**3. Ground motion simulation for the study sites**

The lack of seismic records of significant earthquake events in the NMSZ makes the task of selecting ground motion excitation for response analysis a challenge. The state of knowledge of the causative features of the fault and the expected attenuation of motions from the source has changed over time and remains an area of significant debate and research. Spectral physicsbased parametric source and attenuation models have provided a rational basis for the case studies presented here.

vertical motion was obtained by uniformly scaling the resultant horizontal motion by the

FE Based Vulnerability Assessment of Highway Bridges Exposed to Moderate Seismic Hazard

http://dx.doi.org/10.5772/55334

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In the MEMA UM campus study [17], the input horizontal motion realization for the UM campus was generated by others for M6.3 and *M* 8.3 events having source along the nearest (southernmost) segment of the NMSZ. In the MDOT bridge study [14], software was obtained from the US Geological Survey (USGS) and source model parameters and attenuation relations were identified in consultation with USGS and the University of Memphis enabling simulation of multiple realizations at arbitrary intensities. Events of nominal *M* 6, 7, and 8 were selected in order to capture different response levels. In the MEMA Coldwater River bridges study [16], a FEMA scenario of *M* 7.7 was adopted to be consistent with their results for the multi-state NMSZ region which were based on a distributed source model involving slip along the entire southern segment of the New Madrid fault. Since the study provided only PGA contours, not time histories, the MDOT study realization for the *M* 8 scenario case (Fig. 6) was scaled to achieve an input motion with PGA corresponding to that of the *M* 7.7 scenario at the bridge

Source spectral models for the very large intensity events were such that all ground motions have significant energy in the 1-2 Hz range coinciding with fundamental and low natural

When using FE as the basis of vulnerability assessments, it is important to make several basic decisions regarding modeling approach including probabilistic versus deterministic and simple versus complex. These choices influence at the most general level, the software to be used, and at the most specific level, the key modeling assumptions such as system scope, boundary conditions, incorporation of soil-structure interaction (SSI), and focus on lumped parameter, 2D structural, or 3D continuum finite elements. Rather than propose a compre‐ hensive view on the proper choices for all possible objectives, the select bridge study cases are

In the MEMA UM campus study [17], no prior knowledge existed. As a result of this uncer‐ tainty about what might be expected as well as a strong desire to ensure the safety of the many thousands of students, employees, and visitors to the campus and a major concern about the impact of significant losses to the future functioning of the university enterprise and conse‐ quential economic impacts on the state, the sponsors sought the most realistic view possible given the state of the art at the time. In response to this objective, the analysts committed to full 3D nonlinear dynamic FE simulation including SSI in cases where it might have a signif‐ icant influence on the response. The project was initiated in the mid-1990s when the software ABAQUS [7] provided many desirable features including 3D nonlinear beam-column (struc‐ tural) elements (B33) with user input moment-curvature relations and 3D continuum (solid) "infinite" elements (CIN3D8) with shape functions capturing radiation damping, in effect

commonly assumed factor of 2/3.

site locations (approximately PGA=0.25g).

offered as the possible range one might consider.

frequencies of the bridges.

**4. FE modeling options**

**Figure 6.** resultant horizontal ground acceleration time histories used in FE model analyses; MEMA UM campus study [17]; MDOT study [14]; MEMA Coldwater River bridges study [16]

Figure 6 shows resultant horizontal ground motion realizations generated for the various studies assuming 2D propagation from an assumed epicenter usually taken as Marked Tree, Arkansas, the town nearest to the southernmost position of the New Madrid fault. In the MEMA campus and MDOT bridge studies, orientation of the bridge was considered and component motions were then extracted for application to the FE models. In the absence of a 3D propagation model, requiring definition of layered media in a spherical coordinate system, vertical motion was obtained by uniformly scaling the resultant horizontal motion by the commonly assumed factor of 2/3.

In the MEMA UM campus study [17], the input horizontal motion realization for the UM campus was generated by others for M6.3 and *M* 8.3 events having source along the nearest (southernmost) segment of the NMSZ. In the MDOT bridge study [14], software was obtained from the US Geological Survey (USGS) and source model parameters and attenuation relations were identified in consultation with USGS and the University of Memphis enabling simulation of multiple realizations at arbitrary intensities. Events of nominal *M* 6, 7, and 8 were selected in order to capture different response levels. In the MEMA Coldwater River bridges study [16], a FEMA scenario of *M* 7.7 was adopted to be consistent with their results for the multi-state NMSZ region which were based on a distributed source model involving slip along the entire southern segment of the New Madrid fault. Since the study provided only PGA contours, not time histories, the MDOT study realization for the *M* 8 scenario case (Fig. 6) was scaled to achieve an input motion with PGA corresponding to that of the *M* 7.7 scenario at the bridge site locations (approximately PGA=0.25g).

Source spectral models for the very large intensity events were such that all ground motions have significant energy in the 1-2 Hz range coinciding with fundamental and low natural frequencies of the bridges.
