Frazil ice jam risk assessment method for water transfer projects based on design scheme

Frazil ice jam is a phenomenon in which flowing frazil ice substantially blocks the cross-section of a channel and causes upstream drowning. Frazil ice jam is one of the intense rough ice hazards in rivers and channels. The Yellow River in China has various degrees of ice jams almost every year. In January 1982, the Hequ section formed a dense river ice jam. The villages and farmland within 13 km of the river between Longkou and Beiyuan were flooded during the ice-cover breakup period (Sun et al. 1990). In December 1997, the river at Bada Station formed a severe ice jam, and the water level was as high as 1,054.40 m. The embankment collapsed and inundated 12 villages, and the affected area reached 800,000 km² (Hu 2006). Ice jams may occur in a water transfer project to bring engineering management troubles and threaten safety. As the South-to-North Water Diversion Middle Line Project (MRSNWDP) produced ice jams in winter 2015–2016, there were ice jams in the Puyang River to the north of the Juma River. The water level in the upper reaches of each canal pool was 0.3–0.73 m higher (Duan et al. 2016). So, it is an important question, how to manage a water transfer project with threat of ice jam in winter.

In recent years, researchers have studied the formation mechanism and evolution of ice jams and obtained relevant results. In terms of observations, Wu (2018) studied an accumulation test of ice jams and suggested that when Fr ≥ Frc, ice particles accumulate in the initial ice cover and form ice toes and then progress upstream. Beltaos et al. (2011) noted the dynamic process of water level change and the hydrodynamic characteristics of water waves in the Saint John River during the river thaw period. Wen et al. (2015) observed hydraulics, meteorology and ice conditions along the project and determined the ice regime evolution of the MRSNWDP. In terms of numerical simulation, Shen & Yapa (1984) and Shen (2002) proposed a one-dimensional and two-dimensional ice evolution and unsteady hydraulic process simulation model for rivers. Yan et al. (2014) noted that the formation of ice cover would increase the wet circumference of the section and reduce the hydraulic radius, and then the water level can rise. Sui et al. (2005) noted that the changes in canal water level were influenced by ice jam thickness, Froude number and ice flow. Duan et al. (2016) suggested that juxtaposition ice cover formation conditions were less than 0.4 m/s and 0.35 m/s for a canal pool upstream cross-section and downstream cross-section, respectively, by ice observation at the MRSNWDP. Guo et al. (2011) and Zhou et al. (2016) proposed controlled flow and water level operation schemes to improve safety for MRSNWDP operation in winter. In terms of risk assessment, Luo et al. (2016) adopted the gray correlation decision-making method based on regret theory to evaluate the possibility of ice jams in three sections of the Ningxia–Neimeng reach of the Yellow River, solving a problem of disaster assessment with incomplete information. As of now, the MRSNWDP still operates with smaller flow than its design flow in winter.

While frazil ice jam is a risk for the water transfer project, risk assessment is an important tool for risk prevention and control and is becoming the focus of risk research in the field of engineering construction. Therefore, it is important for the safe and efficient operation of the project to carry out a risk assessment study of ice jams in the water diversion project in winter, propose a reasonable assessment system, identify the main risk factors and conduct risk grading for the whole section of the project.

Risk Management Risk Assessment Technology (2016) of China points out that risk assessment is a complete process composed of risk identification, risk analysis and risk assessment. Common risk assessment methods include Fault Tree, Analytic Hierarchy Process (AHP) and so on. For example, Li et al. (2017) established an ice damage risk assessment model for the South-to-North Water Diversion Project, constructed an index system based on channel characteristics, and determined the spatial distribution of ice jams; Jiang et al. (2014) used ANP (Analytic Network Process)–gray fuzzy theory to establish an early warning model of risk for hydropower project groups; Huang & Song (2013) used expert scoring methods and AHP to propose reservoir risk assessment methods; Li et al. (2019) used variable fuzzy theory and AHP to establish a comprehensive evaluation model to assess the risk of dam breakage; Yang (2015) established a BP (Back Propagation) neural network model for water conservancy engineering risk and proposed suggestions for the corresponding risk assessment and rectification; and Hu et al. (2013) proposed a risk assessment method for hydraulic engineering, based on direct fuzzy set theory, and quantitative analysis was performed on each index in the index assessment system. Yoshimatsu & Abe (2006) established the risk assessment model of geological landslides, took the topographic factors of hazardous areas as evaluation indexes, and applied the AHP to assess the risk of geological landslides. The AHP method is the basis of the ANP method and fuzzy-AHP. The method decomposes the objects to be evaluated into target level, criterion level and index level. It has been widely used in risk assessment, especially in safety risk and environmental risk assessment, and can effectively determine the weight of each index by layering the complex system.

In summary, the existing risk analysis methods are diverse, but a complete evaluation system has not been established for the ice jam risk of water diversion projects. Therefore, this study proposed a frazil ice jam risk assessment indicator system and standard assessment system based on the water transfer project design conditions, and the AHP method was used to ensure the canal risk level to support the prevention of frazil ice jams in canal design or operation.

The MRSNWDP is a long-distance super-large-scale water transfer project across multiple provinces and cities from north latitude 33° to 40° in China, and its total length is 1,432 km. The project starts from Taocha of the Danjiangkou Reservoir, passes through Henan Province and Hebei Province along the way, and finally reaches the Beijing Regiment. The design flow at Taocha is 350 m³/s, and the design annual average water diversion capacity is 9.5 billion m³. The project is divided into 63 canal pools by 64 control gates, and all of the gates are automatically controlled by remote computers centralized in government offices.

The northern canal pools from Anyang experience varying degrees of ice conditions every year in winter, as shown in Figure 1. Duan et al. (2016) noted that the largest ice cover was 0.28 cm, and some frazil ice jam incidents with the largest ice jam thickness of approximately 3.0 m occurred in 2016. For the long-distance canal control system, free water canal pools, frazil ice canal pools and floating ice-covered canal pools may exist simultaneously. Ice jams can be formed with large scope, and when ice jams are formed at any place, the hydraulic response processes of the whole canal system are influenced. All of the gates should be operated at the same time, and the chance of more ice jam formation may be increased. Therefore, it is a complicated problem to simultaneously satisfy the water requirements of users and engineering safety in winter.

A part of the canal system from the Guyunhe gate to the Beijuma gate was used to study the canal system frazil ice jam risk assessment. The data were the initial design conditions, and the studied section of the canal system has a total length of approximately 217.73 km and is divided into 13 canal pools. The spatial distribution of gates is shown in Figure 2. The approximate water flow at each gate usually adopted in winter, which is much less than the design flow, is shown in Table 1.

The study object of the canal system is a canal pool in a canal system as shown in Figure 2. A canal pool is the part of the canal between two adjacent canal gates.

The calculation process of the frazil ice jam risk assessment method is shown in Figure 3. There are three important steps in the process including establishing an assessment indicator system and the risk assessment criteria for each indicator, making sure of the weight of each indicator, and calculating the frazil ice jam risk level. Expert consulting and AHP methods were used in the process.

There are usually ice conditions in rivers north of 30° north latitude in China, and ice generation and disappearance are related to thermal factors, channel characteristics and hydraulic characteristics (Fu et al. 2013). Liu et al. (2020) pointed out that frazil ice jam formation requires a large amount of frazil ice, submerged ice and insufficient capacity in the canal to transport frazil ice. Therefore, the study selected three aspects, including ice production factors, special hydraulic structures and basic design parameters based on canal design data, to construct the assessment indicator system.

The main factors affecting the amount of ice production are the length of open channels and the temperature zone in which the channels are located.

• (1)

  Length of open channel

Under the influence of heat exchange between the water surface and air atmosphere, supercold water easily appears in the channel, and ice occurs when the water body continues to lose temperature. Under the influence of water and atmospheric heat exchange, the longer the channel is, the larger is the range in the temperature of the water body, and the greater is the ice production. Therefore, the length of an open channel is selected as the risk evaluation indicator to classify the ice production capacity.

• (2)

  Temperature zone

The latitude position is a significant factor affecting the distribution of temperature in China. The Middle Route of the South-to-North Water Transfer Project from Taocha at the Danjiangkou Reservoir to the end of Tuancheng Lake in Beijing spans eight degrees of latitude from south to north. The average temperature along the route basically shows a decreasing pattern from south to north. Therefore, the temperature zone is chosen as one of the risk evaluation indexes in this paper.

Aqueducts and inverted siphons are common hydraulic structures in water transfer projects. Limited by economic factors and engineering safety factors, compared with that of the channel, the aqueduct has the following characteristics in design: the slope is larger than that of the upstream and downstream channels, the cross-section of the front of the aqueduct is narrow and the rear section of the aqueduct widens. These factors increase the possibility of ice blockage and congestion.

Huang et al. (2019) showed that in the winter of 2015–2016, the downstream region of the Caohe aqueduct, due to the length of the aqueduct and its proximity to the downstream control gate, caused an ice flow to cross the aqueduct, hit the ice barrier, break the ice and form a certain scale of ice jam. For an inverted siphon, the main purpose is to prevent flow ice from entering the interior of the inverted siphon. A small amount of frazil ice will damage the inner structure of an inverted siphon, and more ice flows will easily cause ice flow blockage. Due to the smaller cross-section of the inverted siphon than that of the surrounding open channels, the degree of blocking of the inverted siphons with the same amount of frazil ice is obviously greater than that of open channels. Therefore, in this paper, the aqueduct and inverted siphon are included in the ice jam risk evaluation indexes, and the number and location of the structures should be considered when the indexes are defined.

The basic parameters of the canal system include slope change, section change and hydraulic parameters.

• (1)

  Bottom slope changes

If the cross-section size of the channel reach remains unchanged, when the bottom slope of the channel changes from steep to gentle, the flow velocity will decrease, resulting in insufficient ice transport capacity. When the bottom slope of the channel gradually becomes steeper, the flow velocity of the water will increase, which will cause the flow velocity to exceed the submerged value and support the formation of a frazil ice jam.

• (2)

  Cross-section narrowed

If the bottom slope of the channel remains unchanged, when the upstream of the water delivery channel is wide and the downstream is narrow, a large amount of ice from upstream easily jams in the narrow section, which easily causes ice jams. In addition, the narrow section beam will increase the section velocity and provide conditions for the formation of the ice slug body. Therefore, in this paper, the rate at which the channel reach width beam narrows is regarded as one of the indexes of ice jam risk assessment for a single-channel pool. When this rate is used for risk analysis, only the section of an open channel reach is considered, not the transition section of the canal system of crossing structures, such as an aqueduct, and the inverted siphon and the changes in the structures themselves are considered.

• (3)

  Hydraulic parameters

The design of water depth, discharge and canal system controllability is considered by channel hydraulic parameters. The designed water depth is small and easily produces bottom freezing. With the same designed water depth, the greater the flow is, the greater is the risk of an ice jam; with the same designed flow, the lower the designed water level is, the greater is the risk of an ice jam. A large amount of flow ice is collected in front of the control gate, which increases the risk of an ice jam in front of the control gate. An ice sluice in front of the control gate can lower the risk of ice accumulation in front of the control gate and improve operational safety. The factors described above should be taken into account in the identification of ice jam risk factors.

The frazil ice jam risk assessment indicator system of the hierarchy model for the water transfer project is shown in Figure 4. Seventeen indicators were used for frazil ice jam assessment, and the indicators were determined directly by the canal design data.

Based on the above established index system and through expert consultation, the risk assessment criteria of each index are determined as shown in Table 2, and risk factor indicators are assigned on a five-point scale.

The frazil ice jam risk level standard of the water transfer project is presented in Table 3, which is divided into five levels.

For the water transfer project in the design stage, ice jam risk assessment grades are categorized as grade I, II and III, and when grade III is assessed, a risk monitoring and emergency system shall be established. If grade IV or V is assessed, detailed demonstration and adjustment shall be conducted on the design conditions.

For a constructed project, if the frazil ice jam risk level is grade III or below, the conventional ice condition monitoring and emergency management system just needs to be established. If the risk grade is IV, ice condition prediction, engineering operation process in winter, engineering measures for disaster reduction and emergency plan refinement need to be strengthened to improve operational safety in winter. If the risk grade is V, the project needs to be modified by demolition and partial reconstruction.

Five senior professional title experts in the study field conducted the risk degree of indicators in the secondary level. The degrees of risk were scored on a scale of 1–9. According to the arithmetic mean value of the risk degree, the pairwise comparison of factors in this layer is carried out, and a judgment matrix is constructed to obtain the weight of factors in this layer using the analytic hierarchy process method. The judgment matrix of each level can be seen in Tables 4–7.

Above all, the layer corresponding factor weight of each index and the risk factors for the total sequencing weight are shown in Table 8. In terms of total order weight, the average weight is 0.059, which is more than the average weight because the main risk factors include the temperature zone, length of the channel, number of aqueducts and the position and number of inverted siphons and locations. For the first-level index, the weights of the indexes are in order from large to small, including special structures, basic design parameters and ice production factors. Therefore, it can be seen that the risk of ice jams can be reduced by the judicious selection of structures and design parameters.

Take the Guyunhe to Hutuohe canal pool as an example. Because the canal pool was 9.8 km long and located in the warm temperate zone, the degree of risk was 2 and 3 for C1 to C2, respectively. Because there was no flume or turnout in the canal pool, and one inverted siphon was placed at the front of the downstream gate, the degree of risk was 0, 0, 1, 5, 0 and 0 for the third-level indicators from C3 to C8 of the special hydraulic structures. Because the bottom slope of the canal pool changed 29 times, and the maximum change rate was 12.978, and the cumulative value was 29.178, the corresponding risk degrees were 3, 3 and 5 from C9 to C11. Because the cross-section narrowed three times in the canal pool, the minimum value of the cross-section narrowness rate was 0.904, and the cumulative value was 2.764, the degrees of risk were 2, 2 and 4 for C12 to C14, respectively. Because the design water depth was 5 m, the design flow and water depth ratio was 33 m²/s, and there was no ice outlet in the pool, the risk degree was deemed to be 1, 5 and 4 from C15 to C17, respectively. Finally, the degrees of the 17 indicators for the 13 pools were obtained, as shown in Table 9.

In accordance with Tables 4 and 5, the frazil ice jam degree of risk was calculated by the analytic hierarchy process method, and the results are shown in Figure 5. Then, in accordance with Table 3, the risk level can be directly determined. The results show the risk levels of the 13 pools between risk level II and risk level IV, in which one pool was rated at risk level II, ten pools were rated at risk level III, and two pools were rated at risk level IV.

The risk levels of the eighth pool and thirteenth pool reach IV with the highest risk degrees of 3.5 and 3.3, respectively. Huang et al. (2019) reported that more serious frazil ice jams had formed from Puaynghe to Gangtou and Fenzhuanghe to Beijuma than in the other canal sections in the 2015–2016 winter based on field ice observations. Both the observation and the risk assessment points to the eighth and thirteenth pools as the highest risk pools in the study canal system. So, more attention should be given to the monitoring of ice conditions, the improvement of the canal system operational process and the development of emergency management plans to reduce the risk level to help the whole canal system achieve the water transfer target safely.

In terms of engineering design data, there were three similarities between the two most risky pools: the length was more than 20 km, there were special hydraulic structures concentrated downstream of the pool, and the slope and section changed frequently and greatly. These commonalities can provide a design reference for the design stage of the water transfer project.

Frazil ice jam prevention is a task through the life-cycle of some water diversion project construction. Suggestions follow for water diversion projects at design stage and operation stage.

The ice jam risk analysis should be advanced to the engineering design stage. Through design scheme review and optimization, the ice jam risk of the design scheme can be reduced. So, this work can reduce or eliminate the ice jam risk prevention and control pressure in the project operation stage.

• (1)

  Strengthen the research on ice jam risk assessment based on design scheme

It is important to suggest a frazil ice jam risk assessment method for a water diversion project design scheme in the form of the national standard. And the frazil ice jam risk assessment should be a common design and design scheme review task according to the national standard for the water diversion project with ice conditions in winter.

• (2)

  Improve the pertinence of engineering design scheme optimization

When the frazil ice jam risk level is higher than III, there is a suggestion to optimize the design scheme. Based on the weight order of risk assessment indicators, a decision-making model should be established to guide the scheme optimization. By comparing the ice jam risk level, scheme feasibility and project cost corresponding to different adjustment schemes, the scheme with the lowest ice jam risk and project cost can be selected.

• (1)

  Implementation of ice jam comprehensive risk grading management

For the built project in the operation stage, if ice jam risk assessment was not considered in the design stage, the method in this paper should be used for risk assessment and risk grading management should be implemented. It is necessary to adopt a different project operation scheme in winter according to the risk assessment results. All of the project operation scheme should be institutionalized.

• (2)

  Establishing emergency management mechanism for ice jam disaster

Disaster can be prevented and controlled. For ice jam disaster in winter, the water diversion project should focus on disaster prevention and control, predicting and analyzing the possibility and consequences of ice jam disaster in advance, and establishing the emergency management mechanism for the ice jam disaster. When the disaster is about to happen, it can be used for quick response to reduce the impact of the disaster and ensure the safety of the project.

• (3)

  Adopting ice jam prevention and control measures

In view of the risk factors with large weight, measures should be taken to reduce the possibility of ice jam, including ice condition monitoring, setting ice ropes, ice melting, water disturbance, ice discharged from canal pools and reducing water flow in winter.

Based on the basic design scheme of the water diversion project and the AHP method, this paper proposes a frazil ice jam risk assessment method for water diversion projects, and the main conclusions are as follows.

Firstly, a frazil ice jam risk assessment indicator system, bottom indicator risk degree standard and risk level decided standard were obtained. There were 17 third-level indicators in total. And special hydraulic structures are the most important first-level index, and air temperature zone, length, the number and location of aqueducts and the number and location of inverted siphons were the main risk factors for frazil ice jams in water transfer projects.

Secondly, the risk levels of the 13 pools of the Middle Route of the South-to-North Water Transfer Project were evaluated. It was considered that most of the pools were below risk level III, and only two pools were at risk level IV. The canal pools with the highest risk level were the eighth and thirteenth pools, which was consistent with the relevant prototype observation conclusion, so, it was considered that this method had certain applicability in the evaluation indicator system, indicator weight and indicator grading standards for both the built–operating stage and the design stage of water transfer projects.

Finally, the study showed that it is necessary to address frazil ice jam at the design stage of a water diversion project, and a method was suggested to do the task well, but the method application results can be influenced by project characteristics, indicator system and grading standard adaptability, and the number of experts consulted. We hope that the readers can provide suggestions about these for us.

This study was supported by the National Natural Science Foundation of China (Grant No. 51779196, 51309015).

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