Государственный комитет Республики Узбекистан

Figure 8.37 Saltwater-freshwater interface in an unconfined coastal aquifer (a) under hydrostatic conditions; (b) under conditions of steady-state seaward flow (after Hubbert, 1940).
Under hydrostatic conditions, the weight of a unit column of fresh water extending from the water table to the interface is balanced by a unit column of salt water extending from sea level to the same depth as the point on the interface. With reference to Figure 8.37(a), we have
(8.75)
or
(8.76)
For ρ_f = 1.0 and ρ_s = 1.025,
(8.77)
Equation (8.77) is often called the Ghyben-Herzberg relation.
If we specify a change in the water-table elevation of Δz_w, then from Eq. (8.77), Δz_s = 40 Δz_w. If the water table in an unconfined coastal aquifer is lowered 1 m, the saltwater interface will rise 40 m.
In most real situations, the Ghyben-Herzberg relation underestimates the depth to the saltwater interface. Where freshwater flow to the sea takes place, the hydrostatic assumptions of the Ghyben-Herzberg analysis are not satisfied. A more realistic picture was provided by Hubbert (1940) in the form of Figure 8.37(b) for steady-state outflow to the sea. The exact position of the interface can be determined for any given water-table configuration by graphical flow-net construction, noting the relationships shown on Figure 8.37(b) for the intersection of equipotential lines on the water table and on the interface.
The concepts outlined in Figure 8.37 do not reflect reality in yet another way. Both the hydrostatic analysis and the steady-state analysis assume that the interface separating fresh water and salt water in a coastal aquifer is a sharp boundary. In reality, there tends to be a mixing of salt water and fresh water in a zone of diffusion around the interface. The size of the zone is controlled by the dispersive characteristics of the geologic strata. Where this zone is narrow, the methods of solution for a sharp interface may provide a satisfactory prediction of the fresh-water flow pattern, but an extensive zone of diffusion can alter the flow pattern and the position of the interface, and must be taken into account. Henry (1960) was the first to present a mathematical solution for the steady-state case that includes consideration of dispersion. Cooper et al. (1964) provide a summary of the various analytical solutions.
Seawater intrusion can be induced in both unconfined and confined aquifers. Figure 8.38(a) provides a schematic representation of the saltwater wedge that would exist in a confined aquifer under conditions of natural steady-state outflow. Initiation of pumping [Figure 8.38(b)] sets up a transient flow pattern that leads to declines in the potentiometric surface on the confined aquifer and inland migration of the saltwater interface. Pinder and Cooper (1970) presented a numerical mathematical method for the calculation of the transient position of the saltwater front in a confined aquifer. Their solution includes consideration of dispersion.