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The theory of groundwater flow systems proposed by Tóth, which was based on the two-dimensional profile flow field, has become the theoretical basis for studying basin-scale groundwater circulation.The stagnation points on the two-dimensional profile can be used to accurately divide the spatial distribution of groundwater flow systems.However, the spatial distribution of groundwater flow systems and whether stagnation points exist in the 3D domain remain unknown.In this study, two typical three-dimensional basins, namely foreland-like basins with undulations only in the x direction and dune-type basins with undulations in both x and y directions, are used as typical examples.By using a combination of cosine functions to characterize the undulating water table, analytical solutions of head distribution in the two basins are derived.Moreover, by employing the TECPLOT software, the spatial distribution of the 3D groundwater flow systems is clearly shown.It is found out that stagnation points can develop in two basins.The stagnation points in the foreland-like basin constitute a horizontally extending stagnation line, which controls the spatial distribution of four flow systems in the basin, while the stagnation points in the dune-type basin form an arc-shaped stagnation line, which controls the spatial distribution of six flow systems in the basin.By studying the distribution of stagnation line in 3D basins and successfully dividing flow systems by using the stagnation line, this study leads to a deepened understanding of groundwater circulation in 3D basins.

Groundwater age and groundwater residence time contain important information about groundwater circulation and evolutionary processes, and have been widely used in the study of groundwater circulation patterns in basins.In this paper, we simulated a three-stage flow system model through a multi-stage groundwater flow system demonstrator, and simulated the groundwater age distribution and groundwater residence time distribution based, and found that the bottom of the basin, the downstream of the regional flow, and the basin retention area responded the latest.The local flow system in the shallow part has relatively low concentration values after stabilization, the intermediate flow system is also relatively low compared to the regional flow system in the deep part, and the stagnant zone has relatively large concentration values due to salt accumulation.The groundwater age distribution curves are single-peaked, and the circulation time of the regional flow system is greater than that of the intermediate flow system than that of the local flow system.The residence time distribution monitored in the discharge zones shows that different levels of recharge will produce early, middle and late peaks, and the peaks correspond exactly to the level of the groundwater flow system.It can be judged from the peaks in the discharge zones that the groundwater is recharged from the local, intermediate or regional flow system, and thus the source of contaminants can be determined.The present research results have some significance for the evolution of groundwater circulation and the improvement of groundwater flow system theory.

Identifying the permeability structure of the dam foundation rock mass is important for the formulation of seepage control schemes. For the horizontally-stratified red-bed rock mass of the Yellow River Guxian Dam foundation, this paper adopted a "continuous, high-resolution" water pressure test data processing method to analyze the relationships between rock mass permeability and elevation, lithology and shear zones, clarifiy the permeability structure of the dam foundation rock mass, and propose seepage control advice. The results indicate that the Guxian Dam foundation rock mass is characterized by a structural and random permeability behavior. The structure shows that the permeability decreases with elevation. The randomness shows that the permeability randomly fluctuates due to lithology and shear zones. For the river-bed dam foundation rock mass, the bottom elevation of the weathering and unloading zone is 450 m or so, and the 1Lu bottom boundary is at the elevation of approximately 340 m. For the rock mass of the dam abutment, the 3Lu bottom boundary is located at the elevation of 560～580 m. The section of 350～360 m elevation has a certain thickness of soft rock, a poor development of shear structure, and a low permeability. It can be regarded as a confining layer and a potential target for the optimization of seepage control schemes. In view of the universal applicability, the method proposed in this paper can be used for reference in similar projects.