Geological disposal of HLW in the form of a \"multi-barrier system\" design comprising both man-made and natural barriers has been adopted for disposal repositories [7]. HLW such as spent fuel and vitrified glass are stored in waste cans and wrapped with buffer/backfill materials, and the outermost layer of nuclear wastes is the surrounding rock (including granite or clay rock, among others). To safely assess the most important \"multi-barrier\" repository, migration of radionuclides (RNs) in groundwater environments, the unique properties of radionuclides exhibit adequate physical and chemical behavior, including radiation activation, adsorption capacity, and surface behavior (interaction of clay or rock barriers) for migration in deep geological environments [8,9]. Safety assessments (SAs) of the final disposal of high-level radioactive waste (HLW) in geology require research on migration of important radionuclides in the surrounding environment. Generally, several important parameters for migration of radionuclides are applied in the transport of geological media for SAs, including the hydrodynamic dispersion coefficients (\(D\)), the diffusion coefficients (\(D_{\rm e}\)), the retardation factor (\(R\)), and the distribution coefficients (\(K_{\rm d}\)). The advection and dispersion behavior of radionuclides in granite fractures are of importance to maintaining the safety of geological disposal. Radionuclides not only can transport into the pore network of fractures or rock matrices, but also can sorb onto rock particles, in turn delaying their transport through the geosphere. The transport of radionuclides in the cracks in crystalline rocks can be described using a dual-porosity model [10]. These studies demonstrate that RN migration is dominated by various micro-processes, including anion exclusion, rock interactions, and diffusion in the rock matrix [11]. In view of the complexity of interactions between RNs and the mediums, knowledge about the migration behavior of RNs in granite fractures is far from complete. Cs is a highly yielded fission product containing up to 6.5% \({}^{135}\)Cs (t\({}_{1/2}\) = 2.0 \(\times\) 10\({}^{6}\) years), and \({}^{79}\)Se is also a fission product with a long half-life of 3.56 \(\times\) 10\({}^{5}\) years. Both Se and Cs belong to anion and cation respectively, as well as having high water solubility in groundwater, and Se and Cs can also be easily incorporated into terrestrial and aquatic organisms, such as occurred after the Fukushima accident, where radioactive wastewater leaked into the Pacific Ocean [12,13]. Granite is considered a potential host rock for disposing of spent nuclear fuel in China and several other countries. The fracturing of granite is the dominant pathway through which radionuclides transport from repositories to the biosphere. In this study, column experiments conducted in laboratories are used to study the retardation factors (\(R\)). By packing crashed granite samples into a column and conducting an advection-dispersion experiment at a low flow rate, it is possible to simulate the transport of radionuclides thats determine the \(R\). In order to develop a reliable model and obtain various parameters for long-term safety assessments, it is necessary to determine and quantify such advection and dispersion processes related to fractures or rock matrices. The free pore spaces between these granitic grains and intragranular secondary pores form water-filled, heterogeneous networks with varying geometric factors, such as constrictivity and tortuosity [14; 15]. Non-equilibrium transports are widely applied and studied in the literature [16; 17] and can be classified into two models: the so-called physical non-equilibrium model and the chemical non-equilibrium model. The physical non-equilibrium model assumes that the porous media consists of mobile and immobile zones. Solute exchanges between these two zones follow a diffusion-controlled process. Sorption in these two zones is assumed to be instantaneous.