The permeability coefficient of saturated clay plays a crucial role in practical engineering applications. In this paper, based on the fractal geometry theory and combined with the relationship between the flowing water volume and non-flowing water volume in saturated clay, the theoretical formulas for the effective pore specific surface area and the effective void ratio of saturated clay are established. Based on the capillary seepage channel model of saturated clay, combined with Poiseuille’s law and the concept of equivalent hydraulic radius, the theoretical formula for the permeability coefficient of saturated clay is established. Finally, the physical parameters of the remolded clay samples are measured and substituted into the modified Kozeny–Carman equation and the equivalent capillary seepage equation of saturated clay before and after the modification. Through the comparative analysis of the above theoretical values and the measured values of indoor seepage tests, it is found that the saturated clay seepage equation established in this paper is more suitable for dense saturated clay with relatively small pores. It has the characteristics of higher calculation accuracy and easier acquisition of basic parameters. The research results provide important references for practical engineering and the study of saturated clay seepage theory, and have broad prospects for practical engineering applications.