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The mean squared deviation between acceleration time histories (of soil-system test replicas) is expressed as a unique aggregate of three discrepancy measures associated with shape, phase, and frequency-shift. The shape-measure quantifies the deviations associated with dissimilarities in form and amplitude. The phase-measure estimates the deviations associated with differences in phase angle. The frequency-shift-measure quantifies the deviations associated with differences in frequency components. These measures were used to assess the discrepancies among six replicas of a centrifuge experiment of a liquefiable soil tested at six different facilities. A sensitivity analysis was thereafter used to assess the effects of input motion discrepancies on a liquefiable soil response. The conducted analysis showed that the acceleration response of the analyzed soil is more sensitive to discrepancies in input motion frequency than in phase or amplitude. 

A decomposition is used to express the mean squared deviation, quantifying the dissimilarities between time histories of input (or response) quantities of multiple replicas of a soil system centrifuge test, as a unique aggregate of three discrepancy measures associated with shape, phase and frequency-shift. The shape measure quantifies the deviations associated with dissimilarities in form and amplitude. The phase measure estimates the deviations associated with differences in phase angle. The frequency-shift measure quantifies the deviations associated with differences in frequency components. These measures are illustrated using simple synthetic motions and used to assess the discrepancies among six replicas of centrifuge input motion achieved at six different facilities. The conducted analysis shows that the proposed decomposition accurately quantifies the different types of discrepancies in input or response time histories.