1. Project Goals/Objectives:

The primary objective of this research project is to incorporate several of the most efficient ground motion intensity measures (IM’s), such as Sa(2T) and Ia, and the well-used IM PGA into a full probabilistic seismic hazard assessment (PSHA) of problems of interest to PEER, e.g. the seismic displacement of non-liquefiable earthen slopes. For example, based on the research of Travasarou and Bray (2003), their simple model of an earthen slope will be incorporated in a full probabilistic seismic hazard assessment (PSHA) with a focus on the engineering demand parameter (EDP) of seismic permanent displacement. The consequences of calculating these respective EDP’s and the uncertainty associated with them for these problems directly through a single PSHA calculation as opposed to indirectly through a PSHA on a relevant IM and then through a relationship developed to estimate the desired EDP based on the specified IM will be explored. This research will allow a more in-depth examination of the first part of the PEER probabilistic framework equation. In addition, a secondary objective of this research is to examine the implications of how earthquake ground motions with identical IM’s are specified for dynamic analysis requiring input acceleration-time histories.

2. Role of this project in supporting PEER’s mission (vision):

This project supports the PEER development and implementation of the Probabilistic-Based Earthquake Engineering methodology through examination of efficient intensity measures for characterization of earthquake ground motions and proper definition of “rock” motions for input to advanced analysis of soil-structure interaction problems.

3. Methodology Employed:

The basic framework for PEER’s performance-based earthquake engineering efforts requires explicit consideration of uncertainties in the seismological, geotechnical, structural, and economic analyses required for comprehensive performance-based seismic evaluation. The reliability of performance predictions will be improved by any reductions in the uncertainties of the parameters used as input to these analyses. Significant uncertainties exist in each of these areas, but perhaps none are as significant as the uncertainties in earthquake ground motions.

Uncertainties in ground motions can be reduced by the identification and subsequent use of ground motion parameters (or Intensity Measures, IM) that correlate well to performance through Engineering Demand Parameters (EDP), and then to “damage.” It is recognized that performance, and the occurrence of “damage” is complex and that no single ground motion parameter will correlate well to all forms of damage. Consequently, through PEER-sponsored research, a number of promising ground motion IMs were identified by several research teams.

The promising IMs are categorized as period-dependent IMs (such as spectral acceleration at the initial elastic fundamental period of the system, i.e. Sa(T), or at some multiple of this period to account for nonlinear response of the system) and period-independent IMs (such as Arias Intensity (Ia) for short-period systems, i.e. T < 0.7 s, and Housner’s Spectral Intensity (SI) for long-period systems, i.e. T > 0.7 s). It was found that Sa(T) or Sa(xT), where x is some multiple such as 2, were the most efficient IMs for predicting a range of EDPs for several classes of problems, such as the seismic performance of bridges, buildings, and earth slopes. Of course, this IM requires specification of the fundamental period of the system T. For classes of problems where T is not well-known or numerous systems of differing T require evaluation, Ia was found to be efficient for cases where T<0.7 s, so an empirical attenuation relationship was developed to estimate Arias Intensity and the uncertainty of its estimate.

However, no intensity measure was found to be fully sufficient for all cases, so some guidance needs to be given regarding the selection of the acceleration-time history required for dynamic analysis. Moreover, the implication of the selection of a particular IM or a vector of IMs in terms of the overall probabilistic seismic hazard analysis has not been evaluated. Hence, this work, which follows from previously funded PEER research, is required to address issues such as these.

The amount of the nonzero seismic displacement for an earth slope can be computed using:


(1) where: c₁= -1.64, c₂₁= -3.57, c₂₂= -0.478, c₂₃= 0.825, c₃₁= 3.75, c₃₂= -0.33, c₄₁= 0.872, c₄₂= -0.082, and c₅= 0.30 are the coefficients determined by the regression and e is a normally-distributed random variable with zero mean and standard deviation s = 0.77. The residuals of Equation (1) are plotted in Figure 1 versus the predictive variables where it can be seen that it captures the data well.

Figure 1. Residuals (d_data – d_predicted) of Equation (1) plotted versus magnitude,
rupture distance, the yield coefficient and the initial fundamental period.

The following tasks will be completed as part of this two-year research project:

4. Brief Description of past year’s accomplishments (Year 6) & more detail on expected Year 7 accomplishments:

This effort did not receive support in Year 6. Instead, it builds upon the Years 3-5 project on identification of efficient intensity measures for earthquake ground motions and development of ground motion attenuation relationships for efficient intensity measures. This project developed several insights regarding optimal intensity measures such as spectral acceleration at a degraded period of the system and Arias Intensity. The accomplishments are described in two conference papers and one journal article.

Anticipated Year 7 accomplishments include preparing a conference paper to be presented at the 12th World Conference on Earthquake Engineering that describes a probabilistic methodology for estimating seismic slope displacements. This effort illustrates the use of the PEER PBEE methodology. Additionally, guidelines for developing rock motions for use in numerical simulations will be developed.

5. Other Similar Work Being Conducted Within and Outside PEER and How This Project Differs:

This project interacts with ongoing work being performed by Ahmed Elgamal and Joel Conte, among others, on the development of input motions for the Humbolt Bay bridge testbed and with Ross Boulanger and Sashi Kunnath, among others, on the I-800 interchange testbed. With its focus on efficient intensity measures for earthquake ground motions it continues the interaction with others in PEER working on this topic, including Allin Cornell, Helmut Krawinkler, Bozidar Stojadinovic, and Joel Conte, among others. This PI is conducting no similar work outside of PEER.

6. Plans for Year 8 if project is expected to be continued:

A Year 8 effort would extend the results of this study to address the special characteristics of near-fault motions.

7. Describe any actual instances where you are aware your results have been used in industry:

A software developer for a well-used probabilistic seismic hazard assessment program contacted me to obtain the attenuation relationship for Arias Intensity that we developed in our Year 3-5 effort. Additionally, a number of practicing engineers have used this attenuation relationship. The results from the Year 7 project are described in a paper to be published in August 2004, so widespread dissemination of the methodology has not occurred. However, the methodology has been used to develop a probabilistic estimate of seismic displacement of a municipal solid-waste landfill for a client who became aware of the project through email exchanges with the PI.

8. Expected Milestones & Deliverables:

The deliverable for this project will take the form of a technical report that will summarize the research methods used and present the results of the research as well as implications for the use of the PEER probabilistic performance-based framework for similar classes of problems.