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Analysis and modeling of flooding in urban drainage systems
Theo G. Schmitt a,*, Martin Thomas a, Norman Ettrich b
aFG Siedlungswasserwirtschaft, Kaiserslautern Technical University, Postfach 3049, D -67653 Kaiserslautern, Germany
bFraunhofer Institut fu?r Techno – und Wirtschaftsmathematik ITWM, Gottlieb -Daimler -Stra?e 49, D -67663 Kaiserslautern, Germany
Abstract
Urban flooding is a global problem and can have significant economic and social
consequences. The main objective of this paper is the development of an integrated planning
and management tool to allow cost effective management for urban drainage systems and
prevention of urban flooding .
This paper follows European Standard EN 752 defining flood
frequen cy as the one hydraulic performance criterion. Dual drainage modeling is used here to
analyze urban flooding caused by surcharged sewer systems in urban areas . A dual drainage
simulation model is described here in details based upon hydraulic flow routing procedures
for surface flow and pipe flow. Special consideration is given to the interaction between
surface and sewer flow in order to most accurately compute water levels above ground as a
basis for further assessment of possible damage costs.
The model application is presented for
small case study in terms of data needs, model verification and first simulation results .
1. Introduction
Climate change is altering precipitation patterns across the globe. Every year, rainstorms and
flooding events are increasing in both frequency and severity. With municipal water utilities
already strained by decades of underinvestment and aging infrastructure, they now face a whole
new spectrum of c hallenges due to climate change and growing urb an populations . So
prev ention of flooding in urban areas has become an important issue. However, drainage
systems designed to cope with the most extreme storm conditions would be too expensive to
build and operate. In establishing tolerable flood frequencies, the safety of the r esidents and the
protection of their valuables must be in balance with the technical and economic restrictions.
According to European Standard EN 752, urban drainage systems should be designed to
withstand periods of flooding in the range of 10 50 years, d epending on the type of urban area
and traffic infrastructure served . In the following, the major issues of this standard will be
briefly discussed in conjunction with an analysis of urban flooding. A simulation model to
assess the hydraulic performance of sewer systems and the risk of flooding caused by system
surcharge will be described afterwards. Its app lication and data need is demon strated in a case
study.
2. Analysis of flooding phenomena
Flooding in urban drainage systems as defined above may occur at different stages of hydraulic
surcharge depending on the drainage system (separate or combined sewers), general drainage
design charac teristics as well as specific local constraints.
When private sewage drains are directly connected to the public sewer system without
backwater valves, the possible effects of hydraulic surcharge depend on the levels of the lowest
sewage inlet inside the house (basement), the sewer line and the water level during surcharge,
respectively. Whenever the water level in the pub lic sewer exceeds the level of gravity inlets in
the house below street level, flooding inside the house will occur due to backwater effects. In
such a case flooding is possible without experiencing surface flooding. In the same way,
hydraulic surcharge in the sewer system might produce flooding on private properties via storm
drains, when their inlet level is below the water level of the surc harged storm or combined
sewer.
In both cases, the occurrence of flooding, being linked directly to the level of inl ets versus water
level (pressure height) in the sewer can be easily predicted by hydrodynamic sewer flow
simulations, assuming the availability of physical data of the private drai ns and the public sewer
system.
Distinct from the situations described ab ove, the occurrence and possible effects of surface
flooding depend much more on local constraints and surface characteristics, e.g. street
gradient, sidewalks and curb height. These characteristics, however, are much more difficult
described physically, a nd these data are usually not available in practice. In addition, todays
simulation models are not fully adequate to simulate the relevant hydraulic phenomena
associated with surface flooding and surface flow along distinct flow paths.
2.1 . Consequences of flooding
Flooding in urban areas due to the failure of drainage systems causes large damage at
buildings and other public and private infrastructure. Besides, street flooding can limit or
completely hinder the functioning of traffic systems and has indi rect consequences such as
loss of business and opportu nity. The expected total damage direct and indirect monetary
damage costs as well as possible social consequences is related to the physical properties of
the flood, i.e. the water level above ground le vel, the extend of flooding in terms of water
volume escaping from or not being entering the drainage system, and the duration of flooding.
With sloped surfaces even the flow velocity on the surface might have an impact on potential
flood damage .
3. Methodology
I. Rainfall -Runoff Simulation : The RisUrSim model first transforms rainfall into
effective runoff using standard methods for interception, depression storage and soil
infiltration (previous areas only) as described in literature (e.g. Akan, 1993; Ashley et
al., 1999). Surface runoff would then be handled in distinct detail depending on the
specific situation of a single runoff area. For areas not considered for detailed surface
flow simulation, e.g. roof areas, RisoReff uses a unit -hydr ograph method to compute
surface runoff as input to the sub -surface sewer system (uni -directional flow ).
II. Hydraulic surface flow modeling : The RisoSurf approach includes detailed
hydraulic considerations for areas where surface flow occurs. Hydraulic (sur face) flow
modeling is generally based upon conservation laws of fluid flow expressed in the
Navier Stokes equations. The fact that in surface flow the vertical dimension is much
smaller than typical horizontal scale allows a simplified two -dimensional
rep resentation, the so -called shallow water flow equations (Hilden, 2003). The
application of this detailed hydraulic method would be restricted to small areas only.
Therefore, it only served as a benchmark for a further simplified two -dimensional
approach.
Rainfall -Runoff
Simulation
Hydraulic
Surface Flow
Modeling
Dynamic
Sewer Flow
Modeling
Coupling of
Modules
Modeling
Interaction of
Surface and
Sewer Flow
III. Dynamic sewer flow modeling: Sewer flow is simulated applying fully
dynamic flow routing of unsteady, gradually varied flow and solving Saint -Venant –
Equations numerically in an explicit difference scheme. The explicit difference
scheme is applied in variable time steps that are permanently adjusted to the
COURANT -criterion, guaranteeing numerical stability (Schmitt, 1986).At each time
step, the proced ure of dynamic flow routing starts by computing flow values for each
conduit (sewer segment between nodes) based upon momentum equation and
instantaneous water levels at the nodes at the end of the last time step. In the next step
of the dynamic flow routi ng procedure the flow volume is balanced at each node,
taking into account inlets from house drains and all surface inlets connected, as well as
inflows and outflows from sewers connected at the nodes. The resulting change of
volume is drawn to free water surface available at the node, thus producing a change
of water level at the node. In order to improve numerical stability, the two phases are
applied in a half -step full -step procedure during each time step as described in
Roesner et al. (1988) and Schm itt (1986). The underground sewer system is
represented by a network of nodes and conduits (sewer segment between nodes). In
contrast to conventional modeling, not only manholes but also street inlets and house
drains are considered as extra nodes to fully achieve the connection of surface and
underground drainage system at all locations where interaction between surface and
sewer flow and potentially flooding might occur. This will be further discussed in
context with the case study below.
IV. Modeling intera ction of surface and sewer flow : The simulation of the
interaction between surface and sewer flow is based upon the definition of exchange
locations. Each runoff area is allocated to one specified exchange l ocation as
illustrated in Fig. 1 . Here, all re levant information for surface and sewer flow
simulation (instantaneous runoff, water level, exchange volume) is available at the
beginning of each time step for all simulation modules and is renewed at the end of the
time step in the following way:
? The hy drologic runoff model RisoReff only supports uni -directional
flow and is applied to all areas not considered for surface flow.
Computed runoff from those hydrologic areas is passed to the single
exchange location to which the area is connected. The excha nge
volume would be the runoff volume in the according time step.
? Areas simulated with the hydrologic model approach can be connected
to the underground drainage system in two alternative ways :
(a) hydrologic areas directly discharging to the sewer system vi a surface inlets or private
drains (se rvice pipes);
(b) hydrologic areas discharging to surface areas where surface flow is considered by
hydraulic model RisoSurf .
? The hydraulic surface flow module RisoSurf allows bi -directional
exchange of runoff volume:
(a) from the surface area to the sewer system, if there is sufficient sewer capacity;
(b) from the sewer to the hydraulic surface in case of sewer surcharge when the water
level in the sewer system rises above ground level.
? In case of surcharge, water level above ground as provided by surface
flow simulation module RisoSurf at exchange nodes would be used by
dynamic sewer flow module HamokaRis in the momentum equation in
the following time step. If the balance of flow volume at the nodes in
HamokaRis results in a w ater level above ground, the associate d surplus
volume would be transfer ed to the surface flow simulation by storing
this volume in the exchange location
Fig. 1 . Possible links and interaction of surface runoff, Fig. 2 . Procedure to synchronize time steps of
surface flow and sewer flow at exchange nodes. Simulation modules RisoSurf and HamokaRis
in simulation tool RisUrSim.
V. Coupling of modules RisoSurf and HamokaRis : The implementation of
coupled hydraulic flow routing for surface and sewer flow modules RisoSurf and
HamokaRis requires particular consideration of numeric stability and observation of
continuity as well. Numeric stability has been secured by a synchro nized
administration of dynamic time step selection according to F ig 2 .
Fig. 3 . Overall structure of the RisUrSim simulation tool
4. Model application case study : One of the test areas to prove the concept of the
RisUrSim method is a sub -catchment in th e city of Kaiserslautern (Fig. 4 ). Some of the
houses in the southern street of the test -area have been subject to basement flooding during
heavy rainfall in the past. To prepare the model application, detailed surveying has been
carried out to accurately describe flow -relevant surface a reas. Besides, a flow monitoring
device has been installed to gather data during rainfall events for model calibration under
surcharge conditions. This, however, has not been successful as during the period of
monitoring not a single surcharge or even floo ding event occurred .
Fig. 4 . Test case area KL -Erzhuetten (Germany).
Fig. 5 . Mathematical representation of the street surface in a triangular network in surface flow module RisoSurf.
5. Simulation results : Due to the fact that no surcharge or flooding event could be monitored,
the RisUrSim Software has been applied to a variety of test scenarios using synthetic design storms.
These applications have been done to verify the most crucial model features of hydr aulic surface flow
simulation and the interaction between surface flow and sewer flow under surcharge and flooding
conditions. The simulation results of the real -case system Erzhuetten are shown the Fig. 10 in terms of
water level distribution along the st reet surface at 15 and 25 min simulation time, respectively. In this
system the surface elevation decreases from north -east (right) to south -west (left) while the sewer –
system flow direction is oriented in the opposite direction. This has led to problems w ith flooding in
this area in the past. The representation of simulated water levels in the manholes and on the street
surface illustrates the surface flow pattern from surcharged, flooded manholes to street areas with
lower surface levels (on the left side of the graph). This proves that with the RisUrSim Software the
surface flooding could be reproduced realistically.
Fig. 6 . Water level distribution as simulated for the test case system KL -Erzhuetten during a synthetical design
storm after 15 and 25 min.
6. Conclusions : It has been shown that European Standard EN 752 triggers more intense
consideration of the flooding phenomenon in urban drain flow modeling. In the RisUrSim
approach particular recognition is given to deta iled surface flow simulation and the interaction
between surface and sewer flow during times of surcharged sewers. This approach is dual –
drainage concept .
References
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