33] [43] Use packing factor (PF) to control the content of fine and coarse aggregate in mixture proportion Use software to design SCC based on the compressible packing model (CPM) Use a combination of the excessive paste theory and ACI guidelines to design self-consolidating lightweight concretes Based on FN EN 206-1 standard, compressible packing mode (CPM) and packing factor (PF) [44] [46] [3] 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] 1999 Obtain a statistical relationship between five mixture parameters and the properties of concrete [49] 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) 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 [52] Avoid segregation of the aggregates as a critical design parameter, then a new segregation-controlled design methodology is introduced for SCC 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 Steel fiber-reinforced self-compacting concrete based on the paste rheology model [54] Bouziani 2013 Saak, Jennings, and Shah Bui, Akkaya, and Shah 2001 Ferrara, Park, and Shah 2007 2002 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 NO [36] Measured properties > required ones˛ YES SCC Fig Mixture design procedure proposed by Edamatsa 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 [47] [53] [55] [57] 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 formwork and completely fill all spaces under its own weight; (2) passing 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 requirements 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 materials, 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 modified Brouwers’ method exhibited satisfied workability with recommended 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 aggregates have been used in SCC [26–28] It is reported that the strength of SCC improved with the increasing content of superplasticizer C Shi et al / Construction and Building Materials 84 (2015) 387–398 Flowability test of cement paste: Flowability test of cement mortar: Determine water demand; Determine optimum sand content 389 Determine optimum SP dosage Control mortar Metakaolin mortars Absorption of mortar mixtures Setting time test Compressive strength of mortar Flowability & filling ability of mixtures: Determine the mortar mixtures: Determine optimum replacement level of optimum SP dosage and replace powder mortars different level of pozzolan Control Concrete Optimum MK Concrete Fresh tests of concrete mixes: Accepted results according to Slump flow cone, V-funnel box, typical acceptance criterion L-box, and segregation sieve for SCC Fig Flow chart of mixture design procedure of the approach proposed by Khaleel (modified based on Ref [37]) Specify concrete properties: Filling ability, passing ability and Segregation resistance Materials information Recommend of uniform criterion, specific design parameters or factors to evaluate 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 categories 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 scientific bases for selection of suitable mixture design methods of SCC Coarse aggregate content Vca values Mixture design methods Fine aggregate content: Vfa (%)=0.45(100-Vca) Paste volume: Vpa (%)=100-Vca-Vfa W/P and SP dosage: the spread and V-funnel tests Trial concrete mixtures Fig Mixture design procedure of UCL method (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 significantly 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 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 aggregate 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 mixtures 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 literatures are summarized in Table 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 390 C Shi et al / Construction and Building Materials 84 (2015) 387–398 Required Maximum weight of W/C, water and compressive water and air content cement contents strength of Gravel content NO SCC Measured Powder content Fine aggregate content properties>required ones ? YES SCC Fig Mixture design procedure of the method proposed by Ghazi Table SCC compressive strength versus W/C (Table in Ref [39]) fc (MPa) W/C 15 0.8 20 0.7 25 0.62 30 0.55 35 0.48 40 0.43 material contents and superplasticizer dosage to determine the initial mixture proportions The best estimates of the mixture proportions 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 following 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 selfcompactability This approach is very easy to follow, but there were no parameters describing the properties of aggregate In order to obtain higher workability and moderate viscosity, higher dosage of superplasticizer must be used, which could result in retarding of concrete 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 shows 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 Select components 45 0.38 50 0.35 55 0.34 60 0.33 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 Fix the GGBS percentage Determine water and calculate efficiency content of content of GGBS at 28 days mixture NO Check with YES Go for the development of SCC 75 0.29 2.2 Compressive strength method or cementitious EFNARC guidelines 70 0.31 with coarse aggregates of different properties The mixture design procedure is shown in Fig 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 shows the procedure of this method In this method, only standard tests for fresh concrete are needed and other complicated 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 satisfactory mixture proportions Besides that, changes in raw materials will need intensive re-testing and adjustments Fix the total powder Re-design mixture 65 0.32 Determine sand/total Determine superplasticizer dosage Trial mixtures and tests Determine final mixture on SCC properties composition aggregate ratio using standard gradation curves Fig Outline of the mixture design method for SCC containing GGBS (modified based on Ref [33]) 391 C Shi et al / Construction and Building Materials 84 (2015) 387–398 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 presented 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 minimizes the need for trial mixtures In addition, the proposed method takes into consideration the gradation of fine and coarse aggregates or the contributions of pozzolanic materials to the properties of concrete However, one of its weekness is that it requires adjustments to all ingredients like sand, coarse aggregate, superplasticizers and water, to achieve an optimal mixture proportion 2.3 Close aggregate packing method Fig The procedure of aggregate packing (modified based on Ref [42]) 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 in Fig The original ACI 211.1 method covers the design of compressive strength from 15 to 40 MPa However, this method expanded compressive strength range from 15 to 75 MPa for SCC, with maximum W/C as shown in Table This method also needs to use some relevant 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 in Fig 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 determined 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 This type of mixture design method determines mixture proportions 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 investigated [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 in Fig 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 by 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 in Fig 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 Select proper material source; Obtain the maximum density by Obtain material information iterative packing of aggregate Assign volume of paste Calculate the least void VV amount VP=nVV Calculate the volume of aggregate Vagg Determine the SP and water content Measured NO properties>required ones ? YES SCC Fig The gradation curves of three packing types (modified based on Ref [42]) Fig Mixture design procedure of the method proposed by Hwang 392 C Shi et al / Construction and Building Materials 84 (2015) 387–398 Construction Criteria 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 lubricating layer around each particle In this method, the risk of blocking was calculated using the following equation Blacking Criteria Void Content Paste Volume Risk of blocking ẳ Mortar volume 1ị where Vai is the volume of aggregate group i and Vabi is 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 in Fig 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: Coarse aggregate content, SP dosage Measured properties>required X ðV =V abi Þ NO ones ? YES Wanted SCC Fig Mixture design procedure of the method proposed by Petersson (modified based on Ref [43]) W r ¼ PF  W rL  ð1  S=aị W s ẳ PF  W sL  S=a to fill the void between aggregates and cement paste to attain ‘‘the least void’’ The procedure of this method is shown in Fig The SCC designed by the DMDA is high flowable, cost-effective and durable It overcomes concrete problems due to shape, particles distribution, 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 ð3Þ where Wr is the content of coarse aggregates in SCC (kg/m ); Ws is the content of fine aggregates in SCC (kg/m3); WrL is the unit volume mass of loosely piled saturated surface-dry coarse aggregates in air (kg/m3); WsL is the unit volume mass of loosely piled saturated 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 in Fig 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 Required workability Required strength Packing factor PF Water to cement ratio Wc/C Fine aggregate Coarse aggregate content Af content Ac Cement content C Water content Wc Pozzolanic paste volume Vpp Fly ash content F Water content Wf ð2Þ GGBS content S SP dosage Water content Ws Total water content W Fig 10 Mixture design procedure of method proposed by Su et al (Fig in Ref [45]) C Shi et al / Construction and Building Materials 84 (2015) 387–398 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 Measured NO properties>required ones ? YES Check rheological behavior Fig 11 Mixture design procedure of the method proposed by Sedran (modified based on Ref [46]) determine the optimum sand to aggregate ratio or the packing factor 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 process 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 in Fig 11 [46] The method focuses on optimizing the granular skeleton of concrete 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 lightweight 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 procedure of this method is shown in Fig 12 The designed SCLC mixtures 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 in Fig 13 The W/C was selected accoring to Fig 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 in Fig 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 natural 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-topowder 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 conventional 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 Determine the void volume in the Determine optimum Determine cement content and dry binary aggregate mixtures combination of coarse W/C according to strength according to ASTM C29 and fine aggregates requirement and ACI 211.2, Determine mineral Determine volume of excess admixtures content paste through experiment NO Measured properties>required ones ? 393 YES SCLCs Fig 12 Mixture design procedure of the method proposed by Shi 394 C Shi et al / Construction and Building Materials 84 (2015) 387–398 Calculate fine and coarse Use Rene-LCPC to calculate aggregate the experimental packing Calculate content, cement content: C=fc’/0.14 according to (2) and (3) density of the binary mixture NO Select W/C according Measured YES SCC to Fig 14 properties>required ones ? Calculate silica fume: Use marsh cone to obtain the SF/(SF+C)=0.10 optimum dosage of SP And (W/b)max=0.45 Fig 13 Mixture design procedure of Sebaibi’s method Compressive strength/MPa Age 28d 60 50 40 30 20 10 0.2 0.3 0.4 0.5 0.6 0.7 W/C Fig 14 Relationship between compressive strength and water-to-cement ratio 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 Select materials 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/m3 of 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 target when bringing the performance value to the target ones Another advantage is that the optimum working conditions determined from the laboratory can also be reproduced in full scale production Physical characterization tests Determine of aggregate substitution ratio Determine aggregate and Select of correction Measure particle packing: cement content lubrication factor Void volume; Particle packing NO Determine paste volume Check with Determine water and EFNARC guidelines YES POC SCC Design additional powder content Verification test - Trial mix Excess paste effect Fig 15 Flowchart of achieving and verifying the mixture design for SCC using POC aggregate (modified based on Ref [48]) C Shi et al / Construction and Building Materials 84 (2015) 387398 Cẳ q ỵ m  1Þ! m!ðq  1Þ! 395 ð4Þ 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 nonindependent variables (proportions of RS, CS and DS) and five levels, as expressed as follows: Y ẳ b1  RS ỵ b2  CS ỵ b3  DS ỵ b4  RS  CSị ỵ b5  RS  DSị ỵ b6  ðCS  DSÞ Fig 16 Illustration of the simplex-lattice design with three factors (RS, CS and DS) and five levels (Fig in Ref [53]) 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 components (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: ð5Þ 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 mixture 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, deformability, 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 Fresh SCC Solid phase (fine and Design and Liquid phase (cement, air coarse aggregates) Construction criterion and admixtures) Criteria for solid phase Criteria for liquid phase (aggregate blocking model) (paste model) Water to binder ratio, Minimum paste volume, Coarse - total aggregate ratio Adjust W/B Adjusted or paste Paste rheology Superplasticizer volume Unsatisfactory Adjusted Concrete trial If no OK Final mixture proportion (High performance and economic efficiency) Fig 17 Flow chart for mixture design procedure using rheology models (Fig 13 in Ref [55]) 396 C Shi et al / Construction and Building Materials 84 (2015) 387–398 Select raw materials for Select fine and coarse cement paste aggregate, and fibers Model for rheological behavior Optimal grading of solid skeleton: of cement paste: Average diameter of particle: dav Mini-cone flow test: rheometer test Measure void ratio: Vvoid Assess paste volume ratio Vp Assess solid volume ratio Vsolid Average spacing of solid particles dss 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 Optimally graded rheological properties Mix-design of solid skeleton for the of cement paste and SCSFRC given paste/solid ratio select its composition Fig 18 Flow chart for mixture design of SCSFRC (modified based on Ref [57]) 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 average diameter of the solid skeleton particles is defined as: P di mi dav ẳ Pi i mi 6ị where di is the average diameter of aggregate fraction i and mi is 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 enveloping the particles, thick enough to ensure the required deformability and segregation resistance of concrete Hence, the average aggregate spacing dss [56], defined as twice the thickness of the excess paste layer enveloping the aggregates: "sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi # V paste  V void dss ¼ dav 1ỵ 1 V concrete  V paste 7ị This can be hence regarded as an indicator of the degree of suspension 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 spacing and average aggregate diameter can be applied for different coarse-to-total aggregate ratios, cement contents, and water-tobinder 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-fibers ¼ 3Lf cfiber ỵ dLf caggregate f 8ị C Shi et al / Construction and Building Materials 84 (2015) 387–398 where Lf and df are the length and diameter of the fibers, respectively, cfiber is the specific weight of fibers and caggregate is the weighted average specific weight of all the aggregates For the fiber-reinforced skeleton, the ‘‘average equivalent diameter of solid particles’’ can be expressed as: P dav ¼ i di mi P ỵ deq-fibers mfibers ỵ mfibers i mi ð9Þ where di, mi and deq-fibers are defined as above; mfibers is the mass of the fibers Optimization of rheological properties of cement paste and choice of its volume ratio stand as further keys of the method The model proved to be an efficient tool for designing fiber-reinforced SCC mixtures with selected fresh state properties, employing different ratios and types of steel fiber reinforcement The procedure of this method is shown in Fig 18 Conclusions Based on the extensive review on different SCC mixture design methods in the literatures, the following conclusions can be drawn: (1) The empirical design method is easy to follow However, intensive laboratory testing on available raw materials are needed to obtain satisfactory mixture proportions (2) The compressive strength method presents a clear and precise procedure to obtain specific quantities of ingredients and minimizes the need for trial mixtures Besides that, the gradation of fine and coarse aggregates, and contributions of pozzolanic materials to the properties of SCC is taken into consideration However, this method requires adjustments to all the ingredients to achieve an optimal mixture proportion (3) The close aggregate packing method mainly considers the relationships between paste and aggregate Hence, this method is simpler and requires a smaller amount of binders However, SCC produced based on this method tends to segregate easily, which is a problem for construction (4) The method based on statistical factorial model can simplify the test protocol required to optimize a given mixture by reducing the number of trial batches to achieve a balance among mixture variables However, establishment of statistical relationships needs intensive laboratory testing on available raw materials (5) The method based on rheology of paste model can reduce the laboratory work and materials, and provide the basis for quality control and further 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International RILEM symposium on selfcompacting concrete RILEM Publications SARL; 2003 [36] Edamatsu Y, Nishida N and Ouchi M A rational mix -design method for selfcompacting concrete considering... [34] Okamura H, Ozawa K Mix design for self- compacting concrete Concr Lib JSCE 1995;25:107–20 [35] Edamatsu Y, et al A mix -design method for self- compacting concrete based on mortar flow and funnel