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A Transfer Function Model for Deformation Hazard Analysis of Earthen Dams


Dynamic analysis of earthen dams is performed to assess the seismic stability and vulnerability of dams during earthquakes, and a useful engineering demand parameter for this assessment is the shear-induced deformation of the dam. Although deformation assessments have historically been based on deterministic approaches, it is possible to combine the seismic hazard and dam response to compute the probabilistic deformation hazard of the dam. A significant challenge to quantifying probabilistic deformation hazard for an earthen dam is the need to perform hundreds of dynamic analyses to capture the response of the dam across the full range of ground motion intensities. When probabilistic deformation hazard assessments are used to prioritize resources for a portfolio of dams, there is the additional need to carry out the analyses with a consistent methodology that provides a basis for comparisons between dams. The objective of this research is to develop a simplified method that can be used to estimate shear-induced deformations with a large suite of ground motions, for the purpose of performing probabilistic deformation hazard assessments for earthen dams in a consistent manner.

The proposed methodology involves estimating the transfer function for a potential sliding mass of an earthen dam, which is applied to a user-defined input ground motion to estimate the average acceleration time history of the sliding mass and calculate a shear-induced deformation. The estimated transfer functions are defined at all frequencies and have a physical basis that captures the key mechanisms through which nonlinearity affects soil behavior, including dam period shift and damping increase. The methodology accommodates the entire time history of the ground motion, allowing the user to take advantage of available seismic hazard characterization through the use of site-specific ground motions. The proposed method is utilized to develop a transfer-function model, which represents one implementation of the methodology for a given set of assumptions about the characteristics of the earthen dam. The developed transfer-function model is based on a synthetic dataset generated by performing equivalent-linear dynamic analyses on two-dimensional finite element models of representative earthen dams. The shift in dam period and increase in damping observed in the modeled transfer functions is controlled by the shear-modulus reduction and material damping curves employed in the dynamic analyses, and adjustments can be made to the transfer-function model for alternative nonlinear behavior.

Implementation of the transfer-function model is demonstrated through two case histories where the estimated deformations from the model are compared with the observed shear-induced deformations at Austrian and Lexington Dams during the Loma Prieta earthquake. The analyses indicate that the estimated deformations are not only sensitive to the record chosen to represent the ground motions at the site, but also the azimuth of the input ground motion. The natural period of the sliding mass, represented in the model by the period corresponding to the peak of the transfer function, also has a large impact on the calculated deformations. Implementation of the transfer-function model in a probabilistic framework is then demonstrated for a hypothetical dam in the Sierra Mountain Region of California. The results from a site-specific probabilistic seismic hazard analysis are used to capture the expected ground motions at the dam site, the transfer-function model is used to perform incremental dynamic analyses for the dam, and the seismic hazard results are combined with the dynamic analyses results to compute probabilistic deformation hazard curves. Epistemic uncertainty in the deformation hazard is presented through alternative deformation hazard curves that reflect uncertainties in the seismic hazard and dam response. Epistemic uncertainty in the seismic hazard, which is characterized by different fractile hazard curves, is a significant contributor to the uncertainty in the deformation hazard. The nonlinear behavior of the transfer function model and yield coefficient of the sliding mass also contribute to the uncertainty in deformation hazard.

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