Abstract
In the present paper, two models based on artificial neural networks (ANN) and gene expression programming (GEP) for predicting splitting tensile strength and water absorption of concretes containing ZnO2 nanoparticles at different ages of curing have been developed. To build these models, training and testing using experimental results for 144 specimens produced with 16 different mixture proportions were conducted. The used data in the multilayer feed forward neural networks models and input variables of genetic programming models are arranged in a format of eight input parameters that cover the cement content (C), nanoparticle content (N), aggregate type (AG), water content (W), the amount of superplasticizer (S), the type of curing medium (CM), Age of curing (AC) and number of testing try (NT). According to these input parameters, in the neural networks and genetic programming models, the splitting tensile strength and water absorption values of concretes containing ZnO2 nanoparticles were predicted. The training and testing results in these two models have shown the strong potential of the models for predicting the splitting tensile strength and water absorption values of concretes containing ZnO2 nanoparticles. Although neural networks have predicted better results, genetic programming is able to predict reasonable values with a simpler method rather than neural networks.
neural networks; genetic programming; nanoparticles; concrete; tensile test; water permeability
Prediction the effects of ZnO_{2} nanoparticles on splitting tensile strength and water absorption of high strength concrete
Ali Nazari^{*}* email: alinazari84@aut.ac.ir; Tohid Azimzadegan
Department of Materials Science and Engineering, Saveh Branch, Islamic Azad University, Saveh, Iran
ABSTRACT
In the present paper, two models based on artificial neural networks (ANN) and gene expression programming (GEP) for predicting splitting tensile strength and water absorption of concretes containing ZnO_{2} nanoparticles at different ages of curing have been developed. To build these models, training and testing using experimental results for 144 specimens produced with 16 different mixture proportions were conducted. The used data in the multilayer feed forward neural networks models and input variables of genetic programming models are arranged in a format of eight input parameters that cover the cement content (C), nanoparticle content (N), aggregate type (AG), water content (W), the amount of superplasticizer (S), the type of curing medium (CM), Age of curing (AC) and number of testing try (NT). According to these input parameters, in the neural networks and genetic programming models, the splitting tensile strength and water absorption values of concretes containing ZnO_{2} nanoparticles were predicted. The training and testing results in these two models have shown the strong potential of the models for predicting the splitting tensile strength and water absorption values of concretes containing ZnO_{2} nanoparticles. Although neural networks have predicted better results, genetic programming is able to predict reasonable values with a simpler method rather than neural networks.
Keywords: neural networks, genetic programming, nanoparticles, concrete, tensile test, water permeability
1. Introduction
Strength assessment of concrete is a main and probably the most important mechanical property, which is usually measured after a standard curing time. Concrete strength is influenced by lots of factors like concrete ingredients, age, ratio of water to cementitious materials, etc. The pore structure determines the transport properties of cement paste, such as permeability and ion migration. Permeability of cement paste is a fundamental property in view of the durability of concrete: it represents the ease with which water or other fluids can move through concrete, thereby transporting aggressive agents. It is therefore of utmost importance to investigate the quantitative relationships between the pore structure and the permeability. Through experimental studies and then numerical simulations of the pore structure and the permeability of cementbased materials, a better understanding of transport phenomena and associated degradation mechanisms will hopefully be reached^{1}.
Conventional methods of predicting various properties of concrete are generally based on either water to cement ratio rule or maturity concept of concrete^{2}. Over the last two decades, a different modeling method based on neural networks (NNs) has become popular and used by many researchers for a wide range of engineering applications. NNs are a family of massively parallel architectures that solve difficult problems via the cooperation of highly interconnected but simple computing elements (or artificial neurons). Basically, the processing elements of a neural network are analogous to the neurons in the brain, which consist of many simple computational elements arranged in several layers^{3}. The concrete properties could be calculated using the models built with NNs. It is convenient to use these models for numerical experiments to review the effects of each variable on the mix proportions^{46}. Besides ANNs, genetic programming (GP) has begun to arise for the explicit formulation of the properties and the performances of concrete recently^{7,8}. Genetic programming offers many advantages as compared to classical regression techniques. Regression techniques are often based on predefined functions where regression analyses of these functions are later performed. On the other hand, in the case of GP approach, there is no predefined function to be considered. In this sense, GP can be accepted to be superior to regression techniques and neural networks. GP has proven to be an effective tool to model and obtain explicit formulations of experimental studies including multivariate parameters where there are no existing analytical models^{7,8}.
In our previous works, the effects of different types of nanoparticles on physical and mechanical aspects of concrete specimens were studied^{927}. The aim of this study is to predict splitting tensile strength and water absorption of several types of concrete with and without ZnO_{2} nanoparticles by ANNs and GP. Totally 144 splitting tensile strength and 144 percentages of water absorption data from 16 different concrete mixtures were collected, trained and tested by means of different models. The obtained results have been compared by experimental ones to evaluate the software power for predicting the properties of concrete.
2. Experimental Procedure
2.1. Materials
Two series of concrete were made in the laboratory. The first was normally vibrated concrete (NVC) series with ordinary river sand as aggregates and the second self compacting concrete (SCC) series with limestone aggregates. The utilized materials are as below:
Ordinary Portland Cement (OPC) conforming to ASTM C150^{[28]} standard was used as received. The chemical and physical properties of the cement are shown in Table 1.
ZnO_{2} nanoparticles with average particle size of 15 nm and 45 m^{2}.g^{1} Blaine fineness producing from Suzhou Fuer Import & Export Trade Co., Ltd was used as received. The properties of ZnO_{2} nanoparticles are shown in Table 2.
Locally available natural sand with particles smaller than 0.5 mm and fineness modulus of 2.25 and specific gravity of 2.58 g.cm^{3} was used as fine aggregate for NVC series concrete. Crushed basalt stored in the laboratory with maximum size of 15 mm and specific gravity of 2.96 g.cm^{3} was used as coarse aggregate in NVC series concrete.
Crushed limestone aggregates were used to produce selfcompacting concretes, with gravel 4/12 and two types of sand: one coarse 0/4, for fine aggregates and the other fine 0/2, with a very high fines content (particle size < 0.063 mm) of 19.2%, the main function of which was to provide a greater volume of fine materials to improve the stability of the fresh concrete. A polycarboxylate with a polyethylene condensate defoamed based admixture (Glenium C303 SCC) was used. Table 3 shows some of the physical and chemical properties of polycarboxylate admixture used in this study.
2.2. Mixture proportions
Totally 6 series of mixtures were prepared and tested experimentally. C0 series mixtures were prepared as control specimens. The control mixtures were made of natural aggregates, cement and water. C0 series mixtures were cured in water (W) and saturated limewater (LW) and designated as C0W and C0LW series, respectively. N series were prepared with different contents of ZnO_{2} nanoparticles. The mixtures were prepared by the cement replacement of 0.5, 1.0, 1.5 and 2.0 weight percent. N series mixtures were also cured in water (W) and saturated limewater (LW) and designated as NW and NLW series, respectively.
C0SCC series mixtures were prepared by cement, fine and ultrafine crushed limestone aggregates with 19.2% by weight of ultrafine ones and 1.0 weight percent of polycarboxylate admixture replaced by water. NSCC series were prepared with different contents of ZnO_{2} nanoparticles. The mixtures were prepared with the cement replacement by ZnO_{2} nanoparticles from 1 to 5 weight percent and 1 weight percent polycarboxylate admixture.
The water to binder ratio for all mixtures was set at 0.40. The binder content of all mixtures was 450 kg.m^{3}. The proportions of the mixtures are presented in Table 4.
2.3. Test procedure
For NVC series concrete, Cylinders with the diameter of 150 mm and the height of 300 mm were cast and compacted in two layers on a vibrating table, where each layer was vibrated for 10 seconds. SCC series mixtures were prepared without subsequent vibration. The moulds were covered with polyethylene sheets and moistened for 24 hours. Then the specimens were demolded and cured in water and saturated limewater at a temperature of 20 °C prior to test days.
Splitting tensile tests were carried out according to the ASTM C 496^{[29]} standard. After the specified curing period was over (7, 28 and 90 days for NVC series and 2, 28 and 90 days for SCC series), the concrete cubes were subjected to splitting tensile test by using universal testing machine. The tests were carried out triplicately.
Water permeability tests are performed with several methods. In this work, water absorption has been selected to evaluate the water permeability of the specimens. Water absorption values samples were measured as per ASTM C 642^{[30]} after specified curing time in cold water. The tests were carried out triplicately.
3. Experimental Results
The splitting tensile strength results of the specimens are shown in Table 4. Table 4 shows that the splitting tensile strength increases with adding nano ZnO_{2} particles up to 1.0% in NW series. It is shown that using 2.0% ZnO_{2} nanoparticles decreases the splitting tensile strength to a value which is near to the control concrete. This may be due to the fact that the quantity of nano ZnO_{2} particles is higher than the amount required to combine with the liberated lime during the process of hydration thus leading to excess silica leaching out and causing a deficiency in strength as it replaces part of the cementitious material but does not contribute to strength^{31}. Also, it may be due to the defects generated in dispersion of nanoparticles that causes weak zones. The high enhancement of splitting tensile strength in the N series blended concrete are due to the rapid consuming of Ca(OH)_{2} which was formed during hydration of Portland cement specially at early ages related to the high reactivity of nano ZnO_{2} particles. As a consequence, the hydration of cement is accelerated and larger volumes of reaction products are formed. Also nano ZnO_{2} particles recover the particle packing density of the blended cement, directing to a reduced volume of larger pores in the cement paste.
On the other hand, for the specimens saturated in limewater, the splitting tensile strength increases by adding up to 2.0 weight percent ZnO_{2} nanoparticles. Lime reacts with water and produces Ca(OH)_{2} which needs to form strengthening gel. When ZnO_{2} nanoparticles react with Ca(OH)_{2} produced from saturated limewater, the content of strengthening gel is increased because of high free energy of nanoparticles which reduces significantly when reacts by Ca(OH)_{2}. Table 4 also shows the water absorption in C0 and N series concrete. The results indicate similar results to splitting tensile strength.
Table 4 also shows the splitting tensile strength of C0SCC and NSCC specimens at 2, 7 and 28 days of curing. The results show that the splitting tensile strength increases by adding ZnO_{2} nanoparticles up to 4.0 weight percent replacements (N4SCC series) and then it decreases, although adding 5.0 percent ZnO_{2} nanoparticles produces specimens with much higher splitting tensile strength with respect to C0SCC and NSCC specimens with 1.0, 2.0 and 3.0 weight percent ZnO_{2} nanoparticles.
To show that nanoparticles are capable to improve the mechanical properties of concrete specimens significantly, the compressive strength of the specimens has been illustrated in Table 4. It is obvious that nanoparticles have a key role on increasing the compressive strength of the specimens.
Table 4 also shows the water absorption in C0SCC and NSCC series concrete. The results indicate improvement by adding nanoparticles similar to splitting tensile strength.
The mechanism that the nanoparticles improve the strength and resistance to water permeability of concrete specimens can be interpreted as follows^{32}: Suppose that nanoparticles are uniformly dispersed in concrete and each particle is contained in a cube pattern, therefore the distance between nanoparticles can be determined. After the hydration begins, hydrate products diffuse and envelop nanoparticles as kernel^{32}. If the content of nanoparticles and the distance between them are appropriate, the crystallization will be controlled to be a suitable state through restricting the growth of Ca(OH)_{2} crystal by nanoparticles. Moreover, the nanoparticles located in cement paste as kernel can further promote cement hydration due to their high activity. This makes the cement matrix more homogeneous and compact. Consequently, the strength and resistance to water permeability of concrete is improved evidently such as the concrete containing nano ZnO_{2} in the amount of 1% by weight of binder^{32}.
With increasing the content of ZnO_{2} nanoparticles more than a specific weight percent (based on the concrete type), the improvement on the strength and resistance to water permeability of concrete is weakened. This can be attributed to that the distance between nanoparticles decreases with increasing content of nanoparticles, and Ca(OH)_{2} crystal cannot grow up enough due to limited space and the crystal quantity is decreased, which leads to the ratio of crystal to strengthening gel small and the shrinkage and creep of cement matrix increased^{33}, thus the strength and resistance to water permeability of cement matrix is looser relatively.
On the whole, the addition of nanoparticles improves the strength and resistance to water permeability of concrete. On the one hand, nanoparticles can act as a filler to enhance the density of concrete, which leads to the porosity of concrete reduced significantly. On the other hand, nanoparticles can not only act as an activator to accelerate cement hydration due to their high activity, but also act as a kernel in cement paste which makes the size of Ca(OH)_{2} crystal smaller and the tropism more stochastic.
4. Artificial Neural Networks
ANNs were developed to model the human brain^{34}. Even an ANN fairly simple and small in size when compared to the human brain, has some powerful characteristics in knowledge and information processing because of its similarity to the human brain. Therefore, an ANN can be a powerful tool for engineering applications^{35}. McCulloch and Pitts^{36} defined artificial neurons for the first time and developed a neuron model as in Figure 1. McCulloch and Pitts' network^{36} formed the basis for almost all later neural network models. Afterwards, Rosenblatt^{37} devised a machine called the perceptron that operated much in the same way as the human mind. Rosenblatt's perceptrons^{37} consist of "sensory" units connected to a single layer of McCulloch and Pitts^{36} neurons. Rumelhardt et al.^{38} derived a learning algorithm for perceptron networks with constituted hidden units. Their learning algorithm is called backpropagation and is now the most widely used learning algorithm. As a result of these studies, together with the developments in computer technology, using ANN has become more efficient after 1980^{[39]}.
As it can be seen from Figure 1, an artificial neuron is composed of five main parts: inputs, weights, sum function, activation function and outputs. Inputs are information that enters the neuron from other neurons of from external world. Weights are values that express the outcome of an input set or another process element in the preceding layer on this process element. Sum function is a function that calculates the effect of inputs and weights completely on this process element. This function computes the net input that approaches to a neuron^{40}. The weighted sums of the input components (net)_{j} are calculated using Equation 1 as follows:
where (net)_{j} is the weighted sum of the jth neuron for the input received from the preceding layer with n neurons, W_{ij} is the weight between the jth neuron in the previous layer, x_{i} is the output of the ith neuron in the previous layer^{39}. b is a fix value as internal addition and represents sum function. Activation function is a function that processes the net input obtained from sum function and determines the neuron output. In general for multilayer feedforward models as the activation function sigmoid activation function is used. The output of the jth neuron (out)_{j} is computed using Equation 2 with a sigmoid activation function as follows^{41}:
where is constant used to control the slope of the semilinear region. The sigmoid nonlinearity activates in every layer except in the input layer^{39}. The sigmoid activation function represented by Equation 2 gives outputs in (0,1). If it desired, the outputs of this function can be adjusted to (1,1) interval. As the sigmoid processor represents a continuous function it is particularly used in nonlinear descriptions. Because its derivatives can be determined easily with regard to the parameters within (net)_{j} variable^{39}.
LMBP is often the fastest available backpropagation algorithm, and is highly recommended as a firstchoice supervised algorithm, although it requires more memory than other algorithms. The standard LMBP training process can be described in the pseudocode of Figure 2^{[42]}.
4.1. Neural network model structure and parameters
ANN model is carried out in this research has eight neurons in the input layer and one neurons in the output layer as demonstrated in Figure 3. The values for input layers were cement content (C), nanoparticle content (N), aggregate type (AG), water content (W), the amount of superplasticizer (S), the type of curing medium (CM), Age of curing (AC) and number of testing try (NT). The values for output layer were splitting tensile strength (f_{S}) data in one set and water absorption (f_{W}) in the other set. Two hidden layer with ten and eight neurons were used in the architecture of multilayer neural network because of its minimum absolute percentage error values for training and testing sets. The neurons of neighboring layers are completely interconnected by weights. Finally, the output layer neurons produce the network prediction as a result.
In this study, the backpropagation training algorithm has been utilized in feedforward two hidden layers. Backpropagation algorithm, as one of the most wellknown training algorithms for the multilayer perceptron, is a gradient descent technique to minimize the error for a particular training pattern in which it adjust the weights by a small amount at a time^{42}. The nonlinear sigmoid activation function was used in the hidden layer and the neuron outputs at the output layer. Momentum rate and learning rate values were determined and the model was trained through iterations. The trained model was only tested with the input values and the predicted results were close to experiment results. The values of parameters used in neural network model are given in Table 5.
To make a decision on the completion of the training processes, two termination states are declared: state 1 (ANNI model) means that the training of neural network was ended when the maximum epoch of process reached (1000) while state 2 (ANNII model) means the training ended when minimum error norm of network gained.
5. Genetic Programming
Genetic programming (GP) proposed by Koza^{43} is an extension to Genetic Algorithms (GA). Koza^{43} defines GP as a domain independent problemsolving approach in which computer programs are evolved to solve, or approximately solve, problems based on the Darwinian principle of reproduction and survival of the fittest and analogs of naturally occurring genetic operations such as crossover and mutation. GP reproduces computer programs to solve problems by executing the steps in Figure 4. This figure is a flowchart showing the executional steps of a run of GP. The flowchart demonstrates the genetic operations in addition to the architecture chancing operations. Also, this flowchart demonstrates a two offspring version of the crossover operation.
Gene expression programming (GEP) software which is used in this study is an extension to GEP that evolves computer programs of different sizes and shapes encoded in linear chromosomes of fixed length. The chromosomes are composed of multiple genes, each gene encoding a smaller subprogram. Furthermore, the structural and functional organization of the linear chromosomes allows the unconstrained operation of important genetic operators such as mutation, transposition, and recombination^{4446}. The two main parameters GEP are the chromosomes and expression trees (ETs)^{4446}. Two languages are utilized in GEP: the language of the genes and the language of ETs. A significant advantage of GEP is that it enables to infer exactly the phenotype given the sequence of a gene, and vice versa which is termed as Karva language.
For each problem, the type of linking function, as well as the number of genes and the length of each gene, are a priori chosen for each problem. While attempting to solve a problem, one can always start by using a singlegene chromosome and then proceed by increasing the length of the head. If it becomes very large, one can increase the number of genes and obviously choose a function to link the subETs. One can start with addition for algebraic expressions or for Boolean expressions, but in some cases another linking function might be more appropriate (like multiplication or IF, for instance). The idea, of course, is to find a good solution, and GEP provides the means of finding one very efficiently^{44}.
5.1. Genetic expression programming structure and parameters
In this study, as seen in Figures 58, the expression trees of two different GEP approach models namely GEPI and GEPII were constructed for splitting tensile strength and water absorption. d0, d1, d2, d3, d4, d5 d6 and d7 in Figures 58 represent C, N, AG, W, S, CM, AC and NT, respectively. In the GEPI and GEPII, as the number of genes used 3 and 4 genes (SubETs), and as linking function used addition and multiplication, respectively. In training and testing of the GEPI and GEPII approach models constituted with two different SubETs and linking function C, N, AG, W, S, CM, AC and NT as input data and f_{S} and f_{W }as independent output data. Among 144 experimental sets, 117 sets were randomly chosen as a training set for the GEPI and GEPII modeling and the remaining 27 sets were used as testing the generalization capacity of the proposed models.
For this problem, firstly, the fitness, f_{i}, of an individual program, i, is measured by:
where M is the range of selection, C_{(i,j)} is the value returned by the individual chromosome i for fitness case j (out of C_{t} fitness cases) and T_{j} is the target value for fitness case j. If C_{(ij)}  T_{j} (the precision) is less than or equal to 0.01, then the precision is equal to zero, and f_{i} = f_{max} = C_{t}M. In this case, M = 100 was used, therefore, f_{max} = 1000. The advantage of this kind of fitness functions is that the system can find the optimal solution by itself^{44,47}.
Afterwards the set of terminals T and the set of functions F to create the chromosomes are preferred, namely, T = {C, N, AG, W, S, CM, AC, NT} and four basic arithmetic operators (+, , *, /) and some basic mathematical functions (Sqrt, x^{3}) were used.
Another major step is to choose the chromosomal tree, i.e., the length of the head and the number of genes. The GEPI and GEPII approach models initially used single gene and two lengths of heads, and increased the number of genes and heads, one after another during each run, and monitored the training and testing sets performance of each model. In this study, for the GEPI and GEPII approach models observed the number of genes 3 and 4, and length of heads 10 and 12, respectively. In addition, for the GEPI and GEPII approach models determined the linking function multiplication and addition, respectively.
Finally, a combination of all genetic operators (mutation, transposition and crossover) was utilized as set of genetic operators. Parameters of the training of the GEPI and GEPII approach models are given in Table 6. For the GEPI and GEPII approach models, chromosome 30 and 40 were observed to be the best of generation individuals predicting f_{S} and f_{W}. Explicit formulations based on the GEPI and GEPII approach models for f_{S }and f_{W} were obtained by:
Figures 5 and 6 show the expression trees with 3 and 4 gens respectively for splitting tensile strength prediction and Figures 7 and 8 show the expression trees with 3 and 4 gens respectively for water absorption prediction. The related formulations could be obtained by the procedure shown in Figure 9^{[7]}.
6. Results
6.1. Artificial neural network
In this study, the error arose during the training and testing in ANNI and ANNII models can be expressed as absolute fraction of variance (R^{2}) which are calculated by Equation 8^{[48]}:
where t is the target value, o is the output value and p is the pattern.
All of the results obtained from experimental studies and predicted by using the training and testing results of ANN I and ANN II models, for f_{S} are given in Figures 10a, b, respectively and for f_{W} in Figures 11a, b, respectively. The linear least square fit line, its equation and the R^{2 }values were shown in these figures for the training and testing data. As it is visible in Figures 10 and 11 the values obtained from the training and testing in ANNI and ANNII models are very close to the experimental results. The result of testing phase in Figures 10 and 11 shows that the ANNI and ANNII models are capable of generalizing between input and output variables with reasonably good predictions.
The performance of the ANNI and ANNII models for f_{S} and f_{W} is shown in Figures 10 and 11, respectively. The best values of R^{2} are 98.29 and 98.89% for training set in the ANNII model, respectively for splitting tensile strength and water absorption. The minimum values of R^{2} are 92.09 and 94.79% for testing set in the ANNI model, respectively for splitting tensile strength and water absorption. All of R^{2} values show that the proposed ANNI and ANNII models are suitable and can predict f_{S} and f_{W} values for every age very close to the experimental values.
6.2. Genetic programming
Once again, in this study, the error arose during the training and testing in GEPI and GEPII models can be expressed as R^{2} which are calculated by Equation 8. All of the results obtained from experimental studies and predicted by using the training and testing results of GEPI and GEPII models, for f_{S} are given in Figures 12a, b, respectively and for F_{W} in Figures 13a, b, respectively. The linear least square fit line, its equation and the R^{2 }values were shown in these figures for the training and testing data. As it is visible in Figures 12 and 13 the values obtained from the training and testing in GEPI and GEPII models are very close to the experimental results. The result of testing phase in Figures 12 and 13 shows that the GEPI and GEPII models are capable of generalizing between input and output variables with reasonably good predictions.
The performance of the GEPI and GEPII models for f_{S} and f_{W} is shown in Figures 12 and 13, respectively. The best values of R^{2} are 97.82 and 94.99% for training set in the GEPII model, respectively for splitting tensile strength and water absorption. The minimum values of R^{2} are 90.93 and 93.13% for testing set in the GEPI model, respectively for splitting tensile strength and water absorption. All of the statistical values show that the proposed GEPI and GEPII models are suitable and can predict f_{S} and f_{W} values for every age very close to the experimental values.
7. Discussion
Artificial neural networks are capable of learning and generalizing from examples and experiences. This makes artificial neural networks a powerful tool for solving some of the complicated civil engineering problems. In this study, using these beneficial properties of artificial neural networks in order to predict the splitting tensile strength and water absorption values of concretes containing ZnO_{2} nanoparticles without attempting any experiments were developed two different multilayer artificial neural network architectures namely ANNI and ANNII. In two models developed in ANN method, a multilayered feed forward neural network with a back propagation algorithm was used. The models were trained with input and output data. Using only the input data in trained models the splitting tensile strength and water absorption values of concretes containing ZnO_{2} nanoparticles were found. The splitting tensile strength and water absorption values predicted from training and testing, for ANNI and ANNII models, are very close to the experimental results. Furthermore, according to the splitting tensile strength and water absorption results predicted by using ANNI and ANNII models, the results of ANNII model are closer to the experimental results. R^{2} values that are calculated for comparing experimental results with ANNI and ANNII model results have shown this situation.
In addition, this study reports a new and efficient approach for the formulation of concrete containing ZnO_{2} nanoparticles using GEP. Two different GEPI and GEPII approach models are proposed in order to predict splitting tensile strength and water absorption values of concrete containing ZnO_{2} nanoparticles. The proposed models are empirical and based on experimental results. The models developed in this study are used to be the number of genes 3 and 4, and the linking function addition and multiplication, respectively. All of the results obtained from the models show excellent agreement with experimental results. The statistical values of R^{2} have shown this situation. Also, the proposed models are so simple that they can be used by anyone not necessarily familiar with GEP. Moreover, it is concluded that GEP is a good soft computing technique for use in concrete properties prediction. As a result, GEP may serve as a strong approach model and it may open a new area for the accurate and effective explicit formulation of many civil engineering problems.
From the predicted results for splitting tensile strength and water absorption, it is concluded that ANN models are more suitable for prediction the concrete properties. This conclusion is made on the R^{2} values obtained from different applied models. However, application of GEP as a result of its simplicity is a relatively suitable approaches for prediction the concrete properties. The results show that both ANNs and GEP models have different R^{2} values for splitting tensile strength and water absorption fitting in both training and testing data sets. This may be due to very close data in both splitting tensile strength and water absorption results. However, as mentioned, all of the predicted results fall in acceptable ranges.
As author's literature survey shows, there are no works for prediction the effects of nanoparticles on properties of concrete specimens by the other researchers. However, as mentioned by the other authors ANNs^{[2,3]} and GEP^{[6,7]} are suitable soft computing tools for prediction the properties of concrete specimens. The results obtained from this work also indicate these findings.
8. Conclusions
ZnO_{2} nanoparticles showed its influence on splitting tensile strength and percentage water absorption up to 1.0 weight percent in NW series concrete, up to 2.0 weight percent in NLW series concrete and finally up to 4.0 weight percent in NSCC series concrete. The deficiency in dispersion of nanoparticles more than the mentioned values causes the reduction of nanoparticles effects on improving splitting tensile strength and percentage water absorption results.
ANN and GEP can be an alternative approach for the evaluation of the effect of cementitious material on the splitting tensile strength and percentage water absorption. There is an optimum replacement ratio of ZnO_{2} nanoparticles existed; this value can be predicted using ANN and GEP models.
ANN and GEP are efficient for predicting the splitting tensile strength of ZnO_{2} nanoparticles concrete. Comparison between ANN and GEP in terms of R^{2}, showed that ANN provides better results than the GEP results.
Received: September 9, 2010
Revised: April 3, 2012
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Publication Dates

Publication in this collection
07 June 2012 
Date of issue
June 2012
History

Received
09 Sept 2010 
Accepted
03 Apr 2012