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    Probabilistic Estimation of Site Specific Fault Displacements

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    The College of the Redwoods (CR) located near Eureka, California would like to upgrade a series of existing buildings that are unfortunately located on secondary faults associated with the active Little Salmon Fault (LSF) zone. In the early 1990’s a deterministic value of the maximum dip-slip displacement that had occurred on one of these secondary faults located beneath the southeast building corner of the former library was measured to be 1.7 feet. This displacement was resolved into approximately 1.5 feet horizontal offset and 0.8 feet of vertical offset, based on the secondary fault plane dip. Geologically, it has not been possible to establish the actual dates of the occurrence of the displacements on the observed faults, therefore it was assumed that they all had occurred within the last 11,000 years. The structural engineer for the project has indicated that it was not possible to design for the observed ground displacement of 1.7 feet. This limited study was undertaken to assess the variation of ground displacements that were observed over the area of ground occupied by CR’s Administration, Science, and former Library buildings. The purpose of this study was to evaluate the reasonableness of using a deterministically determined maximum value of displacement in estimating, and designing mitigations for, the structural response, or whether a probabilistic approach could be utilized. The only data available within the limited time frame allowed for the study was from a series of trench logs made as part of a project for locating building sites on the campus in the early 1990’s. As a first step the frequency distributions of both horizontal and vertical displacements located in a volume of soil comprising the area occupied by the above buildings to a depth of 14 feet were examined. The 14 feet was the maximum depth of the trenches used to provide data for the study. Probability density functions (PDF) versus displacements were developed based on the frequency distributions. The area under the PDF curves between given displacement intervals represents the probability of occurrence (POC) of that displacement. A cumulative probability of occurrence for a displacement interval can be determined by adding the individual POC’s. Based on this it was estimated that a horizontal displacement of ≤ 1.0 foot has a probability of 89% of occurring in the next 11,000 years at the site. In contrast, a vertical displacement of ≤ 1.0 foot has a probability of 88% probability of occurrence
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