Optimal polymer matrix coating for composite railway sleeper Analytic Hierarchy Process

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1 University of Southern Queensland From the SelectedWorks of Wahid Ferdous Summer December 14, 15 Optimal polymer matrix coating for composite railway sleeper Analytic Hierarchy Process Wahid Ferdous Allan Manalo Thiru Aravinthan Gerard Van Erp Available at:

2 The 12th International Symposium on Fiber Reinforced Polymers for Reinforced Concrete Structures (FRPRCS-12) & The 5th Asia-Pacific Conference on Fiber Reinforced Polymers in Structures (APFIS-15) Joint Conference, December 15, Nanjing, China OPTIMAL POLYMER MATRIX COATING FOR COMPOSITE RAILWAY SLEEPER ANALYTIC HIERARCHY PROCESS Wahid Ferdous 1, Allan Manalo 1, Thiru Aravinthan 1 and Gerard Van Erp 2 1 Centre of Excellence in Engineered Fibre Composite (CEEFC), School of Civil Engineering and Surveying, University of Southern Queensland, Toowoomba, QLD 435, Australia md.ferdous@usq.edu.au; allan.manalo@usq.edu.au and thiru.aravinthan@usq.edu.au 2 Former Professor, Centre of Excellence in Engineered Fibre Composite (CEEFC), University of Southern Queensland, Toowoomba, QLD 435, Australia Keywords: Polymer matrix, Optimal design, Analytic hierarchy process, Railway sleeper ABSTRACT The deterioration of the mechanical properties due to environmental exposures is now becoming an issue in the use of fibre composite materials in civil infrastructure. In this study, seven polymer mixes with different percentages of epoxy resin-to-filler ratio has been considered as a coating material for composite railway sleepers. Selecting a particular one from the seven mixes has become a major challenge as the variation on the filler content enhanced some of the physical and mechanical properties of the polymer matrix but degrade some important properties at the same time. To obtain the most suitable polymer coating and to utilise its maximum benefits, the Analytic Hierarchy Process (AHP) was implemented to select the optimal polymer mix for coating of a composite railway sleeper. Initially, three suitable mixes were shortlisted out of total seven based on their satisfaction of the performance requirements of a timber replacement composite railway sleeper. The AHP method was then applied to select the best suited mix out of three alternatives based the thermal, physical, mechanical, durability and cost properties. The results of this analysis found the polymer mix with a resin-to-filler ratio of 7:3 is the most preferred coating when mechanical properties are given the highest priority followed by cost, durability, thermal and physical properties for composite sleeper application. 1 INTRODUCTION Research and development of fibre composite railway sleepers are now looking for a suitable coating material to protect the main structural element from the harsh environments. The superior properties of polymer matrix composed with epoxy resin and light weight filler materials demonstrated a suitable and effective material to serve this purpose. Polymer matrix can be prepared with different resin-to-filler ratios on which their properties are primarily dependent. Recent study by the authors on polymer matrix has shown that the gradual increase of filler materials can improve the thermal, durability and cost properties but degrade physical and mechanical properties. To establish a good balance among all properties, there is a need for optimal design. The main objectives of this study is to determine an optimal polymer matrix using analytic hierarchy process. Analytic Hierarchy Process (AHP) is a multi-criteria decision making method based on mathematics and psychology, developed by Thomas L. Saaty [1] in the 197s. The basic concept of this method is the relative importance of one attribute over other. The main advantage of this method is its capability to check and reduce the inconsistency of the judgement. A little inconsistency, usually less than 1% is acceptable. The hierarchical network is constructed with different hierarchy levels such as (a) goal or objective- upon which the best decision should be made is placed, (b) criteria- contributes to the quality of the decisions, (c) sub-criteria- contributes to the quality of the product and (d) alternatives- the available choices. AHP has been extensively used to select one alternative from many available. It is successfully applied in the broad area of business, industry, government and the military [2]. This method is also useful for strategic transportation planning [3], selecting an appropriate items [4], condition evaluation of existing structure [5], safety risk assessment [6] and so on. In this research, AHP is applied to select the most suitable polymer mix from a group of mixes.

3 Wahid Ferdous, Allan Manalo, Thiru Aravinthan and Gerard Van Erp 2 THEORETICAL BACKGROUND OF ANALYTIC HIERARCHY PROCESS Analytic Hierarchy Process (AHP) is the multi criteria decision making method that derive ratio scales from paired comparisons. The relative importance among attributes can be expressed by the fundamental scale of AHP method proposed by Saaty and Vargas [1]. The number 1, 3, 5, 7 and 9 represents verbal judgments equal importance, moderate importance, strong importance, very strong importance and extreme importance respectively; while 2, 4, 6 and 8 are used to express intermediate behaviour. A relative importance matrix can be constructed for n attributes where the relative importance of attribute i with respect to attribute j is represented by a ij. The strong attribute always need to be compared with the weight scale 1 for weak attribute, and hence, all the diagonal entries of the n order square matrix are equal to 1. A typical relative importance matrix A = [a ij ] n n can be expressed by Eq. (1). The matrix has reciprocal properties where, a ji = 1 a ij and a nn = 1. a 11 a 1n A = [ ] 1/a 1n a nn (1) The normalised Eigen vector of matrix A represents the relative weight of the attributes and called the priority matrix. The Eigen vector of matrix A can be determined by manually or using Matlab program and then it can be normalised by diving the sum of all elements in Eigen vector. The elements of normalised Eigen vector can be expressed by Eq. (2). = a ij n a ij i=1 a ij (2) where, a ij is the element of Eigen vector. To ensure a consistent relative weight among attributes, Consistency Ratio (CR) need to be checked. If CR.1, then the values are generally considered inconsistent in pairwise comparison and need to be revised. The CR can be expressed by Eq. (3). CR = CI RI (3) where, CI is the Consistency Index, expressed by Eq. (4) and RI is the Random Index. The average value for RI with respect to n is given in Table 1. CI = λ max n n 1 (4) where, λ max is the Eigen value and n is the number of comparisons. Table 1 Average random index [1] n RI PAIRWISE COMPARISON OF THE ATTRIBUTES The properties of seven different polymer matrices were prepared and investigated and presented in Table 2. The resin-to-filler ratio has been considered the experimental variable on which the properties of the polymer matrix is primarily dependent. The control mix was composed with 1% resin and subsequently filler materials were added up to 6% with an increment of 1% by volume. No further mix was considered beyond 6% filler (that contains 4% resin) as because it was not a workable mix when prepared. The mixes are acronym from F to F 6 depending on the amount of fillers, e.g., mix

4 The 12th International Symposium on Fiber Reinforced Polymers for Reinforced Concrete Structures (FRPRCS-12) & The 5th Asia-Pacific Conference on Fiber Reinforced Polymers in Structures (APFIS-15) Joint Conference, December 15, Nanjing, China containing 3% filler and 7% resin is represented as F 3. Several fundamental properties have investigated including: generation of heat during mixing and glass transition temperature under thermal; density and porosity under physical; flexural and compressive behaviour under mechanical; and the effect of ultraviolet radiation under durability properties. The experimental investigation conducted for characterising those properties are beyond the scope of this paper. The target values for fulfilling the requirements of polymer matrix as coating of railway sleeper are also presented in the last column in Table 2. Table 2 Performance comparison and the requirements of polymer matrix Performance Measurements F F 1 F F 3 F 4 F 5 F 6 Target Heat generation ( C) < 35 Glass transition temp. ( C) > 6 Density (gm/cm 3 ) to 1.5 % Porosity < 1 Flexural strength (MPa) > 4 % Failure strain in flexure > 1 Compressive strength (MPa) > 4 % Strength reduction by UV < 1 Relative cost comparison As low as Based on the targets in Table 2 it was observed that, only the mixes containing filler from 3% to 5% were fulfilling all the requirements. Challenge still remain in selecting the most suitable one out of shortlisted (F 3, F 4 and F 5) polymer mixes because some of the properties were dominated by F 3 whereas some others by F 5. To select the best mix from those three, AHP was applied. The hierarchy of the analysis has been divided into criteria, sub-criteria and alternatives. The key factors such as thermal, physical, mechanical, durability and cost properties are the main drivers under criteria. The criteria has been sub-divided into more specific properties, e.g. heat generation and glass transition temperature under thermal, density and porosity under physical, flexural strength, failure strain and compressive strength under mechanical and finally the UV resistance falls under durability criteria. Each of the sub-criteria has three alternative polymer mixes (F 3, F 4 and F 5). 3.1 Relative intensity among criteria Criteria is the main driver for selecting optimal mix. In this stage, a small change in the intensity has a significant effect on the final output. Therefore, two cases have been studied by interchanging the highest priority between mechanical properties and cost which are the most dominant among the five investigated properties. In case-1, the highest priority is given in mechanical properties followed by cost, durability, thermal and physical properties. On the other hand, cost is given the highest priority in case- 2 followed by mechanical, durability, thermal and physical properties. The relative importance and intensity in different properties are given in Table 3. Table 3 Pairwise comparison among criteria Criteria Case-1 Case-2 A B Important Intensity Important Intensity Thermal Physical A 3 A 3 Thermal Mechanical B 7 B 5 Thermal Durability B 3 B 3 Thermal Cost B 5 B 7 Physical Mechanical B 9 B 7 Physical Durability B 5 B 5 Physical Cost B 7 B 9 Mechanical Durability A 5 A 3 Mechanical Cost A 3 B 3 Durability Cost B 3 B 5

5 Wahid Ferdous, Allan Manalo, Thiru Aravinthan and Gerard Van Erp 3.2 Relative intensity among sub-criteria The criteria thermal, physical and mechanical has their sub-criteria. The glass transition temperature has given a strong preference over heat generation as the former measures the quality of the product. Porosity is slightly important than density under physical properties. In case of mechanical properties, failure strain is more important when compared with flexural or compressive strength as because the polymer matrix should have sufficient flexibility which depends on the failure strain. However, the flexural strength is slightly important than compressive strength as a coating of polymer railway sleeper. Table 4 measures the relative weight between sub-criteria. Table 4 Pairwise comparison among sub-criteria Criteria Sub-criteria A B Important Intensity Thermal Heat generation Glass transition temperature B 5 Physical Density Porosity B 2 Flexural strength Failure strain B 2 Mechanical Flexural strength Compressive strength A 2 Failure strain Compressive strength A Relative intensity among alternatives The relative weight among the alternative mixes are calculated based on their performance provided in Table 2. As it is mentioned, no further mix can be produced beyond F 6, therefore, the best and the worst possible results are already obtained either in F or in F 6. The intensity of the worst mix (either F or F 6) in a particular investigation in Table 2 is given 1 and the intensity is given 9 for the best. Using this concept the normalised relative intensity of the shortlisted mixes can be determined and given in Table 5. Table 5 Normalised relative intensity between alternative mixes Measuring criteria F 3 vs F 4 F 3 vs F 5 F 4 vs F 5 F 3 F 4 F 3 F 5 F 4 F 5 Heat generation Glass transition temperature Density Porosity Flexural strength Failure strain in flexure Compressive strength Strength reduction by UV Cost DETERMINATION OF OPTIMAL MIX 4.1 Determination of local priority It is important to note that the efficiency of AHP is greatly depends on the accuracy of relative intensity between attributes. The local priority of each criteria, sub-criteria and alternatives have been evaluated in both cases and presented in Figure 1. It is mentioned that the main driver of this analytical study is the criteria, more specifically mechanical properties and cost which contributes 51.28% and 26.15% respectively in Case-1 and opposite for Case-2. No other cases have been studied as they are not as significant as mechanical properties and cost.

6 % Priority % Priority The 12th International Symposium on Fiber Reinforced Polymers for Reinforced Concrete Structures (FRPRCS-12) & The 5th Asia-Pacific Conference on Fiber Reinforced Polymers in Structures (APFIS-15) Joint Conference, December 15, Nanjing, China C1: Case-1 and C2: Case-2 Figure 1 Local priority 4.2 Determination of global priority The global priority can be determined by multiplying the corresponding local priority and their summation indicates the global priority of each mix. This can be expressed as; Global priority of each mix = [Priority alternative Priority sub criteria Priority criteria ] Figure 2 illustrated the priority of each alternative mix in two different cases. For Case-1, the global priority is obtained maximum for the mix with 3% filler (F 3) with a priority of 38.17%. The priority for other two mixes are relatively close to each other and they are 31.56% and 3.28% for F 4 and F 5 respectively. This is due to the improved mechanical properties of F 3 over F 4 and F 5 mixes which has given the highest priority under criteria. On the other hand, F 5 (34.64%) is slightly preferable than F 3 (32.93%) and F 4 (32.43%) in Case-2. It is observed that the variation of priorities among the alternatives are not significant in second case. This indicates, all three shortlisted mixes have more likely similar priorities from the cost perspective. Therefore, 3% filler containing mix (F 3) which provided the best mechanical properties can be selected as a coating material for railway sleeper F3 F4 F5 F3 F4 F5 Polymer mix Polymer mix (a) preference of mechanical properties (Case-1) (b) preference of cost (Case-2) Figure 2 Percentage priority of the shortlisted mixes

7 % Contribution % Contribution Wahid Ferdous, Allan Manalo, Thiru Aravinthan and Gerard Van Erp The percentage contribution of each property is given in Figure 3. For Case-1, the decision for selecting optimal mix is primarily governed by the mechanical properties. The failure strain, flexural strength and compressive strength contributes 27.67%, 15.23% and 8.38% respectively whereas the cost is dominated by 26.15%. On the other side, cost is the most influencing factor for Case-2 and contributes 51.28%. The preference of cost is given almost twice than the combined priority of mechanical properties, e.g. failure strain (14.11%), flexural strength (7.77%) and compressive strength (4.27%) Individual % contribution Cumulative % contribution Individual % contribution Cumulative % contribution (a) preference of mechanical properties (Case-1) (b) preference of cost (Case-2) Figure 3 Percentage contribution of each property 5 CONCLUSION The main objectives of this study was to determine a suitable polymer matrix for the coating of polymer railway sleepers from a group of mixes. For this purpose, analytic hierarchy process was applied from which the following conclusion were drawn: The polymer matrix containing filler from 3% to 5% can fulfill the requirements of a coating material for manufacturing polymer railway sleepers. The percentage priority of the mix is not fixed in all circumstances and it may vary depending on their application and requirements. In this study, the mix consist of 7% resin with 3% filler (by volume) can be considered as the preferred mix for the coating material of polymer railway sleeper. ACKNOWLEDGEMENTS The first author gratefully acknowledged the financial support by Australian Postgraduate Award (APA) scholarship from the University of Southern Queensland, Australia. REFERENCES [1] T.L. Saaty, L.G. Vargas, Models, methods, concepts & applications of the Analytic Hierarchy Process, 2nd ed., Springer Science & Business Media, New York, USA, 12. [2] L. Bodin, S.I. Gass, On teaching the analytic hierarchy process, Computers & Operations Research, 3 (3) [3] S.d. Luca, Public engagement in strategic transportation planning: An analytic hierarchy process based approach, Transport Policy, 33 (14) [4] N. Kursunoglu, M. Onder, Selection of an appropriate fan for an underground coal mine using the Analytic Hierarchy Process, Tunnelling and Underground Space Technology, 48 (15) [5] S. Sasmal, K. Ramanjaneyulu, Condition evaluation of existing reinforced concrete bridges using fuzzy based analytic hierarchy approach, Expert Systems with Applications, 35 (8) [6] S. Aminbakhsh, M. Gunduz, R. Sonmez, Safety risk assessment using analytic hierarchy process (AHP) during planning and budgeting of construction projects, Journal of Safety Research, 46 (13)