Geoscience Reference
In-Depth Information
The governing equations are the continuity equation and the momentum
equation expressed below as follows:
Continuity equation
A
d
H
d
t
=
Q
i
+
Q
ins
;
A
=
A
f
:
h<D,
A
=
A
s
:
h
≥
D,
where
A
is the effective base area of storage pond,
H
the water stage,
Q
i
the inflow discharge from
i
th adjacent storage pond, and
Q
ins
is the
lateral inflow discharge from the ground surface.
h
is the water depth and
D
is the ceiling height of the storage pond.
A
f
is the area related to the
storage pond shape and
A
s
is the slot area.
Momentum equation
L
gA
b
d
Q
d
t
=∆
H
−
αLQ
|
Q
|
,
where
Q
is the discharge,
g
the gravity acceleration, and
L
is the distance
between the base area centroids of adjacent storage ponds.
A
b
is the cross-
sectional area of adjacent storage ponds, and it is determined according
to the water depths in the adjacent storage ponds. ∆
H
is the water level
difference between the adjacent storage ponds and
α
is the loss coecient
associated with Manning coecient.
At the inflow position from the ground surface to the underground space
and the dropping position from the upper floor to the lower floor in multi-
story underground space, the following step flow formula is applied.
Q
=
B
e
µ
0
h
e
gh
e
,
where
B
e
is the effective width of entrance,
µ
0
the discharge coecient, and
h
e
is the water depth in the upper storage pond. If the lower storage pond
is pressurized, then the above momentum equation is applied.
3. Application to Fukuoka City
3.1.
Studied area and computational conditions
Figure 2 shows the studied ground area of about 2.8 km
2
and Fig. 3 shows
the ground elevation distribution. The ground elevation becomes lower from
the Mikasa River to the direction of JR Hakata station. Figure 4 shows the
underground space under JR Hakata station. (JR denotes Japan Railway.)
The subway track space is assumed a storage pond with large volume. The
total area and volume of underground space except subway railroad space
are about 5
.
2
×
10
4
m
2
and 16
.
9
×
10
4
m
3
, respectively.
