Water Resour Manage https://doi.org/10.1007/s11269-017-1835-y Rehabilitation of Urban Drainage Systems Using a Resilience-Based Approach J. Yazdi 1 Received: 2 April 2017 / Accepted: 13 October 2017 # Springer Science+Business Media B.V. 2017 Abstract Highly efficient methods are needed to mitigate negative impacts of urban storms such as flooded roads and damage to properties and infrastructures. A rehabilitation approach based on resiliency is proposed in this paper for urban drainage systems using structural improvement of bottlenecks. The resilience-based approach enhances system capability to act very flexible against exceptional loads such as bridge/culvert blockage during the floods. The approach integrates a multi-objective evolutionary algorithm (MOEA) and EPA-SWMM simulation model to find cost-effective rehabilitation measures under structural failure of critical elements in the network. It is applied to the western part of Tehran Stormwater Drainage System (TSDS) to attain optimal measures by minimizing the costs and flood volumes. The approach outperforms the conventional methods (particularly compared to a previous rehabilitation proposal for the study area) when the system encounters unexpected blockage conditions. Results show that the optimal design obtained by the proposed approach can decrease network flooding from 3.5 × 106 m3 to near zero with at most 23% lower investment costs relative to the traditional design. Keywords Resiliency . Flood . Urban drainage system . Optimization . Rehabilitation 1 Introduction In recent years, flood intensity and frequency has been increased due to urbanization and climate change (Yazdi et al. 2014). Urban floods lead to serious problems such as damages to properties and infrastructures, traffic loads, loss of lives, environmental risks and health issues. Therefore, development of a comprehensive surface runoff collective system to safely transfer stormwater while satisfying the economic and * J. Yazdi j_yazdi@sbu.ac.ir 1 Faculty of Civil, Water and Environmental Engineering, Shahid Beheshti University, Tehran, Iran Yazdi J. administrative constraints is of great importance. Traditional methods of design/ rehabilitation of urban drainage systems (UDSs) are based on providing a sufficient hydraulic capacity for conveyance of design flood discharge. That is to say, design and rehabilitation of UDSs is often carried out with the aim of making a sufficient hydraulic capacity within a deterministic or stochastic approach. The latter, which is also called risk-based method assumes one or more stochastic variables for the system and using the approaches such as sampling techniques gives the probabilistic characteristics of the system output while the former usually considers a fixed design rainfall with a predefined return period. Although, risk-based approach could provide a design with balancing the construction costs and flood damages, in many countries the return period method is used in practice due to difficulty of risk analysis task. Both approaches, integrated by mathematical simulation models and optimization methods, have been applied for design/rehabilitation of UDSs and discussed sufficiently in the literature. Delelegn et al. (2011) used the return period method for design of detention ponds in urban areas by coupling Non-dominated Sorting Genetic Algorithm II (NSGA II) and a 1D-2D hydraulic model. Similarly, Park et al. (2012) applied GA for optimization of the storage capacity, diameter of outlet structures and number of detention ponds in an urban area, South Korea. Sun et al. (2011) proposed a risk-based approach and found the optimal size of pipe diameters and their slopes in an UDS using genetic algorithm (GA). Oraei Zare et al. (2012) optimizes the placement of low impact development (LID) practices in Tehran city considering three different criteria including costs, improvement of quality indices and quantity of surface runoff. They used two widely used multi objective evolutionary algorithms (MOEAs): NSGA-II and multi objective particle swarm optimization (MOPSO) and reported that NSGA-II outperforms MOPSO according to several residual metrics. Karamouz et al. (2013) studied the impacts of climate change on urban floods and capacity of UDSs using general circulation models (GCMs) and developed a deterministic model to find optimal adaption strategies for flood mitigation. Yazdi et al. (2015) optimizes the renewal pipe diameters of a sewer network by linking the EPA-SWMM hydraulic model with three different MOEAs including NSGA-II, MOPSO and NSHS for the rehabilitation of UDSs under a fixed design storm. Fu and Butler (2014) studied the dependence structure of rainfall variables using copula method and showed that considering these dependences in Monte Carlo Simulation have noticeable effects on the magnitude of urban floods. Vojinovic et al. (2014) developed a risk-based approach for the rehabilitation of UDS using MCS and allocating Gaussian probability density functions (PDFs) to the main sources of uncertainty including climate change effects, urbanization, population growth and pipe obsolescence. According to the risk-based approach, they presented the rehabilitation practices using an optimization tool. Yazdi and Kim (2015) used Harmony Search (HS) for the optimal operation of detention ponds and pumps in UDSs. They introduced an active control approach for the gate and pump manouver based on hydrological/ hydraulic modeling and updated rainfalls in real time. Many of the methods and research proposed so far for the rehabilitation of UDSs (such as those enumerated above) are based on providing sufficient hydraulic capacity. The major weakness of these methods is neglecting the impact of unexpected events on reducing the system capacity. Decreasing the system capacity may be originated from Rehabilitation of Urban Drainage Systems Using a Resilience-Based... the accidental incidents (such as channel blockage due to sedimentation) or structural failure of the key elements like pumps in the system during the floods. Traditional methods are only based on the hydraulic reliability while in most of the time, structural failure is responsible for the undesirable performance of the system. Therefore, it is of a major importance to consider the resiliency of UDSs under unforeseen loads such as structural failure when these systems are rehabilitated. Some aspects of the UDS resiliency have been occasionally studied in the literature. For example, Butler et al. (2014) proposed definitions of resilience, reliability and sustainability and discussed what engineering, organizational and/or social options can potentially develop the degree of resilience and sustainability needed to deal with threats such as urban floods. Mugume et al. (2015) proposed a novel approach based on resiliency for the analysis of the UDS performance when they are subject to a large number of structural failures. Their results showed that decentralized small detention ponds provide considerable increase in resiliency of the network compared to a large centralized detention during the flood periods. Tahmasebi Birgani and Yazdandoost (2016) studied the resiliency of urban drainage networks under different rainfalls from the social and economic point of view and introduced several indicators for considering social, environmental, technical and economical criteria on selecting the best set of best management practices (BMPs). They introduced total suspended solid (TSS) as the environmental index, the ability of BMPs for the beauty of the city as the social index, BMP costs as the economical index and flood volume as the technical index. Karamouz and Zahmatkesh (2016) studied the resiliency of urban drainage systems under the condition of costal floods. They introduced and categorized several vulnerability indices and obtained a resiliency criterion quantified as a function of four metrics of robustness, redundancy, rapidity and resourcefulness. Although the concept of resiliency and its application to UDSs is introduced in the literature, most quantitative studies however tend to focus on investigating the social and administrative aspects and do not consider technical factors such as structural failure or exceptional loads. Considering these concerns, the aim of this research is presenting a resilience-based method of rehabilitation to improve UDS flexibility and resiliency under structural failure. The developed approach is applied to a part of the main drainage network of Tehran, capital city of Iran and the effectiveness of the approach is examined. Through this resilient framework, the optimal rehabilitation measures are determined using a multiobjective evolutionary algorithm (MOEA) and rainfall-runoff modeling. 2 Materials and Methods 2.1 Resiliency Review of the relevant literature shows that most of previous research for design/ rehabilitation of urban drainage systems are based on hydraulic capacity which leads to a lack of consideration to other sources of urban flooding such as equipment failure (like pumps and gates), disability of a part of the drainage network and its closure. This Yazdi J. means that traditional design/rehabilitation approaches only consider functional resiliency and usually neglect the structural reliability (Mugume et al. 2015). However, urban flooding not only originates from external loads (like heavy rainfalls and urbanization), but they are also related to internal system threats such as malfunction of facilities and blockages. Structural failures can originates from sudden and unexpected collapse like pump failure or chronic and long-term pressures such as pipe obsolescence and sedimentation. These internal factors decrease system service level and may result in severe flooding. Resiliency here is referred to Bthe state of the system that enables it limit failure duration and magnitude to any threat^ (Mugume et al. 2015). The approach proposed in this research work is optimal increase of redundancy and flexibility on the system by making parallel channels and axillary tunnels in throats or bottlenecks as well as by adding detention ponds on the suitable places of the network. Throats or Bottlenecks refer to critical points of the drainage network which have small cross sections and high probability of blockage in severe floods such as culverts, bridges and underground channels with small capacity of flood discharge. In this methodology, bottlenecks are subsequently closed in the simulation model and subsequent flooding is calculated by model execution. The optimal rehabilitation action is a set of parallel culverts/tunnels and detention ponds that could more efficiently reduces flooding under all combinations of bottlenecks closure. To find this optimal intervention, simulation and optimization models are needed. 2.2 Simulation Model A simulation model is employed to model rainfall-runoff process and predict the response of urban drainage network under external (design rainfall) and internal loads (blockages of bridges/culverts). Simulation model has two major modules: rainfallrunoff and flood routing. The former simulates the process of converting rainfall to the surface runoff and estimates sub-catchments hydrograph while the latter is responsible for flood routing in the channels and conduits to convey surface runoff into the catchment outlet. HEC-HMS (USACE 2008) and EPA SWMM (Rossman 2008) models are used here for rainfall-runoff modeling and flood routing, respectively. 2.3 Optimization Model Design, construction, operation and maintenance of urban flood control systems need large resources of investments. Therefore, one of the goals of system management is to provide maximum protection with minimum costs. Many researches show that optimization techniques can noticeably help to find the optimal strategies for the design/rehabilitation of flood control systems. These techniques can also be used to find optimal policies of the system operation. Optimization tools are used here to determine optimal size of axillary tunnels, detention ponds and control structures such as weirs to improve the performance of urban flood management system considering two or more criteria simultaneously. Here, minimizing the costs and resiliency index are considered as two conflicting objective functions. In the urban drainage systems, resiliency indices include the effects of Bflooding duration^ and Bintensity of discharges exceeded the system capacity^. In the present study, these two features have been considered as Btotal flooding^ as resiliency index calculated during and after Rehabilitation of Urban Drainage Systems Using a Resilience-Based... design rainfall. The mathematical form of the optimization problem can then be expressed as: ! i i i n h m h 00 K h 000 0 min f 1 ¼ C T ¼ ð1 þ αÞ: ∑ C i Li f ðH i ; W i Þ þ C i LWi hi þ ∑ C j A j H D; j þ ∑ C k Lk Dk ð1Þ i¼1 min f 2 ¼ 8 < j¼1 k¼1 NT w1 tw2 ∑ Q f ;N −QCr; f ;N f ;N ; Q f ;N > QCr; f ;N : N ¼1 0; ð2Þ Q f ;N ≤ QCr; f ;N Subject to : va ≤vmax H i ∈fH 1 ; H 2 ; …; H M g W i ∈fW 1 ; W 2 ; …; W M g LWi ∈fLW1 ; LW2 ; …; LWM g hi ∈fh1 ; h2 ; …; hM g ð3Þ where CT and VfT are total rehabilitation costs and total flooding, respectively as the objective functions. It should be noted that in this context, flooding or flood volume refers to a part of surface runoff hydrograph which exceeds the hydraulic capacity of the urban drainage system. Li, Hi and Wi are length, height and width of ith axillary culvert/bridge, respectively; hi and LWi are the height and length of ith side weir, respectively. M is the number of discrete values that Li, Hi, Wi, hi and LWi can take. These parameters are a part of decision variables in optimization 0 problem which schematically shown in Fig. 1. Ci and C i are unit cost of culvert/bridge and side weir construction. va is the velocity in ath channel of the network and vmax is the maximum permissible velocity which is considered 6 m/s based on local standards (MGCE 2011a). n and NT are the number of bridge/culverts and nodes in the network, respectively. m and K are the 00 000 number of detention pond and axillary channels, respectively. C j and C k are unit cost of jth detention pond and kth axillary channel, respectively. Aj, HD, j, Lk and Dk are the area and depth of jth detention pond and length and diameters of kth axillary channel, respectively. Depth of detention ponds and diameter of axillary channels are also of decision variables in this problem. α is a constant to consider the maintenance and operation costs of the interventions. It was assumed 1.3 based on the local standards (Bureau of Technical Affairs and Standards 2001). Qf, N, QCr, f, N and tf, N are simulated discharge at location N, maximum discharge capacity at location N, and duration of flooding at location N of the network, respectively. w1 ≥ 1 and w2 ≥ 1 are weighting coefficients used to control effects of failure magnitude (flooding discharge) and failure duration/recovery time (flooding duration) on W H h LW Q Fig. 1. A schematic view of parallel culverts/bridges and associated decision variables Yazdi J. the resiliency index, respectively. With increase of w1 and decrease of w2, the role of an acute flood (a flood with higher amount of magnitude and lower amount of duration) becomes more important on selecting the optimal size of interventions. In adverse, a larger amount of w2 and lower w1 leads to increase effects of chronic floods (floods with the smaller amount of magnitude and the larger amount of duration) on the resiliency index (and size of rehabilitation measures). By assuming w1 = w2 = 1 in the present paper, flood duration and magnitude have the same contribution to the resiliency of the network and previous equation is simplified as: min f 2 ¼ 8 < NT NT ∑ Q f ;N −QCr; f ;N t f ;N ¼ ∑ V f ;N ; Q f ;N > QCr; f ;N : N ¼1 0; N ¼1 ð4Þ Q f ;N ≤ QCr; f ;N where V f ;N (m3) is flood volume exceeded from the Nth channel of the drainage network and f2 is considered as total flood volume exceeded from the whole of the network. Objective functions in this study do not have an explicit mathematical form of decision variables and for objective function evaluation, running the rainfall-runoff model is needed. On the other hand, decision variables can take only discrete values in the problem studied. For these categories of optimization problems, evolutionary algorithms are best-suited. Therefore, an MOEA known as Non-dominated Sorting Differential Evolution (NSDE) is used here to solve the above optimization problem and to attain the optimal strategies of rehabilitation. Details of this algorithm including the concepts and main steps can be found in the work of Yazdi et al. (2016). 2.4 Case Study The main drainage network of Tehran, the capital city of Iran, includes four independent and separate catchments with their own borders and drainage systems without hydraulic connection to each other. Each catchment has its own urban and rural (or mountainous) sub-catchments. The study area here is the western catchment of Tehran main drainage system. Mean annual rainfall in Tehran varies at 200 mm in southern parts of the city to 500 mm in the north (MGCE 2011b). For example, the mean annual rainfall in three meteorological stations of the region, called Mehr_Abad, Latyan Dam and Karaj Dam stations, was obtained 248, 420 and 424 mm during 1971 to 2006 based on recorded rainfalls between 1971 and 2006, respectively (MGCE 2011c). The studied drainage system mostly includes open channels with 119 km length in which 8.8 km of the channels do not have enough hydraulic capacity to safely convey stromwater runoff related to design rainfall. This network drains 156 km2 area and includes 42 subcatchments and 132 conduits. Figure 2b shows the layout of main urban drainage network of the west zone in SWMM-EPA model and critical reach of the bottlenecks. On the west zone network, there are six critical bridges/culverts that their deck heights occupied a considerable percentage of the useful channel height. Considering the high sediment load of the main channels during flood periods, these bottlenecks are likely to block the flow path and causes the urban flooding in surrounding areas. Experiences of urban flooding in Tehran city confirmed this problem (MGCE 2011a). Location of the bottlenecks in west zone is shown in Fig. 2b and their dimensions are presented in Table 1. According to the urban planning studies, three locations on the catchment were Rehabilitation of Urban Drainage Systems Using a Resilience-Based... (a) Legend Subcatchment Outlet Drainage System SubCatchment Tehran Border Fig. 2 a West zone of Tehran main drainage network, b location of bottlenecks in hydraulic model of the west zone Yazdi J. (b) D1 Axillary Channel D3 D2 Reach with bottlenecks problems Fig. 2 (continued) found to be suitable for constructing detention ponds illustrated in Fig. 2b. Moreover, based on socio-economical studies and lack of hydraulic capacity in local parts of the network, an axillary channel was also suggested for an upstream conduit of the network which its location is indicated in Fig. 3b. 2.5 Model Set Up Model setup and calibration for the west zone of TSDS has been already carried out by Mahab Ghods Consultant Engineers (MGCE 2011a, b) and here the same modeling approach and calibrated parameters have been used for the model preparation. The first step for rainfallrunoff modeling was determination of design rainfall including rainfall depth and duration with its spatial-temporal pattern. Rainfall depth can be achieved from the Intensity-DurationFrequency (IDF) curves, extracted from the recorded rainfalls. According to the previous studies (MGCE 2011a), design rainfall with 50 years return period has been recommended by the authorities for rehabilitation and thus here this return period is selected. The rainfall Rehabilitation of Urban Drainage Systems Using a Resilience-Based... Table 1 Dimensions of critical bridge/culverts on the UDS studied Bridge/Culvert No. Height (m) Width (m) Length (m) Deck thickness (m) 1 2 3 4 5 3.3 5 5 5 4.5 6 7 7 7.5 9.5 10 14.5 6 330 22 0.4 0.5 0.4 1 0.4 duration is suggested to be at least equal to time concentration that this travel time for the studied urban area was estimated 150 min. After a sensitivity analysis on the severity of produced runoff from rainfalls with different durations, six-hour duration has been recognized as the critical value and has been selected for design rainfall duration. According to the meteorological data, recorded rainfalls in nine precipitation gauges inside the city have been analyzed and the following formula has been proposed for short-term rainfalls (MGCE 2011b): i ¼ C Alt:RP D−0:645 ð5Þ where i = the rainfall intensity (mm/h), D = rainfall duration (min) and CAlt. RP = a coefficient associated with return period of design rainfall and the mean height of the sub-catchment. Therefore, the spatial variations of rainfall throughout the catchment is manipulated by the above equation using the average height of sub-catchments. The value of CAlt. RP is determined using a lookup table according to the rainfall return period and the average height of sub-catchment. In fact, Eq. (5) is the Intensity-DurationFrequency (IDF) curve for 50-year return period obtained by frequency analysis of the recorded rainfalls in nine rainfall stations in Tehran. A set of approaches has been also proposed in the literature to determine temporal pattern of design rainfall. Some of the relevant approaches are local pattern, Hershfield method, Huff method, SCS depth-duration curves and some other standard types of patterns such as Euler-II, DVWK and uniform patterns (German ATV Rules and Standards 1999) used in England and German guidelines. Since, UDS should safely pass the peak discharge of design rainfall, the Pareto Front Selected Solutions MGCE design 3500 Flood Volume (1000 m3) 3000 2500 2000 1500 1000 500 0 0 500000 1000000 1500000 Costs ($US) Fig. 3 Pareto front obtained by running NSDE-EPA SWMM framework 2000000 2500000 Yazdi J. most critical temporal pattern producing the maximum peak discharge is selected as temporal pattern in order to provide higher reliability or safety factor for evacuating design flood. A sensitivity analysis has been carried out on the abovementioned methods and the Blocal pattern^ method has been found to be able producing the largest peak runoff at different point of drainage network and therefore temporal pattern obtained by this method has been selected as the relevant temporal pattern of short-term rainfalls in Tehran. In brief, from the IDF Eq. (5), the design rainfall with a 50-year return period was obtained between 27 and 60 mm according to the average height of sub-catchments for a duration of six hours. This rainfall depth was distributed by Blocal pattern^ in six hours. No snow was assumed in the surface of the city during the rainfall. The NRCS curve number method, introduced by U.S. Natural Resources and Conservation Service (NRCS), was set up in HEC-HMS for estimating the precipitation losses based on the local land use and soil type properties (USACE 2008). Furthermore, in order to transform excess precipitations into surface runoff, SCS unit hydrograph was utilized. According to the land uses and soil types, totally 42 sub-catchments were considered in hydrological modeling. After calculating sub-catchment surface runoff by model execution, they were introduced to the hydraulic model of the urban drainage network, here EPA’s Storm Water Management Model (SWMM), for flood routing in the channels and conduits of the network. As mentioned earlier, the parameters of both models (HEC-HMS and SWMM) were set as those of calibrated models reported by MGCE (2011a, b). To solve the optimization problem, a widely used evolutionary algorithm known as Nondominated Sorting Differential Evolution (NSDE) is used. This algorithm combines nondomination and crowding distance (Deb et al. 2002) with DE operators to solve multiobjective optimization problems (Yazdi et al. 2016). The parameters of NSDE was set as those widely used in the literature: crossover probability = 0.7, scaling factor = 0.5, and with a population size and number of iterations equal to 100. 3 Results and Discussion The actions considered for the rehabilitation include constructing parallel culverts/bridges in bottlenecks and common methods of channel enlargement and constructing detention ponds in possible locations. The aim of the provided models is determining the best set of rehabilitation actions among considered axillary culverts, channels and detention ponds with their optimal sizes so that the resiliency of studied UDS is improved. To find optimal rehabilitation actions, NSDE linked to SWMM was coded in Matlab Environment and executed. According to the mentioned computational efforts (a population size and no. of iterations equal to 100), the running time was nearly 140 h on a computer Pentium® Dual-Core CPU 3.00 GHz with 4.00 GB RAM. Figure 3 shows the Pareto optimal solutions obtained after 100 iterations. There are obviously two distinct clusters of solutions in the Pareto front. The reason of clustering the optimal solutions into two groups is the high cost of the fourth rehabilitation action -i.e. parallel culvert (tunnel) related to one of the bottlenecks, respect to the other actions. This results in higher costs for the solutions in the second group which include this parallel tunnel relative to those of the first group. As Fig. 3 shows, NSDE could sufficiently provide diversity in the population from near zero cost to the zero flooding. The location of the proposed design by MGCE including three detention ponds and one axillary channel is Rehabilitation of Urban Drainage Systems Using a Resilience-Based... also showed in the objective functions space (Fig. 3). It can be seen that all optimal designs absolutely outperform the MGCE proposal in terms of both cost and flooding values when blockage scenarios are considered in the drainage system. Specifically, this figure shows that the most costly optimal design obtained by proposed approach can decrease network flooding from 3.5 × 106 m3 to near zero with at most 23% lower investment costs relative to the traditional design. The MGCE proposal includes an axillary channel with 1700 m length and 2 m diameter and three detention ponds with 6000, 40,000 and 25,000 m2 area and 3, 3.5 and 3 m depth, respectively (see Fig. 2b). To analyze the results, five representative solutions from the Pareto front are selected based on clustering and presented in Table 2 illustrating in Fig. 3 with solid red circles. The figures in Table 2 indicate that detention pond no 2 have better performance relative to two other considered detention ponds since it appears more in the optimal solutions. But, roughly, considered detention ponds and axillary channel have lower efficiency in terms of flooding compared to the bypath line actions (i.e. parallel bridge/culverts in the bottlenecks). Solution 5 indicates that making a parallel bridge in locations of bridge no. 1 and no.3 are the most efficient actions among the others to improve the resiliency under cost limitation and thus, only these two actions are emerged in this optimal solution (with the minimum cost). On the other hand, because of the high length of bypath line no. 4 (and its relatively high costs), this option appears in the optimal solutions only when there is enough available funds (only solution no. 5 among the Table 2 Selected solutions from the Pareto front Strategy No.: S1 S2 S3 S4 S5 Height of Bypath 1 (m) Width of Bypath 1 (m) Height of Bypath 2 (m) Width of Bypath 2 (m) Height of Bypath 3 (m) Width of Bypath 3 (m) Height of Bypath 4 (m) Width of Bypath 4 (m) Height of Bypath 5 (m) Width of Bypath 5 (m) Height of Weir 1 (m) Height of Weir 2 (m) Height of Weir 3 (m) Height of Weir 4 (m) Height of Weir 5 (m) Length of Weir 1 (m) Length of Weir 2 (m) Length of Weir 3 (m) Length of Weir 4 (m) Length of Weir 5 (m) Storage Depth of Pond 1 (m) Storage Depth of Pond 2 (m) Storage Depth of Pond 3 (m) Axillary Channel Diameter (m) Total Costs ($US) Total flooding (1000 m3) 4.5 5 3.5 5 4 7 3.5 5 3.5 8 2.1 4.4 4.55 2.6 3.2 4.2 8.4 3.3 8.7 9.3 – 2.7 – – 1,281,543 682.6127 5 10 4.5 5 3.5 6 – – 4.5 7 4.5 1.6 3.5 – 1.9 3.9 8.7 5.1 – 9 4.5 3.6 1.35 0.3 877,078.6 1504.95166 4 6 4 5 5 7 – – 4 6 2.55 2.15 4.25 – 3.65 6.3 8.7 6.6 – 5.4 – 2.7 – – 327,958.3 1751.366 3.5 6 4.5 5 5 10 – – 4 5 2.1 2.45 4.25 – 4.25 3.3 3.3 5.4 – 3 – – – – 185,859.8 2237.644 3.5 5 – – 3.5 7 – – – – 1.3 – 5 – – 4.2 – 4.2 – – – – – – 54,299.75 2670.886 All actions 682.61 1,281,543 – – – – Scenario: Flooding (1000 m3) Costs ($US) Increased flooding (1000 m3) Decreased costs ($US) Relative increased flooding (%) Relative decreased costs (%) 1087.32 1,247,145 404.71 34,397.78 59.29 2.68 Remove bypath1 1164.04 1,237,030 481.43 44,512.98 70.53 3.47 Remove bypath2 1781.42 1,256,813 1098.81 24,729.93 160.97 1.93 Remove bypath3 Table 3 Sensitivity analysis over the efficiency of different actions in the optimal solution no. 1 (Table 2) 2074.28 324,643.6 1391.67 956,899 203.87 74.67 Remove bypath4 2202.91 1,195,564 1520.29 85,978.78 222.72 6.71 Remove bypath5 1615.15 1,146,518 932.54 135,024.1 136.61 10.54 Remove detention pond no. 2 Yazdi J. Rehabilitation of Urban Drainage Systems Using a Resilience-Based... selected solutions). Assessing Table 2 contents and checking the solutions in the Pareto front proves that during exceptional events, the type of actions which increase the redundancy in the critical part of the system are more efficient for flood mitigation than the usual methods of system rehabilitation such as enlarging the channels and detention pond construction. To compare the performance of bypath lines respect to each other in terms of flood mitigation, a sensitivity analysis was also conducted over the options in the optimal solution no.1 which includes all bypaths. To do so, flooding of optimal solution no. 1 was re-calculated several times, in each round, one of the actions was removed from the optimal solution. The results are presented in Table 3. According to this table, bypath4 and bypath5 are the most efficient actions for the flood mitigation under blockage load scenarios. The reason is that they are located in downstream of tributaries and receive higher flood volume and therefore, they are able to pass larger amounts of floods. Bypath3 and detention pond no.2 are in the next scores and bypath 1 and 2 are the inferior options. Bypath4 however has a large construction cost (because of its high length) and thus may be discarded by decision makers. Generally, this table shows the relative importance of different options in the selected optimal design in terms of both flooding and construction costs. 4 Conclusion In this paper, a resilience-based optimization model was proposed for the rehabilitation of urban drainage systems and improvement of system performance under unexpected blockage incidents. The experimental results on the west zone of TSDS show that proposed approach can effectively find the optimal set of actions for flood mitigation under a significant number of blockage scenarios at the bottlenecks. Particularly, some of optimal designs are able to reduce flood volumes to almost zero. The results also indicate that ordinary actions of hydraulic capacity improvement such as enlarging the channel sizes and constructing detentions ponds cannot act effectively during unexpected collapse like bridge/culvert blockage. To enhance system performance in real situations, adding the redundancy to the system such as parallel culverts and tunnels especially in critical points is more important and this noticeably increases the resiliency of the system against unexpected internal loads. In this study, external load was assumed constant equal to a predefined design rainfall. But, generally the external and internal loads of the system are uncertain and there is a positive correlation between them. Considering the uncertainty of both internal and external loads and their relations on the modeling is an important issue which can be the subject of future research. 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