BRIDGE PERFORMANCE LEVELS, DVS, AND DMS Keith Porter, 5/14/02
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
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
Keith Porter, 5/14/02
P. 2 of 4
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?]
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
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
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
IO O LS CP Collapse
Lifetime-maximum peformance level
Figure 1. Schematic illustration of DV1.
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  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
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
5. What level of traffic in vehicles/day can be used as the breakpoint between heavy and light
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?
1. Harrington, T., (Office Chief, Caltrans Division of Structure Maintenance), 22 April 2002, personal
2. Porter, K.A., 2002, Minutes of Caltrans & PEER Meeting 2/25/02 regarding I-880