Elsevier

Materials & Design

Volume 32, Issue 7, August 2011, Pages 3966-3979
Materials & Design

Computer-aided design of the effects of Fe2O3 nanoparticles on split tensile strength and water permeability of high strength concrete

https://doi.org/10.1016/j.matdes.2011.01.064Get rights and content

Abstract

In the present paper, two models based on artificial neural networks and genetic programming for predicting split tensile strength and percentage of water absorption of concretes containing Fe2O3 nanoparticles have been developed. To build these models, training and testing of the network by using experimental results from 144 specimens produced with 16 different mixture proportions were conducted. The data used in the multilayer feed forward neural networks models and input variables of genetic programming models have been arranged in a format of eight input parameters that cover the cement content, nanoparticle content, aggregate type, water content, the amount of superplasticizer, the type of curing medium, age of curing and number of testing try. According to these input parameters, in the two models, the split tensile strength and percentage of water absorption values of concretes containing Fe2O3 nanoparticles were predicted. The training and testing results in the neural network and genetic programming models have shown that every two models are of strong potential for predicting the split tensile strength and percentage of water absorption values of concretes containing Fe2O3 nanoparticles. Although neural network has predicted better results, genetic programming is able to predict reasonable values with a simpler method rather than neural network.

Highlights

Nanoparticles in concrete. ► Mechanical properties of concrete in presence nanoparticles. ► Physical properties of concrete in presence nanoparticles. ► Artificial neural network for design. ► Genetic programming for design.

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 cement-based 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 [4], [5], [6]. 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].

The aim of this study is to predict split tensile strength and percentage of water absorption of several types of concrete with and without Fe2O3 nanoparticles by ANNs and GP. Totally 144 split 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.

Section snippets

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 [9] standard was used as received. The chemical and physical properties of the cement are shown in Table 1. The particle size distribution pattern of the used OPC has been illustrated

Experimental results

The split tensile strength results of the specimens are shown in Table 4. Table 4 shows that the split tensile strength increases with adding nano-Fe2O3 particles up to 1.0% in N-W series. It has been shown that using 2.0% Fe2O3 nanoparticles decreases the split tensile strength to a value which is near to the control concrete. This may be due to the fact that the quantity of nano-Fe2O3 particles is higher than the amount required to combine with the liberated lime during the process of

Artificial neural networks

ANNs were developed to model the human brain [15]. 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 [16]. McCulloch and Pitts [17] defined artificial neurons for the first time and developed a neuron model as in Fig. 4. McCulloch and Pitts’ network [17] formed the basis for

Genetic programming

Genetic programming proposed by Koza [21] is an extension to Genetic Algorithms (GA). Koza defines GP as a domain independent problem-solving 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 Fig. 8. This figure is a

Artificial neural network

In this study, the error arose during the training and testing in ANN-I and ANN-II models can be expressed as absolute fraction of variance (R2) which are calculated by Eq. (8) [27]:R2=1-i(ti-oi)2i(oi)2where 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 fS are given in Fig. 14a and b, respectively and for fW in Fig. 15a and b,

Discussion

Artificial neural networks are capable of learning and generalizing from examples and experiences [16]. This makes artificial neural networks a powerful tool for solving some of the complicated civil engineering problems [17]. In this study, using these beneficial properties of artificial neural networks in order to predict the split tensile strength and percentage of water absorption values of concretes containing Fe2O3 nanoparticles without attempting any experiments were developed two

Conclusions

  • (1)

    Fe2O3 nanoparticles showed its influence on split tensile strength and percentage water absorption up to 1.0 wt.% in N-W series concrete, up to 2.0 wt.% in N-LW series concrete and finally up to 4.0 wt.% in N-SCC series concrete. The deficiency in dispersion of nanoparticles more than the mentioned values causes the reduction of nanoparticles effects on improving split tensile strength and percentage water absorption results.

  • (2)

    ANN and GEP can be an alternative approach for the evaluation of the

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