Sorption Behavior of Radionuclides on Engineered and Natural Barriers and Prediction of Sorption Distribution Coefficients Using Support Vector Regression

. A low-and intermediate-level radioactive waste repository contains various types of radionuclides and organic complexing agents. Their chemical interaction within the repository can lead to the formation of radionuclide-ligand complexes, in ﬂ uencing the limited retention behaviors of radionuclides. This study focuses on the sorption behavior of radionuclides on both engineered (concrete) and natural barriers (sedimentary rock and granite), as well as the prediction of sorption distribution coe ﬃ cients ( K d ) using support vector regression. Batch studies were conducted to determine the K d values for three radionuclides ( 99 Tc, 137 Cs, and 238 U) under di ﬀ erent conditions, including pH, temperature, and the presence of organic ligands (such as ethylenediaminetetraacetic acid, nitrilotriacetic acid, and isosaccharinic acid). The K d values for 238 U exhibited a sharp decrease with increasing concentrations of organic ligands. In contrast, the K d values for 99 Tc showed only a slight reduction at higher organic ligand concentrations. Meanwhile, the K d values for 137 Cs remained relatively unchanged, regardless of the type and initial concentration of organic ligands. This suggests a high level of retention for 137 Cs in the rock samples. The support vector regression model with a radial basis kernel function proved e ﬀ ective in predicting the K d values under di ﬀ erent experimental conditions. This enhancement in predicting accuracy contributes valuable insights into understanding the sorption processes involved in radionuclide behavior. Overall, this study advances our knowledge of radionuclide behavior on both engineered and natural barriers while providing a reliable prediction tool for estimating sorption distribution coe ﬃ cients.


Introduction
The systematic design and efficient management of a radioactive waste repository are of utmost importance worldwide.The repository must incorporate multiple barriers to ensure the public health and environmental protection [1].To ensure safe disposal, concrete-based materials are used as engineered barriers, surrounded by sedimentary rock and granite acting as natural barriers [2].This layered construction effectively prevents the mobility of radionuclides into the geosphere and biosphere, minimizing potential adverse impacts on human health and the environment.
Low-and intermediate-level radioactive waste (LILW) is commonly generated by nuclear power stations, research institutes, and medical facilities.These waste materials are stored in the radioactive waste repository located in Wolsong, Gyeongju, South Korea [3].Radioactive isotopes such as technetium ( 99 Tc), cesium ( 137 Cs), and uranium ( 238 U) are representative components of LILW, posing risks of environmental pollution and severe health issues due to their unstable nature and emission of ionizing radiation (α-, β-, or γ-) during radioactive decay [4][5][6][7].Both 99 Tc and 137 Cs are fission products, characterized by long halflives ( 99 Tc: 211,100 years; 137 Cs: 30 years), high yields, and significant environmental mobility [8,9]. 238U, with its extremely long half-life (44 68 × 10 8 years) and existence in multiple chemical species under varying environmental conditions, also exhibits high mobility in the geosphere [8,10].Considering the inherent properties of these radionuclides, various factors such as groundwater and rainwater intrusion, inadequate maintenance, safety accidents, and natural disasters may potentially lead to the release of these radionuclides from the repository during long-term storage.
The repository also encompasses various organic wastes, including decontamination agents, cellulosic materials, oils, and spent liquid scintillators [11,12].Within these wastes, substances such as ethylenediaminetetraacetic acid (EDTA) and nitrilotriacetic acid (NTA) are used for decontamination purposes on reactor surfaces [13].Under high alkaline conditions, the degradation of cellulosic waste leads to the generation of isosaccharinic acid (ISA) [14].Generally, these organic ligands have the potential to enhance the transport behavior of cationic radionuclides from the barriers due to the formation of strong radionuclide-ligand complexes in the groundwater [15,16].Additionally, anionic radionuclides can compete with organic ligands for surface interactions on the barriers, given the prevalence of anionic species over neutral forms [17,18].The active exploration of interactions between radionuclides and organic ligands, as well as their impacts within and around the repository, is driven by the unique properties exhibited by these substances [18][19][20][21][22][23][24].
The adsorption process plays a critical role in the immobilization of radionuclides within the repository.Among several evaluation methods, the sorption distribution coefficient (K d ) serves as an important factor for investigating the transport behavior of radionuclides between rock barriers and groundwater.Specifically, K d is defined as the ratio of radionuclide concentration between two phases (rock barriers and groundwater) at equilibrium [25].Investigating the transport behavior of radionuclides can be challenging due to various factors that affect adsorption performance, and experimental studies often require significant resources and effort [26].
Support vector regression (SVR) stands as a robust statistical learning method employed in data analysis and pattern recognition [27].It serves as a potent tool capable of capturing intricate relationships and making predictions from nonlinear regression data in diverse fields such as flood prediction [28], earthquake prediction [29], and water purification optimization [30,31].Originating from a network architecture, SVR involves computing linear regression functions within a high-dimensional feature space.Input data is mapped to this space through nonlinear functions, causing data points to be dispersed across both highdimensional and low-dimensional realms [32].This outcome yields linear separability in space and minimizes training errors for data analysis optimization.Moreover, the model showcases excellent generalization capabilities and can effectively curb overfitting, distinguishing itself from artificial neural networks.
In this study, we aimed to replicate the environmental conditions of an actual repository by using both the rock materials and groundwater from the repository located in South Korea.Various analyzers were employed to geochemically characterize the samples.The adsorption behavior of 99 Tc, 137 Cs, and 238 U on concrete, sedimentary rock, and granite was investigated using batch systems (Figure 1).The study focused on understanding the effects of organic ligands such as EDTA, NTA, and ISA, as well as the influence of pH levels ranging from 7 to 13 and temperatures ranging from 10 to 40 °C on the transport behavior of these radionuclides.By considering these factors, we aimed to elucidate their impact on the sorption behavior.To explore the sorption behavior under varied conditions, we employed SVR modeling for each individual radionuclide.This allowed us to predict and analyze the adsorption performance of the radionuclides under different experimental scenarios.Overall, this study provided valuable insights into the adsorption behavior of 99 Tc, 137 Cs, and 238 U on concrete, sedimentary rock, and granite, taking into account the effects of organic ligands, pH levels, and temperature.The application of SVR modeling enhanced our understanding of the sorption processes involved in the transport of these radionuclides., 99%) were acquired from the Sigma-Aldrich products (Seoul, South Korea).

Preparation of Groundwater and Rock Materials.
The groundwater, sedimentary rock, and granite samples were collected near the Wolsong site in Gyeongju, South Korea.The groundwater was pretreated using qualitative filter papers (2-3 μm), and various hydrochemical parameters were measured (Table S1).Afterward, the groundwater sample was sealed and refrigerated for storage until further use.For the sedimentary rock and granite, they were ground into small particles ranging from 53 to 150 μm.The ground rock samples were stored in plastic containers for subsequent use in the experiments.The concrete synthesis process is outlined in Figure S1.Portland cement, fly ash, and fine and coarse aggregates were utilized for the preparation of the concrete.Following the mix ratio described in previous studies [33,34], these materials were 2 International Journal of Energy Research mixed in specific proportions.The resulting concrete pastes were poured into cylindrical molds with a diameter of 10 cm and a height of 20 cm.They were then cured for 28 days at a temperature of 20 °C.After the curing process, the surface of the concrete was carefully polished to eliminate impurities and measure its compressive strength.The compressive strength of the prepared concrete was determined to be 26.60 MPa, which was consistent with the values reported in previous studies [33][34][35].The concrete was also ground to a particle size of 53-150 μm and stored in a plastic container for subsequent use in the experiments.

Pretreatment of Rock Materials.
To minimize changes in solution pH and chemical composition during the adsorption reaction, the three rock samples were pretreated according to the ASTM D4319-93 method from the American Society for Testing and Materials [35].First, 45 mL of groundwater was added to 50 mL conical tubes with 4.5 g of the rock samples.The samples were then shaken at 180 rpm at a temperature of 25 °C for a duration of 2 hours.After shaking, the samples were subjected to centrifugation at 8000 rpm for 30 minutes, and the supernatant from each tube was carefully removed.This procedure was repeated several times until the pH level of the supernatant was similar to that of the groundwater, with the exception of the concrete samples.Concrete has a strong alkaline nature, making it difficult to achieve the same pH level as the groundwater.Therefore, the concrete samples were washed as many times as the other samples during the pretreatment process.Finally, all the samples were dried overnight in a dryer at a temperature range of 30 to 40 °C.By following this pretreatment method, the potential influence of solution pH and chemical changes on the adsorption reactions was minimized.This ensured that the subsequent experiments accurately reflected the sorption behavior of the radionuclides on the rock samples.

2.4.
Characterization.An X-ray diffractometer (XRD, D/ Max-2500) and an X-ray fluorescence spectrometer (XRF, GN006) were utilized to determine the mineralogical structure and major geochemical compositions of the rock samples.The Fourier-transform infrared spectrometry (FTIR) (Spectrum 100) was employed to observe various functional groups present in the rock samples.For microimages and chemical composition analysis of the rock surface, a scanning electron microscopy-energy dispersive X-ray spectrometer (SEM-EDS, SU8220) was employed.The zeta potential of the rock surface was measured using a zeta potential analyzer (ELSZ-2000) within a pH range of 7-13.To calculate the BET surface area of the rock samples, nitrogen adsorption/desorption curves were obtained at 77 K using a Brunauer-Emmett-Teller (BET, BELSORP-MAX) instrument.3 International Journal of Energy Research polypropylene conical tubes, containing rock samples at concentrations of 10 g/L ( 137 Cs or 238 U) or 100 g/L ( 99 Tc), under shaking conditions at 180 rpm for a maximum duration of 10 days.The initial concentrations of 99 Tc, 137 Cs, and 238 U, based on groundwater, were 0.016 mg/L (10 Bq/ mL), 0.003 μg/L (10 Bq/mL), and 0.241 mg/L (0.003 Bq/ mL), respectively.To simulate the pH changes in cement porewater caused by groundwater, the solution pH was adjusted from 7 to 13 using 2 M NaOH and 2 M HNO 3 .Temperature effects were investigated at 10, 20, and 40 °C, reflecting a significant heat increase during the cement hydration process.The mobility of radionuclides through the rock samples in the presence of organic ligands such as EDTA, NTA, and ISA was examined within the range of 10 - 5 to 10 -2 M.After reaching adsorption equilibrium, the tested solution was sampled and filtered using syringes and 0.45 μm membrane filters.The activity concentration of 99 Tc and 137 Cs was determined using a liquid scintillation counter (LSC, Quantulus GCT 6220), with 1 mL of the sample mixed with 10 mL of scintillation cocktail (Hionic-Fluor).The concentrations of 238 U were analyzed using an inductively coupled plasma-mass spectrometer (ICP-MS, ICAP-Q).
Based on the collected data, the sorption distribution coefficient (K d , m 3 /kg) was calculated using the following formula: where C i (mg/L or Bq/mL) or C (mg/L or Bq/mL) represent the initial or final radionuclide concentration in the groundwater, respectively.m (kg) is the dosage of the used rock sample, and V (m 3 ) is the initial volume of groundwater containing the radionuclide.Furthermore, species distributions of radionuclides were simulated using PHREEQC version 3.4.0[36].This simulation is aimed at exploring the impact of retention mechanisms between rock samples and radionuclides.The modeling encompassed a pH range of 7 to 13 and an initial inorganic ligand concentration ranging from 0 to 10 -2 M, all at a temperature of 20 °C.These parameters were selected based on the concentrations of Ca 2+ and CO 3 2-found in the groundwater surrounding the disposal site (Table S1).To investigate the retention mechanism, a sorption complexation model was employed.This model delved into the surface complexation of various species onto the hydroxyl groups of rock samples under diverse environmental conditions.

ε-Insensitive Support Vector Regression (ε-SVR).
The SVR model is a supervised learning algorithm that extends the concept of support vector machines for nonlinear regression [37].It employs a mathematical technique called the kernel method to transform input data into a higherdimensional space, where a linear regression model can be applied.The SVR model incorporates the concept of ε insensitive loss function, allowing for a certain amount of training error, ε.The combination of the SVR model and ε insensitive loss function is known as ε insensitive SVR (ε-SVR) [29].The ε-SVR model function is defined in Eq. ( 2) and involves Lagrange multipliers (β i * and β i ) and bias b.
where ŷ represents the predicted value, w denotes the weight factor, K x i •x represents the kernel function, and N denotes the number of training data.
The ε-SVR model architecture comprises three layers: the input layer, hidden layer, and output layer (Figure S2).In the hidden layer of the ε-SVR model architecture, the kernel function and nonlinear kernel weights, expressed by Lagrange multipliers, are incorporated.Among the various types of kernel functions, the radial basis function (RBF) kernel is particularly effective in handling nonlinear problems, as it can map input data into an infinitedimensional space [32].For this study, the RBF kernel presented in Eq. ( 3) was employed.
where x i •x represents the inner product of x i and x and γ is a tunning parameter that determines the amplitude of kernel function as a hyperparameter of ε-SVR model.The ε-SVR is aimed at minimizing both the generalization error and the model complexity, as it is based on the concept of structural risk minimization.The model complexity is influenced by the kernel function and the weight factor w, while the prediction error is controlled by the ε-insensitive loss function (Eq.( 4)) [38].To develop an effective model for nonlinear regression while minimizing the risk of overfitting, the ε-SVR strives to strike an optimal balance between these two factors.Therefore, the objective function of the ε-SVR model can be mathematically expressed in Eq. ( 5) as a quadratic optimization problem with inequality constraints.This problem can be solved by constructing the Lagrange formulation [32].
where y i represents the experimentally measured value and ζ i and ζ * i represent errors that are less thanε and errors greater than +ε, respectively.The regularization parameter C determines the extent of penalized loss when training error occurs.4 International Journal of Energy Research After solving the quadratic optimization problem and obtaining the dual set of the Lagrange multipliers (β * i and β i ), the weight factor w can be calculated using Eq. ( 6).This allows us to determine the model parameters, which include the Lagrange multipliers and bias b.
According to the Karush-Kuhn-Tucker complementarity conditions [39], the differences between the dual set of the Lagrange multipliers (β * i − β i ) within the ε-insensitive tube are zero.This implies that each Lagrange multiplier is equal.Consequently, the support vectors are identified as the data points that satisfy the nonzero Lagrange multipliers, and only the nonzero coefficients (β * i − β i ) have an influence on training the ε-SVR model [38].As a result, the index i presented in Eqs.(( 2)-( 6)) can be replaced by another letter that represents the support vector.

ε-SVR Model Development.
A database comprising 1620 data sets, which were obtained through batch adsorption experiments, contained information on the type of organic ligands, rock samples, temperature, pH, initial concentrations of organic ligands, and K d values.To convert textual variables such as organic ligands and rock samples into numerical variables related to K d values, the average K d value of each variable was utilized.In addition, a mass concentration variable that accounts for the molecular weight of the organic ligands was added to the database.To handle the variability of the variable values, the logarithm base 10 (log 10 ) transformation was applied to the six variables.Consequently, a database with 12 independent variables and log 10 K d as the dependent variable was constructed.In cases where a variable had a value of zero, it was computed as log 10 (10 -6 ).
Individual ε-SVR models using the RBF kernel were developed to predict K d values for 137 Cs, 99 Tc, and 238 U radionuclides.Each ε-SVR model was trained using a dataset consisting of 540 experimental results, which were randomly divided into an 80% training set and a 20% test set.Prior to model training, the hyperparameters C, ε, and γ needed to be set, and they were optimized using a grid search algorithm with 10-fold Venetian blind cross-validation.The optimal combination of hyperparameters was selected based on the minimum mean squared error during crossvalidation.The ranges for the hyperparameters were C from 10 -2 to 10 4 , ε from 10 -4 to 1, and γ from 10 -4 to 10.Before model training, all variables were normalized.
In order to assess the performance of the ε-SVR K d prediction model developed in this study, several statistical criteria such as root mean squared error (RMSE), coefficient of determination (R 2 ), and relative absolute error (RAE%) were employed.These criteria compare the experimentally measured values with the model's predicted values.The equations for these criteria are as follows: where N represents the number of data points, y i and y i represent the experimental and predicted values, respectively, and y denotes the average of the experimental data.
The prediction models and computations were developed using MATLAB software (MathWorks, Inc., Natick, MA, USA) along with the Parallel Computing Toolbox and PLS Toolbox version 9.1 (Eigenvector Research, Inc., Manson, WA, USA).

Results and Discussion
3.1.Characterization.Rock samples were geochemically characterized by XRD (X-ray diffraction), XRF (X-ray fluorescence), FTIR (Fourier-transform infrared spectroscopy), SEM-EDS (scanning electron microscopy-energy-dispersive X-ray spectroscopy), Zeta potential analyzer, and BET (Brunauer-Emmett-Teller) analysis.Figure 2(a) displays the typical XRD peaks of concrete, sedimentary rock, and granite that were matched using the X'Pert HighScore program.All rock samples exhibited the presence of various minerals commonly found in geological structures in South Korea, including quartz, albite, amphibole, calcite, phlogopite, and feldspar [40,41].
For concrete, characteristic peaks of calcium silicate were observed at 5.8 °, 10.6 °, 26.5 °, 37.3 °, and 50.2 °.Peaks corresponding to anorthite were observed at 23.4 °, 24.5 °, and 27.9 A small peak at 35.5 °was attributed to ettringite, while peaks at 54.5 °and 64.5 °were assigned to ettringite as well.The presence of calcium silicate, anorthite, ettringite, portlandite, and calcite in the concrete confirms the successful synthesis of the material, which is consistent with previous studies [42][43][44].In the sedimentary rock and granite, typical peaks such as chlorite and illite were identified in a broad range of 5-50 ° [45][46][47][48].The observed peaks in granite at 35.4 °, 43.1 °, and 56.9 °were attributed to magnetite.Signals of biotite, commonly found in granite, were indicated at 34.2 °, 41.6 °, 54.9 °, and 60.2 °.These XRD analyses provide valuable information about the mineral composition of the rock samples, confirming the presence of specific minerals and aiding in the understanding of their geological characteristics.
The geochemical composition of the rock samples is summarized in Table S2.The SiO 2 and Al 2 O 3 content were significantly higher compared to other minerals in all rock samples, indicating the presence of aluminosilicate precursors such as quartz, albite, amphibole, phlogopite, and feldspar [49].The concrete exhibited a higher CaO content, two to three times higher than the other rocks, 5 International Journal of Energy Research The FTIR spectra of the rock samples were recorded between 4000 and 400 cm -1 (Figure 2(b)).The hydroxyl functional group (O-H) was observed in all samples as a band around 3410 cm -1 , which can be attributed to water molecules and O-H groups on the mineral surface or interlayer [50][51][52].In the concrete, an absorption band at 1650 cm -1 was observed, indicating the presence of O-H groups in ettringite [53].The carbonate functional group (CO 3
SEM images of concrete, sedimentary rock, and granite are also presented in Figure S4.All rock samples exhibited distinct surfaces with numerous pores, cracks, and fractures.The concrete surface displayed various microscopic crystals, including needle-shaped ettringite, plate-shaped portlandite, and dense seed-shaped calcium silicate hydrate (C-S-H) (Figure S4 (a-c)) [63].As shown in Figure S4 (d-f), the sedimentary rock exhibited smooth structures, conchoidal fractures, and angular edges.The surface of the granite, captured in Figure S4 (g-i), also shared similar features with the sedimentary rock.However, the thin layered structure derived from biotite was only observed in the granite [64,65].
The nitrogen adsorption and desorption isotherms, BET surface area, pore volume, and average pore size of the three rock samples were analyzed using a BET instrument (Figure 2(c), Figure S5, and Table S3).According to the International Union of Pure and Applied Chemistry classification of isotherms, their adsorption/desorption isotherms exhibited a shape resembling a typical type IV isotherm with a type-H4 hysteresis loop (Figure 2(c)).This finding indicates that the rock samples contained both micro-and mesoporous structures with pore sizes below 50 nm.Pore size distributions in the rock samples were analyzed using the BJH model.The analysis revealed the presence of micro-, meso-, and macroporous structures within the rock samples.The average pore sizes of concrete, sedimentary rock, and granite were also measured at 28.93, 19.30, and 14.60 nm, respectively.Furthermore, the specific surface areas of concrete, sedimentary rock, and granite were found to be 6.12, 1.71, and 4.08 m 2 /g.The zeta potential values of the rock surfaces were uniformly negative at pH 7, 9, 11, and 13 (Figure 2(d)).In addition, these values remained almost constant regardless of changes in pH.This result can be attributed to the deprotonation of hydroxyl groups, such as Si-OH, Al-OH, and Ca-OH, above pH 7 [66,67].The charge characteristics of the rocks are consistent with those reported in previous studies [23,68,69]. 99Tc through Rock Barriers.As shown in Figure 3(a), the impact of initial pH on 99 Tc mobility was investigated.The K d values of 99 Tc in all rock samples gradually decreased as the pH increased from 7 to 13.It has been observed that 99 Tc exhibits relatively low  -ions for sorption sites on the rock surfaces [71].The transportation behavior of 99 Tc was influenced by temperature variations (Table S4).The K d value of concrete increased from 4 42 × 10 −5 m 3 /kg to 4 82 × 10 −5 m 3 /kg as the temperature rose from 10 to 40 °C.Similarly, the K d value of the sedimentary rock (or granite) increased from 2 59 × 10 −5 m 3 /kg (or 5 87 × 10 −5 m 3 /kg) to 1 35 × 10 −4 m 3 /kg (or 1 36 × 10 −4 m 3 /kg) with an increase in temperatures.According to the Van't Hoff equation, the calculated enthalpy values (ΔH °) for the sorption process onto the rock samples were found to be positive (Table S5).

Retention Behavior of
These results provide confirmation of the endothermic nature of the 99 Tc adsorption onto the rock samples.Overall, concrete exhibited a higher retardation of 99 Tc compared to sedimentary rock or granite.However, it is evident that 99 Tc displayed high mobility relative to other radionuclides due to its low adsorption onto minerals or rocks [2,72].
Furthermore, the study also examined the effects of organic ligands such as EDTA, NTA, and ISA.As depicted in Figure 4, the K d values of 99 Tc showed a slight decrease with increasing initial concentration of organic ligands.It is well-known that TcO 4 -does not typically form complexes with organic ligands and does not coprecipitate with particles, as this ion remains in its most stable form in aerobic aqueous solutions (Figures S8 and S9) [73].According to the sorption complexation model, TcO 4 -ions have the potential to interact with hydroxyl groups, resulting in the  S7).Nonetheless, the observed low K d values of 99 Tc suggest that the occurrence of these complex formations is relatively rare.Additionally, the influence of organic ligands should be considered.These ligands might compete with anionic TcO 4 2-ions for sorption sites on the rock surfaces, particularly given the prevalence of anionic species above pH 7 [18].As a result, it can be inferred that 99 Tc demonstrated minimal interaction with the organic ligands. 137Cs through Rock Barriers.The retardation results of 137 Cs in rock barriers are presented in Figure 3(b) and Table S4.The K d values of 137 Cs were found to be the highest for granite, followed by sedimentary rock, and concrete.The removal efficiencies of all rock samples were also approximately above 60%.This can be attributed to the presence of silicate groups derived from minerals like biotite, quartz, and calcium silicate, which possess a strong adsorption capacity for cesium ions [74,75].Biotite, specifically found in granite, exhibits a high adsorption capacity for 137 Cs through surface complexation and ion exchange, resulting in a pronounced retardation behavior of 137 Cs in granite [76].

Retention Behavior of
Minimal changes in 137 Cs adsorption were observed across the tested pH ranges.Cesium ions tend to be hydrated under neutral or alkaline conditions, which is their most stable form.Consequently, hydrated cesium ions readily adsorb onto the rock surfaces within the pH range of 7 to 13.Furthermore, the K d values of 137 Cs remained relatively constant regardless of temperature variations.The negative ΔH °values of the 137 Cs sorption onto rock samples were −4 07 × 10 −2 kJ/mol (concrete), −1 16 × 10 −2 kJ/mol (sedimentary rock), and −9 98 × 10 −3 kJ/mol (granite), indicating the exothermic nature of the reaction (Table S5).The effects of organic ligands on the transport behavior of 137 Cs are illustrated in Figure 4.It can be observed that the presence of excess NTA or EDTA did not significantly affect the mobility of 137 Cs.This can be attributed to the very weak stability constants of Cs-ligand complexes (Cs-NTA: 0.84, Cs-EDTA: 1.05) [22].Similarly, ISA showed no significant impact on the mobility of 137 Cs, as ISA tends to react strongly with di-, tri-, and tetravalent cations at high pH [77].This fact has also been substantiated by analyzing the  S11).The modeling revealed that 137 Cs exhibited minimal formation of complexes with EDTA or ISA, with its predominant presence as Cs + ions.Moreover, Table S6 shows the limited occurrence of complexes between Cs + ions and the rock sample surfaces due to the low stability constants (log K = 2 05 or -5.50).These findings suggest that the adsorption of 137 Cs onto rock samples is primarily governed by mechanisms such as physical adsorption, electrostatic forces, and ion exchange.

Retention
Behavior of 238 U through Rock Barriers.The results of the mobility test for 238 U on rock barriers are presented in Figure 3(c) and Table S4.Concrete is known to have a high uranium adsorption capacity through coprecipitation (calcium-uranyl-silicates and calciumuranate), surface sorption, and physical encapsulation [78,79].In the case of concrete, the K d value of 238 U remained relatively constant within the pH range of 7 to 11 but sharply decreased with further increases in pH.The sharp reduction at pH 13 can be attributed to enhanced electrostatic repulsion caused by the hydrolysis of UO 2 (OH) 3 -to UO 2 (OH) 4 2-as the pH increases [21].Although sedimentary rock and granite had lower K d values compared to concrete, they exhibited similar trends to that of concrete.The effect of temperature was prominent and followed the order: concrete, granite, and sedimentary rock.For all rock samples, the ΔH °values of 238 U were consistently negative, suggesting an exothermic nature of the sorption reaction.
Among the three investigated radionuclides, the migration transport of 238 U in rock samples was most strongly influenced by the presence of organic ligands (Figure 4, Figure S6, and Figure S7).The K d values of concrete decreased rapidly from 10 -3 M to 10 -2 M. The qualitative degree of reduction was significant, with a 10-fold reduction for EDTA, a 5-fold reduction for NTA, and a 3-fold reduction for ISA.The extent of quantitative reduction was predicted based on the change in slope observed as the initial organic concentration increased from 10 -4 M to 10 -2 M. The slope values followed this order: EDTA > NTA > ISA, indicating that EDTA had the most pronounced effect on concrete (Figure S12).
To understand the retention mechanism of 238 U, we analyzed the distribution of uranium species and employed a surface complexation model (Figure S13-14 and Table S6).Figures S13 and S14 illustrate the significant influence of Ca 2+ , CO 3 2-, EDTA, and ISA on uranium speciation.Interestingly, when the initial EDTA concentration was below 10 -4 M, EDTA had little impact on uranium speciation across all pH levels.Instead, uranium species were primarily influenced by Ca 2+ and CO 3 2-.However, as the initial EDTA concentration increased to 10 -3 M and 10 -   12 International Journal of Energy Research 2 M, UO 2 (EDTA) 2-complexes started to form, showing strong stability at pH 7.This resulted in increased uranium mobility within rock samples (UO 2 (EDTA) 2-: 13.7) [22].NTA, while less influential than EDTA, also interacted with uranium to form UO 2 (NTA) -complexes with higher stability (UO 2 (NTA) -: 10.85) [22].At pH 13, 238 U exhibited high mobility because species like UO 2 (OH) 4 2and UO 2 (OH) 3-hardly formed surface complexes with rock samples, as indicated by the sorption complexation model (Table S6).Furthermore, stable UO 2 (OH) 4 (HISA) 3- complexes gradually dominated at pH 13 with an increasing initial ISA concentration, resulting in low retardation within rock samples [24].

Prediction Performance of ε-SVR Model. Table S7
provides the optimal combinations of hyperparameters for each individual radionuclide.The optimal value of the regularization parameter C can be explained by considering the trade-off inherent in the objective function of the ε-SVR model.As the value of C increases, the contribution of the error term to the objective function (Eq.( 5)) also increases.This places more emphasis on minimizing errors outside of the ±ε tube and may lead to increased overfitting.Conversely, if C is too small, the objective function tends to regress with larger errors, potentially resulting in underfitting and rendering the concept of ε meaningless.
Similarly, as the value of the permissible error range ε increases, the allowable range of error for the model also increases.This means that the model becomes more tolerant to errors within the training data, which reduces the number of support vectors required to define the model.On the other hand, as the tuning parameter γ is large, the kernel function becomes narrower, and each support vector has a more localized influence on the model output.This is because γ controls the shape and width of the kernel function [80].Consequently, a larger number of support vectors are needed to accurately capture the complexity of the underlying data distribution.Conversely, if γ is too small, the kernel function becomes wider [32], resulting in smoother model that is less prone to overfitting but may not accurately capture the underlying data distribution.Therefore, it is crucial to select appropriate values for the hyperparameters that strike a balance between the model's complexity and its generalization ability.Figure 5 illustrates the linear relationship, on a decimal logarithmic scale, between the experimentally measured K d values and the predicted values obtained from the ε-SVR model for each individual radionuclide.The correlation coefficients (R 2 ) between the experimental and predicted data were 0.979 for 238 U, 0.999 for 99 Tc, and 0.999 for 137 Cs.Although the K d prediction model for 238 U exhibited a most noticeable deviation from the 45-degree line, the R 2 in the test set remained sufficiently high, indicating a  13 International Journal of Energy Research reasonable fit.Therefore, it can be concluded that the ε-SVR model proved robust in predicting K d values for all radionuclides.The performance of the ε-SVR models developed for each radionuclide was evaluated using actual measured K d values and antilogarithm values of predicted K d based on various criteria, as shown in Table 1.The results indicate that the ε-SVR model developed for 137 Cs demonstrated the best prediction performance in terms of R 2 and RAE%, while the model developed for 99 Tc exhibited the lowest RMSE.However, the RAE% of 99 Tc in the test set was found to be the highest at 25.40%.On the other hand, the ε-SVR model developed for 238 U displayed the lowest prediction performance based on RMSE and R 2 .It is important to note that the discrepancies in RMSE and RAE% results may be attributed to differences in the datasets used to develop the ε-SVR model for each radionuclide.
Figure 6 depicts three-dimensional response plots, based on the ε-SVR model with temperature kept constant with variation of the other two variables within the experimental range.In Figure 6(a), the effect of pH and EDTA concentration on the K d values of 99 Tc in the sedimentary rock was investigated keeping the temperature at 20 °C.In the sedimentary rock, 99 Tc exhibited the highest K d value of about 3 16 × 10 −5 m 3 /kg under pH 7 and 10 -6 M of an initial EDTA concentration.Figure 6 6(c)).In addition, 238 U showed that the lowest K d values at an initial ISA concentration were 10 -2 M regardless of pH and temperature, indicating that 238 U could potentially exhibit relatively higher mobility during the initial or final degradation stages of concrete, especially with an increased ISA generation in the engineered barrier.The reliability and performance of the developed model were reaffirmed through the overlap between the simulation results and the training/test datasets.Therefore, the developed ε-SVR K d prediction models have the potential to serve as critical tools for predicting the retardation or mobility of each radionuclide in rock barriers.

Conclusion
In this study, the transport behavior of radionuclides was investigated using groundwater and engineered and natural rock barriers, mimicking conditions similar to an actual disposal site.The obtained data were utilized to develop an ε-SVR model for predicting K d of radionuclides.The experimental results clearly suggested that the mobility of 238 U was significantly influenced by the presence of organic ligands compared to 137 Cs and 99 Tc.The impact of organic ligands followed the trend EDTA > NTA > ISA, particularly in the case of concrete.On the other hand, 99 Tc exhibited substantial mobility in both engineered and natural barriers, regardless of the absence or presence of organic ligands.The retardation of 137 Cs was found to be higher than that of other radionuclides, even in the presence of organic ligands, and showed excellent performance, particularly in granite.These findings highlight that the transport behavior of 238 U in the geosphere and biosphere could be accelerated by the presence of organic ligands.In contrast, 99 Tc may easily migrate from rock barriers under various environmental conditions due to its anionic nature and high solubility in groundwater.Finally, the proposed ε-SVR model was effective to predict K d of radionuclides and can serve as a valuable tool to understand the potential release of radionuclides from a radioactive waste repository.International Journal of Energy Research granite. Figure S5: BJH pore size distribution of rock samples.Figure S6: effect of (a) EDTA, (b) NTA, and (c) ISA on retention behavior of radionuclides on sedimentary rock at pH 7 and 20 °C: 99 Tc (•), 137 Cs (inverted red triangle) 238 U (green square), no ligand at 99 Tc (─), no ligand at 137 Cs (""), and no ligand at 238 U ( ---). Figure S7: effect of (a) EDTA, (b) NTA, and (c) ISA on retention behavior of radionuclides on granite at pH 7 and 20 °C: 99 Tc (•), 137 Cs (inverted red triangle) 238 U (green square), no ligand at 99 Tc (─), no ligand at 137 Cs (""), and no ligand at 238 U ( ---).

Figure 1 :
Figure 1: A schematic diagram of investigating sorption behaviors of radionuclides in the repository.

Figure 3 :
Figure 3: Effect of pH on retention behavior of (a) 99 Tc, (b) 137 Cs, and (c) 238 U on the rock samples.

Figure 6 :
Figure 6: Three-dimensional response plots under various conditions: (a) the mutual interaction effect of pH and EDTA concentration on K d values of 99 Tc (sedimentary rock, 20 °C), (b) the mutual interaction effect of pH and NTA concentration on K d values of 137 Cs (granite, 20 °C), and (c) the mutual interaction effect of pH and ISA concentration K d values of 238 U (concrete, 40 °C).
(b) shows the effect of initial NTA concentration and pH on the K d values of 137 Cs in the granite.The K d values of 137 Cs were significantly influenced by the changes in pH, but the effect of initial NTA concentration on the K d values of 137 Cs was relatively low compared to EDTA.The highest K d values of 137 Cs occurred at pH 10.5 and an initial NTA concentration 10 -6 M. The K d values of 238 U in the cement were significantly influenced by initial ISA concentration and pH (Figure Figure S8: technetium species distribution in the pH range of 7-13 at 20 °C under various initial EDTA concentrations: (a) 0 M, (b) 10 -5 M, (c) 10 -4 M, (d) 10 -3 M, and (e) 10 -2 M. Figure S9: technetium species distribution in the pH range of 7-13 at 20 °C under various initial ISA concentrations: (a) 0 M, (b) 10 -5 M, (c) 10 -4 M, (d) 10 -3 M, and (e) 10 -2 M. Figure S10: cesium species distribution in the pH range of 7-13 at 20 °C under various initial EDTA concentrations: (a) 0 M, (b) 10 -5 M, (c) 10 - 4 M, (d) 10 -3 M, and (e) 10 -2 M.
Figure S12: changes in slope of uranium distribution coefficient slope in concrete sample as a function of organic ligand concentration.

Table 1 :
Performance evaluation results of ε-SVR models using the measured K d values and the predicted K d values.