Quantifying sediment deposition in sewers through hydraulic performance analysis Open Access

This study investigates the effects of fixed sediment deposition on the hydraulic characteristics of sewer flow to support the diagnosis of sewer blockage. Sediment beds extending over the entire pipe (i.e., continuous deposition) and localized deposits were examined under different flow rates and outlet control conditions. Continuous deposition changes the cross-sectional area of the sewer pipe, while localized deposits act similarly to short bottom obstructions. The energy losses induced by a localized deposit at various locations were found to be nearly identical, particularly in cases with backwater effects. To illustrate the relationships between the flow rate, water level, and deposit characteristics, hydraulic performance curves can be developed. The inverse problem, which involves estimating parameters characterizing sediment deposition using observed flow rates and upstream and downstream water levels, can be solved by matching hydraulic performance curves with numerous scatter points from actual monitoring data to obtain the best fit. As there is a wide range of sediment deposition patterns that result in the same overall energy loss, the concept of equivalent sediment bed height is introduced to be applied in real-world scenarios.

A

flow cross-sectional area, m²;

A_c

flow cross-sectional area corresponding to the critical depth y_c, m²;

D

pipe diameter, m;

g

acceleration of gravity, m/s²;

h

height of sediment, m;

F_r

Froude number;

H

water level of the manhole, m;

ΔH

total head difference between the upstream manhole and the registered location near the pipe end, m;

l

length of sediment, m;

L

pipe length, m;

n

composite roughness;

n_s

sediment bed roughness;

n_w

pipe wall roughness;

NSC

Nash–Sutcliffe coefficient;

P

wetted perimeter, m;

P_s

wetted perimeter related to the sediment bed, m;

P_w

wetted perimeter related to the pipe wall, m;

Q

approaching flow rate, m³/s;

Q_nmax

maximum steady, uniform flow discharge that the sewer can convey when the flow attains a full-pipe condition, m³/s;

Q*

dimensionless approaching flow rate, Q*=Q/Q_nmax;

S₀

pipe slope;

S_f

friction slope;

T_c

width of the water surface corresponding to the critical depth y_c, m;

x

longitudinal coordinate, m;

x_b

deposit location, m;

y

flow depth, m;

y_c

critical depth at localized deposit location, m;

y_dm

flow depth above pipe invert at pipe outlet, m;

Y

water level in the pipe, m;

Y_n

normal water level in the pipe, m;

Ŷ

calculated the value of the pipe water level, m;

Y̅

average value of the measured water level in the pipe, m;

ΔY

upstream and downstream water level difference, m;

z

elevation difference between the pipe invert and the bottom of the manhole, m;

ζ

coefficient for inlet head loss

d

downstream of the pipe system;

u

upstream of the pipe system;

After prolonged periods of continuous sediment deposition and erosion in the sewer, the sediment height may eventually reach an equilibrium state (Lange & Wichern 2013; Berzio et al. 2017; Tang et al. 2020). During dry weather conditions, with increasing accumulation time, sediments undergo cohesion, consolidation, and organic matter accumulation, thereby becoming resistant to erosion and flushing, which significantly reduces the hydraulic capacity of sewer systems (Butler et al. 2003; Ota & Nalluri 2003; Jain & Kothyari 2009; Li et al. 2013; Seco et al. 2014; Regueiro-Picallo et al. 2020). Substantial research efforts have been devoted to investigating sediment deposition, transport, and erosion within sewer pipelines, including studies by Perrusquía (1991), Ashley & Verbanck (1996), Bertrand-Krajewski et al. (2006), and Banasiak & Verhoeven (2008), among others. The majority of these studies have focused on elucidating the mechanisms of solids movement, thereby establishing a robust theoretical foundation for understanding particulate matter transport processes. However, a critical challenge in sewer maintenance and management remains the development of effective diagnostic methodologies for quantifying the extent of sediment deposition and blockage.

Deterministic sediment transport modeling and the application of numerical models serve as valuable tools for estimating the spatial distribution of deposition in sewer systems and managing sewer systems effectively (Mark et al. 1996; Mannina et al. 2012; Murali et al. 2019). In recent years, there have been some studies on predictive sediment transport modeling using data-driven approaches such as artificial neural networks (Ebtehaj & Bonakdari 2013). In spite of significant advances in sediment transport mechanisms, however, the challenges to reliable sewer sediment modeling persist due to the complexity arising from the variability of particle properties and their interactions during the motion process (Murali et al. 2019). Burgan (2022), through long-term observations, demonstrated that sediment data exhibits significant seasonal fluctuations. Traditional numerical models require precise calibration of particle properties and boundary conditions, yet field monitoring data remains scarce. In addition, real-time monitoring data have not been systematically leveraged to quantify deposition parameters, hindering smart decisions. Therefore, for maintenance purposes, an initial assessment of the overall characteristics of the sediment bed in sewers is essential, and direct monitoring and/or diagnosis may then emerge as an effective strategy.

Recent advancements in monitoring technologies have facilitated improved sewer management. Smart monitoring systems are capable of providing real-time data that include water levels, flow velocities, and a variety of water quality parameters. Proper analysis of the observed data enables operators to identify and diagnose aberrant operational conditions. In sewer networks, the detection of anomalies in the patterns of pump station inflow can be utilized to detect sewer blockages (Januszek et al. 2021). With the proper deployment of monitoring sensors, real-time blockage detection can be achieved through the use of frequency domain analysis and phase portraits (Hamilton 2023). For individual sewer pipes, Stevens & Schutzbach (1998) developed a regression-based method utilizing an iterative curve fitting to characterize flow monitoring data according to Manning's equation for sewer obstruction detection. This technique has proven to be effective as a straightforward, intuitive tool for inferring sewer performance from flow data in certain scenarios, as confirmed by Enfinger & Kimbrough (2004).

Smart monitoring of sewer systems has become increasingly prevalent in China, with a primary objective being the assessment of sewer sedimentation status through the monitoring of two fundamental hydraulic parameters – water level and flow rate – at upstream and downstream manholes. The method relies on a thorough understanding of the hydraulic performance in the context of immobile deposition. Sedimentation changes the surface condition of the pipe, causing variations in pipe roughness that influence sediment transport capacity (Lange & Wichern 2013; Berzio et al. 2017; Regueiro-Picallo et al. 2020). Therefore, for flow in sewers with a sediment bed, it is imperative to accurately account for the shear stress distribution, which arises from composite roughness, in order to correctly estimate the total shear force (Knight & Sterling 2000; Berlamont et al. 2003). Utilizing a composite roughness resistance factor simplifies open-channel flow computations to one-dimensional analysis, and various methods have been documented, as reviewed by Yen (2002).

Flow delivery curves for a prismatic, mild-slope canal connecting two reservoirs experiencing varying water levels were delineated by Chow (1959). These curves are synthesized into a universal chart that offers a summarized representation of potential flows in a channel for all possible combinations of levels. Yen & Gonzalez (1994) further developed the delivery curves by proposing a method known as the hydraulic performance graph (HPG), which captures the dynamic interplay between water surface elevations at either end of a river segment under varied constant discharge scenarios within the context of gradually varied flow conditions (Yen & González-Castro 2000). The HPG method is also applicable to sewer flow analysis (Yen 2001; Hoy & Schmidt 2006). Special consideration of the transition from gravity flow to full-pipe flow must be incorporated into the HPG for broader applicability (Zimmer et al. 2013).

Flow in sewers in the presence of bed elevation changes or bottom obstructions has been studied by Dey (1998) and Yang et al. (2024), using one-dimensional theoretical analyses based on the control volumes for different flow regimes, which involved an investigation into the interrelationships between hydraulic characteristics and boundary conditions. However, unresolved challenges persist. First, the effects of different fixed sediment types (continuous deposition and localized deposits) and the spatial distribution of sediments on the hydraulic performance of sewers are not known. Second, the hydraulic response of localized deposition to the sewer under downstream backwater effects has received less attention. Furthermore, the current techniques for diagnosing deposition parameters in sewers are not yet sufficiently developed.

This study aims to quantitatively analyze the hydraulic performance of sewer pipes with various patterns of fixed deposited beds and explore the inverse problem of determining the characteristic scales of the deposition based on the observed hydraulic behavior. Systematic laboratory experiments were conducted to develop HPGs for two typical scenarios: continuous deposition and localized deposits. The experiments considered various factors, including flow rates, deposition heights, lengths, locations, and outlet controls. To address the inverse problem of characterizing sediment deposition, a regression-based approach was proposed that utilizes flow rates and water levels measured upstream and downstream of the deposition.

Two types of sediment deposition were examined: continuous sediment bed along the pipe, and localized deposit at a specific segment of the pipe. The sediment deposition was composed of sand particles with an average size of 1.0 mm. The deposition height was 20.0 or 40.0 mm, with a length of 1.00, 2.00, or 8.15 m, as given in Table 1. The continuous deposition bed roughness n_s, 0.0229 and 0.0201 for two deposition heights of 20.0 and 40.0 mm, respectively, was determined according to full-pipe flow experiments. The flow rate varied from 3.0 to 11.0 L/s under various downstream conditions.

The modeling experiments were carried out in gravity-dominated free-surface flow, which satisfies the Froude number similarity principle, and the Reynolds number (R_e > 10⁴) was much larger than 4,000, which aligns with the hydraulic conditions of actual sewer pipes. In order to investigate the hydraulic performance under different depositional conditions, three scenarios were set up. In scenario A, tests were conducted to establish benchmark flow characteristics of the sewer pipe without sediment deposition. Scenarios B and C investigated continuous sediment beds and localized deposits, respectively. Although fixed deposition may not capture all the complexities of real sewer systems, it nonetheless provides valuable fundamental insights into hydraulic performance.

The experimental procedure is outlined as follows: (1) Introduce water at a steady low flow rate of approximately 2.0 L/s, ensuring the calibration and readiness of the measurement apparatus. (2) Gradually increase the flow rate to the predetermined value (3.0 or 5.0 L/s) and await the attainment of a stable flow state. Measure the water depth in the manholes and along the pipe utilizing pressure transducers and/or wrapped measuring tapes. (3) Upon acquiring the necessary data, the measurement under the current flow rate is concluded. (4) Repeat steps (1)–(3) for a fresh set of measurements of the predetermined flow rate. (5) When the maximum water depth in the test pipeline reaches 0.82D, denoting full-pipe flow as per established criteria (Chow 1959; Yen 2001; Hager 2010), the measurement of this scenario is concluded. To ensure experimental reproducibility, each test case was replicated a minimum of three times.

The presence of a continuous sediment bed significantly alters the cross-sectional shape of the flow, as shown in Figure 1. The height of the sediment bed is a pivotal factor influencing the flow. In the scenario of a free outflow condition with an approaching flow rate of Q = 7.0 L/s (Q*=Q/Q_nmax = 0.54, where Q_nmax is the maximum uniform flow capacity, i.e., the maximum steady, uniform flow discharge that the sewer can convey when the flow attains a full-pipe condition), a notable increase in the free surface elevation and upstream manhole water level is observed as the height of the sediment bed h increases from 0 to 20.0 mm and subsequently to 40.0 mm. It should be noted that the roughness of the sediment bed surface differs from that of the sewer pipe's inner wall. Therefore, composite roughness constitutes another pivotal factor influencing the flow.

For small slopes and large lengths of sewer pipes, the upstream may be at normal water level Y_n. Therefore, at the same flow rate, when the downstream water level changes, it does not affect the upstream water level, and some or all of the hydraulic performance curves in Figure 3(a) can be described as straight lines. When the downstream water level is held constant, an increase in flow rate and sediment bed height significantly raises the upstream water level, making the system susceptible to surcharging. It should be emphasized that the scope of this study is limited to free-surface flow. Nonetheless, the described analytical framework has the potential to be adapted to surcharged conditions, and the transition from free-surface to pressurized flow can also be estimated using linearization techniques, as suggested by Zimmer et al. (2013).

HPGs can be established with the known characteristic parameters of the pipe and the sediment bed (pipe diameter D, pipe length L, slope S₀, wall roughness n_w, sediment bed height h, and roughness n_s). However, for the inverse problem, the sediment bed height h and roughness n_s are unknown. In practice, the flow rate Q, the upstream manhole water level H_u, the upstream water level Y_u, and the downstream water level Y_d can be obtained by monitoring. In this study, a method was used to predict the height of the sediment bed based on monitoring flow data as follows:

• (1) Assume a sediment bed height h, which can be initially estimated from the energy equation as follows:

  

  (4)

  where z is the elevation difference between the pipe invert and the bottom of the manhole, Y is the water level in the pipe, A is the pipe flow cross-sectional area, ζ is the coefficient for inlet head loss, set at 0.5 based on experimental tests in this study and also from Hager (2010), and the subscripts u and d denote upstream and downstream of the system, respectively. Additionally, the minimum value of the upstream and downstream monitored water levels can be used as an upper limit for the sediment bed height.

• (2) The sediment bed roughness n_s can be evaluated with the given monitoring data (Q, Y_u, Y_d) by using Equations (1) and (2).

• (3) The HPG then can be built. A sufficiently large set of monitoring data (Q, Y_u, Y_d) was compared with the hydraulic performance curves, and the goodness of fit can be assessed based on the Nash–Sutcliffe coefficient (NSC) calculated by the following formula:

  

  (5)

  where Y_u is the measured value of the upstream water level in the pipe, Y̅_u is the average value of the measured upstream water level in the pipe, and Ŷ_u is the calculated value of the upstream water level in the pipe, which is calculated from the monitoring data Y_d by Equations (1) and (2). An NSC value of 1.0 indicates a perfect fit, indicating that all measured data align with the corresponding curves.

When the flow rate is not monitored, Equation (2) will have two unknown parameters, Q and h, where Q varies under different conditions. Even if multiple monitoring data points (Y_u, Y_d) are used, Equation (2) cannot be solved, and additional conditions need to be introduced. Further analysis revealed that the C-curve in the HPG, unlike the N-line, varies with sediment height. Consequently, Equation (3) was introduced to solve with Equation (2) to evaluate the flow rate and the sediment height. Nevertheless, the C-curve represents the critical condition, and only monitoring data for the free outflow can be used.

In comparison with flow through a clear conduit, a deposit alters the free-surface profiles. Specifically, under conditions of free outflow, an increase in the height of the deposit not only extends the length of the choked-flow region but also elevates the maximum water level upstream of the deposit's apex, as illustrated in Figure 9(a). Deposits at different spatial locations induce specific alterations in flow, provided they do not interfere with boundary conditions, as shown in Figure 9(b). Even though varying spatial distributions of sedimentation significantly alter water surface profiles, a consistent effect on the upstream manhole has been noted. This suggests that energy losses incurred by identical deposits situated at different locations are almost the same. When compared to a clean pipe, sedimentation with a height of h = 20.0 mm and a length of l = 2.0 m causes the water level at the upstream manhole to increase by approximately 0.01 m. Nonetheless, this elevation in water level is about 0.01 m lower than what is observed with continuous deposition of the same height.

Consideration of backwater effects is imperative for accurate hydraulic analysis in sewer systems, as highlighted by Sevük & Yen (1982). Figure 9(c) presents a comparison of water surface profiles under a flow rate of Q = 7.0 L/s, featuring a deposit with a height of h = 20.0 mm located at x_b/D = 17.0, against varying outlet control water depths: free outflow and controlled depths of 0.092, 0.107, and 0.140 m. The impact of the backwater effect gradually increases from downstream to upstream as the controlled depth increases. While for y_dm = 0.092 m, the influence of the backwater was confined to the region downstream of the deposit and insufficient to modify the hydraulic characteristics upstream. However, when the downstream water level (y_dm = 0.140 m) surpasses a specific threshold, the water surface only forms a depression as it crosses the localized deposit, and the displacement of the deposit exerts a negligible influence on the overall flow within the conduit, as evidenced in Figure 9(d).

The water surface profile in the upstream choked-flow region resulting from a localized deposit conforms to the M1 type for mild-slope sewers, as described in Castro-Orgaz & Hager (2019). As described by Yang et al. (2024), the continuity and energy equations without considering the effects of energy loss and deposition length can be applied to predict the free-surface profile for sewer pipes where the localized deposit height and location are known.

Accurately pinpointing the location of sediment deposits through monitoring data requires adherence to specific conditions. First, the site for monitoring the upstream water depth needs to be situated within the choked-flow region, as this location is critical for determining the backwater curve. The choked-flow region increases as the controlled depth increases, which is more conducive to the prediction of deposits. It should also be noted that for smaller deposit heights, the flow regime does not change. In the context of practical applications, choosing monitoring locations is of paramount importance. Understanding the interplay between these parameters and conducting the requisite analyses is essential.

In actual sewers, the presence of various types of deposits and the difficulty in quantitatively analyzing local energy losses render diagnosis and identification virtually impractical in real-world applications. However, it was found that localized deposits can be equivalently converted to continuous sediment beds, provided that the total energy loss remains the same. By employing this method, analyzing HPGs and flow data enables the estimation of the degree of sewer deposits.

Continuous deposition and localized deposits both significantly changed the hydraulic characteristics of sewers but influenced them in different manners. Continuous deposition primarily changed the cross-sectional area of the flow, while localized deposits functioned as a bottom obstruction, resulting in choking and backwater effects. These findings were consistent with previous studies by Berzio et al. (2017) and Regueiro-Picallo et al. (2020). The HPGs established for depositional conditions extend this understanding by providing a quantitative framework for predicting sediment deposition from monitored flow data.

Traditional studies have mostly focused on dynamic deposition-erosion processes, but there is a lack of quantitative characterization of the hydraulic characteristics of fixed sediments (passive layer in MIKE or InfoWorks ICM). This study provided an important addition to the existing studies in the field of sediment hydraulic analysis. The application of the HPG, compared to the regression method of Stevens & Schutzbach (1998) based on Manning's equation, was not constrained by uniform flow and allowed for a more intuitive correlation of flow rate, water level, and deposition. The proposed method could be applied to an online monitoring system, and the real-time data could be used to determine sediment deposition and optimize maintenance strategies.

It should be noted that the equivalent sediment bed height simplified the complex three-dimensional pattern of localized deposit into a one-dimensional parameter through the principle of energy loss equivalence. When the local deposition height in the experiment was 40.0 mm, the equivalent height was 35.0 mm (Figure 13(b)), and this parameter can effectively characterize the effect of deposition on the overall hydraulics despite an error of about 12.5%. Such simplification significantly reduces the difficulty of data collection and model calibration, which is especially suitable for practical engineering scenarios where detailed data on sediment patterns are not available.

Given x_b = 50.0 m, h = 200.0 mm, and other parameters are identical to the previous case, as shown in Table 3. The deposition height h and the location x_b can be identified as follows:

• (1) Assuming x_b = 20.0 m and h = 120.0 mm, Equation (2) can be applied to establish an HPG combining the continuity and the energy equations and match it with the scatter plot formed by (Q, Y_u, Y_d). Meanwhile, Ŷ_u was calculated based on the known Y_d, as shown in Table 3, and NSC = 0.76.

• (2) Repeat the above steps and continue assuming different x_b and h. For example, assuming x_b = 50.0 m, h = 150.0 mm, x_b = 50.0 m, h = 200.0 mm, and x_b = 80.0 m, h = 250.0 mm, NSC = 0.92, 1.0, and 0.92 were then obtained, respectively. Multiple assumptions need to be made to obtain the closest match. The range of x_b and h can be evaluated based on NSC to reduce the number of assumptions.

• (3) Determine the optimal result after multiple assumptions. For this case, x_b= 50.0 m, h= 200.0 mm, and the corresponding HPG is shown in Figure 14(b).

It is important to note that the NSC obtained when using actual monitoring data are nearly always less than one. However, given a sufficient amount of monitoring data (Q, Y_u, Y_d), the observed data should converge to the HPG with a reliable NSC value. In most practical applications, estimating the equivalent sediment bed height is sufficient, and this inverse problem can be solved without significant difficulties.

The findings of this study can be applied to steady flow conditions, as well as to scenarios with slowly varying daily flows (quasi-steady flows) in the sewer network, such as sunny days or light rain events. In the majority of cases, sanitary sewer flow exhibits a limited variation (typically less than 10%) within a few minutes, thereby justifying the assumption of quasi-steady flow conditions. However, when unsteady flow conditions predominate, as in stormwater systems, the method's applicability may become significantly limited.

This study focuses on exploring the fundamental flow behaviors, patterns, and hydraulic properties related to fixed sediment beds and their inverse problems to provide valuable insights for the operation and maintenance of sewer systems. Consequently, specific and controlled sediment bed types were selected. The results can be applicable to conventional bottom sediment beds. However, it is not necessarily applicable to depositional structures such as gradually convergent, asymmetric, or oblique shapes and non-bottom depositional locations (Defina & Viero 2010). The influence of these factors was also not investigated in this study.

The methods applied to the prediction of localized deposits are constrained by the idealized assumptions of the 1D model, including steady-state conditions, simplified boundary conditions, neglect of energy losses, certain geometric properties of the sediment bed cross-section (Yang et al. 2024). These assumptions facilitate the theoretical computational analyses but may not comprehensively reflect the highly dynamic and non-uniform environment of the sewer system. Consequently, when the actual situation deviates from these idealized conditions, the accuracy or reliability of the results will be reduced. In addition, the placement of monitoring locations and the selection of monitoring data are limited by the actual site. In light of these considerations, it is important to exercise caution when extending the results of this study to practical applications.

This study presents a novel method for estimating sediment deposition in sewers by integrating hydraulic performance analysis with monitoring data. The method addresses a significant gap in current maintenance practices and provides a systematic approach to sediment deposition assessment. Laboratory experiments across various flow conditions and sediment configurations validated the method's effectiveness, particularly for steady-state conditions with regular sediment patterns.

The method demonstrates high accuracy in predicting both uniform bed deposits and localized accumulations, with relative errors consistently maintained between 5 and 15% under typical operating conditions. A key finding reveals that under strong downstream backwater conditions, deposit location minimally affects flow characteristics, and energy loss becomes the primary diagnostic indicator for localized deposits. The study introduces an innovative approach for determining equivalent deposited bed height, simplifying the assessment of complex deposition patterns in operational sewer systems.

The practical value of this method lies in its ability to optimize maintenance strategies through quantitative estimation of sediment accumulation. While the method shows promise for standard operating conditions, its application during extreme events or with complex sediment geometries requires further validation. Future research should expand this methodology to include unsteady flow conditions and diverse sediment patterns, with potential integration into real-time monitoring systems. These developments would strengthen the method's role in comprehensive sewer system management.

This study was supported by the National Key R&D Program of China (2022YFC3203200), the Zhejiang Provincial Natural Science Foundation of China (LMS25E090005), and the Ningbo Young Technology Innovation Leading Talent Program (2023QL029).

All data, models, or code generated or used during the study are available from the corresponding author by request.

The authors declare there is no conflict.