Geoscience Reference
In-Depth Information
10.24
Reduce the linearized Boussinesq equation (10.88) to an ordinary differential equation, which can
describe the short-time outflow behavior with boundary conditions (10.53). Hint. Follow the same
steps as those used to obtain Equation (9.13).
10.25
Multiple choice. Indicate which of the following statements are correct. In the case of steady
ground water flow above a horizontal impermeable layer, the hydraulic ground water theory implies
that:
(a)
the streamlines are orthogonal to the free surface;
(b)
the pressure distribution is hydrostatic in the vertical;
(c)
the equipotentials (lines or surfaces of constant hydraulic head) are horizontal;
(d)
ground water recharge at the free surface cannot be taken into account;
(e)
potential flow theory with Laplace's equation is still applicable;
(f)
the horizontal scale of the problem is of the same order of, or smaller than, the vertical scale
(e.g. the depth of the impermeable layer);
(g)
the flow region is fully saturated;
(h)
the water table is a true free surface;
(i)
effects of horizontal anisotropy can still be taken into account by adjusting the Boussinesq
equation (10.31); in other words, if
x
and
y
are horizontal coordinates,
k
xx
need not be
equal to
k
yy
,
and they can be used to replace
k
0
in the formulation;
(j)
however, flow in a soil profile with vertical anisotropy (i.e., when
k
xx
=
k
yy
=
k
zz
) cannot
be described by hydraulic ground water theory.
