Kenji Kawaike*, Kazuya Inoue**, Keiichi Toda** and Tsutomu Nakai***
*Graduate school of Engineering, Kyoto University, Japan
**Disaster Prevention Research Institute, Kyoto University, Japan
***Faculty of Engineering, Kyoto University, Japan
Gokasho,
Uji, Kyoto 611-0011, Japan
Tel +81-774-38-4137; Fax +81-774-38-4147
E-mail kawa@taisui5.dpri.kyoto-u.ac.jp
Abstract: In this paper, an inundation flow model in hillside cities is developed considering the effects of sediment. In this model, the studied area is divided into upstream area (mountainous area) and downstream area (urban area). In the mountainous area, which comprises tributaries, slopes (without sediment) and main stream (with sediment on the bed), the runoff discharge and sediment concentration hydrograph at the downstream end of main stream are calculated using the kinematic wave model and the one-dimensional dynamic wave model. In the urban area, applying these hydrographs as the boundary conditions at the upstream end, the two-dimensional inundation flow analysis is conducted using unstructured meshes. The meshes for computation are divided into three types of categories; river, street and flood plain. In order to consider the effects of streets and buildings in urban area, the occupying ratio and the invasion ratio are introduced, and roughness coefficient is changed according to the mesh category. The above model is applied to Ikuta River basin in Kobe city, Japan. The obtained results show that the scale of inundation is much larger than that of the case without sediment. Therefore, it is very significant to consider the effects of sediment in the inundation flow analysis in hillside cities.
Keywords: hillside cities, sediment yield, inundation flow analysis, unstructured meshes
Recently in Japan, most of the loss of lives by flood disaster is caused by sediment disaster. Sediment disaster is not limited in mountainous areas only. In fact, severe sediment disasters occurred in the hillside cities such as Kobe in 1938, Nagasaki in 1982 and Hiroshima in 1999. In this paper, a two-dimensional inundation flow model considering the effects of sediment is developed using unstructured meshes and applied to Ikuta River basin in Kobe city, Japan.
A river basin studied here is divided into upstream part (mountainous area) and downstream part (urban area). The framework of the model is shown in Fig.1 and the studied area is shown in Fig.2. The reason why Ikuta River was selected in this study is that this river, running through the center of Kobe city, seems to have the potential of causing the severe flood and sediment disaster. Fig.2 shows the mountainous area and the urban area. There is some area which is not included in the Ikuta River basin but whose rainfall flows out directly into the studied urban area. This is the ‘hilly area’ shown in Fig.2.
The river in the mountainous area is divided into ‘tributary’ and ‘main stream’. First, runoff discharge without sediment yield from tributaries and slopes directly connected with the main stream is calculated using the kinematic wave model. As the governing equation, assuming that the bed slope and the friction slope of the St. Venant equation are dominant, the following one is used.
where
q is water discharge per unit width in
the longitudinal direction of slopes or where q is water discharge per unit width in the longitudinal direction of
slopes or tributaries, h is flow
depth,
and m
are the coefficients. When using the Manning’s formula, m
is defined as m=5/3, and
is defined as
where
is the bed slope, and n
is roughness coefficient. Along the tributaries, the following continuity
equation is also used.
where qs is lateral inflow per unit length from side slopes, and B is river width.
Next, adding these runoff discharges as lateral inflows, the water discharge and the sediment concentration hydrograph at the downstream end of the main stream are calculated using the one-dimensional dynamic wave model considering sediment yield from the main stream bed.
The governing equations used here are as follows.
<continuity equation>
<momentum equation>
<continuity
equation for sediment component>
<equation
for bed surface elevation>
where
M is x-component
of discharge flux, u is x-component
of flow velocity, i is deposition or
erosion velocity,
is momentum correction coefficient,
g is gravity acceleration, H
is flow surface elevation,
is bottom shear stress, and
is density of the flow with water
and sediment. C and C*
are volume concentration of sediment in the fluid and volume concentration of
the solids in the bed, respectively, and zb
is deposition or erosion thickness measured from the original bed elevation. In
this study, sediment yield from tributaries or side slopes is not taken into
account.
In the urban area, the studied area is divided into arbitrary-shaped unstructured meshes. Using the runoff discharge and sediment concentration hydrograph as the boundary conditions at the upstream end, the two-dimensional inundation flow analysis based on the Finite Volume Method is conducted1). The governing equations used here are the same as those of Nakagawa et al2) and they are as follows.
<continuity
equation>
<momentum equation>
<continuity equation for sediment component>
<equation for bed surface elevation>
where qrain is rainfall per unit time. As for the location of unknown values, flow depth h, volume concentration of sediment C and deposition or erosion velocity i are defined at a centroid of polygon mesh and discharge flux M, N and flow velocity u, v are defined at the middle point of side of polygon, as shown in Fig.3. The meshes for computation and the original bed elevation used in this study are shown in Fig.4. These meshes are grouped into three types of categories; river, street and flood plain. Fig.5 shows the distribution of these mesh categories. As the boundary condition, the above mentioned hydrographs are imposed at the upstream end of Ikuta River. At the mesh side adjacent to hilly area, the runoff discharge (without sediment) obtained by the kinematic wave model is imposed. At the other boundaries of rivers and river mouth, the discharge flux is calculated by using drop formula. The studied area is highly urbanized, so the effects of factors in urban area such as streets and buildings should be taken into consideration. Here, according to Inoue et al3), the occupying ratio (the ratio of the buildings area to the mesh area) and the invasion ratio (the ratio of the side length, through which inundation water can come into or out the mesh, to the total side length) are introduced. Also, different values are given to the roughness coefficient n depending on the mesh categories.
In the analysis here, the rainfall record in 1938 at Kobe meteorological
station is used. The total computation time is 108 hours (4.5 days). Fig.6 and
Fig.7 show the discharge hydrograph without sediment and the discharge
hydrograph with sediment and the sediment concentration, respectively. The
difference between these discharge hydrographs is due to the sediment volume.
The
maximum inundation water depth without sediment is shown in Fig.8. The inundated
area where the maximum water depth is more than 0.5m is very limited. Fig.9
shows the maximum inundation water depth considering both runoff discharge and
sediment yield, and Fig.10 shows the thickness of sediment deposition at
t=108hr. Fig.10 shows that the sediment deposition
area is widely extended on both sides of Ikuta River. Especially around the
Nunobiki intersection, thickness of deposition amounts to more than 3m. This may be due to the reason that the river bed slope becomes abruptly mild around there. From the comparison between Fig.8 and Fig.9, the computed inundated area with consideration of the sediment effects is larger than that without it, because Ikuta River bed arises due to the sediment deposition, which causes much overflow discharge from the river. Therefore, in the inundation flow analysis in hillside cities with mountainous area on its back such as Kobe, it is very important to consider the sediment yield effects. These figures also indicate that the damage due to inundation could be much reduced by controlling the sediment yield from the mountainous area.
The conclusions obtained from this study can be summarized as follows.
(1) An inundation flow model considering the effects of sediment yield has been developed, which can be applicable to hillside cities.
(2) From the comparison of the results between the case with and without sediment yield, the inundation flow behavior is much influenced by the sediment in hillside cities.
References
[1] Kawaike, K., Inoue, K. and Toda, K.: Inundation Flow Modeling in Urban Area Based on the Unstructured Meshes, Hydrosoft 2000, Hydraulic Engineering Software, VIII, WIT press, pp.457-466, 2000.
[2] Nakagawa, H., Takahashi, T., Sawada, T. and Ishibashi, A.: Estimation of a Debris Flow Hydrograph and Analysis of Evacuation Action Using GIS, Journal of Hydroscience and Hydraulic Engineering, JSCE, Vol.17, No.1, pp.73-85, 1999.
[3] Inoue, K., Kawaike, K. and Hayashi, H.: Numerical Simulation Models on Inundation Flow in Urban Area, Journal of Hydroscience and Hydraulic Engineering, JSCE, Vol. 18, No.1, pp.119-126, 2000.