Limit States

The IAB seismic damage limit states that track inelastic bridge behavior are divided into three categories based on their desirability; ideal, acceptable, and unacceptable. Ideal limit states act as fuses and protect other more critical bridge components. The ideal limit states typically cause minimal damage or damage to components that are easily replaceable or repairable, so that a bridge can remain functional immediately after an earthquake. Acceptable limit states do not involve severe damage, but the damage occurs in components that are difficult to inspect or replace. Damage from acceptable limit states still allows for immediate use of a bridge after an earthquake for emergency services. Unacceptable limit states are those involving severe damage that renders a bridge unusable for even emergency services immediately after a seismic event. A list of the potential limit states in an IAB model and their associated abbreviations are presented in Table 2.3.

Table 2.3: IAB Model Limit States

Ideal Limit States Acceptable Limit States Unacceptable Limit States

Backfill Mobilization – BF Abut. Pile Yielding – APY Bearing Unseating – BU

Retainer Engagement – RE Abut. Pile Local Buckling – APB Severe Steel Pier Damage – SS Retainer Yielding – RY Abut. Pile Soil Mobilization –

APS

Severe Concrete Pier Damage - CS

Retainer Fusing – RF Pile Cap-Abut. Interface Failure – PA

Abut. Pile Rupture – APR

Fixed Bearing Yielding – FY Pier Pile Yielding – PPY

Fixed Bearing Fusing – FF Pier Pile Soil Mobilization– PPS Bearing Sliding – BS Moderate Steel Pier Damage –

SM

Light Steel Pier Damage - SL Moderate Concrete Pier Damage - CM

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The limit states for light, moderate, and severe pier column damage are presented in Table 2.4. Reinforcing steel damage corresponds to the beginning of yielding for light damage, the end of yielding for moderate damage, and rupture for severe damage. Concrete damage is

represented by concrete cracking and concrete spalling for light and moderate damage,

respectively. Severe concrete damage is defined as strains beyond the limit where the concrete would still be repairable, and so the column would need to be replaced (Kowalsky, 2000).

Table 2.4: Corresponding Strain Values for Pier Column Limit States

Limit State Concrete (compression) Reinforcing Steel (Tension)

Light Damage -0.005 < εconc ≤ -0.002 0.0021 ≤ εrebar < 0.015

Moderate Damage -0.018 < εconc ≤ -0.005 0.015 ≤ εrebar < 0.06

Severe Damage εconc ≤ -0.018 0.06 ≤ εrebar

Nine limit states are classified as ideal limit states. Mobilization of the backfill soil at the abutments (BF) is indicated to have occurred when one of the backfill springs achieves its ultimate capacity. Three retainer limit states are included: engagement (RE), yielding (RY), and fusing, which occurs at an anchor bolt fracture (RF). Fixed bearings also experience yielding (FY) followed by fusing, when anchor bolt fracture occurs (FF). Damage to the retainers or fixed bearings leads to the onset of sliding. The bearing sliding limit state (BS) occurs if a bearing reaches the kinetic/sliding portion of bearing friction behavior. Light damage to the reinforcing steel (SL) and unconfined concrete (CL) of the column piers is also classified as ideal. These are not fuse limit states, but indications of minor damage to the pier columns.

Eight limit states are classified as acceptable. Moderate damage to the reinforcing steel (SM) and unconfined concrete (CM) of the pier columns indicates that there is a significant amount of damage in the columns, yet not enough to cause collapse. Yielding of the piles at the

abutment (APY) and pier (PPY) foundations is indicated by yielding of the material of any of the fibers in the steel pile cross-section. Local buckling of the abutment piles (APB) is estimated to occur when the strain in any pile fiber reaches 20 times the strain at expected yield (yield strain). This value of 20 times the yield strain has been identified as the onset of local buckling through a combination of cyclic pile loading experiments and analyses (Frosch et al., 2009). The soil surrounding the piles may also be mobilized by reaching its capacity in the abutment (APS) and pier (PPS) foundations. The onset of the PA limit state occurs upon failure of the dowels. Four limit states are classified as unacceptable due to the likelihood of a loss of bridge span should any of them occur. The first limit state is bearing unseating (BU), which occurs if a bearing displaces a distance larger than the seat width. The seat width dimension is calculated per the IDOT Bridge Manual (IDOT, 2012a). A loss of span may also occur if there is severe damage to the pier columns. Severe damage to the reinforcing steel (SS) or unconfined concrete (CS) of the pier columns, as indicated by achieving the strains in Table 2.4, could compromise the vertical load-carrying capacity of the column and make travel on a bridge

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dangerous immediately after an earthquake. The occurrence of any of these three

unacceptable limit states during an earthquake would result in a dangerous bridge that could not be crossed and would significantly hinder emergency response.

The rupture of the abutment piles (APR) is also identified as an unacceptable limit state due to a bridge becoming dangerous to use once piles have cracked and ruptured. The APR limit state identified in this study is based on judgement and the strain at which the ultimate stress of the steel is expected to occur. APR is estimated to occur when the strain in any pile fiber reaches a value of 40 times the yield strain of the steel.

Most of the ideal and acceptable limit states directly correspond with a change in analytical behavior occurring in the component models. Unlike those limit states, the unacceptable limit states do not correspond to any changes in modeled behavior. Instead, they only identify when certain strain or displacement limits are reached. Given this, the bridge model continues to behave normally once these limit states occur despite severe adverse effects occurring in actual bridges should these strains or displacements be achieved. Any analytical behavior beyond the occurrence of the first unacceptable limit state is therefore not clearly meaningful and

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