ARTIFICIAL NEURAL NETWORK FOR CONCRETE MIX DESIGN

ARTIFICIAL NEURAL NETWORK FOR CONCRETE MIX DESIGN

M Monjurul Hasan1, Ahsanul Kabir2

1. Z H Shikder University of Science & Technology Shariatpur, Bangladesh

2. Bangladesh University of Engineering and Technology Dhaka, Bangladesh

ABSTRACT. Concrete mix design is complicated, time consuming, experience based and uncertain task. Most of the time to achieve the designed strength, one has to depend on the past experience in mix design process and some sort of trial and error methods. The final acceptance comes after the quality control test results. In mix design, the main task is proportioning the ingredients of concrete (water, cement, coarse-aggregate and fine-aggregate) to achieve the desired strength. In this paper, an artificial neural network is being used to predict the concrete mix ratio to achieve the desired strength. The parameters such as, 28-day strength, maximum gravel size, presence of air, fineness modulus of sand, gravels dry-rod unit weight, water cement ratio are used to predict mix ratio (weight basis) in terms of fine aggregate-cement ratio and coarse aggregate-cement ratio. It is always convenient to work with unit-less parameters and concrete mix ratio is a number without any unit attached to it. The artificial neural network was trained just to predict two parameters only, which simplifies the architecture of the network and decreases the number of iteration for training and also the training time. The experimental investigation shows that the neural network model successfully predicts the mix ratios with great efficiency (99.5%) and the network has the potential to perform different parametric studies. Keywords: Concrete, Mix Ratio, Mix Design, Neural Network. M Monjurul Hasan is a lecturer in the Department of Civil Engineering, Z H Shikder University of Science & Technology at Shariatpur in Bangladesh. His research interest includes concrete mix design, strength prediction and use of recycled aggregates in concreting. Dr Ahsanul Kabir is a Professor of Civil Engineering at Bangladesh University of Engineering and Technology, Dhaka, Bangladesh. He is a life fellow of the Institution of Engineers (Bangladesh), Member ACI, Member ISSMFE and Member Bangladesh Society of Geotechnical Engineering. His research interests are nonlinear analysis of concrete structures, concrete mix design with brick and recycled concrete aggregates, concrete strength predictions, deep beams, retrofitting and up-gradation of concrete structures.

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INTRODUCTION Concrete is the most common and one of the major construction materials which is widely used in the world for its performance in the construction practice. In case of designing a concrete structure we need to use the design strength of the concrete. In practice we have to achieve this strength in the field by some mix design procedure. Mix design is a process of selecting appropriate ingredients of concrete in right proportion. Coarse aggregate (CA), fine aggregate (FA), cement (C) and water (W) are the basic ingredients of concrete. There are other materials which can be considered as the ingredients of concrete like fly ash, silica fume, perlite, super plasticizer etc. because of their frequent and purposeful use to modify quality and strength of concrete. Mix design, in the other sense is a process to find required mix ratio of coarse aggregate and fine aggregate with respect to cement in order to achieve a target concrete strength. This is not an easy task. Most of the time, we have to depend on experience and the trial and error process. There are many factors which influence the mix design process and most of the time their mutual relationship is complex. For that reason, an exclusive mathematical approach has not yet been established for concrete mix design. So, there are continuous efforts to develop expert systems for concrete mix proportioning and adjustments [1]. This study is an attempt to evaluate the performance of artificial neural network (ANN) as a smart system for mix design problem, minimizing various uncertainties and errors. Previously ANN was used to predict the concrete compressive strength for specific mix proportions of the ingredients of the concrete [2, 3]. In reality, the necessity of prediction comes later. The first challenge is to do proper mix design in the field condition satisfying the desired strength considering all other criteria like quality of the ingredients and required workability. Predicting the proper mix ratio becomes more important for this reason. Some studies were performed previously to predict the mix proportion (cement, fine aggregate and coarse aggregate content per unit volume of the concrete) of the concrete mixes using ANN [4] to satisfy the desired strength of concrete. In this study ANN is used to determine the mix ratios [fine-aggregate to cement ratio (FA/C) and coarse-aggregate to cement ratio (CA/C)] of the concrete ingredients instead of finding the mix proportions. Individually four back-propagation algorithms are used to train the ANN and prediction performances of the networks are checked. Use of mix ratio [a unit-less parameter] instead of using the mix proportion of the normal weight concrete ingredients simplifies the ANN architecture and reduces the training time and subsequently from the mix ratio, it easy to calculate the amount of the ingredients required per unit volume of concrete. Total 93 mix design data used here are taken from the previous study by Malasri et al [2]. The mix design method adopted by them was that of the American Concrete Institute and the study was performed considering only the coarse-aggregate (CA), fine-aggregate (FA) and cement (C) as the major ingredients of the normal weight concrete.

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CONCRETE Concrete is an inert mass which grows from a cementing medium, became very popular because of its versatile use. Concrete is made up with two major components. One is the cement paste and other is the inert material. The cementing medium is made up of water and cement; coarse aggregate and fine aggregate occupies the section of the inert material. In the properly mixed concrete, these materials are completely surrounded and coated by the cement paste filling all the void space between the particles. With time the setting process of the concrete starts and it gradually gain its strength. In practice, 28 days cylinder crushing strength tests ensure the concrete compressive strength as per design/construction code requirements. Concrete Strength Strength is the most valuable property of the concrete that is used for design works. In practice, concrete is designed for a specific strength with desired workability. Durability, impermeability and volume stability can be important for some cases but these are usually of secondary importance. Further, good strength itself is an indicative measure of these additional properties. The factors which influence the strength of the concrete are water-cement ratio, density, aggregate-cement ratio and the aggregate properties. The percentage of water has great influence on concrete. A minimum amount of water is needed for the proper chemical action (called hydration) of cement in concrete; on the other hand excess water increases the workability but reduces strength. Amount of water content per unit volume of concrete is an indicator of the workability for normal weight concrete Concrete Mix Ratio Finding out concrete mix (ingredient) ratio is the main task of concrete mix design. The purpose of the mix design is to find out the proper proportion of cement, fine aggregate, coarse aggregate and water for the concrete mass to satisfy the design strength, at the same time economy and workability should also be achieved. Workability is more or less ensured by the water-cement ratio and the next step is to find out the right proportion of cement and aggregate content. This task may be simplified by finding out the relative proportion of coarse and fine aggregate with respect to the cement content (CA/C, FA/C). From the relative proportions of the concrete ingredients, the actual amount of these aggregates and cement per unit volume can be calculated. As the mix ratio is a unit-less parameter the quantity conversion can easily be made to any convenient unit which enhances the versatility of using this form [5].

ARTIFICIAL NEURAL NETWORK An artificial neural network (ANN) is the branch of artificial intelligence where the basic idea of formation comes from the human brain system. ANN has the model like the human brain consisting of small information processing elements named artificial neuron interconnecting together. A human brain learns from experience and takes decisions from judgments. These


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concepts are being used in forming ANN. The ANN is nothing but to delegate power to take decision from experience. For this reason the network is trained first from similar kinds of incidental data. After the training, it becomes capable of behaving according to its learning. ANN performs its task through the proper division of tasks among the small units of artificial neurons and becomes an expert system because it learns from the existing data and parameters. In recent years, ANN is widely used for modeling behavior of many physical phenomena [6], even in civil engineering [7]. ANN for Mix Ratio In case of mix design problem, practical knowledge, judgments and trial and error process are the main basis. If a system is established that can do these entire functions mentioned above with greater efficiency, it will be a great help to solve the mix design problem. This is the prime reason for choosing ANN to solve this problem with increased efficiency. Mix proportion prediction (by weight) has been already verified [4] and the water-cement ratio [W/C], fine-aggregate percentage, unit water content, unit cement content and unit coarse-aggregate content [total six parameters] are calculated from the ANN program. The input values were compressive strengths, maximum size of the aggregate, slump and fineness modulus of the fine-aggregate. This paper contributes to predict only two mix ratio [FA/C, CA/C] from the input of specified concrete compressive strength, maximum size of aggregate, fineness modulus of the fine-aggregate, dry-rod unit weight, presence of air and water cement ratio (W/C). Actual amount of the ingredients[C, FA, CA] per unit volume of concrete can be calculated easily from these mix ratios in any unit. Figure 1 shows the simplified ANN diagram of the prediction.

Figure 1 Simplified diagram of the ANN for predicting the mix ratio. Here, ANN is designed to predict only two unit-less parameters which not only simplifies the ANN architecture but also reduce the training time and increases the efficiency of the neural network system.


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ANN Architecture Architecture of a neural network is structured, based on two important things. One is, the neurons have to be arranged in layers and the other is that each neuron to be interconnected with all the neurons of the adjacent layers. Generalized structure of an artificial neuron and an ANN architecture is shown in Figure 2 and Figure 3 respectively [3].

Figure 2: Structure of an Artificial Neuron

Figure 3: Architecture of ANN

The descriptions of the variables shown in the Figure 2 –

• an input vector,

• a weight vector,

• a bias,

• a network potential,

• an activation function,

• an output vector,

The function of an artificial neuron is to receive inputs under an input receiving unit and carry them inside the neuron for processing and finally give an output, so each neuron can classify in some part as the input unit, one summation block, one activation block and finally one result processing unit. The ANN that has been developed for this case study has one input layer, one hidden and one output layer [Figure 1]. The neurons of each layer are interconnected to every neurons of the adjacent layer. Back-propagation network [8, 9] is used to solve this particular problem. It is the most popular and widely used basic algorithm to solve the problems.


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ANN Training During training process, data are passed to the input layer and then it passes from layer to layer maintaining the system of forward pass. In this system, each neuron in the hidden layer receives inputs from input layer’s neurons which are already being multiplied by the adjacent weight and then summed up, in some case it is modified by adding bias. Afterwards it passes through the transfer function and delivers it for the output layer for preparing results maintaining same procedures. Comparing the output values with the target values, errors are calculated. Errors are minimized with the process of iteration and in case of Back-propagation, these are propagated backward to adjust or update the weight for gaining better accuracy. Following this system, a Back-propagation network gets trained. Training of the network is nothing but adjusting the weights between the connections of the neurons. The whole process is summarized below with a simple flow diagram (Figure 4):

Figure 4 Training process of an ANN

EXPERIMENT WITH ANN In total 93 data sets are used for this study. Among them 74 data sets are used for training and the remaining 19 data sets are used for testing the effectiveness. Data used for testing the trained ANN are selected randomly. Table 1 summarizes the ranges of material properties of different data sets used for the study Four Back-propagation algorithms [8] are used to train the network and to check the performance of ANN for this particular case of Mix Design prediction problem. These are:–

• Levenberg-Marquardt (LM) Algorithm

• Resilient Back-propagation (RB) Algorithm

• Variable Learning Rate (VLR) Algorithm

• Conjugate Gradient (CG) Algorithms


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Table 1 Summary (Range) of Concrete Mix Ratio Data Set

Property Names Unit Maximum Minimum

Strength of concrete (28 day) MPa 27.58 13.79 Cement (C) Kg/m3 420 229 Water (W) Kg/m3 202 160 Coarse-aggregate (CA) Kg/m3 1145 692 Fine-aggregate (FA) Kg/m3 1072 679 Gravel dry-rod weight Kg/m3 1762 1442 W/C ratio - 0.82 0.48 CA/C ratio - 5 1.76 FA/C ratio - 4.38 1.82 Presence of air - Yes No Fineness modulus of FA - 3.0 2.4

Performance Evaluation Data are used to train the ANN with Back-propagation algorithms and tasted for the best performance. The performances of the algorithms are evaluated by four expressions, mean absolute error (MAE), root mean square error (RMSE), correlation coefficient (R) and normal efficiency (EF).

Here,

• Ai = Actual value. • Pi = Predicted value. • n = 1, 2, 3, …….., n, …


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A statistical comparison between the actual and ANN predicted mix ratio (using different Back-propagation algorithms) are given in the Table 2 for the19 test data sets and in the Table 3 for all the 93 data.

Table 2 Prediction accuracy of different Back-propagation algorithms for 19 test data sets

NAME OF ALGORITHMS

EF (%) RMSE MAE R

FA/C CA/C FA/C CA/C FA/C CA/C FA/C CA/C Levenberg-Marquardt (LM)

99.93 99.96 0.0035 0.0018 0.0017 0.0011 1.0000 1.0000

Resilient Back-propagation (RB)

99.42 99.38 0.0220 0.0254 0.0171 0.0196 0.9993 0.9995

Variable Learning Rate (VLR)

97.38 96.73 0.1053 0.1224 0.0781 0.941 0.9844 0.9876

Scaled Conjugate Gradient (CG)

99.76 99.77 0.0084 0.0087 0.0069 0.0063 0.9999 0.9999

Table3 Prediction accuracy of different Back-propagation algorithms for all 93 data sets

NAME OF ALGORITHMS

EF (%) RMSE MAE R

FA/C CA/C FA/C CA/C FA/C CA/C FA/C CA/C Levenberg-Marquardt (LM)

99.92 99.95 0.0037 0.0016 0.0019 0.0011 1.0000 1.0000

Resilient Back-propagation (RB)

98.46 98.24 0.2537 0.2429 0.0469 0.0544 0.9215 0.9559

Variable Learning Rate (VLR)

97.29 97.23 0.1063 0.1158 0.765 0.779 0.9832 0.9895

Scaled Conjugate Gradient (CG)

99.25 98.94 0.1471 0.2136 0.0229 0.0321 0.9709 0.9659

It can be observed from the above tables that the Levenberg-Marquardt Back-propagation algorithm performs best among the four Back-propagation algorithms studied. The performance of Scaled Conjugate Gradient (CG) back-propagation method is also reasonably close to the Levenberg-Marquardt (LM) Back-propagation algorithm. Figure 4 compares the efficiency of prediction for all the four back-propagation algorithms considered in this study. The bar chart shown compares the efficiency for the 19 test data sets. The minimum efficiency is about 97% for Variable Learning Rate Back-propagation (VLR) algorithm. Efficiency is found to be 99% for the other three Back-propagation algorithms studied. Performance of ANN trained (using LM Back-propagation) in predicting the Coarse Aggregate to Cement (CA/C) ratio and Fine Aggregate to cement (FA/C) ratio for all the 19 test sample data are compared in the Figure 5. The exhibited correlation between prediction and actual can be termed quite well.


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Figure 4 Efficiency of different Back-propagation algorithms for the test data

Figure 5 Comparing ANN trained algorithm in predicting the Coarse Aggregate to

Cement and Fine Aggregate to cement ratios for the test data samples

CONCLUSION

This study demonstrates that the ANN can be a very convenient tool for the purpose of solving mix design problems. ANN can be used effectively for complete design of concrete mixes with great efficiency. An earlier work was aimed at predicting the mixing proportions of the ingredients like Coarse Aggregate, Fine Aggregate and cement content per unit volume of the concrete. In this study emphasis is given to predict the mix ratio, like the CA/C ratio and FA/C ratio and from there the amount (weight) of the ingredients are to be determined. This model of predicting the mix ratio was preferred because it deals with dimensionless quantities and it is convenient to work with dimensionless quantities compared to those with dimensional units. The


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choice of mix ratios increases the performance of the ANN because this model of ANN predicts only two parameters which give a simple and less complicated ANN architecture, thus takes less time to train the network and also increases the efficiency of ANN as a mix design tool. It presents ANN as a powerful tool for mix design problems and different parametric studies of concrete behavior. However, it needs mentioning that the accuracy of ANN’s prediction depends on the number of training data and its variations. More reliable prediction can be made with more data with wide variations.

ACKNOWLEDGEMENT The data reported in this study is based on information provided from several research projects. Authors acknowledge the support from the Department of civil engineering of Bangladesh University of Engineering and Technology (BUET), Dhaka.

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9. RUMELHART D E, HINTON G E AND WILLIAM R J, Learning Internal Representations by Error Propagation. D.E. Rumelhart and J. McClelland, editors, Parallel Distributed Processing, The M.I.T. Press, Cambridge, MA, 1986, pp. 318-362.


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ARTIFICIAL NEURAL NETWORK FOR CONCRETE MIX DESIGN

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