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9th International Conference on Urban Drainage Modelling
Belgrade 2012
1
Modelling Internal Boundary Conditions of a Sewer
Network
Nuno Melo1 , Jorge Leandro2, James Shucksmith3, Matteo
Rubinato3, Slobodan Djordjevic4, Adrian J. Saul3, Helena Ramos5,
Joo L. M. P. de Lima2
1 UDI Research Unit for Inland Development, Polytechnic
Institute of Guarda, Portugal, [email protected] 2 IMAR Institute of
Marine Research, University of Coimbra, Portugal,
[email protected], [email protected] 3 University of Sheffield,
United Kingdom, [email protected],
[email protected],
[email protected] 4 University of Exeter, United Kingdom,
[email protected] 5 IST Instituto Superior Tcnico,
Technical University of Lisbon, Portugal, [email protected]
ABSTRACT
Due to the increased frequency of rainfall events caused by
climate change, flooding in urban areas are becoming increasingly
frequent. Thus the accurate modelling of drainage systems is a
fundamental tool to enable operators to minimize flooding. In this
paper we compare the experimental data obtained from a facility in
the University of Sheffield with the numerical results obtained
with two one-dimensional numerical models (1D), SIPSON and SWMM.
The experimental facility is a scaled model of an urban drainage
system located in the north of England. The inputs of the scaled
model were taken from two rainfall events that occurred on the 12th
December 2008 and on the 17th January 2009 (data measured by a rain
gauge installed in the basin). It was found that SIPSON internal
boundary conditions at the manhole level represented well the head
losses of the flow inside the manhole, thus the model was able to
reproduce fairly well the water depths along the drainage
system.
KEYWORDS
Numerical modelling, urban flooding, urban drainage, internal
boundary conditions
1 INTRODUCTION
The risk of flooding in urban areas is directly related to the
capacity of the sewer system to convey or hold the excess runoff
generated by a particular rainfall event. Accurate modelling of
these systems is a fundamental tool for real time management,
enabling operators to take advantage of the systems full capacity
and minimize flooding.
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Some national regulations for preliminary design of stormwater
drainage systems is based on the concept of uniform flow with a
filling ratio of approximately 85%, for which the discharge is
equal to the full pipe discharge. This concept was tested in the
past and is still the basis of the present guidelines, although
this is only strictly true for subcritical flow (Gargano and Hager,
2002). The free surface of supercritical flow is dominated by shock
waves due to flow perturbations. For example, in a manhole
connected to both up-and downstream sewers, there are changes of
cross-sectional shape from the circular to the U-shaped profiles of
equal diameter, which generates shock waves within the flow
(Gargano and Hager, 2002).
Manholes allow the aeration of the drainage system and its
inspection and maintenance. Regulations request that they should be
placed whenever sudden changes along the system occurs, e.g. in
terms of diameter, bottom slope, discharge addition or reduction,
or changes in boundary roughness. Typically, the spacing of
manholes in meters should be equal to the sewer diameter in
centimetres, and not exceed 100m (Del Giudice et al., 2000; Hager,
1999).
Free surface flow, as occurs in partially filled sewers, depend
essentially on the Froude number. For subcritical flow,
disturbances propagates also in the upstream direction, such that
these flows must be computed against the flow direction. In
contrast, the computational and the flow directions are identical
for supercritical flows, for which the average-flow velocity V is
larger than the wave celerity c (Hager and Gisonni, 2005). Hager
(1999) proposed a simplification to calculate the Froude number F
for circular sewers in terms of discharge Q, gravitational
acceleration g, sewer diameter D and flow depth h for sewer filling
y=h/D between 20% and 95% (Equation 1).
214/F gDhQ (1)
This is similar to the expression for the rectangular channel,
yet with a larger effect of flow depth, or relative sewer filling
y. For complete sewer filling, i.e. the transition from free
surface to pressurized
pipe flow (y=1), (1) degenerates to the so-called pipe
(subscript D) Froude number 215D )/(F gDQ (Hager and Gisonni,
2005).
Loss coefficients at the manholes can be split into inlet and
outlet coefficients being the global
coefficient of the manhole obtained by InOut (Merlein, 2000).
Losses at sewer junctions
depend on flow rate, junction geometry, and the change in pipe
diameter between the inflow and outflow lines (Wang et al.,
1998).
According to Leandro et al. (2009) the head losses investigation
at sewer junctions have been made through experimental studies for
a better understand of the hydraulic conditions for both
subcritical and supercritical flows. However most of these studies
remain purely experimental and often they do not translate back
into commercial urban flood models.
The aim of this work is to compare the observed flow in a scale
model of an urban drainage system, with the results obtained using
two one-dimensional (1D) numerical models, SIPSON and SWMM, in
order to validate the internal boundary conditions. The calibration
of the models is done using the experimental data of the two storm
events occurred on 12th December 2008 and 17th January 2009 (data
measured by a rain gauge installed in the basin), thus validating
the internal boundary conditions. The facility is a scale model of
an urban drainage system located in the North of England, UK, being
this composed of three inlet pipes fed from a header tank, and six
manholes (diameter of 240 mm), connected to each other by five
circular pipes of two sizes (diameters of 75 and 100 mm).
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2 METHODOLOGY
2.1 Physical model
The physical model used in this study represents a section of an
urban drainage system located in the North of England, UK, which
can record water depths and flow in real time. The facility was
constructed in the laboratorial facilities of the Department of
Civil and Structural Engineering of the University of Sheffield.
The installation is composed by three inlet conduits (A, B and C)
75mm, six manholes and two CSO (Combined Sewer Overflow), as shown
in Figure 1. The six manholes and the two CSO are connected to each
other at the bottom level by five pipes 75mm, and the last manhole
(M6) is connected to the Frontal and Lateral CSO by two pipes of
100mm. The first leaves the M6 at the bottom level and the second
90mm above the bottom level. The bottom level of the manholes is
equal for all. Every manhole has an internal diameter of 240 mm.
This facility is supplied by a header tank of constant level, which
in turn is supplied by the water that is recirculated from de CSO
tanks.
Figure 1. Scheme of the facility (M stands for manhole).
In each inlet of the facility the flow is controlled by
calibrated butterfly valves, remotely controlled from a computer.
The flow in each pipe is varied independently in real time, thereby
enabling the simulation of a variety of precipitation events.
Through the system, non-intrusive pressure transducers are
installed, which enable the acquisition of pressure data in real
time, and six transducers are located within the manholes, which
allow determining the flow depth at these sites by depth versus
pressure relationships. The installation has also three flow
meters, one at each inlet pipe system.
2.2 Hydraulic Numerical Models
To model the system two one-dimensional models, SIPSON and SWMM
were used.
SIPSON is a 1D/1D integrated hydraulic model developed by
Djordjevic (2001) at the University of Belgrade. The acronym SIPSON
stands for Simulation of Interaction between Pipe flow and Overland
flow in Networks. SIPSON, besides being a hydraulic model, also
incorporates a
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hydrologic model (rainfall runoff), called BEMUS, which is used
for calculating the surface runoff input to the hydraulic model. A
GIS interface, named 3DNet, works as the platform for management
and editing of data and visualization of the SIPSON results. The
hydraulic model is based on the Preissman finite difference method
and the conjugate gradient method, solving simultaneously the
continuity equations for network nodes, the complete St. Venant
equations for the 1D networks and the links equations (Djordjevic
et al., 2005).
The modelling of head losses in manholes (in SIPSON) is done by
choosing for each manhole, one of five options (high head loss,
normal head loss, special type 1, special type 2 and special type
3) ordered by degree of head loss.
Storm Water Management Model (SWMM) is a dynamic rainfall-runoff
model. The component of runoff operates on a collection of
sub-catchment areas that receive precipitation and generate runoff.
The routing of the SWMM runoff is done through the system of
channels, pipes and devices. The flow routing in this case is
calculated, using the complete one-dimensional Saint Venant flow
equations (Dynamic Wave Routing) (Rossman, 2010). This routing
method can account for channel storage, backwater, entrance/exit
losses, flow reversal, and pressurized flow (Rossman, 2010).
The modelling of the head losses in manholes (in SWMM) is done
introducing in the pipes, local loss coefficients at entry and exit
of this.
2.3 Data Analysis
Modelling using SIPSON and SWMM was based on the geometric
characteristics of the installation, pipe materials and inflow
hydrographs at each inlet pipes of the system (branches A, B and
C). Calibration was based on the results obtained experimentally
and the reported storm events (12th December 2008 and 17th January
2009) (Figure 2), acting on the roughness of the pipes and head
losses in the manholes to minimize difference in the manholes
depths. The final Manning roughness coefficient of the pipes was
0.01 m-1/3s.
a)
b)
Figure 2. Inflow hydrographs at each inlet pipes of the system,
a) event of 12th December 2008 and b) event of 17th January
2009.
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3 RESULTS AND DISCUSION
Figures 3 to 8 show the variations of the water depth in the
manholes over the simulated events. In each graph the results
obtained experimentally in the scale model and the results obtained
by the modelling made on SIPSON and SWMM are compared. Two cases
are analysed, first considering only the continuous head losses and
a second case considering the continuous head losses and the local
head losses at the manholes.
It was found that the flow Froude number is always less than
unity irrespectively of the event (and regardless of local head
losses at the manholes), indicating that we are in the presence of
subcritical flow. According to Zhao et al. (2006) subcritical flow
in sewer junctions has relatively small energy losses and may be
described as an open-channel ow junction. In SIPSON the head losses
in the manholes was Special Type 3 (least energy loss). In SWMM for
the inlet pipe it was set equivalent to the passage in sharp edge
of a pipe to a reservoir (K =1), for the outlet pipe it was set
equivalent to the sharp edge passage from a reservoir to a conduit
(K= 0.5) (Quintela, 1981).
Regarding the water depths found in manholes 1, 2 and 3 we
verified that for the event of 12th December 2008, the software
that best reproduced the experimental data was SIPSON by neglecting
the head losses in the manholes, including the reproduction of the
maximum peak recorded in the manholes. It was verified that SWMM
had a higher peak damping. Nonetheless and in terms of flow regime
near to steady-state the results obtained by both models were
approximately equal. For the event of the 17th of January 2009, the
conclusions are approximately the same. Nonetheless in this case
both SIPSON and SWMM overshoot the time of peak obtained when
compared with the experimental data.
Manholes 4 and 5 are typical of a situation of confluence of two
pipes in a single manhole, one aligned with the outlet conduit
(main flow direction) and the other with an angle of 45 degrees
with the main direction of flow. For the two simulated events, it
was verified that for the situation where the head losses in
manholes are no considered:
In manhole 4 there was a significant gap between the simulated
and experimental depths. This could be justified by the fact that
the flow of the pipe that enter the manhole with an angle of 45 to
be greater than 1/3 of the flow that circulate in the main flow
direction; it may cause higher turbulence inside the manhole and a
consequent increase in the water level, a situation that is not
reproduced by the models.
In manhole 5 the flow depths resulting from SIPSON fit
relatively well to the experimental data. Contrarily to the
previous case, here, the incoming lateral flow is smaller than 25%
of the flow that circulates in the main flow direction.
a)
b)
Figure 3. Variation of water depth at manhole 1, a) event of
12th December 2008 and b) event of 17th January 2009.
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a)
b)
Figure 4. Variation of water depth at manhole 2, a) event of
12th December 2008 and b) event of 17th January 2009.
a)
b)
Figure 5. Variation of water depth at manhole 3, a) event of
12th December 2008 and b) event of 17th January 2009.
a)
b)
Figure 6. Variation of water depth at manhole 4, a) event of
12th December 2008 and b) event of 17th January 2009.
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a)
b)
Figure 7. Variation of water depth at manhole 5, a) event of
12th December 2008 and b) event of 17th January 2009.
a)
b)
Figure 8. Variation of water depth at manhole 6, a) event of
12th December 2008 and b) event of 17th January 2009.
In the case of manhole 6 (Figure 8), for both simulated events,
the water depths obtained by the numerical models are higher than
the ones obtained by the experimental data. A possible
justification is the position of the pressure sensor that is next
to the downstream pipe. This is the only manhole that the
downstream pipe has a larger diameter than 75mm, i.e. 100mm.
In Figures 9 to 12 the flow rate variations obtained using the
models SIPSON and SWMM for the different simulation conditions are
presented (with and without head losses in manholes).
Comparing the flow rates obtained with both rainfall events, it
was verified that the values resulting from the modelling on the
SIPSON are larger than those obtained by SWMM.
Comparing the flow rates obtained for each model for the
situation without head losses in manholes and with head losses in
manholes, SIPSON results did not show significant differences,
since the loss of energy introduced in manholes was very small,
thus only a small influence on the flow variation occurred. On the
other hand SWMM results of the level of the flow in the facility
are increased, which caused a diminished of the flow peaks due to
the effect of storage observed in the system.
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a)
b)
Figure 9. Variation of flow rate at manholes, for the situation
without considering head losses in manholes for the event of 12th
December 2008, a) SIPSON results and b) SWMM results.
a)
b)
Figure 10. Variation of flow rate at manholes, for the situation
considering head losses in manholes for the event of 12th December
2008, a) SIPSON results and b) SWMM results.
a)
b)
Figure 11. Variation of flow rate at manholes, for the situation
without considering head losses in manholes for the event of 17th
January 2009, a) SIPSON results and b) SWMM results.
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a)
b)
Figure 12. Variation of flow rate at manholes, for the situation
considering head losses in manholes for the event of 17th January
2009, a) SIPSON results and b) SWMM results.
In SWMM is not possible to define the size of the junctions
(diameter), which does not allow that the effects of storage on
these components to be taken, unless junctions are changed to
Reservoirs; and even so only if the reservoir diameter is larger
than 1.2m, which is much larger than the 0.24m of the manholes of
the facility (Figure 13).
Figure 13. Comparison of the variation of water depth at manhole
6 for the event of 12th December 2008, for two different
simulations (with junctions or reservoirs to modelling the manholes
in SWMM).
It was found that SIPSON calculated the flow depth inside
manholes taking into consideration the depth increase due to
transfer of kinetic energy to potential energy. This was verified
by looking at the water depth in the pipes upstream and downstream
of the manholes and verifying that the depth of the flow inside the
manhole was greater than the depth of the flow in the pipe upstream
or downstream.
A similar analysis was done to the SWMM results and it was found
that the depth of the flow within the manhole was an average
between the depths of the flow in conduits that are upstream and
downstream of the manhole.
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4 CONCLUSION
In this paper we compared the experimental data obtained from a
facility in the University of Sheffield with the numerical results
obtained with two one-dimensional numerical models (1D), SIPSON and
SWMM.
When modelling the experimental facility it was found that
SIPSON reproduced fairly well the water depths in the manholes of
the drainage system. In SWMM the results are less representative,
in part, due to the limitations to define the size of the junctions
(diameter).
5 ACKNOWLEDGEMENT
This research was supported by projects PTDC/ECM/105446/2008 and
PTDC/AAC-AMB/101197/2008, funded by the Portuguese Foundation for
Science and Technology (FCT) and by the Operational Programme
Thematic Factors of Competitiveness (COMPETE), shared by the
European Regional Development Fund (ERDF).
The first author is also grateful to UDI Research Unit for
Inland Development, Polytechnic Institute of Guarda, Guarda
(Portugal), by the support to this work.
6 REFERENCES
Djordjevic S. (2001). A mathematical model of the interaction
between surface and buried pipe ow in urban runoff and drainage.
PhD thesis, University of Belgrade, Belgrade, Serbia.
Djordjevic S., Prodanovic D., Maksimovic C., Ivetic M. and Savic
D. (2005). SIPSON - simulation of interaction between pipe flow and
surface overland flow in networks. Water Science and Technology,
52(5), 275-283.
Gargano R. and Hager W. H. (2002). Supercritical flow across
sewer manholes. Journal of Hydraulic Engineering, 128(11),
1014-1017.
Del Giudice G., Gisonni C. and Hager W. H. (2000). Supercritical
flow in bend manhole. Journal of Irrigation and Drainage
Engineering, 126, 48-56.
Hager W. H. (1999). Wastewater Hydraulics: Theory and Practice.
New York: Springer, Berlin.
Hager W. H. and Gisonni C. (2005). Supercritical flow in sewer
manholes. Journal of Hydraulic Research, 43(6), 660-667.
Leandro J., Abreu J. M. and de Lima J. L. M. P. (2009).
Laboratory set-up to validate a dual drainage concept numerical
model. In 8th International Conference on Urban Drainage Modelling,
Tokyo, Japan.
Merlein J. (2000). Flow in submerged sewers with manholes. Urban
Water Journal, 2(3), 251-255.
Quintela A. C. (1981). Hidrulica (Hydraulics). 1st ed, Fundao
Calouste Gulbenkian, Lisboa.
Rossman, L. A. (2010). Storm Water Management Model - User's
manual (Version 5.0). Cincinnati, Environmental Protection
Agency.
Wang K. H., Cleveland T. G., Towsley C. and Umrigar D. (1998).
Head loss at manholes in surcharged sewer systems. Journal of the
American Water Resources Association, 34(6), 1391-1400.
Zhao C., Zhu D. and Rajaratnam N. (2006). Experimental study of
surcharged flow at combining sewer junctions. Journal of Hydraulic
Engineering 132(12), 1259-1271.
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9th International Conference on Urban Drainage Modelling
Belgrade 2012
1
Automated Pipe-sizing of Storm Sewer or Combined Sewer Systems
Based on Hydrodynamic Modelling Kegong Diao1, Michael Mair2,
Michael Mderl3, Manfred Kleidorfer4, Robert Sitzenfrei5, Christian
Urich6, Wolfgang Rauch7
1 University of Innsbruck, Innsbruck, [email protected] 2
University of Innsbruck, Innsbruck, [email protected] 3
University of Innsbruck, Innsbruck, [email protected] 4
University of Innsbruck, Innsbruck, [email protected] 5
University of Innsbruck, Innsbruck, [email protected] 6
University of Innsbruck, Innsbruck, [email protected] 7
University of Innsbruck, Innsbruck, [email protected]
ABSTRACT
This paper introduces a method for automated pipe-sizing of
storm sewer or combined sewer systems based on hydrodynamic
modelling. The methodology includes three steps. Initially, graph
theoretical description of network topology (e.g. Strahler number)
is utilized for classification of the studied sewer networks
topology. Then, the network is decomposed hierarchically into a
number of subsystems based on the network topology. Finally, the
pipe sizing is carried out subsystem by subsystem with no flooding
in the whole system as the objective. To verify the results of the
method, the algorithm is tested on a real world sewer network, and
then the solution is compared with the global optimal solution. As
proved by the case study, the author-designed method could
guarantee a near-optimal solution that is very close to the global
optimal solution, while requires dramatically less computational
effort than global optimization method. Compared with evolutionary
methods, the method has its own advantages, since it does not
require any parameter for configuration and execution control, and
could produce unique solutions as long as the design principles are
fixed.
KEYWORDS
Automated pipe-sizing; combined sewer system; hydrodynamic
modelling; storm sewer system; SWMM
1 INTRODUCTION
Regarding flood protection-based sewer network design, the task
is to minimize the construction costs whilst ensuring no flooding.
The design problem was mostly handled as a pipe sizing and slope
design problem for sewer networks with a fixed plan layout. There
are two major kinds of methodologies for
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solving this problem. The first kind of methodologies is based
on estimating a fixed design discharge for each pipe. The developed
models mainly resort to the application of dynamic programming
(Mays and Wenzel, 1976; Walters and Templeman, 1979; Yen et al.,
1984; Kulkarni and Khanna, 1985), linear programming (Deininger,
1966; Dajani and Hasit, 1974; Elimam et al., 1989), and non-linear
programming (Holland, 1966; Price, 1978; Gidley, 1986). But, as
commonly known, the system capacity can accommodate a considerable
surcharge before surface flooding occurs. Hence, these approaches
may result in a serious over dimensioning of the system capacity.
To deal with this problem, the second kind of methodologies could
be used to achieve good system performance (e.g., no flood
occurrence) based on assessing system performance as a whole under
a predefined design storms. As the optimal pipe sizing is an
NP-hard (non-deterministic polynomial-time hard) problem (Yates et
al. 1984), approximation methods are required to solve the
optimization problem. In this regard, the evolutionary methods have
performed well. For instance, Savic and Walters (1997) have
successfully applied the GA method (Goldberg, 1989) for this task.
Other techniques, such as the ant colony optimisation method
(Zecchin et al., 2006), the particle swarm optimisation method
(Izquierdo et al., 2008) and the cellular automata (Guo et al.,
2007) have also been applied successfully.
Although the evolutionary methods are proved to be efficient and
robust in finding near optimal solutions, they are suffering from
several drawbacks. Firstly, this kind of algorithms usually
requires the users to establish several parameters related to
configuration and execution of the algorithm. Nevertheless, no
general rule is available for the determination of these parameters
and pipe-sizing cannot be linked to existing design standards which
have to be regarded. Hence, a large number of trial-and-error tests
are unavoidable to find appropriate parameter values. Secondly, the
methods (especially, GAs) always entail a high computational cost
in order to achieve a sound level of good solutions. Thirdly, the
methods are inherently stochastic even though it finds out the
solution with real minimization of costs for each run, i.e.
different solutions would be produced after different
implementations.
Given the limitations of currently available methods, a novel
automated pipe-sizing method is developed in this study. Compared
with evolutionary methods, the method introduced in this paper has
the following advantages. First of all, there is no need of
parameters for configuration and execution control. So, no large
amounts of pre-runs are necessary. Secondly, the method is
deterministic, i.e. the optimization results are unique as long as
the design principles (described e.g. by legal regulations) are
fixed. The method simply imports a model input file (e.g. SWMM
file, Rossman, 2010) of the studied network for optimization. The
optimization process could start with the sizes of all pipes being
set to the minimum required value. It could also run based on a
pre-designed layout and then further optimize the pipe-sizing to
improve the system performance. Admittedly, the implementation of
this method could be computational costly as well but it is
possible to improve the efficiency using thread-safe version or a
parallel version of SWMM (Burger and Rauch, 2012).
2 METHODOLOGY
With surcharging, the intrinsic storage capacity of the system
(before surface flooding occurs) can be increased dramatically
beyond (e.g. even doubled) the design capacity (Butler and Davies,
2000). The method introduced in this paper is hence applying
automated pipe-sizing based on hydrodynamic modelling so that the
storage capacity of pipes and manholes could be utilized in a
near-optimal way.
To optimize the storage capacity, the key issue is to determine
where are the proper locations to store excess water. If surcharges
are allowed, network discharge could flow reversely against the
slope due to the backwater effect and thus be stored in upstream
pipes. Therefore, the basic principle of the
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method developed in this study is to maximize the storage
capacity of upstream pipes so that the sizes of downstream pipes
can be minimized. Since the sizes of downstream pipes are commonly
much larger (and more costly) than that of upstream pipes, the
method might be able to reach near-optimal solution with nearly
minimized cost by always avoiding increasing the size of downstream
pipes.
The method includes three steps: 1) Sewer branch order; 2)
Network decomposition; 3) Pipe sizing.
2.1 Sewer branch order
The Sewer branch order is used to describe the network topology
(Sitzenfrei et al., 2012; Urich et al., 2010). In this way, the
Strahler numbers are assigned to each pipe (Strahler, 1952; Urich
et al., 2010). An example of Strahler numbers determination is
given in Figure 1.
Figure 1. An example of Strahler numbers assignment for a small
network. The meaning of all the symbols remains unchanged for all
the rest figures unless otherwise specified.
2.2 Network decomposition
Based on the Strahler numbers, the system is hierarchically
decomposed into a number of subsystems labelled as PSN(i). The
superscript SN refers to the level of decomposition. The index i
refers to the ID of each subsystem at the same level. Except the
top level, all subsystems at each level are comprised of pipes with
Strahler numbers being equal to or smaller than the current level
(SN) and a downstream pipe at the higher level connected to them.
For the top level, the corresponding PSN is the whole drainage
system and the downstream pipe is the outlet pipe of the system.
The sizes of those downstream pipes are set to be infinite (e.g.
>100m). Thus, flooding appears only when the capacity of the
corresponding subsystem is not sufficient, since the back water
effects from the downstream of PSNs have been eliminated. As an
instance, Figure 2 illustrates the decomposition of the small
network shown in Figure 1. For combined sewer systems, notice that
the system would be decomposed according to the locations of CSO
(Combined Sewer Overflow) structures first, and then be further
divided into PSNs.
Figure 2. Decomposition of the small network shown in Figure
1.
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2.3 Pipe sizing
The automated pipe sizing procedure is illustrated as a
flowchart in Figure 4. As it can be seen from the flowchart, the
procedure optimizes the capacity of each subsystem step by step
following the hierarchical structure of the studied network. Take
the network in Figure 2 as an example, the method starts from
analyzing subsystems at the first level of decomposition (PSN=1)
till there are no flooding in all the subsystems (PSN=1(1),...,
PSN=1(5)). Subsequently, the same process would be repeated for the
two subsystems PSN=2(1) and PSN=2(2) at the second level, and then
the PSN=3. Applying this strategy ensures the storage capacity of
the upstream subsystems to be maximized. As discussed above, no
flooding in subsystems at the current level of decomposition is the
prerequisite for the next step. For this reason, if pipes in the
PSN=1(1) are enlarged further during the optimization for PSN=2(1),
this means the capacity of PSN=1(1) is further increased to not
only deal with the local flooding in its served region but also to
accommodate the excess flows from downstream due to the back water
effect.
In the application, the so called infinite size should be
defined with care. On the one hand, it must be large enough to
eliminate the backwater effects from the downstream PSN (higher
level) to the upstream PSN and the interactions between PSNs. On
the other hand, it can also not be too large as to avoid
computation errors. However, the value of infinite size can be
determined based on a few trial-and-error tests, using a
hydrodynamic model.
J and C in Figure 3 and 4 refers to junctions and pipes
respectively. Regarding the JF and CF, JF is the most upstream
flooding node in the studied PSN. CuF is the most upstream pipe
with JF being one end. CF is the first downstream pipe of CuF, and
CdFs are downstream pipes of CF (Figure 3B).
A JS node refers to a node with the following two principles
being satisfied. As shown in Figure 3(A), first the upstream pipe
(Cus) connected to a JS node has its capacity (Ca = actual
Depth/Max. Depth) being equal to 1; second the downstream pipe
(Cds) connected to that node has a larger size (Max. Depth) than
Cus. This is to ensure that only pipes without enough capacity are
enlarged, and the upstream pipes are always preferable. All of the
variables above are defined just for facilitating the
implementation of the method.
Figure 3. Definition of JS, JF, and CF.
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Figure 4. The flowchart of the automated pipe-sizing
procedure.
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3 RESULTS AND DISCUSSION
A case study of a real-world storm sewer network (Example USER1,
Rossman, 2006) is carried out to test the method. The case study
network serves for a 175 hectare drainage area, divided into 58
subcatchments. The network layout is given in Figure 5(A), in which
there are 59 circular pipes connected to 59 junctions and to a
single outfall. The elevation profile of the trunks drops almost 19
meters over a distance of 2.5 km (see Figure 5(B)). Figure 5(C)
describes the design storm used for the simulation. The system was
solved using the software SWMM with a 5 second flow routing time
step for a 7 hours duration with a 1 minute reporting time
step.
Figure 5. (A) Schematic of the case study drainage network. (B)
Elevation profile of the main stem of the case study drainage
network. (C) Rainfall hyetograph for the design storm used for the
case study drainage network. The figures are cited from Rossman
(2006).
As for the case study, the method is implemented based on using
the default pipe sizes specified in the model as initial estimates.
For a new layout, however, the initial pipe sizes could also be
determined by using the time area method. For the optimization of
each subsystem, all pipes except the one with infinite size are
selected as decision variables. The values available for the
decision variables are listed in Table 1. Two design principles are
imposed in this investigation, one allowing surcharge and the other
not. This is to confirm whether the method works for both cases and
can determine logic correct solutions. A comparison between the two
alternative solutions could be found in Figure 7.
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7
Figure 6. Decomposition of the case study drainage network.
Table 1. Price list of reinforced concrete pipes (Cited from Con
Cast Pipe Pricelist, 2012)
Size (mm)
Unit mass (kg/m)
Class 50-D ($/m)
Size (mm)
Unit mass (kg/m)
Class 50-D ($/m)
300 225 65.9 1350 1939 713.3 375 306 81.4 1500 2123 872.4 450
381 83.9 1650 2500 1,044.70 525 470 91.5 1800 2865 1,262.40 600 578
131.5 1950 3324 1,464.10 675 691 201.6 2100 3807 1,680.00 750 780
265.7 2250 4311 1,909.30 825 912 308.3 2400 4869 2,234.70 900 1039
369.8 2550 5179 2,516.90 975 1195 405.7 2700 5752 2,793.30 1050
1277 464.6 3000 7043 3,420.60 1200 1561 582.3
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8
Figure 7. Comparison between alternative design strategies: (A)
With surcharging (B) Without surcharging.
The further verification of the method is to compare its
solution with the global optimal solution. In this study, a brute
force method is applied to the case study network to get the global
optimal solution (simply testing all possible options in the
parameter space). The objective is also to ensure no flooding
occurs during the whole simulation period. Surcharges are allowed
in this case according to the design principle. For the sake of
saving computational cost, however, only the group of pipes resized
by the method developed in this study are chosen as decision
variables. This simplification is introduced because the other
pipes have enough capacity and there is no necessity to enlarge
them. Also, there is no de-sizing procedure involved in the current
algorithm. The range for all decision variables is from 0.3 m to
1.2 m with the same stepsize specified in Table 1. Comparison
between the authors solution and the global optimal solution is
provided in Table 2.
Table 2. Comparison between the global optimal solution and
authors solution
PipeID Initial Max. Depths (m)
Global optimal
Authors' method
PipeID Initial Max. Depths (m)
Global optimal
Authors' method
25 0.600 0.675 0.675 47 0.500 0.825 0.825 26 0.600 0.675 0.675
48 0.600 0.900 0.825 29 0.400 0.450 0.450 49 0.600 0.900 0.825 30
0.450 0.600 0.600 64 0.450 0.750 0.750 31 0.500 0.600 0.600 65
0.450 0.750 0.750 41 0.300 0.525 0.825 66 0.450 0.750 0.750 42
0.230 0.525 0.750 68 0.450 0.750 0.750 43 0.300 0.525 0.750 69
0.300 0.675 0.750 44 0.300 0.450 0.600 70 0.300 0.675 0.675 45
0.500 0.600 0.750 71 0.300 0.600 0.675 46 0.500 0.825 0.825 72
0.300 0.600 0.450
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9
As shown in Table 2, the differences between the two solutions
are not significant for 85% of resized pipes in the network. In
terms of the cost, the authors solution is about 2% higher than the
optimal solution. Regarding the computational expense, the
author-designed method takes about 5 min when it was executed on a
desktop computer configured with Intel(R) Core(TM) i5-2400 CPU @
3.10GHz 3.10 GHz, and 4.00 GB RAM. In the same environment,
however, the brute force method consumes 11 hours. As proved by
this case study, the method developed in this research might
guarantee a near-optimal solution that is very close to the global
optimal solution, while requiring dramatically less computational
effort than global optimization method.
At present the methodology has some shortcomings that will be
addressed in subsequent studies. Firstly, the qualities of the
results highly depend on the computation accuracy of hydrodynamic
simulation. Although it is rarely difficult to limit the errors to
a rather small quantity, a slight difference in the accuracy could
also lead to tremendous oversize problems for some pipes. In this
case, three pipes (41, 42, and 43) are considerably oversized (more
than 0.2 m larger than necessary) by the authors method for
instance. Two factors are attributing to this problem. On the one
hand, the usage of pipes with infinite size causes an increase in
flow routing errors. On the other hand, the computation error of
the SWMM engine may also be a reason. The authors witnessed that
enlarge of a pipe using a reasonable increment may consequently
cause flooding at upstream nodes, which might not be logic.
Secondly, the initial estimates for the pipe sizes have
considerable effects on the final solution. One solution for this
problem is to use network layouts with well-defined pipe sizes
according to time area method (Urich et al., 2010) and engineering
guidelines. Another solution is to simply use the minimum allowed
pipe sizes as initial estimates, e.g. 300 mm. Further work is
essential for addressing this problem in more details.
Thirdly, oversizing of pipes at some places is unavoidable.
Rules or constraints taking into account economic factors could be
imposed on the mechanism of the method. However, a good point is
that the economic factor is somehow considered implicitly by this
method. Since the method could be understood as to address a
certain amount of storage capacity in the most proper location in a
sewer system with surcharge being accepted, the increase on the
size for a long pipe would be definitely smaller than that for a
short one as the storage capacity required is the same.
4 CONCLUSIONS
A method for flood protection-based sewer network design is
introduced in this paper. The method is developed for optimal pipe
sizing for both storm sewer network and combined sewer network. On
the basis of system decomposition according to Sewer branch order,
the automated pipe-sizing for a studied network could be executed
to optimize the capacity of each subsystem in the network step by
step following the hierarchical structure of the network.
The reliability of the method is examined through a case study
using a real world drainage system. The case study network includes
59 junctions, 59 circular pipes and one outfall. To implement the
method, the system was decomposed into 17 subsystems belonging to
three levels respectively. The default pipe sizes specified in the
model are utilized as initial estimates. For the optimization of
each subsystem, all pipes are selected as decision variables.
Commercial pipe sizes (Table 1) are used as the available values
for decision variables.
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10
The solution for the case study was then compared with the
global optimal solution achieved using the brute force method. The
differences between the two solutions are not significant for 85%
of resized pipes in the network. Only three pipes are oversized by
more than 40% in the authors method. However, the loss of accuracy
is compensated by the reduced computational expense, since the
author-designed method takes less than 1% than the brute force
method. Compared with evolutionary methods, the method also has its
considerable advantages, since it does not require any parameter
for configuration and execution control, and could produce unique
solutions as long as the design principles are fixed.
5 REFERENCES
Butler, D. and Davies, J. (2000). Urban drainage. E & FN
Spon, London, UK.
Burger, G. and Rauch, W. (2012). Parallel Computing in Urban
Drainage Modeling: A Parallel Version of EPA SWMM. 9th
International Conference on Urban Drainage Modelling.
Con Cast Pipe website. (2012).
http://www.concastpipe.com/pricing/CC_2012Pricelist.pdf (accessed
19 March 2012)
Dajani, J. S. and Hasit, Y. (1974). Capital cost minimization of
drainage networks. J. Environ. Eng.-ASCE, 100(2), 325-337.
Deininger, R. A. (1966). Computer aided design of waste
collection and treatment systems. Proc. 2nd Annual Conf. of
American Water Resources, Chicago, USA, 247-258.
Elimam, A. A., Charalambous, C., and Ghobrial, F. H. (1989).
Optimum design of large sewer networks. Journal of Environmental
Engineering, 115(6), 1171-1190.
Gidley, J. S. (1986). Optimal design of sanitary sewers. Proc.
4th ASCE Conf. on Computing in Civil Engineering, Boston, USA,
162-177.
Goldberg, D. E., (1989). Genetic algorithms in search,
optimization and machine learning. MA: Kluwer Academic Publishers,
Boston.
Guo, Y. G., Walters, G. A., Khu, S. T., and Keedwell, E. C.
(2007). A novel cellular automata based approach to storm sewer
design. Engineering Optimization, 39 (3), 345364.
Guo Y. G., Walters G. A., and Savic D. A. (2008). Optimal design
of storm sewer networks: Past, Present and Future. 11th
International Conference on Urban Drainage, Edinburgh, Scotland,
UK, 2008.
Holland, M. E. (1966). Computer models of wastewater collection
systems. PhD dissertation, Harvard University, Cambridge,
Massachusetts, USA.
Izquierdo, H., Montalvo, I., Perez, R., and Fuertes, V. S.
(2008). Design optimization of wastewater collection networks by
PSO. Computer and Mathematics with Applications, 56(3),
777-784.
Kulkarni, V. S. and Khanna, P. (1985). Pumped wastewater
collection systems optimization. Journal of Environmental
Engineering, 111(5), 589-601.
Mays, L. W. and Wenzel, H. G. (1976). Optimal design of
multi-level branching sewer systems. Water Resour.Res., 12(5),
913-917.
Price, R. K. (1978). Design of storm water sewers for minimum
construction cost. Proc. 1st Int. Conf. on Urban Strom Drainage,
Southampton, UK, 636-647.
Rossman, L. A. (2006). STORM WATER MANAGEMENT MODEL QUALITY
ASSURANCE REPORT: Dynamic Wave Flow Routing. Water Supply and Water
Resources Division National Risk Management Research Laboratory
Cincinnati, OH 45268, USA.
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11
Rossman, L. A. (2010). Storm Water Management Model users manual
(version 5.0). U.S. Environment Protection Agency, Cincinnati,
USA.
Savic, D. A. and Walters, G. A. (1997). Genetic algorithms for
least cost design of water distribution networks. Journal of Water
Resources Planning and Management, 123(2), 67-77.
Sitzenfrei, R., Urich, C., Mderl, M. and Rauch, W. (2012).
Assessing the efficiency of different CSO positions based on
network graph characteristics. 9th International Conference on
Urban Drainage Modelling, Belgrade 2012.
Strahler, A. N. (1952). Dynamic basis of geomorphology. Geol.
Soc. Am. Bull. 63, 923-938.
Urich C., Sitzenfrei R., Moderl M. and Rauch W. (2010). An
agent-based approach for generating virtual sewer systems. Water
Sci Technol, 62 (5), 1090-7.
Walters, G. A. and Templeman, A. B. (1979). Non-optimal dynamic
programming algorithms in the design of minimum cost drainage
systems. Eng. Optimiz., 4, 139-148.
Yates, D. F., Templeman, A. B., and Boffey, T. B. (1984). The
computational complexity of the problem of determining least
capital cost designs for water supply networks. Engineering
Optimization, 7(2), 142-155.
Yen, B. C., Cheng, S. T., Jun, R. I., Voorhees, M. L., Wenzel,
Jr, H.G., and Mays, L. I. (1984). Least Cost Sewer System Design
Model. Users Guide. Illinois Austin, TX.
Zecchin, A. C., Simpson, A. R., Maier, H. R., Leonard, M.,
Roberts, A. J., and Berrisford, M. J. (2006). Application of two
ant colony optimization algorithms to water distribution system
optimization. Mathematical and Computer Modelling, 44 (5-6),
451-468.
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9th International Conference on Urban Drainage Modelling
Belgrade 2012
1
Parallel Computing in Urban Drainage Modeling:
A Parallel Version of EPA SWMM
Gregor Burger1, Wolfgang Rauch2
1 University of Innsbruck, Austria, [email protected] 2
University of Innsbruck, Austria, [email protected]
ABSTRACT
The hydrodynamic rain-fall run-off simulation model SWMM is
state of the art in research and practice. In order to reduce the
burden of long simulation runs and use the extra power of modern
multi-core computers a parallel version of SWMM is presented. The
challenge was to modify the software in such a minimal way that the
changes may find its way into the several commercial and
non-commercial tools that depend on SWMM for its calculations. A
pragmatic approach to identify and enhance the most runtime intense
parts of the software was chosen in order to keep the code changes
as low as possible. The enhanced software was then benchmarked on
four different input scenarios ranging from a very small village to
a medium sized city. In the investigated sewer systems a speedup of
six to ten times on a twelve core system was realised, thus
decreasing the execution time to an acceptable level even for
tedious system analysis.
KEYWORDS
Multi-Core, OpenMP, Parallel Computing, SWMM, Urban Drainage
Modelling
1 INTRODUCTION
The Storm Water Management Model (SWMM) is a dynamic
rainfall-runoff simulation model used for single event or long-term
simulation of runoff quantity and quality from urbanized areas
(Huber 1995). SWMM was developed by the US EPA and therefore the
code it is built upon is in possession of the public domain. The
fact that a code of such a high quality model is available for
everyone to use and alter, made the tool very popular in research
and in the applied civil engineer field.
Nowadays numerical models like SWMM are not just used in
run-once scenarios but in sensitivity analyses (C.B.S. Dotto et al.
2011; Mair et al. in press), uncertainty analyses (Kleidorfer,
Deletic, et al. 2009; Kleidorfer, Mderl, et al. 2009; Cintia B.S.
Dotto et al. 2012) and vulnerability analyses (Mderl et al. 2009).
All of those requiring a multitude of execution runs. In fact, a
comparison of different uncertainty assessment techniques (GLUE,
Bayesian methods, etc) revealed that the number of simulation runs,
depending on which technique used, ranged in that particular
example from 1600
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2
to over 30000 runs, but the mean is around 3500 runs, until the
uncertainty of the different system parameters is devised (Cintia
B.S. Dotto et al. 2012).
Given the fact that these analyses are essential for a deeper
understanding of the underlying model and input system there is an
imminent need for action. For researchers applying these analyses a
way to reduce the time spent for computer simulation is to restrict
the system parameters or to reduce the size/resolution of the input
system. Both solutions are suboptimal and may degrade the quality
of the results which in the best case can cause additional
simulation runs or in the worst case a publication/assessment with
imprecise or wrong results.
A better way to reduce the run-time of the simulations is to
improve the performance of the underlying simulation codes. One
step in this direction has already happened. CITYDRAIN (Achleitner,
Moderl, and Rauch 2007), a hydrological model developed at the
University of Innsbruck, was redesigned and rewritten into
CityDrain3. CityDrain3 was designed from the ground up to have
native performance instead of interpreted MATLAB and use all the
extra parallel computing power that is available in modern
multi-core computers (Burger et al. 2010). In this paper we will
outline the efforts of bringing one of the most prominent
hydrodynamic codes, namely SWMM, into the multi-core era. In the
course of this manuscript we describe what parallel computing is,
what challenges there are, why it is essential to do it nowadays,
how a parallel version of SWMM looks like and how much performance
there is to be expected from a parallel SWMM.
Beside the apparent reason of an immediate performance gain that
is due to parallel computing there is a not so obvious second
reason for parallelizing simulation software and software in
general. Semi conductor researchers are hitting hard physical
limits that prevent them to scale in single thread performance.
They cannot reduce the chip size indefinitely neither can they
increase the speed of light. In order to keep customers satisfied
and stay true to Moores law, which states that the transistor count
doubles roughly every two years, they needed to make radical
changes (Moore 1998). For chipmakers, the way out of this misery
was to pack several cores onto one die. The multi-core era was born
and now they can again - double the number of cores every two years
(Olukotun et al. 1996).
Although multi-cores solve the problem for the hardware
industry, the real problem was shifted onto the software
developers. Every application out there must be altered in order to
take advantage of the extra cores that are now built into every
CPU. Software is not getting faster anymore on modern CPUs as it
was the case before the multi-core era. In a very famous paper
called the free lunch is over Herb Sutter describes it in an even
more drastic way and states that the performance of software that
does not take advantage of parallel computing is not only
stagnating but will degrade on future many-core devices (Sutter
2005). Many-core devices and hybrid solutions is the future that
software developers will face. In a recent article the same author
describes the complexity and diversity of the modern and future
parallel computing landscape (Sutter 2011).
2 METHODOLOGY
The architectural landscape that parallel computing is applied
to, can be quite widespread nowadays; ranging from dual-core phones
up to the overly hyped cloud-computing architecture (Sutter 2011).
Beside all the hype of cloud computing, urban drainage simulations
are used by engineers, infrastructure planners and researchers in
the field of urban drainage for which the desktop computer is still
the preferred computing platform. A state of the art, off-the shelf
desktop computers hosts a CPU with up to six or eight cores.
Therefore, we focused on this parallel computing (PC) architecture
called multi-core computing (Olukotun et al. 1996). The advantage
of focusing on the multi-core architecture
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3
is that it is readily available and that the porting overhead is
much lower compared to other parallel computing architectures like
GPUs or cloud based systems.
SWMM has a very mature code base that is tested and verified.
The code is heavily used in its stand-alone version and included in
commercial applications. We wanted to have as little impact as
possible on the code structure. The idea was that such minimal code
changes would result in a higher confidence and understanding of
the changes so that adoption of the code or even inclusion in the
main SWMM code can happen. This minimal impact requirement and the
fact that a mature code needs to be portable drove us to decide on
OpenMP as a base parallel application programming interface
(API).
OpenMP is a compiler extension that allows parallelizing of new
and old code. In the best case the already existing code only needs
to be decorated with parallel instructions and synchronization
primitives. Therefore, OpenMP allows us to have the minimum code
changes as described in the previous paragraph. Another reason for
choosing OpenMP was that it is supported by most compilers and it
has matured into a well understood and standardized parallel
computing API for which a lot of performance and testing tools are
available.
Figure 1 Profile of the sequential SWMM code.
The first step for a parallel SWMM was to search for performance
sensitive spots. It makes no sense to parallelize a code that does
only take five percent of the overall SWMM runtime. After intensive
profiling the critical parts for performance where identified. As
expected, the routing of the conduits and sewers are the most time
intensive tasks. A profile as shown in Figure 1 reveals exactly at
which line the most time is spent. For someone not familiar with a
code base, as it was the case in this work, this is very helpful.
The profile shows that the function getConduitFlow is responsible
for 65% of the overall run-time. This function is called by the
execRoutingStep function that iterates over all conduits and calls
find/getConduitFlow for each link.
In the first step we identified parts of the code that have the
potential to run parallel. The code is already in a structure that
allows easy parallelisation. In execRoutingStep a loop iterates
over an array of Link structures. Each link is then argument to the
getConduitFlow function that calculates the new flow for each Link.
The most challenging part in this step was to check if each Link
can be updated separately. (Rossman 2006) states that SWMM solves
the Saint Venant equations with a finite difference scheme. In the
first step the flow for each link is being calculated. After that
the hydraulic
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4
head (elevation head plus any possible pressure head) for each
node is updated. The model of SWMM is that links are conduits and
nodes are junctions in the graph describing the wastewater system.
This is already a first hint that a parallelization at the level of
each conduit and link is possible.
The ultimate proof, though, is the code. This means that each
and every line of code that may be executed in the course of the
call of findConduitFlow needs to be checked for race-conditions and
critical sections. As one can imagine reading and understanding
other people code and then checking for parallel programming errors
is a very tedious, time consuming task that needs full attention.
An error in this part can lead to undefined behaviour, data
corruption, wrong results or even crashes of the program. The
problem with these errors is that they may not be triggered for a
long time and are hard to reproduce. Besides fixing the introduced
race-conditions, the code also contained non reentrant functions
that needed to be fixed so that multiple threads do not interfere
with global variables in a multi-threaded simulation.
The same procedure described in the previous section for
findConduitFlow has been applied to findNonConduitFlow,
initNodeState, link_setOutFallDepth and setNodeDepth by means of
several benchmarking, implementation and testing cycles.
3 RESULTS
The benchmarks were performed on a Dual Xeon System. Each
processor featured six hyper-threaded cores resulting in up to 24
virtual threads for the whole system. Each core runs with a clock
frequency of 2.67 GHz. The cores of each CPU package share a 12Mb
L3 cache, enhancing further the parallel performance of the CPU.
The system was equipped with 24 GB of main memory. The system was
operated by Linux with a kernel at version 3.2.
Each input system was run with one thread as a base measurement,
followed by runs with increasing thread count up to the 24 maximum
threads the system features. A step size of two was chosen because
an uneven thread number is not ideal in a hyper-threaded system.
The average run-time of four runs was then taken as the resulting
run-time (left images). The speedup refers to how much a parallel
algorithm is faster than a corresponding sequential algorithm
(right images).
The four input systems are in an increasing number of nodes and
links, i.e. they are getting bigger. The general trend that the
benchmarks show is that the bigger a system the better the parallel
version of SWMM scales. A reason for this is that there is a
sequential part in the routing algorithm that cannot be
parallelized. This sequential part seems to be more or less
independent of the system size. Amdahls law states that the bigger
the sequential part of a parallel algorithm is, the worse is the
scaling of the speedup (Amdahl 1967; Hill and Marty 2008).
Table 1 Number of Elements per Input System Input System Nodes
Links Sub catchments Population
Artificial 50 49 42 Unknown
Village 1709 1722 440 10760
Small Town 1254 1274 3062 12695
Town 5485 5834 4498 120147
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5
In order to show at what system size it is feasible to use the
parallel SWMM code we used sewer systems of different extension.
This first benchmark system is an artificially generated system
having an alpine character. The system was generated using the Case
Study Generator (Moderl, Butler, and Rauch 2009). The next three
benchmarks systems, listed in Table 1, are in order of population.
All four systems have an alpine character, which means they are
more or less in a tree structure with only few loops. Nevertheless
as the dynamic wave routing was optimized and used in the benchmark
systems loops do not necessarily have an influence on the
performance. The village module represents a small village in a
rural area, the small town is in a suburban area and the town is a
regional capital city. Beside the dynamic wave routing, Horton
infiltration was used in the SWMM options, allow ponding was
disabled and skip dry weather periods was disabled in the input
systems.
3.1 Artificial
As mentioned previously the artificial system was chosen to see
how the optimizations perform when a small input system is used. In
a small system the parallel overhead and the sequential part of the
parallel algorithm are high compared to the part of the algorithm
that runs in parallel. Figure 2 shows how this influences the
overall runtime and speedup. Up until eight threads the runtime
decreases but then rises again. Although the speedup is not good
there are no signs of a slowdown, which means that there is no
disadvantage of using the parallel version of SWMM.
Figure 2 Runtime and Speedup for the Artificial input
system.
3.2 Village
The village system is the first one having enough runtime to
cover the overhead and sequential parts of the routing algorithm.
Up until twelve threads the parallel SWMM version shows a very good
speed-up and the code is 8.3 times faster. At 24 threads the
minimum runtime is reached and a maximum speed-up of 9.5 times.
This means that a parallel version of SWMM is almost 10 times
faster at 24 threads than the standard SWMM. The speed-up curve in
Figure 3 has a slight kink at twelve threads. This kink is because
up until twelve threads the Linux scheduler can schedule all
threads on real hardware threads, beginning with the 13th thread
the virtual hyper-threads must be used, which causes an additional
overhead in the CPU if an application is floating point intensive.
The overhead stems from the fact a real- and a hyper-thread share
the floating point unit. Because of this additional over-head the
speedup-up curve is shallower beginning with the 13th thread.
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6
Figure 3 Runtime and Speedup for the Village input system.
3.3 Small Town
The small town input system shows a slight worse speed-up than
the village. Although the system has a higher population the
modeller chose a lower resolution for links and nodes but a higher
resolution for sub-catchments. As stated in the previous sections
the primary target of parallelization was the routing of the
channels so therefore the scaling is better when more pipes and
less sub-catchments are in the system. Nevertheless parallel SWMM
version reduces the simulation time 6 times from 36 seconds town to
6 seconds.
Figure 4 Runtime and Speedup for the Small Town input
system.
3.4 Town
The town input system is the biggest and most detailed system.
With around 5000 links and nodes the sequential runtime is over 3.5
minutes. With the parallel SWMM code this runtime is reduced to 26
seconds resulting in a speedup of 9.3 times. At the University
Innsbruck this sewer system was heavily used and analysed including
vulnerability and sensibility analyses. These analyses require
several runs, up to the hundreds, of a slightly modified input
system. One can imagine what a ten time reduction in run-time could
mean to such analyses, heavily bound on the run-time of a single
simulation (e.g. long-term simulations could be feasible).
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7
Figure 5 Runtime and Speedup for the Town input system.
4 CONCLUSION AND DISCUSSION
Take for example the uncertainty assessment described in the
introduction where the analysis took around 3500 iterations to
evaluate the uncertainty of five system parameters for the given
case. When a single simulation run takes around five minutes,
researchers must wait twelve days until she/he can finally
interpret the results. The processing unit running this simulation
is blocked for twelve days. And five minutes is not even a long run
for an urban drainage simulation. Applying the techniques described
in this paper one can reduce the runtime of this uncertainty
simulation down to 29 hours. Although it should not be, but such
delays do affect the decisions of researchers whether they run such
analysis or just skip them because they cannot sacrifice twelve
days of their precious time. A parallel version of SWMM also opens
ways to longer and more detailed simulations. And in case of a
certain pressure more money for some extra cores can speed up the
simulation additionally. Without a parallel version of SWMM the
performance of hydrodynamic simulations will stagnate or may even
degrade on future computing technologies.
In this paper we outlined the fundamentals of parallel coding
for the well known hydrodynamic software SWMM. We demonstrated that
a rather small part of the code is decisive for the execution time.
The change of this part of the code into a parallel version
resulted into a significant speedup in the execution. The speedup
is not linear but increases both with the complexity of the system
(the more pipes the better) and the number of threads. In the
investigated real world systems the speedup amounted to 6 to 10
times on a PC with 12 threads.
5 ACKNOWLEDGMENT
This work has been financially funded in the course of the
PaCoWaDi project by the Bundesministerium fr Verkehr, Innovation
und Technologie in the program FIT-IT/ ModSim (FFG projectnumber
2059687).
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8
6 REFERENCES
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Burger, G., S. Fach, H. Kinzel, and W. Rauch. 2010. Parallel
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Dotto, C.B.S., M. Kleidorfer, A. Deletic, W. Rauch, D.T.
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9th International Conference on Urban Drainage Modelling
Belgrade 2012
1
Modelling of percolation rate of stormwater from
underground infiltration systems
Ewa Burszta-Adamiak1, Janusz Lomotowski2
1 Wroclaw University of Environmental and Life Sciences, Poland,
[email protected] 2 Wroclaw University of
Environmental and Life Sciences, Poland,
[email protected]
ABSTRACT
Underground or surface stormwater storage tank systems with
infiltration of water into the ground constitute the basic elements
used in Sustainable Urban Drainage Systems (SUDS). So far, the
methods of designing such facilities have not taken into account
the phenomenon of ground clogging during the infiltration of
stormwater. Sealing of the top layer of the filter bed influences
the infiltration rate of water into the ground.
This study presents an original, mathematical model describing
the changes in the infiltration rate in the phases of filling and
emptying of storage and infiltration tank systems, which enables to
determine the degree of clogging of the top layer of the ground.
The input data for modeling were obtained from studies conducted on
experimental sites on objects constructed in semi-technological
scale.
The tests have proved that the developed model is useful on the
stage of designing stormwater infiltration facilities and that it
helps to control the degree of clogging of absorptive surfaces
during the exploitation of such facilities.
KEYWORDS
clogging; hydraulic resistance; modelling; storm water
management; underground infiltration system
NOMENCLATURE
F , bottom surface of infiltration facility (cm2)
0H water level in the infiltration module at the end of the
filling phase (cm)
)(tH water level in the infiltration module at time t (cm)
sH water level above ground surface (cm)
fh negative pressure head at wetting front (cm)
)(tI accumulated water infiltration into the ground (cm)
fK wetting zone hydraulic conductivity (cm min-1),
Q infiltration flow (cm3 min-1),
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2
FQ variable parameter used in model (10) (cm min-1),
)(tq infiltration rate at time t (cm min-1),
R substituted hydraulic resistance (min) t time (min)
)(tZ depth of wetting front (cm)
1 INTRODUCTION
Stormwater management is becoming aimed at local infiltration or
retention. Such tasks can be realised with use of underground or
surface storage and infiltration systems. In spite of a growing
interest in the application such facilities, they are still
designed and exploited without taking into consideration the
process of clogging during usage. Assuming, for calculation
purposes, the lowest value of the filtration coefficient from the
collection of results obtained during geotechnical studies, does
not correspond to the dynamic changes in the filtration coefficient
caused by the clogging process. The assumption that the filtration
coefficient remains fixed throughout the exploitation period is not
only incorrect, but also harmful, as with time the need occurs to
modernize existing elements of the system and to invest additional
funds. Numerous studies (Burszta-Adamiak, 2005; Burszta-Adamiak and
omotowski, 2005b; Mallin et al., 2009; Marla and Lee-Hyung, 2010;
Rupak et al., 2010; Zhuanxi et al., 2012) have shown that water
flowing into the facilities contains a significant amount of
pollutants, which deteriorate the infiltration parameters of the
infiltration modules. With time of exploitation of infiltration
modules, layers of sediments start to form on the bottom and side
walls of such reservoirs, and soil pores are being sealed. This
process is known as ground clogging. We distinguish between
physical, biological and chemical clogging. In fact, the process is
a very complex one, being a resultant of specific individual
processes. Physical clogging during the infiltration of stormwater
is caused by additives that remain in a suspended state. Rain
washes out of the air the molecules remaining in gaseous state,
aerosols and dusts, of natural or anthropogenic origin. Physical
clogging can also be caused by bubbles of gas exuded from water or
from the soil. The development of biofilm in the sediment zone and
in the layer adjacent to soil contributes to biological clogging.
Chemical clogging takes place when suspensions or insoluble
minerals are deposited on grains of soil. Chemical clogging is
mainly caused by calcium carbonate and insoluble ferrite compounds
deposited from the water (Hua et al., 2010; Nivala et al., 2012;
Skolasiska, 2006; Vigneswaran and Suazo, 1987).
The phenomenon of clogging occurs on infiltration water intakes,
during the filtration of water through rapid and slow filters, in
the course of exploitation of underground water intake facilities
(clogging of well filters and drains), trickling filters, sand
filters and subsurface wastewater infiltration systems (Oe et al.,
1996; Rinck-Pfeiffer et al., 2000; Hiscock and Grischek, 2002,
Lloyd et al., 2009; Mays and Asce, 2010; Pedretti et al., 2012).
Regardless of the type of the given infiltration system, clogging
is an undesirable phenomenon (Bouwer, 2002; Bouwer et al., 2001;
Gautier et al., 1999). The thickness of the clogging layer can
range from several millimetres to several centimetres or even
decimetres, for larger amounts of accumulated sediments (Bouwer,
2002). The phenomenon of clogging develops at various rates.
Usually, in the first year of exploitation of infiltration
facilities, no significant decrease in water infiltration to the
ground is observed, although in the subsequent years of usage such
decrease can reach even up to 50% of the initial permeability(
Balades et al., 1995). On the other hand, Geiger and Dreiseitl
(1999) disagree, claiming that the phenomenon of clogging of
stormwater infiltration facilities is the most intense during the
start-up phase. During that time the adjacent area is usually not
yet overgrown by plants, but heavily polluted with fine dust that
appears as
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3
a result of construction works. Erosion causes soil particles
and other pollutants to enter the filtration zone together with
stormwater, causing rapid mechanical sealing.
The basic technological parameter that is taken into account
during the process of designing artificial infiltration systems is
the infiltration rate. The first model of infiltration of water
into the ground was developed by Green and Ampt in the year 1911
(Ravi, 1998; Williams et al., 1998; Ying et al., 2010). The model
is based on the assumption that the water penetrates into the
ground according to Darcy law, whereas the infiltration rate is
determined by head loss in the saturated and wetted zones Z:
ff
fsfsf KKtZ
hH
tZ
htZHK
dt
tdItq
/)()(
)()()(
( 1 )
Assuming that: Z(t)=Zconst
( 2 )
and introducing a parameter R defined by the ratio: R=Zconst/Kf.
( 3 )
equation (1) will has the form:
ffs K
R
hHtq
)(
( 4 )
The Green-Ampt model offers a good description of measurement
results in cases characterised by stable inflow conditions, i.e.
when a fixed layer of water remains on the ground surface. For
variable inflow conditions (which are typical for stormwater
infiltration facilities due to the random nature of rainfall) the
error in transient infiltration rate prognosis and accumulated
infiltration of water into the ground increases. A well-known model
that describes the mechanical clogging of filter beds while taking
into account the changes in the concentration of suspended solids
in liquid during the flow through porous media is the Iwasaki
equation, developed in 1937 (Iwasaki, 1937 in: Tesaik ,1980). Some
examples of models describing chemical and biological clogging can
be found, among others, in the works of Vandevivere et al. (1995),
Teylor and Jaffe (1990), Taylor et al. (1990), Prez-Paricio (2001)
and Seki and Miyazaki (2001). In spite of the fact that numerous
models have been developed that allow for a better understanding of
the nature of phenomena occurring in porous media, the process of
clogging in stormwater infiltration facilities is still typically
evaluated by means of an evaluation of the changes in the
infiltration intensity during a given test period (Raimbault et
al., 1999). The intensity of infiltration decreases gradually,
until, with time, a layer of low-permeable soil is created that
does not meet design requirements (Balades, 1995). This can be
illustrated by the equation used for the hydraulic evaluation of
the functioning of clogged infiltration systems, which was
developed by Bouwer (1969). Numerous variations of the Bouwer model
can be found, among others, in the works of Dechesne et al. (2004)
where it has been applied for the purposes of evaluation of
infiltration basins with a clogged sediment layer on the bottom and
by Gautier et al. (1999), who tested and then described the process
of infiltration of water through absorptive surfaces, dividing the
flow into infiltration through the clogged bottom and banks of the
basin. The models used to evaluate the phenomenon of clogging in
stormwater infiltration facilities presented in literature are
developed basing on the results of tests performed on surface
infiltration systems. Due to the fact that the area designed for
the construction of infiltration systems is often limited, it is
quite often required to use underground infiltration systems, e.g.
in form of infiltration module systems or infiltration trenches,
etc. These facilities function properly when there is a need to
absorb a larger amount of water than the infiltration and retention
capabilities of the adjacent land allow to absorb in a
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4
specific period of time. Underground storage facilities first
store the collected inflow of stormwater and then enable free
infiltration of water into the ground. The evaluation of the
progress of the clogging phenomenon in underground storage
facilities is difficult due to the fact that the layer of suspended
solids and/or biomass is deposited on the infiltration surface
located below land surface, thus in this type of facilities it is
difficult or even impossible to perform any declogging activities
that are traditionally performed in surface infiltration
systems.
Insufficient information concerning the hydraulic fundamentals
of designing underground stormwater infiltration facilities lead to
experiments. The aim of the analyses was to develop simple models
describing the changes in the infiltration rate in the phase of
filling and emptying of retention and infiltration reservoirs and
to test their usability in the evaluation of the progress of
clogging.
2 METHODS
2.1 Characteristics of the model
The water volume balance equation for infiltration module
systems with an absorptive surface F which is filled at a constant
rate Q, without taking into account the impact of infiltration
through side walls can be formulated as follows:
dttqFdtQtdHF )()( ( 5 )
where the left side of the equation describes the increase in
water volume in the infiltration module and the right side
describes the volume of water flowing into the reservoir, less the
amount of water infiltrating into the ground. This is illustrated
in Figure 1
Figure 1. Sample drawing illustrating momentary water volume
balance during the process of water infiltration from the
module.
Assuming that:
fKR
tHtq
)()( ( 6 )
and introducing a parameter defined by the ratio:
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5
F
QQF ( 7 )
it is possible to determine the equation describing the changes
in water surface level in an infiltration module for water flowing
in at a constant rate:
R
tRK
R
tRQtH fF exp1exp1)( ( 8 )
In the case if water will not be flowing into the module, a
decrease in the water level due to filtration will be observed. The
function of change of the water surface level in the module in the
emptying phase will be described by the following equation:
R
tRK
R
tHtH f exp1exp)( 0 ( 9 )
During the infiltration of water containing suspension a
significant decrease of the filtration coefficient of the top layer
of soil is observed. In the case if the value of the product of the
Kf R constants is close to 0, equations (8) and (9) will have the
respective forms:
R
tRQtH F exp1)( ( 10 )
R
tHtH exp)( 0 ( 11 )
2.2 Description of the experimental site and methodology
The experimental sites were constructed with use of
prefabricated openwork modules. The side walls of those modules
contain apertures that enable the infiltration of inflowing water
into the ground. Modules were wrapped in 1.6 mm thick geotextile
made from polypropylene, characterised by perpendicular water
permeability of 0.0026 m/s. The dimensions of the infiltration
modules are 500x1000x400 mm (length x height x width). These are
systems prepared for the management and infiltration of stormwater,
commonly used in engineering practice.
Infiltration modules were placed in the ground according to the
guidelines provided by the manufacturer. Prior to the beginning of
the experiments, geotechnical tests were conducted in the site
where the modules were located. Lithological profiles of the soil
on the site of experiments are presented in Table 1. Below the
bottom of experimental site no.1 there was a deposit of sandy clay,
covered by medium sand reaching up to the surface of the soil.
Experimental site no 2 was located on cohesive clay, covered by
sandy clay up to the depth of 0.4 m below land surface. Above that
depth, it was covered with a deposit of fine sand.
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6
Table 1. Lithological profiles of the soil on the site of
experiments.
In order to prepare the clogging agent (dispersion suspension),
kaolin clay was used on both experimental sites. The kaolin clay
suspension used for the tests was determined basing on two years
studies of the grain size distribution and concentration of
suspensions present in rainfall, snowfall and roof runoff. These
study was conducted with use of a laser particle sizer Mastersizer
2000 manufactured by Instruments Ltd. Samples were collected both
on the site where later studies on infiltration modules were
conducted, and in several other Polish cities. The preliminary
studies show that the average respective concentrations of
suspensions in samples of rainfall, snowfall and roof runoff were
0.0075% vol., 0.0082% vol. and 0.012% vol. By referring the
obtained results to the concentration of kaolin clay suspension and
the volume of suspension introduced into the test sites, it can be
stated that one year of conducted analysis corresponds to
approximately five years of exploitation in real conditions. The
use of higher concentrations of kaolin clay suspension resulted
from the need to intensify the studies of the clogging process,
which is much slower in real conditions. The particle size of the
clogging agent fell within the range from 0.25 to100 m. These
particles accounted for approximately 60 % of the pollutants
present in rainwater. Sample particle size distribution of the
pollutants present in stormwater and in kaolin clay is presented in
Figure 2. The selection of a model suspension characterised by a
particle size composition similar to that of stormwater enabled us
to model the processes occurring in nature in a more precise way.
Modules were each time filled with 60 dm3 of suspension of the
concentration of 2.5 g/dm3. Suspension used for the tests was
prepared on the basis of tap water, after several days of soaking
in order to eliminate the process of expansion of minerals. The
filling lasted for 8-10 minutes, and the infiltration time- from
0.5 hours at the beginning of the test period to 9 hours after a
year of exploitation. The tests on the sites were conducted in the
period from 18.06.2003 to 14.06.2004. During that time the storage
and infiltration modules were filled on the average once a week.
During the tests the duration of the experiment was measured, along
with the changes in the level of water with kaolin clay suspension
in the modules in the filling and infiltration stages.
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7
0
20
40
60
80
100
0,1 1 10 100 1000 10000
Perc
ent f
iner by w
eig
ht, %
Particle Size, mmSample 1 Sample 2 Sample 3
Sample 4 Kaolin clay
Figure 2. Particle size distribution in suspensions present in
rainwater collected at the location of the measurement sites and in
kaolin clay used for the tests.
3 RESULTS AND DISCUSSION
Due to a large amount of factors influencing clogging and to
their significant variability in time, it is practically impossible
to model the processes occurring in nature. The construction of a
simplified experimental model, together with the application of a
dispersion suspension characterised by an adequate concentration
and size of particles enables us to model processes that would take
even several or over ten years in objects functioning in the real
world, in short periods of time.
The impact of infiltration through side walls was omitted in
calculations, as the scanning photos of the sediment deposited on
the surface and inside the geotextiles, collected from the bottom
and walls of the sites after the tests were ended, show that the
flow of suspension occurred mainly through the bottom, which is
proved by a larger amount of sediments deposited in this part of
the sites (Figure 3). This is mainly a result of the mechanisms of
the sedimentation process, which is one of the specific processes
occurring during the infiltration of polluted waters. In
experimental site no.1, as much as 88.4% of the total mass of
kaolin clay sediments deposited in the module clogged the bottom,
while only 11.6 % was deposited on the walls. A similar situation
was observed in experimental site no. 2, where 90.1% of the total
mass of kaolin clay was deposited on the bottom in form of
sediment, while 9.9 % was found in the geotextile covering the
walls.
Figure 3. Scanning photos of kaolin clay sediment deposited in
the geotextile on the bottom of the module (left image) and on the
side walls of the site (right image) magnified 1000 times
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8
3.1 Changes in the water level during filling and
infiltration
Sample diagrams showing the measured change in water levels in
the infiltration module systems during filling and infiltration as
well as regression functions described by the general models
(equation 10 and 11) calculated with use of STATISTICA 10.0 PL
software are shown, respectively, on Figures 4, 5 and 6, 7.
0 2 4 6 8 10
Time, min
0
5
10
15
20
25
Wa
ter
leve
l, c
m
0 2 4 6 8 10 12
Time, min
0
5
10
15
20
25
30
35
Wa
ter
leve
l, c
m
Figure 4. Comparison of the changes in water levels during the
filling of experimental site no.1, measured on the 15.09.03 (left)
and the 10.12.03 (right) with a regression function described by
the general model (10)
0 2 4 6 8 10
Time, min
0
5
10
15
20
25
30
Wa
ter
leve
l, c
m
0 2 4 6 8 10
Time, min
0
5
10
15
20
25
30
Wa
ter
leve
l, c
m
Figure 5. Comparison of the changes in water levels during the
filling of experimental site no. 2, measured on the 11.07.03 (left)
and the 18.08.03 (right) with a regression function described by
the
general model (10)
0 5 10 15 20 25 30
Time, min
0
5
10
15
20
Wa
ter
leve
l, c
m
0 5 10 15 20 25 30 35 40
Time, min
0
5
10
15
20
25
Wa
ter
leve
l, c
m
Figure 6. Comparison of the changes in water levels during the
infiltration in experimental site no.1, measured on the 30.07.03
(left) and the 11.08.03 (right) with a regression function
described by the general model (11)
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9
0 20 40 60 80 100 120 140 160 180 200 220 240
Time, min
0
5
10
15
20
25
Wa
ter
leve
l, c
m
0 20 40 60 80 100 120 140 160 180 200 220
Time, min
0
5
10
15
20
25
30
Wa
ter
leve
l, c
m
Figure 7. Comparison of the changes in water levels during the
infiltration in experimental site no. 2, measured on the 09.07.03
(left) and the 14.07.03 (right) with a regression function
described by the
general model (11)
The calculated regression functions describe the water level
fluctuations in time in tested underground facilities very well, as
is proved by high values of determination coefficients obtained for
these functions, falling within the range from 0.858 to 0.999 for
modelling with use of equation (10) and from 0.845 to 0.992 when
model (11) was used to describe the process of water infiltration.
During the evaluation of the measured water layer fluctuations
during the emptying of the test infiltration modules, an
acceleration of the transient infiltration rate was noted at the
end of the infiltration phase. In the analysed test sites the
change in the gradient of transient infiltration rates occurred at
water level between 4-6 cm. This phenomenon was noted for all
measurements. It could be explained by an increase in the suction
power of the soil located below the geotextile. At high transient
infiltration rates the thickness of fully saturated zone
stabilises. When the transient infiltration rate decreases, the
thickness of the fully saturated zone starts to decrease, as more
water flows out than it flows in from the land surface direction in
the zone that has not been fully saturated with water. This causes
a decrease in soil moisture and an increase of suction pressure
below the surface of sediments. The decrease in th