A system dynamics simulating model of groundwater level changes and its impacts on land uplift

Land uplift due to mine flooding has become a significant challenge with extensive historical mining activities, particularly in Germany’s Ruhr district. The cessation of coal mining operations has led to a gradual rise in groundwater levels, altering geotechnical and hydrological conditions and causing surface uplift. This study develops a system dynamics (SD) model to investigate the dynamic interactions of influential variables such as groundwater levels, total stress, porosity and permeability with land uplift over time. The model integrates causal loop diagrams (CLD) and stock flow diagrams (SFD) to comprehensively understand the system’s behavior. SFD illustrated that for a 10 percent increase in groundwater level, the land uplift increased by about +6 percent, and a rise of 200 percent in total stress caused an 18 percent increase in effective stress, which decreased the land uplift by about 20 percent. This study highlights the importance of dynamic modeling in informing land-use planning and mitigating the long-term impacts of land uplift after mine closures. Introduction Mine flooding, a consequence of coal mine closures, affects the local stress state and induces surface movements. Understanding the interrelated geotechnical and hydrological parameters influencing land uplift is crucial for accurate predictions and effective land management. The SD approach offers a robust framework for analyzing these complex interactions, allowing the study of individual and combined effects of variables. Fig. 1 The CLD of the effective stress and its impacts on the land upliftover abandoned mines. Methodology This study employs SD modeling to simulate land uplift dynamics. The CLD provides a qualitative framework for understanding the feedback loops within the system, while the SFD enables quantitative simulation. The modeling framework accounts for groundwater infiltration, stress redistribution and land subsidence mitigation strategies. The analysis considers historical and projected data from the Eastern Ruhr region in Germany, allowing for scenario-based simulations. Fig. 2 The SFD of the effective stress and its impacts on the land upliftover abandoned mines.. The developed CLD of land uplift is illustrated in Fig. 1. The red arrow in Fig. 1 represents the indirect interactions between two variables, while the blue arrow indicates the direct impact. Understanding these interactions enables managers to identify the causal and dynamic interrelationships between groundwater levels in abandoned mines and land uplift. Fig. 3 A 10 percent increase in groundwater elevationand its consequences on the land uplift rate. Figure 2 presents the SFD illustrating the mathematical model related to Fig. 1. The mathematical equations define the interaction between each pair of variables in Fig. 2. The SFD in Fig. 2 provides simulation and scenario analysis. Effective stress, σ’, is determined by total stress, σ, and pore water pressure, µ. If the effective stress stays negative, land uplift will occur. An increase in groundwater level increases pore water pressure, leading to surface uplift. The model simulates changes in land uplift based on variations in permeability, porosity and total stress. The results indicate that an increase in porosity intensifies land uplift due to reduced effective stress, while higher total stress counteracts uplift by increasing vertical compaction. The interaction between groundwater levels and land uplift follows an exponential trend, meaning that even minor changes in permeability can significantly impact surface movements. Figure 3 depicts the impact of a 10 percent increase in groundwater level on land uplift. The results demonstrate a +6 percent increase in land uplift, with a delayed response time of approximately 30 years. Groundwater infiltrates horizontally before saturating vertical strata, indicating a non-immediate effect on surface movement. The simulations emphasize that land uplift follows an exponential rather than linear trend, meaning that after a specific time, small increases in groundwater levels may lead to disproportionately large land uplift over time. Stabilizing groundwater pumping rates and controlling infiltration can significantly reduce land uplift risks. The long-term impact suggests that immediate mitigation strategies, such as controlled groundwater extraction, should be employed to delay uplift acceleration and prevent infrastructure damage. The delayed response time in uplift effects highlights the necessity for long-term monitoring and adaptive management strategies. Controlling stress redistribution and mitigating subsurface porosity increases will be critical in maintaining surface stability. Conclusion and managerial insights The SD model provides a valuable tool for predicting and managing land uplift due to mine flooding. Key managerial insights include: Groundwater level fluctuations have a long-term and nonlinear effect on land uplift, necessitating continuous monitoring. Increasing total stress through surface stabilization methods can reduce land uplift risks. Controlling porosity, for example, through soil compaction techniques, can mitigate excessive uplift. Strategic groundwater pumping can delay uplift onset and reduce peak uplift magnitudes. Implementing long-term stress redistribution strategies can mitigate the delayed impact of groundwater level rise on land uplift. This research underscores the importance of system dynamics modeling in post-mining and land uplift management. Future work should incorporate variables such as climate-change effects and soil heterogeneity to enhance predictive accuracy. The insights derived from this study will assist policymakers and engineers in developing sustainable land-use plans in regions affected by post-mining uplift phenomena. References A list of all references is available in the full paper.

A system dynamics simulating model of groundwater level changes and its impacts on land uplift

Authored by: Mir Ahmad Mohammadi

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