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Nansha clay is an interactive marine and terrestrial deposited soft clay that is widely spread in Guangzhou, Pearl River Delta, China. To avoid excessive settlement after construction, there is a need for better quantifying the time-dependent deformation of the soft clay. This paper presents a preliminary study to predict the one-dimensional compression of Nansha clay using fractional derivatives. A fractional Merchant model was introduced to describe the time-dependent settlement, and analytical solutions were obtained in terms of the Mittag-Leffler function. The oedometer test results were presented to validate this model. Compared with classical rheological models, the fractional derivative-based model enabled close estimation of the one-dimensional compression with fewer parameters. The meaning of the order of fractional derivative and its relationship with the clay physical properties were explored. It shows that a smaller value of this order corresponded to a higher coefficient of consolidation and a lower coefficient of secondary consolidation. The amplitude of both the primary and secondary consolidation of clay may be estimated quantitatively by the order of fractional derivative. Taken together, these results may open up new avenues for theoretical and empirical modeling of rheological phenomena in clay using fractional derivatives. [ABSTRACT FROM PUBLISHER]