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The effect of beach slope variation on saltwater intrusion dynamics in the unconfined coastal aquifer (experimental and numerical)
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Abstract: Over-exploitation of groundwater resources often causes seawater to intrude into coastal aquifers. This study aims to evaluate how different beach slopes (90°, 75°, 60°, and 45°) affect the extent and behavior of seawater intrusion in unconfined coastal aquifers under transient conditions. A three-dimensional laboratory model was constructed to simulate seawater intrusion under varying beach slopes. Experimental data were analyzed using image processing techniques, and results were validated using the SEAWAT numerical model. Key parameters—including wedge toe length, height, and area—were measured over time to assess the transient response of the saltwater wedge. The results showed that under static conditions, flatter slopes produced larger saltwater wedges. During transient conditions following a groundwater-level decline, the wedge toe advanced approximately 57% further in the vertical slope than in the 45° slope, while the final wedge size remained smaller on the steeper beach. The wedge height stabilized earlier than the toe length and area during intrusion, whereas in the recession stage, all three indices reached equilibrium almost simultaneously. The geometry of the beach slope has a significant effect on both the extent and temporal behavior of seawater intrusion. The toe length index showed a strong relationship with wedge area and can serve as a reliable indicator of intrusion volume under both steady and transient conditions. These findings emphasize the importance of considering beach slope in the design and management of coastal aquifer systems. Understanding how slope geometry influences the evolution of the saltwater wedge can improve the prediction and control of seawater intrusion in response to groundwater-level fluctuations.
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Key words:
- Seawater /
- Image processing /
- Laboratory model /
- SEAWAT /
- Saltwater wedge
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Figure 4. Laboratory model with porous medium boxes with specific saltwater concentration fourth Steps
Note: After obtaining the numerical value equivalent to saltwater with a concentration of 50% ($ {C}^{50\% } $) and the corrected pixel values of each model image at each time step ($ {C}_{i,j} $), the contour lines of saltwater with 50% concentration were drawn in MATLAB software. After drawing the above contour line, the position of the toe of the saltwater wedge and the height of the wedge are determined.
Figure 5. Conceptual model and boundary conditions used to simulate the numerical model
Figure 6. Laboratory experiments and numerical simulations of the advancing and receding saltwater wedge for a 90° slope beach (C1-90)
Figure 7. Laboratory experiments and numerical simulations of the advancing and receding saltwater wedge for a 45° slope beach (C4-45)
Figure 8. Changes in the saltwater wedge toe length index for beaches with the desired slopes under transient conditions
(a) C1-90, (b) C2-75, (c) C3-60 (d) C4-45, The beginning of the wedge recede stage is from t=45 min
Figure 9. Changes in the saltwater wedge height index for beaches with the desired slopes under transient conditions
(a) C1-90, (b) C2-75, (c) C3-60, (d) C4-45. The beginning of the wedge recede stage is from t=45 min
Figure 10. Changes in the saltwater wedge area index for beaches with the desired slopes under transient conditions
(a) C1-90, (b) C2-75, (c) C3-60, (d) C4-45. The beginning of the wedge recede stage is from t=45 m
Figure 11. Changes in the toe length index of the saltwater wedge for beaches with different slopes during the advance and recede stages of the wedge
Figure 12. Changes in the saltwater wedge toe length index during the advancing process of (a) C1-90, (b) C2-75, (c) C3-60, and (d) C4-45
Figure 13. Changes in the relative displacement of the toe length of the saltwater wedge in the advance and recede stages (a) C1-90, (b) C2-75, (c) C3-60, (d) C4-45
Figure 14. Changes in the relative displacement of the height of the saltwater wedge in the advance and recede stages (a) C1-90, (b) C2-75, (c) C3-60, (d) C4-45
Figure 15. Changes of selected indicators of saltwater wedge over time in the advance stage
(a) C1-90, (b) C2-75, (c) C3-60, (d) C4-45
Figure 16. Changes in selected indicators of the saltwater wedge over time in the recede stage
(a) C1-90, (b) C2-75, (c) C3-60, (d) C4-45
Figure 17. Changes in saltwater wedge indices for beaches with desired slopes in transient conditions
Notes: (a) the toe length of the wedge in the advance stage, (c) the height of the wedge in the advance stage, (e) the area of the wedge in the advance stage, (b) the toe length of the wedge in the recede stage, (d) the height of the wedge in the recede stage, (f) the area of the wedge in the recede stage
Figure 18. Relationships between the relative intrusion length (λ) and the beach angle (α)
(a) The results of Liu et al. (2012) research, (b) The results of this research in steady state conditions
Table 2. Summary of the numerical simulation parameters
Input parameters Value Unit Domain length 110 cm Domain height 42 cm Domain width 40 cm Hydraulic conductivity 33 cm/min Longitudinal dispersivity 0.1 cm Transversal dispersivity 0.01 cm Freshwater density 998 g/L Saltwater density 1024 g/L Saltwater concentration 35 g/L Porosity 0.385 - Saltwater level 37.4 cm Freshwater level 40.5 and 39.5 cm 
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Table 3. Statistical indices values during the advance stage of the saltwater wedge
Cases Indicators of Saltwater Wedge Statistical indicators R2 CE C1-90 Toe length (L) 0.996 0.995 Height (H) 0.974 0.938 Area (S) 0.993 0.832 C1-75 Toe length (L) 0.985 0.983 Height (H) 0.985 0.965 Area (S) 0.971 0.896 C1-60 Toe length (L) 0.978 0.962 Height (H) 0.987 0.881 Area (S) 0.991 0.953 C1-45 Toe length (L) 0.977 0.953 Height (H) 0.982 0.821 Area (S) 0.992 0.929
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Table 4. Statistical indices values during the recede stage of the saltwater wedge
Cases Indicators of Saltwater Wedge Statistical indicators R2 CE C1-90 Toe length (L) 0.976 0.923 Height (H) 0.991 0.940 Area (S) 0.976 0.887 C1-75 Toe length (L) 0.977 0.970 Height (H) 0.980 0.862 Area (S) 0.990 0.889 C1-60 Toe length (L) 0.927 0.921 Height (H) 0.925 0.784 Area (S) 0.947 0.918 C1-45 Toe length (L) 0.973 0.922 Height (H) 0.984 0.905 Area (S) 0.970 0.917
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