Estimating Life Expectancies of Highway Assets, Volume 2: Final Report (2012)

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9 2.1 A Review of Existing Techniques for Life Expectancy Estimation This chapter presents the definitions and measures of asset life expectancy, the highway asset life expectancy values established in past research and practice, the factors that can affect life expectancy, and the statistical and econometric tools that have been used to predict asset life. 2.1.1 Asset Life Definitions and Discussions Asset life in general refers to the time until an asset must be replaced due to substandard performance, technological obsolescence, regulatory changes, or changes in consumer behavior and values (Lemer, 1996). In assessing the life expectancy of highway assets, the asset manager needs to consider the primary reasons for which the agency replaces or retires the asset. These reasons may include 1. Accommodating demands of higher traffic volume from new economic development. 2. Meeting demands of heavier trucks. 3. Eliminating safety problems (e.g., poor alignment or narrow roadways and bridge decks). 4. Reducing the high maintenance costs associated with current design practices. 5. Changes in development patterns that render a road or structure no longer needed. 6. Eliminating potential vulnerability inherent in the current design (e.g., fatigue damage). 7. Eliminating potential vulnerability to extreme events (e.g., floods, earthquakes, or collision). 8. Addressing deterioration that is beyond cost-effective repair/rehabilitation. When designing a new road or bridge, agencies try to account for these factors using the best techniques available at the time. However, many of these factors will change during the asset lifespan, especially for long-lived facilities such as bridges. After a facility is in service, the agency tries to manage risk and deterioration through mitigation actions, maintenance, repair, and reha- bilitation. There are methods for forecasting these factors (e.g., NCHRP Report 495 for fatigue life, hydrological and seismic studies for extreme events, and deterioration models). Ideally, an agency strives to use all such techniques when considering how much longer an asset might last and what additional life might result from agency activity. For deterioration, the agency decision whether to rehabilitate or replace might be based on design details (e.g., access to the deteriorated area). For example, on trusses, the existence of pack rust (corrosion that is inaccessible under gusset plates) might be a reason to replace rather than repair. For pavements, the reason might be subgrade failure. If there is no functional reason to replace a facility, the agency will normally prefer to maintain it forever unless there is irreparable damage. In many cases the motivation to replace a facility is a combination of factors. It is often a matter of benefit/cost analysis in a context of funding constraints and competing projects. An agency C h a p t e r 2 Methodologies for Life Expectancy Estimation

10 estimating Life expectancies of highway assets might band-aid a facility for many years because of a lack of funding to replace it, when other parts of the network have more urgent needs. Asset life is an especially useful consideration for assets where the end-of-life factors listed above are not expected to come into play in the foreseeable future. The goal of the agency, then, is to extend service life indefinitely if possible, until one of the higher level considerations takes precedence. As such, asset life can be viewed from several perspectives as discussed below. • Physical life: The period of time in which the asset is physically standing, with any capabil- ity to provide any type of service. The asset may still physically exist at the site: for example an abandoned road, or a covered bridge that can safely carry pedestrians but can no longer carry vehicles, is still within its physical life; however a bridge that has collapsed, but is not yet removed is past its physical life. • Functional life: The period of time in which the asset satisfies all of its functional require- ments. Functional life may end due to deterioration, traffic growth, extreme events, or changes in requirements. Life extension activities may restore functional life (e.g., bridge widening) or may restore service life without extending functional life (e.g., structural repairs to a narrow bridge). • Service life: The period of time in which the asset is providing the intended type of service, even if at a degraded level of service. A bridge that is posted but open to traffic or a sign that fails retroreflectivity standards but is still in service are past their functional lives but have not reached the end of their service lives. • Economic life: The period of time in which it is economically optimal to keep the asset in service rather than retiring or replacing it. Economic life is a type of service life that takes into account funding constraints and the cost and effectiveness of life extension activities. In other words, it is sensitive to agency decisions. Service life is always less than or equal to physical life. Functional life is always less than or equal to service life. Economic life is usually less than or equal to service life, but may be greater if the facility is removed or replaced prematurely. The above definitions are structured according to the different criteria for end of asset life. Furthermore, the following distinctions are made: • Actual life: The known value of physical, functional, service, or economic life after the asset has actually been retired or replaced. • Estimated life: A forecast of future physical, functional, service, or economic life, which is prepared before the actual life is known. • Target life: A decision about the desired economic life that serves as a basis for planning of design or life extension ac • Design life: A specific type of estimated life and target life that entails a forecast and target for economic life established when the facility is designed. “Actual” and “estimated” can be adverbs applied to any of the asset life definitions (physical, service, functional, economic). Also, treatment life can be defined as the amount of life extension given by a specific treatment. This has to be qualified by the type of life (physical, service, functional, economic) and the per- spective (actual, estimated, target). For example, the physical life of a pavement may be extended by a structural overlay and the functional life of a narrow bridge can be extended by widening. In the Guidebook volume of this report, life expectancy is always an estimate or target, because it is derived from a forecasting and decision support tool. In most contexts in the Guide, asset

Methodologies for Life expectancy estimation 11 life expectancy is an estimate of future service life, taking into account foreseeable deterioration and life extension activities, but not taking into account traffic growth, changes in functional requirements, unforeseeable extreme events, or funding constraints. In the literature, there is also a concept of decay life. This is a life expectancy estimate that considers only deterioration and does not consider life extension activities. It is a notional quan- tity useful as an intermediate result in further life expectancy or lifecycle cost computations. It is most often used in contexts where the analysis period of a lifecycle cost model does not match with the life expectancy of the asset, because the analyst usually will not want to analyze life extension possibilities beyond the end of the analysis period. Other distinctions that are made in the Guidebook, for specific purposes: • Component life versus asset life: components of an asset often have shorter service lives than the asset overall. For example, a bridge deck or pavement wearing surface will have a shorter life compared to the overall bridge or pavement respectively. The Guidebook discusses how to manage component life and life extension activities so as to optimize lifecycle costs for the whole asset. • Asset life versus cohort life: policies of blanket replacement or interval replacement are based on a forecast of population distribution of service life, computed over a population of assets (a “cohort”). Service life is more often used at the asset level, while economic life is more often used at the cohort level, when blanket or interval policies are being considered. In this report, the asset life is referred to in the context of either the physical life or the func- tional life, depending on which asset type is being investigated and which method is being used (interval approach or condition approach) or the type of data available. Figure 1-4 illustrates the different relationships that could exist between the functional life and physical life definitions. C refers to asset construction, PF refers to physical failure of the asset, FF refers to the functional failure of the asset; in this figure, functional failure means end-of-life and is generally consistent with practices where the asset end-of-life is identified on the basis of functional performance criteria. In other practices, functional failure is not an end-of-life criterion but a criterion for identifying when some repair or expansion intervention is needed. In Figure 2-1 (a), the asset first reaches a point where it fails functionally; however, the asset is replaced only after several years; if the asset were not replaced in year AY, it is expected that it would suffer physical failure in year PF. This is the most common scenario for most assets at several agencies. However, in certain cases, a proactive agency can predict the year when the functional threshold will be reached and thus replace the asset before it reaches the threshold (see Figure 2-1 (b)) or just as it reaches the threshold (Figure 2-1 (c)). In Figure 2-1 (d), the asset is replaced a considerable length of time after it has failed both functionally and physically and may or may not have been used after these lives were reached. In certain cases, the asset suffers premature physical failure at year PF due to design or construction flaws, natural disaster, or manmade attacks, and thus is reconstructed; in this case, the anticipated physical life is the same as the actual (or observed) life. If the asset did not fail, it would have reached functional failure at the predicted year FF and physical failure at the design year, PF. The scenario in Figure 2-1 (f) is similar to that in Figure 2-1 (a) and (d) except that the asset replacement occurs at the point of physical failure but is similar to the scenario in Figure 2-1(e) because the actual physical life is the same as the anticipated physical life. For risk analysis for civil infrastructure assets, most existing literature on the subject has focused on physical life solely (Al-Wazeer, 2007). In this report, however, the risk analysis was carried out on the basis of both physical life and functional life because both of these concepts are relevant to asset planning and project programming: identification of the year of asset replace- ment and rehabilitation, and the subsequent agency tasks of work planning and budgeting are

12 estimating Life expectancies of highway assets possible only when the actual physical and functional lives are known with a satisfactory degree of confidence. 2.1.2 Measures of Asset Life A critical consideration in asset life expectancy analysis is the units in which asset life is to be expressed. The most common unit is the asset age in years. However, in recognition that aging is not the only factor of deterioration, asset life can be measured in other units, such as accu- mulated levels of vehicular use (e.g., ADT or VMT); accumulated traffic loading, which is often used for pavements and pavement markings, bridges, and large culverts; and, for all asset types, the accumulated climatic effects (Shekharan & Ostrom, 2002; McManus & Metcalf, 2003). (b)(a) (c) (d) (e) (f) Figure 2-1. Illustration showing different relationships between physical and functional life.

Methodologies for Life expectancy estimation 13 Measures of life expectancy that involve the volume of usage or loading or the climatic effects generally allow for a more profound investigation of the effects of these variables on asset longev- ity. In this report, asset life is expressed in terms of the age (years) of the asset since an agency- specified benchmark such as the initial construction or last reconstruction. This standard is adopted in full recognition that other rationales may exist that have motivated and will continue to motivate the need for carrying out some major action such as replacement/reconstruction or rehabilitation to renew the asset or to restore its functional performance. 2.1.3 Established Life Expectancy Values and Influential Factors In preparation for the development of asset life expectancy models in this report, a synthesis was carried out for the life values established in the literature for the different highway assets using various modeling methods and techniques. As expected, asset life estimates were found to vary significantly across highway agencies due to the differences in environmental conditions, administrative and cultural practices, maintenance strategies and techniques, and other factors. The following subsections present a review of the published literature on asset life expectancy values, most of which were either predicted using statistical models or subjectively estimated from surveys of experienced asset managers. The influential factors of asset life can be categorized as follows: asset characteristics (e.g., age, construction/design type, predominant material, and geometrics); site characteristics (e.g., climate, weather, and soil properties); traffic loading characteristics (e.g., traffic volume and percent trucks); and repair history (e.g., maintenance/rehabilitation intensities and frequencies). A review of such factors follows for each asset class. 2.1.3.1 Bridges Bridge Life Estimates. The actual or functional life expectancy of bridges has been found to vary across countries and across agencies. Some literature focused on the life of the entire bridge while other literature focused on bridge component longevity. In the literature, it is seen that the condition threshold adopted by the agency, as well as the intensity/type/frequency of maintenance and rehabilitation, play a large role in the documented or observed life expectancy of bridge components or bridges. Estes & Frangopol (2001) compiled bridge life expectancy estimates based on data and expert opinion and concluded that reinforced concrete decks survive between 24 to 48 years or 29 to 58 years if NBI condition rating thresholds of 4 and 3 are applied, respectively; steel railings survive 37 years (NBI rating 3 threshold) to 44 years (NBI rating 4 threshold); and reinforced concrete substructures survive 23 to 42 years (NBI rating 4 threshold) and 27 to 50 years (NBI rating 3 threshold). In Indiana, the life of concrete bridge decks was approximated at 50 years (NBI rating 4 threshold) to 60 years (NBI rating 3 thresholds) (Jiang & Sinha, 1989). In Canada, bridge decks have been found to survive 38 to 45 years (Morcous, 2006). In Florida, concrete decks were estimated to survive a maximum of 146 years; steel decks: 37 years; reinforced con- crete superstructures: 80 years (up to 335 years if prestressed); steel superstructures: 46 years; and substructures: 32 to 46 years depending on the painting regimen (Thompson, et al., 2010). In Massachusetts, a typical bridge life, excluding major maintenance, of 60 years was reported (Massachusetts Infrastructure Investment Coalition, 2005). In Colorado, the median bridge life has been estimated at 56 years (mean life = 76 years) with the deck component surviving 19 years (Hearn & Xi, 2007). Bridges with less common designs may have different life estimates. For example, in Chicago, bascule bridges were found to have an estimated life of 75 to 100 years (Zhang et al., 2008). Bridge decks with stainless steel reinforcement can be expected to last for 75 to 120 years (NX Infrastructure, 2008).

14 estimating Life expectancies of highway assets Bridge life is influenced by the maintenance and preservation history of a bridge. In Indiana, it was found that bridge life can vary between 35 and 80 years depending on the maintenance/ preservation activities performed (Cope, 2009; Sinha et al., 2009). For example, if a major repair (e.g., bridge rehabilitation) is carried out every 20 to 25 years, then a bridge life of 70 to 80 years can be expected in Indiana (Sinha et al., 2005). In Massachusetts, bridges were predicted to last 90 years with a preservation activity at year 35, or 110 years if rehabilitated at year 50 (Massa- chusetts Infrastructure Investment Coalition, 2005). In Indiana, it was estimated that, assuming minor maintenance, concrete and steel bridges would survive 50 and 65 years, respectively (Gion et al., 1993). International estimates of highway bridge life are generally similar. In Sweden, bridges are expected to survive 40 to 150 years—typically, a minimum of 50 years is assumed (Hallberg, 2005). In the Netherlands, bridges are typically designed to survive 80 to 100 years (van Noortwijk & Klatter, 2004). Bridge Life Expectancy Factors. Typically, life expectancy and deterioration models have been calibrated separately for each predominant material type (e.g., concrete and steel struc- tures). Of the models calibrated for concrete structures, the life expectancy factors have included the following: climatic conditions including freeze index and cumulative precipitation, geomet- rics (e.g., span length and number of spans), age (overall and since last treatment), construction technique, wearing surface type, bond strength of overlay with bridge deck, highway functional class, repair history, deck area and percent distressed area (based on spalling or delamina- tion), evaluation methodologies, traffic volume, wheel locations, and accumulated truck loads (Chamberlin & Weyers, 1991; Adams et al., 2002; Testa & Yanev, 2002; Rodriguez et al., 2005; and Chang & Garvin, 2006). The deterioration of concrete bridges has been linked to corrosion, fatigue, temperature, and/ or collision causing changes in strength and stiffness (Lin, 1995). Primarily, concrete deteriora- tion is caused by corrosion of reinforcement steel, which in turn is a function of the chloride concentration, diffusion coefficient, average depth of bar cover, size and spacing of reinforce- ment, concrete type, type of curing, amount of air entrainment, carbonation, and water-to- cement ratio (Estes & Frangopol, 2001; Adams et al., 2002; Kirkpatrick et al., 2002; Liang et al., 2002; Melhem & Cheng, 2003; Nowalk & Szerszen, 2004; Sohanghpurwala, 2006; Hearn & Xi, 2007; Oh et al., 2007; Wood & Dean, 2007; Daigle et al., 2008; and Parameswaran et al., 2008). Chlorides reduce the alkalinity of water solutions, leading to rust, which expands and causes a loss in the effective area of reinforcement, which can lead to distresses in the bridge deck. Chlo- ride content is a function of concrete age, roadway functional class, and salt rate from either bodies of water or de-icing chemicals during winter maintenance (Adams et al., 2002). Chloride content is considered “low” at concentrations less than 2.4 kg/m3, “moderate” when between 2.4 and 4.7 kg/m3, “high” when between 4.7 and 5.9 kg/m3, and “severe” when above 5.9 kg/m3 (Liang et al., 2002). In the case of steel bridges, deterioration and life expectancy have been analyzed on factors including bridge age, volume of truck traffic, truck size distributions, truck axle configuration and weight, cumulative precipitation, freeze index, road classification, type of wearing surface, degradation of individual component, fatigue durability, span length, and high temperatures (Lund & Alampalli, 2004; Lu & de Boer, 2006; Rodriguez et al., 2005; and Lipkus & Brasic, 2007). The main cause of deterioration in masonry arch bridges has been found to be axle loads (Narasinghe et al., 2006). 2.1.3.2 Culverts Culvert Life Estimates. The design life of culverts and storm drains is typically 50 to 70 years (Wyant, 2002). For these structures, a 50-year life was determined on the basis of labora- tory experiments on the corrosion rates of controlled low-strength material (CLSM) fixtures

Methodologies for Life expectancy estimation 15 (Halmen et al., 2008). A 2007 survey of agency estimates for culvert life expectancies indicated slightly lower values, typically ranging from 30 to 50 years for pipe and box culverts (Table 2-1). A 2003 study, however, showed greater variability in culvert life estimates, with predictions ranging from under 40 years to over 100 years, but with most falling between 50 and 80 years (Table 2-2). In comparing state agency estimates of pipe culvert life, it can be inferred that geographically related variations seem to have a significant effect on life. Wyoming DOT expert opinion has estimated the life of pipe culverts in the arid climate of that state at over 75 years (Kidner, 2009). In Florida’s wet and warm climatic conditions, metal and reinforced concrete culverts were estimated to survive 91 years and 208 years, respectively (Thompson & Sobanjo, 2010). In Oregon’s wet but cold climate, concrete culverts were found to have an expected life of 86 years (Hadiprono et al., 1988). In Missouri, culvert life was estimated at 45 to 50 years (Mis- souri Highway and Transportation Department, 1990). In New Jersey, culvert life estimates were found to vary greatly by material type: corrugated steel (30 years); concrete, iron, and aluminum (75 years); and brick/clay culverts (150 years) (Meegoda et al., 2008). In New York, steel pipe culvert life was found to range from 13 to 175 years depending on the geographic region, pipe size, and coating (coating life extension—25 to 35 years) (Wyant, 2002). From these studies, it can be generally inferred that culvert life is highly variable and depends on local conditions. There are relatively few guidelines for predicting culvert life. A survey by Wyant (2002) found that only 7 of 35 DOTs had guidelines for predicting the life of culverts; also, FHWA (2007) reported that several agencies seek models to predict culvert life. As such, the framework provided in later chapters of this report and the accompanying Guidebook are expected to be valuable to agencies that seek to predict culvert life. Pipe Culverts Box Culverts Material Number of Responding Agencies Median Life (years) Material Number of Responding Agencies Median Life (years) Concrete 13 50 Reinforced concrete 15 50 Corrugated metal 16 35 Timber 3 30 Asphalt-coated corrugated metal 5 50 Precast reinforced concrete 1 50 Small diameter plastic 7 50 Polyvinyl chloride 1 50 High-density polyethylene 1 50 Aluminum alloy 1 50 Table 2-1. Survey results for culvert life expectancy estimates for pipe and box culverts (Markow, 2007). No. of Responding Agencies Indicating Assumed Life Range by Pipe Type Life of Pipe Culvert RCP NRCP CMP HDPE PVC < 40 years 1 40 – 50 yrs 3 50 – 60 yrs 2 4 5 3 3 60 – 70 yrs 2 70 – 80 yrs 8 2 4 3 1 80 – 90 yrs 1 1 1 90 – 100 yrs ≥ 100 yrs 4 2 2 1 Total 17 8 13 9 6 Table 2-2. 2003 survey of life expectancy estimates for pipe culverts (Perrin Jr. & Jhaveri, 2004).

16 estimating Life expectancies of highway assets Culvert Life Expectancy Factors. In past studies, factors found to be significant in influ- encing culvert life included culvert age, culvert material type, backfill material type, presence of any pipe protection coatings or systems, pipe flow conditions, pH and electrical resistivity of the backfill soil, pH of the flowing water, chloride content, frequency and intensity of culvert inspec- tions or maintenance, presence and type of culvert coating, and topography (flat versus rolling) (Beaton & Stratfull, 1962; Gabriel & Moran, 1998; California Department of Transportation, 1999; Sagues et al., 2001; Wyant, 2002; Halmen et al., 2008). In certain cases, failed culverts are not reconstructed but closed/filled and left in the field, and a new culvert is constructed near the original location. This action is adopted in cases of serious blockages directly influenced by the opening size and flooding potential (Rigby et al., 2002). Mechanistic studies have found that significant life expectancy factors include the amount of fill; level of antioxidants in the soil; soil compaction; condition state of joints, gaskets, and connections; and deflection of the pipe system (Hsuan, 2010; Pluimer, 2010). 2.1.3.3 Traffic Signs Traffic Sign Life Estimates. In the literature, the life of traffic signs has been carried out from the standpoint of functional performance rather than physical condition and, more specifically, on the basis of the measured retroreflectivity. Often, the life has been established based on dif- ferent sheeting colors; in Oregon, the ASTM, state, and FHWA standards were used to establish the life of traffic sign sheets (Table 2-3). A study on traffic sign assets in North Carolina determined that the performance of these assets generally falls below the FHWA performance standards established for that asset type at ages 8 and 15 years (Immaneni et al., 2009). Considering the high cost of measuring retroreflectivity, some agencies prefer to use assumed point estimates of the life of these assets, which has resulted in blanket cohort replacements at fixed intervals. For instance, the Indiana Department of Transportation (INDOT) has a pol- icy of replacing traffic signs every 10 years, pending no measured violation of the MUTCD retro reflectivity requirements (INDOT, 2008; INDOT). MNDOT replaces signs every 12 years (Nelson, 2011). The Delaware, Kansas, Maine, and North Dakota DOTs assume a life of 10 to 12 years (Wolshon et al., 2002). Also, Indiana, Michigan, and North Carolina are considering mov- ing to a 15-year replacement policy for beaded high-intensity materials (Wolshon et al., 2002). Traffic Sign Life Expectancy Factors. For traffic sign structures, the life expectancy factors in past research have included the structure type (e.g., single or double mast-arm cantilevers, box-trusses, tri-chord, and monotube), natural wind loading characteristics (e.g., direction and strength of local winds), truck-induced wind gusts, and nature of connections (e.g., welded and threaded). For traffic sign sheeting performance, considerations have included age, sheeting grade and type, sign size, roadway speed limit, color, precipitation, orientation to the sun and traffic, and proximity to the roadway (Black et al., 1991; Black et al., 1992; Paniati & Mace, 1993; Hawkins Jr. et al., 1996; Kirk et al., 2001; Hawkins Jr. & Carlson, 2001; Wolshon et al., 2002; AASHTO, 2003; and Hildebrand, 2003). Sheeting Color Retroreflectivity Threshold (cd/lx/m2) Life Estimate (years) White 200 – 250 30 – 70 Yellow 135 – 170 30 – 55 Green 35 – 45 5 – 7 Red 35 – 45 5 – 8 Table 2-3. Oregon traffic sign life estimates by sign sheeting and retroreflectivity thresholds (Kirk et al., 2001).

Methodologies for Life expectancy estimation 17 2.1.3.4 Pavement Marking Pavement Marking Life Estimates. Similar to traffic signs, pavement marking life refers to functional life and not physical life because pavement marking life is often based on retroreflec- tivity performance. Such performance often varies by material type. At least one study found that paints have a life of 6 to 12 months, and thermoplastics, 3 to 7 years (Abboud & Bowman, 2002). Generally, similar results were found using 100 to 120 mcd/m2/lux thresholds: 1 to 2 years of life was found for waterborne paints and 4 to 5 years for thermoplastics (Zhang & Wu, 2006). Pavement Marking Life Expectancy Factors. Pavement marking life expectancy factors were found to include the material type, bead gradations, installation application rates and qual- ity, color, pavement surface type, roadway position (e.g., centerline, edge), climatic conditions (e.g., annual precipitation), frequency of snow plowing, sun exposure, traffic volume and vehicle class distribution, and traffic speed (e.g., life varies between constant sections and acceleration/ deceleration sections) (Bowman et al., 1992; Fish, 1996; Harrison & Thamer, 1999; Henry et al., 1999; Migletz et al., 2001; Migletz & Graham, 2002; Parker, 2002; Parker & Meja, 2003; Kopf, 2004; Zhang & Wu, 2006; Jiang, 2008; Lee et al., 2008; Maurer & Bemanian, 2008; and Sathy- anarayanan et al., 2008). 2.1.3.5 Pavements Pavement Life Estimates. Pavement life expectancy generally refers to a functional life when the intended action at the end of life is one that restores the functional adequacy of the pavement and generally refers to actual life when the intended end-of-life action provides a completely new pavement. Pavement life varies by material type: rigid pavements (Portland cement concrete) are generally expected to outlast flexible pavements (asphaltic). From the perspective of functional life, some studies have provided a range of values: an overall assessment of rigid, composite, and flexible pavements produced a range of asset life values from 6 to 20 years (Lee et al., 2002). Rigid pavements in particular have been found to last approximately 16 to 20 years before joint faulting exceeds 0.1 inch, slab cracking exceeds 12% cracked area, and IRI exceeds 160 in/mi (Flom & Darter, 2005); in certain agencies, these thresholds are established to trigger some preservation action. Flexible pavements in Ohio were found to have an average life of 9 years (Yu, 2005) or 12 to 15 years when a PCR threshold of 60 was assumed (Chou, Pulugurta, & Datta, 2008). Flexible pavements in Kansas were estimated to survive up to 8 years, with end of functional life determined by the level of rutting, transverse cracking, and fatigue cracking level (Gedafa et al., 2009). Pavement Life Expectancy Factors. Pavement life expectancy factors have included sur- face type (rigid, flexible, and composite) and thickness, construction quality, traffic loading and speeds, structure and overlay age, accumulated climate effects, subgrade moisture condi- tions, and frequency and intensity of pavement maintenance and rehabilitation (Attoh-Okine & Roddis, 1994; Vepa et al., 1996; Baker et al., 1998; and Gharaibeh & Darter, 2003). For pave- ments constructed using bituminous asphalt mixes, various factors related to fatigue failure have been identified to be influential to life expectancy (Coetzee & Connor, 1990; Breysse et al., 2005). Environmental effects such as temperature, temperature gradient in the asphalt, and the timing and duration of wet base and subgrade conditions have similarly been found significant for flex- ible pavement life (Zuo et al., 2007). The life expectancy of pavements constructed using porous asphalt has been found to be influenced by mixture properties (Miradi & Molenaar, 2007). The quality and characteristics of aggregates, level of bonding, layer properties, and degree of compaction have also been found to significantly affect the life of asphaltic pavement (Witczak & Bell, 1978; Noureldin, 1997; and Ziari & Khabiri, 2007). Due to such characteristics, differ- ent asphalt mixtures have different life expectancies (e.g., dense-graded conventional asphalt

18 estimating Life expectancies of highway assets concrete and gap-graded asphalt rubber hot mix); and the quality and thickness of the pavement base material have also been identified as influential (Raad et al., 1993; Romanoschi et al., 1999). Similar factors were found in the study by von Quintus et al. (2007) of hot mix asphalt pavement life. For non-overlaid continuously reinforced concrete pavements, early age crack distribu- tion patterns, coarse aggregate type, and the presence of a swelling subgrade have been found significant for predicting remaining life (Easley & Dossey, 1994; Dossey et al., 1996). Addition- ally, pavement life has been linked to traffic speed, precipitation, and drainage (Huntington & Ksaibati, 2007). Pavement studies of asset life expectancy have applied various end-of-life definitions. Com- mon condition/performance measures used to estimate functional life include pavement struc- tural condition (PSC), visual condition index (VCI), distress points/index (particularly rutting, punchouts, transverse, fatigue, and D-cracking distresses), pavement quality indicator (PQI), measures of roughness [e.g., IRI, dynamic load index (DLI), and road quality index (RQI)], effective structural number, and centerline deflection (Fwa, 1991; Attoh-Okine & Roddis, 1994; Henning et al., 1997; Baker et al., 1998; Abdallah et al., 2000; Kuo et al., 2000; Lee et al., 2002; Al-Suleiman & Shiyab, 2003; Gharaibeh & Darter, 2003; Baladi, 2006; Huntington & Ksaibati, 2007; Chou et al., 2008; and Gedafa et al., 2009). 2.1.3.6 Traffic Signals Traffic Signal Life Estimates. For traffic signals, a life expectancy of approximately 15 years was found from a survey of transportation agencies by Markow (2007) (Table 2-4). Flashers are assumed to have similar life expectancies. Review of Traffic Signal Life Expectancy Factors. Factors influencing traffic signal head life have been found to include localized wind/gust strength, dominant wind direction with respect to the signal orientation, structure material type, type of structural connections, and climatic and weather factors (South, 1994; Chen et al., 2001; Kloos & Bugas-Schramm, 2005; Lucas & Cousins, 2005; Schrader & Bjorkman, 2006; Markow, 2007). 2.1.3.7 Roadway Lighting Roadway Lighting Life Estimates. Markow (2007) conducted a survey of agencies on the actual (physical) lives of roadway lighting structures and subsequently established typical estimates that vary between 25 and 30 years (Table 2-5). As stated in a subsequent chapter of this report, Component Nr. of Responding Agencies Median Life (yrs) Structural System Tubular steel mast arm 14 20 Tubular aluminum mast arm 7 20 Wood pole (and span wire) 9 15 Concrete pole (and span wire) 2 12.5 Steel pole (and span wire) 9 20 Galvanized pole and span arm 1 >100 Controller System Permanent loop detector 14 7.5 Non-invasive detector 12 10 Traffic controller 18 15 Traffic controller cabinet 17 15 Twisted copper interconnect cable 11 20 Fiber optic cable 7 2 Signal Display System Incandescent lamps 15 1 Light-emitting diode lamps 18 6.5 Signal heads 15 20 Pedestrian displays 1 15 Table 2-4. Survey of life expectancy estimates for traffic signals (Markow, 2007).

Methodologies for Life expectancy estimation 19 higher life estimates were found for roadway lighting structures using historical data. The lower estimate from expert opinion is probably indicative of the need for improved recordkeeping and data analysis to replace expert opinion or to revise expert opinion predictions. In addition to the surveyed agencies in Markow (2007), New Jersey and Ohio estimate lamp life at 2 to 5 years and 5 to 6 years, respectively (Zwahlen et al., 2003; Szary et al., 2005). In New Jersey, roadway lighting components were estimated to survive 8 to 10 years for batteries and 6 to 24 years for structural systems (Szary et al., 2005). Roadway Lighting Life Expectancy Factors. Significant factors in roadway lighting life have included the pole/bulb type, temperature extremes, and other environmental factors (Zwahlen et al., 2003; Szary et al., 2005). 2.1.4 Methods for Estimating Life Expectancy Both empirical (statistical-evidence-based) and mechanistic (physical-based) models have been applied in the literature of life expectancy estimation. This volume of NCHRP Report 713 focuses on empirical models. However, for the sake of completeness of the information search, mechanistic approaches are summarized below. 2.1.4.1 Mechanistic Methods for Estimating Life Expectancy Mechanistic methods generally involve the use of field or laboratory tests, which can be destructive or non-destructive, to measure a physical property, such as corrosion, stress, or strain of an asset or component thereof. Theories regarding material behavior are then applied to extrapolate fatigue or physical life information. For concrete structures, for example, mecha- nistic approaches and applications that have been used in past research for predicting the life of an asset or its structural components are described in Table 2-6. Of the mechanistic-based methods in Table 2-6, asset life is commonly predicted as a function of corrosion, particularly for assets such as reinforced-concrete box culverts that are susceptible to this mode of deterioration. Corrosion occurs in three stages (Liang et al., 2002): 1. Initiation time—the time for chloride ions to penetrate the concrete surface and onto the passive film surrounding the reinforcement; Component Nr. of Responding Agencies Median Life (yrs) Structural System Tubular steel 12 25 Tubular aluminum 9 25 Cast metal 2 22.5 Wood posts 2 32.5 High mast or tower 11 30 Lamps Incandescent 3 1 Mercury vapor 6 4 High-pressure sodium 15 4 Low-pressure sodium 3 4 Metal halide 9 3 Fluorescent 1 5 Other Components Ballast 9 7.5 Photocells 11 5 Control panels 7 20 Luminaires 2 16.25 Table 2-5. Survey of life expectancy estimates for roadway lighting (Markow, 2007).

20 estimating Life expectancies of highway assets Method R eferences in (Liang et al., 2002) P hysical-mathematical m odel Bazant (1979a,b) A ccelerated durability test method Fagerlund (1979) E valuation of parameters of deterioratio n C ady & Weyers (1984) A ccelerated test and mathematical model Influence or Application Predicted time of t p and t cor Prediction of the service life of a structure depended on minimum load-carrying capacity, maximum acceptable deformation, and permeability Use in formulating repair rehabilitation, replacement policy, underestimated value of t cor Prediction of concrete service life P o mmersheim & Clifton (1985) Probabilistic view Prediction of service life of building materials and component s Sjostrom (1985) Failure probability esign life and durability of concrete structures Somerville (1986) Survey data of bridge decks exposed to deicing salt, coastal buildings, and offshore structures Predicted initiation time Guirguis (1987) “Systematic” approach D S ervice life prediction of building and construction material s Masters (1987) Unsteady-state dynamic analysis (using the semi - infinite solid approximation and the Laplace transform. method) Service life prediction for external vertical walls of RC with external thermal insulations Fukushima (1987) M odified version of Bazant's model Predicted time of t p S ubramanian & Wheat (1989) Predictive service life test, aging test, and mathematical model Service life prediction of building materials and component s Masters & Brandt (1989) E xperimental and field tests Prediction of corrosion depth in concrete Tsaur (1989) E xpanded and Bazant model Prediction of the t p time, the corrosion cracking time, the breaking time of bond between concrete and steel, and the steel area losing time Liu & Mian (1990) A llowable limit and the state of corrosion Prediction of service lives of RC buildings, but the predicted results are always overestimated Predictive service life tests and long term aging, and in- use conditions Systematic methodology for the prediction of service life of building materials and components Morinaga (1990) Sjostrom & Brandt (1990) Mathematical deterioration model expressed the property changing as a functio n of solar ultraviolet rays, heat, and degradation factors Service life prediction system of building materials Tomiita (1990) Mathematical model consists of the assessment of the annual total damage ratio and the esti mati on of the service life To estimate the service life of a bituminous glass-fiber- reinforced multiple waterproof roofing element Ahoz & Akman (1990) Probabilistic approach Service life prediction of ferrocement roof slabs Quek et al. (1990) E xperience, deduction, accelerated testing, mathematical modeling, reliability, and stochastic concept Predicting the service life of concrete Clifton (1990, 1991, 1993) Measurement of the corrosion rate of reinforcing steel Prediction of service lives of RC building Morinaga (1990) A ccelerated corrosion tests and field measurement Measure the rate of steel corrosion in concrete Harn et al. (1991) Gray theory Li (1992) Implementation of Tuntti's m odel [considers effect of temperature, chloride proportion, & humidity in concrete pores (resistivity)] Influence of temperature on the service life of rebars Lopez et al. (1993) Predicts remaining service life of harbor structures Table 2-6. Mechanistic methods for predicting concrete structure life (Liang et al., 2002).

Methodologies for Life expectancy estimation 21 Method Influence or Application References in (Liang et al., 2002) Probability method Service life prediction of existing concrete bridges Qu (1995) Reliability approach chloride ions Prezzi et al. (1996) Fick's second law Predicts service life of concrete structures exposed to Predicts service life of existing concrete exposed to marine environments Maage et al. (1996) Testing, structural, and economic models Service life of existing RC structures Henriksen (1996) Generalization of Markov Chains based on time- dependent reliability theory Prediction of bridge service life Ng and Moses (1996) Long-term economic analysis Service life prediction of concrete road bridges Brito & Branco 1996) Calculation of prestressing cable forces from vibro- wire gauges embedded in bridges Service life prediction of prestressed concrete cantilever bridge Javor (1996) Corrosion damage prediction using electrical potential surveys Service life prediction of concrete bridge deck Kriviak et al. (1996) Utilization of measured stress spectra for predicting fatigue accumulation and crack propagation Service life evaluation of steel or composite bridge; influence of the effective traffic loading on structures Baumgartner et al. (1996) Established a computer- integrated knowledge system Predicting the service life of steel-RC exposed chloride ions Bentz et al. (1996) In situ permeability and strength testing Develop the durability-based design criteria for concrete and assess the remaining life of existing structures Long & Rankin (1997) Cumulative damage theory and accelerating the corrosion of rebar in concrete Service life prediction of rebar-corroded RC structure Ahmad et al. (1997) Mathematical model for accelerated testing for concrete structures in chloride laden environments Predicting the initiation time of concrete structures Liang et al. (1997, 1999a) Mathematical model combined Fick's second law with durability coefficient Predicting the service life of existing RC bridges due to carbonation Liang et al. (1998, 1999b) Time-variant reliability method, Monte-Carlo simulation for finding the cumulative-time system failure probability Service life prediction of deteriorating concrete bridges Enright & Frangopol (1998) Fick's second law incorporated surface environment, chloride transport, temperature of surrounding medium, seasonal effects, and construction variability Predicting the service life of a RC structure in different environments Amey et al. (1998) FBECR (fusion-bonded epoxy-coated reinforcing steel) as a physical chloride barrier system FBECR is not a cost-effective corrosion protection system when compared with bridges built with bare steel in Virginia, because they only provide corrosion protection for 5% of VA's bridge decks Weyers et al. (1998) Time-to-cracking model based on elasticity Corrosion cracking model is dependent on the cover depth, the properties of the concrete and steel/concrete interface, the type of corrosion products, and the size of the reinforcing steel, and is a function of the critical weight of the rust products and corrosion rate Weyers (1998), Liu & Weyers (1998) Time-dependent reliability Service life assessment of aging concrete structures Mori & Ellingwood (1993) Table 2-6. (Continued).

22 estimating Life expectancies of highway assets 2. Depassivation time—the time for the chlorides, transported to the steel by the alkaline hydrated cement matrix, to locally destroy the passive film, leading to pitting corrosion; and; 3. Propagation or corrosion time—the time when corrosion products form and cracking, spall- ing, or sufficient structural damage occurs. Generally, the first two stages are modeled together and can jointly be considered as the ini- tiation time. Attempts to model these time stages are shown in Table 2-7; the asset life is then determined as the sum of the two time periods. Time Prediction Method Formula Reference in (Liang et al., 2002) Initiation Time , t p W eyer s W eyers (1998) LZCL Liang et al. (2001) H ookham H ookham (1992) AJMF Amey et al. (1998) Propagation time, t cor Bazant Bazant (1979b) M odified Bazant Liang et al., 2002 CW C ady & W eyers (1984) Li u Liu (1996) Faraday’s Law Fontana (1987) M angat & Elgarf (1999) Initiation Time , t p Guirgui s Guirguis (1987) Bazant Bazant (1979b) NOTES: C(x,t) = Chlorine content at depth x and time t,; C i = initial Chlorine content of the concrete; C s = Chlorine content of the exposed concrete surface; = Concrete surface concentration coefficient of chloride ions; erf = error function; erfc = complementary error function; k, = Constants; D c = Chloride diffusion coefficient; t co r = corrosion; propagation time; t 1 = corrosion initiation time; t = Total service life of RC structures, t = t 1 +t co r ; Z = Valency of the reacting electrode (steel); F = Faraday’s Constant; st = Density of material (steel); r = st /4; = Density of corrosion product; δ = Material (steel) loss; s = Spacing of bars; A = Atomic weight of iron; L = Concrete cover thickness; Constant; D = Original bar diameter; = Critical value of that produces inclined cracks; = Rate of rust production per unit area; = Bar hole flexibility; = Tensile strength of concrete; = Corrosion current density ; = Thickness of pore band around the steel/concrete interface ; = Threshold value of the chloride concentration ; = Concentration of chloride ions in pores of concrete at the surface. Table 2-7. Prediction of corrosion time stages (Liang, Lin, & Liang, 2002).

Methodologies for Life expectancy estimation 23 The more common techniques for predicting corrosion stage times are Fick’s law (Daigle et al., 2008) and Weyers technique [as used in NCHRP Report 558 (Sohanghpurwala, 2006)]. To slow chloride’s ingress into concrete structures, asset managers have used low-permeability concretes, polymer overlays, deck sealers, increased concrete cover depth, and cathodic protection and have investigated alternative reinforcements (Kirkpatrick et al., 2002). For steel structures, fatigue is more commonly used as a basis for estimating life. Previous experimental studies analyzing fatigue with accelerated loading have included the application of vibration theory, fatigue damage theory, fracture mechanics, the Palmgren-Miner linear damage equation, Miner’s hypothesis test, and finite element-based methods (Coetzee & Connor, 1990; South, 1994; Romanoschi et al., 1999; Lund & Alampalli, 2004; Breysse et al., 2005; Lu & de Boer, 2006; Lipkus & Brasic, 2007; Zuo et al., 2007; Samson & Marchand, 2008). A common method of assessing fatigue involves the use of Miner’s Hypothesis (Tanquist, 2002): n N Ci ii k = = ∑ 1 where n represents the accumulation of loads over cycle i, N represents the maximum allowable load cycles, and C represents the fractional life when C is assumed to be 1. The fatigue life of steel bridges can also be calculated using the AASHTO Guide Specifications for Fatigue Evaluation of Existing Steel Bridges (AASHTO, 1990), which has been used to model the time until an end-of-life criterion occurs (Lund & Alampalli, 2004; Metzger & Huckelbridge Jr., 2006). Another common technique in bridge life estimation is reliability analysis. This term is generally considered synonymous with the empirical techniques that involve survival analysis. However, in the bridge field, the term reliability pertains to some probabilistic, time-variant index based on the interplay between structural resistance, such as shear and moment strength, reinforce- ment strength, spacing, and diffusivity, governed by the LRFD (AASHTO, 2010) on one hand, and demand (e.g., traffic volume or truck weights) on the other hand. The life of the asset is taken as the time until the index reaches a pre-specified target level. These indices can be applied to the overall structure or to multiple bridge components. Studies that examined bridge reliability, par- ticularly with the incorporation of probabilistic material strengths, include Lin (1995), Deshmukh & Bernhardt (2000); Lounis (2000), Akgul & Frangopol (2004), Stewart et al. (2004), Biondini et al. (2006), Saber et al. (2006), Oh et al. (2007), and Strauss et al. (2008). Mechanistic models are typi- cally calibrated using laboratory or field experiments under controlled and accelerated conditions that simulate the deterioration of long-lived assets (Roesler et al., 1999). The reliability of these tests, however, is influenced by the extent to which they mimic real-world conditions. For the purposes of asset management and network-level planning, empirical methodologies, rather than purely theoretical relationships, for life expectancy estimation are considered more appropriate for the practice and consequently is the focus of the analysis in this volume of NCHRP Report 713. 2.1.4.2 Empirical Methods for Estimating Life Expectancy Empirical modeling techniques for estimating life, either directly or via deterioration levels can be divided into four categories. Studies that have used these categories for estimating asset life are as follows: • Statistical regression – Bridges: Polynomial functional form (Agrawal & Kawaguchi, 2009); – Culverts: Linear, log-linear, and exponential functional forms (Hadiprono et al., 1988; Kurdziel & Bealey, 1990; and Halmen et al., 2008);

24 estimating Life expectancies of highway assets – Traffic Signs: Linear, power, exponential, and power functional forms (Kirk et al., 2001; Bischoff & Bullock, 2002; and Immaneni et al., 2009); – Pavement Markings: Exponential and smoothing spline functional forms (Abboud & Bowman, 2002; Zhang & Wu, 2006); – Pavements: Linear, polynomial, exponential, log-linear, power, and sigmoidal functional forms: (Labi, 2001; Lee et al., 2002; McManus & Metcalf, 2003; Flom & Darter, 2005; Yu, 2005; Chou et al., 2008; and Gedafa et al., 2009); – Roadway Lighting: Exponential functional form (Szary et al., 2005). • Markov chains – Bridges: (Jiang & Sinha, 1989; Ng & Moses, 1996; Estes & Frangopol, 2001; Zhang et al., 2003; Hallberg, 2005; Morcous, 2006; Ertekin et al., 2008; and Robelin & Madanat, 2008); – Pavements: (Chou et al., 2008). • Duration models – Bridges: Weibull, Exponential, Rayleigh, and Gamma survival models (Ng & Moses, 1996; Klatter & Van Noortwijk, 2003; van Noortwijk & Klatter, 2004; Hearn & Xi, 2007; Nicolai, 2008; Agrawal & Kawaguchi, 2009); – Pavement Markings: Weibull survival models (Sathyanarayanan et al., 2008); – Pavements: Kaplan-Meier estimate, Cox proportional hazards model, and normal, log- normal, exponential, log-logistic, and Weibull survival distributions (Vepa et al., 1996; Colucci et al., 1997; Eltahan et al., 1999; Romanoschi et al., 1999; Shekharan & Ostrom, 2002; Gharaibeh & Darter, 2003; Bausano et al., 2004; Yu, 2005; Yang, 2007; Yu et al., 2008; Anastasopoulos, 2009; and Irfan et al., 2009); – Culverts: Normal and Weibull survival distributions (Halmen et al., 2008; Meegoda et al., 2008); – Roadway Lighting: Kaplan-Meier estimate (Zwahlen et al., 2003). • Machine learning – Bridges: k-nearest neighbor inference-based learning, inductive learning, and artificial neural networks (Melhem & Cheng, 2003; Narasinghe et al., 2006); – Traffic Signs: Artificial neural network (Swargam, 2004); – Pavements: Artificial neural network (Flintsch et al., 1997; Ferregut et al., 1999; and Abdallah et al., 2000). Generally, it was found that statistical regression is the technique that has been most com- monly applied to predict the performance of relatively less-costly assets such as traffic signs, pavement markings, and pipe culverts. Markov chains applications have been limited mainly to pavements and bridges, likely because their calibration requires extensive inspection rating data. Various survival models have been applied to explain pavement life while structural reliability analysis has been more commonly used for predicting bridge life. Of the survival models, the Weibull distribution is widely used across all asset classes. Machine learning has been applied primarily to bridges and pavements, but to a lesser extent than the other approaches, likely because such estimates are perceived as coming from a “black box.” A more extensive treatment of the probabilistic approaches theory is provided in Section 2.2.4. 2.2 Methodology for Estimating Asset Life In building on the literature, one of the goals of this study was to develop an overarching methodology that could be applied to various asset classes in order to predict highway asset life expectancy. For the methodology used in this study (Figure 2-2), each step is discussed in subsequent subsections.

Methodologies for Life expectancy estimation 25 2.2.1 Identify Replacement Rationale The first step in the developed methodology for predicting asset life expectancy is to identify the rationale for the asset replacement. As discussed in a previous section of this volume of NCHRP Report 713, such rationale may generally include structural adequacy and safety, ser- viceability and functional obsolescence, essentiality for public use, and special reductions. For competing rationales, multiple life estimates can be established for the purposes of comparison. 2.2.2 Define End-of-Life On the basis of the selected rationale, the next step is to select a representative condition or performance measure pertinent to the asset replacement rationale under consideration. Where end-of-life refers to functional life, an appropriate measure of functional performance and an agency-specified performance threshold are needed. For bridge assets, for example, structural adequacy and safety can be represented by the superstructure, substructure, channel, and scour condition ratings; serviceability and functional obsolescence can be represented by the deck con- dition rating and deck geometry rating; essentiality for public use can be represented by ADT; and special reductions can be evaluated based on annual maintenance costs. Given a quantitative measure of the rationale, a minimum acceptable threshold, or trigger, is needed. This threshold typically is chosen to reflect the point at which intermediate maintenance actions are no longer cost-effective (Saito & Sinha, 1989). 2.2.3 Select General Approach The three general life estimation approaches common in the literature are (1) the condition- based approach, (2) the age-based approach, and (3) a hybrid approach. For each of these approaches, the data used could be collected from expert opinion surveys or from data pertain- ing to in-service assets. Generally, it can be found that for lesser-studied assets, life expectancy is often determined on expert opinion or manufacturer-published values. These values are then commonly used to conduct blanket replacements of all assets in a given age cohort of that asset type. This practice, however, places the agency at risk of foregoing the benefits of remaining service life left in some assets and/or allowing some assets to operate at unacceptable levels of service. 2.2.3.1 Condition-based Approach The condition-based approach has been commonly used for estimating the functional life of higher valued assets (i.e., bridges and pavements). These assets are periodically monitored/ inspected with respect to their condition. As such, deterioration models can be readily developed. Figure 2-2. General methodology for estimating highway asset life expectancy.

26 estimating Life expectancies of highway assets The functional life expectancy is then taken as the time from construction or last reconstruction until one or more performance measures trigger some action intended to restore the functional performance, or in extreme cases of functional inadequacy, replacement. For instance, if an agency sets a minimum performance threshold for a pavement’s level of cracking or rutting, then the time when the threshold is first crossed is used (Figure 2-3). Such condition-based life estimates could also be viewed with respect to the occurrence of an extreme event (Sanchez-Silva & Rosowsky, 2008). In cases where replacement decisions are based on some terminal level of performance, such as road sign reflectivity thresholds, the selection of the specific performance measure is influ- enced by the rationale for replacement being considered. If replacement is being considered due to structural adequacy and safety, then, for pavements, an agency may wish to predict rutting, PCR, and percent cracks; for bridges, predictions of discrete NBI ratings for decks, substruc- tures, superstructures, structural evaluation, and scour can be made. For other assets, some visual rating of condition can be predicted. If replacement is being considered due to service- ability or functional obsolescence, then pavements can be modeled to predict IRI or PSR; for bridges, the NBI deck geometry or waterway adequacy could be predicted; for culverts, the per- cent of blockage or channel erosion can be considered; for traffic signs and pavement markings, retroreflectivity can be measured; for traffic signals and roadway lighting, luminescence may be predicted. If “essentiality for public use” requires replacement, then economic development considerations may be used. This could be modeled using traffic forecasts. For special reduc- tions, performance could be based on annual maintenance costs to keep the asset in a serviceable state. Also, multiple rationales could be considered for a given exercise to estimate life expec- tancy. For example, the NBI sufficiency rating for bridges considers all of the above-mentioned replacement rationale. If one combined factor has not been agreed on by an agency, then the minimum of a series of life values may be taken. 2.2.3.2 Age-based Approach In the age-based approach, historical replacement records regarding the year of construction and year of demolition/reconstruction are assessed (Figure 2-4). The actual life is best quantified Performance, condition, or value Age Deterioration model End-of-life threshold Performance, condition, or value Age Decision- sensitive End-of-life threshold Figure 2-3. Condition-based life expectancy (Conceptual Illustration) (Thompson et al., 2011). st Figure 2-4. Age-based life expectancies (Conceptual Illustration).

Methodologies for Life expectancy estimation 27 using this approach. In this approach, the asset life can be directly predicted and easily incorpo- rated into replacement scheduling decisions. The accuracy of age-based predictions is highly dependent on data availability and integrity. Many agencies lack complete historical records relating to the year the asset was built, mainte- nance strategies, traffic volumes, and so on. Without sufficient archival information, the cred- ibility of the results may be brought into question. A key piece of information not available in the collected dataset for this study was the rationale or motive behind the replacement of the assets considered. With such data, agencies could organize calibration datasets for only those rationales considered relevant. For instance, if bridge widening is no longer considered neces- sary, then agencies need only analyze the observed lifespan for an alternative bridge replacement rationale. More generally, the age-based approach assumes that the future will mimic the past, which could be an invalid assumption in light of emerging materials, construction processes, contracting approaches, climate change, and so on. 2.2.3.3 Condition/Age-based Hybrid Approach Combining the two approaches may also be preferred so as to directly make life predictions based on condition. For instance, the time until an inadequate sufficiency rating is obtained for a bridge can be predicted as opposed to predicting a sufficiency rating by age. Combining histori- cal replacement records and observed times until a condition/performance threshold is reached could serve an alternative approach for asset life estimation. 2.2.4 Select Modeling Technique In selecting a modeling technique, agencies should consider three dimensions of analysis. The first dimension relates to the basic asset attributes (e.g., asset class and design/material type). The second dimension relates to the nature of the data (e.g., if the data is cross-sectional, time- series or panel; if the dependent variable is discrete or continuous; if sufficient condition-based, age-based, or hybrid model data are available; the geographic representation of the data; and if explanatory variables are available to be analyzed). The third attribute relates to the model- ing techniques (e.g., if a deterministic or probabilistic model is preferred; the specific statistical technique that is to be used; and the measure of goodness-of-fit used to validate model results). On the basis of the selections made at each level, different approaches in the following dimen- sions may be recommended. For instance, if the asset manager seeks to predict the functional life of a steel box culvert (first level), then a condition-based approach to predict a discrete visual condition rating may be applied to determine the functional life if there is lack of histori- cal replacement data (second level), which would then suggest that a discrete choice model or Markov chain may be the most appropriate (third level). Asset life expectancy models could be developed using local data; that way, it would be pos- sible to avoid using life expectancies derived using assumptions or expert opinion or trans- ferred from other dissimilar regions that do not reflect local conditions. This would have the additional benefit of identifying influential local factors and assessing their sensitivity on the basis of local changes in conditions. Where the agency is particularly interested in uncertainty considerations when assessing the life of its assets, probabilistic empirical modeling techniques are recommended using local data. However, agencies are generally advised to select an appro- priate modeling technique on the basis of the dependent variable and their staff expertise. From the literature review, six modeling techniques were identified for potential application for life expectancy modeling and analysis: • Linear and Non-linear Regression Models—continuous, deterministic model type with direct interpretations of model fit (R2) and parameter strength.

28 estimating Life expectancies of highway assets • Neural Networks—continuous, deterministic model type that relies on hidden relationships between sets of variables in order to make forecasts, but is often viewed as a “black box.” • Discrete Outcome Models—discrete, probabilistic, and parametric model type that can be applied to ordered data to predict condition states. • Markov Chains—discrete, probabilistic, and non-parametric model type that can predict the probability of being in any discrete state at any point in time. • Duration Models—continuous, probabilistic model type that produces non-, semi-, or fully parametric survival curves and allows for capturing covariate influences. • Markov-based Duration Models—fit a continuous, probabilistic, fully parametric survival curve to a Markov Chain estimate. In choosing among the modeling techniques, agencies should consider the availability of data. If, for a given asset type, there exist data on intervals between replacements but no per- formance data, duration modeling could be applied for life expectancy estimation. Duration models can be calibrated to observed historical life. If data on asset condition/performance are discrete in nature and are routinely collected during inspections, Markov-based model- ing could be applied. If the asset condition/performance data is continuous in nature on asset condition/performance and generally not routinely collected, a duration model could be applied to determine the asset life on the basis of the observed or expected time at which the performance threshold is reached. A brief review of these model types is provided in the following subsections. 2.2.4.1 Regression Models Linear and non-linear regression models are the most commonly applied technique by agen- cies for asset performance modeling, due to their ease of application and interpretation, simplic- ity of methodology, clarity of results, and ability to be calibrated with widely available software such as MS Excel. Such models can be applied to (1) predict a continuous performance measure (condition-based) as a function of age and other variables or (2) directly predict asset life as a function of the explanatory variables (age-based). Latent variable and adaptive approaches could also be used to predict condition as a function of past performance and characteristics in a step- by-step fashion. Discrete/continuous modeling could also be applied. With regard to model functional forms and types, the variety of options include Polynomial Y xi i i n = + = ∑β β0 1 If n = 1, then Linear If n = 2, then Quadratic If n = 3, then Cubic Exponential/Logistic Y i i xi i n k = +     = − = ∑β α β0 1 1 1for k or If k = 1, then Exponential If k = -1, then Logistic Gompertz Y ci i i xi i n = = ∑ αβ 1

Methodologies for Life expectancy estimation 29 where Y represents a dependent variable ci, ai, and bi represent estimable parameters and xi represents an independent variable Linear models include various model subtypes (e.g., ordinary, indirect, generalized, two-stage and three-stage least squares, instrumental variables, limited and full information maximum likeli- hood, and seemingly unrelated regression). The most efficient and consistent of these models are the system equation methods commonly applied for simultaneous equations, as opposed to single equation methods: i.e., ordinary least squares (OLS), indirect least squares (ILS), instrumental vari- ables (IV), two-stage least squares (2SLS), and limited information maximum likelihood (LIML). System-of-equation methods include three-stage least squares (3SLS), seemingly unrelated regres- sion estimation (SURE), and full information maximum likelihood (FIML). Such models are better suited for dealing with serial correlation problems (i.e., lack of independence among explanatory variables), heteroskedasticity (i.e., variables with non-constant standard deviations), and mitigat- ing errors created by endogenous variables (i.e., variables where there is not a unidirectional causal relationship from the independent variable to the dependent variable) (Washington et al., 2003). In 3SLS, least squares regression is performed in three stages: (1) obtain the 2SLS estimates of the model system, (2) use the 2SLS estimates to compute residuals to determine cross- equation correlations, and (3) use generalized least squares (GLS) to estimate the model parame- ters as similarly done in SURE (Washington et al., 2003). In other words, 3SLS relies on multiple rounds of OLS to predict instrumental variables (i.e., variables that are “suspected” to be endog- enous) which in turn predict the dependent variable. This process results in a more efficient and consistent linear regression model. Of this set of model subtypes, the 3SLS approach is recommended. Where the data are panel in nature, modeling techniques involving random effects could be incorporated to account for correlation (e.g., multiple inspections for a single structure). Despite their simplicity in interpretation (particularly for linear regression), there are dis- advantages for this general model type. Linear regression methods are only appropriate when the dependent variable has a linear or intrinsically linear relationship with the explanatory vari- ables, which may not necessarily be the case for highway asset performance behavior over time. Furthermore, such models are deterministic and thus yield only a point estimate that may not reflect the true value of the condition or asset life that could be expected. On the other hand, for non-linear models, it is generally far more difficult to develop a set of significant independent variables and, although these models may yield higher coefficients of determination (R2), they typically lack explanatory power due to their composition of fewer significant variables. 2.2.4.2 Neural Networks A second approach to consider is that of artificial neural networks. This non-linear adaptive model predicts asset condition on the basis of what it has “learned” (pattern identification) from past data. Statistically, an artificial neural network is a non-linear form of 3SLS, where appropri- ate “instruments” are used to predict future “events”; in this case, an event is asset life reaching a certain value (Figure 2-5). To facilitate learning, such models are typically Bayesian-based. This approach updates esti- mates (i.e., posterior means) by applying weighted averages based on previous estimates (i.e., prior means). Typically, these weights are based on the number of observations. Activation functions within the network have included hyperbolic tangent, log-sigmoid, and bipolar-sigmoid functions. Such approaches have been found to work well with noisy data and are relatively quick; however, such techniques are better suited for smaller databases (Melhem & Cheng, 2003). These models require more sophisticated software to develop (e.g., Palisade’s @Risk Neural Tools, NeuroXL) and can sometimes be used as a “black box” (i.e., prediction process unknown but assumed appropri- ate). However, the ability to “learn” makes these models particularly useful to asset managers.

30 estimating Life expectancies of highway assets 2.2.4.3 Ordered Discrete Response Models Where asset condition/performance data are discrete in nature, it is considered more appro- priate to apply discrete-outcome modeling techniques. Based on an assumed distribution, these models can be used to calculate the probability of an asset being in any condition state. For instance, the probability of a bridge being in any condition state on the NBI rating scale (0-worst to 9-best) in any future year can be calculated using these models. Also, such models simplify sen- sitivity analysis by enabling analysis of marginal effects (i.e., how probability of a condition state changes given a unit change in one of the inputs). These models can be used for panel, ordered, and/or nested data. Model subtypes are typically of the probit or logit form and can be modified as follows: • Ordered (e.g., NBI condition rating) or unordered (e.g., bridge status—functionally obso- lete, structurally deficient, satisfactory condition); • Nested (e.g., predict status of all concrete bridges at first level, then predict status of pre- tensioned concrete bridges and post-tensioned concrete bridges at the second nest level); or • Mixed, fixed, or random effects incorporated to account for asset heterogeneity for panel data. Probit models assume normally distributed variates, whereas logit models assume extreme value distributions. Depending on the data, similar results may be obtained. Probit P Y x x EXP wi i in i i n( ) = −   = − + +( )Φ β β σ pi 1 1 2 1 2 1 2  −∞ − + +( )∫ dwi xin i x i nβ β σ 1 1 Logit P Y EXP x EXP x i i i i ii n( ) = ( )( ) = ∑ β β 1 For ordered models, the threshold parameters are calibrated to indicate the probability of a condition state. For example, the probability that an asset is in any one of three possible condi- tion states can be computed from an ordered probit model by comparing the model sum (Sbx) to the threshold parameters (µ) (Figure 2-6). Mathematically, the exact probability of such an Instru- ment 1 Instru- ment n Input m Input 1 Input 2 Output Figure 2-5. Example of an artificial neural network.

Methodologies for Life expectancy estimation 31 asset being in any condition state follows the cumulative standard normal distribution with the variable X taking the following forms: P Condition State x N P Condition =( ) = −[ ] ( )∑0 0 1β ~ , State x N x N P Co =( ) = −[ ] ( )− −[ ] ( )∑ ∑1 0 1 0 11µ β β~ , ~ , ndition State x N x=( ) = −[ ] ( )− −[ ]∑ ∑2 0 12 1µ β µ β~ , ~N P Condition State x N 0 1 3 1 0 12 , ~ , ( ) =( ) = − −[ ] (∑µ β ) where x represents the set of independent variables, age, material type, etc.; b represents the set of parameter estimates; µ represents the threshold parameters, which in comparison to parameter estimates and vari- able values, indicate the likelihood of being in a given condition state: X and - = −[ ] =∑µ βx Z X Mean DeviationStandard N(0,1) represents the cumulative standard normal distribution with mean = 0 and standard deviation = 1 These models, however, are only appropriate if the assumed distribution accurately reflects the data. Furthermore, with discrete models, in general, there is a potential for aggregation bias. For example, two culverts may each have a condition rating of say 4 but one may be nearly in a condition state of rating 3 while the other is nearly in a condition state of rating 5. This loss of generality may cause some errors in model calibration. 2.2.4.4 Markov Chains Markov chains are commonly applied for estimating bridge deterioration curves. A Markov chain is a memoryless (i.e., transition probability based solely on the present state and not on past states), stochastic process with a finite integer number of possible non-negative states, that Figure 2-6. Example illustration of a 3-state ordered probit model (Washington et al., 2003).

32 estimating Life expectancies of highway assets is used to predict the probability of being in any state after a period of time. These chains are commonly visualized in terms of a “graph” showing all of the nodes (i.e., condition states) and possible paths (i.e., transitions). Calculations, based on the graph, are carried out using matrix multiplication (Figure 2-7). The transition matrix corresponds to the probability of transitioning after a period of time (with discrete or continuous time intervals), which can be taken on an annual basis or based on inspection frequencies. In modeling deterioration, transitions to an improved state are con- sidered impossible and are assigned a transition probability of zero; likewise, transitioning to a non-subsequent state (for example, a preceding condition state or two subsequent condition states) may be assigned zero probability by some agencies. Transition probabilities, represented by, pij = Pr(Yk+1 = j|Yk = i), can be found via expert opin- ion, optimization (Jiang & Sinha, 1989), statistical modeling based on observed frequencies (i.e., the methodology used in this study), or approximated using pairs of inspections (Thompson et al., 2011). To correct for the fact that deterioration rates are not homogenous throughout the life of an asset, multiple transition matrices are typically established for several age ranges (Jiang & Sinha, 1989). Also, Bayesian techniques could be used to update transition probabilities as well. Predictions at various points in time can be derived from the Chapman-Kolmogorov equation (Weisstein) to yield: p t p t pi i i n( ) = ( )∏ where p(ti) represents the initial state, i, probability vector (e.g., [1, 0, 0] for a new traffic sign on a “good,” “fair,” or “poor” rating system starting at time 0); P represents the transition matrix; n represents the size of the age group interval. 2.2.4.5 Duration Models Duration, sometimes labeled as reliability or survival, analysis is a probabilistic approach for predicting the likelihood of a continuous dependent variable passing beyond or “surviving” at any given unit of time. The survival curve is just one representation of probability which can be applied to asset life (Table 2-8). As shown in Figure 2-8, survival curves can be produced for multiple performance measures or replacement rationales. The leftmost curves are the stochastically dominating functions in a life prediction. Good Fair Poor PGG=95.3 PGF=4.6 PGP=0.1 PFF=93.2 PPP=100.0 PFP=3.9 4.6 93.2 0.1 3.90 95.3 0 0 100.0 Figure 2-7. Example Markov chain graph and transition matrix.

Methodologies for Life expectancy estimation 33 Table 2-8. Representations of probability. Figure 2-8. Asset survival curves using different performance indicators and performance thresholds (Irfan et al., 2009).

34 estimating Life expectancies of highway assets Duration models can be non-parametric, semi-parametric, or fully parametric. Non- parametric methods (e.g., Kaplan-Meier/product-limit estimator or life tables) are less com- monly applied in transportation (more common in medical fields) because they do not retain the param etric assumption of the covariate influence; however, they may be appropriate when there is little knowledge of the functional form of the hazard or if a small number of observa- tions is obtained (Washington et al., 2003). The most common non-parametric estimator is the Kaplan-Meier estimate: S t n d d i i iti t ( ) = − < ∏ where n represents the number of assets available at the start of the time period in less censored cases (such as assets that have left the analysis without a conclusive end value); d represents the number of assets ‘failed’ by the end of the time period. For the lower (L) and upper (U) bounds of a desired confidence level for a non-parametric model, such as the Kaplan-Meier, the following equations are recommended (Newcombe, 1998): L np z z z n p nq n z np z = + − − − − + +( ) +( ) + + 2 1 2 1 4 1 2 2 1 2 2 2 2 + + − + −( )z z n p nq2 2 1 4 1 where n is the number of observations; p is the point estimate of probability (i.e., S(t) for Kaplan- Meier); q is taken as 1-p; z is the Normal distribution test statistic at the desired confidence level. Semi-parametric models (e.g., Cox proportional-hazards), which account for covariate influ- ence and are appropriate when the underlying distribution of the data is unknown, are consid- ered more flexible without the constraint of a fully parametric form. The Cox model approach takes the following form: S t S t EXP xi i i n( ) = ( ) +   = ∑  β β0 1 where S¨ (t) represents a fully parametric survival curve. Fully parametric models (e.g., gamma, exponential/Markov, Weibull, log-logistic, log-normal, Gompertz) are generally recommended in studies of this nature due to the benefits in model efficiency and in reducing bias, but they are influenced by the extent to which the assigned dis- tribution fits the data. As found in the literature review, the Weibull survival curve is one of the most commonly applied distributions (van Noortwijk & Klatter, 2004): S t EXP t y( ) = − −      1 α β where a represents the scaling factor (stretches curve laterally); b represents the shape factor (stretches curve vertically); and g represents the location factor (shifts curve horizontally by representing value at which 100% survival probability occurs).

Methodologies for Life expectancy estimation 35 The Weibull distribution is a more generalized form of the exponential distribution (b=1) that allows for a more flexible means of capturing duration dependence. Explanatory factors can also be incorporated to develop a fully parametric survival curve with a = EXP(b0 + Sni=1 bixi). The hazard function of the Weibull distribution is monotonic, indicating that the hazard never decreases over time (if b>1). For distributions with non-monotonic hazard functions, log-logistic models can be applied (Washington et al., 2003). The model form for this distribution is S t t y ( ) = − + −           − 1 1 1β α A difficulty arises, however, when the location factor takes different values during the life of an asset. Merely changing the value of the location factor does not account for the changing hazard rate associated with the parametric specification (Ng & Moses, 1996). As such, the survival prob- ability of in-service structures can be updated using conditional probability (Bayesian) theory: S t t T S t t T S T S t S T >( ) = ∩ >( )( ) = ( ) ( ) where T represents the age an asset is known to have survived. To compare distributions, chi-squared test statistics can be computed based on the family of the distribution. The test statistic for functions in the same family can be approximated as fol- lows (Washington et al., 2003): χ β β2 2= − ( )− ( )[ ]LL LLA B where c2 represents the chi-squared test statistic; LL(bA,B) represents the log-likelihood of distri- butions A and B (e.g., Exponential and Weibull distributions). In the special case of the Exponential and Weibull distributions, a second technique is to cal- culate a modified t-statistic which assesses the statistical significance of the difference between the shape factors. Modified t statistic SE − = −β 1 where b represents the parameter estimate and SE represents the standard error. If the shape factor is significantly different from 1, then the Weibull distribution may be con- sidered justified; otherwise, the Exponential distribution may be considered a better fit. When comparing distributions from alternative families, an individual chi-squared test sta- tistic should be calculated for each distribution (Washington et al., 2003): χ β2 2 0= − ( )− ( )[ ]LL LL c where LL(0) represents the restricted log-likelihood function and LL(bC) represents the log- likelihood function at convergence.

36 estimating Life expectancies of highway assets Using these test statistics, the Gamma, Weibull, Gompertz, Exponential, Log-Logistic, F, and Lognormal parametric duration models were tested in a subsequent section of this report. Finally, to validate the use of a distribution, the Kaplan-Meier survival curve can be compared to the baseline ancillary survival factors. A further consideration in calibrating duration models is the inclusion of censored data (Figure 2-9). Data can be either left-censored, right-censored, both left- and right-censored, not captured, or completely captured over the period of observation. From interpreting Figure 2-12 in terms of asset life expectancies, the censored data types are as follows: the left-censored data (i.e., t4) indicate that the actual initial construction or reconstruction year is not observed but the time of replacement is; the right-censored data (i.e., t5) indicate that the asset construction year is known but that it has not been replaced during the time of observation; both types of censoring represent data (i.e., t2) where neither the construction/reconstruction year and year of replace- ment are observed; the data not captured (i.e., t1) are those in which neither construction or replacement data are available; and the completely captured data would represent those assets for which knowledge of both the years of construction and replacement are available (i.e., t3). Censored data can be problematic in that it can lead to biased estimates. Yet, it can be helpful in modifying predictions to account for observations that may have dissimilar properties from uncensored data. When more than half of a dataset is censored, the observed average time to failure is no longer predicted by the model and the tail probability estimates are inaccurate (Kim, 1999; Ho & Silva, 2006). To help control bias from censoring, parametric models, or Bayesian infer- ence when the distribution is unknown, are recommended (Kim, 1999). However, when dealing with long-term assets, such as highway infrastructure, right-censored observations are particularly important to account for the data that includes information from more modern designs (Klatter & Van Noortwijk, 2003)—such designs are less likely to have failed within the observational period, resulting in a prediction that does not capture the life expectancies of improved designs. Therefore, in this study, a 50/50 censoring split is assumed appropriate for predicting asset life. 2.2.4.6 Markov-based Duration Models Markov-based duration models are a technique for fitting a parametric model estimate to a non-homogenous Markov chain with an absorbing state. In doing so, a parametric form, known to better represent life, can be calibrated to readily available inspection data and ease the cor- related simulation required in uncertainty analysis. In this sense, the Markovian survival curve is analogous to the Kaplan-Meier estimate with probabilities found via matrix multiplication. Therefore, the Kaplan-Meier estimate is essentially a binary Markov chain with the possible states being “failed” or “survived” (Hosgood, 2002). As such, the goal of fitting a parametric model (or multiple parametric models for intermediate transitions) is to minimize the difference to the non- parametric survival function (Perez-Ocon et al., 2001). 1 2 3 4 5 Figure 2-9. Censoring types in duration modeling (Washington et al., 2003).

Methodologies for Life expectancy estimation 37 Homogenous Markovian probabilities are inherently exponentially distributed (multiplying by one transition matrix n number of times). However, if the duration in each state is non- exponential and data for a duration model are unavailable, then an alternative is needed. While this may be sufficiently mitigated by the use of multiple transition matrices (i.e., piecewise exponential distributions), another technique would be to fit a parametric survival curve to the Markovian survival curve. Semi-Markov processes, commonly applied in power system analysis, have been used to con- vert back and forth between Markov chain models and generalized survival (typically Weibull) functions (Ng & Moses, 1996; van Casteren, 2001; and Thompson et al., 2011). One such tech- nique for this conversion is the equivalent age technique, shown below for a Markov/Weibull model (Thompson et al., 2011): 1. Estimate Markov transition matrix 2. Convert each row of the matrix to a median transition time t p j jj = ( ) ( ) log log 0 5. 3. Allocate a portion of asset life to each condition state, in proportion to transition time, to develop weights w t tj j j k k j N = = ∑1Σ 4. Compute a condition index using Markov predictions and weights, which in turn approxi- mates the Weibull survival probability CI w xj j j = ∑ 5. Use the inverse of the Weibull survival model to calculate equivalent age t CI= − ( )[ ]α β ln 1 6. Optimize to maximize goodness-of-fit between the actual age corresponding to the Markov prediction and the equivalent age Maximize Normal Log Likelihood = − ( )− [ ] −0 5 2 0 5. . ln lnpi σ2 0 5.  Age of ediction Equivalent AgeiMarkov Pr −( )2 2 i n∑ σ Subject to Markov Median Life InverseWeibull Median Life= >β 1 assu g increa g monotonic hazardmin sin ,( ) By changing s, a, b

38 estimating Life expectancies of highway assets This technique, however is more commonly applied when dealing with a time-homogenous Markov chain. For non-homogenous Markov chains, this report recommends an alternative approach that minimizes the root mean square error (RMSE) between the Weibull survival function and Markov chain survival curve by changing the Weibull scaling and shape factors, while maintaining the median life prediction. Markov/Weibull models are particularly useful for infrastructure where deterioration is initially slow and then accelerates with time. For in-service assets, the same techniques can be applied to calibrate Markov/Beta models. The use of a Beta distribution has been recommended in past research for estimating remain- ing asset life (Li & Sinha, 2004) due to its flexibility in accounting for various hazard rates (e.g., change in hazard rate due to maintenance activity). The survival function of the Beta distribu- tion is represented by S t t t dt t t t L H L( ) = − −( ) −( − − − − − ∫ 1 1 1 1 1 2 1 0 1 1 α α γ γ γ α ) >−∫ α α α2 101 1 2 0 dt , , where gL represents the lower bound location factor; gH represents the upper bound location factor; a1, a2 represent non-negative shape factors. The advantages of Markov-based models include a probabilistic estimate, sole dependence on current conditions (i.e., minimal data needs if transition probabilities known), flexibility in modifying state duration, and efficiency in dealing with larger networks. Their disadvantages include their discrete nature, the deterioration of components is described in visual terms only, there is an assumption of constant inspection periods, no consideration of system condition, and their independence from past data if a first order Markov-chain is used (Morcous, 2006; van Noortwijk & Frangopol, 2004). To overcome the assumption of constant inspection periods, Bayesian techniques can be applied (Morcous, 2006). 2.2.5 Model Selection Recommendations The best calibrated model can be identified on the basis of the goodness-of-fit measure (e.g., adjusted R2, McFadden R2, log-likelihood), the significance of the variables based on t-statistics assuming a minimum 90% confidence level, the intuitiveness of the parameter signs, mini- mization of the correlation, and the robustness of the estimate. Considering the uncertainties involved in life expectancy estimation, stochastic methods are preferred. A general procedure by which a highway agency could select the best model is presented in Figure 2-10. It is recommended that the decision be based on the general approach applied, the nature of the dependent variable, the sample size, and the probabilistic/deterministic preference. However, the experience and preferences of agency staff could also be considered in the selection of the best model. 2.2.6 Data Availability Assessment and Grouping of Data As stated in the discussion of approaches for estimating life, the accuracy of predictions hinges on the availability and quality of agency databases. For the purposes of asset life estimation, it is recommended that agencies maintain archival records of life expectancy factors, condition/ performance measures, maintenance activities, year of construction, and the rationale for any replacements or retirements of assets. It may be beneficial to supplement in-house information with data from other agencies. Data from the National Oceanic and Atmospheric Administration

Methodologies for Life expectancy estimation 39 (NOAA) can be used to assess climate factors and National Resources Conservation Service (NRCS) data can be used to assess the influence of soil factors. Such information can be combined with agency databases or overlaid into a geographic information system (GIS) (Chase et al., 2000). For volume of NCHRP Report 713, NOAA and NRCS data were collected at the climate division level in order to calibrate parameter estimates. In analyzing climate data, various groupings of assets should be considered, particularly for any non-covariate approach. If data segmentation is not applied, a biased estimate that is not descriptive of either data segment may be obtained (e.g., life of assets in Group A, 50 years; life of assets in Group B, 90 years. If grouping is not done, the life of all assets in Groups A and B combined, 70 years). Proper groupings of data can lead to more efficient statistical/econometric models and further allow agencies to analyze assets that share similar characteristics (Hanna, 1994). These groupings could be organized by district, climate region, material type, structure type, traffic volume, or repair history. The stratification of data should be arranged so that the heterogeneity within each group is minimized and the heterogeneity between the groups is maximized in order to reduce external effects. For agencies that may seek to establish different groupings, clustering and Delphi techniques can be used. Figure 2-11 shows an example dendo- gram for statistical groupings of regions of similar climate, developed using SPSS. For this report, SHRP-LTPP climate regions were used. - - - Figure 2-10. General guideline for model selection for life expectancy estimation.

40 estimating Life expectancies of highway assets 2.2.7 Incorporating the Impacts of Preservation into Life Expectancy Models There are at least three key application attributes of preservation over the asset life cycle: occur- rence, frequency, and intensity. Occurrence is a binary variable referring to whether the asset receives any preservation over its entire life. Frequency is the number of times the asset receives some preservation activity within a certain time period or the interval between the same or different activities. Intensity is a continuous variable that describes the effort associated with preservation and can be measured in terms of the material quantities used or the average annual expenditure (e.g., added thickness of pavement in a structural overlay, $/lane-mile or $ per ft2 of deck area expended on maintenance of pavements and bridges, respectively). So, it is possible for an asset to receive, for example, low frequency but high intensity or high frequency or low intensity. There are two contexts of incorporating the effects of preservation into life expectancy models. The first context, addressed in this section (Section 2.2.7), is the determination of the influence of preservation on asset life expectancy. The second context, addressed in Section 4.2.1.7 in Chap- ter 4, is similar to the first—albeit in the reverse direction: the determination of the effect of supe- rior assets (i.e., those built with long-lived materials, superior designs and innovative construction processes) on preservation application (intensity and frequency) over asset life. For example, the use of stainless steel for deck reinforcement in place of traditional epoxy-coated steel, while more costly, generally leads to longer life expectancies (FHWA, 1988; Yunovich et al., 2002) and has been shown to be more cost-effective in the long term (Cope et al., 2011). Similarly, the construction of French drains under highway pavements has been shown to greatly increase the life of pavement assets (Christopher and McGuffey, 1997). Numerical examples for the second context are provided in Section 4.2.1.7 of Chapter 4. The rest of this section addresses the first context. As demonstrated in this report, the life expectancy of a highway asset is often influenced by the application of preservation it receives over its lifecycle. From the perspective of preservation frequency and intensity, there could be at least three potential cases: when preservation of the asset over its life cycle is (1) performed at the frequency and intensity as specified or assumed by the designer in the lifecycle cost analysis, (2) performed at a lower frequency and/or intensity than is assumed by the designer, (3) performed at a higher frequency and/or intensity than speci- fied or assumed by the designer in the lifecycle cost analysis. 2.2.7.1 Effect of Different Levels of Preservation on Asset Life: A Conceptual Discussion For the condition-based approach, performance curves can be developed by agencies for indi- vidual or sets of assets. If the effectiveness of a preservation activity is known, it is possible to Figure 2-11. Example dendogram developed using cluster analysis.

Methodologies for Life expectancy estimation 41 extrapolate how the performance curve will be modified beyond the preservation year and hence the effect on asset life (Lytton, 1987; Markow, 1991; Mamlouk & Zaniewski, 1998). As shown in Figure 2-12(a), for instance, the effectiveness of a preservation activity can be captured in terms of a performance jump for non-increasing performance indicators and/or a reduced rate of deterioration (i.e., change in the slope of the deterioration curve). With knowledge of the jump and/or change in deterioration rate, the life extension can be calculated (i.e., asset life with preservation activity—asset life without preservation activity). Furthermore, the effec- tiveness can be captured on the basis of the intensity of the activity. As seen in Figure 2-12(b), more intense preservation activities such as asset rehabilitation lead to greater jumps in perfor- mance (i.e., greater reductions in deterioration). Also, more intense or more frequent preserva- tion activities lead to more gentle performance curves (i.e., greater reduction in the deterioration rate compared to less intense or less frequent activities). The timing of the preservation activity then could be scheduled on the basis of the knowledge that the preservation action will “buy” additional time for the asset life. Further discussion of incorporating asset life expectancy into scheduling preservation activities, as well as performing lifecycle cost analysis, are provided in Chapter 4. Prior to such example applications, a dem- onstration of the best fitting survival models fitted to the data is presented in Chapter 3. The effect of different levels of preservation received by an asset over its lifecycle on its longev- ity can be modeled in one of at least two ways: • Capturing the preservation impacts on asset longevity using preservation occurrence versus frequency/intensity as independent variables • Capturing the preservation impacts on asset longevity by developing separate post-application performance models for different preservation treatments, intensities, and/or frequencies. (b) Impacts of Increasing Intensity and Frequency of Preservation on Asset Life (a) Different Mechanisms of the Impact of Preservation on Asset Life 1 3 2 3 2 1 Figure 2-12. Conceptual illustrations of preservation effect on asset longevity (Labi, 2001).

42 estimating Life expectancies of highway assets Each of these ways of assessing preservation impacts on asset life are explained in Sections 2.2.7.2 and 2.2.7.3, respectively. 2.2.7.2 Capturing the Preservation Impacts on Asset Longevity Using Preservation Occurrence vs. Frequency/Intensity as Independent Variables As explained earlier, the life expectancy model could be performance based (where the response variable is an asset performance indicator) or interval based (where the response is a time interval between successive replacements or retirements). If the approach were interval based, then the model would be one that estimates asset life directly as a function of preserva- tion effort and other attributes; in that case, taking the marginal effects of the preservation term would yield the impact of each level of the preservation effort on the asset life expectancy (e.g., 2 additional years of asset life for every inch of pavement overlay or 5 additional years for every $1000 per lane-mile expended on preventive maintenance). The associated non-linearities and scale economies (or diseconomies) could be captured using an appropriate functional form for the model. On the other hand, if the approach were performance based, then the model would be one that estimates asset performance and consequently, on the basis of the threshold perfor- mance, can be used to derive asset life; in such a case, the effect of increased maintenance occur- rence or frequency/intensity would be to slow the rate of deterioration, thus delaying the time the performance curve reaches the threshold and thus increasing asset life as seen in Figure 2-12. Preservation Occurrence: The impact of whether preservation occurs or not, over asset life- cycle can be captured by the use of an indicator variable in a statistical asset life expectancy model. Mohamad et al. (1997) developed a model to investigate the effect of maintenance on the level of pavement performance; maintenance was considered a discrete event representing a binary choice of its being performed on a pavement section or not, and pavement perfor- mance levels were represented by roughness numbers. Other variables included were pavement thickness, pavement loading, and a regional factor. The researchers also addressed the issue of simultaneity bias that often arises in such solution contexts. Preservation Intensity/Frequency: Other researchers have modeled the changes in asset per- formance due to maintenance. For example, Sinha et al., 1988 expressed maintenance effective- ness as the change in pavement roughness, R, as follows: R = a + b*log10M +c*S +d*(log10M*S), where S is a dummy variable representing pavement location, M is the unit routine maintenance expenditure. Used in the appropriate context, these models can be used to derive the expected increase in asset performance (and hence the increase in time to reach performance threshold) due to an expected menu of maintenance actions over several years. Labi (2011) assessed the impact of different levels of maintenance (in terms of $/lane-mile) on the longevity of rehabili- tated pavement assets, for each level of truck loading and climatic severity. 2.2.7.3 Capturing the Preservation Impacts on Asset Longevity by Developing Separate Post-application Performance Models for Different Preservation Treatments, Intensities, and/or Frequencies A post-preservation performance model for the asset specific can be developed for each type, or intensity/frequency level of the preservation treatment, as conceptually illustrated in Figure 2-12. Using data for the different types, intensities, or frequencies of preservation effort, the analyst can develop different asset performance curves, M1, M2, and M3. Generally, higher intensities and frequencies would translate into performance curves that have slower rates of deterioration, and thus, greater life. Methodologies and numerical for determining the asset life from a given asset performance curve are provided in this report and in the Guidebook that accompanies this report. This section develops a methodology that can be used by an agency to assess the impact of different post-preservation application performance curves on asset life extension.

Methodologies for Life expectancy estimation 43 Figure 2-13 (Labi et al., 2008) presents a blown-up portion of a kink in a typical infrastructure performance curve (the kink reflects the application of an intervention, that is, a preservation treatment). In (a), the figure is shown for the so-called “non-increasing” measures of perfor- mance that decrease with asset age, such as Pavement Condition Rating (PCR), Present Service- ability Index (PSI), Sign retroreflectivity, Bridge Sufficiency Rating, mobility index, and safety rating, whose increasing values indicate better performance. In (b), the figure shows typical trends of so-called “non-decreasing” measures of performance that increase with asset age (e.g., surface roughness, faulting index, rut index, bridge vulnerability index, congestion index, crash rating, or some index whose increasing values indicate worsening performance). The functions f1(t) and f2(t) represent the infrastructure performance (or deterioration) model just before preservation and just after preservation, respectively. Typically, f1(t) is steeper than f2(t), but it is not unusual to encounter cases where they have similar slopes. Symbols used in the figure have the following meanings: t = accumulation of some temporal attribute such as time, usage, or climate effects. For sim- plicity, such temporal attributes are collectively referred to as “time” in the rest of this section. ta = time at which the preservation treatment was applied to the asset. This typically corre- sponds to a specific threshold level of service established by the infrastructure agency. Depend- ing on funding availability, actual values of ta may not be constant from year to year, but may rather deviate from established thresholds. tb = time at which the asset reaches a critical replacement threshold level of service if it had not received the preservation treatment. tc = time at which the asset, after preservation treatment, reaches the same level of service at which it received the preservation treatment. te = time at which the asset, after preservation, reaches a critical replacement threshold level of service if it does not receive any other preservation. td = time at which the asset reaches a zero level of service if it had not received the preservation. tf = time at which the asset, after the preservation, reaches a zero level of service if does not receive another preservation. ym = LOS at which the preservation is carried out (this may or may not be equal to the pres- ervation “trigger” or “threshold” value). yc = minimum LOS at which the asset needs replacement or reconstruction, often referred to as the replacement or reconstruction “trigger” or “threshold” value. TL = preservation life, i.e., the time that elapses between preservation and when the asset reaches a state that is the same as the state at which it received the preservation. LE = asset life extension, i.e., the time between the attainment of a critical replacement thresh- old LOS assuming no preservation and the time between the attainment of a critical replace- ment threshold LOS assuming no subsequent preservation. From Figure 2-13, the following basic relationships and assumptions can be established: 1. LE = te - tb 2. f1(tb) = yc = f2(te) 3. TL = tc - ta 4. f1(ta) = ym = f2(tc) 5. TL is solely dependent on the nature of f2(t) and the numerical values of PJ and ym 6. LE is dependent on the nature of f1(t), f2(t) and the numerical values of ym and yc. On the basis of these basic relationship and assumptions, Labi et al. (2008) showed the fol- lowing relationships between preservation intensity (represented by the performance jump and the shape of the post-preservation function) and extension in asset life (Table 2-9). Using these relationships, an agency can quantify the impact of asset preservation treatments on the

44 estimating Life expectancies of highway assets (a) Non-decreasing Performance Attributes (b) Non-increasing Performance Attributes f1(t) ta ym yc f2(t) tetctb A D td tf f1(t) ta f2(t) tetctb A D Accumulated Usage, Weather Effects, or Time (t) Accumulated Usage, Weather Effects, or Time (t) ym yc Performance Jump (PJ) Performance Jump (PJ) Intervention (e.g., rehabilitation or maintenance treatment) Extension in Asset Life (LE) Extension in Asset Life (LE) Intervention Life (IL) Intervention Life (IL) Asset Performance/ Condition Asset Performance/ Condition - - - Figure 2-13. Relationships between performance jump, preservation treatment life and asset life extension (Labi et al., 2008).

Methodologies for Life expectancy estimation 45 1 2 Abbreviations: LE = Extension in Asset Life; IL = Intervention life or preservation Life; PJ = Performance jump (preservation-induced increase in asset performance); y = performance indicator. - - - 1 2 1 2 1 2 1 2 1 2 1 2 Table 2-9. Estimating the increase in asset life due to preservation actions, for different pre- and post-preservation performance functional forms (Labi et al., 2008).

46 estimating Life expectancies of highway assets extension of asset life. This is shown for different pre- and post-preservation performance func- tional forms. Higher levels of preservation intensity translate into higher performance jumps and more gentle deterioration slopes as represented by the post-preservation functional form f2(t) and its parameters. Agencies can apply these relationships to ascertain the increase in asset life due to their dif- ferent preservation actions. To do this requires the following data: (1) a function that describes the rate of the asset performance deterioration before the preservation, (2) a function that pre- dicts the expected jump in asset performance due to the preservation, and (3) a function that describes the expected rate of performance deterioration after the preservation. If such functions are not available, data could be collected to develop them. The results are demonstrated using data from approximately 100 flexible pavement sections in Indiana. For purposes of simple illustration, the following performance model was developed: PSI = 4.4908 - 0.0642 (AGE) A review of the state of practice showed that, on the average, thin overlay preservations had been applied to such pavements at an average condition of 3.1 PSI units (hence ym = 3.1). Also, available pavement condition guides in use in Indiana suggest that interstate pavements are due for replacement when the PSI falls below 2.5 units (therefore yc = 2.5). A recent study in Indiana showed that thin overlay treatments, on the average, offer pavements a 0.87 PSI jump in pave- ment performance. From this information, the life of thin overlay treatments in Indiana can be estimated using the relationships presented in Table 2-9. In other words, the time interval that elapses after such preservation until such time that a similar preservation is needed can be estimated. Assuming that both pre- and post-preservation performance functions are linear (at least within the immediate time vicinity of the preservation application), the appropriate equation in Table 2-9 can be used to determine the preservation life given the performance jump of thin overlay treatments, as follows: IL PJ m = − = − − = 2 0 87 0 0642 13 6 . . . years From a review of literature on the subject, such a result is consistent with field observations of the actual lives of thin overlays, particularly for pavements with relatively low traffic loading and weather severity. A questionnaire survey of pavement professionals at Indiana districts found that thin overlays have had a 10 to 15 yearly interval between applications for AC pavements (Labi and Sinha, 2002). Raza (1994) stated that thin overlays have had a treatment life of up to 11 years. Also, the Indiana DOT design manual suggests a preservation life of 15 years for thin overlays, for the purposes of lifecycle costing (INDOT, 2002). The role of thin overlays, like all preventive maintenance activities, is to extend pavement life (O’Brien, 1989; Mamlouk and Zaniewski, 1998) thereby deferring the need for major rehabilita- tion (Geoffroy, 1996). From the given performance model and threshold data for AC pavements in Indiana, it is also possible to estimate the extension in the pavement asset life due to thin overlay treatments. In other words, it is possible to determine the reduction in pavement life had it not received the thin overlay treatment: LE y y m m PJ m mm m c = −( ) −( )− = −( )( )−2 1 1 1 2 3 1 2 5 0 0 . . .87 0 0642 0 0642 0 0642 13 6   −( ) = . . . . years The extension in asset life, in this example, is equal to the intervention (preservation treat- ment) life. However, this is not always the case. This result was obtained in this example only

Methodologies for Life expectancy estimation 47 because it was assumed that the pattern of deterioration before preservation is the same as that after preservation—both before- and after-preservation functions were assumed to be linear with identical parameters. In reality, it would be realistic to expect that the deterioration slope after preservation is gentler than that before preservation, thereby causing a greater value of asset life. 2.2.7.4 Concluding Remarks for Section 2.2.7 Clearly, it can be beneficial for agencies to model the impacts of preservation occurrence, frequency, and/or intensity on asset longevity. This can be done using preservation occurrence versus frequency/intensity as independent variables or by developing separate post-application performance models for different preservation treatments, intensities, and/or frequencies. The data needed to carry out this analysis is minimal: annual performance data and contract records that indicate the year of asset construction and the year(s) of subsequent preservation treatment applications. Unfortunately, not many agencies have kept a very good record of their asset preservation histories, particularly, contract records that show year of construction and preservation. There are encouraging signs that agencies have realized the need for doing so and are undertaking such effort in earnest. As data on preservation history becomes increasingly available through increased collection and management of such data, it will be possible for agen- cies to develop these models that can help them ascertain the impact of different maintenance various to build models. 2.3 Summary A review of the literature and the developed methodology for estimating highway asset life was presented in this chapter. From the literature, it was found that references to asset life can be generally broken down as follows: physical, functional, service, treatment, design, residual, and actual (or observed) life. These lifespans are typically quantified by a temporal metric; however, some practitioners pre- fer the use of a maximum number of accumulated loadings to represent life. It was determined that past researchers had generally estimated the life of highway assets as follows: overall bridge life = 50–60 years, bridge deck life = 25–45 years, culvert life = 30–50 years, traffic sign life = 10–20 years, pavement markings life = 1–5 years, pavement life = 10–20 years, traffic signal life = 15–20 years, and roadway lighting life = 25–30 years. These estimates were found to be highly variable and subject to the end-of-life definition used, climatic conditions, material/ design types, and maintenance/preservation intensity. Techniques to model highway asset life have included both mechanistic (e.g., corrosion time models, Miner’s hypothesis test, and finite- element models) and empirical (e.g., statistical regression, Markov chains, duration models, and machine learning) methods. The factors used for data segmentation or as inputs to the models generally included asset characteristics (e.g., age, construction/design type, predomi- nant material, and geometrics), site characteristics (e.g., climate, weather, and soil properties), traffic loading characteristics (e.g., traffic volume and percent trucks), and repair history (e.g., maintenance/rehabilitation intensities and frequencies). On the basis of the findings in the literature, a general methodology is presented in this chap- ter. The steps include: (1) identify replacement rationale, (2) define end-of-life, (3) select general approach, (4) select modeling technique, and (5) fit model to data. Replacement rationales were noted to possibly include structural adequacy and safety, serviceability and functional obsoles- cence, essentiality for public use, and special reductions. In defining end-of-life, it was recom- mended to select a performance measure for the selected replacement rationale and to define life as the time until a particular metric drops below a pre-determined threshold. This threshold

48 estimating Life expectancies of highway assets could represent a minimum level of service or the time at which preservation activities are no longer financially viable. Three general approaches were recommended on the basis of agency preference and data availability: age-based (life predicted based on historical records of fully observed life), condition-based (condition predicted as a function of time with life inferred from threshold), and hybrid-based (time until condition threshold is reached) approaches. Based on the preference for probabilistic models, two empirical techniques were recommended, which included the calibration of covariate, duration models (e.g., Weibull or Log-logistic functional forms) and non-covariate, Markov-based duration models (e.g., Markov/Weibull or Markov/ Beta). Empirical techniques were applied in this study due to the general lack of network-wide data pertaining to mechanistic factors (the paucity of such data, in turn, is likely due to high costs of collecting that kind of data at a network level), exclusiveness to a deterioration-based rationale, and the difficulty of incorporating them into an asset management framework (Yu, 2005). Yet, mechanistic techniques for asset life estimation are considered more appropriate at the level of individual asset (i.e., facility level). The final step in the developed framework deals with model fitting. The best model is considered to be that which maximizes a goodness-of-fit measure, has intuitive parameter signs, and yields results that can be validated with past esti- mates of life or non-parametric analyses of the data. Furthermore, this chapter discussed how assets could be placed into clusters for purposes of enhancing the estimation of their lives. Also, considering that asset life is highly dependent on preservation received by the asset, additional details were provided to assist agencies in predict- ing asset life under various scenarios related to asset preservation frequency and intensity.