Integrated modeling of urban mobility, flood inundation, and sewer hydrodynamics processes to support resilience assessment of urban drainage systems Open Access

Flooding is a significant natural disaster with severe socio-economic impacts on urban buildings, interiors and urban mobility, even threatening residents' lives (Leandro et al. 2020; Dong et al. 2022; Xing et al. 2023). With the increasing frequency of extreme weather and a deeper understanding of disasters, there is a recognition that disasters are unavoidable and the focus should shift toward the sustainability of system functions in disasters (Meerow et al. 2016). In this context, the concept of resilience has been widely considered (Hosseini et al. 2016; Büyüközkan et al. 2022).

The urban drainage system is a vital infrastructure serving people. One of its main functions is to protect people from the impact of flooding or minimize the impact of flood. Considering that resilience is an evaluation of system functions under shocks, resilience assessment of drainage systems requires a simulation model between people and facilities to simulate the process of facilities resisting disasters, and, most importantly, the disaster threats to people. However, existing research has to make a series of simplifications on the simulation model between people and facilities. Some studies have focused solely on facilities for resilience assessment, and some have considered the relationship between people and facilities, however, the effects of rainfall impacts on human mobility behavior have not been included in these studies.

The studies on the resilience assessment of urban drainage systems are mostly indirect assessments that did not simulate human behavior affected by flooding or semi-quantitative assessments that did not build dynamic simulation models. There are a few studies using indices such as the volume ratio of flood to runoff and inundation duration under rainfall events to assess the system resilience (Lee et al. 2017; Casal-Campos et al. 2018; McClymont et al. 2020; Mohammadiun et al. 2020). Guptha et al. (2021) used total flood volume, total inflow into the system, maximum nodal flooding duration, and mean nodal flooding duration to assess the system resilience. Lee et al. (2017) used total runoff and flooding volume to assess the resilience of urban drainage systems. These statistical indicators are positively correlated with the impact of flooding on urban mobility and property losses, thereby indirectly reflecting the resilience of the drainage system under rainfall impact. Nonetheless, given the spatial heterogeneity of assets, pedestrian and vehicular traffic, the severity of property damage and traffic disruption can markedly differ based on the flooding location (Gerges et al. 2022). Consequently, despite similarities in the total volume and duration of flooding, the severity of asset losses and traffic disruption resulting from floods in various locations may differ and result in different resilience. Some studies assessed the system resilience using indicators like the ability to raise disaster relief funds and residential disaster resistance (e.g., household income, health status) through questionnaires and interviews (Cashman 2011; Polonenko et al. 2020; Behboudian et al. 2021). McClymont et al. (2020) used runoff volume and others to assess the resilience indirectly and make semi-quantitative assessments of improved quality of life caused by urban drainage systems using indicators such as Thermal Comfort. While this method can more directly reflect the system's ability to resist and recover from disasters, the assessment of resilience is semi-quantitative and the study cannot simulate the entire disaster process (Yabe et al. 2022).

There are also some studies that do not focus on resilience, but comprehensively consider the relationship between people and facilities, but these studies still make a series of simplifications. Some studies have calculated the loss of building property caused by flooding based on the surface water depth simulated by the network-surface coupling model or surface overland flow model, reflecting the function of the drainage system in ensuring the safety of residents' property (Carisi et al. 2018; Figueiredo et al. 2018). There are also studies based on simulated water depth and flow velocity to calculate the stability of people and vehicles and the vulnerability of buildings to obtain the threat degree to human life and property (Dong et al. 2022; Xing et al. 2023). However, this type of research does not model human movement behavior, but only models facilities and surface hydraulic processes. There are also some studies that model people's mobility behavior through smartphone-location data (Rong et al. 2023), and some of these studies further calculate people's accessibility to infrastructure (Fan et al. 2022), people's behavior after power outages (Jiang et al. 2016), and so on. However, they also did not simulate the impact of rainfall on people's mobility behavior. All in all, existing research has simplified the modeling of interrelationships between people and facilities. The lack of integrated models of people and facilities is one of the important reasons why drainage system resilience assessments are mostly indirect or semi-quantitative assessments.

In this article, we propose a resilience assessment framework to directly quantify the functionality of drainage systems in sustaining urban mobility and protecting property during rainfall incidents. This framework addresses the issue of existing research making simplifications in the simulation model between people and facilities, and the reliance on mostly indirect resilience assessments. The study develops an integrated model that encompasses urban mobility, flood inundation, and sewer hydrodynamics processes for drainage systems, taking into account processes like surface migration, runoff into pipes, flooding overflow, urban mobility, and residential water usage. Utilizing this model, the study chose Baqiao District of Xi'an in China as the study case area and calculated the resilience of the drainage system under different design rainfall events. Subsequently, the study analyzed the impact of different rainfall characteristics and occurrence time on the resilience of urban drainage systems. The article is presented as follows: Section 2 introduces the resilience assessment and integrated model; Section 3 analyzes the calculation results of resilience under typical rainfall events, the impact of rainfall occurrence time on resilience, and the impact of rainfall characteristics on resilience; and Section 4 presents the research conclusions.

This study developed a dynamic urban drainage system simulator (UDSSimtor) that includes three major modules: urban mobility, surface flood inundation, and sewer hydrodynamics processes. UDSSimtor can simulate the impact of rainfall on people's mobility behavior and full process including rainfall, runoff generation, runoff entering pipes, node overflow, pluvial flood migration, urban mobility, and residential water usage.

First, the agent-based urban mobility model is introduced. Urban mobility in this study refers to the change in location caused by urban residents during or at the end of their commute. Urban mobility is a macro expression and refers to commuting behavior and movement trajectories of each resident. Residents' commuting routes have some individual differences and randomness, but as a whole, there are rules to follow. For example, when the distance between the workplace and residence is very close, residents may prefer to walk to and from work, and if the distance is too far, they may drive to and from work. When mobility is difficult (such as when there is water on the road), residents may cancel some trips, such as outings and shopping. Also residents generally move on the road and tend to choose closer routes to the workplace/residence.

Based on this, the study puts forward some hypotheses: (1) During rainfall, the study only considers the movement of people caused by work commuting, and does not consider the movement of people caused by recreational activities such as outings. (2) The study considers four modes of commuting, walking, riding bicycles, riding electric vehicles, and taking cars or bus (driving, taking a taxi or taking public transportation, etc.). The mode of commute is determined based on the distance between the residential and workplace, and the mode and travel speed of each commuting mode are shown in Table 1. (3) Different land use types correspond to different movement costs. Roads have the lowest access costs, followed by residential and commercial land, and water bodies are inaccessible. When there is no rainfall, residents move along the path with the lowest total move cost, which is recorded as the ‘lowest-cost locus (no rain)’. (4) Considering different water depths correspond to different movement costs, the path with the lowest total move cost changes when it rains, recorded as the ‘lowest-cost locus (current rain)’. (5) After rainfall occurs, if residents do not know the distribution of flooding, they default to moving along the ‘lowest-cost locus (no rain)’. If flooding occurs in front of the path, residents will examine the surrounding environment and may change routes based on the impact of water depth on movement (the cost of movement caused by water depth). People may also move along the original ‘lowest-cost locus (no rain)’, depending on the impact of water depth on the path.

It should be noted that the determination of various costs and the selection of commuting modes have strong subjective factors. The values mentioned in this part are determined based on principles that are consistent with common sense and the results of the questionnaire survey (see Supplementary material for details).

Next, the surface flood inundation module is introduced. The Horton equation is used for infiltration simulation and the algorithm of CADDIES (Guidolin et al. 2016) is used for surface water flow migration simulation. It should be noted that the simulation method of runoff generation and runoff entry pipes used in this study is different from that of traditional sub-catchments simulation method. If the catchment-based modeling method is used, the runoff generated by each catchment flows directly into the corresponding node or another catchment. However, in this study, there is no catchment. After rainfall falls on the cell, the infiltration simulation is performed. The runoff migrates on the surface, and when runoff flows to the cell where the drainage system node is located, if the drainage system still has capacity, runoff will enter the urban drainage systems through the node. The CADDIES model is a surface water depth simulation model based on a metacellular automation, which uses Manning's formula to calculate the flow flux calculations between the metacells, and then, based on the connectivity of cells, calculates the change in the water volume of each cell, updating the depth of each cell at the next moment in time. In terms of the sewer hydrodynamics processes model, the hydraulic process of pipelines, pumping, etc., is simulated based on the Saint-Venant equations.

UDSSimtor is developed based on the SWMM (storm water management model) source code and expands the urban mobility and flood inundation module modules and related interfaces. The coding language is a mixture of C ++ and C.

UDSSimtor's urban mobility, surface flood inundation, and sewer hydrodynamics processes modules are closely integrated, and there is information and data interaction between modules at each step. After rainfall occurs, infiltration simulations are conducted in the flood inundation module, which calculates the runoff volume generated on each cell. The runoff flows through the cell automation-based water flow migration module, and upon reaching the cell where the node is located, it enters the sewer hydrodynamics processes module. The sewer hydrodynamics simulation is conducted based on the Saint-Venant equations. When flooding occurs at a node, the floodwater enters the flood inundation module and continues to infiltrate. The inundation depth on the surface affects residents' travel and commuter trajectories can be obtained through the urban mobility module. Based on this, the research can simulate flood depths and if they exceed danger levels, residents will detour. Then, the locations of residents' workplaces or residences will affect residential water use, which may impact the spatial distribution of urban flooding and in turn affect urban mobility.

After rainfall occurs, the model takes the land use data, elevation data, residential and workplace location data, urban drainage system construction data, etc., as inputs, and the outputs are hydraulic information such as water level and pipe flow of each pipe, inflow and outflow of each node, etc., the water depth time sequences of each cell, as well as the agents' location and detours under each step.

The study assessed the resilience of UDS based on UDSSimtor. One of the critical functions of a drainage system is to eliminate the hazards of flooding, ensuring residential safety, property safety, and maintaining travel order. In this study, resilience refers to the ability of the population to resist and recover from the impacts of flooding. The loss of functionality (or the functionality impairment) has a significant impact on residential safety, property safety, and normal urban mobility.

The rainfall events used in the study consist of two sets. One set is the Chicago design rainfall with five typical return periods of 0.5, 1, 5, 20, and 100 years. The duration of all rainfall events is 2 h and the rainfall occurrence time is set at 0:00 and 6:00. The other set contains 36 design rainfall events with three different rainfall patterns (uniform, unimodal, and bimodal). The rainfall duration includes 2, 6, and 12 h. The rainfall amounts include 2.5, 10, 22.5, and 50 mm, which correspond to light rain, moderate rain, heavy rain, and torrential rain, respectively.

In order to validate the model, the study collected inflow data with hourly precision from wastewater treatment plants, outflow data from two rainwater discharge monitoring outlets, and video data from two cameras.

For surface water depth validation, the difference between the simulation and the actual observation results is less than 5 cm at 68.1% of the moments and the difference is less than 15 cm at all time. For hydraulic validation of the pipes, the Nash efficiency coefficient of inflow to the wastewater treatment plant is 0.85 ∼ 0.91, and the Nash efficiency coefficient of the rainwater discharge outlets is 0.87. For urban mobility validation, we distributed questionnaires to find out the detours of the residents in the case area, and the detour times obtained from the simulation were close to the results of the questionnaire interviews. Detailed model verification results are shown in Supplementary material.

The urban mobility under different Chicago design rainfalls were calculated in this study.

The social resilience of the drainage system under the Chicago design rainfalls was calculated for each return period in the study.

The analysis reveals that the system functionality curve is not monotonically changing during the resistance and recovery process. In the recovery phase, the functionality values of the drainage system exhibit oscillations. The property loss resilience curve displays a single valley, showing an initial decrease in functionality due to flooding, followed by a gradual restoration as the surface water recedes. In contrast, the functionality curve of urban mobility shows multiple valleys, corresponding to the faster recovery cycle. This difference is attributed to the fact that urban mobility is only affected by flooding during commuting hours. During commuting hours, detours due to flooding lead to reduced functionality, which is restored once the commute is completed.

The study finds that 1–2 days after the rainfall event, the functionality of property safety nearly recovers, while that of urban mobility remains impaired. For example, within 12 h (0:00–12:00) of a 5-year rainfall event, the minimum values of the functionality of property safety and urban mobility are 0.825 and 0.912, respectively, with property safety being more severely affected. However, during the evening rush hour (18:00–19:00) of the same day, the functionality of property rises to 0.997, while that of urban mobility is at 0.992, indicating more significant impairment in mobility. One possible reason is that the presence of roadside curbs can delay flooding near houses and buildings by directing water onto roads. This phenomenon exacerbates traffic disruption as pedestrians are forced to detour.

The functionality, a dimensionless variable ranging from 0 to 1, cannot be compared across different dimensions. Therefore, the study conducted an economic conversion of resilience, revealing that the total economic losses from rainfall events with return periods of 0.5, 1, 5, 20, and 100 years are 0.5, 10.2, 113.1, 255.5, and 462.9 million, and the losses caused by traffic obstruction were 0.1, 0.4, 4.2, 8.1, and 10.7 million, accounting for 21.8, 4.0, 3.7, 3.2, and 2.3%, respectively. Except for rainfall with a return period of half a year, the time loss caused by traffic obstructions under each rainfall did not exceed 5%.

In Section 3.1, we discover that for rainfall events with return periods of 1, 5, 20, and 100 years, the proportion of building property loss all exceeds 95%. The phenomenon is partly attributed to the high value of building properties and the fact that property losses caused by heavy rainfall exceed daily GDP which is used to measure the time cost of detours. Additionally, the occurrence time of the simulated rainfall events, which is midnight to 2:00, leads to building property losses but has a lesser impact on commuting due to partial subsidence of the floodwater during peak travel time. For further findings, the study compares the resilience and the economic conversion results of resilience for rainfall events occurring at midnight (0:00–2:00) and before the morning rush hour (6:00–8:00).

Table 4 presents the resilience assessment results and their economic conversions for different return periods and rainfall occurrence time. The occurrence time has a negligible effect on building property loss but significantly affects the time cost of detours (significant level less than 0.05). Detour losses caused by midnight rainfall are much lower than those during commuting times, with proportions ranging from 15.0 to 65.1%. This is because building property loss is calculated based on loss rates and asset amounts, which are not influenced by time. However, commuting occurs at fixed times, and the rainfall occurrence time affects the flooding depth at that moment, thus impacting urban mobility.

As the return periods increase, the proportion of building property losses in total losses is greater. For smaller rainfalls, if the occurrence time is close to commuting hours, the time cost of detours can even exceed building property losses, which cannot be ignored. Moreover, for rainfall events with the same occurrence time but different return periods, as the periods increase, the resilience of property safety decreases monotonically. However, the resilience of urban mobility does not decrease monotonically with increasing return periods. Taking the example of a 0.5-year and a 100-year event during the morning rush hour, the former only affects one commute, and the average commute time increased by 2.3 min. Rainfall with a return period of 100 years affected at least six commutes. The commuting time in the morning and evening peaks on the rainy day increased by an average of 31.1 and 27.3 min, respectively. The average increase time in the subsequent four commutes was 9.04, 7.8, 7.13, and 6.64 min, with serious tailing. If the operation and maintenance emergency department does not take any measures to drain flooding in low-lying areas, commuting will continue to be affected 3 days after the rainfall occurs.

It was found that when it rains at midnight, the expectation of total loss is 101.6 million, and the expectation of annual detour loss is 3.5 million Yuan, accounting for 3.4%. When it rains before the morning peak, the expectation of total loss is 106.8 million Yuan, the expectation of annual detour loss is 8.9 million Yuan, accounting for 8.3%, the property loss is 98.0 million Yuan, and the detour loss is 9.1% of the property loss. The calculations of the building property damage calculations in this study are consistent with similar studies (Li et al. 2022).

It can be concluded that the impact of rainfall occurrence time on resilience is significant for urban mobility and the detour costs caused by a 0.5-year event can even exceed building property losses. Since rainfalls with lower return periods are more likely to occur in cities, the impact of rainfall on urban mobility should not be underestimated.

The study established four precipitation levels: light rain (2.5 mm), moderate rain (10 mm), heavy rain (22.5 mm), and torrential rain (50 mm), as well as three rainfall durations of 2, 6, and 12 h, and three rainfall patterns: uniform, unimodal and bimodal, resulting in a total of 36 simulated rainfall events. When the total rainfall is 2.5 mm, regardless of how the rainfall duration and rain pattern are adjusted, the minimum value of the function (minQ) in each dimension is greater than 0.999.

Light rain has a negligible impact on property safety and urban mobility. Moderate rainfall affects urban mobility with an average detour minQ of 0.998, while the property losses are minimal (average property minQ of 1.000). Correspondingly, the average property losses during moderate rain are 24.3 thousand Yuan, with detour time costs amounting to 161.3 thousand Yuan. During heavy rainfall and torrential rainfall, despite a higher minQ for property safety (0.995 under heavy rain, 0.889 under torrential rain) compared with minQ for urban mobility (0.966 under heavy rain, 0.806 under torrential rain), property losses (3.9 million Yuan under heavy rain, 104.9 million Yuan under torrential rain) exceed detour time costs (1.2 million under heavy rain, 7.1 million under torrential rain).

In terms of rainfall patterns, the study finds that under the same amount and duration of rainfall, unimodal rainfall events have a more substantial impact on drainage systems than bimodal rainfall events, which in turn have a greater impact than uniform rainfall. Under heavy and torrential rain, the average minQ for unimodal events (0.892) is 0.033 less than that for bimodal events (0.925), and the average minQ for bimodal events is 0.018 less than that for uniform events (0.943). Specifically, when we refer to property safety resilience, the impact of rainfall patterns on minQ is consistent with the overall trend. For instance, under torrential rainfall, the average minQ for unimodal events (0.854) is 0.044 lower than that for bimodal events (0.898), which in turn is 0.018 lower than that for uniform events (0.916). This indicates that, despite the same total rainfall amount and duration, the average property loss rate is different. Under torrential rain, the average building property losses in unimodal rainfall exceed that in uniform rainfall by 56.4 million Yuan, and exceed the property losses in bimodal rainfall by 41.5 million Yuan.

In terms of rainfall duration, shorter rainfall durations result in greater impacts on urban drainage systems. When the total rainfall amount is fixed, rainfall with shorter durations is characterized by ‘short duration, high intensity’, which generates large amounts of runoff in a brief period. This can exceed the conveyance capacity of drainage systems, resulting in urban flooding. The conclusion that extreme rainfall with short duration will lead to more severe flooding is consistent with similar studies (Fowler et al. 2021). Notably, uniform heavy rainfall with a duration of 12 h yields a minQ of 0.999, higher than that of any 2-h moderate rainfall events, regardless of the rainfall pattern (minQ ranging from 0.996 to 0.999), and the minQ under uniform rain pattern and torrential rain lasting 12 h is 0.956, which is greater than the minQ (0.944) under unimodal heavy rain lasting 2 h. Despite the common practice of classifying rainfall events and corresponding disaster response measures based on total rainfall volume, this approach does not adequately reflect the severity of urban flooding. The results suggest that rainfall classification should also incorporate rainfall duration, pattern, and occurrence time, so as to obtain a more appropriate disaster classification and take corresponding response measures to provide better support for urban disaster management.

The urban drainage system has multiple functions such as timely transportation and treatment of rainwater and sewage, elimination of waterlogging, and protection of water environment health. However, rainfall shocks can affect the resilience of drainage systems in many aspects, such as increasing the use time of pumping stations and increasing its probability of failure, as well as non-point source pollution leading to poor water quality in receiving water bodies (Adams et al. 2020; Xu 2021).

In terms of the urban traffic disruption caused by flooding, the study only considered the detour time cost due to traffic obstruction. The study also statistically found that the agents did not walk to the area where the water depth could threaten their lives (the agent would choose to detour when encountering such an area), but the probability of falling down and being subjected to injury and mental illness would change in the rainfall events (Du et al. 2010; Bich et al. 2011). However, there is a lack of probabilistic models to describe the relationship between the water depths and falling and there is also a lack of research on detour probability based on social psychology, so it is difficult to quantitatively assess health damage. This has led studies to underestimate the cost of traffic disruption.

This study obtained some quantitative results, such as the expectation of annual detour loss being 9.1% of the expectation of annual property loss. However, different cities have different road distribution, urban layout, asset characteristics, etc., and quantitative results, such as the proportion of detour losses, will change. If resilience assessment or calculation of property losses and detour costs for other cities is needed, data should be collected which include job and residential location, drainage system construction data, drainage system monitoring data, flood depth monitoring data, surface elevation data, land use data, road network data, and building data to conduct a resilience assessment and loss calculation for the city. This methodology can assess the impact of flood from the perspectives of property loss and urban mobility. Quantitative assessment results such as loss amount and commuting time change ratio provide a basis for their decision-making, including whether to use some traditional and non-traditional measures, such as expanding pipes, building real-time flooding maps, working from home, etc.

Urban drainage system resilience assessments are mostly indirectly quantitative or qualitative, while more effective disaster management requires direct quantitative assessments of resilience. To address this need, we proposed a resilience assessment method to directly and quantitatively assess the resilience of urban drainage systems in terms of protecting residents' property safety and ensuring the normal operation of urban mobility. The study also constructed a functionality loss assessment method to calculate losses in different aspects so that resilience in different dimensions can be compared. Existing models cannot support this assessment method. To address this need, the study established an integrated urban drainage system model coupling urban mobility, flood inundation, and sewer hydrodynamics processes. On this basis, we constructed multiple rainfall events and analyzed the impact of rainfall occurrence time, rainfall duration, and other rainfall characteristics on resilience.

The study took Baqiao District, Xi'an City, Shaanxi Province, China as a case area to evaluate the resilience of the urban drainage system under various rainfall events. The average percentage increase in commuting time under different return periods of rainfall ranged from 6.4% (return period of half the year at midnight) to 203.9% (return period of 100 years before the morning commuting peak). The assessment for the Baqiao district shows that while property losses are generally greater than the disruption to traffic order under rainfall events, the latter can exceed the former when the return period is short (biannual) and the rainfall occurrence time is close to peak commuting hours. The annual expected loss in urban mobility is 9.1% of the annual loss of property if the rainfall is timed near the morning commuting peak. In such cases, measures such as enhanced drainage or the use of flood barriers can mitigate the impact on urban traffic, and some non-traditional measures, such as building real-time flooding maps and working from home, may also be effective in reducing urban mobility losses. Additionally, the study indicates that traditional rainfall classifications based solely on precipitation may not fully represent the severity of the rainfall impact, which is also influenced by rainfall patterns and duration. The findings suggest a comprehensive approach to classifying rainfall events for disaster management, incorporating factors such as intensity, pattern, and duration.

However, our study only considers the aspects of life, property safety, and urban mobility. Future work should aim to incorporate additional aspects of resilience, such as water quality and health risks, to provide a more holistic assessment.

Data cannot be made publicly available; readers should contact the corresponding author for details.

The authors declare there is no conflict.