Mathematical modelling of urban floods with solid material embodiment representing flow obstruction

Transcription

1 2002 WT Press, Ashurst Lodge, Southampton, SO40 7AA, UK. All rights reserved. Paper from: The Sustainable City, CA Brebbia, JF Martin-Duque & LC Wadhwa (Editors). SBN Mathematical modelling of urban floods with solid material embodiment representing flow obstruction F. C. B, Mascarenhas,M. G, Miguez, R. O. G. Campos Computational Hydraulics Laboratory, COPPE Department of Water Resources and Environment, EE Federal University of Rio de Janeiro, UFM, Brazil Abstract The urban flood problem has becoming very frequent at great cities in developing countries, The interest in the mitigation of the related effects has been widely increased due mainly to hazardous situations that arise in wet seasons. Those urban floods have been aggravated either in magnitude and frequency because of problems related to disordered urban land occupation and to inefficient drainage system, An important cause of those problems is frequently associated to the lack of public services integration and poor substructure for the city growth. The drainage system of an urban watershed is not designed to work at very unfavorable conditions related to the presence of all sort of solid material mixed with the water flow. The general picture becomes more significant when the urban waste is added to the basin wash load, due to inefficient urban garbage collect system, and the water flow may be contaminated, favouring proliferation of diseases through the city inhabitants. Regarding the mathematical flood flow modelling, most models are not able to simulate the solid material embodiment. The usual approaches consider only the flood flow running through full hydraulic transverse sections and by increasing the roughness coefficient to simulate flow restrictions. When communities occupy watershed slopes not provided of basic substructure services, there are source of garbage and solid material whose will be added to the water flow along the drainage net. This work presents a mathematical cell model capable to represent the presence of solid material combined with the water flow. This is done through the introduction of a time varying reduction factor for the

2 2002 WT Press, Ashurst Lodge, Southampton, SO40 7AA, UK. All rights reserved. Paper from: The Sustainable City, CA Brebbia, JF Martin-Duque & LC Wadhwa (Editors). SBN discharge, function of quantities such as basin concentration time, distance between cells and real time simulation. 1 ntroduction The disordered urbanizing processes that take place in developing countries have great influence on the urban floods, both in their frequency and flow patterns. At those countries the urbanisation is highly affected by the movement of people from rural areas to the cities, looking for better life conditions. However the substructure developing does not accomplish the fast city growth, and the urban basin is subjected to natural vegetation cover reduction, to imperviousness increasing and to other factors, turning worse the problem of urban floods, mostly at the lower level zones of the watershed. This problem is not new and causes many hazards to the inhabitants, with material losses and even human lives. The social hazards are very strong and one may observe landslides, proliferation of diseases and building destruction to name but a few. The problem is aggravated by the addition of solid material to the water flow, resulting from the basin wash load, from bad planned land occupation and from garbage deposition in the drainage system. MaPQ?tu4tMM Figure 1: Debris accumulation in Faria-Timbo River, Rio de Janeiro, Brazil. Large quantities of garbage added to the flow generate barriers when the river reaches a small bridge constraint, City Hall photograph. 2 The urban flood problem At great cities of developing countries this problem is directly associated to the disordered occupation of the urban environment, when the chaotic urbanizing process promotes all sort of disturbances, The people living at rural areas usually move to urban zones searching for better life conditions related to government assistance, transportation, education, sanitary services, among other conditions, that are absent in rural areas. As a consequence the land occupation is modified, together with the increasing of land imperviousness and natural vegetation cover

3 2002 WT Press, Ashurst Lodge, Southampton, SO40 7AA, UK. All rights reserved. Paper from: The Sustainable City, CA Brebbia, JF Martin-Duque & LC Wadhwa (Editors). SBN The.$mtaimble City removing. The water resources parcels of the water balance at the region are modified, the infiltration soil capacity is reduced and the water volume available for the surface runoff is increased as well the flow velocities and the flood peaks. The modified drainage system has to work under new and stronger conditions and the flood movement is modified with an increasing of the flood plain areas and flood frequency. On the other hand, the sediment load of the basin is affected and more solid material is added to the flow, silting up greater areas of the watershed. Another problem is related to the fact that in the cities of developing countries the waste collection is inefficient, and the garbage is also added to the flow mixture, decreasing the hydraulic conveyances of the flow. t is then usual to notice that rivers, channels and storm drains are obstructed by solid material. Besides, flow sections may suffer reduction by illegal constructions and bad designed embankments. All those singularities are turned to be more favorable to overflowing and solid material accumulation. When the suspended sediment load reaches a channel restriction, garbage and solid material accumulate and become to act as contention barriers to the channel flow, as can be seen in Figs. 1 and 2. The Fig. 3 shows street inlets in the same situation. As the progressive obstruction of the street inlets does not allow the water flow to run to the micro drainage, the waterfall over the basin promotes more inundation. n the same way, the obstruction of the drain galleries contributes for the returning of exceeding water to the surface through the street inlets, Thus it is easy to see that the general picture is filled with flooded areas not seen before the urbanizing process of the watershed. Figure 2: Pipes crossing transverse section of a drain gallery and some garbage material trapped, Rio de Janeiro City Hall photograph, Brazil.

4 2002 WT Press, Ashurst Lodge, Southampton, SO40 7AA, UK. All rights reserved. Paper from: The Sustainable City, CA Brebbia, JF Martin-Duque & LC Wadhwa (Editors). SBN lit.smtaimble Ci(v Figure 3: Street inlets partially obstructed by solid material and waste, Rio de Janeiro City Hall photograph, Brazil. 3 Case study: City of Rio de Janeiro, in Brazil The city of Rio de Janeiro in Brazil presents a set of peculiarities that influence the floods behaviour in its urban basin. The city geographic location is characterised by a very wet climate in the summer season. The topography of the basin, narrowed by mountains and the sea is very favorable to floods occurrence. The disordered urbanizing process already mentioned is also source of related problems. Regarding one of the major sub basin of the city, named Joana, the main drainage is done by the Canal do Mangue, a channel located practically at the outlet of the sub basin crossed by Joana river, n this basin there is an area historically flooded, named Praca da Bandeira which is a city square in an intense commerce region. The area is strongly occupied and is located at a lower level near the city centre, To that square one can notice the convergence of several rivers draining an area of about 42 square kilometres, where the imperviousness is very high, There are slope areas at some boundaries, occupied by lower income inhabitants and basic substructure is practically absent. Several tourist attractions are located inside the basin, such as Maracana soccer stadium and the former zoological garden. The Rio de Janeiro State University is also located inside the are% near the stadium, The characteristics presented turn the area very important to the city and also subjected to floods with solid material added to the flow.

5 2002 WT Press, Ashurst Lodge, Southampton, SO40 7AA, UK. All rights reserved. Paper from: The Sustainable City, CA Brebbia, JF Martin-Duque & LC Wadhwa (Editors). SBN The proposed mathematical model The Sust~limble ( ip The mathematical model proposed and used in this work is the two-dimensional flow cell model, detailed in Miguez and Mascarenhas [2]. The choice of this model was made due to its capacity in representing the watershed in an integrated way, giving the same importance to the flow occurring in the micro and macro drainage net, interacting with each other, and also in the city streets, working as artificial channels. The area is divided into cells and their communications are done by hydraulic links, like free flow, flow over weirs, flow through orifices and so on, Therefore the natural elements of a city landscape are treated in a hydraulic way, regardless their original purposes, The model is also able to simulate the influence of engineering works on the flow through the watershed. The starting point is that the basin can be divided into homogeneous compartments, called flow cells, The cells arrangements are done bearing in mind that the flow patterns may be correctly reproduced by the model, departing from the interactions between cells, forming a topological scheme. The model allows that each flow cell communicates with its neighbors, following a set of hydraulic relations for discharge exchanges ([1], [5]). Thus the flow between cells can be related to links representing weirs, orifices, street and channel flow and free or drowned flow (e.g. under pressure). The model also allows communications between surface and micro drainage nets, through links simulating street inlets. The model is described in more detail in Miguez and Mascarenhas [2]. Usually the effects of solid material embodiment to the flow are represented by an increasing of resistance to the water discharge, through the adoption of high values of the Manning roughness coefficient [4]. This means to say that local head losses are added to the distributed ones in the modelled flow stretch. However, there is a need in representing the effects of the solid material in the flow in a better way, but still treating the fluid as Newtonian. The approach used in this work takes into account a set of modifications introduced in the computer model routines, briefly described as follows. During the flood flow there is a progressive increasing of the presence of sediments and garbage in the flow, The simulating scenarios are gradually changed, starting from an initial condition of full flow discharge until the moment in which the drainage system becomes to work suffering the influence of a partial obstruction by the residuals, To achieve this improvement it was adopted a negative exponential time varying reduction factor for the discharge exchanges between cells. The reduction factor is also timction of the total simulation time, the concentration time of the cell with respect to a slope neighbour cell, taken as the source of solid material and garbage, a constant K for each type of link and the rainfall beginning time.

6 2002 WT Press, Ashurst Lodge, Southampton, SO40 7AA, UK. All rights reserved. Paper from: The Sustainable City, CA Brebbia, JF Martin-Duque & LC Wadhwa (Editors). SBN Joam River Fhwiombic Gage mo~ ?s T% S(rp 40 ~ ~ a-rkrbank + Cdbmion Values ~ hhmod Vahes 5 Simulations and results Figure 4: Calibration results and measured values There are water levels measurements in the lower part of the Joana River sub basin. There is also a rainfall station at one of its quarters, essential to evaluate the rainfall amounts occurred in the basin during the measured flood events. The rainfall used for the model calibration occurred in 16 February The main calibration parameters were the Manning roughness coefficients for each link between cells and the constant K for each link between them. The results for the station of river Joana, with calibrated values of the constants K, can be seen in Fig. 4. The calibration procedure for the constants K was based on a trial and error procedure, analysing the drainage system behaviour for each change in the values of those constants. All model links present some reduction factor applied to the exchange discharge capacities, The strongest case is related to a gutter link, which simulates the working conditions of the street inlets. n this case, for a 10 years design rainfall, atler 6 hours of real simulation time the capacity of discharge exchange between the surface area and the associated drain gallery is reduced to about only 14 percent of its original capacity, The remaining links present a reduction of about 10 percent in their flow effectiveness at the end of the simulation. For validation purposes it was used another available event with less intensity occurred in March 2000, The validation results were considered satisfactory and the figure 6 shows the water level hydrography for that event. The analyses of the results were based on the comparison between two scenarios, as follows. t was taken the 10 years recurrence time for a supposed uniform rainfall over the basin, at a critical design condition. This considered rainfall was supposed to have temporal distribution, according the procedure suggested by

7 2002 WT Press, Ashurst Lodge, Southampton, SO40 7AA, UK. All rights reserved. Paper from: The Sustainable City, CA Brebbia, JF Martin-Duque & LC Wadhwa (Editors). SBN lh(.yl(sfciit](tblf ( it) 577 the U. S, Soil Conservation Service [3] for the design rainfall computed through an equation of intensity-duration-frequency for a rain gauge located inside the basin., Scenario 1: Present situation, simulation of the watershed of river Joana with an exponential reduction factor for the discharges, This scenario was taken as reference., Scenario 2: Present situation without discharge reduction factor; simulation done using as basis the present situation with all constants K for discharge reduction equal to zero for all links, e,g, there is no exponential reduction factor for the discharges. Thus, for this second scenario the reduction factor is always equal to 1, meaning that the discharges occurring in the links between cells are unchanged. This situation is a simulation where the drainage system is supposed to work in perfect conditions and the progressive embodiment of solid material to the flow, due to garbage and slope erosion, is avoided. The measures taken to assure this ideal working are related to an efficient garbage collection system and the implementation of a set of solid material retaining disposals, such as sand boxes and protection grilles. The results are presented in Figs. 5 through 9, showing graphs where the water levels at some cells centres, located at streets crossing points, are plotted as functions of simulation time. +== ==== ~ Jam RiverFl@xa@ic Gmge a70~ _ _ T z T~SteF6 3 L Figure 5: Model validation results and measured values

8 2002 WT Press, Ashurst Lodge, Southampton, SO40 7AA, UK. All rights reserved. Paper from: The Sustainable City, CA Brebbia, JF Martin-Duque & LC Wadhwa (Editors). SBN h,.$t{s[(lit~([fd(>( it>... Uubwtiwrmderthe*ngufTeudorodaSitva andmencktavamstmek 19fL, --- \ L - 1 ~ 19m+ -o&4 i02waticm dlmt Ckhatge - t],m / ---- rsbktim 1902 L...~ ,&mj : -----l 18K~ ~Scmwbl:Res.91t WEticm o a s) mrsslsp Drain gallery in the Urubus river. The scenario without discharge restrictions presents greater water volumes due to the better working of the drainage system. Crossing of Teodoro da Silva and Mendes Tavares streets Xl x] 55!r A --- o Scenario 2: Situation, ~ 2050 /-.. u without dkcharge ~ 2045 ;. --. : restrictions ~ Scenario 1.Present 1,1 ~ ( i ::1- -: --~=i 2030 # ; 2025 & - _ - --J m 80 Co 120 Time Steps, _ Figure 7: Surface cell above that of the preceding figure. t can be observed that the street inlets present a good working when they are subjected to maintenance. The scenario 2, with no discharge restrictions, allows the street inlets to work in their entire capacity.

9 2002 WT Press, Ashurst Lodge, Southampton, SO40 7AA, UK. All rights reserved. Paper from: The Sustainable City, CA Brebbia, JF Martin-Duque & LC Wadhwa (Editors). SBN w.sll.s[llill(lhlc ( it> Crc4Qti%. cksofrancko andb. * ~ wjssanssimds.. a ~ _ ,$1j 2,6al~+L 7!j. ; s.- h55 ~ ~. -d [ 16( ,55 ---_ E ~ r ~ -~.< 0 B 40 &l 83 Km ml Timsep oscemi02muatkm hut diwbge iw.fctiins ~ %7Eak 1:REsalt Situatwn Figure 8: The flood on the urban plain presents water levels decreasing due to the maintenance of the street inlets discharge capacities, This cell is almost dry at the final simulation time, meaning that the well designed drainage system, together with the maintenance of its ideal working conditions, generates favorable results to urban the flood control, Crossing of Vise. da Sta. sabeland Em liasarrpaio Stresis 24.@..- 24,55~.. 24,% : L 24.35_?L-_ v K 2425 ~.~ Q kentio2 Situation without d~chwge restrictions x %mafio Situakn 1: Resent 24,05l ~ J o B so lime steps. -- Figure 9: The same pattern as above for another cell.

10 2002 WT Press, Ashurst Lodge, Southampton, SO40 7AA, UK. All rights reserved. Paper from: The Sustainable City, CA Brebbia, JF Martin-Duque & LC Wadhwa (Editors). SBN Conclusions Floods at urban areas are becoming more frequent, and in developing countries they are aggravated by the embodiment of solid material to the water flow. The disordered urbanizing process turns worst the problem, increasing the erosion of slope areas and adding garbage to the mixture that flows through the urban basin. The mathematical model developed to simulate the effects of solid material in the flow was able to represent different degrees of the drainage obstruction, through the adoption of an exponential time varying reduction factor for the discharge exchanges between cells. The actual situation at the street inlets was represented, for different obstruction beginning times associated to each cell of the modelled basin, those times being function of the distance between the considered cell and the slope areas contributing with solid discharge. When the drainage system of an urban basin is subjected to maintenance, avoiding obstruction in the drain disposals, the fluid that flows is basically water, and the flooding areas will present their water levels decreased, reducing the general overflowing. n this situation the exceeding water stored at some areas of the basin are better conveyed to the outlets of the watershed. The use of the proposed model in those conditions can show clearly that it is very important to plan interventions and procedures to prevent and to decrease the garbage and solid material embodiment to the flow, The integrated analysis, regarding sanitary aspects and the systemic approach for the watershed, where the city landscape interacts with the drainage system, allows the modeller and the planner to achieve the sustainability concept. References [1] Cunge, J. A.; Holly JR., F. M.; Verwey, A., Practical Aspects of Computational River Hydraulics London, Pitman Advanced Publishing Program, 1980, [2] Miguez, M. G. & Mascarenhas, F. C, B,, MathematicalModelling of Urban Floods Through a Cell Scheme Brazilian Journal of Water Resources, v, 4, n, 1, pp , January-March, 1999, SSN X (in Portuguese). [3] Soil Conservation Service, Design of Small Dams - A Water Resources TechnicalPublicationof The United States, Department of The nterior and Bureau of Reclamation, first edition, [4] Tucci, C. E. M.; Porto, R, La Laina; Barros, M. T., Urban Drainage, ABRH Publishers, 1995 (in Portuguese), [5] Zanobetti, D.; Lorgere, H.; Preissmann, A.; Cunge, J. A., Mekong Delta Mathematical Program Construction, Journal of the Waterways and Harbours Division, ASCE, v, 96, n. WW2, pp , 1970.