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Lightweight concrete design using gene expression programing
Construction and Building Materials 139 (2017) 93–100
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Lightweight concrete design using gene expression programing Saeed Jafari a, Seyed Saeed Mahini b,⇑ a b
Department of Civil and Environmental Engineering, Shiraz University of Technology, Shiraz, Iran Discipline of Civil and Environmental Engineering, University of New England, NSW, Australia
a r t i c l e
i n f o
a b s t r a c t
Article history: Received 9 August 2016 Accepted 27 January 2017
The use of lightweight concrete (LWC) in earthquake resistant buildings is beneficial because of the weight and mass reduction of the structures. LWC has been used in the construction industry for many years and while attempts have been made to develop a practical and reliable code for lightweight concrete design worldwide a satisfactory, practical standard for mix design is required. There are a few standards which present methods for designing the mix of LWC such as ACI 211.2. However, in these standards the proposed compressive strength and density determinations cannot be used for all types of lightweight aggregates. The aim of this study is to provide references for three types of lightweight concretes containing clay and natural (mineral) pumice aggregates with the maximum nominal sizes of 12.7 mm (½ in.) and 19.2 mm (¾ in.) respectively. With this intent, hundred specimens of lightweight concrete were made and then tested in the laboratory using these aggregates. After presenting a standard for propositioning and adjusting propositions of the concrete mix three equations were derived using Gene Expression Programing (GEP) to obtain the compressive strength of a specific mixture. Comparison between the actual properties and their predicted counterparts indicated that the proposed derivations are a useful and reliable practical method for use by practicing engineers when designing lightweight concrete mixes. Ó 2017 Elsevier Ltd. All rights reserved.
Keywords: Lightweight concrete Lightweight concrete mix design Gene expression programming Derivations Compressive strength
1. Introduction Structural lightweight aggregate concrete is an important and versatile material for use in modern construction. It has many and varied applications including multistory building frames and floors, bridges, offshore oil platforms, and prestressed or precast elements of all types. Many architects, engineers, and contractors recognise the inherent economies and advantages offered by this material as evidenced by the many impressive lightweight concrete structures found today throughout the world [1]. For more than 80 years structural lightweight aggregate concrete has solved weight and durability problems in buildings and exposed structures [2]. Lightweight concrete has strengths comparable to normal weight concrete, yet is typically 25–35% lighter. Structural lightweight concrete offers design flexibility and substantial cost savings by providing: less dead load, improved seismic structural response, longer spans, better fire ratings, and thinner sections, decreased story height, smaller size structural members, less reinforcing steel, and lower foundation costs. Lightweight concrete
⇑ Corresponding author. E-mail addresses: (S.S. Mahini).
[email protected]
(S.
http://dx.doi.org/10.1016/j.conbuildmat.2017.01.120 0950-0618/Ó 2017 Elsevier Ltd. All rights reserved.
Jafari),
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precast elements offer reduced transportation and placement costs [3]. The use of lightweight structural concrete to reduce the weight of earthquake resistant buildings is useful material having many applications. Therefore, research on the properties of different types of lightweight concretes and the evaluation of the corresponding concrete strength has been considered by many researchers [4,5]. Research has been conducted worldwide on a large number of natural and artificial lightweight aggregates used in the manufacture of mortar and concrete. Natural lightweight aggregates include diatomite, pumice, scoria, sawdust, oil palm shells, bottom ash, and starch-based aggregates. Artificial aggregates include expanded shale, slate, perlite, sintered fly ash, bonded fly ash, solidified blast furnace slug, and vermiculite. Use of natural lightweight aggregates instead of processed artificial aggregates can significantly reduce the cost of such concretes [6]. Shannag [7] investigated the properties of fresh and hardened concretes containing locally available natural lightweight aggregates, and mineral admixtures. Test resulted indicated that replacing cement in the structural lightweight concrete developed, with 5–15% silica fume on weight basis, caused up to 57% and 14% increase in compressive strength and modulus of elasticity, respectively, compared
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S. Jafari, S.S. Mahini / Construction and Building Materials 139 (2017) 93–100
List of notation FC W S L C
is is is is is
the compressive strength of concrete water sand lightweight aggregate cement
to mixes without silica fume. In a study, the surface of large pumice aggregate was coated with cement + colemanite (CLM) dual mixtures (0%, 7.5%, 12.5% and 17.5%). Lightweight concretes were produced by using coated aggregates. Then by exposing to temperatures at 20 °C (Control), 200 °C, 400 °C and 600 °C, the unit weight, compressive strength, ultrasonic pulse velocity and weight loss of concrete samples were determined. As a result of the study, the optimum value was obtained from 12.5-CLM samples. It is determined that the lightweight concretes that would be produced with pumice aggregates coated with cement + colemanite dual mixture would have a high performance against high temperature [8]. Gene expression programming (GEP) is, like genetic algorithms (GAs) and genetic programming (GP), a genetic algorithm as it uses populations of individuals, selects them according to fitness and introduces genetic variation using one or more genetic operators [9]. The fundamental difference between the three algorithms resides in the nature of the individuals: in GAs the individuals are linear strings of fixed length (chromosomes); in GP the individuals are non-linear entities of different sizes and shapes (parse trees); and in GEP the individuals are encoded as linear strings of fixed length (the genome or chromosomes) which are afterwards expressed as non-linear entities of different sizes and shapes (simple diagram representations or expression trees) [10]. Through artificial neural networks and using ultrasonic pulse velocity Kewalramani and Gupta tried to predict the compressive strength of concrete and compared the results of neural networks and multiple variable regressions [11]. Through Programming in the MATLAB environment and considering the number of parameters of concrete Trtnik et al. provided a model for concrete compressive strength based on neural networks and using ultrasonic pulse velocity [12]. Also Mousavi et al. proposed a new model for predicting the compressive strength of high performance concrete using gene expression programming [13]. In another study Hadianfard and Jafari suggested some equations to predict compressive strength of lightweight aggregate concrete using the ultrasonic pulse velocity test through gene expression programming [14]. The purpose of this study is to provide three specific applicable references for selecting and adjusting mixture proportions for three types of lightweight concrete made using three different lightweight aggregates. Discussion in this study is limited to lightweight concrete containing clay, natural (mineral) pumices with the maximum nominal size of 12.7 mm (½ in.) and with the maximum nominal size of 19.2 mm (¾ in.) as lightweight aggregates. Structural LWC has an in-place density (unit weight) of the order of 1440–1840 kg/ m3 (90 –115 lb/ft3) compared to normal weight concrete with a density in the range of 2240 –2400 kg/m3 (140 –150 lb/ft3). For structural applications the concrete strength should be greater than 17 MPa (2500 psi) [15]. The concrete mixture is made with a lightweight course aggregate. In some cases a portion or the entire fine aggregates may be a lightweight product. Lightweight aggregates used in structural lightweight concrete are typically expanded shale, clay or slate materials that have been fired in a rotary kiln to develop a porous structure. Other products such as
LWA GEP GP GA
is is is is
the the the the
lightweight aggregate gene expression programming genetic programming genetic algorithm
air-cooled blast furnace slag are also used. There are other classes of non-structural LWC with lower density, made with other aggregate materials and higher air voids in the cement paste matrix, such as in cellular concrete [16]. Samples made by natural pumices are considered structural lightweight concrete and samples containing clay are considered nonstructural lightweight concrete. The use of pozzolanic and chemical admixtures is not covered in this study, nor do the samples include non-air entertained concrete. Lightweight concretes have been proportioned by the weight method described in ACI 211.2-98. The best approach to making a first trial mixture of lightweight concrete, which has given properties and uses a particular aggregate from a lightweight aggregate source, is to use proportions previously established for a similar concrete using aggregate from the same aggregate source. Such proportions may be obtained from the aggregate supplier and may be the result of either laboratory mixtures or of actual mixtures supplied to jobs. However, a purpose of this study is to provide a guide to proportioning a first trial mixture where such prior information is not available. Changing the lightweight materials in LWC changes other properties of LWC like compressive strength and density which is not predictable for all types of lightweight aggregates. Accordingly for each kind and size of lightweight aggregate a new standard is needed. In this paper by making different samples according to the standard described in ACI 211.2-98 three type of Iranian lightweight aggregates are studied and their new properties obtained through experiment in order to determine three new standards which can provide guidance in the selection of mix proportions having the required specified properties. Through gene expression programing three equations have been derived for all three kinds of concretes which predict the compressive strength of each kind of concrete according to their proportions. 2. Experimental program To study the above-mentioned issues three types of lightweight aggregate concrete were made and tested. The lightweight aggregates used were in compliance with the standard ASTM C330 [17] and determination of the lightweight aggregate concrete mixing ratio was based on standard ACI 211.2 [18]. Measuring, mixing, transporting, and placing operations for lightweight concretes are similar to the procedures for normal weight concrete. However, there are certain differences, especially in proportioning and batching procedures that should be considered to produce a finished product of the highest quality [19]. In this study more than 100 concrete samples have been tested. The batches were made in Shiraz University of Technology laboratory using the specific gravity method. The weight method procedure is applicable to sand-lightweight concrete comprised of lightweight coarse aggregate and normal weight fine aggregate. Estimating the required batch weights for the lightweight concrete involves determining the specific gravity factor of lightweight coarse aggregate and from this the first estimate of the weight of fresh lightweight concrete can be made. Also the absorption of lightweight coarse aggregate may be measured by the method
S. Jafari, S.S. Mahini / Construction and Building Materials 139 (2017) 93–100
described in ASTM C 127 [20]. When concrete was made with lightweight aggregates that have low initial moisture and relatively high rates of absorption they were mixed with one-half to two-thirds of the mixing water for a short period prior to the addition of cement to minimise slump loss. In addition the specific gravity of the lightweight aggregates were determined at the moisture content anticipated prior to use. For convenience each type of concrete mix was named. The concrete made of expanded clay was named lightweight aggregate (LWA)01, the concrete made of natural (mineral) pumices with the maximum nominal size of 12.7 mm was named LWA02, and the concrete made of natural pumices with the maximum nominal size of 19.2 mm was named LWA03. In all concrete mixes sand was used as the fine aggregate and expanded clay, mineral pumice size 12.7 mm or mineral pumice size 19.2 mm as the coarse aggregate.
3. Material properties and mix design Before any amendment the fineness modulus of the fine sand used was 3.46 which reached to 3 after sifting and amendment. For the experiments undertaken the sand moisture content was 1%. In the mix design the saturated surface dry (SSD) condition for the sand was 6% water. The specific gravity of the fine sand was 1717.65 Kg/m3, which was determined in accordance with ASTM C 29 [21]. In the standard ASTM C 330 there are some implications and requirements for gradation of lightweight aggregates. The gradation of aggregates was based on these requirements [17]. The lightweight aggregates used in this study were coarse aggregates with the sizes of 19.2 mm and 12.8 mm of mineral pumices and 9.6 mm for expanded clay. Specific gravity for the expanded clay was 365.72 Kg/m3. Also the specific gravity for mineral pumice with the nominal sizes of 12.7 mm and 19.2 mm was 693 and 653 Kg/ m3 respectively. For expanded clays and mineral pumices the humidity of the aggregates in the natural environment was zero in order to be used outside and exposed to the sun. Also for the experiments undertaken for the aggregates of expanded clays and mineral pumices to reach to the SSD condition 13% and 15% of water was needed respectively. Pycnometric specific density factor for expanded clays was 1.1. In addition the pycnometric specific density factor for mineral pumices with the sizes of 12.7 mm and 19.2 mm was 1.69 and 1.59 respectively. The proportioning follows a sequence of straightforward steps that, in effect, fit the characteristics of the available materials. The first step in the study was to choose a slump based on the type of construction being considered, which in this case, comprised beams, reinforced walls and buildings columns. The next step was to choose one of the maximum size of lightweight aggregates mentioned in previous paragraphs. Based in these two initial steps the appropriate amount of mixing water was determined. The fourth step involved selection of the approximate water-cement ratio based on the expected compressive strength of the concrete. Assessment of the cement content was the next step, with the amount of cement per unit volume of concrete being fixed by the decisions made in Steps 3 and 4. The next step was estimating the lightweight coarse aggregate content based on the maximum size of aggregates and volume of oven-dry loose coarse aggregates per unit volume of concrete for different fineness moduli of sand. With the quantities of water, cement, and coarse aggregate established, the remaining material, fine aggregate content, was estimated in the last step. The concrete mix designs and density of the hardened concretes are presented in the Table 1. All the weights are for making 1m3 of fresh concrete and all weights are based on saturated surface dry (SSD) aggregates.
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4. Experimental results The compressive strength of concrete is the most common performance measure used by engineers in designing buildings and other structures [22]. The compressive strength is measured by breaking cylindrical concrete specimens in a compression-testing machine [23]. For convenience a few cylindrical samples were made of WLA01, WLA02 and LWA03 in order to find coefficients which would convert the compressive strength results of cubic samples to that of cylindrical samples. Fig. 1 shows the hydraulic jack and the failed specimens of all three types of concrete. The measurement method of concrete compressive strength was assessed according to the standard ASTM C 39-83b [24]. Loading rate was considered constant ranging from 0.15 to 0.34 MPa/s. The laboratory velocity of 0.3 MPa/s was used to break the samples. The type of lightweight aggregate and its volume fraction in a mix determined the density of lightweight concrete [25]. Customarily the theoretical density is a laboratory determination; for which the value is assumed to remain constant for all batches made using identical component ingredients and proportions. It is calculated from ASTM C 138/C 138 M [23]. The compressive strengths and densities of samples of the hardened concretes are presented in the Table 2.
5. Factors affecting the compressive strength and density of lightweight concrete According to the Table 2 it can be seen that by increasing the maximum size of the lightweight aggregates the density and compressive strength decrease. The reason for this is that by increasing the maximum size of lightweight aggregates, the structure of the lightweight aggregate gets weaker and lighter. Concrete made by expanded clay is lighter and has a lower compressive strength and therefore can be used for nonstructural purposes. Conversely concrete made using pumice has a strength which makes it suitable to be used as structural concrete. The price of pumice is 20 percent of expanded clay but pumices need to be crushed to get standard sizes (12.7 mm and 19.2 mm). Accordingly concrete made using pumices are cheaper but more difficult to make. Fig. 2 shows diagrams for the average of the weight ratios of lightweight aggregate to all aggregates and the average of the concrete compressive strengths (MPa) for LWA01, LWA02 and LWA03 concrete (in SSD condition). This diagram indicates a clear relationship in relation to different mixes of lightweight concretes and their corresponding compressive strengths. By increasing the weight ratio of lightweight aggregate to all aggregates concrete compressive strengths decrease with an inverse relationship between them. In Fig. 3, the diagram shows that increasing the weight ratio of lightweight aggregates does not have a significant effect on density. This relationship was predictable because of the fact that all samples have been designed for a determined density and because by increasing the lightweight portion the amount of sand decreases and the amount of cement increases. Fig. 4 shows the relationship between the concrete compressive strength and the different water-cement ratios for all of the samples. This diagram indicates that increasing the water-cement ratio results in a decrease in the compressive strength of the concrete. The concrete mixing ratio of the samples were designed according to ACI 211.2 but the compressive strength and density do not correspond to those presented in the standard. It is obvious that as the type of lightweight aggregate changes the other properties of the concrete will change. In this regard this study provides three
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Table 1 Summary of the concrete mix design and density of the lightweight concretes. Name of samples
Type of LWA
Water Cement Ratio
WaterWW (kg)
CementWC, (kg)
SandWS, (kg)
LWAWL, (kg)
Density(kg/m3)
LWA01
Expanded Clay
0.4 0.6 0.8
210 230 210
525 380 260
710 835 975
155 155 155
1659 1529 1631
LWA02
Natural Pumice½ in
0.4 0.6 0.8
212 212 212
530 353 265
737 913 1002
371 371 371
1878 1898 1836
LWA03
Natural Pumice¾ in
0.4 0.6 0.8
212 212 212
530 353 265
619 795 884
539 539 539
1718 1840 1781
Fig. 1. (a) The hydraulic jack; (b) Failed LWA01; (c) Failed LWA02; (d) Failed LWA03.
references for lightweight concretes made by three types of lightweight aggregates. As the mix designs of these samples cover the whole standard range of concrete which may be made these references can be used instead of the methods presented in ACI 211.2 for concretes containing clay, natural (mineral) pumices with the maximum nominal size of 12.7 mm and natural pumices with the maximum nominal size of 19.2 mm as lightweight aggregates. 6. Comparing the mix design used in this study to other research results In experimental work by Bastos et al. [26] to introduce a method for the design of lightweight concrete with expanded clay aggregates 28 lightweight concrete sample mixes using four different quantities of cement (126, 155, 185 and 214 kg/m3) with densities between 853 and 1418 kg/m3 were made by expanded clay (LECA Portugal) and tested. In comparison with the study referred in this paper the size of the lightweight aggregates were smaller and in some samples they were used as fine aggregates. In Fig. 5, the results for both works are shown. Samples in the study referred to in this paper have higher densities and compressive strengths than those of the study by Bastos et al. [26]. In a paper presented by Yohannes [27] the use of Ethiopian pumice and scoria aggregates for lightweight concrete in ribbed
slab construction was described. The experimental program was aimed at studying design for the production of all-lightweight structural concrete and included full size ribbed slab testing. In this study, with the mix design explained in the paper, pumice cannot be used as structural concrete. The coarse aggregate and fine aggregate were respectively, scoria and pumice [27]. The selected water cement ratios for the mix design were 0.45–0.5 but in this study the water cement ratios were 0.4, 0.5, 0.6, 0.7 and 0.8. Table 3 shows the results from Yohannes’ study compared with this study. Fig. 5 and Table 3 shows that the mixes designs used in the study addressed in this paper proved that samples had higher compressive strength when the fine aggregates are normal sand and the coarse aggregates are lightweight materials although these samples are heavier in comparison to the results of other researchers. 7. Prediction of compressive strength of concrete by using GEP GP is a subset of genetic algorithms (GAs). It is a modern regression technique with a great ability to automatically evolve computer programs [28]. The evolutionary process followed by the GP algorithm is inspired from the principle of Darwinian natural selection. GP was introduced by Koza [29] in the late 1980 s after experiments on symbolic regression. This classical GP technique
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S. Jafari, S.S. Mahini / Construction and Building Materials 139 (2017) 93–100 Table 2 Compressive strength and density of samples. Comp. strength (MPa)
Density (kg/m3)
No. of sample
Comp. strength (MPa)
Density (kg/m3)
No. of sample
Comp. strength (MPa)
Density (kg/m3
No. of sample
Comp. strength (MPa)
Density (kg/m3)
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
15.15 12.55 12.43 7.6 9.21 14.01 12.84 12.16 9.52 6.95 13.87 10.39 11.82 9.76 8.95 15.42 13.68 12.84 9.98 8.51 15.79 13.75 13.19 12.29 10.33
1742.2 1724.1 1770.4 1597.3 1613.6 1689.2 1641.2 1601.5 1501.0 1660.7 1666.4 1665.5 1642.4 1664.6 1664.9 1743.4 1676.4 1693.3 1610.1 1647.1 1715.9 1642.7 1371.9 1675.9 1559.4
26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50
11.32 9.13 16.47 15.99 13.15 10.24 9.29 24.07 22.92 22.07 20.99 20.27 25.1 23.18 21.87 20.99 20.31 25.26 23.74 21.88 21.1 20.4 25.62 22.89 21.64
1634.1 1638.8 1700.7 1689.2 1656.9 1688.0 1645.0 1894.2 1888.0 1880.0 1879.4 1879.4 1917.0 1876.4 1939.6 1919.4 1881.2 1928.0 1891.9 1930.1 1942.2 1941.9 1901.6 1922.1 1940.1
51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75
21.12 20.56 26.88 23.89 22.77 21.58 20.8 27.47 23.79 21.8 21.84 20.87 28.82 24 21.64 20.89 24.17 22.26 21.75 20.06 18.34 24.29 22.54 21.82 20.06
1914.4 1858.1 1921.5 1896.0 1916.7 1873.8 1881.2 1865.2 1914.4 1956.1 1949.6 1842.7 1903.4 1918.2 2000.9 1973.6 1960.9 1961.5 1938.7 1974.2 1998.2 1978.4 1974.2 1998.2 1978.4
76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100
18.65 24.38 22.82 21.85 20.07 19.04 24.7 22.97 22.02 20.09 19.24 26.73 22.97 22.08 20.4 19.28 27.14 23.05 22.23 21.15 20.85 29.89 24.08 21.6 20.02
1936.0 1980.7 2005.6 1967.4 1997.0 1968.3 1961.5 1917.0 1979.9 1975.7 1985.2 1917.0 1928.6 1970.1 2003.9 1929.5 1964.4 1985.2 1927.4 1946.7 1937.8 1930.4 1980.7 1961.5 1961.5
Average of compressive strength of concrete (MPa)
No. of sample
W/C : 0.4 , 0.5, 0.6, 0.7, 0.8
30
LWA01
LWA02
LWA03
20 10 0
0.184902673 0.165194149 0.153023186 0.145585139 0.140195274
Average of the weight ratio of lightweight aggregate to all aggregates
LWA01
Density (kg/m3)
2500
LWA02
LWA03
2000 1500 1000 500 0
0
0.1
0.2
0.3
0.4
0.5
0.6
The weight ratio of lightweight aggregate to all aggregates Fig. 3. The weight ratio of lightweight aggregate to all aggregates and density.
is also called tree-based GP [27,29]. The main difference between the GA and GP approaches is that the evolving programs in GP are parse trees rather than fixed-length binary strings in GA [28,30]. Gene Expression Programming (GEP) is an evolutionary algorithm that incorporates both the idea of a simple, linear chromosome of fixed length used in Genetic Algorithms (GAs) and the
Compressive strength of concrete (MPa)
Fig. 2. Shows the diagrams for the weight ratio of lightweight aggregate to all aggregates and density (kg/m3).
LWA03
35
LWA02
LWA01
30 25 20 15 10 5 0 0.1
0.3
0.5
0.7
0.9
water cement ratio Fig. 4. The concrete compressive strength against different water-cement ratios.
tree structure of different sizes and shapes used in Genetic Programming (GP) [10,31]. GEP is a new subarea of GP which was first invented by Ferreira [31]. Function set, terminal set, fitness function, control parameters, and termination condition are the major elements of GEP. The difference between GP and GEP lies in the representation of the solution. GEP creates a fixed length of charac-
S. Jafari, S.S. Mahini / Construction and Building Materials 139 (2017) 93–100
Compressive strength of concrete (MPa)
98
Bastos et al.'s Work
20
Experimental Results
15 10 5 0
Fig. 6. Example of expression trees (ETs) [29].
0
500
1000
1500
2000
Density (Kg/m3) Fig. 5. Comparison of the concrete compressive strength against density obtained from experimental results of this study and the other study by Bastos et al. [26].
Table 3 A comparison between Yohannes’ work and experimental work in this study [27]. Lightweight Concrete
W/C
Average of fc (MPa)
Average of density (kg/m3)
Yohannes’ work made by pumices
0.45 0.48 0.5
15.30 18.31 14.875
1389.3 1325.5 1198.45
LWA02
0.4 0.5 0.6 0.7 0.8
26.18317 22.95386 21.957 20.488 19.347
1904.414 1901 1927.1 1925.671 1894.014
LWA03
0.4 0.5 0.6 0.7 0.8
26.17414 23.48714 22.00517 21.32329 20.584
1956.186 1964.686 1963.617 1976.771 1959.5
ter strings to represent the solutions. These solutions are further shown as computer models in tree-like structures. These trees are termed expression trees (ETs) [28,30]. On the other hand, the solutions created by GP are represented as tree structures and expressed in a functional programming language [29,30]. In GEP, the genetic operators act on the chromosome level. This leads to an extreme simplification in the creation of genetic diversity. GEP has a multi-genic nature. Thus, more complex programs with several subprograms can be generated during the evolutionary process. A gene in GEP is composed of a list of symbols. The symbols are elements from function or terminal sets. Each of the functions takes any value of data type which can be returned by a function or assumed by a terminal [28,30]. A typical GEP gene is as given below:
þ
p
a3b
ð1Þ
p where a, b and 3 are elements of the function set; +, and are the terminal nodes, and ‘‘.’’ is the element separator for easy reading. The above expression is called Karva notation or K-expression [10]. A K-expression can be represented by a diagram as an ET. As an example, Fig. 6 illustrates the expression tree of the above sample gene. The first position in the K-expression denotes the root of the ET. The transformation process starts from the root and reads through the string one by one [30]. The size of the corresponding ETs changes during the GEP evolutionary process. The valid length of each expression is equal to or less than the length of the gene. The validity of a randomly selected genome is certified by a head–tail method. Each GEP gene has a head and a tail. The head may be composed of both function and terminal symbols. The tail, on the other hand, may only contain
terminal symbols [30]. A roulette wheel sampling with elitism strategy is employed by GEP to select and copy the individuals. Single or several genetic operators such as crossover, mutation and rotation are used for introducing variations in the population. Note that the rotation operator rotates two subparts of the genome with respect to a randomly chosen point. Further descriptions of GEP can be found in [28,30]. The gene expression programming method has been used to estimate the compressive strength of lightweight aggregate concrete. The fit function (name Mean Squared Error) and the correlation coefficient were used to illustrate the accuracy of the relationship. The MSE assesses the quality of an estimator (i.e. a mathematical function mapping a sample of data to a parameter of the population from which the data is sampled) or a predictor (i.e. a function mapping arbitrary inputs to a sample of values of some random variable) [32]. In statistics, the mean squared error (MSE) or mean squared deviation (MSD) of an estimator measures the average of the squares of the errors or deviations, that is the difference between the estimator and what is estimated [33]. The Eq. (2) is obtained for LWA01 concrete. In this and following equations, the compressive strength of the 28-day concrete sample is measured in MPa and the propositions are measured in kg. Also the accuracy and the correlation coefficients are presented under the formula. In these equations Fc W, S, C and L are compressive strength, the amount of water, sand, cement and the lightweight aggregate, respectively.
Fc ¼
pffiffiffiffiffiffiffiffiffiffiffiffiffi 1 C 4:64S þ þ qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 8:25 ð2W þ 8:35 SÞ ðC LÞ C þ C:L 0:95
1 þ ðS ð4:15L þ C þ 7:25ÞÞ
ð2Þ
In which, Fitness Function: MSE, Fitness: 620.87, R-square: 0.90 The relation for the LWA02 shown in Eq. (3).
Fc ¼
pffiffiffi pffiffiffi pffiffiffi S þ 8W 9:88 S: 4C 1 C L þ þ þ C þ C ðC WÞ 3:32ðS CÞ C
ð3Þ
In which, Fitness Function: MSE, Fitness: 908.46, R-square: 0.98 The relation for the LWA03 shown in Eq. (4).
S5 Fc ¼
L
6:8 þ
þ 2:35 þ
1 C þ 8:26 pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi þ C þ 6:83 CS 2:71W
1 3S 6:72W
ð4Þ
where Fitness Function: MSE, Fitness: 798.81, R-square: 0.96 Figs. 7, 8 and 9 show the relationships between the actual compressive strength and the predicted compressive strength using equations derived from GEP. The equations are acceptable and they can be used to generate the different mixture designs.
S. Jafari, S.S. Mahini / Construction and Building Materials 139 (2017) 93–100
Predicted compressive strength
17
y = 0.928x + 0.8825 R² = 0.9046
15 13 11 9 7 5
5
7
9
11
13
15
17
19
Actual compressive strength
Predicted compressive strength
Fig. 7. The relationship between actual compressive strength and predicted compressive strength for LWA01
y = 1.0018x - 0.0338 R² = 0.9785
28 26 24 22 20 18 18
20
22
24
26
28
30
Actual compressive strength Fig. 8. The relationship between actual compressive strength and predicted compressive strength for LWA02.
Predicted compressive strength
There are two methods for designing and selecting the proportions for lightweight concrete described in ACI 211.2 in which the compressive strength and density are presented. This study shows that these features change for each lightweight concrete depending on the type of lightweight aggregate used in making the concrete. This study provides three references for three kinds of lightweight concretes made by expanded clays, natural (mineral) pumices with the maximum nominal size of 12.7 mm and natural pumices with the maximum nominal size of 19.2 mm. These three references are considered to be more reliable than that those for the lightweight concretes given in ACI 211.2. Using GEP programming generates equations that can predict compressive strength when there is not a specific standard to select proportions for lightweight aggregate concretes made using clay, natural (mineral) pumices with the maximum nominal size of 12.7 mm and natural pumices with the maximum nominal size of 19.2 mm as lightweight aggregates. References
30
29 y = 0.9402x + 1.3157 R² = 0.9604 27 25 23 21 19 17
99
17
19
21
23
25
27
29
Actual compressive strength Fig. 9. The relationship between actual compressive strength and predicted compressive strength for LWA03.
8. Conclusions By examining the results of tests and the presented graphs it can be concluded that reducing the nominal maximum size of aggregate used in lightweight aggregate concrete will increase the density and compressive strength of the lightweight concrete. Because the grain size of the expanded clays is smaller than the natural pumices the concrete made of expanded clays has a smoother surface than concrete made of mineral pumices. For a specific material increasing the maximum size of aggregates will decrease the density and the compressive strength of the concrete. This is because there is a weakening of the aggregate structure with an increase in maximum size of the aggregate.
[1] ACI 213R–14, Guide for Structural Lightweight Aggregate Concrete, Reported by ACI Committee 213, 2014. [2] R.D. Sturm, N. Mc Ashkill, R.G. Burg, D.R. Morgan, Evolution of Lightweight Concrete Performance in 55 to 80 Year Old Ship. ACI Publication, SP 189-7. [3] L. al-Jaberi, Z.W. Abbas, E.K. Jaffar (Effect of volume of steel fiber on the punching shear behavior of hybrid reinforced concrete flat slab), Eng. Dev. 20 (2015). 02. [4] T. Gonen, Mechanical and fresh properties of fiber reinforced self-compacting lightweight concrete, Scientia Iranica, A 22 (2015) 313–318. [5] J.A. Bogas, M.G. Gomes, A. Gomes, Compressive strength evaluation of structural lightweight concrete by non-destructive ultrasonic pulse velocity method, Ultrasonic 53 (2013) 962–972. [6] K.M.A. Hossain, M. Lachemi, Mixture design, strength, durability, and fire resistance of lightweight pumice concrete, ACI Mat. J. 104 (2007) 449–457. [7] M.J. Shannag, Characteristics of lightweight concrete containing mineral admixtures, Constr. Build. Mater. 25 (2) (2011) 568–662. [8] S. Bideci, Ozlem, The effect of high temperature on lightweight concretes produced with colemanite coated pumice aggregates, Constr. Build. Mater. 113 (2016) 631–640. [9] M. Mitchel (An introduction to Genetic Algorithm), MIT Press Paperback, 1998. [10] C. Ferreira, Gene expression programming: a new adaptive algorithm for solving problems, Complex Syst. 13 (2) (2001) 87–129. [11] M.A. Kewalramani, R. Gupta, Concrete compressive strength prediction using pulse velocity through artificial neural networks, Autom. Constr. 15 (2006) 374–379. [12] G. Trtnik, F. Kavacˆicˆ, G. Turk, Prediction of concrete strength using ultrasonic pulse velocity and artificial neural networks, Ultrasonic 49 (2009) 53–60. [13] S.M. Mousavi, P. Aminian, A.H. Gandomi, A.H. Alavi, H. Bolandi, A new predictive model for compressive strength of HPC using gene expression programming, Adv. Eng. Software 45 (2012) 105–114. [14] M.A. Hadianfard, S. Jafari (Prediction of lightweight aggregate concrete compressive strength using ultrasonic pulse velocity test through gene expression programming), Int. J. Sci. Technol. Civ. Eng. Trans. (2015). [15] S. Kenneth, P.E. Harmon, Engineering Properties of Structural Lightweight Concrete, Carolina Stalite Company, United States, 1999. [16] CIP 36, Structural Lightweight Concrete, National Ready Concrete Association, Concrete in Practice, NRMCA, 2003. [17] ASTM C 330-5, Standard Specification for Lightweight Aggregates for Structural Concrete, ASTM International, 2002. [18] ACI 304.5R91, Batching, Mixing and Job Control of Lightweight Concrete, Reported by ACI Committee 304, 1997. [19] ASTM C 127, Standard Test Method for Density, Relative Density (Specific Gravity) and Absorption of Coarse Aggregate, ASTM International, 2007. [20] ASTM C 29, Standard Test Method for Bulk Density and Voids in Aggregates, ASTM International, 2007. [21] M. Hasan, A. Kabir (Early age tests to predict 28 days compressive strength of concrete), AWAM Int. Conf. Civ. Eng. Geohazard Informational Zonation (2013) 234–241. [22] CIP 35, Testing Compressive Strength of Concrete, National Ready Concrete Association, Concrete in Practice, NRMCA, 2003. [23] ASTM C 138/C 138 M, Standard Test Method for Density (Unite Weight), Yield and Air Content (Gravimetric) of Concrete, ASTM International, 2001. [24] ASTM C 39, Standard Test Method for Compressive Strength of Cylindrical Concrete Specimens, ASTM International, 1983. [25] J.Y. Yoon, J.H. Kim, Y.Y. Hwang, D.K. Shin, Lightweight concrete produced using a two-stage casting process, Material 8 (2015) 1384–1397. [26] A.M. Bastos, H. Sousa, A.F. Melo (Methodology for the design of lightweight concrete with expanded clay aggregates), TSM J. (2005). [27] M. Yohannes, Investigation on the suitability of pumice and scoria aggregates in ribbed-slab construction, Civ. Eng. Res. 5 (4) (2015) 75–82.
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[28] A. Mollahsani, A.H. Alavi, A.H. Gandomi, Empirical modeling of plate load test moduli of soil via gene expression programming, Comput. Geotech. J. 10 (2010) 1016. [29] J. Koza (Genetic programming, on the programming of computers by means of natural selection), MIT Press. 11, Cambridge (MA), 1992. [30] S.S. Sadat Hosseini, A.H. Gandomi, Short-term load forecasting of power systems by gene expression programming, Neural Comput. App. 21 (2012) 337–389.
[31] Q. Zhang, Ch. Zhou, W. Xiao, P. Nelson, W. (Improving Gene expression programing performance by using differential evolution), in: Sixth International Conference on Machine Learning and Applications, 2007, pp. 31–37. [32] The free encyclopedia, Mean Squared Error, 2016. https://en.wikipedia.org/ wiki/Mean_squared_error. (Accessed 08.09.16). [33] E.L. Lehmann, second ed., Theory of Point Estimation, Springer, New York, 1998. MR 1639875.
Contents lists available at ScienceDirect
Construction and Building Materials journal homepage: www.elsevier.com/locate/conbuildmat
Lightweight concrete design using gene expression programing Saeed Jafari a, Seyed Saeed Mahini b,⇑ a b
Department of Civil and Environmental Engineering, Shiraz University of Technology, Shiraz, Iran Discipline of Civil and Environmental Engineering, University of New England, NSW, Australia
a r t i c l e
i n f o
a b s t r a c t
Article history: Received 9 August 2016 Accepted 27 January 2017
The use of lightweight concrete (LWC) in earthquake resistant buildings is beneficial because of the weight and mass reduction of the structures. LWC has been used in the construction industry for many years and while attempts have been made to develop a practical and reliable code for lightweight concrete design worldwide a satisfactory, practical standard for mix design is required. There are a few standards which present methods for designing the mix of LWC such as ACI 211.2. However, in these standards the proposed compressive strength and density determinations cannot be used for all types of lightweight aggregates. The aim of this study is to provide references for three types of lightweight concretes containing clay and natural (mineral) pumice aggregates with the maximum nominal sizes of 12.7 mm (½ in.) and 19.2 mm (¾ in.) respectively. With this intent, hundred specimens of lightweight concrete were made and then tested in the laboratory using these aggregates. After presenting a standard for propositioning and adjusting propositions of the concrete mix three equations were derived using Gene Expression Programing (GEP) to obtain the compressive strength of a specific mixture. Comparison between the actual properties and their predicted counterparts indicated that the proposed derivations are a useful and reliable practical method for use by practicing engineers when designing lightweight concrete mixes. Ó 2017 Elsevier Ltd. All rights reserved.
Keywords: Lightweight concrete Lightweight concrete mix design Gene expression programming Derivations Compressive strength
1. Introduction Structural lightweight aggregate concrete is an important and versatile material for use in modern construction. It has many and varied applications including multistory building frames and floors, bridges, offshore oil platforms, and prestressed or precast elements of all types. Many architects, engineers, and contractors recognise the inherent economies and advantages offered by this material as evidenced by the many impressive lightweight concrete structures found today throughout the world [1]. For more than 80 years structural lightweight aggregate concrete has solved weight and durability problems in buildings and exposed structures [2]. Lightweight concrete has strengths comparable to normal weight concrete, yet is typically 25–35% lighter. Structural lightweight concrete offers design flexibility and substantial cost savings by providing: less dead load, improved seismic structural response, longer spans, better fire ratings, and thinner sections, decreased story height, smaller size structural members, less reinforcing steel, and lower foundation costs. Lightweight concrete
⇑ Corresponding author. E-mail addresses: (S.S. Mahini).
[email protected]
(S.
http://dx.doi.org/10.1016/j.conbuildmat.2017.01.120 0950-0618/Ó 2017 Elsevier Ltd. All rights reserved.
Jafari),
[email protected]
precast elements offer reduced transportation and placement costs [3]. The use of lightweight structural concrete to reduce the weight of earthquake resistant buildings is useful material having many applications. Therefore, research on the properties of different types of lightweight concretes and the evaluation of the corresponding concrete strength has been considered by many researchers [4,5]. Research has been conducted worldwide on a large number of natural and artificial lightweight aggregates used in the manufacture of mortar and concrete. Natural lightweight aggregates include diatomite, pumice, scoria, sawdust, oil palm shells, bottom ash, and starch-based aggregates. Artificial aggregates include expanded shale, slate, perlite, sintered fly ash, bonded fly ash, solidified blast furnace slug, and vermiculite. Use of natural lightweight aggregates instead of processed artificial aggregates can significantly reduce the cost of such concretes [6]. Shannag [7] investigated the properties of fresh and hardened concretes containing locally available natural lightweight aggregates, and mineral admixtures. Test resulted indicated that replacing cement in the structural lightweight concrete developed, with 5–15% silica fume on weight basis, caused up to 57% and 14% increase in compressive strength and modulus of elasticity, respectively, compared
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List of notation FC W S L C
is is is is is
the compressive strength of concrete water sand lightweight aggregate cement
to mixes without silica fume. In a study, the surface of large pumice aggregate was coated with cement + colemanite (CLM) dual mixtures (0%, 7.5%, 12.5% and 17.5%). Lightweight concretes were produced by using coated aggregates. Then by exposing to temperatures at 20 °C (Control), 200 °C, 400 °C and 600 °C, the unit weight, compressive strength, ultrasonic pulse velocity and weight loss of concrete samples were determined. As a result of the study, the optimum value was obtained from 12.5-CLM samples. It is determined that the lightweight concretes that would be produced with pumice aggregates coated with cement + colemanite dual mixture would have a high performance against high temperature [8]. Gene expression programming (GEP) is, like genetic algorithms (GAs) and genetic programming (GP), a genetic algorithm as it uses populations of individuals, selects them according to fitness and introduces genetic variation using one or more genetic operators [9]. The fundamental difference between the three algorithms resides in the nature of the individuals: in GAs the individuals are linear strings of fixed length (chromosomes); in GP the individuals are non-linear entities of different sizes and shapes (parse trees); and in GEP the individuals are encoded as linear strings of fixed length (the genome or chromosomes) which are afterwards expressed as non-linear entities of different sizes and shapes (simple diagram representations or expression trees) [10]. Through artificial neural networks and using ultrasonic pulse velocity Kewalramani and Gupta tried to predict the compressive strength of concrete and compared the results of neural networks and multiple variable regressions [11]. Through Programming in the MATLAB environment and considering the number of parameters of concrete Trtnik et al. provided a model for concrete compressive strength based on neural networks and using ultrasonic pulse velocity [12]. Also Mousavi et al. proposed a new model for predicting the compressive strength of high performance concrete using gene expression programming [13]. In another study Hadianfard and Jafari suggested some equations to predict compressive strength of lightweight aggregate concrete using the ultrasonic pulse velocity test through gene expression programming [14]. The purpose of this study is to provide three specific applicable references for selecting and adjusting mixture proportions for three types of lightweight concrete made using three different lightweight aggregates. Discussion in this study is limited to lightweight concrete containing clay, natural (mineral) pumices with the maximum nominal size of 12.7 mm (½ in.) and with the maximum nominal size of 19.2 mm (¾ in.) as lightweight aggregates. Structural LWC has an in-place density (unit weight) of the order of 1440–1840 kg/ m3 (90 –115 lb/ft3) compared to normal weight concrete with a density in the range of 2240 –2400 kg/m3 (140 –150 lb/ft3). For structural applications the concrete strength should be greater than 17 MPa (2500 psi) [15]. The concrete mixture is made with a lightweight course aggregate. In some cases a portion or the entire fine aggregates may be a lightweight product. Lightweight aggregates used in structural lightweight concrete are typically expanded shale, clay or slate materials that have been fired in a rotary kiln to develop a porous structure. Other products such as
LWA GEP GP GA
is is is is
the the the the
lightweight aggregate gene expression programming genetic programming genetic algorithm
air-cooled blast furnace slag are also used. There are other classes of non-structural LWC with lower density, made with other aggregate materials and higher air voids in the cement paste matrix, such as in cellular concrete [16]. Samples made by natural pumices are considered structural lightweight concrete and samples containing clay are considered nonstructural lightweight concrete. The use of pozzolanic and chemical admixtures is not covered in this study, nor do the samples include non-air entertained concrete. Lightweight concretes have been proportioned by the weight method described in ACI 211.2-98. The best approach to making a first trial mixture of lightweight concrete, which has given properties and uses a particular aggregate from a lightweight aggregate source, is to use proportions previously established for a similar concrete using aggregate from the same aggregate source. Such proportions may be obtained from the aggregate supplier and may be the result of either laboratory mixtures or of actual mixtures supplied to jobs. However, a purpose of this study is to provide a guide to proportioning a first trial mixture where such prior information is not available. Changing the lightweight materials in LWC changes other properties of LWC like compressive strength and density which is not predictable for all types of lightweight aggregates. Accordingly for each kind and size of lightweight aggregate a new standard is needed. In this paper by making different samples according to the standard described in ACI 211.2-98 three type of Iranian lightweight aggregates are studied and their new properties obtained through experiment in order to determine three new standards which can provide guidance in the selection of mix proportions having the required specified properties. Through gene expression programing three equations have been derived for all three kinds of concretes which predict the compressive strength of each kind of concrete according to their proportions. 2. Experimental program To study the above-mentioned issues three types of lightweight aggregate concrete were made and tested. The lightweight aggregates used were in compliance with the standard ASTM C330 [17] and determination of the lightweight aggregate concrete mixing ratio was based on standard ACI 211.2 [18]. Measuring, mixing, transporting, and placing operations for lightweight concretes are similar to the procedures for normal weight concrete. However, there are certain differences, especially in proportioning and batching procedures that should be considered to produce a finished product of the highest quality [19]. In this study more than 100 concrete samples have been tested. The batches were made in Shiraz University of Technology laboratory using the specific gravity method. The weight method procedure is applicable to sand-lightweight concrete comprised of lightweight coarse aggregate and normal weight fine aggregate. Estimating the required batch weights for the lightweight concrete involves determining the specific gravity factor of lightweight coarse aggregate and from this the first estimate of the weight of fresh lightweight concrete can be made. Also the absorption of lightweight coarse aggregate may be measured by the method
S. Jafari, S.S. Mahini / Construction and Building Materials 139 (2017) 93–100
described in ASTM C 127 [20]. When concrete was made with lightweight aggregates that have low initial moisture and relatively high rates of absorption they were mixed with one-half to two-thirds of the mixing water for a short period prior to the addition of cement to minimise slump loss. In addition the specific gravity of the lightweight aggregates were determined at the moisture content anticipated prior to use. For convenience each type of concrete mix was named. The concrete made of expanded clay was named lightweight aggregate (LWA)01, the concrete made of natural (mineral) pumices with the maximum nominal size of 12.7 mm was named LWA02, and the concrete made of natural pumices with the maximum nominal size of 19.2 mm was named LWA03. In all concrete mixes sand was used as the fine aggregate and expanded clay, mineral pumice size 12.7 mm or mineral pumice size 19.2 mm as the coarse aggregate.
3. Material properties and mix design Before any amendment the fineness modulus of the fine sand used was 3.46 which reached to 3 after sifting and amendment. For the experiments undertaken the sand moisture content was 1%. In the mix design the saturated surface dry (SSD) condition for the sand was 6% water. The specific gravity of the fine sand was 1717.65 Kg/m3, which was determined in accordance with ASTM C 29 [21]. In the standard ASTM C 330 there are some implications and requirements for gradation of lightweight aggregates. The gradation of aggregates was based on these requirements [17]. The lightweight aggregates used in this study were coarse aggregates with the sizes of 19.2 mm and 12.8 mm of mineral pumices and 9.6 mm for expanded clay. Specific gravity for the expanded clay was 365.72 Kg/m3. Also the specific gravity for mineral pumice with the nominal sizes of 12.7 mm and 19.2 mm was 693 and 653 Kg/ m3 respectively. For expanded clays and mineral pumices the humidity of the aggregates in the natural environment was zero in order to be used outside and exposed to the sun. Also for the experiments undertaken for the aggregates of expanded clays and mineral pumices to reach to the SSD condition 13% and 15% of water was needed respectively. Pycnometric specific density factor for expanded clays was 1.1. In addition the pycnometric specific density factor for mineral pumices with the sizes of 12.7 mm and 19.2 mm was 1.69 and 1.59 respectively. The proportioning follows a sequence of straightforward steps that, in effect, fit the characteristics of the available materials. The first step in the study was to choose a slump based on the type of construction being considered, which in this case, comprised beams, reinforced walls and buildings columns. The next step was to choose one of the maximum size of lightweight aggregates mentioned in previous paragraphs. Based in these two initial steps the appropriate amount of mixing water was determined. The fourth step involved selection of the approximate water-cement ratio based on the expected compressive strength of the concrete. Assessment of the cement content was the next step, with the amount of cement per unit volume of concrete being fixed by the decisions made in Steps 3 and 4. The next step was estimating the lightweight coarse aggregate content based on the maximum size of aggregates and volume of oven-dry loose coarse aggregates per unit volume of concrete for different fineness moduli of sand. With the quantities of water, cement, and coarse aggregate established, the remaining material, fine aggregate content, was estimated in the last step. The concrete mix designs and density of the hardened concretes are presented in the Table 1. All the weights are for making 1m3 of fresh concrete and all weights are based on saturated surface dry (SSD) aggregates.
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4. Experimental results The compressive strength of concrete is the most common performance measure used by engineers in designing buildings and other structures [22]. The compressive strength is measured by breaking cylindrical concrete specimens in a compression-testing machine [23]. For convenience a few cylindrical samples were made of WLA01, WLA02 and LWA03 in order to find coefficients which would convert the compressive strength results of cubic samples to that of cylindrical samples. Fig. 1 shows the hydraulic jack and the failed specimens of all three types of concrete. The measurement method of concrete compressive strength was assessed according to the standard ASTM C 39-83b [24]. Loading rate was considered constant ranging from 0.15 to 0.34 MPa/s. The laboratory velocity of 0.3 MPa/s was used to break the samples. The type of lightweight aggregate and its volume fraction in a mix determined the density of lightweight concrete [25]. Customarily the theoretical density is a laboratory determination; for which the value is assumed to remain constant for all batches made using identical component ingredients and proportions. It is calculated from ASTM C 138/C 138 M [23]. The compressive strengths and densities of samples of the hardened concretes are presented in the Table 2.
5. Factors affecting the compressive strength and density of lightweight concrete According to the Table 2 it can be seen that by increasing the maximum size of the lightweight aggregates the density and compressive strength decrease. The reason for this is that by increasing the maximum size of lightweight aggregates, the structure of the lightweight aggregate gets weaker and lighter. Concrete made by expanded clay is lighter and has a lower compressive strength and therefore can be used for nonstructural purposes. Conversely concrete made using pumice has a strength which makes it suitable to be used as structural concrete. The price of pumice is 20 percent of expanded clay but pumices need to be crushed to get standard sizes (12.7 mm and 19.2 mm). Accordingly concrete made using pumices are cheaper but more difficult to make. Fig. 2 shows diagrams for the average of the weight ratios of lightweight aggregate to all aggregates and the average of the concrete compressive strengths (MPa) for LWA01, LWA02 and LWA03 concrete (in SSD condition). This diagram indicates a clear relationship in relation to different mixes of lightweight concretes and their corresponding compressive strengths. By increasing the weight ratio of lightweight aggregate to all aggregates concrete compressive strengths decrease with an inverse relationship between them. In Fig. 3, the diagram shows that increasing the weight ratio of lightweight aggregates does not have a significant effect on density. This relationship was predictable because of the fact that all samples have been designed for a determined density and because by increasing the lightweight portion the amount of sand decreases and the amount of cement increases. Fig. 4 shows the relationship between the concrete compressive strength and the different water-cement ratios for all of the samples. This diagram indicates that increasing the water-cement ratio results in a decrease in the compressive strength of the concrete. The concrete mixing ratio of the samples were designed according to ACI 211.2 but the compressive strength and density do not correspond to those presented in the standard. It is obvious that as the type of lightweight aggregate changes the other properties of the concrete will change. In this regard this study provides three
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Table 1 Summary of the concrete mix design and density of the lightweight concretes. Name of samples
Type of LWA
Water Cement Ratio
WaterWW (kg)
CementWC, (kg)
SandWS, (kg)
LWAWL, (kg)
Density(kg/m3)
LWA01
Expanded Clay
0.4 0.6 0.8
210 230 210
525 380 260
710 835 975
155 155 155
1659 1529 1631
LWA02
Natural Pumice½ in
0.4 0.6 0.8
212 212 212
530 353 265
737 913 1002
371 371 371
1878 1898 1836
LWA03
Natural Pumice¾ in
0.4 0.6 0.8
212 212 212
530 353 265
619 795 884
539 539 539
1718 1840 1781
Fig. 1. (a) The hydraulic jack; (b) Failed LWA01; (c) Failed LWA02; (d) Failed LWA03.
references for lightweight concretes made by three types of lightweight aggregates. As the mix designs of these samples cover the whole standard range of concrete which may be made these references can be used instead of the methods presented in ACI 211.2 for concretes containing clay, natural (mineral) pumices with the maximum nominal size of 12.7 mm and natural pumices with the maximum nominal size of 19.2 mm as lightweight aggregates. 6. Comparing the mix design used in this study to other research results In experimental work by Bastos et al. [26] to introduce a method for the design of lightweight concrete with expanded clay aggregates 28 lightweight concrete sample mixes using four different quantities of cement (126, 155, 185 and 214 kg/m3) with densities between 853 and 1418 kg/m3 were made by expanded clay (LECA Portugal) and tested. In comparison with the study referred in this paper the size of the lightweight aggregates were smaller and in some samples they were used as fine aggregates. In Fig. 5, the results for both works are shown. Samples in the study referred to in this paper have higher densities and compressive strengths than those of the study by Bastos et al. [26]. In a paper presented by Yohannes [27] the use of Ethiopian pumice and scoria aggregates for lightweight concrete in ribbed
slab construction was described. The experimental program was aimed at studying design for the production of all-lightweight structural concrete and included full size ribbed slab testing. In this study, with the mix design explained in the paper, pumice cannot be used as structural concrete. The coarse aggregate and fine aggregate were respectively, scoria and pumice [27]. The selected water cement ratios for the mix design were 0.45–0.5 but in this study the water cement ratios were 0.4, 0.5, 0.6, 0.7 and 0.8. Table 3 shows the results from Yohannes’ study compared with this study. Fig. 5 and Table 3 shows that the mixes designs used in the study addressed in this paper proved that samples had higher compressive strength when the fine aggregates are normal sand and the coarse aggregates are lightweight materials although these samples are heavier in comparison to the results of other researchers. 7. Prediction of compressive strength of concrete by using GEP GP is a subset of genetic algorithms (GAs). It is a modern regression technique with a great ability to automatically evolve computer programs [28]. The evolutionary process followed by the GP algorithm is inspired from the principle of Darwinian natural selection. GP was introduced by Koza [29] in the late 1980 s after experiments on symbolic regression. This classical GP technique
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S. Jafari, S.S. Mahini / Construction and Building Materials 139 (2017) 93–100 Table 2 Compressive strength and density of samples. Comp. strength (MPa)
Density (kg/m3)
No. of sample
Comp. strength (MPa)
Density (kg/m3)
No. of sample
Comp. strength (MPa)
Density (kg/m3
No. of sample
Comp. strength (MPa)
Density (kg/m3)
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
15.15 12.55 12.43 7.6 9.21 14.01 12.84 12.16 9.52 6.95 13.87 10.39 11.82 9.76 8.95 15.42 13.68 12.84 9.98 8.51 15.79 13.75 13.19 12.29 10.33
1742.2 1724.1 1770.4 1597.3 1613.6 1689.2 1641.2 1601.5 1501.0 1660.7 1666.4 1665.5 1642.4 1664.6 1664.9 1743.4 1676.4 1693.3 1610.1 1647.1 1715.9 1642.7 1371.9 1675.9 1559.4
26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50
11.32 9.13 16.47 15.99 13.15 10.24 9.29 24.07 22.92 22.07 20.99 20.27 25.1 23.18 21.87 20.99 20.31 25.26 23.74 21.88 21.1 20.4 25.62 22.89 21.64
1634.1 1638.8 1700.7 1689.2 1656.9 1688.0 1645.0 1894.2 1888.0 1880.0 1879.4 1879.4 1917.0 1876.4 1939.6 1919.4 1881.2 1928.0 1891.9 1930.1 1942.2 1941.9 1901.6 1922.1 1940.1
51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75
21.12 20.56 26.88 23.89 22.77 21.58 20.8 27.47 23.79 21.8 21.84 20.87 28.82 24 21.64 20.89 24.17 22.26 21.75 20.06 18.34 24.29 22.54 21.82 20.06
1914.4 1858.1 1921.5 1896.0 1916.7 1873.8 1881.2 1865.2 1914.4 1956.1 1949.6 1842.7 1903.4 1918.2 2000.9 1973.6 1960.9 1961.5 1938.7 1974.2 1998.2 1978.4 1974.2 1998.2 1978.4
76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100
18.65 24.38 22.82 21.85 20.07 19.04 24.7 22.97 22.02 20.09 19.24 26.73 22.97 22.08 20.4 19.28 27.14 23.05 22.23 21.15 20.85 29.89 24.08 21.6 20.02
1936.0 1980.7 2005.6 1967.4 1997.0 1968.3 1961.5 1917.0 1979.9 1975.7 1985.2 1917.0 1928.6 1970.1 2003.9 1929.5 1964.4 1985.2 1927.4 1946.7 1937.8 1930.4 1980.7 1961.5 1961.5
Average of compressive strength of concrete (MPa)
No. of sample
W/C : 0.4 , 0.5, 0.6, 0.7, 0.8
30
LWA01
LWA02
LWA03
20 10 0
0.184902673 0.165194149 0.153023186 0.145585139 0.140195274
Average of the weight ratio of lightweight aggregate to all aggregates
LWA01
Density (kg/m3)
2500
LWA02
LWA03
2000 1500 1000 500 0
0
0.1
0.2
0.3
0.4
0.5
0.6
The weight ratio of lightweight aggregate to all aggregates Fig. 3. The weight ratio of lightweight aggregate to all aggregates and density.
is also called tree-based GP [27,29]. The main difference between the GA and GP approaches is that the evolving programs in GP are parse trees rather than fixed-length binary strings in GA [28,30]. Gene Expression Programming (GEP) is an evolutionary algorithm that incorporates both the idea of a simple, linear chromosome of fixed length used in Genetic Algorithms (GAs) and the
Compressive strength of concrete (MPa)
Fig. 2. Shows the diagrams for the weight ratio of lightweight aggregate to all aggregates and density (kg/m3).
LWA03
35
LWA02
LWA01
30 25 20 15 10 5 0 0.1
0.3
0.5
0.7
0.9
water cement ratio Fig. 4. The concrete compressive strength against different water-cement ratios.
tree structure of different sizes and shapes used in Genetic Programming (GP) [10,31]. GEP is a new subarea of GP which was first invented by Ferreira [31]. Function set, terminal set, fitness function, control parameters, and termination condition are the major elements of GEP. The difference between GP and GEP lies in the representation of the solution. GEP creates a fixed length of charac-
S. Jafari, S.S. Mahini / Construction and Building Materials 139 (2017) 93–100
Compressive strength of concrete (MPa)
98
Bastos et al.'s Work
20
Experimental Results
15 10 5 0
Fig. 6. Example of expression trees (ETs) [29].
0
500
1000
1500
2000
Density (Kg/m3) Fig. 5. Comparison of the concrete compressive strength against density obtained from experimental results of this study and the other study by Bastos et al. [26].
Table 3 A comparison between Yohannes’ work and experimental work in this study [27]. Lightweight Concrete
W/C
Average of fc (MPa)
Average of density (kg/m3)
Yohannes’ work made by pumices
0.45 0.48 0.5
15.30 18.31 14.875
1389.3 1325.5 1198.45
LWA02
0.4 0.5 0.6 0.7 0.8
26.18317 22.95386 21.957 20.488 19.347
1904.414 1901 1927.1 1925.671 1894.014
LWA03
0.4 0.5 0.6 0.7 0.8
26.17414 23.48714 22.00517 21.32329 20.584
1956.186 1964.686 1963.617 1976.771 1959.5
ter strings to represent the solutions. These solutions are further shown as computer models in tree-like structures. These trees are termed expression trees (ETs) [28,30]. On the other hand, the solutions created by GP are represented as tree structures and expressed in a functional programming language [29,30]. In GEP, the genetic operators act on the chromosome level. This leads to an extreme simplification in the creation of genetic diversity. GEP has a multi-genic nature. Thus, more complex programs with several subprograms can be generated during the evolutionary process. A gene in GEP is composed of a list of symbols. The symbols are elements from function or terminal sets. Each of the functions takes any value of data type which can be returned by a function or assumed by a terminal [28,30]. A typical GEP gene is as given below:
þ
p
a3b
ð1Þ
p where a, b and 3 are elements of the function set; +, and are the terminal nodes, and ‘‘.’’ is the element separator for easy reading. The above expression is called Karva notation or K-expression [10]. A K-expression can be represented by a diagram as an ET. As an example, Fig. 6 illustrates the expression tree of the above sample gene. The first position in the K-expression denotes the root of the ET. The transformation process starts from the root and reads through the string one by one [30]. The size of the corresponding ETs changes during the GEP evolutionary process. The valid length of each expression is equal to or less than the length of the gene. The validity of a randomly selected genome is certified by a head–tail method. Each GEP gene has a head and a tail. The head may be composed of both function and terminal symbols. The tail, on the other hand, may only contain
terminal symbols [30]. A roulette wheel sampling with elitism strategy is employed by GEP to select and copy the individuals. Single or several genetic operators such as crossover, mutation and rotation are used for introducing variations in the population. Note that the rotation operator rotates two subparts of the genome with respect to a randomly chosen point. Further descriptions of GEP can be found in [28,30]. The gene expression programming method has been used to estimate the compressive strength of lightweight aggregate concrete. The fit function (name Mean Squared Error) and the correlation coefficient were used to illustrate the accuracy of the relationship. The MSE assesses the quality of an estimator (i.e. a mathematical function mapping a sample of data to a parameter of the population from which the data is sampled) or a predictor (i.e. a function mapping arbitrary inputs to a sample of values of some random variable) [32]. In statistics, the mean squared error (MSE) or mean squared deviation (MSD) of an estimator measures the average of the squares of the errors or deviations, that is the difference between the estimator and what is estimated [33]. The Eq. (2) is obtained for LWA01 concrete. In this and following equations, the compressive strength of the 28-day concrete sample is measured in MPa and the propositions are measured in kg. Also the accuracy and the correlation coefficients are presented under the formula. In these equations Fc W, S, C and L are compressive strength, the amount of water, sand, cement and the lightweight aggregate, respectively.
Fc ¼
pffiffiffiffiffiffiffiffiffiffiffiffiffi 1 C 4:64S þ þ qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 8:25 ð2W þ 8:35 SÞ ðC LÞ C þ C:L 0:95
1 þ ðS ð4:15L þ C þ 7:25ÞÞ
ð2Þ
In which, Fitness Function: MSE, Fitness: 620.87, R-square: 0.90 The relation for the LWA02 shown in Eq. (3).
Fc ¼
pffiffiffi pffiffiffi pffiffiffi S þ 8W 9:88 S: 4C 1 C L þ þ þ C þ C ðC WÞ 3:32ðS CÞ C
ð3Þ
In which, Fitness Function: MSE, Fitness: 908.46, R-square: 0.98 The relation for the LWA03 shown in Eq. (4).
S5 Fc ¼
L
6:8 þ
þ 2:35 þ
1 C þ 8:26 pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi þ C þ 6:83 CS 2:71W
1 3S 6:72W
ð4Þ
where Fitness Function: MSE, Fitness: 798.81, R-square: 0.96 Figs. 7, 8 and 9 show the relationships between the actual compressive strength and the predicted compressive strength using equations derived from GEP. The equations are acceptable and they can be used to generate the different mixture designs.
S. Jafari, S.S. Mahini / Construction and Building Materials 139 (2017) 93–100
Predicted compressive strength
17
y = 0.928x + 0.8825 R² = 0.9046
15 13 11 9 7 5
5
7
9
11
13
15
17
19
Actual compressive strength
Predicted compressive strength
Fig. 7. The relationship between actual compressive strength and predicted compressive strength for LWA01
y = 1.0018x - 0.0338 R² = 0.9785
28 26 24 22 20 18 18
20
22
24
26
28
30
Actual compressive strength Fig. 8. The relationship between actual compressive strength and predicted compressive strength for LWA02.
Predicted compressive strength
There are two methods for designing and selecting the proportions for lightweight concrete described in ACI 211.2 in which the compressive strength and density are presented. This study shows that these features change for each lightweight concrete depending on the type of lightweight aggregate used in making the concrete. This study provides three references for three kinds of lightweight concretes made by expanded clays, natural (mineral) pumices with the maximum nominal size of 12.7 mm and natural pumices with the maximum nominal size of 19.2 mm. These three references are considered to be more reliable than that those for the lightweight concretes given in ACI 211.2. Using GEP programming generates equations that can predict compressive strength when there is not a specific standard to select proportions for lightweight aggregate concretes made using clay, natural (mineral) pumices with the maximum nominal size of 12.7 mm and natural pumices with the maximum nominal size of 19.2 mm as lightweight aggregates. References
30
29 y = 0.9402x + 1.3157 R² = 0.9604 27 25 23 21 19 17
99
17
19
21
23
25
27
29
Actual compressive strength Fig. 9. The relationship between actual compressive strength and predicted compressive strength for LWA03.
8. Conclusions By examining the results of tests and the presented graphs it can be concluded that reducing the nominal maximum size of aggregate used in lightweight aggregate concrete will increase the density and compressive strength of the lightweight concrete. Because the grain size of the expanded clays is smaller than the natural pumices the concrete made of expanded clays has a smoother surface than concrete made of mineral pumices. For a specific material increasing the maximum size of aggregates will decrease the density and the compressive strength of the concrete. This is because there is a weakening of the aggregate structure with an increase in maximum size of the aggregate.
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