mix design of normal concrete considering maximum density & min cement content

Wang et al. / J Zhejiang Univ-Sci A (Appl Phys & Eng) in press

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Journal of Zhejiang University-SCIENCE A (Applied Physics & Engineering) ISSN 1673-565X (Print); ISSN 1862-1775 (Online) www.zju.edu.cn/jzus; www.springerlink.com E-mail: [email protected]

Mix proportioning of normal concrete considering maximum packing density and minimum cement content: a fuzzy approach

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Jafar SOBHANI†1, Ali Akbar Shirzadi JAVID2, Parviz GHODDOUSI2 (1Department of Concrete Technology, Building and Housing Research Center, Tehran 13145-1696, Iran) (2School of Civil Engineering, Iran University of Science and Technology, Narmak, Tehran, Iran) †

E-mail: Jafar [email protected]; [email protected]

Received Feb. 13, 2012; Revision accepted May 8, 2012; Crosschecked

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Abstract: Concrete mix proportioning could be referred to as the process of determining the quantities of concrete ingredients, using local materials, to achieve the specific characteristics of the concrete. Among the most important parameters affecting the performance of concrete are the packing density and corresponding grading curve of aggregates. Better packing of aggregates improves the properties of concrete such as strength, durability, elastic modulus and creep. Also with the increase of packing density, cement content could be reduced, which results in less damage to the environment. This paper presents the development of a novel technique for mix proportioning of normal concrete considering higher packing density and lower cement content. The proposed system utilizes four sub-fuzzy systems to quantify the concrete mixture properties including target compressive strength, water to cement ratio, ideal grading curve and free water. The obtained results with proposed fuzzy systems were compared with the concrete mix proportioned by field experts and were found to be remarkably close to each other. Also the proposed system has less cement and higher packing density of aggregate compared with other mix proportioning methods. Key words: Concrete mix proportioning, Packing density, Modeling, Fuzzy systems. doi:10.1631/jzus.A1200040 Document code: A CLC number:

1 Introduction

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Concrete as the most important material for a construction process is usually made by a mixture of fine aggregate, coarse aggregate, cement, water and admixtures. This material could become hard both in the air and water. Concrete is one of the most popular building materials and engineering materials considering inorganic nonmetallic materials, and is popularly used in construction, water conservation , roads, petroleum, chemical engineering and military engineering applications etc. Concrete mix design could be defined as the process of selecting suitable ingredients of concrete and determining their relative proportions. This process is based on sound technical principles and heuristics and the object of

© Zhejiang University and Springer-Verlag Berlin Heidelberg 2012

proportioning is attaining required strength and durability of concrete (ACI 211.1, 1997; Nataraja et al., 2006; Akhras et al., 1994; Mohd et al. 2005) Today, many researchers believe that planning concrete mix design is an art and it extremely depends on the expert who wants to provide the mix design. It is important to stress that there are many uncertainties in the concrete mix proportioning. Some of these uncertainties are: compressive strength, water to cement ratio, cement content, level of workability, quality of work shop and durability of concrete (Tesfamariam et al., 2007; Simon, 2003). In this regard, suitable methods are needed in order to handle the involved linguistic and probabilistic nature of concrete mix proportioning. Fuzzy set theory was inspired by Zadeh (Zadeh, 1967) in 1965 as a natural way of dealing with the imprecision and uncertainty that is often present in real-world applications (Tanyildizi, 2009; Akkurt et al., 2003). Here,

Deng et al. / J Zhejiang Univ-Sci A (Appl Phys & Eng) 2011 12(8):605-615

2 Components of proposed fuzzy system In this research, the needed parameters for concrete proportioning were stated as fuzzy sets in various sub-fuzzy systems. Fig.1 shows a schematic of fuzzy system interfaces to determine the concrete ingredients. It could be seen that the proposed model utilizes four sub-fuzzy systems as follows:  Target compressive strength fuzzy system (TCSFS), for quantifying the target compressive strength of concrete.  Water to cement ratio fuzzy system (WCRFS), for determining the water to cement ratio of concrete  Ideal grading curve fuzzy system (IGCFS), to quantify and draw the ideal grading curve and then estimate the volume of coarse and fine aggregate  Free water fuzzy system (FWFS), for estimating the free water of concrete The choice of the membership functions is based on the experiences gained, and their base values were selected so that they were concentrated on more sensitive regions (Ozcould et al., 2009). Taking into account the experience of experts that have the experience of concrete mix design for several years, trapezoidal or triangular membership function was used. All of the sub-fuzzy systems are of Mamdani-type with And method: min, Or method: max, Implication: min, Aggregation: max, Defuzzification: Centroid. Matlab software and its fuzzy logic toolbox are also utilized in order to implement the inference system of fuzzy logic.

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uncertainties do not mean random, probabilistic and accidental variations, which are related to the numerical data. Fuzzy set theory provides a regular calculus and performs numerical computation by using linguistic labels stimulated by membership functions (Sardemir et al., 2009, Topcu et al., 2008). Therefore, one of the best existing methods to realize this goal is to apply the fuzzy logic. In 1974, Mamdani (Mamdani, 1976), by exerting Zadeh’s theories and fuzzy inference system, successfully used the ‘IF-THEN’ rules on the automatic operating control of a steam generator (Tanyildizi, 2009, Ozcould et al., 2009). Today, the fuzzy logic is widely applied in various sciences because of its high capability of defining uncertain properties and it’s also being used widely in civil engineering (Saltan et al., 2007; Anoop et al., 2002; Sobhani and Ramezanianpour, 2011; Anoop et al., 2007; Zhao and Chen, 2001; Sasmal et al., 2006). In this paper, a fuzzy approach is presented in order to proportion ingredients of concrete. Recently, concrete technology experts have tended to proportion concrete with high value of aggregates packing density and, consequently, less amounts of cement because of the world’s yearly cement production of 1.6 billion tons accounts for about 7% of the global loading of carbon dioxide into the atmosphere (Ji, 2006; Wong and Kwan, 2006). Also Portland cement is one of the most energy-intensive materials of construction. Therefore production cost and resource consideration will require us to minimize Portland cement use while meeting the future demands for more concrete. This must be the top priority for a viable concrete industry as a part of sustainable development (Mehta, 1999; Mehta, 2001). Hence in this research, an ideal grading curve based on fuzzy system is attained and then, proper volumes of coarse and fine aggregates fully compatible with this curve are determined. In this way, the packing density of the aggregates could be increased and the amount of cement could be decreased. As a result, a type of concrete is produced, which has a reduced environmental impact. (Mehta, 2001). This is one of the concrete proportioning advantages that is proposed here. Description of fuzzy inference model is given in section 2. Results and discussions are presented in section 3. Conclusions are presented in section 4.

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3. Proposed fuzzy systems 3.1. Target compressive strength sub-fuzzy system (TCSFS) TCSFS is defined to determine the target compressive strength of concrete at the age of 28 days. The quality of produced concrete and the workshops (S) and the given compressive strength (fc) were the inputs of this sub-fuzzy system and its output was fcm. Defined set for fuzzy label S is as follows: S= {High Quality, Moderate Quality, Low (1) Quality} Also fuzzy label fc, is defined as the following set:


(2)

where fc=16 represents needed an approximate specific compressive strength of 16 Mega Pascal at the age of 28 days. The output fuzzy label (fcm) is defined in following set: fcm = { 21, 24, 27,30,33,36,39,42,45,48,51}

(3)

IF S is High quality AND fc is around 30 THEN fcm is around 37.

Membership functions for inputs and output parameters used for TCSFS Fuzzy system are given in Fig. 2.

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18 rules were written for this fuzzy inference system. All of these rules are discussed by consulta-

tion with specialists and experts who have experience of 20 years in concrete mix design. For example one of these rules was:

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fc= {16, 20, 23, 26, 30, 35, 38}

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Fig. 1. Schematic representation of fuzzy system for proportioning of concrete ingredients

Fig. 2. Designed fuzzy system for determining target compressive strength (TCSFS)

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3.2. Water to cement ratio sub-fuzzy system (WCRFS)

gate grading curve should be modified by so called Fuller-Thompson relation tunable by specifying power parameter n as follows:

In this sub-fuzzy system water to cement ratio (w/c) is determined. The first input here was target compressive strength (fcm) which was determined from TCSFS. The second input was the cement type that its fuzzy label set is defined as follows:

P

(4)

For instance, C325 shows that the compressive strength of cubic cements mortar has been about 325 kg/cm2, during 28 days. Third input of sub-fuzzy system was the shape of aggregates which its fuzzy label is defined in the following set: (5)

where P is cumulative passing percentage from each sieve size, d is sieve size and D is maximum size of aggregates (MSA). Parameter n could be specified such that the grading curves the ideal one for maximum packing density and determination of fine to coarse aggregate ratio. It is known that this process improves the concrete properties like workability, compressive strength and durability indexes (Abdel-Jawad and Abdullah, 2002). In Fig. 4, a schematic of the ideal grading curve fuzzy system (IGCFS) is shown. Having two input parameters including maximum aggregate size and regarded slump level, and one output representing appropriate parameter n, pseudo trapezoidal fuzzy membership functions for input parameters and output parameter is shown in Fig. 4. The fuzzy label set of maximum size of aggregates (MSA) and slump level and n parameters are defined as follows:

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Shape of aggregates= {Rounded, Sub-Angular, Angular}

Fourth input of sub-fuzzy system was the environmental condition. The fuzzy label set for this input is defined as follows: Environmental condition= {Mild, Moderate, Severe, Very Severe}

(6)

Consequently, the output fuzzy label set of systems is defined as follows:

(7)

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w/c= {0.3, 0.31, 0.32, 0.33,……….., A0.57, A0.58, A0.59, A0.6}

Membership functions for inputs and output fuzzy labels used for WCRFS system are shown in Fig. 3. It could be mentioned that 648 rules were defined for WCRFS system. A sample of them is: IF fcm=Around 32 AND cement type=C425 AND shape of aggregates=sub-angular AND environmental condition= severe THEN w/c is 0.45.

3.3. Ideal grading (IGCFS)

curve

sub-fuzzy

system

Considering maximum packing density, aggre-

(8)

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Cement Type= {LC325, C325, C425, C525, HC525}

 d  n  0.075  n         n  D    D   0.075  1    D  100%

MSA= {9.5, 12.5, 19, 25, 37.5}

(9)

Slump level= {S1, S2, S3, S4}

(10)

n= {0.1, 0.15, 0.2, 0.25, 0.3, 0.35, 0.4, 0.45, 0.5, 0.55, 0.6, 0.67}

(11)

25 rules were defined, which the following is a sample rule: IF MSA= 125 and slump=S2 THEN n=0.38

After determining the value of n in this sub-fuzzy system and utilizing in the Fowler-Thompson (Eq. (8)), the ideal grading curve could be gained as depicted in Fig. 5 assuming that maximum size of aggregates is 19 millimeter and value of n=0.35.

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Fig. 3. Designed fuzzy system for determining water to cement ratio (WCRFS)

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Fig. 4. Designed fuzzy system for determining ideal grading curve (IGCFS)

Fig. 5. Grading curve drawn for n=0.35

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Now, it is possible to determine the percentage of volume of coarse and fine aggregates in a way that it gets it as close as possible to this curve. 3.4. Free water fuzzy system (FWFS) FWFS is defined to determine the free water of concrete. The fineness modulus of aggregates (F.M.) according with ASTM C136 and target slump value and shape of aggregates were the inputs of this sub-fuzzy system and free water of concrete was its output. Defined fuzzy label set for F.M. and free water of concrete are as follows: (12)

Free Water= {103, 113, 123, 133,………, 273, 283, 293, 303}

(13)

75 rules were defined in this fuzzy inference system. A sample of this is as follows: IF F.M. is 0.4 AND slump is S3 AND shape of aggregates is sub-angular THEN Free Water is 226.

Considering the determined water to cement ratio and the amount of free water, the amount of cement could be calculated through the following equation: Cement content= amount of free water/ water-cement ratio

(14)

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If the content of cement and free water calculated in this stage of the mix design is higher than those contents required to provide structural details and durability of concrete element, then it can be reduced by using a suitable superplasticizer in a constant water to cement ratio and slump. At the final stage, the weight of aggregates (Wagg) could be defined from the following formula:

(15)

In the case of applying other admixtures in producing concrete, they could also be placed in equation (15). Note that in this equation, the amounts of Pagg, Pcem and Pwater were respectively the specific gravity of aggregates in saturated condition with dry surface, specific gravity of cement and density of water which are obtained through performing some tests before starting the mix design. Membership functions for inputs and output parameters used for IGCFS Fuzzy system are given in Fig. 6. 3.5. Modification of mix design in the laboratory or the site

After preparing a concrete mix design by the proposed fuzzy system, the resulting mix design must be made real on the site or the laboratory and fresh concrete testing like slump test should be done. If the value obtained with the slump test and the target slump value (as an input in the water to cement ratio sub-fuzzy system (WCRFS)) are different, then some modification should be applied in the mix design to achieve the desired result as follows:

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F.M. = {3, 3.5, 4, 4.5, 5, 5.5, 6, 6.5, 7}

(Wagg/Pagg) + (Wcem/Pcem) + (Wwater/Pwater) + (Vair) =1

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IF the slump test value is less than the target slump value, THEN one of the following actions are performed

o One percent is added to the water to cement ratio and then the modified amount of cement and aggregates are calculated from equations 14 and 15. Although it may be observed that a little decrease in the compressive strength of concrete occurs with this measure. o The small amount of plasticizer admixtures use in concrete to adjust the slump value on site or laboratory. o If the slump test value is higher than the target slump value, then one percent is decreased from water to cement ratio and the modified amount of cement and aggregates are calculated from equations 14 and 15.

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Table 1 General inputs required for creating a mix design

Maximum size of

Specific compressive strength

Target slump

Quality of

Aggregate

Mix

aggregate (mm)

(MPa) at 28 days

(mm)

workshop

shape

Mix 1 Mix 2 Mix 3 Mix 4 Mix 5 Mix 6

19 19 9.5 37 25 25

20 30 20 30 35 25

70 140 70 100 90 120

Low Quality High Quality Low Quality Moderate QualHigh Quality Low Quality

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Rounded Sub-Angular Rounded Sub-Angular Angular Rounded

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Fig. 6. Designed fuzzy system for determining the free water (FWFS)

Fig. 7. Cement content calculated by proposed fuzzy model and ACI method

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Table 2 Comparison of mix design of fuzzy model with those specified by expert

Cement (kg/m3) 313

Coarse aggregate (kg/m3) 928

Fine aggregate (kg/m3) 928

Free water ( kg/m3) 164

Expert

0.530

310

941

923

164

Fuzzy model

0.48

404

1025

683

194

Expert

0.49

404

1020

687

198

Mix 3

Fuzzy model

0.53

358

439

1318

190

Expert

0.53

356

441

1312

189

Mix 4

Fuzzy model

0.55

322

1134

644

177

Expert

0.55

320

1137

645

176

Mix 5

Fuzzy model

0.415

400

1154

628

166

Expert

0.42

400

1149

631

168

Mix 6

Fuzzy model

0.485

353

1059

718

171

Expert

0.48

350

1063

723

168

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Mix 2

Table 3 Laboratory results of compressive strength and slump values of mix design by fuzzy model

Mix Mix Mix 2 Mix 3 Mix 4 Mix 5 Mix 6

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Water to cement ratio 0.525

Concrete mix design Mix 1 Fuzzy model

compressive strength (MPa) at 28 days 21 32 23 30 38 26

slump (mm) 74 143 72 103 88 119

The results of compressive strength and slump tests of mixes that is designed by fuzzy model are presented in Table 3. Comparing these results with the target values in Table 1 shows that the fuzzy model is able to provide a mix design in accordance with the plan. Furthermore, it is able to attain the target values of compressive strength and slump. For example, the target values of compressive strength and slump for mix 2 are 30 MPa and 140 mm in accordance with Table 1; while the laboratory results for this parameters for the mix 2 are 32 MPa and 143 mm.

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4. Results and discussion

4.1. Validation and feasibility of fuzzy system In order to evaluate the feasibility of the proposed fuzzy inference system, samples of concrete mix design are compared with a traditional method (ACI method) provided by an expert through. Table 1 shows inputs required for creating a mix design. Results of a concrete mix proportioned using proposed fuzzy model and also results from a traditional mix, designed by concrete technology experts, are presented in Table 2. As seen in Table 2, the values associated with the concrete ingredients designed using fuzzy system are in a good agreement with the ingredients proportioned by an experienced concrete technology expert.

4.2. Comparison of proposed system based on packing density As it was mentioned, today, concrete technology experts and civil engineers are focused on using lesser amount of cement and thus decreasing harmful effects on the environment. In order to achieve this goal, grading of the aggregates must be done in a way that creates the least amount of voids between the aggregates and maximizes the volume of the solid grains (aggregates) which is also known as "packing density" (Abdel-Jawad and Abdullah, 2002; Pofale and Deo, 2010; Kwan and Fung 2009; Shen, 2010; Brouwers and Radix, 2005). Hence, the value of aggregate packing density (according to the standard


5. Conclusions

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In this study, fuzzy systems were proposed for mix design of normal concrete considering the maximum packing density and minimum cement content. Based on the findings of this research, the following conclusions can be drawn from the research: 1- Due to the involvement of various uncertainties like linguistic terms, the application of fuzzy systems is an excellent approach on mix design of concrete. 2- Results of modeling with the proposed fuzzy system are found to be satisfactory and fully in agreement with the results of concrete mix design specified by field experts of concrete technology. Therefore it could be inferred that the proposed fuzzy model is a reliable one. 3- Comparison of the results gained by the proposed system considering the ideal aggregates grading curve with traditional ACI mix design method, revealed that by application of the proposed system, the amount of cement used could be decreased and on the other hand, the amount of packing density would be enhanced which means more aid in reducing pollution of cement production and also improvement of concrete durability.

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test method for bulk density (“unit weight”) and voids in aggregate (ASTM, 1998)) and the cement content used in the mix proportioned from fuzzy system, with those of American Concrete Institute (ACI 211.1, 1991) method presented in (Table 4). The reason for choosing the ACI mix design method for this comparison is that, this method is one the most common and customary methods employed for this purpose. As illustrated in this paper, the packing density value by proposed the fuzzy system is greater than the packing density resulting from the ACI method. Moreover, the cement content used in the mix design by the fuzzy system is less than its content by the ACI method (Fig. 7). The reason for this difference is that as a part of the fuzzy model (used in this research), a method is employed by means of which, after calculating and drawing the ideal grading curve in the mix design (by calculating the value of parameter "n" and using its associated equation), it is possible to choose a volume for coarse and fine aggregates that is most compatible with this curve. In addition, voids created between aggregates in this method are also less than the ACI mix design method. As a result, packing density of aggregates and the amount of cement in the proposed fuzzy model are respectively more and less than those of other methods.

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Table 4. Voids percent and packing density of aggregates

Fuzzy system

Condition

Voids (%)

Packing density

Loose

0.301

0.699

Rodded

0.228

0.772

Mix 3

Mix 2

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Mix 1

Aggregate mix

ACI

Fuzzy system ACI

Fuzzy system ACI

Loose

0.304

0.696

Rodded

0.243

0.757

Loose

0.284

0.716

Rodded

0.228

0.772

Loose

0.298

0.702

Rodded

0.237

0.763

Loose

0.300

0.700

Rodded

0.237

0.763

Loose

0.304

0.696

Rodded

0.245

0.755

Acknowledgements

The authors gratefully acknowledge Dr. Mohsen Tadayon and Dr. Hormoz Famili for providing the needed data and prescribing the concrete mix designs for this study and their valuable comments on this paper. References

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mix design of normal concrete considering maximum density & min cement content

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