
==== Front
Heliyon
Heliyon
Heliyon
2405-8440
Elsevier

S2405-8440(24)13479-2
10.1016/j.heliyon.2024.e37448
e37448
Research Article
Bank erosion under the impacts of fluvial erosion, frost heaving/freeze-thaw process of rivers in seasonal frozen regions
Yang Jun ab
Jia Dongdong ddjia@nhri.cn
ac⁎
Zhai Biyao a
Chen Xiaona ab
Wang Jinyang ab
a Key Laboratory of Port, Waterway and Sedimentation Engineering of Ministry of Transport, Nanjing Hydraulic Research Institute, Nanjing 210029, China
b The National Key Laboratory of Water Disaster Prevention, Hohai University, Nanjing 210098, China
c Yangtze Institute for Conservation and Development, Nanjing 210098, China
⁎ Corresponding author. Key Laboratory of Port, Waterway and Sedimentation Engineering of Ministry of Transport, Nanjing Hydraulic Research Institute, Nanjing 210029, China. ddjia@nhri.cn
06 9 2024
15 9 2024
06 9 2024
10 17 e374487 4 2024
30 8 2024
4 9 2024
© 2024 The Author(s)
2024
https://creativecommons.org/licenses/by-nc-nd/4.0/ This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).
Bank erosion is a key feature of channel evolution in alluvial rivers, and will occur under the combined effect of hydraulic erosion and frost heave/freeze-thaw process of rivers in seasonal frozen regions. However, most research on bank erosion modeling has seldom considered the impact of the frost heave/freeze-thaw process. Therefore, the variation in the mechanical characteristics of riverbank soil under the freeze-thaw cycle was investigated firstly in the current research and then used in the modeling of bank erosion processes at typical sections of the Songhua River. Additionally, a sensitivity analysis of riverbank stability was conducted using orthogonal experiments. The results indicate that after 7 freeze-thaw cycles, the soil cohesion and internal friction angle of bank soil decreased by about 10%–47 % and 9%–19 %, respectively. Unlike lowland rivers, bank erosion of rivers in seasonal frozen regions is more likely to occur during the rising water period. The frost heaving/freeze-thaw process will make the bank stability safety coefficient Fs more quickly decrease to the unstable critical value. As compared with the case without considering the frost heaving/freeze-thaw process, the mass failure occurred in advance when the frost heaving/freeze-thaw process was considered, and the calculated bank erosion volume was increased by 11%–51 %, agreeing better with the measured value. The sensitivity ranking of the four influencing factors on riverbank stability under freezing-thawing conditions is as follows: river stage > groundwater level > cohesion > internal friction angle. The current study can provide a reference for research on bank erosion and channel evolution of rivers in seasonal frozen regions.

Keywords

Bank stability
Frost heave/freeze-thaw action
Soil properties
Bank erosion
Sensitivity analysis
Rivers in seasonal frozen regions
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pmc1 Introduction

Bank erosion is an important manifestation of lateral deformation of the alluvial river channel, but may become a natural disaster in a river with a large population on the floodplain [[1], [2], [3], [4], [5]]. Bank erosion will occur under the combined effect of hydraulic erosion and the frost heave/freeze-thaw process of rivers in seasonal frozen regions, leading to frequent bank failure [6]. Taking the Heilongjiang River Basin in northern China as an example, the frost heaving/freeze-thaw action changes the soil structure, resulting in cracks in the bank soil layer and a decrease in shear strength. Under the scouring of water flow, the bank soil is more susceptible to erosion, and the riverbank is more likely to become steep and even experience instability and failure. According to incomplete statistics, bank erosion in the Heilongjiang River has caused an average annual loss of about 7 km2 of farmland [7], which has an important impact on river stability and farmland safety. Therefore, investigating bank erosion of rivers in seasonal frozen regions has important theoretical significance and practical application value.

The mechanism and process of bank erosion is complex, bank erosion is influenced by multiple factors, including in-channel water level, groundwater flow, riparian vegetation, and bank soil properties. Many experts have investigated the mechanism of bank erosion, revealing different factors that affect bank erosion. For example, some scholars found that 80 % of bank erosion in the middle and lower reaches of the Yangtze River occurred at concave bank bends or flow-deflection locations that were heavily eroded by water flow. From the perspective of fluvial dynamics, the nearshore hydraulic erosion has been identified as the primary factor causing bank mass failures [[8], [9], [10]]. Variations in soil compositions, groundwater levels, and in-channel water levels also significant influence the bank erosion process [[11], [12], [13]]. However, their study did not encompass on-site sampling and analysis of the riverbank soil in the study area, nor did it analyze the influence degree of various factors on the stability of the riverbank.

On the other hand, many scholars have constructed numerical models for bank stability with different failure modes based on soil mechanics and bank stability theory [[14], [15], [16], [17], [18], [19], [20], [21], [22]]. Existing bank stability analysis models are generally based on slope stability theory in soil mechanics. Some researchers have proposed a numerical model for the mass failure of viscous banks based on plane sliding theory [23]. Considering the effect of pore water and hydrostatic pressure a cohesive bank failure model was developed [24]. By improving the generalized model of riverbank stability, the failure process of the riverbank with a two-layer soil structure in Jingjiang Reach of the Yangtze River is simulated [[25], [26], [27]].

However, most these research focused on the hydraulic erosion and gravitational collapse of the river bank, with little attention paid to the process of hydraulic erosion -frost heave/freeze-thaw. Studies on the stability behavior of reservoir soil bank slopes under freeze-thaw cycles in cold regions have also been conducted [4,28], but they frequently fail to take into account the effects of water scouring on riverbanks. In addition, for rivers of high-latitude seasonal frozen regions such as the Songhua River, the frost heave/freeze-thaw effect is strong, and bank failure phenomena are common. However, due to limitations in simulation techniques, bank erosion under the impacts of hydraulic erosion, and frost heaving/freeze-thaw process of rivers in seasonal frozen regions have not been well simulated. In particular, the quantitative contribution of frost heave/freeze-thaw action to bank erosion retreat still requires further investigation.

Therefore, this study takes typical cross-sections of the downstream near-dam section of the Dadingzishan Project of the Songhua River as an example. The mechanical properties of the riverbank soil under freeze-thaw cycles are investigated through direct shear tests. An improved BSTEM model is used to calculate the erosion process, and the quantitative analysis of the impact of the frost heave/freeze-thaw action on the bank erosion process is conducted, and then sensitivity analysis of riverbank stability is conducted using orthogonal experiments. The research findings can provide a reference for the study of riverbank erosion and channel evolution of other rivers in seasonal frozen regions.

2 Materials and methods

2.1 Study area

The Songhua River is one of the seven major rivers in China and the largest tributary of the Heilongjiang River in China. The mainstream of the Songhua River is a typical plain alluvial river with a total length of about 940 km and is divided into the upper, middle, and lower Songhua Rivers with boundaries at Harbin and Jiamusi, respectively. The upper reach is from Sanchahe to Harbin, the middle reach is from Harbin to Jiamusi, and the lower reach is from Jiamusi to Tongjiang. The average annual precipitation in the Songhua River Basin is generally around 500 mm. During the flood season from June to September, the precipitation accounts for 60%–80 % of the annual total value, while in winter from December to February, the precipitation only accounts for 5 %. The study area has a continental monsoon climate, with an average annual temperature of 5.6 °C, a maximum temperature of 38 °C, and a minimum temperature of −34 °C. In the seasonal frozen region, the flowing season lasts from April to October, and the frozen period is from November to March of the following year generally. Along the main channel of the Songhua River, there are varying degrees of erosion on the sandbars or banks. The soils on both sides of the main channel are loose, with a low resistance capacity to hydraulic erosion. Unlike southern rivers such as the Yangtze River, the freeze-thaw process of rivers in the seasonal frozen regions changes soil mechanics, inducing substantial differences in the mechanisms behind the bank erosion processes.

The study area is located downstream of the dam of the Dadingzishan Project of the Songhua River (Fig. 1). After the operation of the Dadingzishan Project in 2008, the flow and sediment regime entering the study area has been altered greatly, resulting in more obvious river bed scouring, and intense bank erosion processes in some reaches. According to the observed data, two typical bank erosion sections of DM1 and DM2 (Fig. 1) were selected to perform bank erosion simulations in the current research, and the influence of the frost heave/freeze-thaw process on the bank erosion is being examined.Fig. 1 Sketch maps of the Songhua River.

Fig. 1

2.2 Soil test under freeze-thaw cycle

To analyze the changes in the mechanical properties of the bank soil under freeze-thaw cycles, soil samples from the study area were collected. Direct shear tests were conducted on bank soil samples that have undergone different numbers of freeze-thaw cycles to study the variation of shear strength of riverbank soil under freeze-thaw cycles.

2.2.1 Sample preparation

The surface layer of the study area's banks is predominantly composed of clay or silty clay, while the lower layer is mainly composed of silt or fine sand, with a loose texture and poor resistance capacity to erosion. Bank soil was sampled at the selected sites of DM1 and DM2 locations in December 2021 and May 2022. Indoor geotechnical tests were then carried out to measure the physical and mechanical properties of bank soil. Sieving analysis was adopted to obtain the bank soil gradation, Finally, three kinds of soil with a clay content of 12 %, 23 %, and 33 % (labeled as No.1, 2, and 3) were selected to conduct the freeze-thaw cycles soil test respectively (Fig. 2a). According to the Standard for Geotechnical Testing Method [29], soil samples taken from the riverbank site were sieved through a 2 mm sieve after being sun-dried and air-dried. Each type of soil was then prepared with a water content of 13 %, 18 %, and 40 % respectively. The water was sprayed into the predetermined mass of soil, and the mixture was thoroughly mixed and sealed for 24 h to ensure uniform distribution of moisture in the soil. Based on the field measurements at the riverbank site, the dry density of the prepared samples was set at 1.30 g/cm3. The stratified compaction method was used to prepare the measuring sample, which is 20 mm in height and 61.8 mm in diameter. (Fig. 2b and c). The sample is wrapped with cling film and placed in a sealed bag to ensure that it is isolated from the external environment, preventing moisture loss and external interference.Fig. 2 Sample preparation diagram(a)Bank soil gradations(b)Riparian soil sampling(c)Ring knife sample preparation.

Fig. 2

2.2.2 Test method

In the freeze-thaw test, the soil samples from the riverbank were frozen at −20 °C for 12 h to imitate the freezing process in a natural river. During the melting process, the soil samples of the riverbank were melted at 20 °C for 12 h to imitate the natural melting period. According to the literature [[30], [31], [32]], the physical and mechanical properties of bank erosion stabilize after three to seven freeze-thaw cycles. Therefore, the cycles of the freeze-thaw test are set to 0, 1, 3, and 7 in different cases.

Direct shear tests were carried out on the soil samples following freeze-thaw operations, to determine the cohesion and friction angle of bank soil. The tests were carried out using a strain-controlled direct shear instrument. The vertical pressure of the test samples were 50, 100, 150, and 200 kPa respectively, with a shear rate of 0.08 mm/min.

2.3 Bank erosion modeling

The BSTEM model of the National Sediment Laboratory of the United States was developed based on the stability analysis method proposed by Osman and Thorne [23]. It can consider the effects of lateral water pressure, pore water pressure, and the layering of riparian soil and is one of the most widely used models in this field [33,34].

The model is composed of a bank-toe erosion module and a stability analysis module. The bank-toe erosion module is run by inputting basic data such as typical riverbank profile, river level, gradient, roughness, and layered soil physical and mechanical parameters, and the results are imported into the stability analysis module to calculate the safety factor Fs of bank stability. If the calculated value of Fs was less than the critical value, mass failure would occur.

Frost heave promotes the development of tensile cracks on the bank top, while the freeze-thaw process reduces the mechanical strength of bank soil, both of which can affect the stability of the riverbank. As a result, the effects of frost heave/freeze-thaw should be considered when studying the river bank failure in seasonal freezing rivers (Fig. 3).Fig. 3 Sketch of riverbank failure under freeze-thaw process.

Fig. 3

2.3.1 Fluvial erosion at bank-toe

The lateral erosion of the bank toe is calculated based on the residual shear stress method [35]. The lateral erosion rate of the bank soil is mainly determined by the erosion strength of the flow and the resistance of the soil. Only when the shear stress of the near-bank flow is greater than the critical shear stress of the bank soil, erosion will occur. The erosion width E can thus be expressed as:(1) E=k∙(τ0−τc)∙Δt

where E is the lateral erosion width of the bank (m); k is the erodibility coefficient (m3/(N·s)), which is related to the characteristics of the soil; τ0 is the flow shear stress (N/m2); τc is the critical shear stress of bank soil (N/m2); Δt is the time step(s).

For the calculation of flow shear stress, the division method of the hydraulic radius [36] is used to calculate the average boundary shear stress acting on each node of the riverbank soil:(2) τ0=γωRS

where γω is the unit weight of water (9.81 kN/m3); R is the hydraulic radius (m), approximated by the water depth; S is the longitudinal water surface slope.

Hanson et al. [37] obtained an empirical formula to estimate the critical shear stress of non-cohesive soil, which can be given by:(3) τc=0.044×16.2×d50

where d50 is the median particle size of sediment particles, and the median particle size of bank fine sand near the dam section downstream of the Ddingzishan project is 0.09 mm. The critical shear stress of the lower fine sand is 0.06 N/m2 calculated by equation (3). The erodibility coefficient k is related to the soil's characteristics and shear stress. Here, the erodibility coefficient of non-cohesive soil adopts the empirical relationship [38]k=1×10−7τc−0.5.

For cohesive bank soil, according to the analysis results of Zong et al. [39], the critical shear stress can be calculated by:(4) τc=0.265×ρd3.51

where ρd is the dry density of the soil (t/m3). In addition, the erodibility coefficient of cohesive soil here is calculated by k=7.677×10−6τc−1.949 [39].

2.3.2 Bank stability analysis

The safety factor Fs of bank stability is mainly calculated by the horizontal layer method and vertical slice method (Fig. 4).Fig. 4 Sketch of the force analysis riverbank failure.

Fig. 4

The horizontal layer method is developed from the failure model of Simon et al. [40] and further improves the Osman-Thorne model. The horizontal layer method can divide the river bank into 5 layers at most, with each layer having defined mechanical property indicators. The safety factor Fs can be written as:(5) Fs=∑i=1I(ci′Li+(μa−μw)iLitanφib+[Wicosβ−μaiLi+Picos(α−β)]tanφi′)/∑i=1I(Wisinβ−Pisin[α−β])

where Li is the length (m) of the mass failure surface in the ith soil layer i; uai is the pore air pressure of soil in the ith layer i (kN/m2). uwi is the pore water pressure of soil in the ith layer i (kN/m2). Pi is the hydrostatic pressure (kN/m2) exerted by river flow on the soil of layer i; Wi is the soil weight of layer i (kN). ci' is the effective cohesion of layer i soil (kN/m2). φi' is the effective internal friction angle (°) of layer i soil; φib is the degree to which the apparent cohesion of soil in layer i increases with the increase of matric suction (°). α is the bank slope (°); β is the angle of the failure surface (°); I is the number of bank layers.

The vertical slice method originates from the CONCEPTS model developed by Langendoen and Simon[41]. The horizontal layer method divides the bank soil into five layers, and each layer is further divided into an equal number of soil blocks. To enhance computational accuracy, each soil block is further divided into three soil strips. The calculation formula of the safety factor Fs is as follows:(6) Fs=cosβ∑i=1I(ci′Li+(μa−μw)iLitanφib+[Ni−μaiLi]tanφi′)/sinβ∑i=1I(Ni)−Pi

where Ni is the unit directional force (kN/m) acting on the i-th soil block.

On the one hand, the shear strength of soil decreases when freeze-thaw occurs. on the other hand, under the combined effects of hydraulic erosion and frost heaving, cracks will develop on the top of the bank. According to Rankine's theory of soil mechanics [42], when frost heave is considered, the depth of the tensile crack can be given by:(7) Ht=pd+2cKzγωKz

Where Kz is the active earth pressure coefficient; pd is freeze-thaw force (kPa); c is the effective cohesion of soil (kN/m2).

In the current research, the critical value of Fs for the bank stability safety factor is 1.0., and Fs < 1.0, the bank is unstable, and thus mass failure will occur.

2.4 Model calculation condition

2.4.1 Soil mechanical properties

To obtain the riverbank soil properties, a field survey was conducted out at the typical bank section, and the physical and mechanical properties of each layer of bank soil were obtained by indoor geotechnical tests. The study area longitudinal variation in the soil composition is not significant. Table 1 gives the physical and mechanical characteristics of the riverbank soil in the section of DM1. It can be seen that the upper soil layer is mainly comprised of clay, with an average thickness of about 4.5 m, while the lower soil layer is predominantly sandy soil, with an average thickness of approximately 7 m. In terms of the shear strength of the soil, the indoor shear tests indicate that the cohesion ranges from 0.4 to 17.5 kPa, and the friction angle ranges from 21.2 to 27.9° (Table 1).Table 1 Physical and mechanical parameters of soils in different soil layers of DM1 riverbank.

Table 1Soil layer	Material	Layer thickness/(m)	Unit weight/(kN/m3)	φb/(°)	Internal friction angle/(°)	Cohesion/(kN/m2)	
1	Clay	0.5	16.1	15	21.2	17.5	
2	Clay	2.0	16.7	15	23.6	15.8	
3	Clay	2.0	16.6	15	25.1	4.3	
4	Sandy soil	3.1	18.5	15	27.9	0.4	
5	Sandy soil	3.7	18.5	15	27.8	0.4	

During the calculation, the soil cohesion in April decreased by 28 % (taking the mean value of soil No. 2 and No. 3), and the internal friction angle decreased by 10 %. Besides, according to Li et al. [43], considering the influence of the freeze-thaw process on soil structure in April, the dry density of soil was reduced by 15 %, to consider the impacts of the frost heave/freeze-thaw process during this period. In November, the frost-heaving effect was given by Eq. (7).

2.4.2 Flow condition

According to the hydrograph of the river stage, the hydrological year of 2009 was divided into four different periods, including the dry period (December 16th to March 15th), rising period (March 16th to May 31st), flood period (June 1st to September 30th) and recession period (October 1st to December 15th). The river stage change during the simulation period is shown in Fig. 5. In this simulation, the influence of groundwater level change is also considered. The river bank in the study reach has a relatively high permeability due to the thin upper cohesive soil and the thick lower non-cohesive soil. Therefore, it was assumed that the groundwater level inside the river bank changes synchronously with the in-channel river stage.Fig. 5 Temporal changes in the river stage.

Fig. 5

3 Results

3.1 Soil mechanical properties change

The changes in soil sample cohesiveness and internal friction angle during freeze-thaw cycles are depicted in Fig. 6, Fig. 7. It can be seen that the soil's cohesiveness and internal friction angle generally decrease as the frequency of freeze-thaw cycles increases. The freeze-thaw process causes expansion and contrprocess deformation of the soil, which leads to the production of cracks and significant damage to the soil structure, changing the internal arrangement of the soil particles. The soil's shear strength gradually declines and eventually stabilizes while the freeze-thaw cycles continue.Fig. 6 The variation of cohesion with the number of freeze-thaw cycles.

Fig. 6

Fig. 7 The variation of internal friction angle with the number of freeze-thaw cycles.

Fig. 7

Specifically, in terms of cohesion, the clay content of No. 1 soil is 12 %. After 7 freeze-thaw cycles, soil cohesion at water contents of 13 % and 18 % decreased by about 10 % and 45 %, respectively. The clay content of No. 2 soil is 23 %, and the cohesion decrease rates at water contents of 13 %, 18 %, and 40 % decreased by about 42 %, 28 %, and 28 % after 7 freeze-thaw cycles, respectively. The clay content of No. 3 soil is 33 %, and the cohesions at water contents of 13 %, 18 %, and 40 % after 7 freeze-thaw cycles decreased by about 45 %, 33 %, and 19 %, respectively.

Similarly, in terms of internal friction angle, after 7 freeze-thaw cycles, the decreased range of internal friction angle of soil No. 1 at a water content of 13 % and 18 % are about 19 % and 17 % of the initial values, respectively. The decreased range of soil internal friction angle of soil No. 2 at a water content of 13 %, 18 %, and 40 % are about 14 %, 16 %, and 8 % of the initial values, respectively. The soil internal friction angles of soil No. 3 at a water content of 13 %, 18 %, and 40 % decreased by about 14 %, 9 %, and 19 %, respectively.

In general, after 7 freeze-thaw cycles, the soil cohesion and internal friction angle of different clay contents decreased by 10%–47 % and 9%–19 %, respectively, with different water content. This indicates that the freeze-thaw process has a relatively large effect on soil cohesion, but a relatively minor effect on the internal friction angle.

3.2 Riverbank stability in different periods

The stability of the riverbank at two typical sections downstream of the Dadingzishan Project of the Songhua River was analyzed using the improved BSTEM model, to illustrate how riverbank stability change in different periods. The temporal change of the safety factor Fs was obtained, as shown in Fig. 8. The calculation results of different periods are summarized as follows.(1) During the dry period (December 16th to March 15th), the average water discharge is low, and thus the hydraulic erosion is not intensive, resulting in a high level of bank stability during this period. The variation trend of the bank safety factor Fs changes with the water level of the river stage when considering the freezing/thawing coupling effect in two cross-sections. This is because during this period, the riverbank slope is gentle, the water level in the river channel is low, and the erosion amount is small, resulting in a lower probability of bank failure.

(2) During the rising period (March 16th to May 31st), the melting of ice raises the water level in the river channel, which exacerbates erosion of the lower sandy soil layer along the riverbank. This causes the stability factor of the riverbank to significantly decline, particularly at the DM2 section where a mass failure occurred during the freeze-thaw period of April. In fact, during the ice-thawing period around early April each year, a special spring flood occurs, which adversely affects the stability of the opposite bank in a short period. Thus, there is a higher possibility of bank failure during the rising water period.

(3) During the flood period (June 1st to September 30th), the flow discharge in the river channel increased, and the water level reached the highest in the whole year. As a results of the extensive erosion of the lower sandy bank soil layer, the slope of the river bank became steeper and the overall stability of the river bank decreased. The computation results indicates that throughout the flood period, there are one and five mass failure incidents at DM1 and DM2 sections respectively. After each mass failure, the bank stability will increase correspondingly due to the decrease of bank slope and the cover effect of the failed bank material at the bank-toe. With the further bank toe erosion and the continuous change of the river stage, the Fs value will decrease until the next mass failure again. Overall, the stability of riverbanks during flood periods is generally low, leading to a higher occurrence of bank failure.

(4) During the recession period (October 1st to December 15th), the river stage in the channel decreased rapidly. At the same time, the hydraulic erosion at the bank toe has increased the bank slope. These two processes induced mass failure during the recession period. According to the calculation, there are one and four mass failure events at sections DM1 and DM2 sections, respectively.

Fig. 8 Temporal variation in the safety factor of bank stability Fs.

Fig. 8

3.3 Bank profile processes

Fig. 9 shows the calculated bank profile changes in these two sections. It could be seen that two mass failure events occurred at the section of DM1 in 2009, but the bank profile change was mainly attributed to the hydraulic erosion at the bank toe. The calculated bank erosion width was 2.9 m in this section, which was in good agreement with the measured average width of 3.0 m. Ten mass failure events occurred at the section of DM2, the calculated bank erosion width was 35.12 m at this section, which is in good agreement with the measured failure width (the measured failure width is about 36 m). Besides, the calculated bank profile also agreed well with the measured profile as shown in Fig. 9.Fig. 9 The change process of the bank profile.

Fig. 9

3.4 Bank erosion in different periods

Numerical experiments were conducted for the two conditions—one taking into account the freeze-thaw process in April and the other not taking into account the freeze-thaw process in April—in order to better investigate the impact of frost heave/freeze-thaw process on bank erosion in the research area. The former is referred to as Case 1, and the latter is referred to as Case 2. The following observations can be found:

Fig. 10 gives a comparison between the calculated bank erosion volumes in these two cases during different periods. It can be observed that the bank-toe erosion amount of Case 1 after the freeze-thaw period in April is higher than that of Case 2. The reason is that the freeze-thaw action causes the soil to become loose and the dry density to decrease, resulting in a reduction in the bank's resistance to erosion. As a result, the mobilized shear stress on the soil decreases, making it more susceptible to erosion by water flow.Fig. 10 The amount of bank-toe erosion in different periods Case 1: considering the freeze-thaw process in April; Case 2: without considering the freeze-thaw process in April.

Fig. 10

Furthermore, the total mass failure volume of Case 1 throughout the year is greater than that of Case 2. However, the riverbank mass failure volume of Case 2 during the recession period is greater than that of Case 1 (Fig. 11). When considering freeze-thaw effects, the bank has already experienced one bank failure during the rising period (DM2) or flood period (DM1), resulting in less collapse volume during the recession period.Fig. 11 The amount of mass failure erosion in different periods Case 1: considering the freeze-thaw process in April; Case 2: without considering the freeze-thaw process in April.

Fig. 11

4 Discussion

4.1 Impacts of freeze-heave/freeze-thaw on bank stability

As previously stated, the frost heave/frost thaw action causes riverbanks more prone to collapse. Therefore, studying the stability and morphology of riverbanks with and without considering frost heave/frost thaw action can provide further insights into the variations of rivers in seasonal frozen regions.

Frost heaving/freeze-thaw process caused mass failure to occur earlier at sections of DM1 and DM2. Fig. 12 gives the comparisons between the calculated stability factors of the river bank at sections of DM1 and DM2 in different cases. It was evident that there were more mass failures and that the first mass failure occurred 90 days earlier at DM1 and 80 days earlier at DM2 in Case 2.Fig. 12 Comparison of bank stability with and without the freeze-thaw process Case 1: considering the freeze-thaw process in April; Case 2: without considering the freeze-thaw process in April.

Fig. 12

Fig. 13 gives the comparisons between the calculated profile changes of the river bank at sections of DM1 and DM2 in different cases. When the frost heave/freeze-thaw process is not taken into account, the mass failure widths of the DM1 and DM2 sections are 1.04 m and 30.24 m respectively. After considering the influence of the frost heave/freeze-thaw process, the cumulative mass failure widths increased to 2.91 m and 35.12 m respectively, which were closer to the measured widths (3 m and 36 m, respectively).Fig. 13 Comparison of bank profile with or without the freeze-thaw process.

Fig. 13

As compared with the calculated results of Jia et al. [6], The impacts of the frost heaving/freeze-thaw process caused mass failure to occur in advance, consistent with the conclusions of this study. It should be noted that the DM1 section did not immediately collapse after both the cohesion and internal friction angle of the soil decreased due to freezing and thawing in April. The reason is that riverbank collapse is an accumulative process. At this time, the water flow is relatively small, the river stage is low, and the bank erosion is limited. However, as the toe erosion accumulates and the slope of the bank becomes steeper, the safety factor of the riverbank decreases, making it more prone to reaching the critical value of Fs and mass failure will occur, potentially posing safety hazards for subsequent mass failures.

4.2 Quantitative analysis of freeze-heave/freeze-thaw effects on bank erosion

Previous studies have mostly focused on the hydraulic erosion and gravitational failure of the river bank, while the hydrodynamic-frost heave/freeze-thaw has not been thoroughly considered [17,34]. More research is needed, specifically to determine the quantitative contribution of frost heave/freeze-thaw action to bank erosion still requires further investigation. Therefore, we quantified the total erosion volume of the riverbank at different periods and the quantitative contribution of freeze-thaw action to riverbank erosion.

In terms of the total bank erosion amount, it was increased by 11–51 % at sections of DM1 and DM2 in Case 1, as compared with Case 2, indicating that the freeze-thaw process intensified the bank erosion process. As shown in Fig. 14, the total bank erosion volumes (bank-toe and mass failure erosion) in Case1 and Case 2 at the section of DM1 are 87.06 m3/m and 57.48 m3/m respectively, that is, after considering the effects of frost heave/freeze-thaw, the total amount of bank erosion increases by about 51 %. The total bank erosion volumes in Case1 and Case 2 at the section of DM2 are 87.06 m3/m and 57.48 m3/m respectively, that is, after considering the effects of frost heave/freeze-thaw, the total amount of bank erosion increases by about 11 %.Fig. 14 The total amount of bank erosion (bank-toe and mass failure erosion) in different periods Case 1: considering the freeze-thaw process in April; Case 2: without considering the freeze-thaw process in April.

Fig. 14

Fig. 15 shows the contribution rates of frost heaving/frost thawing to bank erosion at different stages. During the rising period, the total amount of bank erosion at sections of DM1 and DM2 increased by about 111 % and 115 % respectively. During the flood period, the total amount of bank erosion at sections of DM1 and DM2 increased by about 240 % and 8 % respectively. It should be noted that during the recession period, the total amount of bank erosion at sections of DM1 and DM2 increased by about −23 % and −3% respectively. The reason is that when considering frost heaving/frost thawing, the river bank has already experienced one mass failure during the rising period (DM2) or flood period (DM1) in advance (Fig. 12), resulting in relatively less erosion during the recession period.Fig. 15 The total amount of variation of bank erosion in different periods.

Fig. 15

When considering the influence of frost heave/freeze-thaw, the total amount of bank erosion at the section of DM1 had a larger increase than that at the section of DM2. The reasons included: ① the overall bank-toe erosion volume at DM1 in 2009 was relatively small; ② the number of mass failures erosion after considering the freeze-thaw effect (2 times) is one more than when not considering the freeze-thaw effect (1 time), and the amount of mass failure erosion has increased by 17.08 m3/m. This also reflects that the frost heave/freeze-thaw process increases the amount of erosion at the toe of the bank, thereby increasing the likelihood of collapse, posing a serious threat to the safety of riverbank land and people's lives. This indicates that when studying the problem of riverbank erosion in seasonally frozen areas, the influence of freeze-thaw action needs to be considered.

4.3 Sensitivity analysis of riverbanks

4.3.1 Orthogonal experiment

The orthogonal experimental design is a statistical method used to analyze physical experiments with multiple factors. It involves selecting a representative number of experimental groups from a large number of experiments and analyzing the data of the orthogonal experimental results using range analysis. The larger the sensitivity index, the greater the impact of the influencing factor on the stability safety factor of the riverbank, indicating that the bank is more sensitive to this factor.

Considering four influencing factors: river stage, riverbank groundwater level, soil cohesion, and internal friction angle, each factor is set at three levels to conduct orthogonal experiments on the bank with and without freeze-thaw action. The values of the influencing factors are shown in Table 2, and the calculation results of the orthogonal experiments are shown in Table 3.Table 2 Levels of influencing factors.

Table 2Levels	Factors influencing	
River stage/(m)	Riverbank groundwater level/(m)	Cohesion/(kN/m2)	Internal friction angle/(°)	
1	111	111	30	30	
2	109	109	20	25	
3	107	107	10	20	

Table 3 Results of orthogonal experimental design calculation.

Table 3Experimental group	River stage	Riverbank groundwater level	Cohesion	Internal friction angle	Freeze-thaw Fs	Without freeze-thaw Fs	
①	111	111	30	30	3.28	4.17	
②	111	109	20	25	3.52	4.23	
③	111	107	10	20	3.88	4.38	
④	109	111	20	20	1.42	1.82	
⑤	109	109	10	30	1.93	2.26	
⑥	109	107	30	25	3.63	4.36	
⑦	107	111	10	25	0.87	1.07	
⑧	107	109	30	20	2.02	2.53	
⑨	107	107	20	30	2.60	3.05	

4.3.2 Sensitivity analysis of experimental results

The stability safety factor of the riverbank with and without freeze-thaw action, as well as the sensitivity of various influencing factors, are shown in Table 4. ① The sensitivity of riverbank to river stage is the highest, while it is the least sensitive to the internal friction angle, regardless of the with or without freeze-thaw action. The sensitivity ranking of riverbank to the four influencing factors, regardless of the with or without freeze-thaw action, is as follows: river stage > groundwater level > cohesion > internal friction angle. Therefore, attention should be paid to the influence of the river stage on the bank slope to avoid significant extensive erosion and scouring of the river bank when the water level rises. In addition, during the recession water period, attention should be paid to the risk of bank collapse caused by groundwater level. ② Freezing and thawing action can reduce the sensitivity of the riverbank stability safety factor and various influencing factors. The sensitivity reduction effect is most significant for cohesion and internal friction angle, with a decrease of 32.84 % and 24.74 % respectively, indicating that the variation of cohesion and internal friction angle values has a relatively small impact on the stability of river bank slopes in seasonal freezing areas.Table 4 Results of the range analysis.

Table 4Sensitivity of influencing factors	River stage	Riverbank groundwater level	Cohesion	Internal friction angle	
Without freeze-thaw action riverbank	2.0433	1.5767	1.1167	0.3100	
freeze-thaw action riverbank	1.7300	1.5133	0.7500	0.2333	
Reduction in sensitivity to freeze-thaw/(%)	15.33	4.02	32.84	24.74	

It should be noted that the length of time rivers freeze, the date that the ice thaws, and the type of bank soil all vary depending on location. Although there may be variations in particular values, the pattern of reduced cohesiveness as a result of frost heave and freeze-thaw action is consistent with regard to the changes in shear strength of frozen-thawed soil that need special consideration in bank erosion. Therefore, this study takes the Songhua River, a typical seasonal frozen river in China, as an example to quantitatively analyze the impact of frost heave/freeze-thaw action on bank erosion processes. The current study can provide a reference for research on the channel evolution of other rivers in seasonal frozen regions and the establishment of failure pre-warning platforms. However, some major gaps are also identified for the current study, indicating the need for more scientific researches in the near future, such as considering conducting small-scale fluvial erosion experiments that account for freeze-thaw processes, as well as more impact factors should be taken into account on bank stability, and enhancing the applications in different rivers.

5 Conclusion

Taking the typical cross-sections of the downstream near-dam section of the Dadingzishan Project of the Songhua River as an example, the variation in the mechanical characteristics of riverbank soil under the freeze-thaw cycles was investigated firstly in the current research, and then was used in the modeling of bank erosion processes at typical sections of Songhua River, and the quantitative analysis of the impact of frost heave/freeze-thaw process on riverbank erosion is conducted by the improved BSTEM model. The following major conclusions are drawn from the current study.(1) After 7 cycles of the freeze-thaw process, the soil cohesion and internal friction angle of bank soil decreased by about 10%–47 % and 9%–19 %, respectively.

(2) When the impact of the freeze-thaw process is taken into account, the risk of bank mass failure during the rising water phase increases compared to when it is not. But overall, the flood and recession periods are the peak periods for bank mass failure.

(3) The impacts of frost heaving/freeze-thaw action caused mass failure to occur earlier at sections of DM1 and DM2. After considering frost heave/freeze-thaw, the cumulative total amount of bank erosion (ban-toe and mass failure) for DM1 and DM2 increases by approximately 51 % and 11 % respectively throughout the year, bringing it closer to the measured value.

(4) Sensitivity analysis of orthogonal experiments reveals that the sensitivity ranking of the four influencing factors on riverbank stability under freezing-thawing conditions is as follows: river stage > groundwater level > cohesion > internal friction angle.

Compliance with ethical standards

This article does not involve potential conflicts of interest, nor does it involve human or animal research, and is strictly ethical.

Data availability

Data will be made available on request.

CRediT authorship contribution statement

Jun Yang: Writing – original draft, Methodology, Investigation, Funding acquisition, Data curation, Conceptualization. Dongdong Jia: Supervision, Resources, Investigation, Funding acquisition, Conceptualization. Biyao Zhai: Writing – review & editing, Supervision. Xiaona Chen: Writing – review & editing, Investigation. Jinyang Wang: Writing – review & editing, Supervision.

Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgments

This work was supported by the 10.13039/501100012166 National Key Research and Development Program of China (grant number 2023YFC3209501) and the 10.13039/501100001809 National Natural Science Foundation of China (grant numbers 52079080, 52479066, U2040215). Greatly appreciate the careful work and constructive suggestions of the editors and all anonymous reviewers.
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