Measurements of piezometric heads at w ells near the coastline indicate that piezometric heads at points in the salt w ater zone change w ith time and may have an important bearing on the location of the fresh w ater-salt w ater interface. They should be considered in estimating the location of the interface.
Figure 20. 11 show s a fresh w ater-salt w ater interface which generally occurs in a homogeneous unconfined aquifer in a coastal zone. Groundwater flow is in a steady state and discharges into the sea. It is assumed that a piezometer taps any given point A in the salt w ater zone below the interface; hsstands for the elevation of piezometric head of the salt w ater measured at point A above the mean sea level; hfis the elevation of w ater table at point D at the same location of the piezometer above sea level.
Figure 20. 11 Schematic diagram show ing a sharp interface betw een fresh w ater-salt w ater in a coastal unconfined aquifer
At point A，the follow ing relation can be established w hen the subsurface flow system is in an equilibrium state:
w here ρsand ρfare densities of salt w ater and fresh w ater，respectively，Msand M are the depths of point A and the interface at point B below sea level， g is the gravitational acceleration. Rearrangement of Equation ( 20. 18) gives
and the follow ing relation is obtained
or
w here
For any given datum ( Figure 20. 11) ，the follow ing relation can also be established:
w here h'sand h'fare the piezometric heads of salt w ater at point A and w ater table at point D above the datum ，respectively ; M 'sand M ' are elevations of point A and the interface at point B above the datum ，respectively. From Equation ( 20. 23 ) the follow ing relation is obtained
or
Equation ( 20. 25) can be converted into Equation ( 20. 24) by letting h's= hs+ H0，h'f= hf+H0and M' = H0－ M，w here H0is the elevation of the sea level above the datum.Equation ( 20. 21) gives the depth of the interface，w hich is determined by ρs，ρf，hsand hf. According to Equation ( 20. 25 ) the elevation of the interface above the datum can be calculated，w hich is determined by ρs，ρf，h'sand h'f. In particular，if hsequals to zero， Equations ( 20. 20) or ( 20. 21 ) becomes the Ghyben-Herzberg relation. Thus，the Ghyben- Herzberg relation is a special case of Equation( 20. 21) . It is also noted that M in Equations ( 20. 20) or ( 20. 21) is not related to Msand that M' in Equations ( 20. 24) or ( 20. 25) is not related to M's，indicating that the depth or elevation of the interface is independent of the depth or elevation of the measured point in the salt zone below the interface.
For ρf= 1. 0 and ρs= 1. 025，Equation ( 20. 21) becomes
水文地质专业英语
and Equation ( 20. 25) becomes
水文地质专业英语
Figure 20. 12 show s different depths of the interface in an ideal model for different hf( ranging from 0 m to 3 m ) w hen hs= － 1 m，－ 0. 5 m，0 m，0. 5 m and 1 m according to Equation ( 20. 26) . It is seen that the depth of the interface increases with increasing hffor a given hs， and also increases w ith increasing hsfor a given hf. For example，the interface is 121 m and 39 m deep below the sea level for hf= 2 m w hen hs= － 1 m and 1 m，respectively.
Figure 20. 12 Depth of interface for different hsand hfin a theoretical model
Equation ( 20. 26) is used to estimate the depth of the interface in the northw estern coastal zone of Beihai，w here a sharp interface is assumed to exist betw een the fresh w ater and salt w ater. Piezometric heads at w ell cluster H5 are used as the upper Q1z clay terminates near this w ell cluster. Piezometric head at H5-1 stands for the w ater table of the fresh w ater at the w ell and piezometric head at H5-3 represents the hydraulic head of the salt w ater at a point in the salt w ater zone below the interface. Data of piezometric heads at H5-1 and H5-3 are first smoothed using the Haning formula of running average to eliminate the minor fluctuations in the measured piezometric heads ( Figure 20. 13a) . The estimated depths of the interface at w ell H5 during the measurement period are show n in Figure 20. 13b，w hich range from 40 m to 80 m below the sea level. The interface w as deeper in dry season than in rainy season due to the increasing piezometric heads of the salt w ater. Also show n in Figure 20. 13b are the estimated depths of the interface w ith the Ghyben-Herzberg relation. The results estimated w ith the Ghyben- Herzberg relation appear opposite of those calculated w ith Equation ( 20. 26) and are considered to be not as reasonable as the latter，because the Ghyben-Herzberg relation does not take the piezometric head of the salt w ater into account.
Figure 20. 13 Changes in ( a) average piezometric heads at H5-1 and H5-3 and ( b) calculated depth of the fresh w ater-salt interface below sea level from January，1996 to M arch，1997 A—estimated w ith the Ghyben-Herzberg relation; B—estimated w ith Equation ( 20. 26)