SAMPLE DESIGN-LEVEL DYNAMIC ANALYSIS RESULTS

The analysis of the 45 IAB models (note that CtC15F_ and ClC15F_ did not yield results) at the 1000-year return period design-level earthquake hazard, provides information concerning the frequency of occurrence of the various limit states within the bridges. By assessing which limit states occur, and how often they occur, the IABs may be deemed ideal, acceptable, or

unacceptable designs for the current design-level. This section illustrates the results for

StC15EA. Tables are presented that describe the frequency at which each limit state occurs for each IAB out of the 20 ground motions it is subjected to. Additionally, figures presenting typical behavior for the IAB during one of the ground motions are also provided to demonstrate key behavior. The behavior is presented using plots of the center node displacement time history, center node displacement-base shear behavior, overall backfill behavior at one abutment, retainer behavior of all the retainers, stress-strain behavior of the four extreme fibers at the top of one of the abutment piles, and the behavior of the top p-y spring in one of the abutment

0 1 2 3 4 5 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 Period, T (sec) S pec tr al A c c el er at ion, S a ( g ) Mean

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piles. The red dashed lines in the backfill behavior and the top p-y spring behavior plots correspond to the load required to mobilize these components.

Table 3.1: Frequency of Limit State Occurrences for StC15EA Under Design-Level Ground Motions

StC15EA

LS Class _State Limit Long. Tran.

Ide al BF 0% 0% SL 60% 40% CL 35% 10% RE 0% 100% RY 0% 100% RF 0% 0% Ac ce pt abl e APY 100% 100% APB 0% 0% APS 70% 30% PA 0% 0% PPY 0% 0% PPS 0% 0% SM 0% 0% CM 0% 0% Una cc ept . BU 0% 0% SS 0% 0% CS 0% 0% APR 0% 0%

Table 3.1 provides an example of the tables used to describe the frequency of limit state occurrences for IABs under design-level ground motions. The results presented in Table 3.1 indicate that in the longitudinal direction, there is only light pier column steel and concrete damage (SL and CL), as well as the yielding of the abutment piles (APY) and the mobilization of the soil surrounding the piles (APS). In the transverse direction, SL, CL, APY, and APS also occur, in addition to engagement and fusing of the retainers (RE and RF, respectively).

The table of frequency of limit state occurrences is a useful tool in comparing the severity of damage in an IAB during design-level shaking. StC15EA does not have any unacceptable limit states occur, which is encouraging. However, the table allows for observations to be made indicating that the abutment piles always yield in both directions. Although no unacceptable limit states occur, the consistent occurrence of an acceptable limit state is still an interesting result requiring further investigation. The tables are also handy for determining which

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parametric variations aid in the fusing of certain components. An example of this is how the StC15EA results do not indicate any retainer fusing (RF) despite yielding occurring. Comparing the frequency of RF to other IABs allows for conclusions to be made concerning which

parameters aid in allowing the retainers to fuse.

Sample figures that summarize the dynamic behavior of StC15EA and its components are provided in Figure 3.2 and Figure 3.3. These figures facilitate observations to be made

concerning the individual component behavior during a dynamic analysis. The longitudinal plots include information concerning the center node displacement, overall deck displacement vs. total base shear, backfill behavior, the behavior of the four corners of a critical abutment pile, and the behavior of the p-y spring at the abutment. The transverse plots provide the same information with the exception of the backfill behavior being replaced by the retainer behavior. The behavior and time history plots allow for observations to be made concerning limit state occurrences beyond the frequency of limit state occurrence tables. For example, APY is shown to always occur in Table 3.1, and APB never occurs. However, the table is incapable of telling us whether the piles barely yield, or yield and then nearly reach local buckling. Figure 3.2 (d) and Figure 3.3 (d) allow for these gaps in knowledge to be filled in by noting that the maximum pile strain is nearly 5 times the yield strain in the longitudinal direction and only about 3 times the yield strain in the transverse direction. Similarly, Figure 3.3 (c) demonstrates that the retainers do experience significant yielding and are close to fusing despite it never occurring. Other interesting behavior can also be observed, such as the effect of backfill re-engagement in the longitudinal direction and retainer re-engagement in the transverse direction. Both of these occurrences result in the overall deck displacement-base shear response to have a noticeable pinching behavior.

Although the plots described in this section may not be present in the summary of the

parametric study results found in Chapter 4, the complete set of figures describing the design- level dynamic analyses can be found in Appendix C.

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Figure 3.2: Dynamic analysis results for StC15EA subjected to a design-level ground motion in the longitudinal direction.

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Figure 3.3: Dynamic analysis results for StC15EA subjected to a design-level ground motion in the transverse direction.

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