Existing approaches for prediction of seismic ground motion and its associated uncertainties mostly rely on fitting to a recorded motion (usually at the surface) with known earthquake and site characteristics. However, application of such obtained probabilistic ground motion to geotechnical engineering problems, such as free-field probabilistic site response analysis or probabilistic soil-structure interaction analysis, double counts the uncertainties and non-linearities of the soil medium. The goal of this project is to develop a new, physics-based methodology and an attendant computational tool to obtain a complete probabilistic description (probability density function) of site-specific ground motion time-history for a future seismic event by (1) characterizing and quantifying uncertainties in bed-rock motion at a site during future seismic event (right hand side (RHS) uncertainty), (2) characterizing and quantifying uncertainties in site-specific soil properties (left hand side (LHS) uncertainty), and (3) propagating the uncertain bed-rock motion through the uncertain soil. The ability to obtain such probabilistic description of site-specific ground motion time history will not only help in accurately assessing performance of any civil infrastructure object, but also help in critical decision-making process by the project owners, policy makers, and insurance agencies. For example, if the predicted ground motion is too uncertain, then the project owner may ask the following question: what step can be taken to reduce that uncertainty? In answering that question, a process for evaluating the relative contributions of RHS (source and path) and LHS (soil properties) uncertain parameters to overall uncertainty in seismic motions will be demonstrated as well. This will assist the project owners in mobilizing resources for increase understanding of the most significant contributor of uncertainty (source? site? path?), reduce the knowledge uncertainty, and subsequently reduce the overall ground motion uncertainty. In addition, the proposed development of theoretical capability to systematically propagate different sources of uncertainties through the governing equation of mechanics will greatly benefit the empirical modeling community in developing attenuation models especially for the regions where there are limited or no data (for example, eastern United States). Even for western United States, it will help the empirical modelers in better constraining their models. Further, the proposed technique will also provide insight in understanding spatial variation of ground motion and its associated uncertainties (covariance structure), which are under renewed interest in the research community, especially due to their effects on seismic performances of lifeline structures.
This project will combine the state-of-the-art stochastic calculus with the principles of mechanics in developing a finite element based stochastic computational framework to propagate random waves through random non--linear heterogeneous media. It, to best of our knowledge, is the first attempt to simulate wave propagation through nonlinear (elastic--plastic) heterogeneous medium in the stochastic space considering both LHS and RHS uncertainties. Since uncertainties in material properties and external forces are present in all fields of engineering, the impact of this project will be much wider than just in the area of geotechnical engineering. In order to ensure future of developments from this project, high school science and mathematics teachers will be involved (via RET supplement) through summer workshops so that they can transmit their experiences to high school classrooms. The objective here is to emphasize the importance of mathematics and physics in modeling physical phenomena such as earthquake and plant an early seed among the future engineers to seek a career in this field.
