State-of-the-art hydrogeological investigations use transient calibrated numerical flow and transport models for multiple scenario analyses. However, the transient calibration of numerical flow and transport models still requires consistent long-term groundwater time series, which are often not available or contain data gaps, thus reducing the robustness and confidence of the numerical model. This study presents a data-driven approach for the reconstruction and prediction of gaps in a discontinuous groundwater level time series at a monitoring station in the Allertal (Saxony-Anhalt, Germany). Deep Learning and classical machine learning (ML) approaches (artificial neural networks (TensorFlow, PyTorch), the ensemble method (Random Forest), boosting method (eXtreme gradient boosting (XGBoost)), and Multiple Linear Regression) are used. Precipitation and groundwater level time series from two neighboring monitoring stations serve as input data for the prediction and reconstruction. A comparative analysis shows that the input data from one measuring station enable the reconstruction and prediction of the missing groundwater levels with good to satisfactory accuracy. Due to a higher correlation between this station and the station to be predicted, its input data lead to better adapted models than those of the second station. If the time series of the second station are used as model inputs, the results show slightly lower correlations for training, testing and, prediction. All machine learning models show a similar qualitative behavior with lower fluctuations during the hydrological summer months. The successfully reconstructed and predicted time series can be used for transient calibration of numerical flow and transport models in the Allertal (e.g., for the overlying rocks of the Morsleben Nuclear Waste Repository). This could lead to greater acceptance, reliability, and confidence in further numerical studies, potentially addressing the influence of the overburden acting as a barrier to radioactive substances.

Pipe leakage from defect subsurface gravity sewer pipe networks potentially contaminates soil and groundwater. In recent times, an increasing number of numerical pipe leakage models incorporating pipe flow, saturated-unsaturated flow in the subsurface, and exchange fluxes from and to leaky pipes have been developed. Numerical benchmarks are required in order to demonstrate result accuracy of these models. The present technical note represents a novel numerical benchmark of the pipe leakage problem describing pipe water exfiltration into horizontal unsaturated-saturated soil. The present benchmark enables to test the accurate calculation of the spatial potential distribution in the soil, which is affected by the water level in the leaky pipe. The derivation of an analytical solution for stationary pipe water exfiltration into a horizontal aquifer and a conceptual model for the setup of a corresponding numerical model is shown. Results of the analytical model are reproduced using the numerical leakage model OGS-HE.

The calculation of radionuclide transport in the subsurface is an important part of analyses to evaluate safety of nuclear waste disposal sites. Such calculations often emphasize on the solute breakthrough in space and time. In this context, unfractured low-permeability porous media represent effective radionuclide retention because diffusion becomes the dominant mode of transport. Under such conditions and for safe containment, diffusion is desired to be smallest, optimally in combination with large retardation by e.g. sorption. The present study investigates timescales and solute breakthrough distances for selected radionuclides in low-permeability porous media. The used mathematical model is the solute transport equation incorporating the processes of diffusion, sorption, and decay. Firstly, published physical through-diffusion experiments are recalculated in order to validate the transport parameters using a numerical simulator. Secondly, timescales and distances of radionuclide breakthrough are calculated using an analytical model. The simulation results indicate that solute breakthrough converges at a certain distance as decay becomes the dominant process limiting transport. For example, the migration of $$^{36}$$ 36 Cl in Opalinus Clay converges at a solute breakthrough distance of approximately 162 m for timescales beyond 10 Mio years. Based on the results, an expression based on the $$2{\text {nd}}$$ 2 nd Damköhler number is introduced and its accuracy is demonstrated. With this simple equation, maximum solute breakthrough distances can be calculated based solely on the input of a dimensionsless number, the effective diffusion coefficient, the effective porosity or capacity factor, and the physical half-life. That expression is accurate ( $$R^2=1.00$$ R 2 = 1.00 ) for non-sorbing radionuclides acting as inert tracers. For sorbing radionuclides, that equation deviates more from simulation results ( $$R^2=0.77$$ R 2 = 0.77 ). Results of the present study contribute to long term safety analyses of nuclear waste disposal sites.

Leakage from aging sewer and stormwater pipes into the subsurface poses significant environmental risks and threatens the integrity of urban infrastructure, primarily through the degradation of groundwater quality and the alteration of urban water balances. While the presence of defects within pipe networks is well‐documented, accurately quantifying volumetric exchange fluxes remains a challenge due to the complex, nonlinear interactions between the pipe, the surrounding variably saturated soil, and the fluctuating groundwater level. Current modeling approaches often overlook the threshold behaviors of these systems, leading to potential inaccuracies in leakage estimation. In this study, we show for the first time that leaky pipes can become hydraulically disconnected from the underlying groundwater, a phenomenon analogous to well‐known river–groundwater interactions that include disconnection. In a sewer–groundwater context, hydraulic disconnection is restricted to point sources and is strongly influenced by colmation/clogging. Through numerical modeling of a hypothetical case study, we show that the leakage flux from the pipe (in absolute terms) initially increases with declining groundwater levels, until a critical depth below the leaky pipe is reached. After this point, the hydraulic communication from the groundwater to the leaky pipe stops and the leakage flux can be considered constant. In a sensitivity analysis, we demonstrate the impact of the individual hydraulic parameters of the leaky‐pipe‐groundwater system on the hydraulic disconnection. We further modify the properties of the aquifer material, resulting in a hydraulic disconnection depth of 0.89 m, 1.77 m and 4.00 m below pipe for sand, loamy sand and sandy loam aquifers, respectively. This insight has important implications for leakage modeling: once hydraulic disconnection occurs, the leakage flux becomes independent of groundwater dynamics. The present study provides a proof‐of‐concept for the mechanism by which leaky sewers hydraulically disconnect from groundwater.

The release and migration of radionuclides towards the biosphere from underground waste repositories may pose a threat to the environment and humans. Therefore, the understanding of transport processes of radionuclides in the subsurface is crucial in order to predict the arrival in the near-surface environment for effectively mitigating and managing associated risk. Processes controlling radionuclide transport may be advection, dispersion, diffusion, sorption and decay, among others.In the context and typical locations of existing waste repositories and test sites, diffusion-dominated transport occurs. Typically, local permeabilities and flow velocities are so small that advection and dispersion would only become significant at very large timescales. The processes of diffusion, sorption (possibly modulated by pressure and temperature) and decay may often be crucial for a) predicting the gradual release and movement of contaminants from the repository into the surrounding geological formations and b) in the geological barrier itself as part of safety analyses. Therefore, understanding of barrier-specific diffusion processes is essential for assessing long-term containment and designing effective concepts to ensure reliable isolation of radionuclides over a time period long enough for their decay to safe levels and to avoid potential environmental risks associated with the disposal of radioactive waste.In the present desktop study, we calculate diffusion-dominated transport of specific radionuclides (Tritium, Technetium, Neptunium a.o.) for various host rocks (tuff a.o.). We calculate radionuclide breakthrough curves and timescales using the 1D analytical model by Lapidus & Amundson (1952), extended for decay in Bear (1972). In order to validate transport parameters for specific radionuclides in specific rock, we analytically try to reproduce physical radionuclide diffusion experiments. Subsequently, we use the validated transport parameters to predict timescales of diffusion-dominated transport.References:Bear, J., 1972. Dynamics of Fluids in Porous Media. American Elsevier, New York.Lapidus, L., & Amundson, N. R. (1952). Mathematics of adsorption in beds. VI. The effect of longitudinal diffusion in ion exchange and chromatographic columns. The Journal of Physical Chemistry, 56(8), 984-988.