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

Life-cycle robustness : quantification and challenges Wendner, Roman; Tamparopoulos, Alexios E.; Bergmeister, Konrad Jul 31, 2015

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12th International Conference on Applications of Statistics and Probability in Civil Engineering, ICASP12Vancouver, Canada, July 12-15, 2015Life–Cycle Robustness: Quantification And ChallengesRoman WendnerResearch Associate, Institute of Structural Engineering, University of Natural Resourcesand Applied Life Sciences, Vienna, AustriaAlexios E. TamparopoulosResearch Associate, Institute of Structural Engineering, University of Natural Resourcesand Applied Life Sciences, Vienna, AustriaKonrad BergmeisterProfessor, Institute of Structural Engineering, University of Natural Resources andApplied Life Sciences, Vienna, AustriaABSTRACT: Life-cycle robustness is achieved when a structural member or a system is designed tomaintain its intended function and required safety level within its desired life-cycle. The different charac-ter of effects that each element of the system needs to undergo (damage, ageing, extreme events, changesin usage) in conjunction with the diversity in the intrinsic material properties, form a demanding problem.Further complexity emerges when one realizes that time is not simply a variable, but a factor permeatingmodel choices and uncertainty representation approaches. Different effects in the load side, and proper-ties in the resistance side develop differently in time. Depending on the scale of the problem, the spatialrandomness of materials such as concrete may be relevant for the accurate quantification of failure prob-abilities, and may require careful modelling, even at a mesoscale. For a long-term analysis, where theinfluence of uncertainties may dominate over predictability, robust design concepts and analyses meth-ods that are relatively insensitive to small variations in variable inputs related to secondary effects andprocesses can prove decisive. On the computational side, challenges are associated with the computa-tional cost of simulations and nonlinear analyses required to determine time-variable reliability profiles,considering all likely scenarios. Furthermore, statistical characteristics of the inputs, in particular theirtail behaviour and their statistical dependence, needs to be properly captured and reproduced while main-taining sufficiently small sample size, and thus acceptable computational cost. Within this contribution, aframework for the quantification of life-cycle robustness is presented in the context of fasteners subjectedto sustained load and extreme events. The emerging challenges are presented and briefly discussed.1. INTRODUCTIONLife-cycle robustness aims to expand the conceptsof safety, sustainability and cost-efficiency of in-frastructure to include highly uncertain and unfore-seen events. In particular, it can be defined asthe ability of a component or a whole system tomaintain its intended function and required safetylevel in spite of damage, ageing, extreme events,or changes in usage throughout its life-cycle. Ro-bustness can have several different aspects, sinceit needs to include installation, operation, demoli-tion, and recycling phases. Each of these perspec-tives faces different challenges, as it is subjected todifferent actions and variations. A careful analysisand synthesis of those aspects reveals more chal-lenges and uncertainties, as the level of detail in-creases. It also discloses the weaknesses of somecurrently adopted assumptions in the context oflife-cycle evaluation and robust design approaches.In the present paper, the requirements of an inte-grated life-cycle robustness design and applicationframework, focusing on fastening systems are dis-112th International Conference on Applications of Statistics and Probability in Civil Engineering, ICASP12Vancouver, Canada, July 12-15, 2015cussed, the major challenges of this concept arebriefly reviewed, and the main expected prospectsthat arise from the application to fastening systemsare outlined (Wendner and Tamparopoulos, 2014).Finally, computational aspects of life-cycle robust-ness on fastening systems are presented.The requirements of life-cycle robustness on fas-tenings cover a broad range of topics that shouldbe addressed by an integrated approach. De-sign requirements aim at formulating consistent de-sign codes through experimentation and verifica-tion. Development may refer to new optimisedproducts, and accelerated production processes forexisting ones. Progress on this front is constantlyrequired, owing to new developments in construc-tion materials with largely unknown long-term be-haviour. Testing methods are required to investigatethe effect of geometrical and material properties,including ageing, on the load bearing capacity. It isimportant to verify numerical computations for thedifferent failure modes, types of systems, base ma-terials, and loading conditions. The type and vol-ume of acquired data often stress the need for dataanalysis methods that go beyond traditional statis-tical inference. In the installation procedure, par-ticularly in critical infrastructure, geometrical toler-ances, variations, and possible human errors need tobe taken into account. Adequate performance lev-els need to be prescribed, varying from serviceabil-ity to ultimate capacity. Sufficient safety marginsare required in order to ensure robustness through-out the whole service life, and issues related to pos-sible secondary consequences, progressive damageand disproportional failure effects should be inves-tigated. Sustainability in the disassembling and dis-posal process should include provisions that extendbeyond the anchor’s life time. Finally, many as-pects are of great importance with respect to cost(experimentation, intervention, optimised mainte-nance planning, rehabilitation, renovation, repair,replacement), when viewed over the intended lifes-pan.In each of the life-cycle robustness perspectives,different challenges may arise. As the level of detailin the investigation increases, more challenges anduncertainties can be disclosed. Temporal effects in-clude processes, actions, influences, and secondaryeffects that develop differently in time. System di-versity emerges from variations in the componentformulation, failure modes, geometry, cracking ofconcrete, reinforcement type, loading type, differ-ent base materials or intended applications. Perfor-mance is assessed in the regimes of small proba-bilities, where the influence of uncertainties can belarge; furthermore, nonlinear complexity, samplesize, model uncertainty, and possible dependencestructure can seriously affect computations. Uncer-tainties of various types are confined in the mechan-ical properties of materials, geometrical tolerancesand installation variations, extreme events, envi-ronmental influences, and degradation processes.Structural and statistical dependence may lead tounrealistic estimations, in particular in the area oflow target failure probabilities, when several inputvariables are considered. Multi-scale modelling ap-proaches aims to connect the two different perspec-tives, namely the macroscopic behaviour of fasten-ing systems, and the micro-scale properties of basematerials, e.g. concrete. The costs resulting fromthe sheer volume of required tests and from theequipment for performing non-destructive testingfor developing accurate models comprise a majorchallenge. A multidisciplinary approach is neededin order to develop an efficient life-cycle robustnessframework.There are several prospects of developing an in-tegrated multidisciplinary approach of life-cycle ro-bustness of fastenings. Firstly, incorporating state-of-the-art in research on concrete behaviour (creep,shrinkage, etc.) and on other base materials willallow for developing much more refined predictionmodels (Wendner et al., 2014). In this context, ex-isting research on physics and material science canbe utilised. The quest for performance-based de-sign concepts, transparent safety levels, and dura-bility can lead to processes that realistically simu-late the behaviour of fastening systems. Stochas-tic models for input variables in space and timeare constantly being developed (Eliáš and Vorˇe-chovský, 2012). Uncertainty importance analysesfocusing on the intended applications can indicatethe parameters that mostly influence the perfor-212th International Conference on Applications of Statistics and Probability in Civil Engineering, ICASP12Vancouver, Canada, July 12-15, 2015mance of fastenings in time. Thus, research effortscan be efficiently allocated to base material prop-erties, time effects, loading scenarios, fracture de-velopment, testing procedures, and representationof spatial or other variations. More practical andno less important prospects include the study ofinstallation, maintenance, repair, and replacementwithin a unified framework. Construction planningcan take great advantage of realistic evaluations ofsystem performance or cost efficiency. Fast and au-tomated construction techniques can be developed,and future market demands can be captured. Theassessment of existing fastening systems can sig-nificantly reduce cost and increase the reliability ofcomplex systems. Currently used reliability indicesreflect only the failure frequency and not the conse-quences of failure. On this front, utility-based per-formance and safety evaluation can facilitate fas-tening applications. In the next years, a more effec-tive use of new laboratory technology is expected.Accurate testing procedures can be formulated, fol-lowing the technological developments in data ac-quisitions equipment and the related analysis meth-ods.2. LIFE-CYCLE ROBUSTNESS QUANTIFICATIONFRAMEWORK FOR FASTENING SYSTEMS2.1. PreliminariesAnchorages are very important for integratingprecast elements, and for strengthening andretrofitting. They allow the connection of new loadbearing structural members with existing elements,as well as the installation of new, not structurallyrelevant, elements, e.g. sunshades. Therefore, fas-tenings are important for any adaptation of existinginfrastructure, and for the life-cycle design of newstructures. The economic significance of fasteningsis indicated by the fact that the potential damagecaused by failed fastening elements can be by sev-eral orders of magnitude higher than the value ofthe products themselves. It is also highlighted bythe use of fastenings as key-elements of critical in-frastructure, such as power plants, hospitals, andutility line systems.The current state of fastening technology reflectsonly 25 years of systematic research. So far, prac-tice has been limited to simple solutions, to naïvemethods for estimating lifetimes, to the assumptionof unreinforced concrete, and to mere addition—as opposed to realistic combination—of safety fac-tors. The load carrying capacity has been mostlystudied under static short-term but not under dy-namic loads. Deeper understanding regarding theload carrying mechanisms faces a number of chal-lenges. More accurate prognostic models can offeran optimised design of new fastening systems, anda reliable assessment of existing systems. There-fore, such models will facilitate efficient mainte-nance management over the full product lifetime.A fastening system is an arrangement of anchorsand other structural members formed into a broaderstructure. The performance of the system is deter-mined by the performance of its individual compo-nents, and by the arrangement layout. In the fol-lowing, we will confine ourselves to a single anchorsystem. In order to realistically assess and predictthe performance of anchors, and formulate modelsfor their life-cycle robustness, it quickly becomesevident that time is not simply a variable, but rathera factor permeating fundamental model choices anduncertainty representation approaches. In fact, thelife-cycle performance and robustness of fasteningsystems is influenced by several time-dependentprocesses, which alter the initially assumed me-chanical characteristics. Some of those effects de-velop monotonically in time—albeit not necessar-ily in a linear fashion—whereas others have a pe-riodical nature. Environmental influences may oc-cur due to concrete carbonation, chloride effects,steel corrosion, UV radiation, and freeze-thaw cy-cles. Concrete creep may have significant influ-ence on the long term performance; therefore, mod-els that accurately describe this phenomenon areneeded (Bažant, 2001). Random actions (imposedby fatigue, fire, earthquakes, explosions, traffic ac-cidents, etc.) cannot always be foreseen and mod-elled akin to the typically encountered loading sce-narios. Monitoring and updating of prediction mod-els can be challenging, since concrete fracture ini-tiates at a very low scale. Finally, possible conse-quences of ageing need to be investigated, not sim-ply in the narrowed view of the fastenings them-selves, but rather with respect to the broader system312th International Conference on Applications of Statistics and Probability in Civil Engineering, ICASP12Vancouver, Canada, July 12-15, 2015which they operate in.Life-cycle robustness design faces a multitude ofaleatory and epistemic uncertainties. The amountof deviation to be expected depends both on therandomness in the applied loads as well as on theamount of uncertainty in the mechanical propertiesof the used materials, due to inherent variabilitiesand heterogeneities. In fact, a significant part ofuncertainty can be attributed to the heterogeneity ofconcrete at lower scale, which is linked to a varietyof macroscopic effects during failure. However, themechanical properties of materials and members af-ter many years of operation are largely unknown.Further uncertainties arise from geometrical toler-ances and variations in the installation procedure.Tolerance against installation inaccuracies (installa-tion robustness) constitutes a major challenge. Fur-thermore, resistance against extreme events or envi-ronmental influences faces the problems of unpre-dictability and intangibles in the account of conse-quences. If the temporal dimension is added to theanalysis (as required for any life-time prediction)the uncertainty associated with the predicted meanresponse increases significantly with the time spanof extrapolation—in particular if degradation pro-cesses and extreme events are to be considered.2.2. Quantification of performanceThe aim of a quantification framework for life-cyclerobustness is to describe a model for the perfor-mance of fastening systems with changing prop-erties, subjected to uncertain load scenarios (sus-tained load and accidental events). The requirementthat resistance is not smaller than action (R ≥ S) isnot straightforward to solve in order to analyticallyobtain failure probabilities. Firstly, both resistanceR(t) and action S(t) are time-dependent. In addi-tion, at any given time t, the system state dependson the load history. This strongly affects, not onlythe resistance, but also the limit state that needs tobe solved to obtain failure probabilities. Hence, Rand S are generally not independent. Finally, thesystem state (reflected mainly as a result of age-ing and degradation) is governed by stochastic pro-cesses in concrete, steel or other materials, largelyunknown to date. Other problems associated withthe system setup include nonlinearity of the systembehaviour, effective load event combination, effi-cient sampling and simulation. A predictive modelcan be supported by observations on fracture or dis-placement to describe the transition of changes inload S to changes in resistance R.The resistance of the system can be written asR = R(t). To emphasise that R is not merely a deter-ministic function of time, but rather a random vari-able dependent on the variable mechanical proper-ties and the load history, one can write:R = R(t|L(t)) = R(t|x˜(t),Stτ=0) (1)where L(t) is the system state at time t, the vec-tor x˜(t) represents the mechanical properties at timet, and Stτ=0 expresses the complete load history.The vector of random mechanical properties x˜ ex-hibits three dimensions: the statistical variability(described e.g. by proper distributions and possi-bly a correlation matrix), the spatial variability (de-scribed e.g. by a random field), and a time depen-dence, since the properties change over time, whiledegradation occurs due to environmental influence.When field data, such as displacement measure-ments, are collected through monitoring, all thosetypes of uncertainties are involved in the observa-tions. Therefore, a mere collection of data is notsufficient, without studying the individual effectsand processes.In terms of remaining lifetime, reliability can bedefined as the probability that the system will per-form its intended function under specified designlimits (Pham, 2006). If T is the random variabledenoting the time-to-failure, with probability func-tion F(t), then the reliability of the system is:F¯(t) = P(T > t), t ≥ 0 (2)Damage models can introduce information on thelifetime T by describing the state of damage of thesystem at a given time t as a random variable Dt(Aven and Jensen, 2013). Then:T = inf{t > 0 : Dt ≥ Du} (3)Therefore, the lifetime is defined as the first timethe (total) damage reaches a given level Du. Here,Du can be a constant or, more general, a random412th International Conference on Applications of Statistics and Probability in Civil Engineering, ICASP12Vancouver, Canada, July 12-15, 2015variable independent of the damage process. In thatcase, the observed damage process does not carrythe entire information about the failure state. Dam-age can be viewed as a cumulative hazard affect-ing the system, and described as a non-decreasingstochastic process (Singpurwalla, 2010). This com-pound process can be viewed as a composition ofthree processes:1. A process X (1)t , representing the occurrence ofextreme loads;2. A process X (2)t , representing the damage evo-lution between X (1)t events;3. A process X (3)t , representing the possible dam-age owing to the occurrence of a X (1)t event attime t.For X (1)t a counting process with constant appear-ance rate λ (e.g. a Poisson process) can be used toexpress the occurrence of events in time:P[N(t + s)−N(t) = n] = e−λ s(λ s)nn!(4)where N is the number of occurrences. In the caseof the system of concern, one can assume more thanone independent processes, in place of X (1)t , to ac-count for the different event types (wind, extremetraffic load, snow, earthquake, etc.) In any case,the occurrence times are given by an increasing se-quence 0 < t1 < t2 < ... of random variables. Eachpoint t j corresponds to a random mark D j that de-scribes the additional damage induced by the jthload event.For X (2)t , the damage evolution between eventscan be modelled as a gamma process, where thenonnegative increments are assumed to be dis-tributed as gamma distributions (Phadia, 2013).Let G(α,β ) denote the gamma distribution withshape parameter α > 0 and scale parameter β > 0,α(t), t ≥ 0 be an increasing left continuous func-tion such that α(0) = 0. Moreover, let Xt , t ≥ 0be a stochastic process such that (i) X0 = 0, (ii) Xthas independent increments in non-overlapping in-tervals, and (iii) for t > s, the increment Xt −Xs isdistributed as G(c(α(t)−α(s)),c), where c > 0 isconstant. Then Xt is said to be a gamma processwith parameters, cα(t) (the mean of the process)and c (the precision or scale parameter). Gammaprocesses have an infinite number of incrementsin a finite interval of time, and are therefore suit-able for describing wear caused by continuous use(Singpurwalla, 2006).For X (3)t , the damage amounts D j induced by therandom events in the simplest case can be modelledas i.i.d. random variables. However, D j dependsalso on the current state of the system, and possiblyon the entire load history, thus:D j(t) = D j(t|x˜(t),Stτ=0) (5)The simulation of the aforementioned compoundprocess can be described as follows: At the timet = 0 the system has a residual damage capacity Duwhen it begins to operate under sustained load andundergoes wear e.g. due to ageing, described by astochastic process of the X (2)t type. The parame-ters of the process depend on the initial state of thesystem. At time t = t1, given by a process of theX (1)t type, an excessive load event occurs; at thispoint, the system state has suffered a damage D01due to ageing, and it has a residual damage capac-ity Du−D01. The extreme event induces a randomdamage D1 that depends on the load history andthe system state. The system undergoes a deteri-oration D12 until the next point t2 where an eventoccurs, inducing an additional damage, and so on.If the residual damage capacity is greater than theultimate level Du, then the process continues, untilfailure.A Monte Carlo simulation of this system canyield the distribution of lifetimes. The availabilityof the lifetime distribution that includes all typesof loading scenarios can allow for estimating safevalues, in the sense of statistical quantiles, with adesired confidence level.3. CONCLUSIONSIn recent years, steadily increasing budgetary con-straints have led to a strengthened awareness re-garding the importance of life-cycle performanceand cost considerations. The tight dependency of512th International Conference on Applications of Statistics and Probability in Civil Engineering, ICASP12Vancouver, Canada, July 12-15, 2015society with the proper functioning of infrastruc-ture, is linked to higher exposure and economic sig-nificance of structural systems. Life time design ofinfrastructure and extension of existing structureshas become increasingly important (Bergmeister,2012). Numerically and experimentally based reli-ability assessment methods with respect to differentactions have been developed (Strauss et al., 2013).However, up to now maintenance aspects hardly en-ter the decision process regarding the constructionof new buildings or structures. Moreover, most ofthe research progress in material science, in sophis-ticated testing procedures, or in uncertainty anal-ysis remain confined to simple theoretical concep-tions. In the present paper, the requirements of a de-sired framework for life-cycle robustness of fasten-ing systems were outlined. Addressing the emerg-ing challenges in this venture can pave the way tonew prospects and theoretical advancements as wellas to novel construction approaches.AcknowledgementsThe financial support by the Austrian Federal Min-istry of Economy, Family and Youth and the Na-tional Foundation for Research, Technology andDevelopment is gratefully acknowledged.4. REFERENCESAven, T. and Jensen, U. (2013). Stochastic Models inReliability. Springer, second edition.Bažant, Z. P. (2001). “Prediction of concrete creep andshrinkage: Past, present, future.” Nuclear Engineer-ing and Design, 203(1), 27–38.Bergmeister, K. (2012). “Life-cycle design for theworld’s longest tunnel project.” Life-Cycle and Sus-tainability of Civil Infrastructure Systems, Strauss, A.,Frangopol, D. M. and Bergmeister, K., eds., Vienna,Austria, Taylor & Francis Group, London, 51–59.Eliáš, J. and Vorˇechovský, M. (2012). “On the ef-fect of material spatial randomness in lattice simu-lation of concrete fracture.” 5th International Con-ference on Reliable Engineering Computing (REC2012), Vorˇechovský, M., Sadílek, V., Seitl, S., Veselý,V., Muhanna, R. L. and Mullen, R. L., eds.Phadia, E. G. (2013). Prior Processes and TheirApplications: Nonparametric Bayesian Estimation.Springer.Pham, H. (2006). Springer Handbook of EngineeringStatistics. Springer.Singpurwalla, N. D. (2006). Reliability and Risk: ABayesian Perspective. Wiley.Singpurwalla, N. D. (2010). “A new perspective on dam-age accumulation, marker processes, and weibull’sdistribution.” Advances in Degradation Modeling:Applications to Reliability, Survival Analysis, and Fi-nance, Nikulin, M. S., Limnios, N., Balakrishnan, N.,Kahle, W. and Huber-Carol, C., eds., Springer, 241–249.Strauss, A., Wendner, R., Bergmeister, K., and Costa,C. (2013). “Numerically and experimentally basedreliability assessment of a concrete bridge subjectedto chloride–induced deterioration.” Journal of Infras-tructure Systems, 19(2), 166–175.Wendner, R., Bergmeister, K., and Sandini, A. (2014).“Life–cycle robustness in fastening technology: Achristian–doppler laboratory.” Proceedings of the 4thInternational Symposium on Life-Cycle Civil Engi-neering, Tokio, Japan.Wendner, R. and Tamparopoulos, A. E. (2014). “Life–cycle robustness: prospects and challenges.” 6thInternational Conference on Reliable EngineeringComputing (REC).6


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