Multi-response optimization of post-fire residual compressive strength of high performance concrete Abdul Rahim a,⇑ , U.K. Sharma a , K. Murugesan b , A. Sharma c , P. Arora c a Department of Civil Engineering, Indian Institute of Technology Roorkee, India b Department of Mechanical & Industrial Engineering, Indian Institute of Technology Roorkee, India c Reactor Safety Division, BARC, Mumbai, India highlights " This research is optimization of mix parameters of HPC to achieve maximum residual strength. " Taguchi method and Utility concept used for optimizing multiple temperature responses. " The study shows that the addition of fly ash reduces the deterioration of HPC at high temperatures. " Important observations made for the effect of key parameters on residual strength of heated HPC. article info Article history: Received 16 March 2012 Received in revised form 18 July 2012 Accepted 4 August 2012 Available online 29 September 2012 Keywords: Compressive strength Elevated temperature High performance concrete Optimization Taguchi method Utility concept abstract This paper presents results of an experimental study undertaken to optimize the residual compressive strength of heated high performance concrete using the Taguchi off-line method and the utility concept. The design of experiments (DoEs) was first carried out by Taguchi method using a standard L 9 (3 4 ) orthog- onal array (OA) of four factors with three material parameter levels. The factors considered in the context of high performance concrete were cement content, fly ash content, super-plasticizer content and fine aggregate content. The cube specimens were cast and heated up to 200 °C, 400 °C, 600 °C and 800 °C tar- get temperatures. They were subsequently tested under axial compressive loads in cooled conditions. Based on the results, the material parameter responses were analyzed by utility concept to reduce the multi-characteristic response and to obtain single setting of optimized parameters in order to maximize the post-fire residual compressive strength of concrete. The results indicate that the best level of control factors paid their own contribution for compressive strength at various elevated temperatures. The cement content was found to be the most influencing parameter followed by fine aggregate content and fly ash dosage. The role of chemical admixture dosage was observed to be relatively less marked on the residual compressive strength of high performance concrete. The confirmation tests corroborated the theoretical optimum test conditions. Ó 2012 Elsevier Ltd. All rights reserved. 1. Introduction High Performance Concrete (HPC) has been widely used as a construction material around the world. The HPC is produced using carefully selected high quality ingredients, low water–cementi- tious materials ratio, high binder content including pozzolans and chemical admixtures. High performance concrete possesses superior performance than normal concrete in many aspects namely strength, durability and workability [1]. The production of high performance concrete incorporating fly ash has proved practical in several countries as an appropriate substitute for nor- mal strength concrete [2]. Further many modern concrete struc- tures are frequently subjected to elevated temperatures due to exposure to an aggressive fire or heat source. The concrete struc- tures including nuclear reactor vessels, clinker silos of cement plants, metallurgical and chemical industrial structures, glass mak- ing industrial structures, storage tanks for hot crude oils, coal gas- ification and liquefaction vessels, reinforced concrete chimneys, tunnels and high rise buildings during an accidental fire are often subjected to elevated temperatures [3]. Therefore, it is important to understand the behavior of HPC exposed to such high tempera- ture situations. An extensive research data are available on the effect of ele- vated temperature on the residual mechanical properties and ther- mal properties of HPC [3–12]. It is reported that when the concrete 0950-0618/$ - see front matter Ó 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.conbuildmat.2012.08.048 ⇑ Corresponding author. E-mail address: [email protected](A. Rahim). Construction and Building Materials 38 (2013) 265–273 Contents lists available at SciVerse ScienceDirect Construction and Building Materials journal homepage: www.elsevier.com/locate/conbuildmat
Transcript
Construction and Building Materials 38 (2013) 265–273
Contents lists available at SciVerse ScienceDirect
Multi-response optimization of post-fire residual compressive strength of highperformance concrete
Abdul Rahim a,⇑, U.K. Sharma a, K. Murugesan b, A. Sharma c, P. Arora c
a Department of Civil Engineering, Indian Institute of Technology Roorkee, Indiab Department of Mechanical & Industrial Engineering, Indian Institute of Technology Roorkee, Indiac Reactor Safety Division, BARC, Mumbai, India
h i g h l i g h t s
" This research is optimization of mix parameters of HPC to achieve maximum residual strength." Taguchi method and Utility concept used for optimizing multiple temperature responses." The study shows that the addition of fly ash reduces the deterioration of HPC at high temperatures." Important observations made for the effect of key parameters on residual strength of heated HPC.
a r t i c l e i n f o
Article history:Received 16 March 2012Received in revised form 18 July 2012Accepted 4 August 2012Available online 29 September 2012
This paper presents results of an experimental study undertaken to optimize the residual compressivestrength of heated high performance concrete using the Taguchi off-line method and the utility concept.The design of experiments (DoEs) was first carried out by Taguchi method using a standard L9(34) orthog-onal array (OA) of four factors with three material parameter levels. The factors considered in the contextof high performance concrete were cement content, fly ash content, super-plasticizer content and fineaggregate content. The cube specimens were cast and heated up to 200 �C, 400 �C, 600 �C and 800 �C tar-get temperatures. They were subsequently tested under axial compressive loads in cooled conditions.Based on the results, the material parameter responses were analyzed by utility concept to reduce themulti-characteristic response and to obtain single setting of optimized parameters in order to maximizethe post-fire residual compressive strength of concrete. The results indicate that the best level of controlfactors paid their own contribution for compressive strength at various elevated temperatures. Thecement content was found to be the most influencing parameter followed by fine aggregate contentand fly ash dosage. The role of chemical admixture dosage was observed to be relatively less markedon the residual compressive strength of high performance concrete. The confirmation tests corroboratedthe theoretical optimum test conditions.
� 2012 Elsevier Ltd. All rights reserved.
1. Introduction
High Performance Concrete (HPC) has been widely used as aconstruction material around the world. The HPC is produced usingcarefully selected high quality ingredients, low water–cementi-tious materials ratio, high binder content including pozzolansand chemical admixtures. High performance concrete possessessuperior performance than normal concrete in many aspectsnamely strength, durability and workability [1]. The productionof high performance concrete incorporating fly ash has provedpractical in several countries as an appropriate substitute for nor-
ll rights reserved.
mal strength concrete [2]. Further many modern concrete struc-tures are frequently subjected to elevated temperatures due toexposure to an aggressive fire or heat source. The concrete struc-tures including nuclear reactor vessels, clinker silos of cementplants, metallurgical and chemical industrial structures, glass mak-ing industrial structures, storage tanks for hot crude oils, coal gas-ification and liquefaction vessels, reinforced concrete chimneys,tunnels and high rise buildings during an accidental fire are oftensubjected to elevated temperatures [3]. Therefore, it is importantto understand the behavior of HPC exposed to such high tempera-ture situations.
An extensive research data are available on the effect of ele-vated temperature on the residual mechanical properties and ther-mal properties of HPC [3–12]. It is reported that when the concrete
266 A. Rahim et al. / Construction and Building Materials 38 (2013) 265–273
is subjected to fire or high temperatures, the significant changes inphysical and chemical composition of concrete occur, which leadsto progressive degradation of mechanical properties and durabilityof concrete. The extent of strength loss of concrete due to hightemperature depends on many internal and external parameterssuch as constituents of concrete mix, properties of the constitu-ents, grade of concrete, heating rate, peak temperature, coolingrate, shape and size of member, methods of heating, cooling, etc.The pozzolonic concretes perform better and show higher residualcompressive strength compared to concretes prepared without anypozzolana [13–15]. However the improvement of strength wasshown to be more significant at temperatures below 400 �C dueto formation of tobermorite gel as primary contributor to struc-tural properties. The previous research indicates that the un-stressed residual specimens have the lowest strength comparedwith the stressed and unstressed specimens tested at high temper-atures [4]. In unstressed residual test method, the concrete speci-men is heated without a preload, at constant rate of temperature,which is maintained until a thermal steady state is reached withinthe specimen. Load or strain is then applied after cooling to roomtemperature at prescribed rate until failure. In stressed test meth-od, a pre-load generally in the range of 20–40% of the ultimatecompressive strength of concrete is applied at ambient tempera-ture to the specimen prior to heating and the load is sustained dur-ing the heating period. Heat is applied at a constant rate until atarget temperature is reached, and the temperature is maintaineduntil a thermal steady state is achieved. The compressive load is in-creased at a prescribed rate until the specimen fails. In unstressedtest at elevated temperature, the specimen is heated without a pre-load and then it is tested in heated condition. While the influenceof various concrete grades, aggregate types, various heatingparameters and structural parameters on the residual compressivestrength of concrete has been investigated in the previous litera-ture, the role of various concrete mix parameters has not beenstudied conclusively in the past [16,17]. The basic influential mixdesign parameters of concrete are water–cement ratio (W/C),water content, cementitious material content, mineral admixturecontent, chemical admixture content, fine aggregate content,coarse aggregate content and binder to aggregate ratio, etc.
2. Research significance
The present study was aimed to investigate the influence of var-ious mix parameters on residual performance of high performanceconcrete. The main objective was to improve the residual compres-sive strength of concrete by optimizing the various concrete mixdesign parameters. A large number of trial experiments are usuallyrequired to fix-up a suitable mixture combination for getting thetargeted requirements. Thus lot of attempts have been made bymany researchers in the past to make use of optimization tech-niques to obtain optimum content of concrete mix proportions atroom temperature to achieve maximum strength for a given setof materials and exposure conditions [18–20]. The pervious litera-ture indicates that Taguchi method has been extensively and suc-cessfully employed to optimize various parameters that affect theperformance of concrete under ambient conditions [18–20] and to
a very limited extent at elevated temperatures [21–25]. Further,the Taguchi technique is best suited for products with a singlequality response or characteristic optimization. However, most ofthe real situations have multiple characteristics or responses ofinterest. The particular single quality response optimized by Tagu-chi technique, may not give desired results for other parameters ofthe products. In such cases, multi response optimization may bethe solution to obtain a single optimal setting of the processparameters.
3. Experimental program
An experimental program was designed to determine the optimum mix propor-tions of high performance concrete for obtaining maximum residual compressivestrength and minimum deterioration effect of heat when exposed to elevated tem-peratures ranging from room temperature to 800 �C. To this end, the design ofexperiments based on Taguchi off line method was formulated using standardL9(34) orthogonal array considering four parameters (mix constituents) at three lev-els with a maximum of nine mixture trials [21]. The aim was to achieve maximumcompressive strength using larger-the-better criterion. Using the resulting mix de-signs, the experiments were carried out and the results were further analyzed sta-tistically by analysis of variance (ANOVA) to find out the significant factors affectingthe residual compressive strength of concrete. The details of casting, experimentaltest runs, Taguchi optimization procedure and the results obtained are discussed inthe following sections.
3.1. Materials
The constituent materials of concrete were tested for required physical proper-ties and proportioned before starting the key operations of the experimental inves-tigation. A locally manufactured commercially available ordinary Portland cement(OPC) of 43 grade complying with IS 8112:1989 [26] was used for preparing highperformance concrete mixes. In this study, indigenously available fly ash from near-by thermal plant was used as mineral admixture to prepare the high performanceconcrete. The fine aggregate used was naturally available river sand conformingto the zone II of IS 383-1970 [27]. The fineness modulus and specific gravity of sandwere 2.8 and 2.67 respectively. Locally available crushed siliceous type gradedcoarse aggregate of 12.5 mm nominal size was used. Fineness modulus and specificgravity of coarse aggregate were 7.14 and 2.67 respectively. Both sand and coarseaggregate were used in saturated surface dry (SSD) conditions for preparing themixes. A commercially available high range water reducing admixture based onmodified poly-carboxylic either (PCE) polymer with solid content of 9.2% was usedto prepare the concretes for the required workability. A slump of 150–180 mm wasmaintained in all the mixes.
3.2. Design of mixes – Taguchi’s methodology
The design of experiments (DoEs) is a powerful scientific systematic statisticaltechnique for determining the optimal factor settings of a process and therebyachieving improved process performance, reduced process variability and improvedmanufacturability of products and processes. Taguchi’s such approach is a powerfultool for the successful design application of high quality experimental procedure forquality products [28]. Taguchi’s technique focuses on off-line experiments of singlequality characteristic optimization for a product or a process that needs improve-ment leading to controlling factors determination and subsequent regulation, man-aging to adjust their influence even under a very noisy environment.
The first step in Taguchi’s statistical design is the selection of levels and theirfactors. In the present research, cement content, fly ash content (FA), super-plasti-cizer dosage and fine aggregate content were considered as parameters. Based onthe available literature and laboratory trials, various levels of these mix parameterswere chosen. Table 1 shows the chosen factors and their levels. A standard L9(34)orthogonal array (OA) was selected for the design of experimental trial runs withfour factors and three levels, giving rise to a total of nine combination of trial mixesas shown in Table 2. The code numbers and absolute values of all the four factorsare also shown in Table 2. Cube specimens of size 100 mm were cast and testedto evaluate the influence of the various mix parameters and thereby to optimize
Super plasticizer content (C) (L/m3) Fine aggregate content (D) (kg/m3)
4.888 619.9195.512 627.0456.096 633.711
Table 2Design matrix of L9 (34) orthogonal array with parameters and their coding.
Details of mixes Factors and their coded levels and absolute values
Cement content Fly ash content Super-plasticizer content FA content
A. Rahim et al. / Construction and Building Materials 38 (2013) 265–273 267
the strength of heated concrete. A total of 150 cubes were tested under this pro-gram including 135 cubes corresponding to nine different mixes and five differenttemperatures and 15 cubes for confirmation of the optimized mixes. The specimenswere cast in triplicate to obtain the average of three results for each mix combina-tion and corresponding to each exposure temperature.
3.3. Testing
The concrete specimens were de-molded 24 h after casting and placed in thewater tank for curing. After 13 days of water curing the cubes were removed fromthe curing tank and stored for another 14 days in the laboratory ambient conditionsbefore testing. After 28 days, the specimens were heated in an oven at 105 ± 5 �C for24 h to remove excess moisture in order to avoid undue thermal spalling. Thereaf-ter, the specimens were heated in an electric high temperature muffle furnace tothe desired target temperatures. The rate of heating was kept at 5 �C/min with eachtemperature level maintained for 2 h and then the furnace was switched off. Theheating rate was chosen on the basis of the fact that normally, for fire protection,a heating rate of 5 �C/min is adopted [29,30]. After that the furnace was kept inclosed condition for 1 h before opening the door of the furnace for further coolingto room temperature. Subsequent to a single cycle of heating and cooling, theuni-axial conventional destructive compressive strength tests were conducted onthe specimens using Amsler make compression testing machine. Three specimenswere tested for each result and the average values of the compressive strengthare given in the Table 3.
4. Results and discussion
4.1. Optimization by Taguchi technique
There are three categories of performance characteristics forevaluating the performance of parameters namely larger-the bet-ter, smaller-the better and nominal-the better [31]. In the presentstudy, the aim was to determine the best possible concrete mixproportions in order to achieve the maximum residual compres-sive strength of heated concrete. So, the ‘larger the better’ type ofquality characteristic situation was evaluated in terms of signalto noise ratio (S/N) using the following equation:
Larger the better S=NðdbÞ ¼ �10� log101n
Xn
i¼1
1y2
i
!ð1Þ
where Yi is a performance value of the ith trial and n is the numberof repetitions for an experimental combination.
In the Taguchi method, the test trials corresponding to mostfavorable working conditions may not have been carried out dur-ing the experimentation process. In such cases the correspondingvalue to the most favorable working situations can be predictedby utilizing the balanced characteristic of the orthogonal arrayusing the following equation [32]:
Yi ¼ lþ Xi þ ei ð2Þ
where l is the overall mean of performance value; Xi is the fixed ef-fect of the parameter level combination used in the ith experiment;and ei is the random error in the ith experiment.
The confirmation experiments are conducted validating theoptimal values calculated using experimental results data in orderthe results are meaningful or not. The confidence interval (CI) at achosen error level may be estimated by the following equation.
CI ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiFða;1; feÞVe
1Neffþ 1
R
� �sð3Þ
where F (a, 1, fe) is the F value from the F table from any statisticalbook at the required confidence level and at a degree of freedom(DOF) of 1, Ve is the variance error, R is the number of replicationsand Neff is the effective number of replications. In this experimentalstudy, the interaction effects of parameters were not considered.
A statistical analysis was performed to determine the significantfactors statistically. The optimum conditions were arrived at usingthe loss function as larger-the better, which is a quality characteris-tic function to maximize the compressive strength of post-heatedconcrete specimens. The mean numerical values of main effects ofeach parameter and temperature of exposure are given in Fig. 1shows the effects of mean values of main effects at all the three lev-els for the various chosen factors i.e. cement content, fly ash (FA)content, super-plasticizer content and fine aggregate content. Itcan be observed from Fig. 1a that the maximum of mean values ofmain effects at room temperature was obtained for cement content
(a) Room temperature
(b) 200 C
(c) 400 C
(d) 600 C
(e) 800 C
Fig. 1. (a–e) Mean values of main effect of parameters on the performance characteristic of heated concrete.
268 A. Rahim et al. / Construction and Building Materials 38 (2013) 265–273
at Level A1 (434.449 kg/m3), for fly ash content at Level B2
(131.240 kg/m3), for super-plasticizer dosage at Level C3 (6.096 L/m3) and for fine aggregate content at Level D2 (627.045 kg/m3).The cement content, super-plasticizer content and fine aggregatecontent were observed to be acting as main influencing parameters
at room temperature. The strength decreased with increase in the flyash content and fly ash content did not show any significant effect atroom temperature conditions.
The parameters appeared to change their influence on theresidual compressive strength of concrete with the change in tem-
A. Rahim et al. / Construction and Building Materials 38 (2013) 265–273 269
perature of exposure. At 200 �C exposure, the optimum valueswere obtained for cement content at Level A1 (404.449 kg/m3),for fly ash (FA) content at Level B1 (108.612 kg/m3), for super-plas-ticizer content at Level C1 (4.888 L/m3) and for fine aggregate con-tent at Level D3 (633.711 kg/m3). The main influencing parametersat 200 �C exposure were super-plasticizer content, cement contentand fine aggregate content as evident from Fig. 1b. The increaseddosage of the super-plasticizer shows relatively negative effects atthis temperature condition. The residual strength of high perfor-mance concrete decreased with increase in the amount of flyash content. However, the residual compressive strength of con-crete exposed to 200 �C increased in the range of 15–46% com-pared to room temperature strength irrespective of the level ofany parameter. It is believed that this strength gain may be dueto the formation of tobermorite gel, due to reaction between theunhydrated fly ash particles and calcium at elevated temperatures[14]. The increase of compressive strength may also be due tohardening of the cement paste during the evaporation of freewater, which attenuates surface (Van der Waal’s) forces betweenthe cement gel particles, making the particles close to each other[33,34]. The optimum conditions for specimens exposed to 400 �Ctemperature were obtained for cement content at Level A3
(355.618 kg/m3), for fly ash content at Level B3 (152.408 kg/m3),for super-plasticizer dosage at Level C3 (6.096 L/m3) and for fineaggregate content at Level D2 (627.045 kg/m3). Fly ash contentand the fine aggregate content were observed to be the maininfluencing parameters on the compressive strength at 400 �Cexposure as shown in from Fig. 1c. It is evident that the higherstrength was retained by the high performance concrete contain-ing 30% of fly ash. At 400 �C temperature, all the fly ash concretemix specimens exhibited much better fire resistance and theresidual strength compared to their performance under room tem-perature. However a strength reduction was observed for all thespecimens heated at 400 �C compared to the correspondingstrengths at 200 �C. This may be due to the pore structure coars-ening and complete dehydration of concrete when exposed tohigh temperatures [33]. Mild hair line cracks were also observedon the surface of specimens heated to 400 �C.
The post-fire residual strength values severely reduced for thevarious mixes as the temperature of exposure increased to600 �C. The maximum residual strength of concrete at this temper-ature was obtained for cement content at level A2 (393.720 kg/m3),for fly ash content at level B3 (152.408 kg/m3), for super-plasticizercontent at level C1 (4.888 L/m3) and for fine aggregate content atlevel D1 (619.919 kg/m3). The cement content was observed to bethe most influencing parameter and the fly ash content, super-plasticizer dosage and fine aggregate content were observed tobe relatively less effective. Overall at 600 �C, the fly ash high per-formance concrete performed better and showed reduced crackingand spalling. The average loss of residual strength was in the rangeof 23.5–41% for high performance concrete exposed to 600 �C. It isbelieved that at temperature as high as 600 �C, the major hydratesof concrete known as C–S–H gel decompose, causes the loss ofcementing ability of binding material.
Table 4Optimal setting of process parameters (phase I) and optimal vales of individual quality ch
At 800 �C temperature exposure, a severe strength loss and dete-rioration was observed in all the specimens due to further decompo-sition of the C–H–S gel and disintegration of concrete at such hightemperatures. The optimum conditions at 800 �C exposure were ob-tained for cement content at level A2 (393.720 kg/m3), for fly ashcontent at Level B3 (152.408 kg/m3), for super-plasticizer contentat level C3 (6.096 L/m3) and for fine aggregate content at level D2
(627.045 kg/m3). The cement content and fine aggregate contentwere observed to be the main influencing parameters as shown inFig. 1e. It is observed that the increased amount of cement contentand fine aggregate content leads to reduction of strength at suchhigh temperatures. It is therefore noticed that all nine trial mixescould only maintain a minor part of their original compressivestrength after exposure to 800 �C. Table 5 displays the individualoptimal values and the corresponding optimal settings of processparameters for the entire range of heated concrete.
4.2. Application of the utility concept for multi response optimization
The optimum mix conditions of the fly ash HPC were obtainedfor a given temperature of exposure as explained above. In thisexperimental study, the Taguchi off-line approach is employed toobtain best suited mono characteristic response optimization ofconcrete mix proportions. From the results of the above technique,five dissimilar optimum mix proportions were obtained to maxi-mize the post-fire residual compressive strength of fly ash HPC atdifferent exposures of elevated temperatures. The five dissimilaroptimum mix proportions obtained are shown in Table 4. The con-ventional trial and error method cannot be implemented in order toobtain the best combination of process parameters, since there aremulti-response parameters that are to be optimized. In multi-re-sponse problems the objective is to determine the optimal settingsof factors or process variables which will simultaneously optimizeseveral responses. For this purpose, the Taguchi technique usingutility concept has been employed simultaneously to optimize themultiple responses of HPC mix parameters exposed to differenttemperatures [35]. The published literature revels that the multipleresponse characteristics have been investigated by number ofresearchers in the past [36–38]. The present experimental workwas designed with an objective of arriving at optimum proportionsof mix parameters for maximum residual compressive strength ofHPC at all temperatures. These mix parameters can be determinedby applying the utility concept. In the application of utility conceptall S/N ratios of mix parameters optimized at different temperaturesare computed for larger the better optimization criterion. Assumingequal weights at all temperatures, the weighted S/N ratios obtainedfor different temperatures are summed up and with these data themean process parameters are determined. Using the significantcontribution of mean utility values of main effects, the optimal set-ting process parameters are determined. These concepts were ap-plied to the present problem and an absolute optimumproportion of mix parameters for HPC were obtained at differentexposures of elevated temperatures. The method applied in thepresent research can be explained as follows:
aracteristics.
of Predicted confidence intervals of qualityracteristics
a Indicates best performance of signal to noise (S/N) ratio values for differenttemperature of exposures.
270 A. Rahim et al. / Construction and Building Materials 38 (2013) 265–273
If Xi represents measure of proportion of mix parameters of ithmix proportion level and n represents number of mix proportionlevels, then the overall utility function can be expressed as [35]
where Ui (M1, M2,. . . Mn) is the overall utility of n parameterresponses.
The function may be rewritten to optimize the proportion ofmix parameters and the weights are assigned according to their re-sponses for the individual utility index. So, the general form ofweighted utility equation can then be written as
UðM1;M2; � � � ;MnÞ ¼Xn
i¼1
Wi UiðMiÞ ð5Þ
where Wi is the weight assigned to the mix parameters i and thesum of the weights for all mix parameters is equal to 1.
The experimental results of five different temperatures of eachtrial mix of L9 (34) orthogonal array are summarized in Table 3. TheTaguchi technique uses the signal-to noise ratio values to evaluateand interpret the results for optimizing process, which reflectsboth the mean and variation of the process parameters. The sumof composite measures of overall maximized signal-to-noise ratiovalues are summarized in Table 5.
The multi-response S/N ratio of the overall utility value is givenby
g ¼WRoomg1 þW200�Cg2 þW400�Cg3 þW600�Cg4 þW800�Cg5 ð6Þ
where WRoom, W200�C, W400�C, W600�C and W800�C are weights as-signed to the responses of the mix design parameters. The weight-ing is done to satisfy the test of indifference on the various mixparameters. In this study equal importance has been given to theweighting factors. Therefore WRoom, W200�C, W400�C, W600�C andW800�C = 0.2
The utility value of the composite measure is then calculatedusing the following equation (overall utility function):
where n is the trial number, R is the replication number.Thus, the data obtained by transforming the experimental re-
sults for various mix proportions is known as utility data. This datais subsequently analyzed by appropriate statistical techniques forarriving at the optimal setting of mix proportion.
A preference scale is constructed for determining the utility va-lue of HPC for each temperature. The mix proportion parametersare assigned as preference number of nine for best optimal valuesof mix parameters. If a logarithmic scale is chosen, then the prefer-ence number (Pi) is given as [35]:
Pi ¼ C logMi
M0i
ð9Þ
where Mi is the value of mix proportion parameter i, M0i is the min-
imum acceptable value of the mix proportion level i and C is a con-stant of preference scale number equal to 9.
Following are the details of calculation for the preference scalevalue P(28�C) expressed on a logarithmic scale for compressivestrength of concrete at room temperature.
X� = optimum value at room temperature is 73.537 MPa (referTable 4).X0 = minimum acceptable value at room temperature is 50 MPa(all the observed values in Table 3 lie between 58 MPa and74 MPa).
Using the above values and the Eqs. (7) and (8), the preferencescale for room temperature was constructed as
Pð28�CÞ ¼ 53:72 logXð28�CÞ
50
� �ð10Þ
In a similar way, the preference scale values for other temperatures,namely 200 �C, 400 �C, 600 �C and 800 �C were also calculated. Theselected mix design parameters were assigned equal weights,P(28�C), P(200�C), P(400�C), P(600�C), and P(800�C) respectively.
The below mentioned overall utility function relation was de-ployed to calculate the utility data of HPC at various temperaturesexposure:
where n is the trial number = 1, 2,. . . 9; R is the replication of sam-ples = 1, 2, 3. The calculated utility data are reported in Table 5.
4.3. Data analysis and estimation of optimal mix proportions
The utility values were analyzed using the larger the betterquality characteristic type and were calculated using Eq. (1). Thecalculated values of mean responses (mean utility value) and thesignal to noise ratios (S/N ratio) are given in Tables 6 and 7 respec-tively, and the mean responses of mix proportions of utility valuesare plotted in Fig. 2. This figure depicts clearly that the first level ofcement content (A1 = 434.45 kg/m3), the third level of fly ash con-tent (B3 = 152.41 kg/m3), the third level of super-plasticizer
Fig. 2. Mean responses of main effects of process parameters of utility values.
Table 8Optimal setting of process parameters utility values (phase II).
S. No. Process parameter Level Optimal values (Kg/m3)
A. Rahim et al. / Construction and Building Materials 38 (2013) 265–273 271
content (C3 = 6.096 L/m3) and the second level of fine aggregatecontent (D2 = 627.045 kg/m3) shall yield a best optimal perfor-mance value of the utility function i.e. residual compressivestrength of high performance concrete exposed to different tem-peratures. Table 8 indicates absolute values of optimal values ofmix proportions for optimized high performance concrete mixparameters and their levels of multi-response optimization usingthe utility concept to achieve maximum residual compressivestrength of heated concrete.
4.4. Predicted means (optimal values of mix proportion parameters)
The optimum value of utility (U28�C, 200�C, 400�C, 600�C, 800�C) waspredicted at the selected levels of variables as stated above viz. ce-ment content (A1), fly ash content (B3), super-plasticizer content(C3) and fine aggregate content. The estimated mean of the re-sponse of mix proportion parameters (URoom Temp., 200�C, 400�C,600�C, 800�C) can be determined as:
where T is the overall mean of utility value = 7.473 which is takenfrom Table 5. The values of A1, B3, C3, D2 were taken from Table 6.
The utility values of both the main effects and signal-to-noise(S/N) ratio values of raw data were analyzed at each level of allthe parameters. It is clear from Table 8 and Fig. 2 that the meanutility values of first level of cement content (A1), third level offly ash content (B3), third level of super-plasticizer content (C3)and second level of fine aggregate content (D2) would yield bestperformance in terms of utility value and S/N ratio values for differ-ent temperatures of exposure.
Substituting the values of the above mentioned terms in Eq.(11), we get
Table 9Pooled ANOVA for utility vales of raw data.
A statistical analysis of the data was carried out for the evalua-tion of the significance of each selected parameter for its contribu-tion towards the optimization of residual compressive strength ofhigh performance concrete (31). The analysis of variance (ANOVA)was performed to identify the relative significance and futurepromising direction of the process parameters. Table 9 shows thecomputed results of pooled versions of utility values of the ANOVAat 0.05% level of significance with 95% confidence level. The fisherratios (F-ratio) were calculated to identify the importance of fac-tors from variance within the confidence level and the percent con-tributions of the various parameters as quantified under therespective columns of Table 9. It reveals that cement contentshowed a significant effect on the residual compressive strengthof heated concrete with 65.41% contribution at all the tempera-tures with a maximum influence. The fine aggregate content wasobserved to be the second most influencing parameter with18.78% contribution followed to cement content with respect toresidual compressive strength of heated concrete.
272 A. Rahim et al. / Construction and Building Materials 38 (2013) 265–273
5. Confirmation experiment
An important requirement in Taguchi’s technique and simulta-neous multi-characteristic optimization of utility concept is to con-duct confirmation experiments for validating the predicted results.Hence, in order to test the predicted optimized conditions, confir-mation experiments were conducted by running another threereplications at the optimal mix proportions as determined fromthe analysis (31). Fig. 3 indicates the experimental test results ofnine HPC mixes and their confirmation test. The confirmation testresults are also shown in Table 10 along with the predicted results.The 95% confidence interval (CI) for the predicted mean of opti-mum quality characteristics on confirmation test was estimatedusing Eq. (3). It can be observed From Table 4 that the individualresponse of residual compressive strength values for the specimenstested at room temperature and those exposed to 800 �C, fall with-in the predicted 95% confidence interval of optimal range. The util-ity values obtained at different temperature exposure of concretewere analyzed for different levels of mix parameters. The experi-mentally obtained utility values are shown in Table 11. The valuesare observed to be lying above the predicted 95% confidence inter-val of optimal range utility calculated for the utility function.
6. Conclusions
An experimental study was carried out to optimize the statisti-cally significant parameters of mix proportions of fly ash based
Fig. 3. Mix trials and their confirmation test results.
Table 10Confirmation test results of specimens utility values.
Temperature ranges Confirmation test results (in MPa)
high performance concrete in order to maximize the residual com-pressive strength of heated concrete. While mono performancecharacteristics optimization process was established by Taguchitechnique, multi characteristics data was analyzed by utility con-cept. Based on the results, the following conclusions may bedrawn:
� The detrimental effects of temperature on the residual com-pressive strength of high performance concrete do not mattermuch up to a temperature of 400 �C. Rather the strengthincreases up to a temperature of exposure of 400 �C irrespectiveof the mix parameters considered in the study. It is only in thetemperature range of 600–800 �C that a noticeable degradationin the compressive strength of high performance concrete isobserved.� This study establishes a procedure for computing the optimum
mix conditions for maximum residual compressive strength ofhigh performance concrete exposed to various elevated temper-atures. The results show that the mix parameters change theirinfluence on the residual compressive strength with the changein temperature of exposure. The most influencing parameteraffecting the residual compressive strength of concrete is foundto be cement content under room temperature conditions,super-plasticizer dosage at 200 �C temperature, fly ash contentat 400 �C temperature and cement content at both 600 and800 �C temperatures.� The overall most influencing parameter for achieving a maxi-
mum residual compressive strength of heated high perfor-mance concrete, exposed to any temperature up to 800 �C, isthe cement content. The fine aggregate content is found to bethe second most influencing parameter, which is followed byfly ash content and super-plasticizer dosage. These observationscan be kept in mind while designing the concrete mixes forstructures liable to be exposed to elevated temperatures.
Acknowledgement
The authors thankfully acknowledge the financial support re-ceived from Board of Research in Nuclear Sciences (BRNS) – Mum-bai, India for conducting this research.
References
[1] Mehta PK, Aitcin PC. Principles underlying the production of high-performanceconcrete. Cem Concr Aggr, ASTM J 1990;12(2):70–8.
[2] ACI Committee 232-2R-96. Use of fly ash in concrete. Detroit: Americanconcrete institute; 2006.
[3] Potha Raju M, Srinivasa Rao K, Raju PSN. Compressive strength of heated high-strength concrete. Mag Concr Res 2007;59(2):79–85.
[4] Abrams MS. Compressive strength of concrete at temperatures to 1600 F.Portland cement association. American concrete institute special publicationSP-25; 1973.
[5] Kodur VKR, Phan L. Critical factors governing the fire performance of highstrength concrete systems. Fire Saf J 2007;42:482–8.
[6] Arioz O. Effects of elevated temperature on properties of concrete. Fire Saf J2007;42:516–22.
[7] Phan LT, Carino NJ. Review of mechanical properties of HSC at elevatedtemperature. J Mater Civ Eng ASCE 1998;10(1):58–64.
um 95% of Predicted confidenceintervals of quality characteristics
A. Rahim et al. / Construction and Building Materials 38 (2013) 265–273 273
[8] Phan LT, Carino NJ. Effects of test conditions and mixture proportions onbehaviour of high-strength concrete exposed to high temperatures. ACI Mater J2002;99(1):54–66.
[9] Sarshar R, Khoury GA. Material and environmental factors influencing thecompressive strength of unsealed cement paste and concrete at hightemperatures. Mag Concr Res 1993;45(162):51–61.
[10] Chan YN, Peng GF, Anson M. Residual strength and pore structure of high-strength concrete and normal strength concrete after exposure to hightemperatures. Cem Concr Compos 1999;21:23–7.
[11] Felicetti R, Gambarova PG. Effects of high temperature on the residualcompressive strength of high-strength siliceous concretes. ACI Mater J1999;95(4):395–405.
[12] Chan YN, Luo X, Sun W. Compressive strength and pore structure of high-performance concrete after exposure to high temperature up to 800�C. CemConcr Res 2000;30:247–51.
[13] Khoury GA. Compressive strength of concrete at high strength temperature: areassessment. Mag Concr Res 1992;44(161):291–309.
[14] Poon CS, Azhar S, Anson M, Wong YL. Comparison of the strength anddurability performance of normal- and high-strength pozzolanic concretes atelevated temperatures. Cem Concr Res 2001;31:1291–300.
[15] Balendran RV, Rana TM, Maqsood T, Tang WC. Strength and durabilityperformance of HPC incorporating pozzolans at elevated temperature. StructSurv 2002;20(4):123–8.
[16] Bharathkumar BH, Narayanan R, Raguprasad BK, Ramachandramurthy DS. Mixproportions of high performance concrete. Cem Concr Compos 2001;23:71–80.
[17] Neville AM. Properties of concrete. 4th ed. Pearson Education, Inc. and DorlingKindersley Publishing; 1995.
[18] Erdogan ozbay, Adil Baykasoglu, Ahmed Oztas, Hakan Ozbebek. Anexperimental compression of optimum mix proportions of high strengthconcrete proposed by Taguchi method and genetic algorithm. In: Proceeding of5th international symposium on intelligent manufacturing systems; 2006. p.1062–70.
[19] Erdogan Ozbay, Baykasoglu Adil, Ozbay Ahmed, Ozbebek Hakan. Investigatingmix proportions of high strength self compacting concrete by using Taguchimethod. Constr Build Mater 2009;23:694–702.
[20] Turkmen I, Gul R, Celik C, Demrboga Ramazan. Determination by the Taguchimethod of optimum conditions for mechanical properties of high strengthconcrete with admixtures of silica fume and blast furnace slag. Civ Eng EnvironSyst 2003;20(2):105–18.
[21] Rahim A, Sharma UK, Murugesan K, Sharma A, Arora P. Optimization of post-fire residual compressive Strength of concrete by Taguchi method. J Struct FireEng 2012;3(2):169–80.
[22] Tanyildizi H, Ahmet Coskun. Performance of lightweight concrete with silicafume after high temperature. Constr Build Mater 2008;22:2124–9.
[23] Tanyildizi H, Ahmet Coskun. The effect of high temperature on compressivestrength and splitting tensile strength of structural lightweight concretecontaining fly ash. Constr Build Mater 2008;22:2269–75.
[24] Tanyildizi H. Effect of temperature, carbon fibers, and silica fume on themechanical properties of lightweight concretes. New Carbon Mater2008;23(4):339–44.
[25] Tanyildizi H. Statistical analysis for mechanical properties of polypropylenefibre reinforced lightweight concrete containing silica fume exposed to hightemperature. Mater Des 2008;30:3252–8.
[26] IS 8112-1989 (Reaffirmed 2005). 43 Grade ordinary Portland cement—specification. Bureau of Indian Standards, New Delhi, India.
[27] IS 383-1970. Specification for coarse and fine aggregate from natural sourcesfor concrete. Bureau of Indian Standards, New Delhi, India.
[28] Antony J, Antony JF. Teaching the Taguchi method to industrial engineers.Work Study 2001;50(4):141–9.
[29] Zaidi KA, Sharma UK, Bhandari NM. Effect of temperature on uni-axialcompressive behavior of confined concrete. Fire Saf J 2012;48:58–68.
[30] Zhang B, Bicanic N, Pearce CJ, Balabanic G. Residual fracture properties ofnormal- and high strength concrete subjected to high temperature. Mag ConcrRes 2000;52(2):123–36.
[31] Chaulia PK, Das R. Process parameter optimization for fly ash brick by Taguchimethod. Mater Res 2008;11(2):159–64.
[32] Ranjith Roy. A primer on the Taguchi method. 2nd ed. Society ofManufacturing Engineers. 1990.
[33] Xu Y, Wong YL, Poon CS, Anson M. Impact of high temperature on PFAconcrete. Cem Concr Res 2001;31:1065–73.
[34] Aydin S, Baradan B. Effect of pumice and fly ash incorporation on hightemperature resistance of cement based mortars. Cem Concr Res2007;37:988–95.
[35] Kumar P, Barua PB, Gaindhar JL. Quality optimization (multi-characteristic)through Taguchi’s technique and utility concept. Qual Reliab Eng Int2000;16:475–85.
[36] Singh H, Kumar P. Optimizing multi-machining characteristics throughTaguchi’s approach and utility concept. J Manuf Technol Manage2006;17(2):255–74.
[37] Garg R. Effect of process parameters on performance Measures of wireelectrical discharge machining. Ph.D Thesis. N.I.T Kurukshetra; 2010.
[38] Sibalija Tatjana V. Multi-response optimisation of thermo-sonic copper wire-bonding process with correlated responses. Int J Adv Manuf Technol2009;42:363–71.
