Prediction of Compressive Strength of Concrete from Early Age Test Result Using Design of Experiments (RSM)

Transcription

1 Predictio of Compressive Stregth of Cocrete from Early Age Test Result Usig Desig of Experimets (RSM) Salem Alsausi, Louba Betaher Abstract Respose Surface Methods (RSM) provide statistically validated predictive models that ca the be maipulated for fidig optimal process cofiguratios. Variatio trasmitted to resposes from poorly cotrolled process factors ca be accouted for by the mathematical techique of propagatio of error (POE), which facilitates fidig the flats o the surfaces geerated by RSM. The dual respose approach to RSM captures the stadard deviatio of the output as well as the average. It accouts for ukow sources of variatio. Dual respose plus propagatio of error (POE) provides a more useful model of overall respose variatio. I our case, we implemeted this techique i predictig compressive stregth of cocrete of 28 days i age. Sice 28 days is quite time cosumig, while it is importat to esure the quality cotrol process. This paper ivestigates the potetial of usig desig of experimets (DOE-RSM) to predict the compressive stregth of cocrete at 28th day. Data used for this study was carried out from experimet schemes at uiversity of Beghazi, civil egieerig departmet. A total of 114 sets of data were implemeted. ACI mix desig method was utilized for the mix desig. No admixtures were used, oly the mai cocrete mix costituets such as cemet, coarseaggregate, fie aggregate ad water were utilized i all mixes. Differet mix proportios of the igrediets ad differet water cemet ratio were used. The proposed mathematical models are capable of predictig the required cocrete compressive stregth of cocrete from early ages. Keywords Mix proportioig, respose surface methodology, compressive stregth, optimal desig. C I. INTRODUCTION ONCRETE is the most widely used structural material for costructio today. Traditioally, cocrete has bee fabricated from a few well-defied compoets: Cemet, water, fie aggregate, coarse aggregate, etc. I cocrete mix desig ad quality cotrol, the stregth of cocrete is regarded as the most importat property. The desig stregth of the cocrete ormally represets its 28 th day stregth.i case of costructio work 28 days is cosiderable time to wait for the test results of cocrete stregth, while it also represets the quality cotrol process of cocrete mixig, placig, proper curig etc. If due to some experimetal error i mix desig, the test results fail to achieve the desiged stregth, the repetitio of the etire process becomes ecessary, which ca be costly ad time cosumig. It is ecessary to wait at least Salem Alsausi, Professor, is with the Civil Egieerig Departmet, Uiversity of Beghazi, Beghazi, Libya ( salem.alsausi@uob.edu.ly Luba Betaher, Assistat Lecturer, is with the Civil Egieerig Departmet, Uiversity of Beghazi, Beghazi, Libya. 28 days, thus the eed for a easy ad suitable method. Data used for this study was carried out from experimet schemes at uiversity of Beghazi, civil egieerig departmet. A total of 114 sets of data were implemeted. ACI mix desig method was utilized for the mix desig. No admixtures were used, oly the mai cocrete mixes costituets such as cemet, coarse-aggregate, fie aggregate ad water were utilized i all mixes. Differet mix proportios of the igrediets ad differet water cemet ratio were used. The proposed mathematical models are capable of predictig the required cocrete compressive stregth of cocrete from early ages. Proportios of the igrediets ad differet w/c. estimatig the stregth at a early age of cocrete were ivestigated. A rapid ad reliable cocrete stregth predictio would be of great sigificace. There are may idustrial problems where the respose variables of iterest i the product are a fuctio of the proportios of the differet igrediets used i its formulatio. This is a special type of respose surface problem called a (RSM). Usig polyomial regressios, the DOE approach permits calculatio of the respose surfaces for the parameters uder study over the experimetal domai. Because of the high complexity of the relatio betwee the compressive stregth ad compoet compositio of cocrete, covetioal regressio aalysis could be isufficiet to build a accurate model. This paper ivestigates the potetial of usig desig of experimets (DOE) to predict the compressive stregth of cocrete at 28th day as the respose. Respose surface method (RSM) opes ew possibilities i the classificatio ad geeralizatio of available experimetal results to estimate cocrete stregth from the mix compoets. This work presets ad examies the mix proportioig of ordiary cocrete usig RSM techique to optimize the mixture proportios ad developmet of mathematical model for desired properties of cocrete compressive stregth i terms predictable ad icrease the efficiecy of the predictio [1]. II. EXPERIMENTAL PROGRAM Locally produced Ordiary Portlad Cemet (OPC) was used. The coarse aggregate was 19 to 25 mm maximum size crushed stoe. No admixtures or additives was used i this study oly the ordiary costituets of cocrete (cemet, sad, gravel, water) to study the effect of the ordiary mix proportio o the compressive stregth of cocrete. Specimes were immersed i water util the day of testig at 1559

2 3, 7, 28 days. The experimet work was carried out at uiversity of Beghazi civil egieerig departmet. Total 114 sets of data were used to aalyze the behavior of the cocrete with time (age). ACI mix desig method (ACI ) was used for the mix desig process. The cocrete compressive stregth after 28 day was defied as the stregth obtaied from stadard cubes 150mm. The statistical aalysis was performed usig the computer software (Miitab). Computig the statistical iformatio of the data like the mea, stadard deviatio ad the correlatio coefficiet betwee the variable was preset at Tables I ad II. Geeral costituets of cocrete [cemet(c), coarse-aggregate (CA), fie aggregate (FA) ad water (W)] were used to evaluate the cocrete compressive stregth [2]. TABLE I DESCRIPTIVE STATISTICS INFORMATION'S Variable Quatity Mea StDev Mi. Max. W/C Water cemet ratio W Wight of water, Kg C Wight of cemet, Kg CA Wight of coarse aggregate Kg FA Wight of fie aggregate Kg fc`7 cocrete compressive stregth at 7 day Mpa fc`28 cocrete compressive stregth at 28 day Mpa TABLE II CORRELATION BETWEEN THE VARIABLES USED FOR ANALYSIS W/C W C CA FA fc`7 W 0.52 C CA FA fc` fc` III. METHODOLOGY Respose surface methodology (RSM) cosists of a set of statistical methods that ca be used to develop, improve, or optimize products [3]. RSM typically is used i situatios where several factors ifluece oe or more performace characteristics, or resposes. (RSM) used to optimize oe or more resposes, or to meet a give set of specificatios (e.g., a miimum stregth specificatio or a allowable rage of slump values). There are three geeral steps that comprise (RSM): experimet desig, modelig, ad optimizatio [4]. Cocrete is a mixture of several compoets. Water, portlad cemet, fie ad coarse aggregates form a basic cocrete mixture. Various chemical ad mieral admixtures, as well as other materials such as fibers, also may be added. Choosig the desig correctly will esure that the respose surface is fit i the most efficiet maer. MINITAB provides cetral composite ad Box-Behke desigs [3]. Cosider a cocrete mixture cosistig of q compoet materials (where q is the umber of compoet materials). Two approaches ca be applied to cocrete mixture, the mathematically idepedet variable approach, ad optimizatio the mathematic model. Fig. 1 The research diagram The empirical models are fit to the data, ad polyomial models (liear or quadratic) typically are used. The geeral case of the full quadratic model for k =3 as a example for idepedet variables is show as [3]: (1) I (1), the te coefficiets are represeted by the b k ad e is a radom error term represetig the combied effects of variables ot icluded i the model. The iteractio terms (x i x j ) ad the quadratic terms (x i 2 ) accout for curvature i the respose surface. The cetral composite desig (CCD), a augmeted factorial desig, is commoly used i product optimizatio [2]. The desig cosists of 2k factorial poits represetig all combiatios of coded values x k = ±1, 2*k axial poits at a distace ±α from the origi, ad at least 3 ceter poits with coded values of zero for each x k. The value of α usually is chose to make the desig rotatable, but there are sometimes valid reasos to select other values show i Fig. 3. Fig. 2 Schematic of a cetral composite desig for three factors Optimizatio may be performed usig mathematical (umerical) or graphical (cotour plot) approaches. Numerical optimizatio requires defiig a objective fuctio that 1560

3 reflects the levels of each respose i terms of miimum (zero) to maximum (oe) desirability (D) which is [5]: Several types of desirability fuctios ca be defied. Commo types of desirability fuctios are show i Fig. 4. (2) five compoet cotets ad a 7-day age. The best fit for the compressive stregth was obtaied with a lowest absolute percetage error (MAPE %) ad high coefficiet of efficiecy (E). The summary of the results were preset i Tables II ad IV, scatter diagrams showig i Figs. 4 ad 5. Ofte some of the terms are ot sigificat, the full quadratic model ad for each coefficiet, calculate the t- statistic for the ull hypothesis that the coefficiet is equal to zero. The Model (1) i terms of Mix compoets: Fig. 3 Examples of desirability fuctios Whe the model was completed, sets of tested data are used to determie the accuracy of regressio for comparisos betwee the predicted compressive stregth ad true compressive stregth. The best performaces (observatios) are selected accordig to several criteria. The chose criteria are defied as follows: 1. Mea Absolute Percetage Error MAPE% M APE % 100 = 2. Coefficiet of Efficiecy E E 2 ( xi yi ) = 1 2 ( xi x ) xi y x IV. DEVELOPMENT OF MATHEMATICAL MODEL I a mixture experimet, the respose is observed at all mixture desig poits ad the effects of compoet ad iteractios betwee compoets are ivestigated simultaeously. However, i cocrete mixture desig, certai mixture desig poits are ot possible ad must be omitted. Therefore, a flatteed simplex-cetroid mixture experimet desig was adopted [4]. All compressive stregths were measured o 150 mm x 150 mm cub. These were fully compacted o a vibratig table, moist cured for 24 h r, ad the cured i water at 20 C util testig at 3, 7, ad 28. Therefore, there were 114 traiig data covered six differet levels of stregth, about 15, 20, 25, 30,35ad 40 MPa. It may be certai that these will form a fairly represetative group coverig all the rages of practical use for cocrete mixtures ad will preset the rather complete ad idepedet iformatio required for such a evaluatio. The results of the compressive stregth tests were subjected to polyomial regressio usig a computer program (MINITAB) [6]. Two polyomials were tried to represet the measured compressive stregth data for i i (3) (4) ` (5) TABLE III MIXTURE EXPERIMENT SUMMARY STATISTICS FOR FC`28 DAY MPA STRENGTH FOR MODEL (1) Variable Mea StDev Mi Max FIT fc` MAPE%= 6.42 E= % CI Fig. 4 Measured ad predicted compressive stregth of model 1 The Model (2) i terms of Mix compoets ad the cocrete compressive stregth of fc`7 day: ` ` ` TABLE IV MIXTURE EXPERIMENT SUMMARY STATISTICS FOR FC`28 MPA STRENGTH FOR MODEL (2) Variable Mea StDev Max Mi FIT Fc` MAPE% 4.87 E %CI It ca be see that, the MAPE % for the results is rather low, ad the E for the models are so high as to provide (6) 1561

4 accurate predictios. I other words, the models are good i geeralizatio ad close to the observed value withi the rage of 95% cofidece iterval. However, there is ucertaity i the fitted fuctios, because they are estimated from a sample of data. The ucertaity provided is for a 95 percet cofidece iterval. Fig. 5 Measured ad predicted compressive stregth of model (2) V. OPTIMIZATION Numerical optimizatio usig desirability fuctios ca be used to fid the optimum mixture proportios i this situatio. A desirability fuctio must be defied for each respose (property) [6]. The desirability fuctio takes o values betwee 0 ad 1, ad may be defied i several ways. A several targets were optimizig for 28 fc` cocrete compressive stregth to fid out the proper mix compoet meet the target. I this study, the overall desirability D was defied as the geometric mea of the idividual desirability fuctios d i over the feasible regio of mixtures. Numerical optimizatio for model (1) gave the followig best settigs for this cocrete mixture as show i Table V. TABLE V NUMERICAL OPTIMIZATION FOR MODEL (1) The fc` 28 target W/C W C CA FA VI. SUMMARY AND CONCLUSIONS I this study shows the followig: 1) Data used for this study was take from experimet results were doe at uiversity of Beghazi civil egieerig departmet. Total 114 sets of data were used to aalyze the behavior of the cocrete with time. ACI mix desig method (ACI ) was used for the mix desig process. the cocrete compressive stregth was defied as the stregth obtaied from stadard cubes (150mm) o admixtures or additives were used oly the geeral costituets of cocrete [cemet (C), coarseaggregate (CA), fie-aggregate (FA) ad water (W)]. Differet mix proportios of the igrediets ad differet w/c ratio were used to study the variatios. 2) The statistical error aalysis shows the adequacy of the model obtaied ad also that the terms added to the model have sigificat effects o the respose variable. For both of the models, values of (E) are 0.85 ad 0.91 for the first ad secod models. Therefore, it ca be said that the models established for compressive stregth are adequate. I both of the models, the MAPE% is i reasoable agreemet with the predictio for compressive stregth (MAPE% is 6.7% ad 4.5%). This idicates that the amouts of results obtaied from the models are appropriate. 3) The models are good i geeralizatio ad close to the observed value withi the rage of 95% cofidece iterval. 4) Based o the data obtaied from the RSM models, high correlatios betwee the compressive stregth ad the compoet compositio of cocrete ca be developed usig the geeralizatio capabilities. Such a model ca be efficietly used for simulatig the compressive stregth behavior. 5) The importace of the ifluece of mix costituets o the stregth of cocrete was approved. Two mathematical models for the predictio of cocrete compressive stregth at the age of 28 was proposed ad developed (usig RSM) from the kowledge of the mix costituets, ad stregth at the ages of 7 day. 6) Practical approach has bee described for predictio of 28-day compressive stregth of cocrete ad the proposed techique ca be used as a reliable tool for assessig the desig stregth of cocrete from quite early test results. This will help i makig quick decisio for accidetal poor cocretig at site ad reduce delay i the executio time of large civil costructio projects. 7) A several targets were optimizig for 28 fc` cocrete compressive stregth to fid out the proper mix compoet meet the target. NOMENCLATURE C = cemet Kg/m 3 CA = coarse-aggregate Kg/m 3 D = desirability DOE = desig of experimet E = coefficiet of efficiecy FA = fie-aggregate Kg/m 3 fc`28 = cocrete compressive stregth (MPa) at 28 day fc`7 = cocrete compressive stregth (MPa) at 7day MAPE% = Mea Absolute percetage Error = the umber of data observed q = particle desity RSM = Respose surface method StDev = stadard deviatio W = water Kg/m 3 W/C = water/cemet x i = The observed data = The predicted data y i 1562

5 x = the average of data observed 95%CI =95 percet cofidece iterval MPa REFERENCES [1] Hasa. M ad Kabir, " Predictio of compressive stregth of cocrete from early age test result",4th Aual Paper Meet ad 1st Civil Egieerig Cogress, 2011, 22-24, Dhaka, Bagladesh ISBN: [2] M. Sayed-Ahmed1, "Statistical Modelig ad Predictio of Compressive Stregth of Cocrete" Cocrete Research Letters, 2012, Vol. 3(2). [3] M. J. Simo, "Cocrete Mixture Optimizatio Usig Statistical Methods: Fial Report" FHWA Office of Ifrastructure Research ad Developmet, 6300 Georgetow Pike, 2003, McLea, VA [4] M. T. Ciha et al., "Respose surfaces for compressive stregth of cocrete", Costructio ad Buildig Materials 40, 2013, [5] Murali. ad Kadasamy, " Mix proportioig of high performace selfcompactig cocrete usig respose surface methodology", Joural of Civil Egieerig (IEB), 2009,37 (2), [6] Myers, R. H., ad Motgomery, D. C. "Respose surface methodology", 1995, Wiley, New York. 1563