9th International Conference on Urban Drainage Modelling Belgrade 2012

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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, nuno_melo@ipg.pt 2 IMAR Institute of Marine Research, University of Coimbra, Portugal, leandro@dec.uc.pt, plima@dec.uc.pt 3 University of Sheffield, United Kingdom, j.shucksmith@sheffield.ac.uk, m.rubinato@sheffield.ac.uk,

a.j.saul@sheffield.ac.uk 4 University of Exeter, United Kingdom, S.Djordjevic@exeter.ac.uk 5 IST Instituto Superior Tcnico, Technical University of Lisbon, Portugal, hr@civil.ist.utl.pt

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.

9th International Conference on Urban Drainage Modelling Belgrade 2012

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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, dkg630630@gmail.com 2 University of Innsbruck, Innsbruck, Michael.Mair@uibk.ac.at 3 University of Innsbruck, Innsbruck, Manfred.Kleidorfer@uibk.ac.at 4 University of Innsbruck, Innsbruck, Robert.Sitzenfrei@uibk.ac.at 5 University of Innsbruck, Innsbruck, Michael.Moederl@uibk.ac.at 6 University of Innsbruck, Innsbruck, Christian.Urich@uibk.ac.at 7 University of Innsbruck, Innsbruck, Wolfgang.Rauch@uibk.ac.at

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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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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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

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.

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.

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.

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, gregor.burger@uibk.ac.at 2 University of Innsbruck, Austria, wolfgang.rauch@uibk.ac.at

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

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

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

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

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.

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).

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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6 REFERENCES

Achleitner, S., M. Moderl, and W. Rauch. 2007. CITY DRAIN\copyright-An Open Source Approach for Simulation of Integrated Urban Drainage Systems. Environmental Modelling & Software 22 (8): 11841195.

Amdahl, G.M. 1967. Validity of the Single Processor Approach to Achieving Large Scale Computing Capabilities. In Proceedings of the April 18-20, 1967, Spring Joint Computer Conference, 483485.

Burger, G., S. Fach, H. Kinzel, and W. Rauch. 2010. Parallel Computing in Conceptual Sewer Simulations. Water Science and Technology: a Journal of the International Association on Water Pollution Research 61 (2): 283.

Dotto, C.B.S., M. Kleidorfer, A. Deletic, W. Rauch, D.T. McCarthy, and T.D. Fletcher. 2011. Performance and Sensitivity Analysis of Stormwater Models Using a Bayesian Approach and Long-term High Resolution Data. Environmental Modelling & Software 26 (10) (October): 12251239. doi:10.1016/j.envsoft.2011.03.013.

Dotto, Cintia B.S., Giorgio Mannina, Manfred Kleidorfer, Luca Vezzaro, Malte Henrichs, David T. McCarthy, Gabriele Freni, Wolfgang Rauch, and Ana Deletic. 2012. Comparison of Different Uncertainty Techniques in Urban Stormwater Quantity and Quality Modelling. Water Research 46 (8) (May 15): 25452558. doi:10.1016/j.watres.2012.02.009.

Hill, M.D., and M.R. Marty. 2008. Amdahls Law in the Multicore Era. Computer 41 (7): 3338.

Huber, WC. 1995. EPA Storm Water Management ModelSWMM. Computer Models of Watershed Hydrology 1: 783808.

Kleidorfer, M, M Mderl, R Sitzenfrei, C Urich, and W Rauch. 2009. A Case Independent Approach on the Impact of Climate Change Effects on Combined Sewer System Performance. Water Science and Technology: A Journal of the International Association on Water Pollution Research 60 (6): 15551564. doi:10.2166/wst.2009.520.

Kleidorfer, M., A. Deletic, T. D. Fletcher, and W. Rauch. 2009. Impact of Input Data Uncertainties on Urban Stormwater Model Parameters. Water Science & Technology 60 (6) (September): 1545. doi:10.2166/wst.2009.493.

Mair, M., R. Sitzenfrei, M. Kleidorfer, M. Mderl, and W. Rauch. in press. GIS-based Applications of Sensitivity Analysis for Sewer Models. Water Science & Technology. https://mail.google.com/mail/?shva=1#search/manfred.kleidorfer@uibk.ac.at/13567075afcc7ffe.

Moderl, M., D. Butler, and W. Rauch. 2009. A Stochastic Approach for Automatic Generation of Urban Drainage Systems. Water Science & Technology 59 (6): 11371143.

Mderl, M., M. Kleidorfer, R. Sitzenfrei, and W. Rauch. 2009. Identifying Weak Points of Urban Drainage Systems by Means of VulNetUD. Water Science & Technology 60 (10) (November): 2507. doi:10.2166/wst.2009.664.

Moore, G. E. 1998. Cramming More Components Onto Integrated Circuits. Proceedings of the IEEE 86 (1) (January): 8285. doi:10.1109/JPROC.1998.658762.

Olukotun, Kunle, Basem A. Nayfeh, Lance Hammond, Ken Wilson, and Kunyung Chang. 1996. The Case for a Single-chip Multiprocessor. SIGPLAN Not. 31 (9) (August): 211. doi:10.1145/248209.237140.

Rossman, L.A. 2006. Storm Water Management Model, Quality Assurance Report: Dynamic Wave Flow Routing. Cincinnati,OH: US Environmental Protection Agency, Office of Research and Development, National Research Management Research Laboratory.

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Sutter. 2005. The Free Lunch Is over: A Fundamental Turn Toward Concurrency in Software. Dr. Dobbs Journal 30 (3): 202210.

Sutter. 2011. Welcome to the Jungle. Sutters Mill. http://herbsutter.com/2011/12/29/welcome-to-the-jungle/.

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, ewa.burszta-adamiak@up.wroc.pl 2 Wroclaw University of Environmental and Life Sciences, Poland, janusz.lomotowski@up.wroc.pl

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),

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

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

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:

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.

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.

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

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)

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