Calibrated Fragility Functions for Seismic Loading of Sacramento-San Joaquin River Delta Levees
The Sacramento-San Joaquin River Delta, referred to as the Delta, is of great significance to California in numerous aspects. As one of the largest estuaries in the western United States, the Delta is vital to California’s water supply system. Essential lifelines such as the transportation lines and transmission lines lie across the Delta. Across the Delta, there is also an extensive levee system which helps to maintain the islands and waterways. The levees are at the risk of failure, which have brought great attention because the levee failures could cause severe damage to both economy and environment. Although the levees at the Delta have not been shaken by extremely strong earthquake events, the risk is still high considering that there are quite a few active faults near the Delta. Therefore, it is of great importance to get a better understanding of the seismic fragility of levees in the Delta region. Case histories of Japanese levees are first studied to validate the analysis approach. Three instrumented levee sites are selected where instrumental data and field performance data are available, including Nakashimo site, Yamazaki site and Kozuka site. For each site, a two-dimensional (2D) numerical model is constructed and calibrated using OpenSees. The 2D model is shaken by recorded earthquake events, and the response predicted by the finite element model is compared with recorded response. It is found that the predicted surface motions at the levee crest matches well with the recorded surface motion to a great extent with their response spectra compared. The predicted crest settlement for large earthquake events also agrees well with the reported settlement data. But for small earthquake events, it is unclear if the finite element model over-predicts the crest settlement when there is no reported damage report. At the Nakashimo site, a predicted pore water pressure response is also compared with the actual recording, and the comparison indicates that the finite element is able to predict the building-up of the pore water pressure that is consistent with the recorded response, and the predicted rate of dissipation is slightly faster than the measured rate of dissipation. PGV-based fragility curves are then derived from a large number of numerical simulations by following a calibrated approach of developing fragility function. The derived fragility functions are also compared with empirical fragility functions developed by Kwak et al. (2016). A comparison study shows that the median of the log-normal CDFs for the fragility curve obtained from numerical simulations is quite close to the median of the fragility functions proposed by Kwak et al. (2016), while the standard deviation is slightly smaller. This is likely due to the fact that the approach of deriving fragility functions from numerical simulations does not account for all sources of uncertainty that the empirical fragility functions incorporated. With the analysis approach validated, the levees in the Delta, specifically at the McDonald Island are analyzed. A 2D levee model is constructed following a generic levee cross-section profile, and soil properties are determined from available geotechnical data and geophysical measurements. A group of ground motions are selected to be consistent with seismic hazard at McDonald Island. A ground motion intensity measure selection study shows that PGV of the crest motion from a one-dimensional (1D) model without liquefaction is favored in the fragility function derivations. PGV-based fragility curves are also derived from numerical simulations, and it is found that the medians of the log-normal CDFs for PGV-based fragility curves are found to be smaller than what was proposed in Kwak et al. (2016). This indicates that levees at the McDonald Island are more fragile than Japanese levee sites mostly due to a much higher water level and the peat materials beneath the levee fill. The standard deviation of the log-normal CDFs of the fragility curve, after accounting for motion-to-motion variability, within-cross-section variability, and section-to-section varaibility, corresponds quite well with what was proposed by Kwak et al. (2016). In addition, considering that natural soils are usually heterogeneous, the spatial variablity of soil is often characterized and modeled by a spatially correlated random field. Traditional methods like Cholesky decompostion can be computationally expensive for a random field exceeding certain size. An algorithm that combines both Cholesky decomposition and Kriging is proposed to save some computational cost. Example applications are also introduced to validate the algorithm.