The impact of urban groundwater upon surface water - eTheses ...

6.2.1 Analytical Model, Steady State Solution
GROUNDWATER FLOW MODELLING
The one-dimensional equation for flow in an unconfined aquifer may be expressed as:
dh d ⎡ dh ⎤
Sy = k h b + R
dt dx ⎢ ( − )
⎣ dx ⎥
⎦
Sy = specific yield [-]
k = hydraulic conductivity [L/T]
h = hydraulic head [L]
b = base elevation of the aquifer [L]
t = time [T]
x = distance [L]
R = recharge [L/T]
When Recharge is zero, the hydraulic conductivity and aquifer base elevation are
homogeneous and the boundary conditions are:h = h1 at x = 0 and h = h2 at x = L (Figure 6.1)
the analytical solution is:
h
Datum
2
River
2
2 2
− h
⎡h − h b(
h − h ⎤
1
2 1 2 1)
− b(
h − h1)
= ⎢ − ⎥x
2
⎣ 2L
L ⎦
h 1 h h 2
x
b
Aquifer
L
Figure 6.1 Schematic diagram for the analytical solution of unconfined flow to a river
153
Impermeable base
Equation 6.1