BRIDGE PERFORMANCE LEVELS DVS AND DMS Keith Porter PERFORMANCE

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					    BRIDGE PERFORMANCE LEVELS, DVS, AND DMS                                                   Keith Porter, 5/14/02



                                              PERFORMANCE LEVELS
    In conversations in February and April, 2002 [1, 2], Caltrans engineers discussed how they currently
    describe actual bridge performance. In particular, they spoke about how Caltrans inspectors, examining
    a bridge after an earthquake, describe the bridge’s performance for decision-making purposes. They
    spoke about the available post-earthquake decision alternatives, and how the physical damage and
    consequences for traffic guide decision-making. Let us recast their decision alternatives as performance
    levels, i.e., describe performance in terms of the actions Caltrans engineers would take in light of observed
    damage. It happens that these performance levels generally coincide with those of ASCE/FEMA 356. Let
    us acknowledge this by borrowing names for performance levels from ASCE/FEMA 356. Let us also
    acknowledge that a continuity exists between some of the performance levels. Table 1 is a synthesis of
    the performance levels described in these conversations. It omits the self-evident damage states
    “undamaged” and “collapsed.”


                                  Table 1. Provisional bridge performance levels.

    Performance         Definition                                                 Caltrans action

    1. Immediately      No nonstructural or structural damage significantly        Leave open; repair any
       operational      affects vertical or lateral capacity, e.g., there can be   damage
       (IO)             concrete spalling but no evidence of distress of
                        reinforcement or structural concrete. No significant
                        roadway discontinuities. [“Significant:” > ½-1 in?]
    2. Operational      Same as IO, but there is nonstructural damage or           Close, repair damage, and
       (O)              limited ground failure affecting traffic safety, e.g.,     then reopen
                        roadway discontinuities in excess of ½ in or 1 in, that
                        can be repaired within a short time t (t ≈ 3 days?).
                        [Make list more exhaustive.]
    3. Life safe (LS)   Structural damage exists such that lateral capacity        Close, shore, reopen and
                        has been significantly impaired (perhaps in excess of      repair while open
                        10% reduction in capacity; see “damage measures”
                        for definition of capacity reduction), but vertical
                        capacity has not. Up to 50% reduction in lateral
                        capacity would be acceptable if the bridge were
                        shored to prevent collapse in aftershocks, and up to
                        10-25% reduction in vertical capacity. Damage to
                        bridge bearing pads not considered in vertical
                        capacity.
    4. Collapse         Structural damage exists such that lateral capacity        Close. For critical bridge(1),
       prevention       has been reduced in excess of 50%, vertical capacity       whichever is faster: repair or
       (CP)             has been reduced in excess of 10-25%, or both.             replace. Noncritical bridge(2):
                                                                                   whichever is cheaper,
                                                                                   including indirect cost.
    (1) Critical bridge: normally carrying heavy traffic loads [need to quantify] or lacking redundant routes.
    (2) Noncritical bridge: normally carrying light traffic loads and having redundant routes.




PORTER 14 MAY 2002 BRIDGE DV AND DM.DOC
printed 5/16/02
Keith Porter, 5/14/02
P. 2 of 4



                                          DECISION VARIABLES
The performance levels presented above specify how one would describe the performance of a bridge
after the earthquake has occurred. PEER wishes to describe performance probabilistically, through
parameters referred to as decision variables (DV). That is, the DV represents a pre-earthquake estimate of
the uncertain future seismic performance of a facility. We wish to define these DVs now. The most
straightforward way to parameterize decision variables is via the probability of reaching or exceeding
each performance levels in future earthquakes. That is, either:

    1.   DV1: a probability mass function giving the probability that each performance level would be the
         highest reached during the bridge’s design life T, as a function of the performance level, as
         illustrated conceptually in Figure 1. [T = 100 yr? T depends on traffic and redundancy?]
                                                        or
    2.   DV2: a probability mass function giving the probability that the bridge will reach or exceed a
         performance level during a scenario event (“the earthquake”), as a function of the performance
         level.

The choice of action in the CP performance level depends on repair time and repair cost. Therefore,
additional decision variables are required:

    3.   DV3: probability distribution on repair time, conditioned on experiencing CP performance.

    4.   DV4: probability distribution on repair cost, including indirect cost, conditioned on experiencing
         CP performance.

    5.   DV5: probability distribution on replacement time, conditioned on experiencing CP performance.

    6.   DV6: probability distribution on replacement cost, including indirect cost, conditioned on
         experiencing CP performance.

Scenario event. It has been suggested that “the earthquake” be defined in terms of earthquake magnitude
and distance. The earthquake would be the event whose M and R correspond to the (highest) mode of
the risk-disaggregation diagram. For example, let us create a 3-D bar chart, where the x-axis shows
discrete ranges of magnitude, the y-axis reflects discrete ranges of distance, there is a vertical bar for each
(M, R) pair, and the height of the bar is the probability that during the design life of the bridge (T = 100
yr?), an earthquake of that (M, R) will cause the bridge to reach or exceed a controlling performance level,
e.g., O for critical, LS for noncritical.
Keith Porter, 5/14/02
P. 3 of 4




                               1



                              0.1
              Probability




                             0.01



                            0.001
                                    IO              O            LS            CP      Collapse

                                             Lifetime-maximum peformance level


                                         Figure 1. Schematic illustration of DV1.

                                                 DAMAGE MEASURES
PEER’s methodology calls for estimating damage measures (denoted by DM) that are needed to assess
DV. These would be:

    1.   DM1. Residual vertical “capacity.” There are several ways to parameterize this. Caltrans
         discussion [1] seemed to be in terms of strength. Thus, post-earthquake capacity could be
         measured as DM1a = Vpost/Vpre, where Vpost = uniform live load required to cause a vertical
         collapse mechanism given the post-earthquake damage, and Vpre = similar, pre-earthquake.
         Another alternative is DM1b = Ppre/Ppost, where Ppre = probability of forming a vertical collapse
         mechanism under DL+LL, given the undamaged bridge and considering the maximum value
         during the design life, and Ppost = similar, given the post-earthquake damage, but considering the
         probability distribution on maximum DL+LL during the earthquake repair period, e.g., 5 yr,
         rather than during the design life of the bridge. DM1 and DM2 (described next) would be used to
         distinguish between damage states 2 and 3, and between 3 and 4.

    2.   DM2. Residual lateral “capacity.” Again, several ways to parameterize this. Could be defined in
         terms of strength: DM2a = Epost/Epre, where Epost = lateral load required to cause a vertical collapse
         mechanism given the post-earthquake damage, and epre = similar, pre-earthquake. Could be
         defined in terms of deformation capacity, DM2b = Dpost/Dpre, where Dpre is median pushover
         displacement associated with collapse in the pre-earthquake bridge condition, and Dpost is
         remaining median pushover displacement associated with collapse, given post-earthquake
         condition of the bridge. A third alternative would be DM2c = Ppre/Ppost, where Ppre = probability
         of forming a lateral collapse mechanism under DL+EQ, given the undamaged bridge and
         considering the maximum value during the design life, and Ppost = similar, given the post-
         earthquake damage, and during the earthquake repair period, e.g., 5 yr.

    3.   DM3. Permanent vertical ground deformation at the abutment.

    4.   DM4. Permanent relative structural deformation at expansion joints. (Difficult to estimate.)
Keith Porter, 5/14/02
P. 4 of 4



                                               OPEN ISSUES
    1.   Caltrans provisional agreement with the performance levels and definitions in Table 1.
    2.   Definition of “significant roadway discontinuity”. What size discontinuity threatens traffic safety
         and would have to be repaired?
    3.   Definition of “short repair time.” Is 3 days a reasonable cutoff?
    4.   What other nonstructural damage commonly occurs and should be listed under performance
         level O?
    5.   What level of traffic in vehicles/day can be used as the breakpoint between heavy and light
         traffic?
    6.   What is the design life T of a highway bridge (other than monumental bridges)?
    7.   Is 5 years a reasonable repair period for DM1b and DM2c?
    8.   Would Caltrans prefer DM1a or DM1b? DM2a, DM2b, or DM2c? Who are the Caltrans decision-
         makers who could offer their preferences?
    9.   Harrington suggested the cutoffs of 10% and 50% capacity reductions noted in performance
         levels 3 and 4 in off-the-cuff conversation. Would he revise these after reflection? Who else’s
         judgment should be sought to assess these cutoffs?


                                               REFERENCES
    1.   Harrington, T., (Office Chief, Caltrans Division of Structure Maintenance), 22 April 2002, personal
         communication

    2.   Porter, K.A., 2002, Minutes of Caltrans & PEER Meeting 2/25/02 regarding I-880