ACI Materials Journal/March-April 1999 167

ACI Materials Journal, V. 96, No. 2, March-April 1999.Received June 23, 1997, and reviewed under Institute publication policies. Copyright

1999, American Concrete Institute. All rights reserved, including the making of copiesunless permission is obtained from the copyright proprietors. Pertinent discussion includingauthors closure, if any, will be published in the January-February 2000 ACI MaterialsJournal if the discussion is received by October 1, 1999.

ACI MATERIALS JOURNAL TECHNICAL PAPER

This paper presents the development of a computer model for theprediction of cement degree of hydration . The model is establishedby incorporating large experimental data sets using the neuralnetworks (NNs) technology. NNs are computational paradigms,primarily based of the structural formation and the knowledgeprocessing faculties of the human brain. Initially, the degree ofhydration was estimated in the laboratory by preparing portlandcement paste with the water-cement ratio (w/c) ranging from 0.2 to0.6, curing times from 0.25 to 90 days and subjected to curingtemperatures from 3 to 43 C (37 to 109 F). A total of 390 specimenswere tested, thus producing 195 data points divided into five sets.The networks were trained using data in Set 1, 2, and 3. Once theNNs have been deemed fully trained, verification of the performanceis then carried out using Set 4 and 5 of the experimental data, whichwere not included in the training phase. The results indicated thatthe NNs are very efficient in predicting concrete degree of hydrationwith great accuracy using minimal processing of data.

Keywords: curing; hydration; models.

INTRODUCTIONHydraulic cements are defined as cements that not only

harden by reacting with water, but also form a water-resis-tant product. Cements derived from calcination of gypsum orcarbonates, such as limestone, are nonhydraulic becausetheir products of hydration are not resistant to water. Anhy-drous portland cement does not bind sand and gravel; itacquires the adhesive property only when mixed with water.This is because the chemical reaction of cement with water,commonly referred to as the hydration of cement, yieldsproducts that possess setting and hardening characteristics.The compounds of portland cement are nonequilibriumproducts of high temperature reactions and are therefore in ahigh-energy state. When cement is hydrating, thecompounds react with water to acquire stable low-energystates, and the process is accompanied by the release ofenergy in the form of heat. The heat of cement hydration isof great significance in concrete technology. In some cases,it can be a hindrance, while in other cases, it can help. Thereactions between cement compounds and water tend to raisethe temperature of concrete. This rise in temperature gener-ally subjects the freshly hardened concrete to both thermaland drying shrinkage.

It is currently well-recognized that drying shrinkage ofconcrete is a property that is affected by several parameters,such as the elastic properties of the paste and aggregate andtheir shrinkage, as well as the restraining imposed by theaggregate and unhydrated cement.1,2 The shrinkage of pasteis also influenced by the relative humidity, drying time,water content, degree of hydration , and admixture.1-3However, and as stated by Almudaiheem,4 the complexityof the subject is such that the effect of the mix design param-eters on equilibrium drying shrinkage of concrete, and the

fundamental shrinkage parameters of the paste are not wellunderstood. Moreover, the uncertainties associated withparameters affecting the drying shrinkage of concrete makeit difficult to estimate exactly how much shrinkage willoccur. Consequently, this paper will introduce a computermodel based on the neural networks (NNs) technology toassess one particular variable that affects concrete shrinkage,namely the degree of hydration.

RESEARCH SIGNIFICANCEThis work will demonstrate that the NNs modeling of

concrete degree of hydration is effective, accurate, andsimple to implement. Only minor processing of the data isnecessary to obtain the degree of hydration for a given set ofeasily accessible conditions with minimal computation time(< 5 msec). This expediency and relatively high accuracy isthe most significant advantage of using NNs. The experi-mental time needed to evaluate the degree of hydration isgenerally several orders of magnitude greater.

THEORETICAL BACKGROUNDTo evaluate the drying shrinkage of concrete, Pickett2

derived a model from the elastic theory based on mix compo-sition and material properties. This model is expressed by

(1)

where c /p is the ratio of the shrinkage of concrete to that ofthe paste, Va is the volume fraction of the aggregate, and isexpressed as

(2)

with and E being, respectively, Poissons ratio andmodulus of elasticity, while subscripts c and a stand forconcrete and aggregate, respectively. Pickett2 found that aconstant value of = 1.7 showed good agreement withshrinkage of paste, even though he realized that it shouldvary. Almudaiheem,4 on the other hand, introduced a modi-fied model in which he replaced Va, a, and Ea by VR, R, andER, respectively, in Eq. (1) and (2), where the subscript R

c

p---- 1 Va( )

=

3 1 c( )

1 c 2 1 2a( )EcEa-----+ +

-----------------------------------------------------------=

Title no. 96-M21

Prediction of Cement Degree of Hydration Using Artificial Neural Networksby Adnan A. Basma, Samer A. Barakat, and Salim Al-Oraimi

ACI Materials Journal/March-April 1999168

denotes the restraining phase. The volume of restraining canbe calculated by4

(3)

where c is the density of concrete, w/c is the water-cementratio, and is the degree of hydration. In Eq. (3), the degreeof hydration is the only parameter that needs to be estimated.This will be done here by conducting an experimental work,as will be seen in a latter section. Once the experimental datais obtained, the NNs are first trained for a specific paradigmusing part of the data. The remainder of the data, to which theNNs were not initially exposed, is then used to test the accu-racy of the developed model. A general description of theNNs and the experimental program follows.

DEFINITION OF NEURAL NETWORKS (NNs)NNs could be defined as information processing structures

that consist of many simple processing elements, i.e.,neurons, with dense parallel interconnections. The connectionsbetween the neurons are called synapses. Each neuronreceives weighted inputs from many other neurons andcommunicates its outputs to many other neurons by using anactivation function f (Fig. 1). Thus, information is repre-sented by a massive cross-weighted neurons interconnec-tions. NNs might be single or multilayered. The single-layer

VR1

1 c w c( )+[ ]----------------------------------- 1 Va( ) Va+=

NNs present processing units of the NNs, which take inputsfrom the outside of the network, and their outputs go to theoutside of the network; otherwise, the NNs are considered asmultilayers.5,6

The basic methodology of NNs consists of three stages:network training, testing, and implementation. The weightsare adjustable through the programming training process,while the training effect is called learning. The learningprocess is done by giving weights and biases computed froma set of training data or by adjusting the weights according toa certain condition. The initial weights and biases joiningnodes of the input layer, hidden layers, and output layer arecommonly assigned randomly. The weights and biases arechanged incessantly for the output of the network to matchthe required data value. As the input data are passed throughthe hidden layers, a sigmoidal activation function is gener-ally used. During the training procedure, the data areselected uniformly. A specific pass is completed when alldata sets have been processed. Generally, several passes arerequired to attain a desired level of prediction accuracy. Thefinal sets of weights and biases comprise the long-termmemory, or synapses of the respective events. Consequently,learning corresponds to determining the weights and biasesassociated with the connections in the networks. The NNsmodel thus determines the structure (adaptively, incremen-tally, and automatically) when the input data is presented.Currently, there are several learning algorithms available inthe literature. However, the most commonly used is theback-propagation paradigm.7 This paradigm works asfollows. The data consist of input-output pairs. The networkwill produce an output vector A(:, j) for each input vector X(:, j).Thus, application of R input vectors would produce an outputmatrix A with S rows and R columns. In the case of multi-layered NNs, layers whose output becomes the networkoutput are called output layers. All other layers (with theexception of the input layer) are termed hidden layers. Atypical three-layer network is shown in Fig. 2. This networkhas R inputs (R = 3), S1 neurons in hidden Layer 1 (S1 = 3)and S2 neurons in hidden Layer 2 (S2 = 1) with a constantinput B fed as biases for each neuron. Observe that theoutputs of each intermediate layer are the inputs of thefollowing layers. Therefore, if X is the input and A1 is theoutput of hidden Layer 1, then A1 will be the input and A2

Adnan A. Basma is an associate professor of civil engineering at Sultan QaboosUniversity. He received his BS, MS, and PhD from the University of Mississippi in1980, 1981, and 1985, respectively. His research interests include reliability-basedstudies and neural networks as applied to structural/geotechnical engineering.

Samer A. Barakat is an assistant professor of civil engineering at Jordan Universityof Science and Technology (JUST). He received his MS from JUST in 1989, and hisPhD from the University of Colorado, Boulder, Colo., in 1994. His research interestsinclude reliability-based structural optimization, earthquake structural resistance,and composite materials.

Salim Al-Oraimi is an assistant professor of civil engineering and Dean of StudentAffairs at Sultan Qaboos University. He received his PhD from the University ofWales, UK. His research interests include fiber reinforced concrete, fracture mechanics,and computer applications to structural engineering.

Fig. 1Schematic diagram of single neuron.

Fig. 2Schematic diagram of typical neural networkstructure with two hidden layers.

ACI Materials Journal/March-April 1999 169

the output of hidden Layer 2. This implies that A2 = Y is thefinal output of the network and is calculated by

(4)

where f1 and f2 are the transformation function that areselected to best suit the used data.

The discrepancy, or delta, between the actual and desiredbehavior of the network is determined by subtracting theoutput vector A from the target or desired vector T. Under thedelta rule, the post-trial change in weight Wij of a connectionbetween the input and output is estimated by

(5)

where represents the trial-independent learning rate. Theweights are continuously adjusted over each training epoch(or iteration) until the difference between the output andtarget values reaches a desired limit or until all trainingpreset numbers of epochs or iterations are completed.

As the name implies, the concept behind the back-propa-gation is to propagate the errors back through the systembased on observed discrepancies. As the weights areadjusted, they are received by the processing elements orneurons to produce an output through an activation or trans-formation function. Several activation functions arecurrently available. However, the two most commonly usedare the log-sigmoidal and tan-sigmoidal transformations.The log-sigmoidal function receives inputs (which may haveany value between minus and plus infinity) and maps theminto the range of 0 to +1. The tan-sigmoidal function, on theother hand, maps inputs into the range 1 to +1. Such func-tions prevent the input signal from growing infinitely as theyare successively summed and passed on to other neurons.Furthermore, they introduce nonlinearity into the network,without which the network output will be severely limited tolinear combinations. The respective graphical representation

Y f2 W2 f1 W1 X B1+( )[ ] B2+{ }=

Wij Tj Aj( )Xi=

of the log-sigmoidal and tan-sigmoidal activation functionsare shown in Fig. 3 and 4.

EXPERIMENTAL WORK TO DETERMINE DEGREE OF HYDRATION

The degree of hydration was estimated in the laboratoryby conducting five sets of tests. In Set 1, 2, and 3, portlandcement paste was prepared, respectively, at the water-cement ratio (w/c) of 0.3, 0.4, and 0.6, while w/c in Set 4 and5 were, respectively, 0.2 and 0.5. For all five sets, severalspecimens were prepared and cured for 0.25, 0.5, 1, 3, 7, 14,28, and 90 days at curing temperatures of 3, 13, 23, 33, and43 C (37, 55, 73, 91, and 109 F) with the exception of 0.25day that was not cured at 3 C. For each set of w/c ratios, twospecimens were prepared and then averaged to assess .Consequently, this laboratory work used a total of 390 spec-imens. The nonevaporated water content wn was used as ameasure to evaluate the degree of hydration. The degree ofhydration was estimated by the following

(6)

where wnu is the nonevaporable water content at completehydration, which was equal to 0.23 g/g of cement.

To determine the nonevaporable water content at aspecific age, small specimens (about 1.5-mm thick) were cutfrom the original sample (50-mm cube) and immersed inmethanol to stop hydration. After about 7 days in methanol,the specimens were oven dried at 105 + 3 C (221 5 F), thenground into fine particles, and a weighted sample was ignitedat 1000 C (1832 F). The nonevaporable water content wn perg of cement was determined from the following equation

(7)

wn

wnu

--------=

wnw1 w2

w2------------------=

Fig. 3Log-sigmoidal transformation function.Fig. 4Tan-sigmoidal transformation function.

ACI Materials Journal/March-April 1999170

where w1 is the oven-dried weight, and w2 is the weight afterignition. The degree of hydration was then calculated by Eq.(5). Fig. 5 to 9 show, respectively, the average measuredvalues of (from two tested specimens) for Set 1 to 5. Ascan be noted from these figures, increases with tempera-ture and curing time, while w/c has a minor effect. In general,however, the degree of hydration was found to remainalmost constant for specimens cured for 28 and 90 days.

NEURAL NETWORKS SOLUTIONAs stated earlier, five sets of experimental data were

obtained. Set 1, 2, and 3 (shown respectively in Fig. 5, 6, and7), with 117 points, were initially used to train the NNs andproduce a model from a certain paradigm recognition.

Consequently, this model is expected to map and transformthe input or causative variable space (curing period, temper-ature, and w/c) into the output or target variable space(degree of hydration ). Once this is achieved, the data inthese sets are thus assumed to have been combined andencased in the derived model to the degree that they can bereplaced by the model.

The software was used to perform the necessary computa-tion. The complete listing of the subroutine used can be seenin the Appendix.* For the purpose of this research work,several single and multilayered NNs with various activationfunctions were used to determine the most appropriate model

*The Appendix is available in xerographic or similar form from ACI headquarters,where it will be kept permanently on file, at a charge equal to the cost of reproductionplus handling at time of request.

Fig. 5Measured degree of hydration with w/c = 0.3 forSet 1 (deg F = 1.8 C + 32).

Fig. 6Measured degree of hydration with w/c = 0.4 forSet 2 (deg F = 1.8 C + 32).

Fig. 7Measured degree of hydration with w/c = 0.6 forSet 3 (deg F = 1.8 C + 32).

Fig. 8Measured degree of hydration with w/c = 0.2 forSet 4 (deg F = 1.8 C + 32).

ACI Materials Journal/March-April 1999 171

to predict the degree of hydration. The best suited NNs archi-tecture was:

1. Three-way back-propagation with adaptive learningrate and momentum;

2. Three input neurons (w/c, curing period tc, and temper-ature Tc);

3. Two hidden layers, with three neurons in the first andone neuron in the second hidden layer;

4. One output neuron (degree of hydration );5. Tan-sigmoidal function in hidden Layer 1 (f1); and6. Log-sigmoidal function in hidden Layer 2 (f2).This architecture can be seen schematically in Fig. 2.The training stage and the associated NNs analyses were

carried out with adaptive momentum factor and learningrate . The optimal values of these latter parameters were

determined as = 0.95 and = 0.02. Training was carriedout for 35,000 epochs or until the average sum square errorsover all training epochs was minimized. Training time on apersonal computer was less than 15 min. The progress of thenetworks training was monitored by observing the learningrate and the output sum-square error after each trainingepoch. Figure 10 shows the training progress of the finalnetwork. This figure was developed using sample-movingaverages of the network output errors obtained at the end ofeach training epoch. The asymptotic shape of the curveimplies that the network learning was notably complete bythe end of the training. Furthermore, this figure indicates thatapproximately 20,000 passes were required for convergence.The final weights and biases produced by the NNs are listedin Table 1(a) and (b). The accuracy of the NNs modelobtained in the training stage was tested versus Sets 4 and 5of the experimental data (Fig. 8 and 9).

PREDICTION ACCURACY OF NEURAL NETWORKS

To check the accuracy of the NNs solution, the finaladopted model was called upon to recall the data used to trainstage, i.e. data Set 1 to 3. Furthermore, the prediction accu-racy of the networks was tested against the data in Set 4 and 5.It should be stressed that all of the data in these latter sets wereinitially withheld from the NNs. In a similar fashion as in therecall test, the input values from these sets of data werepresented to the model to perform the necessary calculationsand produce corresponding outputs. Figure 11 shows a compar-ison between the experimental values of and the recalledand predicted values by the NNs. The closeness of the pointsto the equality line serves only to indicate the validity of theNNs model. A regression analysis of the points in this figurewas performed, and the results are listed in Table 2. The high

Fig. 9Measured degree of hydration with w/c = 0.5 forSet 5 (deg F = 1.8 C + 32).

Fig. 10Variation of sum-squared error and learning ratewith training iterations.

Table 1(a)Connection weights and biases for hidden Layer 1

Hidden neuronConnection weights for

Biasw/c tc Tc1 +0.45498 +0.83475 +0.42987 +0.849072 +0.63014 +0.32891 +0.65910 +0.297353 -0.03594 -0.20280 -0.01644 +0.32447

Table 1(b)Connection weights and biases for hidden Layer 2

Hidden neuronConnection weights for*

BiasHD1-N1 HD1-N2 HD1-N31 1.22227 0.05960 2.46489 0.06590

*HD = hidden layer; N = neuron.

Table 2Regression of predicted -values by neural networks on target experimental values

Neuralnetwork stage

No. of data

points Regression model* r295 percent confidence

intervalTraining 117 Y = 0.973X + 0.011 0.973 0.081Testing 78 Y = 0.877X + 0.049 0.877 0.130

Training andtesting 195 Y = 0.929X + 0.029 0.929 0.107

*Regression analysis performed on data in Fig. 11.Note: X = by neural networks; Y = experimental value of .

172 ACI Materials Journal/March-April 1999

values of the correlation coefficient further substantiate theNNs accuracy.

SUMMARY AND CONCLUSIONSThe work presented herein uses NNs technology to model

and predict concrete degree of hydration. By using such atechnology, the final model is said to have encapsulated the

data sets in such a way that very little prior assumption aboutthe relationship between the data attributes is needed. As longas the important parameters are present in the data analyzed,the training process will enhance the most fundamental rela-tionship(s) on the models long-term memory. Any combina-tion of the data attributes will invoke the appropriate reactionfrom the memory. The final proof of applicability of the NNsmodel is provided through its ability to predict output valuesfrom data that it had never encountered.

Based on the results of this investigation, it was concludedthat the performance of the NNs was superior. The model,including two hidden layers with three nodes per layer, andthe curing period, temperature, and w/c as input variableswere found to be very successful in predicting the degree ofhydration .

REFERENCES1. Carlson, R. W., Drying Shrinkage of Concrete as Affected by Many

Factors, Proceedings, ASTM, V. 38, Part 2, 1939, pp. 419-437.2. Pickett, G., Effect of Aggregate on Shrinkage of Concrete and

Hypothesis Concerning Shrinkage, ACI JOURNAL, Proceedings V. 52,No. 5, 1956, pp. 581-590.

3. Pihlajavaara, S. E., A Review of Some of the Main Results of aResearch on Aging Phenomena of ConcreteEffect of Moisture onConcrete, Cement and Concrete Research, V. 4, No. 1, 1974, pp. 761-771.

4. Almudaiheem, J. A., An Improved Model to Predict the UltimateDrying Shrinkage of Concrete, Magazine of Concrete Research, V. 44,No. 159, 1992, pp. 81-85.

5. Garson, G. D., Interpreting Neural-Network Connection Weights,AI Expert, V. 6, No. 7, 1991, pp. 47-51.

6. Simpson, P. K., Artificial Neural System, Pergamon Press, Inc., NewYork, 1990, 659 pp.

7. McClelland, J. L., and Rumelhart, D. E., Exploration in ParallelDistributed Processing, MIT Press, Cambridge, Mass., 1988.

Fig. 11Recalled and predicted values by neuralnetworks versus experimental data.