Keiichi Toda*, Kazuya Inoue*, Kensaku Kuriyama** and Osamu Maeda***
* Disaster Prevention Research Institute, Kyoto University, Japan
** Graduate school of Engineering, Kyoto University, Japan
*** Tokyo Electric Power Company, Japan
Gokasho, Uji, Kyoto 611-0011, Japan
TEL +81-774-38-4136 FAX +81-774-38-4147
Email toda@taisui5.dpri.kyoto-u.ac.jp
Abstract: Most of large cities in Japan face the potential danger of flood disaster due to river flood and/or storm surge. This paper treats a numerical analysis of inundation flow by a river bank breach in urban areas including underground space. The inundation flow model used here is based on the network model called “Street Network Model” which can express spread of inundation flow along streets. This model is applied to the northern part of Osaka and the volume of inundation water flowing into each underground space is examined. The detailed inundation flow analysis in Umeda underground mall is also executed. The obtained results emphasize the danger of underground space in inundating.
Keywords: street network model, inundation flow analysis, underground space, urban area
In the central district of large cities, a number of buildings stand close together on the land surface, under which underground space facilities such as underground mall and subway are developed. Populations and properties are densely concentrated there. If this area is attacked by overland flood flow due to a bank breach, the flow would extend to underground space, and the damage would be serious. Therefore, it is very significant to predict the flood disaster there, especially the inundation flow behavior accurately from the hydraulic and disaster preventive aspects. In view of this situation, this paper treats a numerical simulation method of inundation flows in urban areas with underground space, and aims at development of inundation flow modeling in underground space.
First, the one-dimensional river flood analysis is conducted by the method of characteristics. Next, assuming a river bank breach in flooding, the inflow discharge into flood prone area is calculated by the overflow formula, which is the boundary condition of inundation flow analysis on the ground surface. In the inundation flow analysis, “Street Network Model 1) ” is applied. The inundation water on the surface flows into underground spaces from stairs and so on. This inflow discharge is calculated by the drop formula, and the capacity of each underground space is taken into consideration.
In urban areas, the inundation water spreads along streets since buildings are constructed closely on both sides of streets. Then, in this model, the studied area is divided into the street part and the other part (named “residence block”). The street part consists of links (streets) and nodes (intersections). The concept of this modeling is shown in Fig.1. In calculation, in link mesh, which is divided into finer meshes, one-dimensional continuity and momentum equations are used as below. In this case, each link is regarded as a uniform rectangular channel and assumed to have an x-positive direction from a start node to an end node.
where h is water depth, u and M are x-directional velocity and discharge flux, respectively, qin is lateral inflow, B is channel width, H is water stage, and g is gravity acceleration. Node mesh or residence block is regarded as one mesh for itself. The water depth there is calculated from the following continuity equation.
where A is area of node or
residence block, Qk is
discharge from the mesh side k, and m
is the total number of the mesh sides. To calculate the discharge flux between
link, node and residence block, the following equation is used.
Fig.2 shows the Yodo river and the flood prone area studied here. The meshes (links, nodes and residence blocks) in the flood prone area are shown in Fig.3. In the Yodo river, Hirakata, 26km upstream from the river mouth and the location 4km downstream from the river mouth are chosen as the upstream and downstream boundaries, respectively. The assumed bank breach points are the three locations of 7.2km, 9.2km, and 10.0km from the river mouth. The flood prone area is about 15km2 and is surrounded by the rivers. The underground spaces considered in this study are Umeda underground mall, the two parking lots and the seven subway lines. The relation of their locations is shown in Fig.4.
The river bank breach is assumed when the flood
with peak discharge 12,000m3/s occurs in the Yodo river. In the river
flood analysis, the computational time step
is 0.05sec, the reach length
is 400m and Manning roughness
coefficient n is 0.03. The rectangular
shaped bank breach condition is assumed and the bank breach proceeds during
5min. The final breach width is about 370m and the final breach bottom elevation
is the same as that at the flood prone area there. In the inundation flow
computation on the surface,
is set 0.05sec, the link length
xl is set about 50m, and n
is 0.03 for link and node and 0.067 for residence block, respectively. The
inflow discharge to the underground is treated as the lateral outflow in the
surface meshes including stairs and so on, and it is evaluated by the drop
formula. In Umeda underground mall, the inflow from the ground surface and the
outflow to the lower subway spaces occur simultaneously. Here, it is assumed
that the outflow to the subway spaces continues until they are filled with water
and that the inflow discharge is not stored in Umeda mall during that time.
First, under the condition that the bank breach point is 9.2km from the river mouth, the inundation flow behavior is examined. Fig.5 shows the inundation water depth distributions on the surface at 1hr and 2hr after the bank breach. In the studied area, as the eastern area is higher than the western area, most of the inundation water flows down in the west or the south-west directions. Inundation water intrudes into the underground when it reaches the underground entrances. Fig.6(a) shows the inundation water volume distribution at 2hr after the bank breach. The size of underground spaces in Fig.6 nearly corresponds to the real size of those. Fig.7 shows the temporal changes of the inflow water discharge from the Yodo river to the flood prone area and the total inflow discharge into the underground spaces. The inflow discharge from the river is almost 2,000m3/s until 3hr after the bank breach, while the inflow discharge into the underground shows its maximum value 1,300m3/s at 2.5hr after the bank breach and it suddenly decreases after that and it becomes very little at 3.0hr after the bank breach. This is due to the reason that as is shown in Fig.6(b), at this time, most of the underground spaces are filled with the inflow water and there is very little inundation water existing over the underground spaces which still have some spare capacities.
Next, the sensitivity of inundation flow behavior is examined by changing the bank breach points. The inflow discharge from the river changes by the difference of river water stage and flood prone area elevation. Also, the way of inundation flow expansion changes. Fig.8 shows the inflow water volume dis- tribution in the five subway lines at 2hr after the bank breach. The water volume changes of Sakaisuji Line and Sennichimae Line which are located at the eastern edge and the western edge in the studied area, respectively, are very sensitive to the bank breach locations. The water volume of the other subway lines also changes to some extent by the bank breach point. These results show that the inundation phenomena in urban areas including underground spaces would become quite complicated if it occured.
The inundation flow analysis in Umeda underground mall is also executed. In this mall, pathways form a network and stores including department stores are located in both sides of them. Therefore, Street Network Model can be applied assuming that a pathway is a link, an intersection is a node and an area including stores and buildings is a residence block. As the underground pathway is about 3m in height, co-existence of free-surface flow condition and pressurized flow one has to be taken into account. In treating this, the slot model 2) with a narrow slot at ceiling has been applied. By this technique, the free-surface and the pressurized flows do not have to be analyzed separately. Once the pathway is primed, then the depth is replaced by the piezometric head acting on the pathway walls at that location. The network used here is shown in Fig.9.
The inflow discharge from the surface area into the underground space is expressed by the drop formula. The outflow discharge from the underground space into the subway station is also expressed in the similar way.
The inundation flow results by the bank breach
at 9.2km are used as the external boundary conditions and
= 0.01sec is used for
computation. Fig.10 shows the temporal change of inundation water depth
distributions. Inundation water intrudes from the northern stairs which are near
to the bank breach point, and extends to the whole mall space. At 30min after
the bank breach, the inundation water depth partially approaches the 3m ceiling
height. Then, at 50min after the bank breach, the inundation water depth becomes
more than 0.5m except for Osaka station building B1F and Dojima underground
mall. Generally, the underground area is very small compared with the surface
area. Therefore, once inundation water intrudes into the underground space, the
water depth tends to rise quickly, which makes the evacuation activities very
difficult.
The inundation flow analysis has been elaborated by considering the effects of streets and underground space. The behavior of inundation water on the surface and inflow water into the underground space would be very complicated in the urban area.
References
[1] 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.
[2] Chaudhry, M.H. Applied
Hydraulic Transients, Van Nostrand Reinhold, pp.422-423, 1979.