## Abstract

Manholes are important structures in urban storm drainage systems connecting roads and underground drainage networks, and they are also an important part of the research on improving urban resistance to storm flooding. Due to cost and space constraints, most of the existing experimental data on manholes come from scale model experiments obtained by scaling according to Froude's similarity criterion, and there is a lack of validation based on full-size experimental data. This also leads to inconsistencies in the form and parameter values of the manhole flow exchange equations derived from different experiments. To remedy this deficiency, a full-scale urban drainage engineering physics model was developed in this study with the aim of investigating the flow exchange of surface water as it flows through manholes into the sewer system. Experiments were conducted under steady flow conditions and compared with predictions from the existing models. The results show that the predictions of the existing model deviate significantly from the measured values when the flow is between free weir flow and submerged orifice flow. Therefore, we constructed a weighting equation based on weir and orifice flows and found that the weighting coefficients decayed exponentially during the transition from weir to orifice flow.

## HIGHLIGHTS

A full-scale physical model of urban drainage was developed in the vicinity of the manholes.

A weighted equation based on a combination of free weir and submerged orifice equations is proposed to represent the experimentally measured rate of flow exchange through a manhole as surface water flow enters the sewer system.

The coefficients in the equation develop exponentially with the flow regime.

## INTRODUCTION

In recent years, the frequency and scale of global urban flooding events have shown a yearly increase (Ceola *et al.* 2014; Liu *et al.* 2020) due to multiple factors such as changing climatic conditions (Centre for Research on the Epidemiology of Disasters United Nations Office for Disaster Risk Reduction 2020), sprawling cities (Liu *et al.* 2020), and prompting the optimization and improvement of theories of urban flooding causation analysis and urban drainage theory (Rubinato *et al.* 2017). The urban surface is usually characterized by high impermeability (Fletcher *et al.* 2013), and the collection, transfer, and transportation of surface runoff are mainly undertaken by the drainage network system that is situated underground. When there is massive precipitation, urban flooding may occur once the rainfall exceeds the capacity of the drainage system (Rubinato *et al.* 2017). In order to describe the evolution of urban flooding and to assess the risk of flooding in cities (Mark *et al.* 2004; Martins *et al.* 2018), this work explores the process based on the dual drainage hydraulic model, which has been widely used in engineering (Schmitt *et al.* 2004; Smith 2006; Beven & Hall 2014; Fraga *et al.* 2017). The basic philosophy of the dual drainage model is to describe surface runoff and pipe flow in a drainage network located underground as two separate processes, which interact with each other through drainage structures, such as manholes (Leandro & Martins 2016). In such models, the computational node representing the manhole/gully couples the flow interaction processes of surface free flow and subsurface pipe flow (Rubinato *et al.* 2017); hence, the accuracy of the steady-state linking discharge equations at the manhole has a significant impact on the accuracy of the overall model system.

The most common flow exchange scenario at the manhole is flow from the surface through the manhole into the subsurface, a process that occurs in almost all urban drainage systems (Chen *et al.* 2007; Rubinato *et al.* 2017). The form of flow exchange at manholes in this process can be broadly classified into three cases: weir flow, submerged weir case, and flooded orifice outflow, depending on the depth of water flowing at the surface (Chen *et al.* 2007; Rubinato *et al.* 2017; Buttinger-Kreuzhuber *et al.* 2022). Therefore, the flow interaction process at the manhole is commonly quantified by equations in the form of a weir/porthole.

The specific form of the linking equations and the values of the parameters can be determined experimentally. Constrained by the cost and the limited space available in the laboratory, most teams use the construction of numerical models to simulate the actual situation and calibrate the numerical results with scaled model experiments. Despite the great breakthroughs made in recent years in improving the accuracy of numerical models (Martins *et al.* 2018), simplifying the numerical models themselves (Leandro *et al.* 2009), and optimizing algorithms to reduce computational effort (Schmitt *et al.* 2004), researchers have not yet reached a unified opinion on the specific form of the flow equations describing the flow at the manhole and the reasonable range of values for the weir/port coefficients used to describe the flow interaction (Li *et al.* 2019). Leandro *et al.* (2010), Lee *et al.* (2012), and Rubinato *et al.* (2017) used geometric scaling of 1/30, 1/20, and 1/6 for homogeneous physical scenarios according to Froude's similarity criterion, respectively, and the range of weir flow or orifice coefficients obtained experimentally at the manhole showed significant disparities. In addition, the validation of the equations and parameter takeoffs of the existing models are mostly obtained based on the scaled scaling models, which lack the support of full-scale experimental data (Li *et al.* 2019).

In order to address this gap, a full-scale physical model is developed in this paper to realize the flow interaction scenario of a single manhole and its surrounding appurtenances (pavement and underground pipes) in an urban drainage system reproduced in the laboratory, and experiments are conducted to validate and evaluate different equation forms and parameter takeoffs. To complete the steady-state experiments conducted under different flow and exchange conditions and to evaluate the applicability of the equation form and parameter takeoffs in representing flow exchange, the covers of the manholes in the experiments have been removed in advance.

## METHODOLOGY

### Setup

*et al.*'s design (Rubinato 2015; Rubinato

*et al.*2017), consists of an unsloped downspout and a shallow tank, corresponding to the underground and surface systems of urban drainage, respectively, both connected by a manhole (Figure 1). The difference is that, on the one hand, the testbed sink mentioned in this paper is unsloped, restoring the manhole located on the horizontal pavement in the actual situation; on the other hand, unlike the scale model, the structure simulating urban drainage in the testbed designed in this paper is built exactly 1:1 according to the actual engineering dimensions to exclude the error caused by the scale effect (Li

*et al.*2019).

A prefabricated plastic manhole is directly purchased for urban drainage project construction with an inner diameter of 700 mm; according to the relevant regulations of urban drainage in China, the downspouts are selected to be built with the specifications appropriate to the above manhole with an inner diameter of 300 mm. The gutter bed is aligned with the top of the manhole and designed according to the width of a single lane, with a width of 3.5 m and a length of 7 m. The gutter bed is 1 m above the water level at the inner bottom of the pipe. To ensure strength, the material of both the sink and the pipe is spiral submerged arc welded steel pipe. The cover of the manhole has been removed in advance, thus allowing flow interaction between the water in the flume (surface system) and the pipe (underground system) to occur through the manhole. The flow into the above-ground and underground systems is controlled by valves and continuously monitored by corresponding electromagnetic flowmeters (–), respectively.

The accuracy of each measurement device has been verified by field calibration after the installation was completed, and the specific parameters are shown in Table 1.

Equipment . | Parameter . | Value . | Parameter . | Value . |
---|---|---|---|---|

Corresponding electromagnetic flow meter () | Model | DKLD-DN-300 | Range of measurement | 25.45–1,300 m^{3}/h |

Corresponding electromagnetic flow meter (, ) | Model | DKLD-DN-300 | Range of measurement | 25.45–1,300 m^{3}/h |

Corresponding electromagnetic flow meter () | Model | LDTHS-500B10177JYLF62015 | Maximum measurable flow | 7,069 m^{3}/h |

Ultrasonic water level meter () | Model | HC175F30GM | Range of measurement | 20–2,000 mm |

I-2000-V1 | ||||

Ultrasonic water level meter () | Model | HC175F30GM | Range of measurement | 20–2,000 mm |

I-2000-V1 | ||||

Pressure sensor () | Range of measurement | −10 to 10 kPa | Output signal | 4–20 mA |

Pressure sensor () | Range of measurement | −0.1 to 1 MPa | Output signal | 4–20 mA |

Pressure sensor () | Range of measurement | −0.1 to 0.1 MPa | Output signal | 4–0 mA |

Equipment . | Parameter . | Value . | Parameter . | Value . |
---|---|---|---|---|

Corresponding electromagnetic flow meter () | Model | DKLD-DN-300 | Range of measurement | 25.45–1,300 m^{3}/h |

Corresponding electromagnetic flow meter (, ) | Model | DKLD-DN-300 | Range of measurement | 25.45–1,300 m^{3}/h |

Corresponding electromagnetic flow meter () | Model | LDTHS-500B10177JYLF62015 | Maximum measurable flow | 7,069 m^{3}/h |

Ultrasonic water level meter () | Model | HC175F30GM | Range of measurement | 20–2,000 mm |

I-2000-V1 | ||||

Ultrasonic water level meter () | Model | HC175F30GM | Range of measurement | 20–2,000 mm |

I-2000-V1 | ||||

Pressure sensor () | Range of measurement | −10 to 10 kPa | Output signal | 4–20 mA |

Pressure sensor () | Range of measurement | −0.1 to 1 MPa | Output signal | 4–20 mA |

Pressure sensor () | Range of measurement | −0.1 to 0.1 MPa | Output signal | 4–0 mA |

### Flow control and test configuration

To make the flow easier to control, the water that forms the surface flow is pumped from the underground reservoir into the inlet tank, where it passes through a manhole after being fully developed. A portion of this passes through the manhole into the underground system, while the other portion continues along the surface and enters the outlet tank. The water in both the underground system and the outlet tank is recycled into the reservoir in a free-flowing manner, creating a cycle. To ensure that the flow in the pipes is in a free state, the valves on the pipes are fully open.

*v*is the surface incoming flow velocity in m/s;

*Q*is the incoming flow rate, which can be obtained from the degree of flow meter , and the unit is taken as ;

*A*is the flow section area in , and is taken in the experiment, where is the shallow flume bed width in m;

*h*is the incoming water depth in . Therefore, the equation of the surface flow rate and flow velocity in the experiment is:

The value of the incoming water depth *h* can be obtained from the sensors , , and , and the results of these three ways of taking values are compared in Section 4.1 of this paper.

From Equation (2), the incoming flow rate is related to both the incoming flow rate and the incoming water depth on a road surface without slope. Therefore, the incoming flow rate can be changed by controlling the valve and adjusting , so that the water depth is always maintained at the set depth, thus obtaining the change of surface and subsurface flow interaction occurring through the manhole under different flow rates corresponding to the same incoming water depth; furthermore, by changing the set incoming water depth, the change of flow exchange occurring at the manhole under different conditions of incoming road surface flow can be obtained.

### Flow exchange equations at the manhole

When the flow is from the surface to the ground, the flow exchange at the manhole is usually described in the form of weir flow or orifice flow, and these two equation forms are chosen conditional on whether the pipe network head exceeds the surface elevation () (Rubinato *et al.* 2013).

#### Free weir scenario

*et al*

*.*(2005) have pointed out that the actual flow exchanged at the manhole is deflected under high-velocity flow, the velocity head is assumed to be negligible in most urban flood models. Therefore, the corresponding equation is:where is the flow rate exchanged at the manhole (), specifying that the direction of flow interaction is from the surface into the pipe network when and

*vice versa*when . is the manhole diameter ().

*h*is the depth of incoming water at the surface (). is the flow coefficient, characterizing the energy loss due to viscous effects. The value of this coefficient varies from researcher to researcher (Table 2).

Source . | Type of flow . | Parameter settings . | Equation . | Parameter value . |
---|---|---|---|---|

Rubinato et al. (2017) | Free weir | Equation (3) | ||

Submerged weir | Equation (4) | |||

Submerged orifice | Equation (5) | |||

Buttinger-Kreuzhuber et al. (2022) | Free weir | Equation (3) | ||

Submerged weir | Equation (4) | |||

Submerged orifice | Equation (5) | |||

Leandro et al. (2010) | – | – | Equation (6) |

Source . | Type of flow . | Parameter settings . | Equation . | Parameter value . |
---|---|---|---|---|

Rubinato et al. (2017) | Free weir | Equation (3) | ||

Submerged weir | Equation (4) | |||

Submerged orifice | Equation (5) | |||

Buttinger-Kreuzhuber et al. (2022) | Free weir | Equation (3) | ||

Submerged weir | Equation (4) | |||

Submerged orifice | Equation (5) | |||

Leandro et al. (2010) | – | – | Equation (6) |

#### Submerged weir scenario

In this case, according to the relationship between the flow depth () of the incoming surface flow and the size parameter of the manhole (, where is the manhole area ()), the relationship can be described by the submerged weir case formula and the flooded orifice formula, respectively (Rubinato *et al.* 2013; Fernández-Pato & García-Navarro 2018). For circular manholes, the size parameter .

*b*is the height from the inner bottom of the piping system to the surface water plane ().

*H*is the head of flow in the piping system ().

#### Orifice scenario

*.*(2010) have proposed an equation describing the flow from the surface to the subsurface system through a circular manhole, which is expressed as follows:

Unlike the previous equation, this equation is used in such a way that it only requires that the flow at the manhole is entering the pipe system from the surface, without concern for the relationship between the water level in the manhole and the surface elevation.

## EXPERIMENTS ON SURFACE FLOW INTO NON-SURCHARGED SEWER

To evaluate the effectiveness of the different equations in Table 2 in describing the flow exchange at the manhole at a real scale and to compare the applicability of different values of each flow coefficient, a series of experiments were conducted using the experimental equipment mentioned in Section 2.1. During the experiments, the piping system is in a completely open state, and no independent incoming flow is set up in the piping in order to ensure that the flow at the manhole always enters the piping system from the surface. The experiments were conducted by adjusting the incoming flow rate from the surface system and the outflow downstream of the surface, thus controlling the flow velocity () and depth () of the incoming surface flow and recording the flow exchange that occurred after the flow reached a steady state.

The head () in the manhole is estimated by the time average of the pressure readings at .

To clarify the reasonable measurement location and the method of surface flow depth (), the measurement values (, , and ) are obtained by three different measurement locations and evaluated by comparing the calculation results after substitution into Equations (3)–(6). is the time average of ultrasonic water level meter readings arranged in the direction of the surface incoming flow. and are measured by the pressure transducers –arranged near the manhole. is the time average of corresponding to the depth of flow, and is the time average of corresponding to the depth of flow.

All data were obtained as time averages recorded continuously for 10 min after the flow rate reached stability.

Table 3 shows the variation of the independent variables controlled in the experiment and the corresponding flow exchange at the manhole. In addition, geometric scaling parameters based on the ratio of the surface flow depth () to the manhole diameter () are given in order to facilitate a better generalization of the results.

Surface flow depth . | Surface flow velocity . | Flow exchange . | Pipe network head . | Scaled flow depth . |
---|---|---|---|---|

[0.389, 0.744] | [0.115, 0.136] | [0.502, 0.786] | ||

[0.414, 0.453] | [0.207, 0.217] | [1.058, 1.153] | ||

[0.317, 0.369] | [0.215, 0.222] | [1.127, 1.206] | ||

[0.213, 0.232] | 0.231 | [1.298, 1.323] | ||

[0.173, 0.176] | 0.238 | [1.388, 1.393] | ||

Surface flow depth . | Surface flow velocity . | Flow exchange . | Pipe network head . | Scaled flow depth . |
---|---|---|---|---|

[0.389, 0.744] | [0.115, 0.136] | [0.502, 0.786] | ||

[0.414, 0.453] | [0.207, 0.217] | [1.058, 1.153] | ||

[0.317, 0.369] | [0.215, 0.222] | [1.127, 1.206] | ||

[0.213, 0.232] | 0.231 | [1.298, 1.323] | ||

[0.173, 0.176] | 0.238 | [1.388, 1.393] | ||

*et al.*2017), in more extreme rainstorms or floods, the water depth on the road is much deeper than one would expect (Doong

*et al.*2016; Zhou

*et al.*2022). Therefore, we have also designed for an extreme situation where the water depth on the roadway reaches 40 cm. The equipment used in the experiment corresponds to the size parameter . According to the classification criteria in Section 2.3, the case of is free weir flow, the case of is close to submerged weir flow, and the rest is submerged orifice flow, which basically coincide with the experimental phenomenon (Figure 4). The power of the water pump is basically unchanged, so the adjustable range of flow rate is small in the case of higher incoming water depth (). Figure 4 also implies that there exists a partial range of flows to satisfy: for the same depth of inlet, if the street surface incoming flow is greater, less flow enters the sewer through the manhole. This phenomenon is consistent with the view proposed by Djordjević

*et al.*(2005).

## DISCUSSION

### Evaluation of surface–subsurface link equations

*et al.*(2017) and the flow parameter values given by Buttinger-Kreuzhuber

*et al.*(2022) are close to each other, both of which have a relatively large deviation from the measured values (Figure 6(a)) and underestimated the discharge capacity of the manhole (). The method given by Leandro

*et al.*(2010) is in better agreement with the measured results for the free weir and orifice states but deviates significantly in the description of the flow states in between. Although the model of Rubinato

*et al.*is lower than the experimentally measured values at their recommended parameters, the measured values are still between the flow ranges estimated by their model for free weir and orifice flow when extending the use of the model for each flow regime to the entire discharge process (Figure 6(b)).

### Equation for the weir flow–orifice transition state

*et al.*(2010) deviate significantly from the measurements is located between the weir and orifice flow states, we define this interval as the transition interval from free weir flow to orifice flow. To characterize this transition process, an achievable solution is to construct the corresponding weight coefficients and based on the equations given by Rubinato

*et al*. (2017) for the free weir flow and the submerged orifice flow, correcting the calculation of the transition process. Assuming that the flow exchange at the manhole in the weir–orifice transition state satisfies the following relation:where represents = Equation (3) and represents = Equation (5). and should be related to the incoming water depth and the size of the manhole, and both are dimensionless parameters. It should be noted that the calculated values for the free weir flow model given by Rubinato

*et al.*are higher than the value of orifice flow for the case of = 0.1 m, contrary to the other conditions. To ensure that the value of is always between 0 and 1, the value of at this point should be taken as its reciprocal (the first point in Figure 7). To determine the values of and , the flow coefficients it is recommended to use the mid-values of the corresponding intervals in Table 2 when calculating , and for the same considerations, the flow coefficients in were obtained in a similar way, i.e., = 0.54 and = 0.167. Combined with the scaled flow depth (Figure 6), this gives:

This means that the weight coefficient , which represents the free weir flow during the transition, decays exponentially with the increase of the dimensionless scale .

*et al.*(2017) with

*α*and

*β*(Figure 8(a)) and compared it with that of Leandro

*et al.*(Figure 5). The corrected results describe the free orifice flow and the transition process more closely to the measured values and can provide a more accurate prediction of the amount of flow discharged from the manhole under the test conditions in this paper (Figure 8(b)). It should be noted that, subject to the limitations of the equations used to describe the orifice flow and free weir flow in the vicinity of the manhole, in the case of free weir flow, the value of should be taken as the inverse of the value of when it is taken as small as , and in the test conditions of the present paper, the critical condition for deciding whether or not to take the inverse value of

*α*lies at a point where is slightly greater than 1/7.

## CONCLUSION

- (1)
According to the existing models that distinguish different flow states of flow at the manhole from the surface into the subsurface, by selecting appropriate flow coefficients, most of the models can predict the flow exchange occurring at the manhole well in the case of free weir flow, but with the increase of surface flow depth, the model predictions of submerged weir case and flooded orifice flow show large deviations from the actual measurements. The model given by Leandro

*et al*. (2010) does not distinguish between flow states and describes the free weir and submerged orifice cases closer to the measured values but is not suitable for predicting the cases in between. - (2)
The state between free weir flow and submerged orifice is defined as the weir–orifice transition state, and the transition state equation is constructed based on the equations for free weir flow and submerged orifice by introducing weighting coefficients and to describe the flow exchange () in the transition state. According to the measured results, the weight coefficient , which represents the weir flow, decays exponentially with the increase of the characteristic water depth (Figure 9).

- (3)
The experimental results show that the transition state equation accurately describes the whole process from free weir flow and submerged weir flow to orifice flow in the manhole drainage process. Influenced by the adopted computational models of weir flow and orifice flow, its parameter should be taken as the inverse in the low condition.

- (4)
The introduced weight coefficients and are only related to the characteristic water depth () of the surface flow, so they are universal and can be directly incorporated into any double drainage model to improve the accuracy of the model prediction.

## ACKNOWLEDGEMENTS

The study was supported by the IWHR Research & Development Support Program (WH0145B022021, WH0145B042021, JZ110145B0022023 and JZ110145B0012021) and the MWR Major Science & Technology Program (SKS-2022007).

## DATA AVAILABILITY STATEMENT

All relevant data are included in the paper or its Supplementary Information.

## CONFLICT OF INTEREST

The authors declare there is no conflict.

## REFERENCES

*Novatech 2010-7ème Conférence internationale sur les techniques et stratégies durables pour la gestion des eaux urbaines par temps de pluie/7th International Conference on Sustainable Techniques and Strategies for Urban Water Management.*GRAIE, Lyon, France, pp. 1–8

*13th edition of the World Wide Workshop for Young Environmental Scientists (WWW-YES-2013)-Urban waters: resource or risks?*HAL-ENPC, France