## 1 Introduction
During the hydration process, the anhydrous OPC forms aqueous and solid cement minerals such as portlandite (Ca (OH)\({}_{2}\), calcium-silicate-hydrate (C-S-H) and other minor phases comprising aluminum, sulfate, and iron, whose surface areas provide the large sorption capacity for dissolved radionuclides [12]. Additionally, the alkaline nature of cement phases provides a favorable environment in which radionuclides are less soluble [7]. The gradual degradation of concrete is based on the assumption that, over time, the disposal facility will deteriorate, allowing rainwater to infiltrate the concrete structures within the disposal facility, as shown in both the conceptual diagram in Figure 1 and in the assumed degradation timeframe in Figure 2. The rainwater with a lower pH will not be in equilibrium with the high alkaline hydrated cement mineral system that makes up the concrete structures [14]; consequently, chemical reactions will occur that gradually alter the aqueous and solid phases of concrete, thereby causing further disintegration of concrete [15]. The reduced pH of infiltrating water will increase radionuclide solubility, leading to the transport of radionuclide ions via an electrochemical potential gradient and an advection caused by a flow of aqueous solution [15]. As depicted in Figure 2, this study assumes that infiltration of water will occur after 300 years of regulatory oversight and that the disposal site will have experienced normal wear, with the possibility of a radionuclide-containing waste drum failing after 100 years of operation, followed by failure of a concrete vault after 300 years, a cover failure after 500 years, and further concrete degradation after 1000 years. The natural deterioration of the disposal site is projected to be caused by, among other things, general influences on construction, lengthy operation periods (>100 years), climate change (e.g., pro-longed flooding), and ground water geochemistry [7]. Literature indicates that concrete deterioration goes through four phases, defined by gradual decrease in pore water pH and calcium to silica (C/S) ratio [11]. The initial state (I) is distinguished by a pH greater than 12.5. This is due to the high amounts of alkalis, including sodium and potassium. In the second state, the pH is around 12.5 and controlled by the solubility of portlandite (Ca (OH)\({}_{2}\) which has the ability to firmly bind metal ions, anions, and halogens by substituting its hydroxyl functional group [11; 16]. The pH of the third state (III) is governed by the equilibrium between Calcium-Silica-Hydrate (C-S-H) and infiltrating water from the surrounding non-cemetitious materials. The packing of the C-S-H tiny polymers into platelets provides the sorption binding surface area in this condition [16].Lastly, in the fourth state (IV), the pH decreases to approximately 10 under the influence of calcite (CaCO\({}_{3}\)) which has a smaller reactive surface area, hence exhibiting lower sorption abilities than the other phases [16]. A few studies evaluating the effect of the pH on the concentration of the species (see Fig. 1) is also performed. Figure 1: Conceptual Model of a near-surface disposal site. Figure 2: Time frame to reflect gradual deterioration of disposal facility. geochemical evolution on concrete barriers have demonstrated that the sorption behaviors of radionuclides vary with the stages of concrete degradation [12]. Sorption refers to the binding of radionuclides on the surface or within the structure of a substance [7]. The radionuclide sorption process on cementitious surfaces is evaluated using the distribution coefficient (K\({}_{d}\)) and diffusion coefficient (D\({}_{s}\)) parameters, which are employed to assess radionuclide migration through the cementitious medium [17]. The distribution coefficient is the ratio of the radionuclide's mass concentration in the solid phase to its concentration in the liquid phase at equilibrium, whereas diffusion is the movement of vapor and ions through concrete [18].