This study presents the potential of Genetic Expression Programming (GEP)
computing paradigm to forecast the Marshall Stability of steel fiber reinforced asphalt
concrete and has various mix proportions has been developed. Experimental details were
used to construct the model. The steel fiber content (0%, 0.25%, 0.50%, 0.75%, 1.0%,
1.5%, 2.0% and 2.5%), percentage of bitumen (5%, 5.5% and 6.0%) and unit weights
(2,465-2,515 (gr/cm3)) was used as input variables and Marshall Stability (kg) values
were used as output variables. The performance of models was comprehensively judged
using several statistical verification tools. Results have shown that developed GEP
model has a strong potential for predicting the Marshall Stability of asphalt concrete
without performing any experimental studies

Morova, Nihat

Saltan, Mehmet

Serin, Sercan

Terzi, Serdal

Epoka University

2nd International Balkans Conference on Challenges of Civil Engineering, BCCCE, 23-25 May 2013, Epoka University, Tirana,Albania.1030Modeling Marshall stability of steel fiber reinforced asphalt concreteby genetic expression programmingSerdalTerzi1, MehmetSaltan1, NihatMorova2, SercanSerin31Department of Civil Engineering, SULEYMAN DEMIREL University, Turkey2Department of Manufacturing Engineering, SULEYMAN DEMIREL University, Turkey3Department of Civil Engineering, DUZCE University, TurkeyABSTRACTThis study presents the potential of Genetic Expression Programming (GEP)computing paradigm to forecast the Marshall Stability of steel fiber reinforced asphaltconcrete and has various mix proportions has been developed. Experimental details wereused to construct the model. The steel fiber content (0%, 0.25%, 0.50%, 0.75%, 1.0%,1.5%, 2.0% and 2.5%), percentage of bitumen (5%, 5.5% and 6.0%) and unit weights(2,465-2,515 (gr/cm3)) was used as input variables and Marshall Stability (kg) valueswere used as output variables. The performance of models was comprehensively judgedusing several statistical verification tools. Results have shown that developed GEPmodel has a strong potential for predicting the Marshall Stability of asphalt concretewithout performing any experimental studies.INTRODUCTIONFlexible pavements are designed so as to have at least 20 years project life. Thecurrent research subjects include the studies focusing on increasing the performance andlifetime off-road pavements. It is aimed to increase the performance and lifetime ofroads by using different additive materials [1].The researchers that previously worked on this subject clearly indicated that theuse of fiber inthe pavements and asphalt mixtures has a strengthening effect. Fibers canbe used especially in the mixtures with continuous grading and in Stone Mastic Asphalt(SMA) mixtures in order to overcome the deterioration of asphalt during carriage andconstruction of the mixture, as well as in asphalt stabilization [2-4]. The use of fibersalters the visco-elasticity characteristics of the mixture [5]; enhances its dynamicmodulus [6], enhances sensibility against humidity[7], enhances flow coherence, andprovides resistance against the rutting [8-9]; as well as decreases the amount ofreflective cracks in asphalt mixtures and pavement [10-12].In recent decade, one of the most important and promising research field has been“Heuristicsfrom Nature”, an area utilizing some analogies with natural or social systemsand using them to derive non-deterministic heuristic methods and to obtain very goodresults. Nowadays Artificial Intelligent methods have been extensively used in civilengineering applications [13-14].The main purpose of this paper is to develop an Genetic Expression Programming(GEP) methodology for estimation of the Marshall Stability of steel fiber reinforcedasphalt concrete.2nd International Balkans Conference on Challenges of Civil Engineering, BCCCE, 23-25 May 2013, Epoka University, Tirana,Albania.1031EXPERIMENTAL PROCEDUREAggregatesCrushed limestone aggregates were used in asphalt mixtures. Aggregate materialtests were carried out based on American Standards, in order to obtain the physical andmechanical characteristics of the materials to be used in the mixtures. Table 1 showsmixture ratios determined for hot mixtures. The physical and mechanical characteristicsof the aggregates used in the mixtures are given in Table 2 [15].Table 1 Mixture ratios determined for hot mixturesSieve Diameters25-4,75mm 4,75-0,075mm FillerBinder 40% 55% 5%Table 2 Physical and Mechanical characteristics of Aggregates [15]Sieve Diameters0-4,75mm4,75-9,5 mm 9,5-25 mm StandartLimit StandartWater Absorption% *  (3,54) 1,63 0,81 Binder; % 2,5 ASTM C 127Abrasion loss (%)(Los Angeles) * * 23,804 Binder; % 35 ASTM C 131Fine Material % *  (14,51) 1,27 0,45 % 0,5 ASTM C 117Organic Material Clear Clear Clear Clear ASTM C 40Freeze-Thaw % * * 6,69 Binder; % 12 ASTM C 88Peeling Strength.% *More than%50More than%50 Binder; % 50HTS Part 403 App-AAverage Density(gr/cm3) 2,576 2,642 2,677 - ASTM C 127Loose specificgravity (gr/cm3) 1,61 1,40 1,41 - ASTM C 29Compact specificgravity(gr/cm3) 1,91 1,62 1,64 - ASTM C 29*Tests not required according to the technical specifications prepared by Highways Commission (Karayolları TeknikŞartname - KTŞ)BitumenAC 60/70 asphalt cement was used in asphalt mixtures as bitumen. The physicalcharacteristics of this selected bitumen are given in Table 3.Table 3 Basic Physical Characteristics of Bitumen [15]Characteristics of BitumenTest Name Average ValuesPenetration (25 ºC) 60-70Flash Point 180ºCFire Point 230 ºCSoftening Point 45,5°CDuctility (5 cm/minute) >100 cmSpecific Gravity 1,034 gr/cm³2nd International Balkans Conference on Challenges of Civil Engineering, BCCCE, 23-25 May 2013, Epoka University, Tirana,Albania.1032Steel FiberIn this study, Dramix RC-80/60-BN fiber was used. The characteristics of thementioned steel fiber are given Table 4 and a photograph of these fibers is available inFigure 1.The characteristics of Dramix RC-80/60-BN Steel Fiber: In the denominationof Dramix steel fibers, R and C define the hook and the admixture features of fiber,respectively, while 80defines the performance class and 60 defines the length of fiber inmm. B stands for Bright. N stands for Low Carbon [15].Table 4 Properties of steel fiberLength Max.DiameterSlendernessRatioSpecificGravityModulus ofElasticity(MPa)TensileStrength(MPa)The Numberof Fiber (kg)60 mm ± %5 0.75 mm ± %5 80 7480 200000 1035 4600Asphalt mixtures were prepared in accordance with the technical specificationsrequired by Highway General Directorate of Turkey [16]. The upper and lower limitsrequired for the mixture grading of aggregate are shown in Figure 2.Figure 1 Steel FibersFigure 2 Gradation curve of the aggregates used in mixture2nd International Balkans Conference on Challenges of Civil Engineering, BCCCE, 23-25 May 2013, Epoka University, Tirana,Albania.1033A series of tests were carried out to determine the optimum bitumen content.Asphalt mixture samples were produced using as 4.5%, 5.0%, 5.5%, and 6.0% bitumencontents. Optimum bitumen content obtained as 5.5%.Based on the obtained optimum bitumen content value, steel fibers were added indifferent ratio in weights (0% - 0.25% - 0.50% - 0.75% - 1.0% - 1.5% - 2.0% - 2.5%) asthree samples for each fiber rate. Maximum Marshall Stability value was obtained for5.5% bitumen content and 0.75% fiber addition [15].GENETIC ALGORITHMSThe fundamental unit of information is in living systems in the gene. In general, agene is defined as a portion of a chromosome that determines or affects a singlecharacter or phenotype (visible property), for example, eye color. It comprises a segmentof deoxyribonucleic acid (DNA), commonly packaged into structures calledchromosomes. This genetic information is capable of producing a functional productwhich is most a protein19.Genetic Algorithm (GA) is inspired by the mechanism of natural selection wherestronger individuals are likely the winners in a competing environment. Here, GA uses adirect analogy of such natural evolution. Through the genetic evolution method, anoptimal solution can be found and represented by the final winner of the genetic game[17].GA presumes that the potential of ant problem is an individual and can berepresented by set of parameters. These parameters are regarded as the genes of achromosome and can be structured by a string of values in binary form. A positive value,generally known as a fitness value, is used to reflect the degree o “goodness” ofchromosome for the problem which would be highly related with its objective value[17].Pragmatic researchers see evolution’s remarkable power as something to beemulated rather than envied. Natural selection eliminates one of the greatest hurdles insoftware design: specifying in advance all the features of a problem and the actions aprogram should take the deal with them. By harnessing the mechanism of evolution,researchers may able to “breed” programs that solve problems even when no person canfully understand their structure. Indeed, these so-called genetic algorithms have alreadydemonstrated the ability to make breakthroughs in the design of such complex systemsas jet engines[18].Genetic algorithms make it possible to explore a far greater range of potentialsolutions to a problem than do conventional programs. Furthermore, as researchersprobe the natural selection of programs under controlled and well-understood conditions,the practical results they achieve may yield some insight into the details of how life andintelligence evolved in natural world[18].Basic Steps of Genetic AlgorithmsGiven a way or a method of encoding solution of a problem into the form ofchromosomes and given an evaluation function that returns a measurement of the costvalue of any chromosome in the context of the problem, a GA consist of the followingsteps (See Figure 3) [19].2nd International Balkans Conference on Challenges of Civil Engineering, BCCCE, 23-25 May 2013, Epoka University, Tirana,Albania.1034Figure 3 Basic Steps of Genetic Algorithm [20]Step 1 : Initialize a population of chromosomes.Step 2 : Evaluate each chromosome in the population.Step 3 : Create new chromosomes by mating current chromosomes; apply mutation andrecombination as the parent chromosomes mate.Step 4 : Delete members of population to make room for new chromosomes.Step 5 : Evaluate the new chromosomes and insert them into the population.Step 6 :If stopping criterion is satisfied, then stop and return the best chromosome;otherwise, go to step 3.Genetic Expression Programming (GEP)The phenotype of GEP individuals consists of the same kind of ramified structuresused in genetic programming. However, these complex entities are encoded in simpler,linear structures of fixed length – the chromosomes. Thus, there are two main players inGEP: the chromosomes and the ramified structures or expression trees (ETs), the latterbeing the expression of the genetic information encoded in the former. Figure 4 showsan example of ETs.Figure 4an example of ETsAs in nature, the process of information decoding is called translation. And thistranslation implies obviously a kind of code and a set of rules. The genetic code is very2nd International Balkans Conference on Challenges of Civil Engineering, BCCCE, 23-25 May 2013, Epoka University, Tirana,Albania.1035simple: a one-to-one relationship between the symbols of the chromosome and thefunctions or terminals they represent. The rules are also very simple: they determine thespatial organization of the functions and terminals in the ETs and the type of interactionbetween sub-ETs in multi-genic systems. In GEP there are therefore two languages: thelanguage of the genes and the language of ETs. However, thanks to the simple rules thatdetermine the structure of ETs and their interactions, it is possible to infer immediatelythe phenotype given the sequence of a gene, and vice versa. This bilingual andunequivocal system is called Karva language. Figure 5 shows an example ofKarvalanguage [21].Figure 5an example of Karva languageDEVELOPED GEP MODELIn this section of the paper, the developed model for the Marshall stability isgiven.In this study developed GEP model is mainly aimed to generate the mathematicalfunctions for the prediction of the Marshall stability of reinforced asphalt concretecontaining steel fiber. In GEP model three input parameters were preferred such aspercentage of bitumen(%), percentage of steel fiber and unit weight (gr/cm3) and outputwas the Marshall stability (kg) of asphalt concrete. So this mathematical function wasgenerated in the form of y = f(bitumen (%),steel fiber (%)and unit weight (gr/cm3) forprediction of Marshall Stability. Table 5 presents the model parameters used for GEPmodel. The relationship between the input parameters and Marshall Stability has beentransformed into the Visual Basic program code based on the GEP model yielding thebest result as follows:GEP MODELThe following variables in the program code stand for the values assigned to themas follows Marshall Stability (MS), POB= Bitumen, SF= Steel Fiber, UW= Unitweight.The mathematical formula of the Visual Basic program code obtained as a resultof the evolutionary programming has been written as follows using abbreviation ofparameters (Eq. (1)):Marshal Stability = (10 ^ ((IIf(Int((POB- UW)) <= UW, Int((POB- UW)) , UW) *Cos((UW* UW))))) + (10 ^ (IIf(UW>Exp(Sin(((SF* SF) + IIf(UW= SF, UW, SF)))) ,UW, Exp(Sin(((SF* SF) + IIf(UW= SF, UW, SF))))))) + (10 ^ ((IIf((10 ^ (1 / (UW))) <UW, (10 ^ (1 / (UW))) , UW) * Cos((UW* UW)))))2nd International Balkans Conference on Challenges of Civil Engineering, BCCCE, 23-25 May 2013, Epoka University, Tirana,Albania.1036Table 5 GEP parameters of the models developed.Population size 50Generation 977Number of the genes 3Length of the gene head 8Linking function +Function set +, -, *, /,√, exp, sin, cos, arctanMutation rate 0,044One-point recombination rate 0,3Two-point recombination rate 0,3Inversion rate 0,1Transposition rate 0,1PREDICTION RESULTS AND DISCUSSIONSIn order to learn the performance of the developed model is, several statisticalverification criteria were used such as coefficient of determination (R2) Eq. (2), rootmean squared error (RMSE) Eq. (3) and Standard Error of the Estimate (SEE) Eq. (4).(2)(3)SEE= (4)Where;n= Total number of dataYi(observed)= Measured (experimental)Yi(model)= Developed model resultTable 6 represent calculated R2, RMSE, SSE and SEE values for training and testgroups of developed GEP model.Table 6 Performance statistics of the modelGEP modelTrainingsetR-square 0.842RMSE 47.32SEE 6.94e+004Test set R-square 0.9219RMSE 44.35SEE 1.18e+004Marshall Stability (MS)values estimated from model were graphically comparedwith the experimental results in Figures 6 and 7 it clearly appears that the results fromthe GEP are in good agreement with the experimental results.2nd International Balkans Conference on Challenges of Civil Engineering, BCCCE, 23-25 May 2013, Epoka University, Tirana,Albania.1037Figure 6 Comparison of experimental results with predicted Marshall Stability valuesfrom GEP Model (training set)Figure7 Comparison of experimental results with predicted Marshall Stability valuesfrom GEP Model (testing set)2nd International Balkans Conference on Challenges of Civil Engineering, BCCCE, 23-25 May 2013, Epoka University, Tirana,Albania.1038CONCLUSIONSIn this work, GEP modeling approach was studied and its prediction capability forMarshall Stability was illustrated. For training set, 33 samples were randomly selectedand the residual data (8 samples) were selected as test set. After finding the best closelyGEP model with experimental, the results of GEP model were compared with theexperimental results. The coefficient of determination (R2), Root mean square error(RMSE) and Standard Error of estimation (SEE) were used as comparison criteria.When predicted and measured values compared in the training set, RMSE and R2were found as 47.32 and 0.842 respectively. These values were found as 44.35 and0.9219 in the test stage respectively. As a result, it can be concluded that GEP is a usefulmethod for this kind of engineering applications.REFERENCES[1] Umar, F., Ağar, E., Pavement Structure, Istanbul Technical University CivilEngineering Faculty Press, Istanbul, 1991.[2] Hassan HF, Oraimi SA, Taha A. Evaluation of open-graded friction coursemixtures containing cellulose fibers and styrene butadiene rubber polymer. 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Modeling Marshall stability of steel fiber reinforced asphalt concrete by genetic expression programming

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Modeling Marshall stability of steel fiber reinforced asphalt concrete by genetic expression programming

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