Performance-Based Seismic Bridge Design (2013)

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37 CHAPTER SIX DAMAGE ANALYSIS Some general observations, taken from Cooper et al. (1994) and Kiremidjian and Basöz (1997), can be made with regard to the observed behavior and performance of bridges in the 1989 Loma Prieta and 1994 Northridge, California, earthquakes: (1) Bridge skew angle, abutment type, pier type, and span continuity showed the highest correlations to damage for given levels of ground shaking, specific details of which can be found in Basöz and Kiremidjian (1998). (2) New bridges (post-1981) performed well, whereas designs of the 1972–1981 vintage had mixed performance. Pre- 1971 designs generally performed quite poorly. This is a direct indicator that the improved seismic design criteria generated after the 1971 San Fernando, California, earth- quake do achieve their performance goals, whereby inelas- tic action is controlled and life safety is maintained. The mixed response of 1972–1981 bridges is due primarily to the transition to the enhanced design criteria precipitated out of the San Fernando earthquake. (3) Retrofit measures, such as joint restrainers, column jacketing, and foundation strengthening, can dramatically improve the response of nonductile bridge designs. Although they are not a guar- antee of perfect performance, seismic retrofits are effective at reducing damage and preventing collapse. (4) The pre- paredness of local jurisdictions and municipalities prior to a significant seismic event is critical to rapid emergency response, inspection, diversion of traffic to alternate routes, and repair/reconstruction efforts. (5) Lessons learned from past earthquakes and experimental research result in tan- gible improvements in performance. Although the seismic design community is still far from a complete understand- ing of structural behavior and performance in response to strong ground shaking, significant progress has been made, and research efforts continue. A detailed review of bridge performance is beyond the scope of this synthesis, but there are many excellent resources. Overviews of bridge damage can be found in Pond (1972), Housner and Thiel (1990), Housner and Thiel (1994), Priestley et al. (1996), Chen and Duan (1999), Kawashima (2000, 2001), Yashinsky and Karshenas (2003), and Palermo et al. (2010), among many others. Perhaps one of the best surveys of bridge damage can be found in the EERI reconnaissance reports published as a part of the Earthquake Spectra series. EERI has conducted close to 300 international postearthquake investigations over the past 40 years as a part of its Learning from Earthquakes (LFE) Fundamental to the PBSD methodology is the need to deter- mine the type of damage and the likelihood that such dam- age will occur in particular components of the structural system. This determination is of vital importance, as the damage sustained by a structure (and its nonstructural com- ponents) is directly relatable to the use or loss of a system after an earthquake. Therefore, there is a need to reliably link structural and nonstructural response (internal forces, deformations, accelerations, and displacements) to dam- age. This is the realm of damage analyses, where damage is defined as discrete observable damage states (e.g., yield, spalling, longitudinal bar buckling, bar fracture). The pri- mary focus of this chapter is on structural components, but similar considerations must be made for nonstructural com- ponents as well. In this chapter, an initial discussion of types of struc- tural damage observed during historic earthquakes and laboratory experiments prefaces the methods that have been developed to predict damage. This discussion is followed by structural details and concepts that can be used to reduce damage even in strong ground shaking. Finally, postevent inspection tools are reviewed. REVIEW OF BRIDGE DAMAGE FROM EARTHQUAKES Bridges have suffered various types of damage in past earthquakes, as evidenced by the San Fernando (1971), Loma Prieta (1989), and Northridge (1994) earthquakes in California; the 1995 Kobe earthquake in Japan; the 1999 Chi Chi earthquake in Taiwan; the 1999 Kocaeli and Duzce earthquakes in Turkey; the 2010 Darfield and 2011 Christ- church earthquakes in New Zealand; the 2010 Maule earth- quake in Chile; and the 2011 Tohoku earthquake in Japan, where virtually every bridge component has experienced some sort of damage—in some cases leading to structural collapse. The following section includes a brief discussion, including photographs, of bridge damage observed in some of these earthquakes. Although there has been extensive laboratory testing on many components and subassem- blages, real earthquakes have a powerful ability to reveal structural weaknesses or design deficiencies. Accordingly, extremely valuable information for the development of PBSD can be gathered from actual bridge performance in past earthquakes.

38 program. Reconnaissance information can be found in the LFE Reconnaissance Archive (http://www.eeri.org/projects/ learning-from-earthquakes-lfe/lfe-reconnaissance-archive/). Another resource provided by EERI is the Earthquake Clearinghouse (http://www.eqclearinghouse.org/), which provides a consolidated repository for brief observations from EERI reconnaissance teams shortly after a significant seismic event. Detailed observations and reports are often linked from the clearinghouse website. The detailed analysis of damaged bridges has become an important component of postevent investigation, as it provides the opportunity for engineers to verify that cur- rent analytical methods are capable of predicting the failure modes observed in the field, as well as ensuring that design details and configurations perform as expected. Several detailed examples from recent earthquakes in California have shown that the observed damage could be explained and predicted by current nonlinear analytical methods as long as appropriate modeling assumptions are made (Hous- ner and Thiel 1990, 1994; Broderick et al. 1994; Priestley et al. 1994; Basöz and Kiremidjian 1998). Such analyses of an entire bridge system helps further interpret the role of individual component damage in the overall damage state and performance of the bridge system. The data reviewed herein are largely concerned with component behavior, yet performance is an attribute of a system. Additionally, dam- age analysis of bridge systems following significant earth- quakes can be used to direct further research and improve design criteria. DAMAGE STATES Past earthquakes have caused significant damage to some bridges, greatly affecting their functionality after ground shaking subsides. Structural damage has been observed in all major bridge components, exhibiting multiple fail- ure modes. Figure 13 shows examples of bridge damage as seen in the 1989 Loma Prieta and the 1994 Northridge earthquakes. Perhaps the most well-known bridge collapse during the Loma Prieta earthquake was that of the Cypress Viaduct, which claimed 43 lives (Priestley et al. 1996). This collapse was largely caused by column joint shear failures, as shown Figure 13a, the result of the lack of a robust load path through the joint preventing force transfer from the col- umns to the crossbeams. Another significant collapse dur- ing Loma Prieta was the Struve Slough Bridge, shown in Figure 13b. In this case, the columns (pile extensions) had minimal transverse reinforcement at the connection to the skewed transverse cap beam. Under strong shaking the soil around the piles deformed significantly, leading to pile-to- cap plastic hinge failures, resulting in the collapse of the central segment of the bridge (Jablonski et al. 1992). The San Francisco–Oakland Bay Bridge was also damaged in this earthquake. The Northridge earthquake was also particularly dam- aging to reinforced concrete bridges, with a number of short-column, brittle shear failures owing to the low trans- verse steel quantities within the columns, as seen in Figure 13c. This problem was exacerbated by geometric effects such as short, stiff columns attracting significant loading. This led Caltrans to develop criteria that holistically treat the bridge system whereby mass and stiffness was bal- anced throughout the bridge. Another design flaw that led in some cases to significant damage were flared columns similar to the one shown in shown in Figure 13d. These architectural column flairs were intended to break away under transverse loading allowing the column to develop a plastic hinge at the top of the column adjacent to the bridge superstructure soffit. However, in several columns the flairs remained intact forcing the plastic hinge to form lower in the column, increasing the rotational demands on the col- umns, which resulted in plastic hinge failures. Also evident is the fractured transverse reinforcement within the plastic hinge. This lack of core concrete confinement led to axial crushing of the plastic hinge. Damage from the Loma Prieta and Northridge earthquakes instigated much of the recent research on bridge components. One of the purposes of conducting laboratory experi- ments on bridge components, subassemblages, and systems is to correlate definable deformation responses, such as strains, curvatures, rotations, and EDPs, with the initiation and progression of damage states, known as DMs. Finally, the DMs can be related to the functionality or loss of the bridge in terms of performance level. These correlations have been defined within the literature, but there is often a disparity in what is reported between researchers, insti- tutions, and organizations. An example of such a correla- tion, which is based on the five-level performance evaluation approach developed and used extensively by the University of California, San Diego (Hose and Seible 1999) and by Cal- trans in their Visual Catalog of Reinforced Concrete Bridge Damage (2006), is presented in modified form in Table 10. Example correlations between damage levels (DLs), hysteresis, and EDPs are given in Figures 14 and 15 and Table 11. The hysteretic response of the specimen is char- acteristic of well-confined, reinforced concrete columns with a near elastic perfectly plastic response and stiffness degradation upon unloading, particularly at high ductility levels. The specimen was able to reach a displacement duc- tility of eight, which corresponds to a drift angle of nearly 9% before bar buckling and fracture occurred. This is well above the displacement ductility demand limits imposed in the AASHTO SGS and the Caltrans SDC. It is also evident that damage levels I through IV are repairable, as the trans- verse and longitudinal steel have not fractured or buckled, and the core concrete remains intact. Damage level V would require significant repair efforts or even complete column or bridge replacement.

39 FIGURE 13 Typical bridge damage: (a) Cypress Viaduct collapse (Loma Prieta, 1989); (b) Struve Slough Bridge (Loma Prieta, 1989); (c) I-10 at Venice Blvd. (Northridge, 1994); and (d) Mission Gothic Bridge (Northridge, 1994). (Courtesy: National Information Service for Earthquake Engineering, EERC, University of California, Berkeley.) (a) (b) (c) (d)

40 TABLE 10 BRIDGE DAMAGE AND PERFORMANCE ASSESSMENT Damage Level Damage Classification Damage Description (Damage Measures) Performance Level I No • Onset of hairline cracks Fully operational II Minor • Crack widening • Theoretical first yield of longitudinal reinforcement Operational III Moderate • Initiation of inelastic deformation • Onset of cover concrete spalling • Development of diagonal cracks Limited damage IV Major • Formation of very wide cracks • Extended concrete spalling Life safety V Local failure/ collapse • Buckling of main reinforcement • Rupture of transverse reinforcement • Crushing of core concrete Collapse TABLE 11 BRIDGE PERFORMANCE/DESIGN PARAMETERS SRPH-1 (HOSE AND SEIBLE 1999) Level Description Steel Strain Concrete Strain % Drift Displacement Ductility i Fully operational <0.005 <0.0032 <1.0 <1.0 ii Operational 0.005 0.0032 1.0 1.0 iii Life safety 0.019 0.01 3.0 2.0 iv Near collapse 0.048 0.027 5.0 6.0 v Collapse 0.063 0.036 8.7 8.0 Comparing the data in the Figure 14 and Table 11 with those in Table 10 reveals that the life safety designation applies at very low displacement or ductility levels in Hose and Seible’s (1999) work, while the Caltrans and AASHTO design procedures would permit much higher displacements. This inconsistency in terminology and nomenclature should be resolved before PBSD can be uniformly applied. In Table 10, life safety has been adjusted upward to reflect the normal application of the term in bridge design practice. The current relationships between damage and perfor- mance levels are somewhat subjective, based on the per- ceived risk and observed actual performance of components and structures in past earthquakes. Accordingly, there is some variation between correlations of damage and perfor- mance, depending on the agency or institution that produces the relationship. One hurdle that must be overcome to a reach a fully developed PBSD methodology is a consensus on what damage and performance levels should be incorporated and what definitions of damage and performance can be used. Regardless of the performance levels chosen, all perfor- mance assessment metrics use visually or analytically deter- minable milestones of damage to quantify an EDP limit. The visual limit state assists postearthquake inspectors in the field, and the analytical limit states assist the designer. Example limit states for reinforced concrete and steel mem- bers will likely include some or all of the damage states listed in Table 12. Although some authors have used as many as five sepa- rate damage levels of interest (Hose and Seible 1999), these could also be distilled down to two for reinforced concrete ele- ments—the onset of cover concrete spalling and the initiation of longitudinal bar buckling—as they represent the flexural damage states that indicate the onset of operability limitations and onset of life safety concerns, respectively (Berry and Eber- hard 2003). A nationwide consensus (among researchers, gov- ernment, and practitioners) is needed on what damage states should be evaluated. This consensus would also assist in set- ting consistent damage state limits for bridges of high and low importance because of postevent operability requirements. FIGURE 14 Typical bridge column performance curves SRPH-1 (Hose and Seible 1999).

41 FIGURE 15 Bridge column damage at various damage levels SRPH-1 (Hose and Seible 1999).

42 TABLE 12 REINFORCED CONCRETE AND STRUCTURAL STEEL MEMBER DAMAGE STATES Reinforced Concrete Damage States Structural Steel Damage States Concrete cracking First yield Cover concrete spalling Local buckling (e.g., flange or web) Core concrete crushing Lateral torsional buckling Yield of the longitudinal reinforcement Brace buckling Fracture of the transverse reinforcement Fatigue cracking Buckling of the longitudinal reinforcement Connection fracture (e.g., bolt or weld) Fracture of the longitudinal reinforcement Gross or net section fracture or tearing Residual deformations Residual deformations An observation or caveat regarding the element correla- tions between EDP and performance level discussed previ- ously is that they are for individual elements or components, not systems. Thus, depending on the redundancy, configu- ration, boundary conditions, and articulation of the bridge system, such damage may not be indicative of the entire bridge and its performance. Often, individual components may experience damage that affects a local region, but the system as a whole may not be at the same damage level. In such situations, a local repair may return the bridge to full service in a short time, even though the component damage could have been severe, even near collapse. This situation produces a challenge in analytically predicting behavior, a priori, and making decisions regarding use before inspecting the bridge postearthquake. A classic example is the collapse of two deck spans at Pier E9 on the East Bay Crossing portion of the San Francisco– Oakland Bay Bridge in the 1989 Loma Prieta earthquake (Housner and Thiel 1990), as shown in Figure 16. The spans were replaced and the bridge was returned to service rela- tively quickly. In no way was the entire bridge system a loss, even though several components reached a collapse damage state. A replacement for the bridge is under construction, but the original bridge has remained in service for many years following the earthquake. DAMAGE PREDICTION In first-generation PBSD, the onset of damage has typically been treated as discrete deformation limits based on strain FIGURE 16 San Francisco–Oakland Bay Bridge Span E-9 Collapse, Loma Prieta Earthquake, 1989. (Courtesy: National Information Service for Earthquake Engineering, EERC, University of California, Berkeley.)

43 (e.g., AASHTO SGS) or rotation (e.g., ASCE 41), which essentially quantifies each damage state deterministically, where the likelihood of damage goes from 0% to 100% the instant a damage limit is reached. Unfortunately, the onset of damage is not a discrete deterministic quantity; there is a distribution of values. In effect, the damage prediction is a probabilistic problem, not a deterministic one. What is not often clear in the codes and some literature is whether the reported deformation limits represent lower bounds, mean, or some intermediate value for the onset of damage. This ambiguity results in a situation where the dispersion of the data and the exact location of the limiting value within the statistical spread are unknown. This ambiguity is perhaps best illustrated through the cover concrete strain at the initiation of spalling in rein- forced concrete columns. One issue that immediately arises is that the concrete strain at spalling is not directly measur- able during an experimental test, and therefore, it has to be either back-calculated or determined using a numerical pre- dictive analysis. To determine the strain at spalling using experimental data, the concrete strain must be calculated based on the experimentally measured curvature and steel strains using a plane-section assumption. While theoreti- cally this approach is simple, such a calculation can intro- duce significant errors with respect to the curvature and the strain recordings due the effects of cracking and bond deterioration. The curvature measured during a test is an average curvature over a specific gauge length, and the steel strain recorded is subject to the proximity of the strain gauge to a crack within the concrete, along with thermal effects because of heat generated during yielding of the steel. These errors make the back calculation of the spalling strain based on experimental data difficult. To circumvent these problems, the nominal strain at spall- ing can be calculated using a predictive analysis of the entire test specimen, which typically uses a moment-curvature analysis, the assumed plastic hinge length, and the second moment area theorem to determine deflections. However, when this is done, there is still a considerable spread in the predicted or calculated concrete strain at the onset of spall- ing, with values ranging from 0.002 in./in. to 0.018 in./in. for circular columns and 0.002 in./in. to 0.01 in./in. for rectan- gular columns (Lehman and Moehle 1998; Hose and Seible 1999; Berry and Eberhard 2003). Relationships between cover spalling and various parameters for spiral columns are shown in Figure 17, generated as a part of the research con- ducted by Berry and Eberhard (2003), where it is clear from the vertical distribution of points that there is a no obvious choice for the strain at spalling. The solid and dashed lines in the figure represent families of specimens that are nominally identical, other than the property defined as the abscissa. All columns included in the data set shown are classified as flex- ure-critical, have an aspect ratio (L/D) greater than 1.95, and the longitudinal reinforcement is not spliced. The variables are defined as follows. spall = Extreme concrete strain at onset of spalling D = Column diameter P = Column axial load L = Length of column cantilever Ag = Gross concrete area db = Longitudinal bar diameter = effective confinement ratio Eq. 1 Where: s = is the volumetric transverse ratio fys = is the yield stress of the spiral reinforcement f 'c = is the concrete compressive strength Eq. 2 Where: l = is the volumetric longitudinal ratio fy = is the yield stress of the longitudinal reinforcement. It is clear that the often-used values of 0.004 to 0.005 extreme compression fiber strain are simplifications of a highly variable quantity, and that there is poor cor- relation between spalling and the correlative secondary variables used in the figures. To further complicate the matter, damage initiation in steel and concrete appears to be dependent on the history of inelastic loading, known as the cumulative damage process (El-Bahy et al. 1999; Moyer and Kowalsky 2003; Tsuno and Park 2004). During seismic attack, the number and magni- tude of inelastic excursions are a function of the ground motion and the structural characteristics (e.g., stiffness, strength, energy dissipation). These excursions can only be accounted for directly using a nonlinear response his- tory analysis, where f lexural damage models (low-cycle fatigue, bar buckling, and cumulative energy dissipa- tion) are employed to predict if the ultimate deformation capacity of the component has been reached. Further- more, the interaction between bar buckling, bar fracture (as result of low-cycle fatigue or prior buckling cycles), and transverse steel quantity is complex and is not entirely understood.

44 FIGURE 17 Trends in nominal compressive strain at cover spalling, circular columns (Berry and Eberhard 2003).

45 Although there has been considerable research investi- gating the effects of cumulative damage processes (Manson 1953; Coffin 1954; Manson and Hirshberg 1964; Mander et al. 1994; El-Bahy et al. 1999; Brown and Kunnath 2000; Moyer and Kowalsky 2003; Tsuno and Park 2004; Saisho 2009; Hawileh et al. 2010, among others), research is still ongoing at North Carolina State University by M. Kow- alsky to evaluate current PBSD material strain limits and the relationship between strain and displacement consider- ing the seismic load history and even temperature effects. This research is of critical importance as the preponder- ance of design practice uses monotonic sectional analyses and strain limits to define the performance (and damage) of a structure. The strain limits are currently selected with- out a consistent scientific justification or basis, and a given strain is nonunique to a specific displacement because of the uneven accumulation of tensile and compressive strain under cyclic loading. Cumulative damage/load history effects without question contribute to the uncertainty in damage initiation, but fur- ther research is needed in this area to quantify their partici- pation. Furthermore, load-history effects are significant in the determination of structural performance during strong aftershocks, as the initial conditions of the structure for the aftershock ground motion can be drastically different from those of the undamaged structure. These are potentially major hurdles that must be overcome before PBSD can be fully realized and implemented. Because there is uncertainty or variability within the onset of damage, a conservative, lower-bound estimate is typically used as a discrete deterministic limit. This esti- mate adds conservatism to the solution and reduces the probability of damage occurring at lower deformation lev- els. Although this is certainly a valid methodology and has been used successfully in first-generation PBSD, improve- ments can be made. The prediction of damage can be further refined by employing a probabilistic description for the onset of damage, where deformation limits can be selected using a consistent basis and the inherent uncertainty in damage initiation can be defined. However, before the probabilistic treatment of damage is discussed, a brief aside will draw an analogy to the variation in strength of structural components using structural reliability theory. It is well known in structural design that the strength of any element will fall within a certain distribution clustered about a central tendency (mean or median). The variability in strength is used in LRFD design, where both resistance and loading are treated as random variables described according to a certain distribution or probability density function (e.g., normal Gaussian, lognormal). Structural safety is achieved by selecting a lower-bound element resistance and an upper- bound load effect that will produce an acceptably low prob- ability of failure. Resistance factors (whose values are less than unity) are used to reduce the predicted element strength such that it lies toward the lower bound of the bell-shaped distribution of strength. The distribution of strength (resistance) is shown in Figure 18 as a Gaussian probability density function where mR is the mean resistance, Rn is the nominal resistance, and ΦRn is the design resistance. FIGURE 18 Distribution of resistance (Nowak 1999). Associatively, load factors (whose values are greater than unity) are used to increase the service-level loads so they are representative of the upper bound of com- bined load effect on the element. The distribution of the loading is shown in Figure 19 as a Gaussian probability density function where mX is the mean load, Xn is the ser- vice load, and γXn is the factored load used in strength design checks. FIGURE 19 Distribution of load effect (Nowak 1999). The load and resistance factors are calibrated based on the nature of the loading (e.g., duration, frequency, severity), the variability of component strength (i.e., the dispersion or uncertainty), the component failure mechanism (ductile or brittle), and the desired probability of failure. As long as the design resistance is greater than the factored load, the LRFD equation (ΦRn ≥ γXn) is satisfied, and the design is consid- ered safe. The statistical variability of strength is also included in modern seismic design philosophy of capacity pro- tection, where it is recognized that ductile elements experiencing plastic deformation have an associated dis- tribution of strength with a maximum feasible strength, or “overstrength.” Adjacent nonductile elements are then designed to elastically resist the overstrength forces, thereby capacity protecting them from damage, as higher seismically induced internal forces cannot be generated within the structure.

46 If the distribution of component strength is superim- posed onto the nonlinear force-displacement response of a reinforced concrete column (as in the upper portion of Fig- ure 20), significant strength levels can be identified. The expected (mean) strength of the component is represented by the solid line and is determined using expected material properties (1.3f’c and 1.1fy). This is equal to mR in Figure 18. The maximum feasible strength of the component is repre- sented by the overstrength line and is typically 1.2 to 1.4 times greater the expected strength for reinforced concrete elements, in this case represented by 1.7f’c and 1.3fy. Finally, the nominal strength is determined using nominal material properties. Note that this is the same strength represented by Rn in Figure 18. FIGURE 20 Sources and treatment of uncertainty in strength and damage. It can now be seen that the probabilistic treatment of capacity and demand is nothing new to structural analysis, and it is therefore a simple extension to treat damage accord- ingly. In Figure 20, three damage states have been identi- fied: first yield, spalling, and longitudinal bar buckling. Each damage state is also assigned an expected value, indicated by the vertical dashed line, and a distribution of possible val- ues surrounding the expected value (the probability density function). The uncertainty of each damage state is unique, as indicated by the dispersion or width of the distribution. First yield is relatively well defined, as indicated by the narrow distribution. This means that the variable has little uncer- tainty and, if the dispersion is small enough, it can be treated deterministically. However, the distributions for spalling and bar buckling are much wider, showing that there is sig- nificant uncertainty in their values. If the probability density function is integrated (summed) along its domain, the result is a cumulative distribution function (CDF). In the context of damage analysis, the CDF is known as a fragility function and rep- resents the probability that a certain damage state (known here as DM) will occur given a certain value of an EDP, such as strain, rotation, drift, or displacement. Typically, a lognormal distribution is adopted in earthquake engineer- ing for several key reasons: It fits a wide variety of struc- tural and nonstructural components along with structural collapse, it has a strong precedent in seismic risk analysis, and it has an advantage theoretically because there is zero probability density at and below zero EDP values (Por- ter et al. 2007). However, fragility functions can also be defined using a normal Gaussian distribution. The general mathematical form of a lognormal fragility function is given in Equation 3. Eq. 3 Where P(DM|EDP) is read as “the probability of DM occurring given EDP,” Φ is the normal cumulative prob- ability distribution defined as a function of the median EDP value of the distribution (θ) and the dispersion (β), which mathematically is the logarithmic standard deviation. Fragility functions for the three column damage states are shown in Figure 20, which shows that the fragility func- tion occupies the domain where its respective damage state can occur. High-variability damage have shallow fragility functions, while low-variability damage states have steep fragility functions. While the schematic representation of fragility functions are relatively simple, their derivation and modification from experimental or analytical data or expert opinion can be complex and are outside the scope of this synthesis. However, Kennedy et al. (1980), Krawinkler and Miranda (2004), Porter et al. (2007), and ATC (2011) are excellent references in fragility function theory and development. Care must be taken in developing and applying fragil- ity functions, as they are only as reliable as the data used to develop them. Accordingly, the selection and filtering of the input data are critical so that the fragility function relates only the true uncertainty of the actual component of interest. This uncertainty includes the variability of con- struction quality, actual material properties in relation to the properties assumed in design, and the testing proce- dure (e.g., test setup, loading protocol, boundary condi- tions). In effect, only the variability that cannot be directly accounted for using well-defined engineering principles should be included. Discretion is also required in select- ing the EDP to define the fragility function of a compo- nent. Typically, the EDP with the lowest dispersion will be selected, as this will increase the accuracy of the damage prediction. For columns, this will be the drift ratio or the plastic hinge rotation.

47 The probabilistic treatment of damage can then be applied to PBSD in several different ways. First, the damage fragility functions can be used to generate deformation (strain, rota- tion, or drift) limits that have a uniform probability of occur- rence. For example, if it is acceptable to have a 20% chance of spalling at the design strain limit, the fragility function relating the probability of spalling to extreme cover concrete strain can be used to determine the strain associated with a 20% probability of spalling. This partial implementation would provide a more rigorous basis for discrete determin- istic deformation limits than what is currently employed in first-generation PBSD. Second, fragilities can be used in postearthquake bridge inspection prioritization; this will be discussed later in the chapter. And finally, as discussed in chapter seven, the component damage fragilities can be used during vulnerability or loss analysis in the full probabilistic form of PBSD. For a probabilistic damage analysis methodology to be fully functional, all relevant damage states must be defined for all relevant components, which requires extensive exper- imental and analytical testing and investigation (Krawin- kler and Miranda 2004). This research includes areas such as accelerated bridge construction (ABC) and nonconven- tional ductile components. Although a fully probabilistic PBSD methodology is desirable from a purist perspective, a large data gap waits to be filled. Reinforced concrete col- umns have seen the most laboratory research attention for bridge components. This is evidenced by the wealth of test data as found in the PEER Structural Performance Data- base (http://nisee.berkeley.edu/spd/). The database includes more than 400 cyclic lateral load tests of circular, octagonal, and rectangular columns with various reinforcement con- figurations. The Kawashima Research Group has compiled a similar database of Japanese column tests (http://seismic. cv.titech.ac.jp/). Until fragility relationships are developed for all struc- tural components and the dissemination of the information to structural designers, PBSD has to be implemented using deterministic methods based on the information that is cur- rently available (Priestley et al. 2007). As is evident from the earlier discussion of ATC-58, the building industry has made relatively large strides in the development of a full suite of fragility functions. The bridge industry has only begun this development. Perhaps one of the best recent examples of the development and application of bridge component fragility is the work of Berry and Eberhard (2003) at the University of Washington. They focused on the damage states of cover concrete spall- ing and longitudinal bar buckling for reinforced concrete col- umns. As an input for their work they surveyed more than 100 flexure-critical rectangular and circular bridge column tests with aspect ratios of 1.95 or greater. None of the tests included spliced longitudinal reinforcement. In general, rectangular columns were confined with rectangular hoops or cross ties and the circular columns were confined with spiral or circular hoops. The culmination of their research was the development of expressions that predict the expected column displacement (∆calc) at the onset of spalling and at bar buckling, see Equa- tions 4 and 5, respectively. Eq. 4 Eq. 5 Where ke_bb = 40 for rectangular-reinforced columns, 150 for spiral-reinforced columns, and zero if s/db exceeds 6, and the remaining variables are defined in relation to Figure 17. The probability of damage can then be predicted using the fragility functions, which have been reproduced in Figure 21. The ratio of the seismic demand (∆demand) to the predicted expected displacement at the onset of damage (∆cdc) is entered as the abscissa; then the probability of the respective damage state is read as the ordinate based on fra- gility function. Note that if the seismic demand is equal to the calculated displacement at the onset of damage, there is a 50% probability that damage will have occurred. In gen- eral for this set of data, the fragility functions based on the normal cumulative distribution function (CDF) provide bet- ter estimates of the data than the lognormal CDF; this may not always be the case. Equation 4 has since been adopted to form the basis of the “implicit” displacement capacity expressions that are used in the AASHTO SGS to predict displacement capacity for bridges designed for SDCs B and C, as shown in Figures 4 and 5. DAMAGE REDUCTION Aside from the ability to predict the onset of critical dam- age levels, there is also a need to refine design and detail- ing concepts to mitigate damage within the structure. Two strategies exist, both of which rely on the design philoso- phy of capacity protection. The first strategy is to limit the permissible deformations in order to limit damage. This is typically done by lowering the strain (or other deformation) limit from those found in guidelines such as the AASHTO SGS. This approach can be seen in the current agency- and project-specific criteria that are reviewed in chapters eight and nine of this synthesis. The second approach is to use construction concepts that inherently reduce or prevent damage, even under large deformations and displacements. These concepts include but are not limited to the following: • Transverse steel/confinement requirements in rein- forced concrete members • Isolation and dissipation devices • Residual displacement control

48 • Damage-resistant plastic hinges • Load path control. These concepts will be briefly discussed to show their applicability to increasing the seismic performance of bridge structures. Transverse Steel/Confinement Requirements Perhaps the most complete and widely implemented appli- cation of damage mitigation concepts is that of increased transverse steel requirements in reinforced concrete col- umns. These provisions gradually emerged over the years subsequent to the 1971 San Fernando earthquake until the deployment of the current AASHTO seismic requirements. Experience has shown that reinforced concrete columns with low transverse steel content are susceptible to plastic hinge confinement and shear failures, resulting in signifi- cant damage and even structural collapse. The transverse steel requirements were progressively increased until finally a practical limit was reached, whereby the transverse steel content became so high as to precipitate constructability issues. Criteria such as ATC-32 (1996) pushed the limits on transverse confinement with “anti-buckling steel,” where buckling of the longitudinal reinforcement was suppressed by the transverse steel so that the controlling flexural limit state of the plastic hinge was low-cycle fatigue failure of the longitudinal reinforcement. However, experience proved that too much of a good thing analytically could lead to severe reinforcement congestion. Clearly, performance at large displacements could be enhanced, but at what price? The bridge design community then settled on the transverse steel limits that are included in the current AASHTO speci- fications, which acknowledge that bar buckling is the likely controlling limit state of the plastic hinge. Seismic Isolation and Energy Dissipation Devices Another well-known application of damage mitigation is the use of isolation and energy dissipation devices, also known as base or seismic isolation, to substantially decou- ple the structural response from the earthquake ground motion. Such systems are also referred to as protective systems. This uncoupling is typically accomplished using a system of isolation and dissipation devices strategically located within the structure. The isolation component con- sists of a flexible element that elongates the structure’s fundamental period of vibration or a sliding element that limits the seismic energy that enters into the structure. An energy-dissipating element or damper is then used to reduce the displacements imposed on the isolating ele- ments to a manageable level. The theory behind these con- FIGURE 21 Fragility functions for the onset of spalling and bar buckling for rectangular and spirally reinforced columns.

49 cepts is illustrated in Figure 22, which shows acceleration and displacement elastic response spectra. In general (for smooth or design spectra, short-period range excluded), as the fundamental period increases the spectral acceleration reduces while displacement increases until the constant displacement region of the response spectra is reached. In effect, the period lengthening due to seismic isolation devices trades spectral acceleration for displacement at the isolation plane (i.e., within the isolator). As these displace- ments can get quite large, it is then necessary to introduce supplemental damping to the system, the effect of which is shown by the family of curves in Figure 22, where ζ equals the damping as a percentage of critical. As the damping increases (larger values of ζ), the displacement can be reduced significantly. Therefore, by decoupling the struc- tural response from the ground motion, the design actions (forces and deformations) are limited by the capacity of the isolator system, thereby preventing or reducing damage. In essence, the seismic-isolation system capacity protects the entire structure by acting as a low-strength ductile fuse. Most isolation and energy dissipation systems can absorb energy without incurring damage themselves. This aspect of the devices enables them to substantially improve struc- tural performance over that of conventional structural sys- tems, such as reinforced concrete frames. FIGURE 22 Response modification due to seismic isolation and energy dissipation devices. The relative importance of either the period shift or the increased energy dissipation (damping) can be emphasized, depending on the structural configuration and the site con- ditions, leading in some cases to the exclusive use of either isolators or dampers. In general, however, structures that can accept seismic isolation and dissipation systems exhibit one or all of the following properties: (1) The bridge has stiff piers with a high natural frequency of vibration, (2) the bridge is nonregular (e.g., a combination of very short and very long columns owing to topography), and (3) the expected ground motion is well defined with a dominant high-frequency con- tent, typical of shallow earthquakes, near fault or rock sites (Priestley et al. 1996). Damping devices typically are most effective in flexible structures such as in moment frame con- struction, or of course a structure that has isolation devices. AASHTO SGS supports including protective system devices with a bridge system; they fall into the Type 3 design strategy. There is also an AASHTO Guide Specification deal- ing with analysis, design, and device testing for seismically isolated bridges (AASHTO 2010). The seismic isolation of bridges is often straightforward, with the isolators typically placed between the top of the columns or piers and the super- structure, thereby limiting the forces transmitted from the superstructure to the substructure. In many cases, the seis- mic isolators can simply replace the normal thermal expan- sion bearings. The application of protective system devices to bridges and buildings has reached a relatively mature level, and recommendations for the analysis and design of such structures are well documented (Skinner et al. 1993; Priestley et al. 1996; Naeim and Kelly 1999; Chopra 2007; Christopoulos and Filiatrault 2007; Priestley et al. 2007; among others) and are beyond the scope of this synthesis. Although seismic isolation and dissipation devices might appear to be the panacea for earthquake-induced dam- age, several challenges still exist. First, not all structures will benefit greatly from the inclusion of protective system devices; these are primarily long-period structures, as the period elongation resulting from isolation will typically not significantly reduce the spectral accelerations. Second, the increase in displacement demand can cause practical issues such as the need for large movement joints or moats around the perimeter of the isolated portion of the struc- ture. These can cause maintenance and aesthetic issues. Next, the elongation in the fundamental period can actually cause amplification of accelerations if soft-soil or near-fault forward-directivity (long-period pulse) effects are present. This issue arises from the concept that response spectra for individual earthquakes are not smooth as shown in Figure 22; they are actually quite jagged, and in the case of soft- soil or near-fault directivity effects the long-period accel- erations may be larger than moderate-period accelerations. A poignant example of this is the 1985 Michoacán earth- quake, where the deep deposit of soft lacustrine volcanic clays underlying Mexico City amplified the seismic waves significantly in the 2-second period range. In this situation, if a stiff structure was seismically isolated, the period shift could result in high spectral demands. The evaluation of site effects is therefore of critical importance in the applica- tion of seismic isolation. Furthermore, if the displacement demands of an isolated system are not properly accounted for and are underestimated, the isolation system may fail, loose stability, or run out of travel, which can impart signifi- cant accelerations to the structure. Although seismic isolation and dissipation devices may not be the fix-all for increased seismic performance, they nonetheless provide another set of tools for mitigating earth-

50 quake-induced damage and achieving heightened seismic performance levels. If the structural configuration and site conditions permit, seismic isolation can be an effective and elegant solution for controlling structural performance. Residual Displacement Control The reparability and usability of a bridge after strong ground shaking is often a function of its residual displacement. In some cases, large inelastic displacement demands can result in substantial permanent offset from a plumb condition. Strategies abound for control of residual displacements, including simply limiting normal reinforced concrete col- umn drifts. However, promising purpose-designed struc- tural systems are being developed. The development of unbonded post-tensioned columns to reduce these permanent deformations has seen particu- lar attention in the past decade. Details have been devel- oped for reinforced concrete (RC), steel-jacketed RC, and concrete-filled tube (CFT) columns. The restoring force is provided by unbonded post-tensioning steel, which is anchored into the footing and the pile cap. Energy dissipa- tion is enhanced by including bonded or unbonded mild steel within the plastic hinge region, as described by Mahin et al. (2006) and Cohagen et al. (2009); further details are out- lined in NCHRP Report 681 (Marsh et al. 2011). There are even details for RC or steel-jacketed RC segmental columns, which rely solely on longitudinal unbonded post-tensioning to develop flexural resistance. Shear resistance between the segments is developed by interface shear, with the clamp- ing force provided by the post-tensioning and column dead load (Hewes et al. 2001). The University of Washington is currently conducting experimental tests on pretensioned concrete columns. These systems hold a great deal of prom- ise to recenter the structure after a large seismic event, as indicated by quasi-static and dynamic testing. Although they have been used in the building community, concerns regard- ing long-term durability and inspection of such systems in bridges continue to prevent deployment of the concepts. However, there are still significant challenges in the ability to predict residual displacements even for recenter- ing systems (Mahin et al. 2006). Recent research (Yazgan 2009; Lee et al. 2010) has shown that the predicted residual displacements in RC structures are sensitive to the adopted modeling approach, fiber-discretized sections, or a pre- defined hysteretic rule (e.g., modified Takeda, bilinear). Yazgan (2009) noted that fiber-section elements tend to underestimate residual displacements, whereas the modi- fied Takeda hysteresis overpredicts residual displacements. However, Lee et al. (2010) presented a method that can sub- stantially increase the accuracy of residual displacement prediction in fiber-section elements by modifying the con- fined concrete constitutive model to account for the effects of imperfect crack closure on the transition between unload- ing in tension to reloading in compression. The constitutive model modifications follow the recommendations by Stan- ton and McNiven (1979). Even though prediction of residual displacements is difficult, some agencies—for example, the Japan Road Association—have adopted such strategies to help ensure reparability following strong ground shaking. The accurate prediction of residual displacements is also critical in the determination of structural response and per- formance to strong aftershocks. If significant residual dis- placements exist, bias in the response history may initiate, causing asymmetric “ratcheting” behavior where the struc- ture progressively “walks” towards collapse. Additionally, structures with large residual displacements may not be suitable for postevent use, as the live loading may introduce significant P-∆ forces on the already weakened structure, instigating collapse. Damage-Resistant Plastic Hinges Another damage control or mitigation method is the incor- poration of a deformable, damage-resistant medium into an RC or prestressed concrete plastic-hinge region. These have typically been elastomeric materials placed between a con- crete column member and an adjacent footing or cap beam. These concepts provide structural compliance to accommo- date seismic displacements, but also prevent or delay dam- age to the columns. Jellin (2008) and Stringer (2010) have conducted research on reducing damage in prestressed concrete pile connec- tions. These connections were specifically developed for use in marine wharf and pier structures, but there is overlap for application in pile bents for bridges. Because of the need for thick cover concrete (up to 3 in.) in prestressed piles in saltwa- ter environments, seismic performance is greatly affected by the thick cover concrete spalling away from the pile, with sub- stantial damage to both the pile and the soffit of the deck or pile cap at low connection rotation demands. The aforementioned research was able to greatly delay pile spalling and eliminate soffit spalling by including a thin (0.5 to 0.75 in. thick) elasto- meric (cotton duck or random-oriented fiber) bearing pad at the top of pile cutoff and a soft foam wrap around the perimeter of the embedded length of the pile into the cap. Another example is the ongoing work at the University of Nevada-Reno by Saiidi (as outlined in NCHRP Report 698), where elastomeric bearing materials are built into the portions of columns that would normally experience plastic hinging (Marsh et al. 2011). The substitution of elastomeric material in place of the normally damage-prone RC creates a column that is much more damage resistant than conven- tional columns. Once such novel damage-limiting systems are available for deployment, adequate damage prediction techniques and fragility data will be needed to take such sys- tems into PBSD. Such databases would parallel those being

51 developed by the building community for use in PBSD of buildings, as described earlier. Load Path Control The final method of damage reduction is to control the lateral load path. This method includes fusible shear keys, which provide an isolating effect if proper support lengths are used, and AASHTO SGS Type 2 structures, where all inelastic action is confined to ductile steel diaphragms, whereas the rest of the superstructure and the substructure remain essen- tially elastic. As cross-frames and diaphragms are not direct gravity load-supporting elements, they can be repaired or replaced with relative ease. Type 2 structures are relatively new and have not been implemented in any great numbers. Research into their seismic performance is still ongoing. POSTEVENT INSPECTION State DOTs have recently incorporated damage analysis to aid in postearthquake bridge inspection prioritization. Both Cali- fornia (Turner et al. 2009) and Washington (Ranf et al. 2007) have developed systems based on the USGS ShakeMaps, Haz- ards U.S. (HAZUS, described in chapter seven), and regional experience. Every bridge within a region is assigned a fra- gility function based on the bridge geometry (span lengths, number of spans, column heights, skew), component material types, year of construction, retrofit, construction type, and regional bridge performance in past earthquakes. When a seismic event with a magnitude greater than a preset threshold occurs (typically magnitude 4.0), a ShakeMap is developed for a specified intensity level [0.3 s (Washington) or 1.0 s (Cal- ifornia) 5% damped spectral acceleration], and the program then applies the fragility functions for every bridge within the affected area. This generates a list of bridges that may have incurred damage, including estimates of the potential damage level. Inspectors can use this list to prioritize their inspections, making as efficient use of both time and the state DOT’s limited resources as possible. Another tool developed by Caltrans is the Visual Catalog of Reinforced Concrete Bridge Damage (Caltrans 2006b), which relates field observations to the expected reserve capacity of the system by means of damage level definitions similar to those in Table 10. This is accomplished using photographs from more than 100 RC bridge-column labora- tory tests conducted since 1990 and photographs of actual damage from 14 historic earthquakes worldwide since the early 1970s. Damage is organized according to the failure mechanism, the shape of the hysteretic backbone (ductile, strength degrading, or brittle), and the damage level. This tool is used in training both inspectors and engineers, and it assists inspectors in interpreting the damage that they see in the field. It also helps ensure that different inspectors obtain consistent results. GEOMETRIC CONSTRAINTS AND SERVICE LEVELS Central to the serviceability of bridges are the geometric aspects of the structure, including the approaches, the bridge roadway alignment, and the barrier configuration. Displace- ments that occur during or as the result of an earthquake, whether caused by the structure or the soil around the struc- ture, may affect bridge use. Displacements that occur during the event may affect life safety, and permanent displace- ments that remain after the event may likewise affect the use of the bridge. Therefore, displacements, which are an EDP, affect the performance of the bridge, which in essence is a DM, from which losses, such as loss of service may be determined. These geometric constraints, which may be the result of structural damage, ground movements, or both, are necessary for evaluating the potential for service-level losses or service restrictions. Additionally, the geometric constraints would be expected to inform decision making regarding postearthquake use of a bridge. In 2003, the ATC/MCEER Joint Venture published MCEER/ATC-49 (2003), which provided guidelines for seismic design of highway bridges. The commentary of that document included recommendations for allowable dis- placements relative to two service levels: immediate and sig- nificant disruption. The commentary also provided a list of potential causes for displacements and suggestions for miti- gation or limitation of such displacements, shown in Table 13. The narrative that described the original table is included here verbatim, with the exception of document cross-refer- ences, which are augmented here with text in parentheses. Allowable displacements are constrained by geometric, structural and geotechnical considerations. The most restrictive of these constraints will govern displacement capacity. These displacement constraints may apply to either transient displacements as would occur during ground shaking, or permanent displacements as may occur due to seismically induced ground failure or permanent structural deformations or dislocations, or both. The magnitude of allowable displacements depends on the desired performance level of the bridge design. The following paragraphs discuss the geometric constraints that should be considered in establishing displacement capacities. It should be noted that these recommendations are order of magnitude values and are not meant to be precise. Structural and geotechnical constraints are discussed in (the higher seismic requirements of) Sections 7 and 8. Allowable displacements shown in Table C3.2-1 [Table 13] were developed at a Geotechnical Performance Criteria Workshop conducted by MCEER on September 10 & 11, 1999 in support of the NCHRP 12-49 project. The original intent of the workshop was to develop detailed foundation displacement criteria based on geotechnical constraints. The final recommendation of the workshop was that, except in special circumstances, foundations are able to accommodate large displacements without strength degradation and that displacement capacities are usually constrained by either structural or geometric considerations. The values in the table reflect geometric constraints and are based largely on judgment

52 TABLE 13 BRIDGE GEOMETRIC CONSTRAINTS ON SERVICE LEVEL (MCEER/ATC, 2003) Permanent Displacement Type Possible Causes Mitigation Measures Immediate Significant Disruption Vertical Offset • Approach fill settlement • Bearing failure • Approach slabs • Approach fill stabilization • Bearing type selection 0.083 ft. (0.03 m) 0.83 ft. (0.2 m) (To avoid vehi- cle impact) Vertical Grade Break G1 G2 ∆G • Interior support settlement • Bearing failure • Approach slab settlement • Strengthen foundation • Bearing type selection • Longer approach slab Use AASHTO “Green Book” requirements to estimate allow- able grade break None Horizontal Alignment Offset ∆ • Bearing failure • Shear key failure • Abutment foundation failure • Bearing type selection • Strengthen shear key • Strengthen foundation 0.33 ft. (0.1 m) Joint seal may fail Shoulder width (To avoid vehi- cle impact) Horizontal Alignment Break ∆B B1 B2 ∆ • Interior support failure • Bearing failure • Lateral foundation movement • Strengthen interior support • Bearing type selection • Strengthen foundation Use AASHTO “Green Book” requirements to estimate allow- able alignment break None ∆ = 3.28 ft. (1.0 m) Longitudinal Joint Opening ∆ • Interior support failure • Bearing failure • Lateral foundation movement • Strengthen interior support • Bearing type selection • Strengthen foundation 0.33 ft. (0.1 m) 3.28 ft. (1.0 m) (To avoid vehi- cle impact) Encroachment on Clearance ∆ Clearance Line • Foundation settlement • Lateral foundation movement • Bearing failure • Strengthen foundation • Bearing type selection ∆ (Actual Clearance) Depends on facility being encroached upon Table 13 continued on p.53

53 that represents the consensus opinion of the workshop participants. Geometric constraints generally relate to the usability of the bridge by traffic passing on or under it. Therefore, this constraint will usually apply to permanent displacements that occur as a result of the earthquake. The ability to repair, or the desire not to be required to repair, such displacements should be considered when establishing displacement capacities. When uninterrupted or immediate service is desired, the permanent displacements should be small or nonexistent, and should be at levels that are within an accepted tolerance for normally operational highways of the type being considered. A guideline for determining these displacements should be the AASHTO publication “A Policy on Geometric Design of Highways and Streets”. When limited service is acceptable, the geometric constraints may be relaxed. These may be governed by the geometry of the types of vehicles that will be using the bridge after an earthquake and by the ability of these vehicles to pass through the geometric obstruction. Alternately, a jurisdiction may simply wish to limit displacements to a multiple of those allowed for uninterrupted service. In the case of a no collapse performance objective, when liquefaction occurs, post- earthquake use of the bridge is not guaranteed and therefore no geometric constraints would be required to achieve these goals. However, because life safety is at the heart of the no collapse requirement, jurisdictions may consider establishing some geometric displacement limits for this performance level for important bridges or those with high ADT. This can be done by considering the risk to highway users in the moments during or immediately following an earthquake. For example, an abrupt vertical dislocation of the highway of sufficient height could present an insurmountable barrier and thus result in a head-on type collision that could kill or severely injure occupants of the vehicle. Usually these types of geometric displacement constraints will be less restrictive than those resulting from structural considerations and for bridges on liquefied sites it may not be economic to prevent significant displacements from occurring. Permanent Displacement Type Possible Causes Mitigation Measures Immediate Significant Disruption Tilting of Cross-Section ∆G • Interior support settlement • Bearing failure • Approach slab settlement • Strengthen foundation • Bearing type selection • Longer approach slab ∆ G = .001 radians None Movement into Abutment Fill (Longitudinal) ∆H • Engagement of abutment backfill due to horizontal movement of superstructure • Increase gap between superstructure and abutment backwall • Stiffen interior supports • Increase amount of fill that is engaged ∆ = .02H No Constraint Controlled by Adjacent Seat Width Movement through Abutment Fill (Transverse) ∆ • Transverse movement of strengthened or supplemental interior wingwalls through approach fill • Isolate transverse movement with sacrificial shear keys and/or isolation bearings • Increase transverse strength and stiffness of abutment ∆ = .02H No Constraint Notes: Geometric constraints, with the exception of longitudinal and transverse movement through abutment fill, usually apply to permanent displacements which may be difficult to predict accurately. Therefore, the constraints in this table shall be taken as order of magnitude values. The AASHTO publication “A Policy on Geometric Design of Highways and Streets” (otherwise known as the “Green Book”) specifies criteria for determining vertical curve length based on site distance. This criteria, which is based on design speed and whether the curve is a “crest” or a “sag” can be used to determine the allowable change in grade resulting from support settlement. A curve length equal to the sum of adjacent spans may be used in the case of a continuous superstructure or a zero curve length may be used in the case of adjacent simply supported span lengths. Bridge owners may also wish to consider the AASHTO recommendations on appearance and driver comfort in establishing allowable grade changes. In the case of horizontal curves, minimum curve radius is usually controlled by superelevation and side friction. These radii are specified in the AASHTO “Green Book”. When lateral displacement of an interior support results in an abrupt angle break in horizontal alignment a vehicle shall be able to safely achieve the desired turning radius at design speed within the provided lane width minus a margin of safety at each edge of the lane. Consideration shall also be given to the opening of the expansion joint at the edge of the bridge. Joint seals may be damaged at the immediate service level. If no damage at the seal is desired the designer should check the actual longitudinal and transverse capacity or reduce some of the permissible movements. Table 13 continued from p.52