International Conference on Applications of Statistics and Probability in Civil Engineering (ICASP) (12th : 2015)

Prediction of soil corrosivity index : a Bayesian belief network approach Demissie, Gizachew; Tesfamariam, Solomon; Sadiq, Rehan Jul 31, 2015

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12th International Conference on Applications of Statistics and Probability in Civil Engineering, ICASP12Vancouver, Canada, July 12-15, 2015Prediction of Soil Corrosivity Index: A Bayesian Belief NetworkApproachGizachew DemissiePhD Student, School of Engineering, University of British Columbia, Kelowna, CanadaSolomon TesfamariamAssociate Professor, School of Engineering, University of British Columbia, Kelowna,CanadaRehan SadiqProfessor, School of Engineering, University of British Columbia, Kelowna, CanadaABSTRACT: Soil and their inherent properties play a very significant role in aggravating the corrosionprocess of metallic pipes as they are buried underground. The most common causes of corrosion arelower resistivity of soil; lower and higher pH; presence of sulfate-reducing bacteria, chlorides, sulfateand sulfides; difference in soil composition; and differential aeration of soil around the laid water pipes.The interaction of these variables are highly complex and challenging to predict the degree of corrosiondue to the soil environment. In this paper, a Bayesian belief network (BBN) approach is proposed toaddress the inter-dependency of soil parameters and their effect on the corrosivity of soil. The proposedapproach uses a combination of in situ collected data and expert knowledge of soil parameters to modelthe inter-dependency between soil parameters and predict the SCI using an updating capability of theBBN. The model was developed and trained using soil parameters data collected by the city of Calgary incombination with expert knowledge. The performance of the developed soil corrosivity index-Bayesianbelief network (SCI-BBN) model was evaluated by the BBN model sensitivity analysis. In order todemonstrate the developed approach, the SCI-BBN model output was converted into five indexes, whichare very high to very low, so that the decision makers clearly understand their system’s situation. Finally,the linguistic soil corrosivity indices of each pipes were mapped using a geographic information system(GIS) platform in order to indicate its spatial representations.1. INTRODUCTIONSoil corrosivity is a complex phenomena which hasa significant impact on buried metallic water pipesystems. The metallic water pipe corrosion processis facilitated predominantly due to the corrosive na-ture of the surrounding soil. It is a naturally oc-curring process in which the surface of a metallicpipe structure is oxidized or reduced by chemicalor electrochemical reaction with the soil environ-ment (Hubell, 2003). The material loss, given avery long period of time, can result in a significantreduction of area, which in turn leads to a reductionin the structural capacity of a given metallic pipeelement. At any age of the pipe, by identifying thepotential corrosive environment and taking appro-priate action, water utilities can avoid pipe failuresand save significant future repair and replacementcosts (Sadiq et al., 2004a).Several scoring scales have been developed bydifferent researchers to rate the corrosivity of soiltowards buried metallic pipes. The most widelyknown of these approaches is the 10-point scoringmethod proposed by the American Water WorksAssociation (AWWA) and the American NationalStandards Institute (ANSI) published in the Stan-dard for polyethylene encasement for ductile ironpipe systems (AWWA, 1999). The 10-point sys-tem was proposed not to classify the soil corro-112th International Conference on Applications of Statistics and Probability in Civil Engineering, ICASP12Vancouver, Canada, July 12-15, 2015sivity, rather was used to identify aggressive soilto metallic pipes (Barnard et al., 2005). Consider-ing the weighted aggregation of five soil properties(i.e soil electrical resistivity, soil pH, redox poten-tial, soil sulfides content and soil moisture content),soil of less than 10-point score was considered asnon-aggressive to metallic pipes whereas the soilgreater or equal to 10-points is categorized as ag-gressive to metallic pipes. However, this methoddoes not provide information on the intensity ofsoil corrosivity (Sadiq et al., 2004a). If the ag-gregate points are slightly less than 10, for exam-ple 9.5, it is distinguished as non-aggressive soil tometallic pipes. In order to fill this gap, Spickelmire(2002) proposed a 25-point scoring method. The25-point risk assessment (scoring) method modifiesthe 10-point method by incorporating other soil cor-rosivity factors and additional pipe design/functionfactors. However, due to its data intensive nature,this method is more applicable on large-sized wa-termains than small-sized watermains.Statistical and soft-computing techniques werealso proposed to asses the aggressiveness of soiltowards buried metallic pipes (Cunat, 2001; Sadiqet al., 2004a,b; Najjaran et al., 2006; Kleiner et al.,2010). Sadiq et al. (2004a) and Najjaran et al.(2006) used fuzzy based approaches that considersoil parameters of AWWA (1999) 10-point scoringmethod. On the other hand, Kleiner et al. (2010)used the impact of soil properties on pipe corrosionusing statistical/probabilistic tools to characterizeproperties of corrosion pits. Different authors alsoattempted to discretize the soil corrosivity potential.Sadiq et al. (2004a) discretized the soil corrosivitypotential into non-corrosive, moderately corrosiveand corrosive; however, Najjaran et al. (2006) dis-cretized the soil corrosivity as corrosive and non-corrosive.Previous literature, however, is limited in consid-ering the inter-dependency of soil parameters in theprediction of the soil corrosivity potential. In addi-tion, most of the municipalities have collected lit-tle information about the soil parameters becauseof cost and limited qualified personnel to collect allnecessary information needed to adopt the previousapproaches raised by different researchers. In thispaper, a Bayesian belief network (BBN) approachthat uses a combination of different informationsources is proposed. The proposed approach is usedto understand the effect of interdependency amongsoil parameters and on soil corrosivity index. Inthis approach, a combination of collected informa-tion/data and expert knowledge is employed usinga BBN approach.The first part of this paper summarises the lit-erature review on the soil corrosivity parameters.The next part describes the conceptual backgroundof the BBN. The following part illustrates the pa-rameters considered and techniques used in the de-velopment process of the BBN model. Next, themodel performance evaluation and its result will bediscussed and interpreted, respectively. Finally, thecase study, and summary and conclusion sections,demonstrates the proposed model, and summariseand concludes this paper, respectively.2. SOIL CORROSIVITYSoil and their inherent properties play a signifi-cant role in aggravating the corrosion process ofmetallic pipes as they are buried underground. Thecommon causes of corrosion are low resistivity ofsoil; lower PH; presence of sulfate-reducing bacte-ria, chlorides, sulfate and sulfides; difference in soilcomposition; differential aeration of soil around thepipe; and stray direct current from external forces(AWWA, 1999; Cunat, 2001; Spickelmire, 2002).In this paper, the soil parameters will be categorizedas major and minor depending on their contributionto soil corrsivity. The major soil parameters are soilresistivity, soil pH, redox potential, sulfides and soiltypes or moisture content (AWWA, 1999). The nextsection of this paper discusses the nature of an in-terdependency between soil parameters and on soilcorrosiveness.2.1. Soil resistivitySoil resistivity is affected by the soil solution whichcontain different concentrations of ions (e.g. salts),produced due to the action of the subsurface wateron the chemical minerals and the characteristics ofsoil. The electrical resistivity of soil is influencedby the degree of moisture content in the soil, tem-perature of the soil, degree of compaction of the soil212th International Conference on Applications of Statistics and Probability in Civil Engineering, ICASP12Vancouver, Canada, July 12-15, 2015and concentration of different salts and their move-ments (Doyle et al., 2003; Romanoff, 1957). In thecase of low temperature and low moisture contentof the soil, electrical resistivity of soil is higher andvice versa (Romanoff, 1957). Higher electrical re-sistivity of the soil is also created by high concen-tration of soluble salts and higher compaction of thesoil. Hence, the soil resistivity, in conjunction withminor soil parameters (i.e. availability of salt, tem-perature etc.), is one of the stressors in determiningthe corrosiveness of soil.2.2. Soil moisture contentPrevailing soil moisture content is one of the mostimportant parameter that affects the soil corrosion(AWWA, 1999). At a low percent of soil mois-ture content, the electrical resistivity of soil is veryhigh and vice versa (Romanoff, 1957). A techni-cal manual on soil resistivity by AEMC instruments(AEMC, 2002) also illustrates that, when the soilmoisture content is less than 20%, there will bea rapid change in soil resistivity. However, whensoil moisture content is above 20% the soil resis-tivity seems constant and falls under the categoryof low resistivity, which manifests highly corrosivesoil environment. Soil moisture content is also af-fected by variability of ground water. If the watertable is near the top part of the soil, it would nor-mally indicate that the soil has a high percent ofmoisture content. Higher soil moisture content, onthe other hand, indicate that aeration of soil porousmedia is very low and vice versa.2.3. Soil pHSoil pH is a measure of soil acidity or alkalinity andis the measure of hydrogen ions (H+) and other ionsthat carry currents in the soil. Carbonic acid, var-ious minerals (and/or their leaching), organic andinorganic acid (produced by microbial activities, asa result of waste disposal and acid rain) are used todetermine the pH value of soil (Sadiq et al., 2004a).A high amount of current carrying ions correspondsto a low pH value and low amount of current carry-ing ions indicates a high pH. For the current to flow,there must be a potential difference between twopoints that are electrically connected and immersedin an electrolyte (Hubell, 2003). Most often, corro-sion occurs through the loss of metal ions at anodepoints or areas.2.4. Redox potentialRedox potential is a measure of the attraction ofsubstance to electrons (i.e. its electro-negativity)and measured in volts (V). In soil, the oxygenconcentration and the soil moisture content deter-mine the redox potential. Higher oxygen contentof soil implicates higher redox potential (Pezeshkiand DeLaune, 2012). Lower redox potential in-dicate less aeration in a soil porous media, whichgives a favourable environment for aerobic bacte-ria to act. Rapid changes in the moisture contentalso strongly affects soil aeration status. When thepores in the soil are filled with water, the diffusionof oxygen will be restricted and the consumptionof oxygen will rapidly be facilitated. Fiedler et al.(2007) also described that a fluctuating water tablecauses the buried iron/metallic structures that havecontacts with soil particles to alternate between ox-idized and reduced forms over a period of seasons.This variability in oxidation and reduction, a nat-ural process of redox potential, clearly shows thatthe soil corrosivity potential is developing aroundburied metallic pipes.2.5. Soil sulfides contentThe presence of sulfate and sulfate-reducing bac-teria in the soil might be a risk for buried metal-lic pipes. In a microbial process, sulfate can beconverted to highly corrosive sulfide by anaerobicsulfate-reducing bacteria (Cunat, 2001). Hence, de-tailed analysis and testing for microbial activitiesby analyzing soil samples for presence of sulfidescontent may indicate the corrosiveness of the soildue to the sulfides content (Sadiq et al., 2004a).3. BAYESIAN BELIEF NETWORKBayesian belief network (BBN) is a popular analyt-ical framework in causal studies, where the causalrelations are encoded by the structure of the net-work (Ellis and Wong, 2008). BBN captures ourbelief (which may be uncertain or imprecise) aboutthe relation between a set of variables that are rele-vant to some problem. According to Pearl (1988),BBN is a graphical model that permits a probabilis-tic relation among the set of variables. It is repre-312th International Conference on Applications of Statistics and Probability in Civil Engineering, ICASP12Vancouver, Canada, July 12-15, 2015sented by a direct acyclic graph (DAG), in whichthe nodes represent stochastic variables of interestand the links identify direct causal influences be-tween the linked variables (Krieg, 2001).A distinguishable nature of BBN from othercausal belief networks is its use of Bayesian calcu-lus to determine the state probabilities of each nodeor variable from the predetermined conditional andprior probabilities (Krieg, 2001). The main con-cept of BBN is based on the use of Bayes’ Theorem(Equation 1).p(H|E) =p(E|H)p(H)∫p(E|H)p(H)dH(1)where, p(H) is a prior probability distribution ofhypothesis (H); E is the observed data or evidence;p(E) is the probability that the evidence (E) takesplace; and p(E|H) is the statistical model used todescribe the distribution of the data (E) given thehypothesis (H).BBN forces each node to update the poste-rior probabilities for each of its hypotheses onthe receipt of data messages from its immediateneighbours (Krieg, 2001). BBN also supports thecomputation of the probabilities of any subset ofvariables given evidence about any other subset(Tesfamariam and Martín-Pérez, 2008). These de-pendencies are quantified through a set of condi-tional probability tables (CPT), in which each vari-able is assigned a CPT of the variable given its par-ents.4. SCI-BBN MODEL DEVELOPMENTA soil corrosivity index-Bayesian belief network(SCI-BBN) model was developed by consideringsoil parameters, their interactional relationships andtheir effects on the corrosiveness of the soil. Themajor five soil parameters explained in the previoussection are used to estimate the total AWWA (1999)10-point method’s point value for soil corrosivityindices. In addition, minor parameters (e.g. tem-perature, oxygen contents, presence of acid, sul-fates and sulfate-reducing bacteria’s, etc.), whichhave a direct and indirect impact on soil corrosiv-ity are also considered.Collecting the information about the soil parame-ters is costly and needs qualified personnel. Hence,a technique of incorporating a combination of ex-pert knowledge and collected information for allstates of the considered soil parameters were em-ployed. In the development process of the model,the Norsys Software Corporation’s Netica (Norsys,2014) was used to construct the SCI-BBN modeldue to its flexibility in integrating with MicrosoftExcel. The soil parameters and ranges consideredfor the definition of node states to predict the SCIand the proposed BBN model are briefly presentedin Tables 1 and 2 and Figure 1.Figure 1: Proposed Bayesian belief network model topredict SCI.The SCI node of the SCI-BBN model was trained(i.e. estimation of the CPT) using the five ma-jor soil parameters (i.e. resistivity, moisture con-tent, pH, redox potential and sulfides content) col-lected at different locations by the city of Calgary.Figure 2 shows the normal probability distributionfunction (PDF) of sample input soil parameters andSCI-BBN output. Due to the limitation of trainedpersonnel and cost for collecting information aboutsoil parameters, expert knowledge is considered todetermine the CPT of other soil parameter nodessuch as temperature, sulphates, salts, degree ofcompaction, presence of sulphate-reducing bacte-ria, presence acid, groundwater variability, oxygencontent and aeration of soil porous media.5. SENSITIVITY ANALYSISBBN sensitivity analysis must be carried out in or-der to understand the significance of input parame-412th International Conference on Applications of Statistics and Probability in Civil Engineering, ICASP12Vancouver, Canada, July 12-15, 2015Table 1: Definition of major soil parameters/nodes andtheir states used in BBN model developmentNodes Node states(Discretization)Soil resistivity VH ( ≤ 3,000 )H (2,500 ≤ ρ < 3000)M (2,100 ≤ ρ <2,500)ML (1,800≤ ρ <2,100)L(1,500≤ ρ < 1,800)VL (<1,5000)Redox potential VH (>+100)H ( +50 - +100)L (0 - +50)VL ( <0 )Soil sulphides content Positive (>3mg/kg)Trace (2-3mg/kg)Negative (< 2mg/kg)Soil pH VH (≥ 8.5)H (7.5 ≤ P < 8.5)MH (6.5 ≤ P < 7.5)M (4.0 ≤ P < 6.5)L (2.0 ≤ P < 4.0)VL (P < 2.0)Moisture content Good drainage (H)Fair drainage (M)Poor drainage (L)ters on the final outcomes as prior conditional prob-abilities are implemented in the BBN. In this pa-per, a variance reduction (VR) sensitivity analysismethod is used to determine the absolute degreeand the rank order of influence of parent (soil pa-rameters) nodes on the child (SCI) node. The vari-ance of a continuous node Q or a node Q havinga state value of real number states (e.g. the SCInode), V (Q = f ) given the evidence F (e.g. soil re-sistivity), can be computed as (Pearl, 1988; Norsys,2014):V (Q| f ) =∑q(q| f )[Xq−E(Q|F)]2 (2)E(Q) =∑qp(q)Xq (3)where, q is the state of the node Q; f is the state ofthe varying node; Xq is the numeric real value cor-Table 2: Definition of minor soil parameters/nodes andtheir states used in BBN model developmentNodes Node states(Discretization)Sulfate-reducing bacteria Present (H)Not present (L)Availability of Available (H)sulfate in soil Not available (L)Oxygen in the soil Excess oxygen (H)Low oxygen (L)Temperature of soil (> 0◦C) (H)(≤ 0◦C) (L)Presence of salts H, LPresence of carbonic acid H, LGround water variability Consistent, VariableDegree of Compacted (H)compaction of soil Not compacted (L)Organic/inorganic acid H, LAeration of soil Excess aeration (H)porous media Less aeration (L)Soil corrosivity VH (>13), H(10-13),index (SCI) M (7-10),L (3.5-7.0),and VL (0-3.5)responding to state q; ∑q() means the sum of over-all states q of Q; E(Q) is the expected real valueof Q before any new findings; and E(Q| f ) is theexpected real value of Q after a new finding f fornode F .Table 3 shows result of the computed variancereduction for the soil corrosivity index node. Thevariance reduction of the soil resistivity node wasfound to be the maximum. Therefore, this resultimplicated that the resistivity of the soil has thegreatest contribution to the variability of the SCI.Similarly, soil temperature and redox potential arethe second and third most influential soil parame-ters identified. Presence of carbonic acid is foundto be the least influential soil parameter on the theSCI.6. CASE STUDYThe water supply network (WSN) of the City ofCalgary was used to demonstrate the proposedSCI-BBN model. This network supplies qualitydrinking water to homes, businesses or institutions512th International Conference on Applications of Statistics and Probability in Civil Engineering, ICASP12Vancouver, Canada, July 12-15, 2015 2 4 6 8 10 12ProbabilitySoil sulfide content (mg/Kg) 1500 3000 4500Soil resistivity (Ohm-cm) 7.90 8.30 8.70ProbabilitySoil pH0. 33 43 53Soil moisture content (%) 220 270 320ProbabilityRedox potential (mV) 6 12 18 24SCIFigure 2: PDF of SCI-BBN model sample input soilparameters and SCI (SCI-BBN model output)throughout the city of Calgary for a population ofmore than one million (City of Calgary, 2014).The network consists of over 4650 kms of water-mains of which more than 2035 kms are metal-lic pipes (Brander and Eng, 2004; City of Calgary,2014). The city of Calgary watermains consist ofseveral groups of pipe materials, which includesductile iron (DI), cast iron (CI), steel (ST), copper(CU) and non-metallic (i.e. plastic and cementi-tious pipe). However, only metallic pipes (i.e. CI,ST, and DI) are considered for further analysis inthis study, as these pipes are mostly vulnerable tocorrosion due to soil corrosivity. The coverage ofthe metallic pipes in the city of calgary as sum-marised and depicted in Figure 3, DI is 52%, CI is40% and others (CU and ST) are 8%. Furthermore,Table 3: Sensitivity of SCI node due to finding at theparent nodes.Nodes NormalizedVRSoil resistivity 38.20Temperature of soil 19.57Redox potential 9.64Soil pH 6.81Presence of salts in the soil 5.58Soil sulfides content 5.17Ground water variability 3.27Oxygen content of soil 2.69Aeration of soil porous media 2.57Degree of compaction of soil 2.20Presence of sulfate-reducing bacteria 2.01Availability of sulfate in soil 1.14Soil moisture content 0.53Organic/inorganic acid 0.32Presence of carbonic acid 0.32the figure shows that from the total count of breaksrecorded DI is 53.5%, CI is 39.5% and others (CUand ST) are 7%.The soil electrical resistivity measurement usedto train the model was taken at 1094 points, inwhich almost all the points were distributed aroundthe laid metallic pipes. Tests of redox potential, soilpH, soil moisture contents and soil sulfides contentwere observed at 8 representative points all over thecity of Calgary. A geographic information system(GIS) tool was used to populate these soil informa-tion to the individual pipe.The SCI-BBN model was integrated with GIS asas shown in Figure 4. Spatial features of soil in-formation available in the form of points, lines andpolygons were processed, stored and managed ina GIS platform. Next, information about each soilparameter has been populated to individual metal-lic pipe system to facilitate an input for the SCI-BBN model. Similarly, the output of the SCI-BBNmodel was processed to create the final mapping ofthe SCI to the pipe system. The spatial analysis andmapping of soil parameter inputs to the SCI-BBNmodel and the final mapping of the SCI of the pipesystem were performed using ESRI ArcMap 10.1612th International Conference on Applications of Statistics and Probability in Civil Engineering, ICASP12Vancouver, Canada, July 12-15, 2015015304560CIDISTPercentagePipe materialTotal lengthTotal breaksFigure 3: Percentage of length and total recordedbreaks of metallic pipe of the city of Calgary (1910-2012).Figure 4: Integration of SCI-BBN with GIS.(ESRI, 2012).In order to demonstrate the developed approach,the SCI-BBN model output was converted into fivelinguistic indices, which are very high to very low,so that the decision makers clearly understand theirsystem’s situation. Similarly, a GIS platform wasused to visualize the spatial representation of finallinguistic indices for each pipe in the case studyarea. For example, Figures 5 and 6 show the spa-tial representation of the SCI with respect to eachmetallic pipe and overall composition of linguisticindices in the WSN, respectively. Further steps ofthis study will be scenario analysis of the model,validation of the model with recorded breakagerates of the pipes in the case study area and an ex-tension of this model to assess overall risk of metal-lic pipe deterioration and failure.SCI Very lowLowMediumHighVery highÜ0 5 102.5 KmsFigure 5: Spatial distribution of predicted SCI of metal-lic pipes in the city of Calgary3%21%12%21%43% VHHMLVLFigure 6: Composition of SCI result for metallic pipesof the city of Calgary.7. SUMMARY AND CONCLUSIONThe main objective of this paper was to identifythe soil parameters that contribute to soil corrosiv-712th International Conference on Applications of Statistics and Probability in Civil Engineering, ICASP12Vancouver, Canada, July 12-15, 2015ity and further use this information to predict theSCI. A combination of in situ collected data, expertknowledge and various literature were used to set-up the model node states and train the model. A de-tailed review was under taken to identify and definethe representative nodes of the SCI-BBN modeland their causal relationships and interdependen-cies among the nodes. A BBN sensitivity analy-sis was performed at the SCI node to determine theabsolute degree and rank order of influence of par-ent nodes (soil properties) on the child node (SCI).Finally, the model was used to predict the SCI ofmetallic pipes in the city of Calgary.This paper explicitly demonstrated the value ofcombining different information sources in real sit-uations (condition) where data scarcity is unavoid-able. The model can be used as an aid to implementthe rehabilitation and renewal plan of metallic pipesystems of any water utilities, with the understand-ing that this model needs either quality informationand/or qualified expertise in the field of soil corro-sivity. However, for this model to be effective, itneeds to be validated using recorded data, for in-stance, comparing the spatial distribution of pre-dicted SCI with a spatial distribution of recordedpipe breakage rates of the case study area.8. REFERENCESAEMC (2002). “Why measure soil resitivity?,< Retrived Arril 20, 2014>.AWWA (1999). “ANSI/AWWA C105/A21.5. AmericanNational Standard for Polyethylene Encasement forDuctile-Iron Pipe Systems.” Report No. 43105, Amer-ican Water Works Association, Denver.Barnard, M., Michael, A., and Oliver, G. L. (2005).“Corrosion and corrosion control of iron pipe.” Amer-ican Water Works Association, (June), 88–98.Brander, R. and Eng, P. (2004). “Minimizing failuresto pvc water mains.” Proceedings of Plastic Pipe XIIConference, Milan, Italy.City of Calgary (2014). “Calgary’s water supply,<>.Cunat, P.-J. (2001). “Corrosion resistance of stainlesssteels in soils and in concrete.” CEOCOR: comitéd’étude de la corrosion et de la protection des canal-isations. Journées plénières.Doyle, G., Seica, M. V., and Grabinsky, M. W. (2003).“The role of soil in the external corrosion of cast ironwater mains in toronto, canada.” Canadian geotech-nical journal, 40(2), 225–236.Ellis, B. and Wong, W. H. (2008). “Learning causalBayesian network structures from experimental data.”Journal of the American Statistical Association,103(482), 778–789.ESRI (2012). “ArcGIS 10.1.” ESRI (Environmental Sys-tems Research Institute).Fiedler, S., Vepraskas, M. J., and Richardson, J. (2007).“Soil redox potential: Importance, field measure-ments, and observations.” Advances in Agronomy, 94,1–54.Hubell (2003). “Step 7 - corrosion Guide.” Hubbell, Inc,<>.Kleiner, Y., Rajani, B., and Krys, D. (2010). Impactof soil properties on pipe corrosion re-examination oftraditional conventions. National Research Councilof Canada, Ottawa.Krieg, M. L. (2001). “A tutorial on Bayesian belief net-works.Najjaran, H., Sadiq, R., and Rajani, B. (2006). “Fuzzyexpert system to assess corrosion of cast/ductile ironpipes from backfill properties.” Computer-Aided Civiland Infrastructure Engineering, 21(1), 67–77.Norsys (2014). “Norsys software developement corp.,<>.Pearl, J. (1988). Probabilistic reasoning in intelligentsystems : Networks of plausible inference. San Fran-cisco, CA: Morgan Kaufmann.Pezeshki, S. and DeLaune, R. (2012). “Soil oxidation-reduction in wetlands and its impact on plant func-tioning.” Biology, 1(2), 196–221.Romanoff (1957). External Corrosion and corrosioncontrol of buried water mains (Re-Printed in 2004).AWWA Research Foundation, USA.Sadiq, R., Rajani, B., and Kleiner, Y. (2004a). “Fuzzy-based method to evaluate soil corrosivity for predic-tion of water main deterioration.” Journal of Infras-tructure Systems, 10(4), 149–156.Sadiq, R., Rajani, B., and Kleiner, Y. (2004b). “Prob-abilistic risk analysis of corrosion associated failuresin cast iron water mains.” Reliability Engineering &System Safety, 86(1), 1 – 10.Spickelmire, B. (2002). “Corrosion consideration forductile iron pipe.” Materials Performance, 41, 16–23.Tesfamariam, S. and Martín-Pérez, B. (2008). “Bayesianbelief network to assess carbonation-induced corro-sion in reinforced concrete.” Journal of Materials inCivil Engineering, 20(11), 707–717.8


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