Journal of Advanced Concrete Technology Vol. 6, No. 1, 135-142, February 2008 / Copyright © 2008 Japan Concrete Institute

135

Scientific paper

Artificial Neural Network for Predicting Creep and Shrinkage of High Performance Concrete Jayakumar Karthikeyan1, Akhil Upadhyay2 and Navaratan M. Bhandari3 Received 30 June 2007, accepted 30 December 2007

Abstract Concrete undergoes time-dependent deformations that must be considered in the design of reinforced/prestressed highperformance concrete (HPC) bridge girders. In this research, experiments on the creep and shrinkage properties of a HPC mix were conducted for 500 days. The test results obtained from this research were compared to different models to determine which model was the better one. The CEB-90 model was found better in predicting time-dependent strains and deformations for the above HPC mix. However, in a far zone, some deviation was observed, and to get a better model, the experimental data base was used along with the CEB-90 model database to train the neural network. The developed Artificial Neural Network (ANN) model will serve as a more rational as well as computationally efficient model in predicting creep coefficient and shrinkage strain.

1. Introduction Concrete undergoes volumetric changes throughout its service life. These changes are a result of timedependent deformations (creep and shrinkage). The time-dependent increase in strain in hardened concrete subjected to sustained stress, in excess of shrinkage, is defined as creep. Creep includes basic creep and drying creep. Basic creep occurs under conditions where there is no moisture movement to or from the environment. Drying creep is the additional creep caused by drying. The ratio of creep strain to that of the initial elastic strain due to a sustained stress is used as a measurement of creep deformation. This ratio is called the creep coefficient. Shrinkage is defined here as the time-dependent strain measured at constant temperature in an unloaded and unrestrained specimen. Behind this simple definition there are six different types of shrinkage; plastic shrinkage, thermal shrinkage, chemical shrinkage, autogeneous shrinkage, drying shrinkage and carbonation shrinkage. Various types of shrinkages can be distinguished depending on the cause of moisture loss. Plastic shrinkage takes place due to loss of water during the plastic state of concrete either by evaporation from the surface or absorption in aggregate. Thermal shrinkage takes place during the first few days of placement: generation of heat resulting from hydration and consequent cooling leads to it. Chemical shrinkage results in volume reduction due to hydration. Autogeneous shrinkage

1

Research Scholar, Department of Civil Engineering, Indian Institute of Technology, Roorkee, India. E-mail:[email protected] 2 Associate Professor, Department of Civil Engineering, Indian Institute of Technology, Roorkee, India. 3 Professor, Department of Civil Engineering, Indian Institute of Technology, Roorkee, India.

takes place due to the self-desiccation after final setting. Drying shrinkage is the removal of adsorbed water from the hydrated cement paste when it is exposed to the environment. Carbonation shrinkage is the dissolution of calcium hydroxide and the deposition of calcium carbonate having lesser volume. Shrinkage is expressed as a dimensionless strain. The shrinkage of concrete has a direct influence on prestress losses of prestressed concrete members and the long-term deformation of girders. Several reports have indicated that the shrinkage and creep deformations of HPC are lower than those of normal-strength concrete. This is due to the dense matrix and low-water cementitious material ratio (Huo et al. 2001). The creep and shrinkage strains for the HPC mixture were measured compared to seven different models to determine which models were the most accurate. According to Townsend’s experimental results comparison, American Concrete Institute (ACI)'s ACI 209 model modified by Huo was most accurate in predicting timedependent strains (Townsend 2003). The creep for a light weight high strength concrete mixture was measured and compared with four different models. The models considered were ACI 209, CEB 90, B3 and GL2000. According to Vincent’s measurements, the GL2000 model was the best predictor model, and CEB90 was the best predictor for the total strains (Vincent 2003). Based on his investigation, Huo states that the current ACI 209 model does not accurately predict the material properties for HPC. Huo revised the ACI 209 equations for calculating shrinkage strains and creep coefficient, which can be used for both conventional concrete and HPC. The above revised equations are referred to as ACI 209 modified by Huo, (Huo et al. 2001). A new ANN model is for predicting creep in masonry structures. Few experiments for creep in brick masonry have been carried out. By making use of those test data, Noureldin and Taha has used ANN to generate a new

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model for predicting creep (Noureldin and Taha 2003). In view of the above literature review, the objective of the present study is to investigate the time-dependent properties of HPC such as creep and shrinkage, in order to find out the better predictor model for creep and shrinkage. The better predictor model values along with experimental data generated in this work are used in the ANN and it is validated to generate a new predictive ANN model for creep and shrinkage.

2. Basic approach The above-mentioned objective is achieved through the following steps: a) Preparation of specimens for creep and shrinkage studies of a HPC mix b) Comparison of the predictions of various existing creep and shrinkage models with experimental data to identify the best model having the least deviation. c) Addition of the experimental data and the data obtained from the model having the least deviation from experimental data to get a combined training set for the ANN training, and comparison of the performance of the developed ANN with the experimental results.

3. ANN The ANN, which consists of simplified models of the biological neuron system, is a massively parallel distributed processing system made up of highly interconnected neural computing elements that have the ability to learn by acquiring knowledge and making it available for use. The ANN exhibits characteristics such as mapping capabilities and pattern association, generalization, robustness and high speed information processing. The ANN can be trained with known values from collected data or from the test data; and it can recall full patterns from incomplete, partial, or noisy patterns. The main advantages of the ANN are: a) Once appropriately trained, the ANN works as a model free estimator and it can be effectively used in solving the unknown or untrained instances of the problem. b) The ANN has higher fault tolerance. c) Whenever more data becomes available, further training can be done without starting from scratch. Applications of ANNs in civil engineering have increased in recent years and are continuing to do so. Therefore, all the required patterns can be found from the neural network free estimator. ANNs have been used recently to recognize complicated patterns and find solutions to problems too complex to be modeled accurately by traditional computing methods.

4. Conventional models Of the various varieties of methods proposed for the

prediction creep and shrinkage in concrete, seven are presented in this section: ACI 209, ACI 209 modified by Huo, AASHTO-LRFD, B3, CEB 90, GL 2000 and Tadros. ACI 209 proposes an empirical model for predicting creep and shrinkage strain as a function of time. The models have the same principle: a hyperbolic curve that tends to an asymptotic value called the ultimate value ( φu , (εsh)u ). The shape of the curve and ultimate value depend on several factors such as the curing conditions, age at application of load, mix design, ambient temperature and humidity. Equations 1 and 2 presents the general model for predicting creep coefficients ( φt ) and shrinkage strains (εsh)t . For the detailed expressions, refer to ACI Committee 209 2005.

⎛ (t - t')0.6 ⎞ φt = ⎜ .φu 0.6 ⎟ ⎝ 10 + (t - t') ⎠

(1)

⎛ t - t0 ⎞ (εsh)t = ⎜ ⎟ .(εsh)u ⎝ 35 + (t - t0) ⎠

(2)

where, t = Age of concrete (days), t' = Age of concrete at loading (days), t0 = Age at the beginning of drying (days), φu = Ultimate creep coefficient expression depending on slump, member geometry, humidity, fine aggregate, air content and type of curing, (εsh)u = Ultimate shrinkage strain expression depending on slump, member geometry, humidity, fine aggregate, air content and type of curing. Huo modified the above equations by incorporating a strength correction factor. Modified equations 3 and 4 can be used for conventional concretes as well as HPC for predicting creep coefficients ( φt ) and shrinkage strains ( (εsh)t ). For further details on these expressions, refer to Huo et al. 2001. ⎛ ⎞ (t - t')0.6 φt = ⎜ .φu 0.6 ⎟ (12 0.0725.f c') + (t - t') ⎝ ⎠

(3)

⎛ t - t0 ⎞ (εsh)t = ⎜ ⎟ .(εsh)u ⎝ (45 - 0.3625fc') + (t - t0) ⎠

(4)

fc' =28 days compressive strength (MPa) The AASHTO-LRFD model is similar to ACI 209. However, based on this model slightly different correction factors for slump, member size, type of curing, etc. are proposed in the ultimate creep coefficient and ultimate shrinkage strain expressions. For the expressions, refer to AASHTO-LRFD 2004. The CEB 90 model gives the hyperbolic change over time of creep and shrinkage, and it also uses an ultimate value corrected according to the mix design and environmental conditions. One difference of CEB 90 is that it predicts creep strain rather than creep coefficient. Equations (5), (6) and (7) give the general prediction model for creep strains ( εcr(t, t') ), creep coefficients ( φ28 ), and shrinkage strains ( εs(t, t0) ) respectively. For further details on these expressions, refer to CEB-FIP

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model code 1990.

εcr(t, t') = φ28 = φ0

σc(t') .φ28(t, t') E28 ⎛ ⎜ ⎜ ⎜ ⎜ ⎜ ⎝⎜

(5)

⎞ 0.3

t-t' ⎟⎟⎟ βh +(t-t') ⎟⎠⎟⎟

(6)

εs(t, t0) = εso.βs.(t - t0)

(7)

where, σc(t') = Applied stress (MPa), E28 = 28 days modulus of elasticity (MPa), φ0 = Notional creep coefficient depending on humidity, member geometry, compressive strength and type of curing, βh = Constant depending on member size and relative humidity, εso = Notional shrinkage coefficient depending on the type of cement and compressive strength, βs = A hyperbolic shrinkage function depending on member geometry and time. The B3 model was proposed by Bazant and Baweja in 1995 as a new improvement and an update of previous models such as BP (Bazant and Panula model in 1978) and BP-KX (Bazant, Panula, Kim, Koo and Xi model in 1992). The B3 model is simpler, better theoretically supported and more exact than the previous models. It takes into account basic and drying creep portions. Equations (8), (9), (10) and (11) give the general expression for the creep compliance function ( J(t, t') ), basic creep function ( C0(t, t') ), drying creep function ( Cd(t, t', t0) ) and drying shrinkage ( εsh(t, t0) ) respectively. For further details on these expressions, refer to Bazant and Baweja 1995. J(t, t') = q1 + C0(t, t') + Cd(t, t', t0)

(8)

C0(t, t') = q2.Q(t, t') + q3.In (1+(t+t')n ) + q4In ⎛⎜ t ⎞⎟ ⎝ t' ⎠

(9)

Cd(t, t', t0) = q5. ⎡⎣exp{8.H(t)}−exp{-8.H(t0')}⎤⎦

εsh(t, t0) = -εsh∞.kh.tanh t-t0 τsh

0.5

(10) (11)

where, q1 = Instantaneous strain due to unit stress, t = Age of concrete (days), t' = Age of concrete at loading (days), t0 = Age of concrete at the beginning of drying (days). Gardner and Lockman (GL2000) proposed a more compact model for creep coefficient depending only on relative humidity and member geometry. Equations (12) and (13) give the expression for predicting the creep coefficients ( Ccr(t, t') ) and shrinkage strains ( εsh(t, t0) ). For further details, refer to Gardener and Lockman 2001.

⎡ 2.(t -t')0.3 ⎛ 7 ⎞0.5 ⎛ (t -t') ⎞0.5 ⎤ + ⎜ ⎟ .⎜ ⎢ ⎥ ⎟ 0.3 ⎢(t -t') +14 ⎝ t0 ⎠ ⎝ (t -t')+7 ⎠ ⎥ 0.5 ⎢ ⎛ ⎞ ⎥ 1 Ccr(t,t') = ⎢ ⎜ ⎟ ⎥. Ec28 (12) (t -t') ⎢+2.5.(1-1.086.h2 ).⎜ ⎟ ⎥ 2 ⎢ ⎥ ⎜ V ⎛ ⎞ ⎟ ⎢ ⎜⎜ (t -t')+0.15.⎜ ⎟ ⎟⎟ ⎥ ⎝ S ⎠ ⎠ ⎦⎥ ⎝ ⎣⎢

⎛ ⎞ ⎜ ⎟ (t - t') ⎟ εsh(t, t0) = εshu. (1-1.18.h 4 ) . ⎜ 2 ⎜ ⎛V⎞ ⎟ ⎜ (t - t') + 0.15. ⎜ ⎟ ⎟ ⎝S⎠ ⎠ ⎝

0.5

(13)

where, t = Age of concrete (days), t' = Age of concrete at loading (days), t0 = Age of concrete at the beginning = of drying (days), h = Relative humidity (decimals), V S Volume to surface area ratio (mm), Ec28 = 28 days elastic modulus (MPa), εshu = Ultimate shrinkage strain depending on cement factor and compressive strength. Tadros proposed a simple and compact model to predict the creep coefficient and shrinkage strain. Equations (14) and (15) give the expression for predicting the creep coefficients ( φ(t, ti) ) and shrinkage strains ( εsh ). For further details, refer to Maher.K.Tadros et al. 2003. t ⎛ ⎞ -0.118 φ(t, ti) = 1.9. ⎜ .(1.56 - 0.008H). ⎟ .t ci 610.58f ' + t ⎝ ⎠ (14) 5 ⎞ ⎛ 1064 -3.7(V/S) ⎞ ⎛ ⎜ ⎟.⎜ ⎟ 735 ⎝ ⎠ ⎝ 1+ (0.145fci') ⎠ t ⎛ ⎞ εsh = 480*10-6. ⎜ ⎟ . (2 - 0.0143H). ⎝ 61- 0.58fci' + t ⎠ 5 ⎞ ⎛ 1064 - 3.7(V/S) ⎞ ⎛ ⎜ ⎟. ⎜ ⎟ 735 ⎝ ⎠ ⎝ 1+ (0.145fci') ⎠

(15)

where, H = Relative humidity (decimals), fci' = 28 days compressive strength (MPa), V/S = Volume to surface area ratio (mm).

5. Creep and shrinkage experimental program A HPC mix was adopted for the experiments on timedependent deformation. The mix was designed to have a specified compressive strength of 50 MPa at 28 days. The mix composition is listed in Table 1. The compressive strength and the young’s modulus of the mix at different ages are listed in the Table 2. 150 mm × 150 mm × 150 mm cube specimens were used for testing the compressive strength. 150 mm × 300 mm cylinder specimens were used for testing the modulus of elasticity. Experiments were conducted to get time dependent material properties like modulus of elasticity, creep coefficient and shrinkage strain for the above mix. Three shrinkage specimens of size 150 mm × 150 mm × 600 mm prisms were tested for the above HPC mix with a moist curing duration of 28 days. The specimens were placed at an average room temperature of 20ºC and an average relative humidity of 56%. The dial gauges were placed at the top of the shrinkage rigs to find out the periodic length change of the specimen, from which the shrinkage strains can be calculated. Three creep specimens of size 150 mm × 150 mm × 600 mm prisms were monitored for creep deformation.

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Table 1 Mix design. Cement Kg/m3

Silica fume Kg/m3

Sand Kg/m3

Gravel Kg/m3

Water L/m3

434

32.6

685

1098

158

Super plasticizer L/m3 4

Table 2 Physical properties of the mix. Age (Days) 1 3 7 14 28 56 90 180

Average cube compressive strength (MPa) 22.44 27.86 36.74 41.95 51.11 55.23 58.82 60.44

Modulus of elasticity (GPa) 14.68 16.54 20.975 21.05 21.9 22.83 25.03 27.74

Creep specimens were cast at the same time as corresponding shrinkage specimens were. These three creep specimens were stacked on top of each other in the creep rig. The demountable mechanical gauge (DEMEC) points were attached on the surface of each creep specimen at a spacing of 200 mm at the centre of the specimen in the longitudinal direction. The test setup of the creep specimens is shown in Fig. 1.

6. Analysis and comparison of test results with conventional models The test specimens for creep and shrinkage were moist cured for 28 days and placed to their respective rigs. The creep specimens were loaded at a stress level of 15% of the 28 days compressive strength and maintained a constant temperature of 20±3ºC and relative humidity of 50±6%. The strain readings were taken immediately before and after loading, two to six hours later, then daily for one week, weekly up to the age of one month, monthly up to the age of one year and the readings were taken up to 500 days. The same procedure was also followed for the shrinkage testing. The measurements were taken and displayed in graph form. Figures 2 to 5 present the creep coefficient, total strain, creep strain and shrinkage strain measurements. The total strain is the summation of elastic strain, creep strain and shrinkage strain. Based on the test results, the above values are predicted by seven different models. The predicted strains were calculated using the measured compressive strength and elastic strains. The following models were considered: AASHTO-LRFD, ACI 209, ACI 209 modified by Huo, B3, CEB-90, GL 2000 and Tadros. Figures 2 to 5 show the trend of variation of creep coefficients and strains with age after loading. Shrinkage strain prediction shows less variation between various models in compared to total and creep

Fig. 1 Experimental setup for 150 mm × 150 mm × 600 mm creep specimens.

strain. Creep and shrinkage mainly depend on parameters related with the composition of the concrete incorporating the effect of local materials, local environmental conditions and member loading and geometrical parameters. To facilitate the design of structures, some empirical relations have been developed to predict the creep and shrinkage characteristics for different regions and the same have been incorporated in the respective codes of practices. As the relationships are empirical, it is difficult to bring out a crisp comparison of various conventional models and hence experimental studies are carried out to identify the better predictor. However, qualitatively, it can be observed that the ACI 209 equation underpredicts the creep coefficient compared to the experimental results. The compressive strength of the concrete is not directly included in the equation, but constant values ‘10’ and ‘35’ have been incorporated in the general equation. Huo points out that for HPC, the factors need to be modified, and the model modified by him slightly improves the prediction. Also, the additional correction factors are responsible for under prediction up to some extent. In the AASHTO-LRFD equation, correction factors like slump, air content, etc., have not been considered. The formulation of expressions based on the ACI 209 equation has been slightly revised in AASHTO-LRFD, which results in better prediction compared to the above equations. The B3 model gives large deviation with respect to experimental results. Modeling of parameters and mainly the empirical expressions are the cause for this. The CEB 90 model

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AASHTO-LRFD

ACI 209

ACI 209 (Huo)

B3

CEB 90 Tadros

GL 2000 Experimental

AASHTO-LRFD ACI 209 (Huo) CEB 90 Tadros

ACI 209 B3 GL 2000 Experimental

20 17.5

2.5

15 Strain (10-4)

3

Phi (t)

2 1.5 1

12.5 10 7.5 5

0.5

2.5

0

0

0

100

200

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400

500

0

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200

300

400

500

Age after Loading (Days)

Age after Loading (Days)

Fig. 2 Creep coefficient values for 150 mm specimens.

Fig. 3 Total strain values for 150 mm specimens.

AASHTO-LRFD

ACI 209

AASHTO-LRFD

ACI 209

ACI 209 (Huo) CEB 90

B3 GL 2000

ACI 209 (Huo)

B3

Tadros

Experimental

CEB 90

GL 2000

Tadros

Experimental

7 6

12

5 Strain (10-4)

Strain (10-4)

10 8 6

4 3

4

2

2

1

0

0

0

100

200

300

400

500

Age after Loading (Days)

Fig. 4 Creep strain values for 150 mm specimens.

slightly over predicted at the early age (1 to 3 days) and then showed a close match with the experimental results compared to the other conventional models. The reason for the match is due to the better formulation of expressions for the key parameters like member geometry, humidity, strength, age of loading, etc. GL 2000 model values overpredict and Tadros model values underpredict compared to the experimental results. As the two models consider all key parameters, the mismatch is due to the limited generalization capability of empirical formulations to adopt the local material and environmental conditions in which experiments are carried out. A residual is defined as the algebraic difference between a predicted value and an experimental value. A negative

0

100

200

300

400

500

Age after Loading (Days)

Fig. 5 Shrinkage strain values for 150 mm specimens.

residual indicates that a model underpredicts the experimental data, and a positive residual indicates the model overpredicts the experimental data. A residual squared analysis of the total strain, creep and shrinkage data was performed to determine which model was most accurate. The following formula (16) is the residuals squared method that identifies the better predictor model with the given time.

tf 2 Sum of residual squared = ∑ ( Ret ) T=ti

(16)

where, T = Time after loading, ti = Initial time considered, tf = Final time considered, Ret = Residual time t.

7. Development of ANN model for creep and shrinkage A few conventional models exist for the prediction of creep and shrinkage. As observed earlier, qualitatively the prediction trends are the same but quantitatively differences are observed, due to various empirical formulations developed to suit the local conditions. Better predictor models can be developed for specific locations by using past experimental data that are reflected in the conventional model along with the new experimental data. The trends available in the combined data set can be assessed accurately using ANN, which is a model estimator. The dynamic nature of ANN allows modifying the predictor with the help of new test data generated to grab the new features associated with the environment and developments in material over time. This saves time and experimental efforts required to generate new models. Shrinkage and creep are affected mainly by the composition of the material, time, age of loading and the member geometry. Hence to represent these features, the following key parameters are taken as input parameter for the ANN. a) Relative humidity b) Volume to surface area ratio c) Compressive strength d) Time of loading e) Time at which creep and shrinkage is measured A multi-layer ANN for predicting time-dependent deformations in concrete structures is developed. The ANN presented in this paper is trained based on the experimental results combined with CEB model results, ANN shows better match most of the time with experimental results. However, there is some variation between experimental and CEB 90 model predictions at a later age. The creep and shrinkage prediction neural network consist of an input layer, 2 hidden layers and an output layer, as shown in Fig. 9. The optimum architecture is arrived at trial and error. The network utilizes a tan-sigmoid transfer function and a linear output function. A back propagation training algorithm was used as the learning rule for the network. This algorithm was created by generalizing the Widrow-Hoff learning rule to multiple-layer networks and nonlinear differentiable functions. Input/output data sets are used to train a network until the network can approximate a function.

AASHTO-LRFD ACI 209 (Huo)

ACI 209 B3

CEB 90 Tadros

GL 2000

90 80 70 60 50 40 30 20 10 0 Models

Fig. 6 Total sum of residual squared for 150 mm specimens. AASHTO-LRFD

ACI 209

ACI 209 (Huo)

B3

CEB 90 Tadros

GL 2000

80 70 Sum of Residuals2 Strain (10-8)

Figures 6 to 8 show comparisons of predictions of various conventional models for total strain, creep strain and shrinkage strain with reference to the experimental results developed in the present work. From the above specified reasons, it is inferred that the AASHTO-LRFD, ACI 209, ACI 209 (Huo) and CEB 90 models show less deviation whereas the B3, GL 2000 and Tadros model show more deviation. In all three cases, CEB 90 results shows a better match with the experimental results, having the least sum of squared residual strains.

Sum of Residuals2 Strain (10-8)

J. Karthikeyan, A. Upadhyay and N. M. Bhandari / Journal of Advanced Concrete Technology Vol. 6, No. 1, 135-142, 2008

60 50 40 30 20 10 0 Models

Fig. 7 Creep sum of residuals squared for 150 mm specimens.

AASHTO-LRFD ACI 209 (Huo) CEB 90 Tadros

ACI 209 B3 GL 2000

14 12 Sum of Residuals2 Strain (10-8)

140

10 8 6 4 2 0 Models

Fig. 8 Shrinkage sum of residual squared for 150 mm specimen.

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Properly trained backpropropagation networks tend to give reasonable answers when presented with inputs that they have never seen. Typically, a new input will lead to an output similar to the corrected output for input vectors used in training that are similar to the new input being presented. This generalization property makes it possible to train a network on a representative set of input/output pairs and get reliable results without training the network on all possible input/output pairs. Trainbr is a network training function that updates the weight and bias values according to LevenbergMarquardt optimization (Melin and Castillo 2004). It minimizes a combination of squared errors and weights, and then determines the correct combination so as to produce a network that generalizes well. This process is called Bayesian regularization (MacKay 1992). The Bayesian regularization training criterion was utilized during the learning process of the network with 464 training epochs for achieving a sum of squared error (SSE) of 0.034762 by using MATLAB computer-aided design software. Figure 10 shows the convergence of SSE of the network during training. The horizontal axis in each graph shown in Fig. 10 represents the number of epochs. The vertical axis in top most graph represent SSE, in the middle graph represents sum squared weight (SSW) and in the bottom most graph represent number of parameters. This entire graph jointly used to get indication regarding convergence of the training process having the architecture 5-11-4-2. In Figs. 11 and 12, each figure represents three curves. The first curve is that of CEB 90 model, the second curve is the experimental values, and the third curve is the ANN. The comparison between the experimental and CEB 90 data shows a good match in the initial stages, while in the later stage some difference is observed. After observing this trend, the training database is modified as explained earlier, with the help of experimental data. The accuracy of ANN prediction mainly depends on the quality of the database used for the training of ANN. As the CEB 90 model shows better match with the experimental results, a major part of training data set is obtained using the CEB 90 model. However in the later stage, deviation between experimental values is observed, and so in that stage CEB 90 data are replaced by experimental data. As a result of this exercise, the ANN gives good prediction. The performance of the developed ANN is evaluated by using a test data set that has not been used for training the network. On checking the performance over test data, the mean error was found to be 5.34%, minimum error 0.42%, and maximum error 13%.

8. Conclusions This paper presents the details of experimental work carried out to get the creep and shrinkage behavior of a HPC mix. Comparison of test results with seven different conventional models that are in practice was carried out. The CEB 90 model was found to show better match

First Hidden Layer Input layer RH

Second Hidden layer Output layer

V/S fck

ε Ф

to t Where, RH = Relative Humidity in Decimels, V/S = Volume by surface area ratio in mm, fck = Compressive strength of the concrete at to (MPa), to = Age of loading (Days), t = time at which the creep and shrinkage is measured (Days), ε = Shrinkage Strain and Ф = Creep Coefficient.

Fig. 9 Artificial Neural Networks (ANNs) for predicting creep coefficient and shrinkage strains.

Fig. 10 Convergence of the ANN error during training.

with experimental results. However, at a higher age, some deviation was observed in both creep and shrinkage predictions. For the sake of improvement, the experimental data and CEB 90 predictions were combined to develop an appropriate training set for the ANN. The ANN model developed in this work to predict creep and shrinkage behavior of the designed HPC mix and the predicted CEB 90 data values use the 5-11-4-2 architecture. On checking the performance over test data, the mean error was found to be 5.34%, minimum error 0.42% and maximum error 13%. The developed ANN model is computationally efficient and will be useful in predicting the time-dependent behavior of HPC mixes. Acknowledgement The authors express their sincere thanks to the JACT board and the reviewers for their valuable comments and suggestions. References ACI Committee 209, (1992). “Report on factors

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Shrinkage ANN

Creep ANN

Shrinkage Experimental

Creep Experimental

Shrinkage CEB 90

Creep CEB 90 2.5

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2 Phi (t)

Strain (10-4)

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1.5 1 0.5 0

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Fig. 11 Experimental vs ANN (shrinkage).

affecting shrinkage and creep of hardened concrete.” ACI Manual of Concrete Practice American Concrete Institute: Farmington Hills, MI, USA. AASHTO-LRFD, (2004). “AASHTO LRFD Bridge design specifications.” Third Edition American Association of State Highway and Transportation Officials: Washington. Bazant, Z. P. and Baweja, S. (1995). “Creep andshrinkage prediction model analysis and design of concrete structures – Model B3 RILEM Draft Recommendation.” Materials and Structures, 28, 357-365. Comité Euro-International du Béton (CEB), (1990). “CEB-FIP model code 1990.” Bulletin d’Information No.213/214: Lausanne, Switzerland. Gardener, N. J. and Lockman, M. J. (2001). “Design provisions for drying shrinkage and creep of normal strength concrete.” ACI Materials Journal, 98(2) (159-167). Gilbert, R. I. (1988). “Time effects in concrete structures.” Elsevier Science Publishers: Amsterdam. Huo, X., Al-Omaishi, N. and Tadros, M. K. (2001). “Creep, shrinkage and modulus of elasticity of high performance concrete.” ACI Materials Journal, 98(6), 440-449. MacKay, D. J. C. (1992). “Bayesian Interpolation.” Neural Computation, 4(3), 415-447.

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Age after Loading (Days)

Fig. 12 Experimental vs ANN (creep).

Melin, P. and Castillo, O. (2004). “Soft computing for intelligence control of nonlinear dynamical systems (Invited Paper).” International Journal of Computational Cognition, 2(1), 45-78. Nawy, E. G. (2001). “Fundamentals of high performance concrete.” 2nd ed.John Wiley and Sons: New York. Neville, A. M., Dilger, W. H. and Brooks, J. J. (1983). “Creep of plain and structural concrete.” Construction Press: London. Noureldin, A. and Taha, M. M. R. (2003). “Prediction of creep performance of masonry structures using artificial neural networks.” Proceedings of ICPCM – A New Era of Building, Cairo, Egypt, 1-10. Tadros, M. K., Al-Omaishi, N., Seguirant, S. J. and Gallt, J. G. (2003). “Prestress losses in pretensioned highstrength concrete bridge girders.” NCHRP Transportation Board: Washington. D.C. NCHRP Report 496. Townsend, B. D. (2003). “Creep and shrinkage of ahigh strength concrete mixture.” Thesis (M.S). Virginia Polytechnic Institute and State University, USA. Vincent, E. C. (2003). “Compressive creep of a light weight, high strength concrete mixture.” Thesis (M.S). Virginia Polytechnic Institute and State University, USA.

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Scientific paper

Artificial Neural Network for Predicting Creep and Shrinkage of High Performance Concrete Jayakumar Karthikeyan1, Akhil Upadhyay2 and Navaratan M. Bhandari3 Received 30 June 2007, accepted 30 December 2007

Abstract Concrete undergoes time-dependent deformations that must be considered in the design of reinforced/prestressed highperformance concrete (HPC) bridge girders. In this research, experiments on the creep and shrinkage properties of a HPC mix were conducted for 500 days. The test results obtained from this research were compared to different models to determine which model was the better one. The CEB-90 model was found better in predicting time-dependent strains and deformations for the above HPC mix. However, in a far zone, some deviation was observed, and to get a better model, the experimental data base was used along with the CEB-90 model database to train the neural network. The developed Artificial Neural Network (ANN) model will serve as a more rational as well as computationally efficient model in predicting creep coefficient and shrinkage strain.

1. Introduction Concrete undergoes volumetric changes throughout its service life. These changes are a result of timedependent deformations (creep and shrinkage). The time-dependent increase in strain in hardened concrete subjected to sustained stress, in excess of shrinkage, is defined as creep. Creep includes basic creep and drying creep. Basic creep occurs under conditions where there is no moisture movement to or from the environment. Drying creep is the additional creep caused by drying. The ratio of creep strain to that of the initial elastic strain due to a sustained stress is used as a measurement of creep deformation. This ratio is called the creep coefficient. Shrinkage is defined here as the time-dependent strain measured at constant temperature in an unloaded and unrestrained specimen. Behind this simple definition there are six different types of shrinkage; plastic shrinkage, thermal shrinkage, chemical shrinkage, autogeneous shrinkage, drying shrinkage and carbonation shrinkage. Various types of shrinkages can be distinguished depending on the cause of moisture loss. Plastic shrinkage takes place due to loss of water during the plastic state of concrete either by evaporation from the surface or absorption in aggregate. Thermal shrinkage takes place during the first few days of placement: generation of heat resulting from hydration and consequent cooling leads to it. Chemical shrinkage results in volume reduction due to hydration. Autogeneous shrinkage

1

Research Scholar, Department of Civil Engineering, Indian Institute of Technology, Roorkee, India. E-mail:[email protected] 2 Associate Professor, Department of Civil Engineering, Indian Institute of Technology, Roorkee, India. 3 Professor, Department of Civil Engineering, Indian Institute of Technology, Roorkee, India.

takes place due to the self-desiccation after final setting. Drying shrinkage is the removal of adsorbed water from the hydrated cement paste when it is exposed to the environment. Carbonation shrinkage is the dissolution of calcium hydroxide and the deposition of calcium carbonate having lesser volume. Shrinkage is expressed as a dimensionless strain. The shrinkage of concrete has a direct influence on prestress losses of prestressed concrete members and the long-term deformation of girders. Several reports have indicated that the shrinkage and creep deformations of HPC are lower than those of normal-strength concrete. This is due to the dense matrix and low-water cementitious material ratio (Huo et al. 2001). The creep and shrinkage strains for the HPC mixture were measured compared to seven different models to determine which models were the most accurate. According to Townsend’s experimental results comparison, American Concrete Institute (ACI)'s ACI 209 model modified by Huo was most accurate in predicting timedependent strains (Townsend 2003). The creep for a light weight high strength concrete mixture was measured and compared with four different models. The models considered were ACI 209, CEB 90, B3 and GL2000. According to Vincent’s measurements, the GL2000 model was the best predictor model, and CEB90 was the best predictor for the total strains (Vincent 2003). Based on his investigation, Huo states that the current ACI 209 model does not accurately predict the material properties for HPC. Huo revised the ACI 209 equations for calculating shrinkage strains and creep coefficient, which can be used for both conventional concrete and HPC. The above revised equations are referred to as ACI 209 modified by Huo, (Huo et al. 2001). A new ANN model is for predicting creep in masonry structures. Few experiments for creep in brick masonry have been carried out. By making use of those test data, Noureldin and Taha has used ANN to generate a new

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model for predicting creep (Noureldin and Taha 2003). In view of the above literature review, the objective of the present study is to investigate the time-dependent properties of HPC such as creep and shrinkage, in order to find out the better predictor model for creep and shrinkage. The better predictor model values along with experimental data generated in this work are used in the ANN and it is validated to generate a new predictive ANN model for creep and shrinkage.

2. Basic approach The above-mentioned objective is achieved through the following steps: a) Preparation of specimens for creep and shrinkage studies of a HPC mix b) Comparison of the predictions of various existing creep and shrinkage models with experimental data to identify the best model having the least deviation. c) Addition of the experimental data and the data obtained from the model having the least deviation from experimental data to get a combined training set for the ANN training, and comparison of the performance of the developed ANN with the experimental results.

3. ANN The ANN, which consists of simplified models of the biological neuron system, is a massively parallel distributed processing system made up of highly interconnected neural computing elements that have the ability to learn by acquiring knowledge and making it available for use. The ANN exhibits characteristics such as mapping capabilities and pattern association, generalization, robustness and high speed information processing. The ANN can be trained with known values from collected data or from the test data; and it can recall full patterns from incomplete, partial, or noisy patterns. The main advantages of the ANN are: a) Once appropriately trained, the ANN works as a model free estimator and it can be effectively used in solving the unknown or untrained instances of the problem. b) The ANN has higher fault tolerance. c) Whenever more data becomes available, further training can be done without starting from scratch. Applications of ANNs in civil engineering have increased in recent years and are continuing to do so. Therefore, all the required patterns can be found from the neural network free estimator. ANNs have been used recently to recognize complicated patterns and find solutions to problems too complex to be modeled accurately by traditional computing methods.

4. Conventional models Of the various varieties of methods proposed for the

prediction creep and shrinkage in concrete, seven are presented in this section: ACI 209, ACI 209 modified by Huo, AASHTO-LRFD, B3, CEB 90, GL 2000 and Tadros. ACI 209 proposes an empirical model for predicting creep and shrinkage strain as a function of time. The models have the same principle: a hyperbolic curve that tends to an asymptotic value called the ultimate value ( φu , (εsh)u ). The shape of the curve and ultimate value depend on several factors such as the curing conditions, age at application of load, mix design, ambient temperature and humidity. Equations 1 and 2 presents the general model for predicting creep coefficients ( φt ) and shrinkage strains (εsh)t . For the detailed expressions, refer to ACI Committee 209 2005.

⎛ (t - t')0.6 ⎞ φt = ⎜ .φu 0.6 ⎟ ⎝ 10 + (t - t') ⎠

(1)

⎛ t - t0 ⎞ (εsh)t = ⎜ ⎟ .(εsh)u ⎝ 35 + (t - t0) ⎠

(2)

where, t = Age of concrete (days), t' = Age of concrete at loading (days), t0 = Age at the beginning of drying (days), φu = Ultimate creep coefficient expression depending on slump, member geometry, humidity, fine aggregate, air content and type of curing, (εsh)u = Ultimate shrinkage strain expression depending on slump, member geometry, humidity, fine aggregate, air content and type of curing. Huo modified the above equations by incorporating a strength correction factor. Modified equations 3 and 4 can be used for conventional concretes as well as HPC for predicting creep coefficients ( φt ) and shrinkage strains ( (εsh)t ). For further details on these expressions, refer to Huo et al. 2001. ⎛ ⎞ (t - t')0.6 φt = ⎜ .φu 0.6 ⎟ (12 0.0725.f c') + (t - t') ⎝ ⎠

(3)

⎛ t - t0 ⎞ (εsh)t = ⎜ ⎟ .(εsh)u ⎝ (45 - 0.3625fc') + (t - t0) ⎠

(4)

fc' =28 days compressive strength (MPa) The AASHTO-LRFD model is similar to ACI 209. However, based on this model slightly different correction factors for slump, member size, type of curing, etc. are proposed in the ultimate creep coefficient and ultimate shrinkage strain expressions. For the expressions, refer to AASHTO-LRFD 2004. The CEB 90 model gives the hyperbolic change over time of creep and shrinkage, and it also uses an ultimate value corrected according to the mix design and environmental conditions. One difference of CEB 90 is that it predicts creep strain rather than creep coefficient. Equations (5), (6) and (7) give the general prediction model for creep strains ( εcr(t, t') ), creep coefficients ( φ28 ), and shrinkage strains ( εs(t, t0) ) respectively. For further details on these expressions, refer to CEB-FIP

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model code 1990.

εcr(t, t') = φ28 = φ0

σc(t') .φ28(t, t') E28 ⎛ ⎜ ⎜ ⎜ ⎜ ⎜ ⎝⎜

(5)

⎞ 0.3

t-t' ⎟⎟⎟ βh +(t-t') ⎟⎠⎟⎟

(6)

εs(t, t0) = εso.βs.(t - t0)

(7)

where, σc(t') = Applied stress (MPa), E28 = 28 days modulus of elasticity (MPa), φ0 = Notional creep coefficient depending on humidity, member geometry, compressive strength and type of curing, βh = Constant depending on member size and relative humidity, εso = Notional shrinkage coefficient depending on the type of cement and compressive strength, βs = A hyperbolic shrinkage function depending on member geometry and time. The B3 model was proposed by Bazant and Baweja in 1995 as a new improvement and an update of previous models such as BP (Bazant and Panula model in 1978) and BP-KX (Bazant, Panula, Kim, Koo and Xi model in 1992). The B3 model is simpler, better theoretically supported and more exact than the previous models. It takes into account basic and drying creep portions. Equations (8), (9), (10) and (11) give the general expression for the creep compliance function ( J(t, t') ), basic creep function ( C0(t, t') ), drying creep function ( Cd(t, t', t0) ) and drying shrinkage ( εsh(t, t0) ) respectively. For further details on these expressions, refer to Bazant and Baweja 1995. J(t, t') = q1 + C0(t, t') + Cd(t, t', t0)

(8)

C0(t, t') = q2.Q(t, t') + q3.In (1+(t+t')n ) + q4In ⎛⎜ t ⎞⎟ ⎝ t' ⎠

(9)

Cd(t, t', t0) = q5. ⎡⎣exp{8.H(t)}−exp{-8.H(t0')}⎤⎦

εsh(t, t0) = -εsh∞.kh.tanh t-t0 τsh

0.5

(10) (11)

where, q1 = Instantaneous strain due to unit stress, t = Age of concrete (days), t' = Age of concrete at loading (days), t0 = Age of concrete at the beginning of drying (days). Gardner and Lockman (GL2000) proposed a more compact model for creep coefficient depending only on relative humidity and member geometry. Equations (12) and (13) give the expression for predicting the creep coefficients ( Ccr(t, t') ) and shrinkage strains ( εsh(t, t0) ). For further details, refer to Gardener and Lockman 2001.

⎡ 2.(t -t')0.3 ⎛ 7 ⎞0.5 ⎛ (t -t') ⎞0.5 ⎤ + ⎜ ⎟ .⎜ ⎢ ⎥ ⎟ 0.3 ⎢(t -t') +14 ⎝ t0 ⎠ ⎝ (t -t')+7 ⎠ ⎥ 0.5 ⎢ ⎛ ⎞ ⎥ 1 Ccr(t,t') = ⎢ ⎜ ⎟ ⎥. Ec28 (12) (t -t') ⎢+2.5.(1-1.086.h2 ).⎜ ⎟ ⎥ 2 ⎢ ⎥ ⎜ V ⎛ ⎞ ⎟ ⎢ ⎜⎜ (t -t')+0.15.⎜ ⎟ ⎟⎟ ⎥ ⎝ S ⎠ ⎠ ⎦⎥ ⎝ ⎣⎢

⎛ ⎞ ⎜ ⎟ (t - t') ⎟ εsh(t, t0) = εshu. (1-1.18.h 4 ) . ⎜ 2 ⎜ ⎛V⎞ ⎟ ⎜ (t - t') + 0.15. ⎜ ⎟ ⎟ ⎝S⎠ ⎠ ⎝

0.5

(13)

where, t = Age of concrete (days), t' = Age of concrete at loading (days), t0 = Age of concrete at the beginning = of drying (days), h = Relative humidity (decimals), V S Volume to surface area ratio (mm), Ec28 = 28 days elastic modulus (MPa), εshu = Ultimate shrinkage strain depending on cement factor and compressive strength. Tadros proposed a simple and compact model to predict the creep coefficient and shrinkage strain. Equations (14) and (15) give the expression for predicting the creep coefficients ( φ(t, ti) ) and shrinkage strains ( εsh ). For further details, refer to Maher.K.Tadros et al. 2003. t ⎛ ⎞ -0.118 φ(t, ti) = 1.9. ⎜ .(1.56 - 0.008H). ⎟ .t ci 610.58f ' + t ⎝ ⎠ (14) 5 ⎞ ⎛ 1064 -3.7(V/S) ⎞ ⎛ ⎜ ⎟.⎜ ⎟ 735 ⎝ ⎠ ⎝ 1+ (0.145fci') ⎠ t ⎛ ⎞ εsh = 480*10-6. ⎜ ⎟ . (2 - 0.0143H). ⎝ 61- 0.58fci' + t ⎠ 5 ⎞ ⎛ 1064 - 3.7(V/S) ⎞ ⎛ ⎜ ⎟. ⎜ ⎟ 735 ⎝ ⎠ ⎝ 1+ (0.145fci') ⎠

(15)

where, H = Relative humidity (decimals), fci' = 28 days compressive strength (MPa), V/S = Volume to surface area ratio (mm).

5. Creep and shrinkage experimental program A HPC mix was adopted for the experiments on timedependent deformation. The mix was designed to have a specified compressive strength of 50 MPa at 28 days. The mix composition is listed in Table 1. The compressive strength and the young’s modulus of the mix at different ages are listed in the Table 2. 150 mm × 150 mm × 150 mm cube specimens were used for testing the compressive strength. 150 mm × 300 mm cylinder specimens were used for testing the modulus of elasticity. Experiments were conducted to get time dependent material properties like modulus of elasticity, creep coefficient and shrinkage strain for the above mix. Three shrinkage specimens of size 150 mm × 150 mm × 600 mm prisms were tested for the above HPC mix with a moist curing duration of 28 days. The specimens were placed at an average room temperature of 20ºC and an average relative humidity of 56%. The dial gauges were placed at the top of the shrinkage rigs to find out the periodic length change of the specimen, from which the shrinkage strains can be calculated. Three creep specimens of size 150 mm × 150 mm × 600 mm prisms were monitored for creep deformation.

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Table 1 Mix design. Cement Kg/m3

Silica fume Kg/m3

Sand Kg/m3

Gravel Kg/m3

Water L/m3

434

32.6

685

1098

158

Super plasticizer L/m3 4

Table 2 Physical properties of the mix. Age (Days) 1 3 7 14 28 56 90 180

Average cube compressive strength (MPa) 22.44 27.86 36.74 41.95 51.11 55.23 58.82 60.44

Modulus of elasticity (GPa) 14.68 16.54 20.975 21.05 21.9 22.83 25.03 27.74

Creep specimens were cast at the same time as corresponding shrinkage specimens were. These three creep specimens were stacked on top of each other in the creep rig. The demountable mechanical gauge (DEMEC) points were attached on the surface of each creep specimen at a spacing of 200 mm at the centre of the specimen in the longitudinal direction. The test setup of the creep specimens is shown in Fig. 1.

6. Analysis and comparison of test results with conventional models The test specimens for creep and shrinkage were moist cured for 28 days and placed to their respective rigs. The creep specimens were loaded at a stress level of 15% of the 28 days compressive strength and maintained a constant temperature of 20±3ºC and relative humidity of 50±6%. The strain readings were taken immediately before and after loading, two to six hours later, then daily for one week, weekly up to the age of one month, monthly up to the age of one year and the readings were taken up to 500 days. The same procedure was also followed for the shrinkage testing. The measurements were taken and displayed in graph form. Figures 2 to 5 present the creep coefficient, total strain, creep strain and shrinkage strain measurements. The total strain is the summation of elastic strain, creep strain and shrinkage strain. Based on the test results, the above values are predicted by seven different models. The predicted strains were calculated using the measured compressive strength and elastic strains. The following models were considered: AASHTO-LRFD, ACI 209, ACI 209 modified by Huo, B3, CEB-90, GL 2000 and Tadros. Figures 2 to 5 show the trend of variation of creep coefficients and strains with age after loading. Shrinkage strain prediction shows less variation between various models in compared to total and creep

Fig. 1 Experimental setup for 150 mm × 150 mm × 600 mm creep specimens.

strain. Creep and shrinkage mainly depend on parameters related with the composition of the concrete incorporating the effect of local materials, local environmental conditions and member loading and geometrical parameters. To facilitate the design of structures, some empirical relations have been developed to predict the creep and shrinkage characteristics for different regions and the same have been incorporated in the respective codes of practices. As the relationships are empirical, it is difficult to bring out a crisp comparison of various conventional models and hence experimental studies are carried out to identify the better predictor. However, qualitatively, it can be observed that the ACI 209 equation underpredicts the creep coefficient compared to the experimental results. The compressive strength of the concrete is not directly included in the equation, but constant values ‘10’ and ‘35’ have been incorporated in the general equation. Huo points out that for HPC, the factors need to be modified, and the model modified by him slightly improves the prediction. Also, the additional correction factors are responsible for under prediction up to some extent. In the AASHTO-LRFD equation, correction factors like slump, air content, etc., have not been considered. The formulation of expressions based on the ACI 209 equation has been slightly revised in AASHTO-LRFD, which results in better prediction compared to the above equations. The B3 model gives large deviation with respect to experimental results. Modeling of parameters and mainly the empirical expressions are the cause for this. The CEB 90 model

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AASHTO-LRFD

ACI 209

ACI 209 (Huo)

B3

CEB 90 Tadros

GL 2000 Experimental

AASHTO-LRFD ACI 209 (Huo) CEB 90 Tadros

ACI 209 B3 GL 2000 Experimental

20 17.5

2.5

15 Strain (10-4)

3

Phi (t)

2 1.5 1

12.5 10 7.5 5

0.5

2.5

0

0

0

100

200

300

400

500

0

100

200

300

400

500

Age after Loading (Days)

Age after Loading (Days)

Fig. 2 Creep coefficient values for 150 mm specimens.

Fig. 3 Total strain values for 150 mm specimens.

AASHTO-LRFD

ACI 209

AASHTO-LRFD

ACI 209

ACI 209 (Huo) CEB 90

B3 GL 2000

ACI 209 (Huo)

B3

Tadros

Experimental

CEB 90

GL 2000

Tadros

Experimental

7 6

12

5 Strain (10-4)

Strain (10-4)

10 8 6

4 3

4

2

2

1

0

0

0

100

200

300

400

500

Age after Loading (Days)

Fig. 4 Creep strain values for 150 mm specimens.

slightly over predicted at the early age (1 to 3 days) and then showed a close match with the experimental results compared to the other conventional models. The reason for the match is due to the better formulation of expressions for the key parameters like member geometry, humidity, strength, age of loading, etc. GL 2000 model values overpredict and Tadros model values underpredict compared to the experimental results. As the two models consider all key parameters, the mismatch is due to the limited generalization capability of empirical formulations to adopt the local material and environmental conditions in which experiments are carried out. A residual is defined as the algebraic difference between a predicted value and an experimental value. A negative

0

100

200

300

400

500

Age after Loading (Days)

Fig. 5 Shrinkage strain values for 150 mm specimens.

residual indicates that a model underpredicts the experimental data, and a positive residual indicates the model overpredicts the experimental data. A residual squared analysis of the total strain, creep and shrinkage data was performed to determine which model was most accurate. The following formula (16) is the residuals squared method that identifies the better predictor model with the given time.

tf 2 Sum of residual squared = ∑ ( Ret ) T=ti

(16)

where, T = Time after loading, ti = Initial time considered, tf = Final time considered, Ret = Residual time t.

7. Development of ANN model for creep and shrinkage A few conventional models exist for the prediction of creep and shrinkage. As observed earlier, qualitatively the prediction trends are the same but quantitatively differences are observed, due to various empirical formulations developed to suit the local conditions. Better predictor models can be developed for specific locations by using past experimental data that are reflected in the conventional model along with the new experimental data. The trends available in the combined data set can be assessed accurately using ANN, which is a model estimator. The dynamic nature of ANN allows modifying the predictor with the help of new test data generated to grab the new features associated with the environment and developments in material over time. This saves time and experimental efforts required to generate new models. Shrinkage and creep are affected mainly by the composition of the material, time, age of loading and the member geometry. Hence to represent these features, the following key parameters are taken as input parameter for the ANN. a) Relative humidity b) Volume to surface area ratio c) Compressive strength d) Time of loading e) Time at which creep and shrinkage is measured A multi-layer ANN for predicting time-dependent deformations in concrete structures is developed. The ANN presented in this paper is trained based on the experimental results combined with CEB model results, ANN shows better match most of the time with experimental results. However, there is some variation between experimental and CEB 90 model predictions at a later age. The creep and shrinkage prediction neural network consist of an input layer, 2 hidden layers and an output layer, as shown in Fig. 9. The optimum architecture is arrived at trial and error. The network utilizes a tan-sigmoid transfer function and a linear output function. A back propagation training algorithm was used as the learning rule for the network. This algorithm was created by generalizing the Widrow-Hoff learning rule to multiple-layer networks and nonlinear differentiable functions. Input/output data sets are used to train a network until the network can approximate a function.

AASHTO-LRFD ACI 209 (Huo)

ACI 209 B3

CEB 90 Tadros

GL 2000

90 80 70 60 50 40 30 20 10 0 Models

Fig. 6 Total sum of residual squared for 150 mm specimens. AASHTO-LRFD

ACI 209

ACI 209 (Huo)

B3

CEB 90 Tadros

GL 2000

80 70 Sum of Residuals2 Strain (10-8)

Figures 6 to 8 show comparisons of predictions of various conventional models for total strain, creep strain and shrinkage strain with reference to the experimental results developed in the present work. From the above specified reasons, it is inferred that the AASHTO-LRFD, ACI 209, ACI 209 (Huo) and CEB 90 models show less deviation whereas the B3, GL 2000 and Tadros model show more deviation. In all three cases, CEB 90 results shows a better match with the experimental results, having the least sum of squared residual strains.

Sum of Residuals2 Strain (10-8)

J. Karthikeyan, A. Upadhyay and N. M. Bhandari / Journal of Advanced Concrete Technology Vol. 6, No. 1, 135-142, 2008

60 50 40 30 20 10 0 Models

Fig. 7 Creep sum of residuals squared for 150 mm specimens.

AASHTO-LRFD ACI 209 (Huo) CEB 90 Tadros

ACI 209 B3 GL 2000

14 12 Sum of Residuals2 Strain (10-8)

140

10 8 6 4 2 0 Models

Fig. 8 Shrinkage sum of residual squared for 150 mm specimen.

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Properly trained backpropropagation networks tend to give reasonable answers when presented with inputs that they have never seen. Typically, a new input will lead to an output similar to the corrected output for input vectors used in training that are similar to the new input being presented. This generalization property makes it possible to train a network on a representative set of input/output pairs and get reliable results without training the network on all possible input/output pairs. Trainbr is a network training function that updates the weight and bias values according to LevenbergMarquardt optimization (Melin and Castillo 2004). It minimizes a combination of squared errors and weights, and then determines the correct combination so as to produce a network that generalizes well. This process is called Bayesian regularization (MacKay 1992). The Bayesian regularization training criterion was utilized during the learning process of the network with 464 training epochs for achieving a sum of squared error (SSE) of 0.034762 by using MATLAB computer-aided design software. Figure 10 shows the convergence of SSE of the network during training. The horizontal axis in each graph shown in Fig. 10 represents the number of epochs. The vertical axis in top most graph represent SSE, in the middle graph represents sum squared weight (SSW) and in the bottom most graph represent number of parameters. This entire graph jointly used to get indication regarding convergence of the training process having the architecture 5-11-4-2. In Figs. 11 and 12, each figure represents three curves. The first curve is that of CEB 90 model, the second curve is the experimental values, and the third curve is the ANN. The comparison between the experimental and CEB 90 data shows a good match in the initial stages, while in the later stage some difference is observed. After observing this trend, the training database is modified as explained earlier, with the help of experimental data. The accuracy of ANN prediction mainly depends on the quality of the database used for the training of ANN. As the CEB 90 model shows better match with the experimental results, a major part of training data set is obtained using the CEB 90 model. However in the later stage, deviation between experimental values is observed, and so in that stage CEB 90 data are replaced by experimental data. As a result of this exercise, the ANN gives good prediction. The performance of the developed ANN is evaluated by using a test data set that has not been used for training the network. On checking the performance over test data, the mean error was found to be 5.34%, minimum error 0.42%, and maximum error 13%.

8. Conclusions This paper presents the details of experimental work carried out to get the creep and shrinkage behavior of a HPC mix. Comparison of test results with seven different conventional models that are in practice was carried out. The CEB 90 model was found to show better match

First Hidden Layer Input layer RH

Second Hidden layer Output layer

V/S fck

ε Ф

to t Where, RH = Relative Humidity in Decimels, V/S = Volume by surface area ratio in mm, fck = Compressive strength of the concrete at to (MPa), to = Age of loading (Days), t = time at which the creep and shrinkage is measured (Days), ε = Shrinkage Strain and Ф = Creep Coefficient.

Fig. 9 Artificial Neural Networks (ANNs) for predicting creep coefficient and shrinkage strains.

Fig. 10 Convergence of the ANN error during training.

with experimental results. However, at a higher age, some deviation was observed in both creep and shrinkage predictions. For the sake of improvement, the experimental data and CEB 90 predictions were combined to develop an appropriate training set for the ANN. The ANN model developed in this work to predict creep and shrinkage behavior of the designed HPC mix and the predicted CEB 90 data values use the 5-11-4-2 architecture. On checking the performance over test data, the mean error was found to be 5.34%, minimum error 0.42% and maximum error 13%. The developed ANN model is computationally efficient and will be useful in predicting the time-dependent behavior of HPC mixes. Acknowledgement The authors express their sincere thanks to the JACT board and the reviewers for their valuable comments and suggestions. References ACI Committee 209, (1992). “Report on factors

142

Shrinkage ANN

Creep ANN

Shrinkage Experimental

Creep Experimental

Shrinkage CEB 90

Creep CEB 90 2.5

4.5 4 3.5 3 2.5 2 1.5 1 0.5 0

2 Phi (t)

Strain (10-4)

J. Karthikeyan, A. Upadhyay and N. M. Bhandari / Journal of Advanced Concrete Technology Vol. 6, No. 1, 135-142, 2008

1.5 1 0.5 0

0

100

200

300

400

500

Age after Loading (Days)

Fig. 11 Experimental vs ANN (shrinkage).

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Fig. 12 Experimental vs ANN (creep).

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