以類神經網路評估高性能混凝土的工作度

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以類神經網路評估高性能混凝土的工作度

葉怡成

中華大學資訊管理學系

摘要

本研究建立類神經網以探索類神經網路預測高性能混凝土坍流度的可行性，並以訓練過的類神經網路進行混凝土坍流度的計算模擬。用變化因子的組

合，像水膠比、SP/ 膠結料比、用水量，達到變化混凝土坍流度的效果，產生

了坍流度曲線，以探索水膠比、SP/ 膠結料比、用水量的作用。結果發現 (1) 以

類神經網路預測混凝土坍流度很有潛力；(2) 在水膠比分別為 0.4 和 0.5 下，每

增加百分之一的SP/ 膠結料比，可節省的用水量約為 15 和 10kg/ m³；(3) 增

加SP/ 膠結料比增加了坍流度，然而其效果在高水膠比時遠比低水膠比時來得小。

關鍵詞：高性能混凝土，強塑劑，坍流度，工作度，類神經網路。

NEURAL NETWORKS FOR EVALUATING WORKABILITY OF HIGH-PERFORMANCE CONCRETE

I-Cheng Yeh

Professor, Department of Information Management Chung-Hua University

Hsin Chu, Taiwan 300, R.O.C.

Key Words: high-performance concrete, superplasticizer, slump-flow, worka- bility, artificial neural networks.

ABSTRACT

In this study, an artificial neural network was established to explore the feasibility of using neural networks in predicting the slump-flow of concrete. Computational simulation of concrete slump-flow was performed using the trained neural network. The variation in concrete slump-flow was achieved by varying combinations of factors like the water/binder ratio, SP-binder ratio, and water content. The slump-flow curves under various ratios were generated by the trained neural networks developed in this study to investigate the effects of water/binder ratio, SP-binder ratio, and water content. It was found that (1) the use of a neural network for the modeling of concrete slump-flow looks promising, (2) the water content saved by the use of SP is about 15 and 10 kg/ m³ for every percent of SP / b, at w/b = 0.4 and 0.5, respectively, and (3) an increasing SP/b ratio increased the slump-flow, while the effect was much smaller at high w/b ratio than that at low w/b ratio.

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I. INTRODUCTION

Nowadays the workability of high-performance concrete (HPC) is mainly evaluated by slump tests. However, the validity of a slump test generally only holds for concrete with a slump value ranging from 2.5 to 20 cm, corresponding ap- proximately to a consistency range from low plastic to medium plastic. Therefore, these test methods do not seem ap- propriate to characterize the workability of HPC with high flowability, since its slump value is usually more than 20 cm.

Moreover, it is known empirically that concretes with the same slump value may have different workabilities. To evalu- ate the workability property solely based on slump test results can be misleading. An alternative test method adopted in Ja- pan and Taiwan is the slump-flow test [1], which is simply a measurement of the diameter of the concrete after it has col- lapsed in a standard slump test. The use of slump-flow is more sensitive in characterizing the workability of HPC.

Because of their high fines content, high-strength concrete mixes tend to be quite cohesive, sticky, and viscous.

Experience with high-strength concrete has revealed that even at the same slump value, which is commonly taken as a measure of workability, a higher strength concrete mix is generally more difficult to compact. In other words, a higher strength concrete mix needs a higher slump for proper consolidation.

With the increasingly common practice of designing concrete structures, especially tall concrete building structures, to con- tain congested steel reinforcement, it is inevitably desirable to have, for in situ construction, high-strength concretes that have not only high strength but also high workability [2].

Therefore, there is an urgent need to find a more basic and reliable approach to measure workability.

High-strength concrete has been traditionally produced by lowering the water/cement ratio. This, however, reduces the workability of the concrete mix and renders the concrete mix more difficult to compact. That was why the earliest high-strength concretes were mostly 0-2.5 cm slump "labora- tory concretes". The workability can be restored to a more acceptable level by adding superplasticizer (SP).

The necessity of using a superplasticizer in the manufac- ture of HPC merits brief explanation. Without a superplasticizer, the water content of a mixture cannot be reduced very far as this would result in an unworkable mixture. At the same time, the cement content cannot be raised excessively, not only because of cost, but also because a high cement content may lead to thermal problems. The combination of an upper

limit on the content of cement and a lower limit on the content of water means that, without a superplasticizer, the w/c cannot be reduced below a value of about 0.4 [3].

Experience has shown that it is not always possible to produce HPC that is still workable, using 150kg/ m³of water, by simply choosing a random combination of portland cement and 2% superplasticizer. The reason for this is the interaction between the cementitious material and the superplasticizer, which is rather complex and which can lead to a low slump.

Difficult and poor workability properties are often referred to as barriers to proper utilization of high-strength concrete, but very little information about workability properties of such concrete is available in the literature. A literature search was conducted. Rather than compiling an exhaustive annotated bibliography of the available literature, some im- portant publications were reviewed, and they are listed in the References at the end of the paper [4-8]. Lacking such information, optimization of a concrete mix proportion is rarely attained.

Material models, in general, have been developed in the same way: (1) A material is tested and its behavior is observed; (2) a mathematical model is postulated to explain the observed behavior, and material parameters are determined; (3) the mathematical model is used to predict behavior in yet untested situa- tions; and (4) the mathematical model is then modified to account for behavior observed but unexplained by the model [9].

Neural network-based material models differ in some fundamental ways from the traditional mathematical models.

Neural networks are mathematical entities whose design is motivated, to some extent, by biological processes, but which follow strictly defined rules of behavior. The process by which a neural network’s weights (connection strengths) are established is referred to as ‘training’. In order to train an artificial neural network, there must be a substantial quantity of data available. The data are provided to the network in the form of training pairs, vectors of information consisting of independ- ent input values and their associated output results [10].

Such a trained neural network not only would be able to reproduce the experiment results it was trained on, but through its generalization capability it should be able to approximate the results of other experiments. The degree of accuracy in this generalization depends on how comprehensive the training set is [9]. Some recent applications of neural networks in civil engineering materials include references [8-20] in this paper’s references. However, little research has been done on modeling workability of concrete using neural networks.

In this study, an artificial neural network-based modeling system was established to explore the feasibility of using neu-

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ral networks in predicting the slump-flow of concrete. In addition, the results obtained by neural network were compared with the experimental values and with those determined from a statistical regression model. Computational simulation of concrete slump-flow was performed using the trained neural network by varying combinations of factors like the water/binder ratio (w/b), SP-binder ratio (SP/b), and water content. Finally, some conclusions were deduced from these curves and were discussed.

II. NEURAL NETWORKS

A neural network is a computer model whose architecture essentially mimics the knowledge-acquisition of the human brain. It consists of a number of interconnected processing elements, commonly referred to as neurons. The neurons are logically arranged into two or more layers and interact with each other via weighted connections. These scalar weights determine the nature and strength of the influence between the interconnected neurons. Each neuron is connected to all the neurons in the next layer. There is an input layer where data are presented to the neural network and an output layer that holds the response of the network to the input. It is the inter- mediate layers, also known as hidden layers, which enable these networks to represent and compute complicated associa- tions between patterns [21].

Each hidden and output neuron processes its inputs by multiplying each input by its weight, summing the product, and then passing the sum through a nonlinear transfer function to produce a result. The S-shaped sigmoid curve is commonly used as a transfer function.

The neural network “learns” by modifying the weights of the neurons in response to the errors between the actual output values and the target output values. The neural network para- digm adopted in this study utilizes the back propagation learning algorithm. In back propagation neural networks, the mathematical relationships between the various variables are not specified. Instead, they learn from the examples fed to them. In addition, they can generalize correct responses that only broadly resemble the data in the learning phase [21]. A thorough treatment of the back propagation learning algorithm is beyond the scope of this paper. The algorithm has been covered widely [22, 23] in other publications.

During training the network performance is monitored by Root-Mean-Square (RMS) error to achieve a better under- standing of the network performance [2]. At the end of the training phase, the neural network should correctly reproduce

the target output values for the training data, provided the errors are minimal, i.e., convergence occurs. The associated trained weights of the neurons are then stored in the neural network memory. Once trained, the values for the input parameters for the project are presented to the network. Then the network calculates the node outputs using the existing weight values and thresholds developed in the training process [2].

III. BUILDING NEURAL NETWORKS FOR EVALUATING WORKABILITY

The experimental data include 103 mixtures, which are taken from the tests carried out by Yeh and Chen [24]. The workability of fresh concrete was determined by the conven- tional slump test. However, the slump-flow was measured instead of slump. These data were randomly divided into a training set (78 data points) and testing data (25 data points).

For this slump-flow modeling problem the obvious inputs are the component contents of concrete, including cement, fly ash, slag, water, SP, coarse aggregate (CA), and fine aggregate (FA), and the output is the slump-flow of the concrete.

That is, the neural network developed in the investigation has seven units in the input layer and one unit in the output layer.

The values of network parameters considered in this approach are as follows: number of hidden layers = 0, 1, and 2;

number of hidden units = 5, 7, 10, and 14; learning rate = 0.1, 0.3, 1.0, and 3.0; momentum factor = 0.0, 0.25, 0.5, and 0.75;

and learning cycles = 500, 1000, 2000, and 5000 (each cycle covers the entire database available for training). After a number of trials, based on the R of testing set, the best ² network parameters are as follows: number of hidden layers = 1; number of hidden units = 7; learning rate = 1.0; momentum factor = 0.5; and learning cycles = 2000.

The measured slump-flow collected from the literature [24] is plotted against the predicted slump-flow calculated by the aforementioned neural network model, as shown in Fig.1 and Fig 2. Although the correlation between the measured slump-flow and the predicted values obtained from testing data are somewhat more scattered than that obtained from training data, it is obvious that the rather small scatter of data around the diagonal line confirms the fact that the neural network is an excellent predictor of the slump-flow.

For comparison purposes, the following polynomial regression formula was adopted here:

( ) ∑ ∑ ∑

<

1

=

+

=

i

j i q

j ij q

i i

ix β x x

β y

E ⁽¹⁾

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Table 1 RMS error and R ² of the training and testing results

Neural network Regression model Training set Testing set Training set Testing set RRMS

(cm) 7.19 9.83 10.2 19.5

R 0.797 0.8142 0.621 0.403

where x_i is the ith-component content; β_i andβ_ij are the regression coefficients.

The values of RMS error and R of the training and ² testing results for the neural network models and regression models are also listed in Table 1. It is seen that the neural network model gives a smaller RMS error and a larger R ² for both the training set and the testing set, especially for the testing set.

Ⅳ. EXPLORING WORKABILITY USING NEURAL NETWORKS

In this study, computational simulation of concrete slump-flow was performed using the trained neural network.

The variation in concrete slump-flow was achieved by varying combinations of factors like the water/binder ratio, SP-binder ratio, and water content. The binder means cementitious material, that is, cement plus fly ash and slag. The ranges of each variable are listed as follows:

1. The water-binder ratio (w/b) was varied utilizing 0.3, 0.4, and 0.5.

2. The SP-binder ratio (SP/b), the amount of superplasticizer by weight of binder, was varied using 0, 1, 2, 3, and 4%.

3. The amount of water was varied from 130 to 250kg/ m³. Besides, the fly ash-binder ratio and slag-binder ratios were kept constant at 25% and 25%, respectively, by weight of binder (cement + fly ash + slag); the CA/FA was kept constant at 1.0; the total volume of concrete was 1.000m . ³

From the water content to slump-flow curves generated using trained neural network developed in this study with the above combinations, two sets of curves are shown in Fig. 3 to 5, and Fig. 6 to 10, respectively, to explore the effects of w/b and SP/b. Consider the fact that validity of a slump-flow test is generally recommended for concrete with a slump-flow value ranging from 20 to 80 cm; therefore, those parts of curves outside the range may be unreliable and should be ignored.

20 30 40 50 60 70 80

Measured slump-flow (cm)

Predicted slump-flow (cm)

Fig. 1 The measured and predicted slump-flow of neural network for training set

20 30 40 50 60 70 80

Measured slump-flow (cm)

Predicted slump-flow (cm)

Fig. 2 The measured and predicted slump-flow of neural network for testing set

1. Discussion of Figs. 3 to 5

Figs. 3 to 5 show a large difference in the shape of the slump-flow-water curves between low- and high-w/b concretes for a wide range of SP/b ratio.

(1) The effects of SP/b

Compared to concrete without SP, to retain a high slump-flow (60 cm), at w/b=0.4, the water content saved is about 15, 30, 42, and 51kg/ m³for SP/b=1, 2, 3, and 4%, respectively. Similarly, at w/b=0.5, the water content saved is about 10, 20, 30, and 39 kg/ m³ for SP/b=1, 2, 3, and 4%,

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20 25 30 35 40 45 50 55 60 65 70

100 120 140 160 180 200 220 240 Water Content(kg)

Slump-Flow(cm)

0% SP/b 1% SP/b 2% SP/b 3% SP/b 4% SP/b 5% SP/b

Fig. 3 The water content-slump flow curves at w/b=0.3

20 25 30 35 40 45 50 55 60 65 70

100 120 140 160 180 200 220 240 Water Content(kg)

Slump-Flow(cm)

20 25 30 35 40 45 50 55 60 65 70

100 120 140 160 180 200 220 240 Water Content(kg)

Slump-Flow(cm)

20 25 30 35 40 45 50 55 60 65 70

0% 1% 2% 3% 4% 5% 6% 7%

SP/b ratio

Slump-Flow (cm)

130 140 150 160 170 180 190 200 210 220 230 240 250 water (kg)

Fig. 6 The SP/b-slump flow curves at w/b=0.3

20 25 30 35 40 45 50 55 60 65 70

0% 1% 2% 3% 4% 5% 6% 7%

SP/b ratio

Slump-Flow (cm)

130 140 150 160 170 180 190 200 210 220 230 240 250 water (kg)

20 25 30 35 40 45 50 55 60 65 70

0% 1% 2% 3% 4% 5% 6% 7%

SP/b ratio

Slump-Flow (cm)

130 140 150 160 170 180 190 200 210 220 230 240 250 water (kg)

Slump-flow (cm) Slump-flow (cm) Slump-flow (cm) Slump-flow (cm) Slump-flow (cm) Slump-flow (cm)

Water Content (kg)

Water Content (kg) Water Content (kg)

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respectively. In other words, the water content saved by the use of SP is about 15 and 10 kg/ m³ for every percent of SP/b, at w/b=0.4 and 0.5, respectively.

(2) The effects of w/b

In Fig.3, at low w/b (0.3), the curve of 2% SP/b is close to the lower-right of the diagram, and the curves of 0% and 1% SP/b are outside the diagram. At SP/b

≤

3%, the concrete cannot reach a 60 cm slump-flow even though more than 250kg/ m³of water was used. At SP/b=4%, the concrete requires only 220 kg/ m³ of water to maintain the same slump-flow.

Similarly, at high w/b (0.5) shown in Fig. 5, at SP/b=0%, the concrete requires 230kg/ m³of water to reach a 60 cm slump-flow. At the other extreme, at SP/B=4%, the concrete requires only 180kg/ m³ of water to maintain the same level.

The results can be explained by the fact that the fresh concrete conforms to the criterion that too soft a mortar consistency will cause segregation of the concrete, whereas too sticky a mortar consistency will result in poor flowability.

2. Discussion of Figs. 6 to 8

Figs. 6 to 8 show a large difference in the shape of the slump flow-SP/b curves between low- and high-w/b concretes for a wide range of water contents. As can be seen from these figures, the SP/b ratio had a distinct effect on workability properties at low and high w/b ratio.

(1) At a low water-binder ratio (0.3) shown in Fig. 6, a higher SP/b will result in much lower water content to reach high workability (slump-flow). Without SP (SP/b = 0%), even though the water content is greater than 250kg/ m³, no workability took place. However, with SP/b = 4%, the water required to reach high slump-flow (60 cm) is smaller than 230kg/ m³. (2) At a medium water-binder ratio (0.4) shown in Fig. 7,

the workability of concrete has a similar tendency, the higher the SP/b, the higher the slump-flow, but the effects of SP decreased. Without SP, increasing the water content can still obtain a very high workability. At constant water content, the slump-flow var- ies proportionally with the SP/b ratio because the re- lationship between slump-flow and SP/b is nearly linear. At high SP/b (4%), the water required to reach 60 cm slump-flow is smaller than 180kg/ m³. (3) At a rather high water-binder ratio (0.5) shown in Fig.

8, the tendency is totally different from those shown in Fig. 6 and Fig. 7. While water content is low (un-

der 150kg/ m³), the SP has a small effect on workability; while medium (160~180kg/ m³), the SP has nearly zero effect; while high (above 190kg/ m³), the SP has great effect.

V. CONCLUSIONS

Although the present simulating exploration was based on a limited number of variables, it appears that the following conclusions can be drawn.

1. From the previous discussion, the use of a neural network for the modeling of concrete slump-flow looks promising.

2. In this study the water content saved by the use of SP is about 15 and 10kg/ m³ for every percent of SP/b, at w/b

= 0.4 and 0.5, respectively.

3. An increasing SP/b ratio increased the slump, while the effect was much smaller at high w/b ratio than that at low w/b ratio. That is, SP are most effective in concrete mixtures that are low in w/b ratio, in other words, rich in cement and other cementitious materials.

4. In general, when both w/b ratio and water content remain constant, slump-flow increases with the increase of SP/b ratio.

ACKNOWLEDGMENTS

This work was supported by the National Science Coun- cil, ROC, under Grant NSC-92- 2211-E-216-015.

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